Electric Machinery and Transformers_I. L. Kosow

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Scilab Textbook Companion for

Electric Machinery And Transformers

by I. L. Kosow1

Created byThirumalesh H S

Bachelor of EngineeringElectrical Engineering

Sri Jayachamarajendra College of EngineeringCollege Teacher

R. S. Ananda MurthyCross-Checked by

Lavitha Pereira

August 13, 2013

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the ”Textbook Companion Project”section at the website http://scilab.in

Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

Contents

List of Scilab Codes 5

1 ELECTROMECHANICAL FUNDAMENTALS 11

2 DYNAMO CONSTRUCTION AND WINDINGS 27

3 DC DYNAMO VOLTAGE RELATIONS DC GENERATORS 37

4 DC DYNAMO TORQUE RELATIONS DC MOTORS 49

5 ARMATURE REACTION AND COMMUTATION IN DY-

NAMOS 80

6 AC DYNAMO VOLTAGE RELATIONS ALTERNATORS 84

7 PARALLEL OPERATION 103

8 AC DYNAMO TORQUE RELATIONS SYNCHRONOUS

MOTORS 129

9 POLYPHASE INDUCTION OR ASYNCHRONOUS DY-

NAMOS 182

10 SINGLE PHASE MOTORS 225

11 SPECIALIZED DYNAMOS 234

12 POWER ENERGY AND EFFICIENCY RELATIONS OF

DC AND AC DYNAMOS 241

13 RATINGS SELECTION AND MAINTENANCE OF ELEC-

TRIC MACHINERY 298

14 TRANSFORMERS 317

List of Scilab Codes

Exa 1.1 calculate average voltage . . . . . . . . . . . . . . . . 11Exa 1.2 calculate e and E . . . . . . . . . . . . . . . . . . . . . 12Exa 1.3 calculate E . . . . . . . . . . . . . . . . . . . . . . . . 13Exa 1.4 calculate E for different theta . . . . . . . . . . . . . . 14Exa 1.5 calculate Eperpath Eg Ia Ra Vt P . . . . . . . . . . . 15Exa 1.6 repeated previous eg with 4poles . . . . . . . . . . . . 17Exa 1.7 calculate Eav per coil and per coilside . . . . . . . . . 18Exa 1.8 verify previous eg with phi in webers . . . . . . . . . . 19Exa 1.9 verify eg1 5b with eq1 5a . . . . . . . . . . . . . . . . 20Exa 1.10 calculate Z and Eg . . . . . . . . . . . . . . . . . . . . 21Exa 1.11 calculate F and find its direction . . . . . . . . . . . . 22Exa 1.12 repeat previous eg with angle 75 . . . . . . . . . . . . 23Exa 1.13 calculate counter emf . . . . . . . . . . . . . . . . . . 24

Exa 1.14 calculate Eg phi in linesperpole and mWb . . . . . . . 25Exa 2.1 calculate a for lap and wave windings . . . . . . . . . 27Exa 2.2 calculate generated emf . . . . . . . . . . . . . . . . . 28Exa 2.3 calculate polespan p kp . . . . . . . . . . . . . . . . . 29Exa 2.4 calculate kp . . . . . . . . . . . . . . . . . . . . . . . . 30Exa 2.5 find alpha n theta . . . . . . . . . . . . . . . . . . . . 31Exa 2.6 find n alpha kd for different number of slots . . . . . . 32Exa 2.7 calculate Eg Np kd kp Egp . . . . . . . . . . . . . . . 34Exa 2.8 calculate f S omega . . . . . . . . . . . . . . . . . . . . 35Exa 3.1 calculate I1 If Ia Eg . . . . . . . . . . . . . . . . . . . 37Exa 3.2 calculate Rd Eg . . . . . . . . . . . . . . . . . . . . . 38

Exa 3.3 calculate Vnoload . . . . . . . . . . . . . . . . . . . . 39Exa 3.4 calculate E . . . . . . . . . . . . . . . . . . . . . . . . 40Exa 3.5 calculate Ia Eg . . . . . . . . . . . . . . . . . . . . . . 42Exa 3.6 calculate VR . . . . . . . . . . . . . . . . . . . . . . . 43

Exa 6.8 calculate torqueperphase and total torque . . . . . . . 100

Exa 7.1 calculate I Ia and P . . . . . . . . . . . . . . . . . . . 103Exa 7.2 calculate all currents and power of the generator . . . 106Exa 7.3 calculate VL IL Pg and PL . . . . . . . . . . . . . . . 107Exa 7.4 calculate total load and kW output of each G . . . . . 110Exa 7.5 calculate max and min E and frequency and Epeak and

n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Exa 7.6 calculate max and min E and f and phase relations . . 113Exa 7.7 calculate Is in both alternators . . . . . . . . . . . . . 114Exa 7.8 calculate generator and motor action and P loss and

terminal V and phasor diagram . . . . . . . . . . . . . 116Exa 7.9 calculate synchronizing I and P and P losses . . . . . . 119

Exa 7.10 calculate synchronizing I and P and P losses . . . . . . 122Exa 7.11 calculate mesh currents line currents phase voltages pha-

sor diagram . . . . . . . . . . . . . . . . . . . . . . . . 125Exa 8.1 calculate alpha Er Ia Pp Pt Power loss Pd . . . . . . . 129Exa 8.2 calculate alpha Er Ia Pp Pt Power loss Pd . . . . . . . 132Exa 8.3 calculate Ia PF hp . . . . . . . . . . . . . . . . . . . . 134Exa 8.4 calculate IL Iap Zp IaZp theta deba Egp . . . . . . . . 139Exa 8.5 calculate torque angle . . . . . . . . . . . . . . . . . . 142Exa 8.6 calculate Pp Pt hp internal and external torque and

motor efficiency . . . . . . . . . . . . . . . . . . . . . 144

Exa 8.7 calculate total load I and PF using IM and SM percentreduction in I and overall PF . . . . . . . . . . . . . . 146Exa 8.8 calculate Tp and hp . . . . . . . . . . . . . . . . . . . 150Exa 8.9 calculate original kvar and kvar correction and kVA and

Io and If and power triangle . . . . . . . . . . . . . . . 151Exa 8.10 calculate cost of raising PF to unity and point85 lagging 154Exa 8.11 calculate Po jQo and power triangle . . . . . . . . . . 156Exa 8.12 calculate Pf jQf Pa jQa kVA and draw power tabulation

grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Exa 8.13 calculate Pf jQf Pa jQa kVA and power tabulation grid 159Exa 8.14 calculate original and final kVA kvar P and correction

kvar Sa . . . . . . . . . . . . . . . . . . . . . . . . . . 161Exa 8.15 calculate kVA added Pa and Qa and Pf Qf and PF . 164Exa 8.16 Verify tellegens theorem for kVAs found in Ex 8 15 . . 167Exa 8.17 calculate overall PF using unity PF SM . . . . . . . . 169Exa 8.18 calculate overall PF using point8 PF leading SM . . . 172

Exa 8.19 calculate kVA and PF of system and same for SM . . 175

Exa 8.20 calulate speeds and poles for alternator and motor . . 178Exa 9.1 calculate poles and synchronous speed . . . . . . . . . 182Exa 9.2 calculate rotor speed . . . . . . . . . . . . . . . . . . . 183Exa 9.3 calculate rotor frequency . . . . . . . . . . . . . . . . 185Exa 9.4 calculate starting torque and current . . . . . . . . . . 186Exa 9.5 calculate s Xlr fr Sr . . . . . . . . . . . . . . . . . . . 187Exa 9.6 calculate full load S and Tf . . . . . . . . . . . . . . . 189Exa 9.7 calculate rotor I and PF and same with added Rr . . . 191Exa 9.8 calculate Rx and rotor PF and starting current . . . . 193Exa 9.9 calculate Sr with added Rx . . . . . . . . . . . . . . . 197Exa 9.10 calculate Elr Ir Pin RCL RPD torques . . . . . . . . . 200

Exa 9.11 calculate Elr Ir Pin RCL RPD and torques . . . . . . 202Exa 9.12 calculate s and Sr for Tmax . . . . . . . . . . . . . . . 205Exa 9.13 calculate starting torque . . . . . . . . . . . . . . . . . 207Exa 9.14 calculate full load and starting torques . . . . . . . . . 208Exa 9.15 calculate Ip Ir PF SPI SCL RPI RPD and rotor power

and torque and hp and motor efficiency . . . . . . . . 209Exa 9.16 calculate Ism IL Ts and percent IL and percent Ts . . 215Exa 9.17 calculate T s Sr for different V . . . . . . . . . . . . . 217Exa 9.18 calculate T s Sr for different impressed stator V . . . . 219Exa 9.19 calculate fcon and Scon . . . . . . . . . . . . . . . . . 222

Exa 10.1 calculate total starting current and PF and componentsof Is Ir and phase angle between Is Ir . . . . . . . . . . 225Exa 10.2 calculate Ps Pr Pt and motor efficiency . . . . . . . . 227Exa 10.3 calculate total starting current and sine of angle between

Is Ir . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229Exa 10.4 calculate ratios of T and efficiency and rated PF and hp 232Exa 11.1 calculate S V P T A and B from torque speed relations

fig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Exa 11.2 calculate stepping angle . . . . . . . . . . . . . . . . . 236Exa 11.3 calculate stepping length . . . . . . . . . . . . . . . . 237Exa 11.4 calculate synchronous velocity . . . . . . . . . . . . . . 238

Exa 11.5 calculate slip of DSLIM . . . . . . . . . . . . . . . . . 239Exa 12.1 Pr Ia efficiency . . . . . . . . . . . . . . . . . . . . . . 241Exa 12.2 efficiency at different LF . . . . . . . . . . . . . . . . . 243Exa 12.3 field current Ec Pf . . . . . . . . . . . . . . . . . . . . 245Exa 12.4 Pr variable losses efficiency table . . . . . . . . . . . . 246

Exa 12.5 Ia LF max efficiency LF . . . . . . . . . . . . . . . . . 252

Exa 12.6 Pd Pr efficiency . . . . . . . . . . . . . . . . . . . . . 254Exa 12.7 Pd Pr max and fl efficiency Pk Ia LF . . . . . . . . . . 256Exa 12.8 IL Ia Pd Pr Speed SR . . . . . . . . . . . . . . . . . . 258Exa 12.9 Ec Pd Po Pr To Ia efficiency speed SR . . . . . . . . . 261Exa 12.10 efficiency Pf Pd Pr Ia LF max efficiency . . . . . . . . 263Exa 12.11 efficiency at different LF . . . . . . . . . . . . . . . . . 266Exa 12.12 Ia Ra Pf Pk Pcu efficiencies Pd . . . . . . . . . . . . . 268Exa 12.13 Pf Pcu Zs VR efficiencies Pd . . . . . . . . . . . . . . 272Exa 12.14 Pr Pcu efficiencies hp torque . . . . . . . . . . . . . . 276Exa 12.15 RPO efficiency hp torque compare . . . . . . . . . . . 280Exa 12.16 Ip Ir PF SPI SCL RPI RCL RPD T hp efficiency . . . 283

Exa 12.17 upper and lower limit Is . . . . . . . . . . . . . . . . . 287Exa 12.18 starting I and PF . . . . . . . . . . . . . . . . . . . . 289Exa 12.19 Re1s slip Pcu and Pr at LFs hp T . . . . . . . . . . . 291Exa 13.1 R and reduced life expectancy . . . . . . . . . . . . . 298Exa 13.2 E and increased life expectancy . . . . . . . . . . . . . 299Exa 13.3 E and increased life expectancy classB . . . . . . . . . 300Exa 13.4 ClassB insulation SCIM details . . . . . . . . . . . . . 301Exa 13.5 final temperature . . . . . . . . . . . . . . . . . . . . . 303Exa 13.6 Tf R decreased life expectancy . . . . . . . . . . . . . 305Exa 13.7 rms hp . . . . . . . . . . . . . . . . . . . . . . . . . . 306

Exa 13.8 Vb Ib Rb Rpu . . . . . . . . . . . . . . . . . . . . . . 307Exa 13.9 Rpu jXpu Zpu . . . . . . . . . . . . . . . . . . . . . . 309Exa 13.10 new Zpu . . . . . . . . . . . . . . . . . . . . . . . . . 311Exa 13.11 line and phase Vpu . . . . . . . . . . . . . . . . . . . 312Exa 13.12 Zb Xs Ra Zs P . . . . . . . . . . . . . . . . . . . . . . 313Exa 14.1 stepup stepdown alpha I1 . . . . . . . . . . . . . . . . 317Exa 14.2 turns I1 I2 stepup stepdown alpha . . . . . . . . . . . 318Exa 14.3 alpha Z1 I1 . . . . . . . . . . . . . . . . . . . . . . . . 320Exa 14.4 Z2prime Z3prime Z1 I1 Pt V2 P2 V3 P3 Pt . . . . . . 322Exa 14.5 alpha N2 N1 ZL . . . . . . . . . . . . . . . . . . . . . 324Exa 14.6 Z between terminals A B . . . . . . . . . . . . . . . . 326

Exa 14.7 alpha V1 V2 I2 I1 PL Ps PT efficiency . . . . . . . . . 328Exa 14.8 PL alpha maxPL . . . . . . . . . . . . . . . . . . . . . 331Exa 14.9 Eh El Ih new kVA . . . . . . . . . . . . . . . . . . . . 332Exa 14.10 Piron . . . . . . . . . . . . . . . . . . . . . . . . . . . 334Exa 14.11 I2 I1 Z2 Z1their loss E2 E1 alpha . . . . . . . . . . . . 335

Exa 14.12 ZL ZP difference . . . . . . . . . . . . . . . . . . . . . 338

Exa 14.13 Re1 Xe1 Ze1 ZLprime I1 . . . . . . . . . . . . . . . . 339Exa 14.14 I2 ohmdrops E2 VR . . . . . . . . . . . . . . . . . . . 342Exa 14.15 E2 VR . . . . . . . . . . . . . . . . . . . . . . . . . . 344Exa 14.16 E2 VR . . . . . . . . . . . . . . . . . . . . . . . . . . 345Exa 14.17 Ze1 Re1 Xe1 Ze2 Re2 Xe2their drops VR . . . . . . . 347Exa 14.18 Pcsc . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350Exa 14.19 Ze1drop Re1drop Xe1drop VR . . . . . . . . . . . . . 351Exa 14.20 Re1 Re1 r2 its drop Pc . . . . . . . . . . . . . . . . . 354Exa 14.21 tabulate I2 efficiencies . . . . . . . . . . . . . . . . . . 356Exa 14.22 Zeqpu V1pu VR . . . . . . . . . . . . . . . . . . . . . 363Exa 14.23 Pcu LF efficiencies . . . . . . . . . . . . . . . . . . . . 365

Exa 14.24 efficiencies at differnt LFs . . . . . . . . . . . . . . . . 368Exa 14.25 Zpu2 St S2 S1 LF . . . . . . . . . . . . . . . . . . . . 370Exa 14.26 Vb Ib Zb Z1 Z2 I1 I2 E1 E2 . . . . . . . . . . . . . . . 373Exa 14.27 RL ZbL ZLpu Z2pu Z1pu IbL ILpu VRpu VSpu VS

VxVxpu . . . . . . . . . . . . . . . . . . . . . . . . . . 377Exa 14.28 ZT1 ZT2 Zbline3 Zlinepu VLpu IbL IL ILpu VSpu VS 381Exa 14.29 Z1pu Z2pu Vbline Zlinepu ZMs . . . . . . . . . . . . . 385Exa 14.30 ST ST Sxformer . . . . . . . . . . . . . . . . . . . . . 387Exa 14.31 Wc tabulate allday efficiency . . . . . . . . . . . . . . 389Exa 14.32 I2 Ic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

Exa 14.33 Zeh Zel I2rated I2sc overload . . . . . . . . . . . . . . 396Exa 14.34 PT kVA phase and line currents kVAtransformers . . . 398Exa 14.35 PT ST phase and line currents kVAtransformers . . . 400Exa 14.36 find line currents and their sum . . . . . . . . . . . . . 403Exa 14.37 kVAcarry loadtransformer VVkVA ratiokVA increaseload 406Exa 14.38 IL alpha Ia kVA . . . . . . . . . . . . . . . . . . . . . 409Exa 14.39 VL ST Idc Sac Sdc per line . . . . . . . . . . . . . . . 410

Chapter 1

ELECTROMECHANICAL

FUNDAMENTALS

Scilab code Exa 1.1 calculate average voltage

1 / / E l e c t r i c M ac hi ne ry and T r an s f or m e rs2 / / I r v i n g L k osow3 // P r en t i c e H al l o f I n d i a4 / / 2 nd e d i t i om5

6 / / C ha pt er 1 : E l e c t r o m e c h a n i c a l F un da me nt al s7 / / E xa mp le 1−18

9 clear ; clc ; close ; // C l ea r t he work s p ac e andc o n s o l e .

11 / / G iv en d a ta12 t = 50 e -3; // t = ti m e i n m i l l i s e c o n d13 phi = 8 * 10 ^ 6; / / p h i = u n if o rm m a gn et i c f i e l d i n

m a x w e l l s14

15 / / C a l c u l a t i o n s16 E_av = ( phi / t ) * 10 ^ -8; / / E av = a v er a ge

v o l t a g e g e ne r a t ed i n t he c on du ct or

17 / / i n v o l t

1819 / / D is pl ay t h e r e s u l t20 disp ( ”E x ampl e 1−1 S o l u t i on : ” ) ;

21 disp ( ” A v er a ge v o l t a g e g e n e ra t ed i n t he c on du ct or i s: ” ) ;

22 printf ( ” E a v = %. 2 f V” , E _a v ) ;

Scilab code Exa 1.2 calculate e and E

1011 / / G iv en d a ta12 l = 18; // l = l e n g t h o f t he c on du ct or i n i n ch e s13 B = 5 00 00 ; / / B = u n if o rm m a gn e ti c f i e l d i n l i n e s / sq

−i n c h e s14 d = 720; // d = d i s t a n c e t r a v e l l e d by c on du ct or i n

i n c h e s15 t = 1 ; // t =t i me t ak en f o r t he c on du ct or t o move

i n s ec on d16

17 / / C a l c u l a t i o n s18 v = d / t ; / / v = v e l o c i t y i n i n c he s / s ec on d w it h whi cht h e c o n d u c t o r mo ves

20 / / p ar t a

21 e = B * l * v * 1 0 ^ -8; / / e = i n s ta n t an e o us

i n d u c ed EMF i n v o l t22 / / p ar t b23 A = d * l ; // Area s we pt by t he c o nd u ct o r w h i le

moving24 phi = B * A ; / / p h i = u n i fo r m m a g ne t i c f i e l d25 E = ( phi / t ) * 10 ^ -8; / / E = a v e r a g e i n du c ed

30 printf ( ” \n a : e = %. 2 f V ” , e ) ;31 printf ( ” \n b : E = %. 2 f V ” , E ) ;

Scilab code Exa 1.3 calculate E

1 / / E l e c t r i c M ac hi ne ry and T r an s f or m e rs2 / / I r v i n g L k osow3 // P r en t i c e H al l o f I n d i a

4 / / 2 nd e d i t i om5

11 / / G iv en d a ta12 l = 18; // l = l e n g t h o f t he c on du ct or i n i n ch e s

13 B = 5 00 00 ; / / B = u n if o rm m a gn e ti c f i e l d i n l i n e s / sq−i n c h e s14 d = 720; // d = d i s t a n c e t r a v e l l e d by c on du ct or i n

i n c h e s15 t = 1 ; // t =t i me t ak en f o r t he c on du ct or t o move

i n s ec on d

16 t he ta = 75 // t h et a = a n g l e b et we en t he mo ti on o f t h e c o n d u c t o r a nd f i e l d17 / / i n r a di a ns18

19 / / C a l c u l a t i o n s20 v = d / t ; / / v = v e l o c i t y i n i n c he s / s ec on d w it h whi ch

t h e c o n d u c t o r mo ves21

22 E = B * l * v * 10 ^ -8 * sind ( theta ); / / E =A ve ra ge i n d u ce d EMF i n v o l t

27 disp ( ” Av er ag e i nd uc ed EMF i n v o l t i s : ” )

28 printf ( ” E = %. 2 f V ” , E ) ;

Scilab code Exa 1.4 calculate E for different theta

1011 / / G iv en d a ta12 v = 1.5; // v = v e l o c i t y i n m/ s w it h whi ch t he

c o n du c to r i s moving13 l = 0.4; // l = l e n g t h o f t h e c on du ct or

14 B = 1 ; // B = u ni fo rm f i e l d i n t e n s i t y i n t e s l a

15 t he ta _a = 9 0; // t h e t a a = a n g le b et we en t he mo ti ono f t h e c o n d u c t o r and f i e l d16 t he ta _b = 3 5; / / t h e t a b = a n g le b et we en t he m ot io n

o f t h e c o n d u c t o r and f i e l d17 t h e ta _ c = 1 20 ; // t h e t a c = a n g l e b et wee n t he m oti on

o f t h e c o n d u c t o r and f i e l d18

19 / / C a l c u l a t i o n s20 E_a = B * l * v * sind ( thet a_a ); // V o l ta g e i n du c ed

i n t he c on du ct or f o r t h e t a a21 E_b = B * l * v * sind ( thet a_b ); // V o l ta g e i n du c ed

i n t he c on du ct or f o r t h e t a b22 E_c = B * l * v * sind ( thet a_c ); // V o l ta g e i n du c ed

i n t he c on du ct or f o r t h e t a c23

27 printf ( ” \n a : E = %. 2 f V ” , E _a ) ;

28 printf ( ” \n b : E = %. 3 f V ” , E _b ) ;

29 printf ( ” \n c : E = %. 2 f V ” , E _c ) ;

Scilab code Exa 1.5 calculate Eperpath Eg Ia Ra Vt P

42 disp ( ”E x ampl e 1−5 S o l u t i o n ” ) ;

4344 printf ( ” \n a : E/ p at h = %. 2 f V/ p at h ” , E _p at h ) ;

45 printf ( ” \n b : Eg = %. 2 f V ” , E _ g ) ;

46 printf ( ” \n c : I a = %. 2 f A ” , I _ a ) ;

47 printf ( ” \n d : Ra = %. 2 f ohm ” , R _ a ) ;

48 printf ( ” \n e : Vt = %. 2 f V ” , V _ t ) ;

49 printf ( ” \n f : P = %. 2 f W ” , P ) ;

Scilab code Exa 1.6 repeated previous eg with 4poles

9 clear ; clc ; close ; // C l ea r t he work s p ac e and

c o n s o l e .10

11 / / G iv en d a ta12 n o _ o f _ c on d u c to r s = 4 0;

13 I = 10; // C ur re nt c a r r i e d by e ac h c o nd u tc o r14 R _ pe r _p a th = 0 .0 1; // R e s i s t a n ce p er p at h15 f lu x_ pe r_ po le = 6 .4 8 * 10 ^ 8; // f l u x l i n e s16 P = 2 ; // No . o f p o l es17 p ath = 4; // No . o f p a r a l l e l p a t h s18 t o t a l_ f lu x = P * f l ux _ pe r _p o le ; // T o ta l f l u x l i n k e d

i n one r e v o l u t i o n19 t = 2 ; // t i m e f o r one r e v o l u t i o n20 e _ a v _ p e r _c o n d u ct o r = 6 . 48 ; // A ve ra ge v o l t a g e

g e n e r a t ed p e r c o n du c t or21

22 / / C a l c u l a t i o n s

23 E _ p at h = ( e _ av _ pe r _c o nd u ct o r ) * ( n o _o f _c o nd u ct o rs/ path ) ; / / A v er a ge24 / / v o l t a g e g e ne r a t ed p er pa th25

26 E _ g = E _p at h ; // G en er at ed a rm at ur e v o l t a g e27

28 I_a =( I / path ) * ( 4 * path ) ; // A r mat ur ec u r r e n t d e l i v e r e d t o an e x t er n a l

29 / / l o ad30

31 R_a = ( ( R_ pe r_p at h) / path ) * 10; / / A r ma t ur e

r e s i s t a n c e32

33 V_t = E_g - I_a * R_a ; // T er mi na l v o l t a g e o f g e n e r a t o r

35 P = V_t * I_a ; // G en r at o r p ower r a t i n g36

37 // D is pl ay t h e r e s u l t s38 disp ( ”E x ampl e 1−6 S o l u t i o n ” ) ;

40 printf (” \n a : E/ p at h = %. 2 f V/ p at h ”

, E _p at h ) ;

41 printf ( ” \n b : Eg = %. 2 f V ” , E _ g ) ;

42 printf ( ” \n c : I a = %. 2 f A ” , I _ a ) ;

43 printf ( ” \n d : Ra = %. 3 f ohm ” , R _ a ) ;

44 printf ( ” \n e : Vt = %. 2 f V ” , V _ t ) ;

45 printf ( ” \n f : P = %. 2 f W ” , P ) ;

Scilab code Exa 1.7 calculate Eav per coil and per coilside

1 / / E l e c t r i c M ac hi ne ry and T r an s f or m e rs2 / / I r v i n g L k osow3 // P r en t i c e H al l o f I n d i a4 / / 2 nd e d i t i om

11 / / G iv en d a ta12 N = 1 ; // no . o f t ur n s13 phi = 6.48 * 10 ^ 8; // M a gn e t i c f l u x i n l i n e s14 s = 30 / 60; // No . o f r e v o l u t i o n o f t h e c o i l p e r

s ec o nd ( r e f e r s e c t i o n 1 −14)

1516 / / C a l c u l a t i o n s17 E _a v _ pe r _ co i l = 4 * phi * N * s * 10 ^ -8; //

a ve ra ge v o l t a ge p e r c o i l18 / / f o r abov e e qu at io n r e f e r s e c t i o n 1−1419

20 E _a v_ pe r_ co il _s id e = E _a v_ pe r_ co il * ( 1 / 2) ; //a v er a ge v o l t a g e p er c on d uc to r

22 // D is pl ay t h e r e s u l t s23 disp (

”E x ampl e 1−7 S o l u t i on : ”)

24 printf ( ” \n Eav / c o i l = % . 2 f V/ c o i l ” , E _ a v _p e r _ co i l

25 printf ( ” \n Eav / c o i l s i d e = % . 2 f V/ c o n du c to r ” ,

E _ a v _ p e r _ c o i l _ s i d e ) ;

Scilab code Exa 1.8 verify previous eg with phi in webers

6 / / C ha pt er 1 : E l e c t r o m e c h a n i c a l F un da me nt al s

7 / / E xa mp le 1−88

11 / / G iv en d a ta12 p hi _l in es = 6. 48 * 10 ^ 8; // m ag ne t i c f l u x i n l i n e s13 N = 1 ; // no . o f t ur n s14

15 / / C a l c u l a t i o n s16 p hi = p hi _l in es * 10 ^ -8; // M ag ne ti c f l u x i n weber

1718 omega = ( 30 ) * ( 2 * %pi ) * ( 1 / 60 ) ; //

a ng ul ar v e l o c i t y i n r a d / s19

20 E _a v_ pe r_ co il = 0 .6 36 62 * o me ga * p hi * N ; //a ve ra ge v o l t a ge p e r c o i l

21 // f o r t he abov e f o rm ul a r e f e r s e c t i o n 1−14 e qn (1 −4b )

23 / / D is pl ay t h e r e s u l t24 disp (

”E x ampl e 1−8 S o l u t i on : ”) ;

25 printf ( ” \n Eav / c o i l = % 0 . 2 f V/ c o i l ” ,

E _ a v _ p e r _ c o i l ) ;

Scilab code Exa 1.9 verify eg1 5b with eq1 5a

1 / / E l e c t r i c M ac hi ne ry and T r an s f or m e rs2 / / I r v i n g L k osow

3 // P r en t i c e H al l o f I n d i a4 / / 2 nd e d i t i om5

9 clear ; clc ; close ; // C l ea r t he work s p ac e andc o n s o l e .10

11 / / G iv en d a ta12 P = 2 ; // No . o f p o l es13 Z = 40; // no o f c on du c t o rs14 a = 2 ; // a = P a r a l l e l p a th s15 phi = 6.48 * 10 ^ 8; // m ag ne ti c f l u x16 S = 30; // S pee d o f t h e p ri me mover17

19 E_g = ( ( phi * Z * S * P ) / ( 60 * a ) ) * 10 ^ -8;// a v er a ge v o l t a g e b et wee n

20 / / t h e b r us h es21

24 printf ( ” \n Eg = %. 2 f V b et we en t h e b r u s h es ” , E _g ) ;

Scilab code Exa 1.10 calculate Z and Eg

11 / / G iv en d a ta12 n o _o f _c o il s = 4 0;

13 N = 20; // n o o f t ur ns i n e a c h c o i l

14 o me ga = 2 00 ; // a ng ul ar v e l o c i t y o f a r m a t u r e i n r ad /s15 phi = 5 * 10 ^ -3; // f l u x p e r p ol e16 a = 4 ; // No . o f p a r a l l e l p a t h s17 P = 4 ; // No . o f p o l es18

19 / / C a l c u l a t i o n s20 Z = n o_o f_c oi ls * 2 * N ; // No . o f c o nd u c to r s21

22 E_g = ( phi * Z * omega * P ) / ( 2 * %pi * a ) ; //V o lt ag e g e n er a t ed by t he

23 / / a r ma t ur e b et we en b r u s h e s24

25 // D is pl ay t h e r e s u l t s26 disp ( ”E x ampl e 1−10 S o l u t i o n : ” ) ;

27 printf ( ” \n Z = % d c o nd u ct o rs ” , Z ) ;

28 printf ( ” \n Eg = % . 2 f V b et we en t he b r us h es ” , E _g ) ;

Scilab code Exa 1.11 calculate F and find its direction

c o n s o l e .10

11 / / G iv en d a ta12 l = 0.5; // l e ng t h o f t he c on du ct or13 A = 0.1 * 0.2; // a re a o f t h e p ol e f a c e

14 phi = 0.5 * 10 ^ -3; // m ag ne ti c f l u x i n web er

15 I = 10; // C u rr en t i n t he c o nd u ct o r16

17 / / C a l c u l a t i o n s18 B = ( phi ) / ( A ) ; // Fl ux d e n s i t y19

20 F = B * I * l ; // Mag ni tude o f f o r c e21

22 / / D is pl ay t h e r e s u l t23 disp ( ”E x ampl e 1−11 S o l u t i o n : ” ) ;

25 printf ( ” \n a : F = % . 3 f N” , F ) ;

2627 printf ( ” \n b : The f o r c e on t h e c on du ct or i s % . 3 f N

i n an upward d i r e c t i o n a s shown i n f i g 1−13 c ” ,

Scilab code Exa 1.12 repeat previous eg with angle 75

1 / / E l e c t r i c M ac hi ne ry and T r an s f or m e rs

2 / / I r v i n g L k osow3 // P r en t i c e H al l o f I n d i a4 / / 2 nd e d i t i om5

11 / / G iv en d a ta12 l = 0.5; // l e ng t h o f t he c on du ct or13 A = 0.1 * 0.2; // a re a o f t h e p ol e f a c e14 phi = 0.5 * 10 ^ -3; // m ag ne ti c f l u x i n web er15 I = 10; // C u rr en t i n t he c o nd u ct o r

16 t h et a = 7 5; // a n g l e b et we en t he c o nd u ct o r and t he

f l u x d e ns i t y B17

18 / / C a l c u l a t i o n s19 B = ( phi ) / ( A ) ; // Fl ux d e n s i t y20

21 F = B * I * l * sind ( theta ); // Ma gnitu de o f f o r c e22

26 printf ( ” \n F =% f N i n a v e r t i c a l l y upward d i r e c t i o n

” , F ) ;

Scilab code Exa 1.13 calculate counter emf

11 / / G iv en d a ta12 R _ a = 0 .2 5; // Armature r e s i s t a n c e13 V _a = 1 25 ; // dc bus v o l t a g e

14 I _a = 60; / / A rm at ur e c u r r e n t15

16 / / C a l c u l a t i o n s17 E_c = V_a - I_a * R_a ; / / C ou n te r EMF g e n e r a t e d i n

t h e a rm at ur e c o n d u c to r s o f m oto r

21 printf ( ” \n Ec = % d V ” , E _ c ) ;

Scilab code Exa 1.14 calculate Eg phi in linesperpole and mWb

11 / / G iv en d a ta12 V _a = 1 10 ; // v o l t a g e a c r o s s a rm at u re

13 I _a = 60; / / A rm at ur e c u r r e n t14 R _ a = 0 .2 5; // Armature r e s i s t a n c e15 P = 6 ; // No . o f p o l es16 a = 12; // No . o f p at hs17 Z = 720; // No . o f a rm at ur e c o n du c to r s18 S = 18 00 ; / / S pe ed i n rpm19

20 / / C a l c u l a t i o n s21 E_g = V_a + I_a * R_a ; / / G e n e ra t e d EMF i n t h e

a r m a t u r e

2223 ph i_ li ne s = ( E_g * ( 60 * a ) ) / ( ( Z * S * P ) *

10 ^ -8 ) ;

24 / / Fl ux p e r p ol e i n l i n e s25

26 p hi _W b = p hi _l in es * 10 ^ -8; // Flux p e r p o l e i n

w e b e r s27

31 printf ( ” \n a : Eg = %d V ” , E _ g ) ;

33 printf ( ” \n b : p hi = %f l i n e s / p o l e ” , p hi _l in es ) ;

35 printf ( ” \n c : p hi = %f Wb ”, p hi _W b ) ;

Chapter 2

DYNAMO CONSTRUCTION

AND WINDINGS

Scilab code Exa 2.1 calculate a for lap and wave windings

6 / / C ha pt er 2 : Dynamo C o n s t r u c t i o n and W in di ng s7 / / E xa mp le 2−18

11 / / G iv en d a ta12 m = 3 ; // M u l t i p i c i t y o f t he a rm at u re13 P = 14; // No . o f p o l e s

1415 / / C a l c u l a t i o n s16 a_lap = m * P ; // No . o f p a r a l l e l p a t h s i n t h e

a rm at ur e f o r a l a p w in di ng17 a_w ave = 2 * m ; // No . o f p a r a l l e l p a t h s i n t h e

a rm at ur e f o r a wave w in d in g

22 printf ( ” \n a : a = %d p at hs ” , a _l ap ) ;

23 printf ( ” \n b : a = %d p at hs ” , a _w a ve ) ;

Scilab code Exa 2.2 calculate generated emf

1011 / / G iv en d a ta12 P = 14; // No . o f p o l e s13 p h i = 4 .2 e 6; // Flux p er p o l e14 S = 60; // G e ne r at o r s p ee d15 c oi ls = 4 20 ; // No . o f c o i l s16 t u rn s _p e r_ c oi l = 2 0;

17 c o n d u c t o rs _ p e r_ t u r n = 2 ;

18 a _ la p = 4 2; // No . o f p a r a l l e l p at h s i n t he a r m a t ur ef o r a l ap w in di ng

19 a _ wa ve = 6; // No . o f p a r a l l e l p at h s i n t he a r m a t ur ef o r a wave w in di n g20

21 / / C a l c u l a t i o n s22 Z = c oi ls * t u rn s _p e r_ c oi l * c o nd u ct o rs _ pe r _t u rn ; //

No . o f c o nd u c to r s

23 E _g_l ap = (( phi * Z * S * P ) / ( 60 * a_lap ) ) *10 ^ -8; / / G e n e r a t e d EMF f o r24 / / l ap w i nd in g ( Eq 1−5a )25 E _g _wa ve = ( phi * Z * S * P ) / ( 60 * a_w ave ) *

10 ^ -8; / / G e n e r a t e d EMF f o r26 / / wave w in d in g ( Eq 1−5a )27

31 printf ( ” \n a : Eg = %0 . 1 f V ” , E _ g_ l ap ) ;

32 printf ( ” \n b : Eg = %0 . 1 f V ” , E _g _ wa ve ) ;

Scilab code Exa 2.3 calculate polespan p kp

11 / / G iv en d a ta12 s l ot s = 7 2; // No . o f s l o t s13 P = 4 ; // No . o f p o l es

14 c o il s _s p an n ed = 1 4; // 14 s l o t s a re spa nne d w hi l ew i n d in g t he c o i l s15

16 / / C a l c u l a t i o n s17 P ol e_ sp an = s lo ts / P ; // P o le s pa n

18 p _n ot = c oi ls _s pa nn ed / P ol e_ sp an * 1 80 ; // Span o f

t h e c o i l i n19 // e l e c t r i c a l de gr e e s20 funcprot ( 0) ; // U se t o a vo i d t h i s m es sa ge ” W arning

: r e d e f i n i n g f u n c t i o n : b e t a ”21 b e ta = ( 18 0 - p _n ot ) ;

22 k_p1 = cosd ( beta / 2 ) ; // P it ch f a c t o r u si ng eq(2 −7)

23 k_p2 = sind ( p_not / 2 ) ; // P it ch f a c t o r u si ng eq(2 −8)

25 // D is pl ay t h e r e s u l t s

26 disp ( ”E x ampl e 2−3 S o l u t i on : ” )27 printf ( ” \n a : F ul l −p i t c h c o i l s pa n = %d s l o t s / p o l e

” , P ol e_ sp an ) ;

28 printf ( ” \n b : p = %d d e gr e e s ” , p _n ot ) ;

29 printf ( ” \n c : kp = %. 2 f \ t \ t eq (2 −7) ” , k_p1 ) ;

30 printf ( ” \n d : kp = %. 2 f \ t \ t eq (2 −8) ” , k_p2 ) ;

Scilab code Exa 2.4 calculate kp

c o n s o l e .10

11 / / G iv en d a ta12 f ra ct io na l_ pi tc h = 1 3 / 1 6;

13 s l o t = 9 6; // No . o f s l o t s

14 P = 6 ; // No . o f p o l es

1516 / / C a l c u l a t i o n17 k_p = s in d( ( f ra ct io na l_ pi tc h * 1 80 ) / 2 ) ; //

P it ch f a c t o r18

19 / / D is pl ay t h e r e s u l t20 disp ( ”E x ampl e 2−4 S o l u t i on : ” )

21 printf ( ” \n kp = %. 4 f ” , k _ p ) ;

Scilab code Exa 2.5 find alpha n theta

11 / / G iv en d a ta12 P = 12; // No . o f p o l e s13 t he ta = 3 60 ; // No . o f m ec ha ni ca l d e gr e es o f

r o t a t i o n14 a l p ha _ b = 1 80 ; / / No . o f e l e c t r i c a l d e g r e e s f o r

f i n d i n g c as e b i n t h e q ue st i o n15

16 / / C a l c u l a t i o n s17 alpha = ( P * theta ) / 2; // No . of e l e c t r i c a ld e g r e e s i n one r e v o l u t i o n

18 n = alpha / 360; // No . o f a c c y c l e s19 t heta _b = ( 2 * alp ha_b ) / P ; // No . o f m e ch a ni c al

d e g r e e s o f r o t a t i o n

20 // f o r f i n d i n g c as e b i n t h e q ue st i o n21

22 // D is pl ay t h e r e s u l t s23 disp ( ”E x ampl e 2−5 S o l u t i on : ” )

24 printf ( ” \n a : a l ph a = %d d e g r e e s ” , a lp ha ) ;

25 printf ( ” \n n = %d c y c l e s ” , n ) ;

26 printf ( ” \n b : t h et a = %d m ec h an i ca l d e g r e es ” ,

t h et a _b ) ;

Scilab code Exa 2.6 find n alpha kd for different number of slots

11 / / G iv en d a ta12 P = 4 ; // No . o f p o l e s13 p hi = 3; // No . o f p ha se s14 s l o ts _ ( 1) = 1 2; // No . o f s l o t s f o r c a s e 115 s l o ts _ ( 2) = 2 4; // No . o f s l o t s f o r c a s e 216 s l o ts _ ( 3) = 4 8; // No . o f s l o t s f o r c a s e 317 s l o ts _ ( 4) = 8 4; // No . o f s l o t s f o r c a s e 4

1819 / / C a l c u l a t i o n s20 e l e c t ri c al _ de g re e s = 1 80 * 4 ;

21 i = 1 ; / / where i i s c as e s u b s c r i p t . eg c as e1 , c a se 2 ,e t c

23 while i < = 424 a lp ha _ ( i ) = e l ec t ri c al _ de g re e s / s lo t s_ ( i ) ; //e l e c t r i c a l d e g r e e s

25 // p e r s l o t s f o r c a s e i26 n_ (i ) = slots _( i) / ( P * phi ); // No . o f a c

c y c l e s f o r c a se 127 k_d (i ) = s ind ( n_ (i )*( alpha _( i) / 2 ) ) / ( n_ (

i ) * s in d( a lp ha _ (i ) / 2) );

28 i = i + 1 ;

29 end ;

33 printf ( ” \n a : ” ) ;

34 i = 1 ; / / where i i s c as e s u b s c r i p t . eg c a se 1 , c a se 2 ,e t c

36 while i < = 4

37 printf ( ” \n \ t %d : a l p h a = %. 2 f d e g r e e s / s l o t ”, i , alpha_ (i ) ) ;

38 printf ( ” \n\ t n = %d s l o t s / po l e −p h as e ” ,

n_ ( i) ) ;

39 printf ( ” \n\ t kd = %. 3 f ” , k _d ( i ) ) ;

40 printf ( ” \n” ) ;

41 i = i + 1 ;

42 end ;

44 printf ( ” \n\n\n b : ” ) ;

45 printf ( ” \n \ t \ t n \ t a lp ha i n d e g r ee s \ t \ t kd ” ) ;

46 printf ( ” \n \ t

” ) ;

47 i = 1 ;48

49 while i < = 4

50 printf ( ” \n \ t \ t %d \ t %. 2 f \ t \ t \ t \t% . 3 f ” , n_ (i

) , a lp ha _( i) , k_d ( i) ) ;

51 i = i +1;

52 end ;53 printf ( ” \n \ t

” ) ;

Scilab code Exa 2.7 calculate Eg Np kd kp Egp

11 / / G iv en d a ta

12 s l ot s = 7 2; // No . o f s l o t s13 P = 6 ; // No . o f p o l es14 p h a se = 3; // t h r e e p ha se s t a t o r a rm at ur e15 N _c = 20; // Number o f t u r ns p er c o i l16 pitch = 5 / 6;

17 p hi = 4 .8 e +6 ; // f l u x p e r p o le i n l i n e s18 S = 12 00 ; / / R ot or s p ee d19

20 / / C a l c u l a t i o n s21 f = ( P * S ) / 120; // F re qu en cy o f r o t o r

2223 E_ g_p erc oil = 4.44 * phi * N_c * f *10 ^ -8; //G en er at e d e f f e c t i v e v o l t a g e

24 // p e r c o i l o f a f u l l p it ch c o i l25

26 N_p = ( slots / phase ) * N_c ; // T o t a l number o f

t u rn s p er p ha se27

28 n = slots / ( phase * P ) ; // No . o s s l o t s p e r p ol ep e r p ha se

30 alpha = ( P * 180 ) / slots ; // No . of e l e c t r i c a ld e gr e e s be tw e en a d ja c en t s l o t s

32 k_d = sind ( n * alpha / 2 ) / ( n * sind ( alpha / 2

) ) ; // D i s t r i b u t i o n f a c t o r33

34 sp an = p itc h * 18 0; // S pan o f t h e c o i l i ne l e c t r i c a l d e g r ee s

36 k_p = sind ( span / 2 ) ; // P it ch f a c t o r37

38 E_gp = 4.44 * phi * N_p * f * k_p * k_d * 10 ^ -8;

// T ot al g e ne r a t ed v o l t a g e39 / / p er p ha se c o n s i d e r i n g kp and kd40

41 / / D is pl ay t h e r e s u l t42 disp (

”E x ampl e 2−7 S o l u t i on : ”)

43 printf ( ” \n a : Eg / c o i l = %. 2 f V/ c o i l ” , E _ g_ p er c oi l ) ;

44 printf ( ” \n b : Np = %d t u r n s / p h a se ” , N _ p ) ;

45 printf ( ” \n c : kd = %. 3 f ” , k _ d ) ;

46 printf ( ” \n d : kp = %. 3 f ” , k _ p ) ;

47 printf ( ” \n e : Egp = %. 2 f V/ p h a s e ” , E_gp ) ;

Scilab code Exa 2.8 calculate f S omega

11 / / G iv en d a ta12 P = 8 ; // No . o f p o l es13 S = 900; // Speed i n r e v o l u t i o n s / mi nut e14 f _1 = 50; // F re qu en cy o f g e n er a t ed v o l t a g e from

g e n er a t or 1

15 f _2 = 25; // F re qu en cy o f g e n er a t ed v o l t a g e fromg e n er a t or 2

17 / / C a l c u l a t i o n s18 f = ( P * S ) / 120; // F re qu en cy o f t he g e n er a t ed

v o l t a g e19 S_1 = ( 120 * f_1 ) / P ; / / S pe ed o f g e n e r a t o r ( rpm )

1 t o g e n e r a t e 50 Hz v o l t a ge20 S_2 = ( 120 * f_2 ) / P ; / / S pe ed o f g e n e r a t o r ( rpm )

2 t o g e n e r a t e 25 Hz v o l t a ge21 o mega _1 = ( 4 * %pi * f_1 ) / P ;

// Sp eed o f g e n e r a to r 1 i n r a d / s22 o mega _2 = ( 4 * %pi * f_2 ) / P ; // Sp eed o f

g e n e r a to r 2 i n r a d / s23

26 printf ( ” \n a : f = %d Hz ” , f ) ;

27 printf ( ” \n b : S 1 = %d rpm \n S2 = %d rpm ” , S _ 1 ,

S _2 ) ;

28 printf ( ” \n c : omega1 = %f r ad / s \n omega2 = %f

r a d / s ” , o me g a_ 1 , o m e ga _ 2 ) ;

Chapter 3

DC DYNAMO VOLTAGE

RELATIONS DC

GENERATORS

Scilab code Exa 3.1 calculate I1 If Ia Eg

6 / / C ha pt er 3 : DC Dynamo V o l t a g e R e l a t i o n s − DCG e n e r a t o r s

7 / / E xa mp le 3−18

11 / / G iv en d a ta12 k W = 15 0; // Power r a t i n g o f Shunt g e n e r a to r i n kW13 V_1 = 2 50 ; // V ol ta ge r a t i n g o f Shunt g e n er a t or i n V14 V _a = V_1 ; // V ol ta ge r a t i n g o f Shunt g e n er a t or i n V15 R _f = 50; // F i el d r e s i s t a n c e i n ohm

16 R _ a = 0 .0 5; // Armature r e s i s t a n c e i n ohm

1718 / / C a l c u l a t i o n s19 I_1 = ( kW * 1000 ) / V_1 ; // F u ll −l oa d l i n e c u r r e n t

f l o w i n g t o t h e l o ad i n A20 I_f = V_1 / R_f ; // F i e l d c u r re n t i n A21 I_a = I_f + I_1 ; // Armature c u r r e nt i n A22 E _ g = V _ a + I _ a * R _ a ; // F u ll l oa d g e ne r a t ed

v o l t a ge i n V23

26 printf ( ” \n a : I 1 = %d A ” , I _ 1 ) ;27 printf ( ” \n b : I f = %d A ” , I _ f ) ;

28 printf ( ” \n c : I a = %d A ” , I _ a ) ;

29 printf ( ” \n d : Eg = %. 2 f A ” , E _ g ) ;

Scilab code Exa 3.2 calculate Rd Eg

7 / / E xa mp le 3−28

1011 / / G iv en d a ta12 k W = 10 0; // Power r a t i n g o f t he g e n er a t or i n kW13 V_1 = 5 00 ; // V ol ta ge r a t i n g o f h te g e ne r a t or i n V14 R _ a = 0 .0 3; // Armature r e s i s t a n c e i n ohm

15 R _f = 1 25 ; / / S hu nt f i e l d r e s i s t a n c e i n ohm

16 R _ s = 0 .0 1; // S e r i e s f i e l d r e s i s t a n c e i n ohm17 I _d = 54; // D i ve r te r c u r r e n t i n A18

19 / / C a l c u l a t i o n s20 I_1 = ( kW * 1000 ) / V_1 ; // F u ll −l oa d l i n e c u r r e n t

f l o w i n g t o t h e l o ad i n A21 I_f = V_1 / R_f ; // Shunt F i e l d c u r r e nt i n A22 I_a = I_f + I_1 ; // Armature c u r r e nt i n A23 I_s = I_a - I_d ; // S e r i e s F i e l d c ur r e n t i n A24 R_d = ( I_s * R_s ) / I_d ; // D i v e r t e r r e s i s t a n c e i n

25 E _ g = V _ 1 + I _ a * R _ a + I _ s * R _ s ; / / G e n er a t e dv o l t a g e a t f u l l l oa d i n V

29 printf ( ” \n a : Rd = %. 4 f ohm ” , R _ d ) ;

30 printf ( ” \n b : Eg = %. 2 f V ” , E _ g ) ;

Scilab code Exa 3.3 calculate Vnoload

7 / / E xa mp le 3−3

12 E _ o ri g = 1 50 ; // Armature v o l t a g e o f t he g e n e r a t or

i n V13 S _ o ri g = 1 80 0; // Speed o f t he g e n er a t or i n rpm14 S _ f i n a l_ a = 2 0 00 ; // I n c r e a s ed Speed o f t he g e n er a t or

i n rpm f o r c as e a15 S _ f i n a l_ b = 1 6 00 ; // I n c r e a s ed Speed o f t he g e n er a t or

i n rpm f o r c as e b16

17 / / C a l c u l a t i o n s18 E _f in al _a = E _o ri g * ( S _f in al _a / S _o ri g ) ; / / No−

l oa d v o l t a ge o f t h e g e n e ra t o r19 // g e n er at or i n V f o r c a se a

20 E _f in al _b = E _o ri g * ( S _f in al _b / S _o ri g ) ; / / No−l oa d v o l t a ge o f t h e g e n e ra t o r

21 // g e n er at or i n V f o r c a se b22

25 printf ( ” \n a : E f i n a l = %. 1 f V ” , E _f in al _a ) ;

26 printf ( ” \n b : E f i n a l = %. 1 f V ” , E _f in al _b ) ;

Scilab code Exa 3.4 calculate E

7 / / E xa mp le 3−48

12 S _ f in a l = 1 20 0; // Speed o f th g e n er a t or i n rpm13 E _ o r ig _ a = 6 4. 3; // Armature v o l t a g e o f t heg en er at or i n V f o r c a se a

14 E _ o r ig _ b = 8 2. 9; // Armature v o l t a g e o f t heg en er at or i n V f o r c a se b

15 E _ or ig _ c = 1 62 .3 ; // Armature v o l t a g e o f t heg en er at or i n V f o r c a se c

17 S _ o r ig _ a = 1 20 5; // V ar ie d Speed o f t he g e n er a t o r i nrpm f o r c as e a

18 S _ o r ig _ b = 1 19 4; // V ar ie d Speed o f t he g e n er a t o r i n

rpm f o r c as e b19 S _ o r ig _ c = 1 20 2; // V ar ie d Speed o f t he g e n er a t o r i n

rpm f o r c as e c20

21 / / C a l c u l a t i o n s22 E_1 = E _o ri g_ a * ( S _f in al / S _o ri g_ a ) ; / / No− l o a d

v o l t a ge o f t h e g e ne r a t or23 // g e n er at or i n V f o r c a se a24 E_2 = E _o ri g_ b * ( S _f in al / S _o ri g_ b ) ; / / No− l o a d

v o l t a ge o f t h e g e ne r a t or25

// g e n er at or i n V f o r c a se b26 E_3 = E _o ri g_ c * ( S _f in al / S _o ri g_ c ) ; / / No− l o a dv o l t a ge o f t h e g e ne r a t or

27 // g e n er at or i n V f o r c a se c28

31 printf ( ” \n a : E1 = %. 1 f V a t %d rpm ” , E_ 1 , S _ fi na l

32 printf ( ” \n b : E2 = %. 1 f V a t %d rpm ” , E_ 2 , S _ fi na l

33 printf ( ” \n c : E3 = %. 1 f V a t %d rpm ” , E_ 3 , S _ fi na l) ;

Scilab code Exa 3.5 calculate Ia Eg

7 / / E xa mp le 3−58

11 / / G iv en d a ta12 V = 125; // Rated v o l t ag e o f t he s hu nt g e n er a t or i n

V13 R _ a = 0 .1 5; // Armature r e s i s t a n c e i n ohm14 V _a = 0; // Shunt g e ne r a t or i s l oa de d p r o g r e s s i v e l y

u n t i l t he t e r m i n a l v o l t a ge15 / / a c r o s s t h e l o a d i s z e r o v o l t16 I _1 = 96; // Load c u r r e n t i n A17 I _f = 4; // F i e l d c ur r e nt i n A18

19 / / C a l c u l a t i o n s20 I_a = I_f + I_1 ; // Armature c u r r e nt i n A21 E_g = V_a + I_a * R_a ; // V ol ta ge g e ne r a t ed i n t he

a rm at ur e i n V22

25 printf ( ” \n I a = %d A ” , I _ a ) ;

26 printf ( ” \n E g = % d V ” , E _ g ) ;

Scilab code Exa 3.6 calculate VR

7 / / E xa mp le 3−68

11 / / G iv en d a ta12 V _n 1 = 1 35 ; // No l oa d v o l t ag e o f t he s hu nt

g e n e r a to r i n V13 V _f 1 = 1 25 ; // F ul l l oa d v o l t a ge o f t h e s h u n t

g e n e r a to r i n V

1415 / / C a l c u l a t i o n16 VR = ( V_n1 - V_f1 ) / V_f1 * 100; / / P e r ce n t a ge

v o l t a ge r e g u l a t i o n17

20 printf ( ” \n VR = %d p e r c e n t ” , VR ) ;

Scilab code Exa 3.7 calculate Vnoload

3 // P r en t i c e H al l o f I n d i a

4 / / 2 nd e d i t i om5

7 / / E xa mp le 3−78

11 / / G iv en d a ta12 V R = 0 .1 05 ; // v o l t a ge r e g u l a t i o n

13 V _f 1 = 2 50 ; // F ul l l oa d v o l t a ge o f t h e s h u n tg e n e r a to r i n V

15 / / C a l c u l a t i o n16 V_n1 = V_f1 + ( V_f1 * VR ) ; / / No−l oa d v o l t a ge o f

t h e g e ne r a t or i n V17

20 printf ( ” \n Vn1 = %. 1 f V ” , V_n1 ) ;

Scilab code Exa 3.8 calculate IsNs Rd

6 / / C ha pt er 3 : DC Dynamo V o l t a g e R e l a t i o n s − DCG e n e r a t o r s7 / / E xa mp le 3−88

c o n s o l e .

1011 / / G iv en d a ta12 N _ f = 1 00 0; / / S hu nt f i e l d w i nd i n g t u r n s13 N _s = 4; // S e r i e s f i e l d w in d in g t u r n s14 I_f = 0 .2 ; // F i e l d c ur r e nt i n A15 I _a = 80; // F u ll l oa d a rm at ur e c u r r e nt i n A16 R _ s = 0 .0 5 ; // S e r i e s f i e l d r e s i s t a n c e i n ohm17

18 / / C a l c u l a t i o n s19 d eb a_ I_ f_ N_ f = I _f * N _f ;

20 I _ s_ N _s = d e ba _ I_ f _N _ f ; / / S e r i e s f i e l d a mp ere−t u r n s

21 I_s =( I _s _N _s ) / N_s ; // D es ir ed c u r r e n t i n A i nt he s e r i e s f i e l d r e q u i r e d t o

22 // p ro du ce v o l t a g e r i s e23 I_d = I_a - I_s ; // D i ve r t e r c u r r e n t i n A24 R_d = ( I_s * R_s ) / I_d ; // D i v e r t e r r e s i s t a n c e i n

28 printf ( ” \n a : I s Ns = %d A t ” , I _s _N _s ) ;

29 printf (” \n b : Rd = %. 4 f ohm ”

, R _ d ) ;

Scilab code Exa 3.9 calculate Rd Vnl Vfl

7 / / E xa mp le 3−98

c o n s o l e .10

11 / / G iv en d a ta12 k W = 60; // Power r a t i n g o f t he g e n er a t o r i n kW13 V = 240; // V ol ta ge r a t i n g o f t he g e n er a t or i n V14 I _f = 3; / / I n c r e a s e i n t he f i e l d c u r r e nt i n A15 O C_ V = 2 75 ; / / O ve r Compounded V o l t a g e i n V16 I_l = 2 50 ; // Rated l oa d c u r r e nt i n A17 N_f = 2 00 ; // No . o f t ur ns p er p o l e i n t h e s h u n t

f i e l d w i ndi ng18 N _s = 5; // No . o f t ur ns p e r p ol e i n t h e s e r i e s

f i e l d w i ndi ng19 R_f = 2 40 ; / / Shunt f i e l d r e s i s t a n c e i n ohm20 R _s = 0 .0 05 ; / / S e r i e s f i e l d r e s i s t a n c e i n ohm21

22 / / C a l c u l a t i o n s23 d eb a_ I_ f_ N_ f = I _f * N _f ;

24 I _ s_ N _s = d e ba _ I_ f _N _ f ; / / S e r i e s f i e l d a mp ere−t u r n s25 I_s =( I _s _N _s ) / N_s ; // D es ir ed c u r r e n t i n A i n

t he s e r i e s f i e l d r e q u i r e d t o26 // p ro du ce v o l t a g e r i s e27 I_d = I_l - I_s ;

// D i ve r t e r c u r r e n t i n A28 R_d = ( I_s * R_s ) / I_d ; // D i v e r t e r r e s i s t a n c e i nohm

29 NL_ MMF = ( V / R_f ) * N_f ; / / No−l o a d MMF30 I _ f _N _ f = N L_ M MF ;

31 F L_ MM F = I _f _N _f + I _s _N _s ; // F ul l −l o a d MMF32

35 printf ( ” \n a : Rd = %. 5 f ohm ” , R _ d ) ;

36 printf ( ” \n b : No−lo ad MMF = %d At/ po le ” , N L_ MM F ) ;

37 printf ( ” \n F u l l −lo ad MMF = %d At/ po le ” , F L_ MM F );

Scilab code Exa 3.10 determine approx size of dynamo

7 / / E xa mp le 3−108

11 / / G iv en d a ta12 k W = 5 0; // Power r a t i n g o f t h e dynamo13 V = 125; // Rated v o l t ag e i n V14 S = 18 00 ; // S pe ed o f t h e dynamo i n rpm15 I _ f = 20 ; // E x c i t i n g f i e l d c u r r e n t

16 M a x_ t em p _r i se = 2 5; / / Maximum T e mp e ra t ur e r i s e i nd eg re e c e l s i u s

17 I_l = 4 00 ; // Load C ur re nt i n A18 // INSULATION CLASS A19 // COMPOUND WINDING20

21 / / D is pl ay t h e r e s u l t22 disp ( ”E x ampl e 3−10 S o l u t i o n : ” )

23 printf ( ” \n a : S i n ce t he s pe e d i s r e du ce d i n h al f , wemust r e d uc e t h e kW r a t i n g i n h a l f . C on s eq ue nt ly ,t h e 2 5kW, 9 00 rpm dynamo h a s t h e same s i z e . ” ) ;

24 printf ( ” \n\n b : S i n c e we have c ut t h e s pe ed i n h a l f b ut m a i n t ai n e d t h e same kW r a t i n g , t h e dynamo h a s

t wi ce t h e s i z e a s t h e o r i g i n a l . ” ) ;

25 printf ( ” \n\n c : H a lf t h e s i z e . ” ) ;

26 printf ( ” \n\n d : Same s i z e . ” ) ;

Chapter 4

DC DYNAMO TORQUE

RELATIONS DC MOTORS

Scilab code Exa 4.1 calculate force and torque

6 / / C h ap t er 4 : DC Dynamo T or qu e R e l a t i o n s −DC Motors7 / / E xa mp le 4−18

11 / / G iv en d a ta12 d = 0.5; // d i am e t e r o f t h e c o i l i n m13 l = 0.6; // a x i a l l en gt h o f t h e c o i l i n m

14 B = 0.4; // f l u x d e n s i t y i n T15 I = 25; // c ur r e nt c a r r i e d by t h e c o i l i n A16 t h et a = 6 0; // a n gl e be t we en t he u s e f u l f o r c e & th e

i n t e r p o l a r r e f a x i s i n deg17

19 F = B * I * l ; // f o r c e d ev el op ed on e a c h c o i l s i d ei n N20 f = F * s in d( th et a) ; // f o r c e d ev el op ed a t t h e

i n s t a n t t he c o i l l i e s a t an a ng l e21 // o f 60 w . r . t t h e i n t e r p o l a r r e f a x i s22 r = d / 2; // r ad i u s o f t h e c o i l i n m23 T_c = f * r ; // t or qu e d ev el op ed i n N−m24 T_c1 = T_c * 0 .2248 * 3.281 ; // t o rq u e d e ve l op e d i n

l b − f t b y f i r s t m et ho d25 T_ c2 = T_c * 0 .7 37 56 2 ; // t or qu e d ev el op ed i n l b − f t

by s e c o n d m eth od

29 printf ( ” \n a : F = %d N ” , F ) ;

30 printf ( ” \n b : f = %. 2 f N ” , f ) ;

31 printf ( ” \n c : Tc = %. 2 f N−m ” , T _ c ) ;

32 printf ( ” \n d : 1 . 3 N−m ∗ 0 . 2 24 8 l b /N ∗ 3 . 2 8 1 f t /m =%. 2 f l b− f t ” , T_c1 ) ;

33 printf ( ” \n 1 . 3 N−m ∗ 0 . 7 3 7 5 6 2 l b . f t /N . m = % . 2 f l b − f t ” , T_c2 ) ;

Scilab code Exa 4.2 calculate force and torque

11 / / G iv en d a ta12 d = 1 8 ; // d i am e t e r o f h t e c o i l i n i n c h e s13 l = 2 4 ; // a x i a l l en gt h o f t h e c o i l i n i nc he s14 B = 24000 ; / / Fl ux d e n s i t y i n l i n e s / s q . i n c h e s15 I = 2 6 ; // C u r r e n t c a r r i e d by t h e c o i l i n A16 theta = 60 ; // a n gl e bet w ee n t he u s e f u l f o r c e & th e

i n t e r p o l a r r e f a x i s i n deg17

19 / / C a l c u l a t i o n s20 F = ( B * I * l * 10 ^ -7 ) / 1.13 ; // f o r c e

d e v e l o p e d o n e a c h c o i l s i d e i n l b21 f = F * s in d( th et a) ; // f o r c e d ev el op ed a t t h e

i n s t a n t t he c o i l l i e s a t an a ng l e22 // o f 60 w . r . t t h e i n t e r p o l a r r e f a x i s23 r = d / 2; // r ad i u s o f t h e c o i l i n i nc he s24 T_c = f * ( r * 1 / 12) ; // t or qu e d ev el op ed i n l b .

f t / c o n d u c t o r25

28 printf (” \n a : F = %. 3 f l b ”

, F ) ;

29 printf ( ” \n b : f = %. 2 f l b ” , f ) ;

30 printf ( ” \n c : Tc = %. 3 f l b − f t / c o n d u c to r ” , T _ c ) ;

Scilab code Exa 4.3 calculate average force and torque

11 / / G iv en d a ta12 Z = 700 ; / / no . o f c o nd u c to r s13 d = 2 4 ; // d i am et er o f t he a rm at ur e o f t he dc motor

i n i n ch e s14 l = 3 4 ; // a x i a l l en gt h o f t h e c o i l i n i nc he s15 B = 50000 ; / / Fl ux d e n s i t y i n l i n e s / s q . i n c h e s16 I = 2 5 ; // C u r r e n t c a r r i e d by t h e c o i l i n A17

18 / / C a l c u l a t i o n s19 F_av = ( B * I * l * 10 ^ -7 ) / 1.13 * ( 700 * 0.7

) ; // a v e ra g e f o r c e20 // d e v e l o p e d on e a c h c o i l s i d e i n l b21 r = d / 2; // r ad i u s o f t h e c o i l i n i nc he s22 T_av = F_av * ( r /12 ) ; // a rm at ur e a v e ra g e t o r q ue

i n l b −f t23

26 printf (” \n a : Fav = %. 2 f l b ”

, F_av ) ;

27 printf ( ” \n b : Tav = %. 2 f l b−f t ” , T_av ) ;

Scilab code Exa 4.4 calculate torque developed

4 / / 2 nd e d i t i om5

c o n s o l e .10

11 / / G iv en d a ta12 slots = 120 ; // No . o f a rm at u re s l o t s13 c o nd u ct o rs _ pe r _s l ot = 6 ;

14 B = 60000 ; / / Fl ux d e n s i t y i n l i n e s / s q . i n c h e s15 d = 2 8 ; // d i am et er o f t he a rm at ur e16 l = 1 4 ; // a x i a l l en gt h o f t h e c o i l i n i nc he s17 A = 4 ; // No . o f p a r a l l e l p a t h s18 s pan = 0. 72 ; // P ol e a r c s s pa n 72% o f t he a rm at ur e

s u r f a c e

19 I = 133.5 ; // Armature c u r r e nt i n A20

21 / / C a l c u l a t i o n s22 Z _T a = s lo ts * c on du ct or s_ pe r_ sl ot * s pa n ; / / No .

o f a rm at ur e c o n d u c to r s23 F_t = ( B * I * l ) / ( 1 .13 * 10 ^ 7 * A ) * Z_Ta ;

// F or ce d ev el op ed i n l b24 r = ( d / 2 ) / 12 ; // r a d i u s o f t he a rm at u re i n

f e e t25 T = F _t * r ; // T i t a l t or qu e d ev el op ed26

29 printf ( ” \n T = %d l b− f t ” , T ) ;

Scilab code Exa 4.5 calculate armature current

6 / / C h ap t er 4 : DC Dynamo T or qu e R e l a t i o n s −DC Motors

7 / / E xa mp le 4−5

c o n s o l e .10

11 / / G iv en d a ta12 slots = 120 ; // No . o f a rm at u re s l o t s13 c o nd u ct o rs _ pe r _s l ot = 6 ;

14 B = 60000 ; / / Fl ux d e n s i t y i n l i n e s / s q . i n c h e s15 d = 2 8 ; // d i am et er o f t he a rm at ur e16 l = 1 4 ; // a x i a l l en gt h o f t h e c o i l i n i nc he s17 A = 4 ; // No . o f p a r a l l e l p a t h s

18 s pan = 0. 72 ; // P ol e a r c s s pa n 72% o f t he a rm at ur es u r f a c e

19 T _a = 1500 ; // t o t a l a rm at ur e t or qu e i n l b −f t20

21 / / C a l c u l a t i o n22 Z = s lo ts * c on du ct or s_ pe r_ sl ot ; // No . o f a rm at ur e

c o n d u c t o r s23 r = ( d / 2 ) / 12 ; // r a d i u s o f t he a rm at u re i n

f e e t24 I_a = ( T_a * A * 1.13 e7 ) / ( B * l * Z * r * span

) ; // A rma tu re c u r r e n t i n A25

28 printf ( ” \n I a = %. 1 f A ” , I _ a ) ;

Scilab code Exa 4.6 calculate torque due to change in field flux

7 / / E xa mp le 4−68

11 / / G iv en d a ta12 T_old = 150 ; // To rque d e ve l op e d by a motor i n N−m.13 disp ( ”E x ampl e 4−6” )

14 disp ( ” Given d at a : ” )

15 printf ( ” \n \ t \ t \ t p h i \ t I a \ t T ” ) ;

16 printf ( ” \n \ t \ t \ t ” ) ;

17 printf ( ” \n O r i g i n a l c o n d i t i o n \ t 1 \ t 1 \ t 150 N−m ”) ;

18 printf ( ” \n New c o n d i t i o n \ t \ t 0 . 9 \ t 1 . 5 \ t ? ” ) ;

20 / / C a l c u l a t i o n21 T_new = T_old * ( 0.9 / 1 ) * ( 1.5 / 1 ) ; // New

t o rq u e p ro du ce d i n N−m22

23 / / D is pl ay t h e r e s u l t24 printf ( ” \n\n S o l u t i on : ” )

25 printf (” \n U si ng t he r a t i o method , t he new t o rq u e i st he p ro du ct ” ) ;

26 printf ( ” \n o f two new r a t i o c h an ge s : ” ) ;

27 printf ( ” \n T = %. 1 f N−m ” , T _n ew ) ;

Scilab code Exa 4.7 calculate Ia and percentage change in Ia and E

7 / / E xa mp le 4−7

c o n s o l e .10

11 / / G iv en d a ta12 R _a = 0.25 ; // Armature r e s i s t a n c e i n ohm13 BD = 3 ; // Brush c o nt a ct dro p i n v o l t14 V = 120 ; // A pp l ie d v o lt a g e i n v o l t15 E_a = 110 ; // EMF i n v o l t a t a g i ve n l oa d16 E_b = 105 ; // EMF i n v o l t due t o a p p l i c a t i o n o f

e x tr a l oa d

1718 / / C a l c u l a t i o n s19 I_a_a = ( V - ( E_a + BD ) ) / R_a ; / / A r ma t ur e

c ur r e nt f o r E a20 I_a_b = ( V - ( E_b + BD ) ) / R_a ; / / A r ma t ur e

c ur r e nt f o r E b21 del_E = ( ( E_a - E_b ) / E_a ) * 100 ; / / % c h a n g e

i n c o u n t e r EMF22 del_I = ( ( I_a_a - I_a_b ) / I_a_a ) * 100 ; // %

c ha ng e i n a rm at ur e c u r r e n t23

26 printf ( ” \n a : I a = %d A ” , I _a _a ) ;

27 printf ( ” \n b : At i n c r e a s e d l o ad \n I a = %d A ”, I_ a_ b ) ;

28 printf ( ” \n c : d e l E c = %. 2 f p e r c e nt \n d e l I a =%. 2 f p e r ce n t ” , d el _E , d el _I ) ;

Scilab code Exa 4.8 calculate speed at different loads

4 / / 2 nd e d i t i om5

11 / / G iv en d a ta12 V_a = 120 ; // Rated t e r m in a l v o l t a g e o f t he DC

motor i n v o l t

13 R_a = 0.2 ; // Armature c i r c u i t r e s i s t a n c e i n ohm14 R_sh = 60 ; // S hun t f i e l d r e s i s t a n c e i n ohm15 I_l = 40 ; / / L in e c u r r e nt i n A @ f u l l l o ad16 BD = 3 ; // Brush v o l t a ge dr op i n v o l t17 S _o ri g = 1 80 0 ; // Rated f u l l −l o ad s pe ed i n rpm18

19 / / C a l c u l a t i o n s20 I_f = V_a / R_sh ; // F i e l d c ur r e n t i n A21 I_a = I_l - I_f ; / / A rm at ur e c u r r e n t @ f u l l l o a d22 E _c _or ig = V_a - ( I_a * R_a + BD ) ; // Back EMF @

f u l l l o a d23

24 I_a_a = I_a / 2 ; // Armature c u r r e nt @ h a l f l o ad25 E_c_a = V_a - ( I_a_a * R_a + BD ) ; // Back EMF @

h a l f l oa d26 S_a = S_orig * ( E_c_a / E_c _or ig ) ; / / S pe ed @

f u l l l o a d27

28 I_a_b = I_a * ( 5 / 4 ) ; / / A rm at ur e c u r r e n t @ 1 2 5%o v e r l o a d

29 E_c_b = V_a - ( I_a_b * R_a + BD ) ; // Back EMF @

1 25% o v e r l o a d30 S_b = S_orig * ( E_c_b / E_c _or ig ) ; / / S pe ed @ 1 25

% o v e rl o a d31

32 / / D is pl ay t h e r e s u l t

33 disp ( ”E x ampl e 4−8 S o l u t i on : ” ) ;

3435 printf ( ” \n a : At f u l l l oa d ” ) ;

36 printf ( ” \n S = %. 1 f rpm ” , S _ a ) ;

38 printf ( ” \n b : At 125 p e r c e n y t o v e r l o ad ” ) ;

39 printf ( ” \n S = %. 1 f rpm ” , S _ b ) ;

Scilab code Exa 4.9 calculate speed with increased line current

1011 / / G iv en d a ta12 I _ l _o r ig = 4 0; // o r i g i n a l L i n e c ur r e nt i n A13 I _ l _ fi n al = 6 6; // F i n al L in e c u r r e n t i n A14

15 p hi _o ri g = 1;

16 / / f i e l d f l u x i s i n c r e a s e d by 1 2% s o EMF p ro d uc edand t e r m i n a l

17 / / v o l t a g e w i l l a l s o i n c r e a s e by 1 2%18 p h i_ f in a l = 1 .1 2;

1920 V_a = 1 20 ;

21 R _ s h _o r ig = 6 0; // O r i g i n al F i e l d c k t r e s i s t a n c e i nohm

22 R _s h_ fi na l = 50 ; // D ec re as ed f i n a l f i e l d c kt

r e s i s t a n c e i n ohm

2324 R _a = 0 .2 ; // Armature r e s i s t a n c e i n ohm25 B D = 3; // Brush v o l t a g e dr op i n v o l t26 S _ o ri g = 1 80 0; // Rated f u l l − l o ad s pe ed27

28 / / C a l c u l a t i o n s29 I _ f _o ri g = V _a / R _s h_ or ig ; // O r i g i n al F i e l d

c u r r e n t i n A30 I _a _o ri g = I _l _o ri g - I _f _o ri g ; // O r i g i na l

A rm at ur e c u r r e n t @ f u l l l o a d31 E _c _or ig = V_a - ( I _a_ or ig * R_a + BD ) ; / / B ac k

EMF @ f u l l lo ad32

33 I _f _f in al = V _a / R _s h_ fi na l ; / / F i n a l f i e l dc u r r e n t i n A

34 I _ a _f i na l = I _ l_ f in a l - I _ f_ f in a l ; // F i na lArm atur e c u r r e n t i n A

35 E_ c_ fi na l = V_a - ( I_ a_ fi na l * R_a + BD ) ; //F i n a l EMF i n d u c e d

36 S = S_orig * ( E_ c_ fi na l / E _c _or ig ) * ( p hi _or ig /

p hi _f in al ) ;

37 / / F i na l s pe ed o f t he motor38

41 printf ( ” \n S = %. 1 f rpm ” , S ) ;

Scilab code Exa 4.10 calculate power developed

7 / / E xa mp le 4−108

11 / / G iv en d a ta12 I_a_1 = 38 ; // Armature c u r r e nt i n A @ f u l l −l oa d a s

p e r e xa mp le 4−8a13 E _c _1 = 1 09 .4 ; / / Back EMF i n v o l t @ f u l l − l oa d a s

p e r e xa mp le 4−8a14 S _1 = 1800 ; / / S peed i n rpm @ f u l l − l oa d a s p er

e x am p le 4−8a15

16 I_a_2 = 19 ; / / Armature c u r r e nt i n A @ h a l f −l o a d a sp e r e xa mp le 4−8a

17 E _c _2 = 1 13 .2 ; / / Back EMF i n v o l t @ h a l f −l oa d a sp e r e xa mp le 4−8a

18 S _2 = 1863 ; / / S pee d i n rpm @ h a l f −l oa d a s p ere x am p le 4−8a

20 I _a _3 = 47 .5 ; / / A rma tu re c u r r e n t i n A @ 1 25%

o v e r lo a d a s p er exa mp le 4−8b21 E _c _3 = 1 07 .5 ; / / Back EMF i n v o l t @ 1 2 5% o v e r l o a da s p er ex am pl e 4−8b

22 S _3 = 1769 ; // S pee d i n rpm @ 1 25% o v e r l o a d a s p e re x am p le 4−8b

24 I _a _4 = 63 .6 ; / / Armature c u r r e nt i n A @ o v e r lo a da s p er ex am pl e 4−9

25 E _c _4 = 1 04 .3 ; / / Back EMF i n v o l t @ o v e r l o a d a sp e r e xa mp le 4−9

26 S _4 = 1532 ; // S peed i n rpm @ o v e r l o ad a s p er

e x am p le 4−927

28 / / C a l c u l a t i o n s29 P _d _1 = E _c _1 * I _a _1 ; // A rm at ur e p ow er d e v e l o p e d

@ f u l l − l o a d

31 P _d _2 = E _c _2 * I _a _2 ; // A rm at ur e p ow er d e v e l o p e d@ h a l f −l o a d32

33 P _d _3 = E _c _3 * I _a _3 ; // A rm at ur e p ow er d e v e l o p e d@ 1 2 5 % o v e r l o a d

35 P _d _4 = E _c _4 * I _a _4 ; // A rm at ur e p ow er d e v e l o p e d@ o v e r l o a d

37 // D is pl ay t h e r e s u l t s38 disp ( ” E xa mp le 4−10 S o l u t i o n : ” ) ;

39 printf ( ” \n E xampl e \ t I a \ t Ec \ t S pe ed \ t Pd o r ( Ec∗ I a ) ” ) ;

40 printf ( ” \n

” ) ;

41 printf ( ” \n 4−8a \ t \ t %d \ t %. 1 f \ t %d \ t %d W a tf u l l −l o a d ” , I _a _1 , E _ c_ 1 , S _ 1 , P _ d _ 1 ) ;

42 printf ( ” \n 4−8a \ t \ t %d \ t %. 1 f \ t %d \ t %. 1 f W a th a l f −l o a d ” , I_a _2 , E _c _2 , S _2 , P_ d_ 2 );

43 printf ( ” \n 4−8b \ t \ t %. 1 f \ t %. 1 f \ t %d \ t %d W a t

125 p e rc e nt o v er l oa d ”, I _ a _ 3 , E _ c _ 3 , S _ 3 , P _ d _ 3 ) ;

44 printf ( ” \n 4−9 \ t \ t %. 1 f \ t %. 1 f \ t %d \ t % d W a to v er l oa d ” , I _ a _ 4 , E _ c _ 4 , S _ 4 , P _ d _ 4 ) ;

45 printf ( ” \n

” ) ;

Scilab code Exa 4.11 convert torque readings into Nm and lbft

11 / / G iv en d a ta12 T _a = 6 .5 ; // T or qu e i n d yn e−c e n t i m e t e r s13 T _ b = 1 0. 6; / / T or qu e i n gram−c e n t i m e t e r s14 T _ c = 1 2. 2; // T or qu e i n o un ce−i n c h e s15

16 / / C a l c u l a t i o n s17 T _a _N m = T _a * 1 .4 16 e -5 * 7 .0 61 2 e -3 ; / / T or qu e T a

i n N−m18 T _ b _ N m = T _ b * ( 1 / 7 2 . 0 1 ) * 7 . 0 6 1 2 e - 3 ; / / T o rq u e

T b i n N−m19 T _c _N m = T_c * 7 .0 61 2e -3 ; // Torque T c i n N−m20

21 T _a _l bf t = T _a * 1 .4 16 e -5 * 5 .2 08 e - 3; / / T or qu e T ai n l b − f t

22 T _b _lb ft = T_b * ( 1 / 72.01 ) * 5.208 e -3; / / T o rq u e

T b i n l b − f t23 T _c _l bf t = T _c * 5 .2 08 e - 3; // Torque T c i n l b− f t24

27 printf ( ” \n a : T = %. 1 e N−m ” , T _a _N m ) ;

28 printf ( ” \n T = %. 1 e l b − f t \n ” , T _a _l bf t ) ;

30 printf ( ” \n b : T = %. 2 e N−m ” , T _b _N m ) ;

31 printf ( ” \n T = %. 1 e l b − f t \n ” , T _b _l bf t ) ;

33 printf ( ” \n c : T = %. 3 e N−m ” , T _c _N m ) ;34 printf ( ” \n T = %. 2 e l b − f t \n ” , T _c _l bf t ) ;

Scilab code Exa 4.12 calculate Ist and percentage of load current

11 / / G iv en d a ta12 V_a = 120 ; // Rated t e rm i n al v o l t a g e o f dc s hu nt

n ot or i n v o l t13 R_a = 0.2 ; // Armature r e s i s t a n c e i n ohm14 BD = 2 ; // Brush drop i n v o l t15 I_a = 75 ; // F u l l l oa d a rm at u re c u r r e n t i n A

1617 / / C a l c u l a t i o n s18 I_st = ( V_a - BD ) / R_a ; // C ur re nt @ t he i n s t a n t

o f s t a r t i n g i n A19 p er ce nt ag e = I_ st / I_ a * 100 ; // P e rc en t ag e a t

f u l l l o a d20

23 printf ( ” \n I s t = %d A ( Back EMF i s z e r o ) ” , I_ st ) ;

24 printf ( ” \n P e rc e nt a ge a t f u l l l o ad = %d p e r ce n t ” ,

p e r c en t a g e ) ;

Scilab code Exa 4.13 calculate Rs at various back Emfs and Ec at zero

c o n s o l e .10

11 / / G iv en d a ta12 V_a = 120 ; // Rated t e rm i n al v o l t a g e o f dc s hu nt

n ot or i n v o l t13 R_a = 0.2 ; // Armature r e s i s t a n c e i n ohm14 BD = 2 ; // Brush drop i n v o l t15 I_a = 75 ; // F u l l l oa d a rm at u re c u r r e n t i n A16 I _a_n ew = 1.5 * I_a ; // a rm at ur e c u r r e nt i n A a t

1 50% r a t e d l o a d17

18 E_c_a = 0 ; / / Back EMF a t s t a r t i n g19 E_c_b = ( 25 / 100 ) * V_a ; // Back EMF i n v o l t i s

25% o f Va @ 1 50% r a t e d l o a d20 E_c_c = ( 50 / 100 ) * V_a ; // Back EMF i n v o l t i s

50% o f Va @ 1 50% r a t e d l o a d21

22 / / C a l c u l a t i o n s23 R_s_a = ( V_a - E_c_a - BD ) / I_a _new - R_a ; / / Ra

t ap pi ng v al ue a t s t a r t i n g24 / / i n ohm

25 R_s_b = ( V_a - E_c_b - BD ) / I_a _new - R_a ; / / Rat a p pi n g v a l u e @ 2 5% o f Va

26 // i n ohm27 R_s_c = ( V_a - E_c_c - BD ) / I_a _new - R_a ; / / Ra

t a p pi n g v a l u e @ 5 0% o f Va

28 / / i n ohm

29 E_c_d = V_a - ( I_a * R_a + BD ) ; // Back EMF @f u l l −l oa d w it h ou t s t a r t i n g r e s i s t a n c e30

33 printf ( ” \n a : At s t a r t i n g , Ec i s z er o ” ) ;

34 printf ( ” \n Rs = %. 2 f ohm \n ” , R _s _a ) ;

36 printf ( ” \n b : When b ac k EMF i n v o l t i s 2 5 p e r c e n to f Va @ 150 p e rc e nt r a te d l oa d ” ) ;

37 printf ( ” \n Rs = %. 3 f ohm \n ” , R _s _b ) ;

3839 printf ( ” \n c : When b ac k EMF i n v o l t i s 5 0 p e r c e n t

o f Va @ 150 p e rc e nt r a te d l oa d ” ) ;

40 printf ( ” \n Rs = %. 3 f ohm \n ” , R _s _c ) ;

42 printf ( ” \n d : Back EMF a t f u l l −l o a d w i th o u ts t a r t i n g r e s i s t a n c e ” ) ;

43 printf ( ” \n Ec = %d V ” , E _c _d ) ;

Scilab code Exa 4.14 calculate field flux in percent and final torque de-veloped

7 / / E xa mp le 4−148

12 / / C u m ul a t iv e DC com pound m ot or a c t i n g a s s h u n tmotor13 T _o ri g = 160 ; / / O r i g i na l t or qu e d ev el op ed i n l b . f t14 I _ a_ or ig = 1 40 ; // O r i g i na l a rm at u re c u r r e n t i n A15 p hi _f _o ri g = 1 .6 e +6 ; // O r i g i na l f i e l d f l u x i n

l i n e s16

17 / / R e c o nn e c t ed a s a c u m u l a t i v e DC comp ound m ot or18 T _f in al _a = 1 90 ; / / F i n a l t or qu e d ev el op ed i n l b . f t

( c a s e a )19

20 / / C a l c u l a t i o n s21 p hi _f = p hi _f _o ri g * ( T _f in al _a / T _o ri g ) ; //

F ie l d f l u x i n l i n e s22 p er ce nt ag e = ( p hi _f / p hi _f _o ri g ) * 100 - 100 ; //

p e r ce nt a g e i n c r e a s e i n f l u x23

24 p hi _f _f in al = 1 .1 * p hi _f ; // 10% i n c r e a s e i n l oa dc a u se s 10% i n c r e a s e i n f l u x

25 I_a_b = 154 ; // F i na l a rm at ur e c u r r e nt i n A ( c a se b)

26 T_f = T _fi na l_ a * ( I_a_b / I_ a_o ri g ) * (

p hi _f _f in al / p hi _f ) ;

27 // F i n a l t o rq u e d e ve l op e d28

31 printf ( ” \n a : p h i f = %. 1 e l i n e s \n ” , p hi _f ) ;

32 printf ( ” \n P e r c e n t a g e o f f l u x i n c r e a s e = %. 1 f p e r c e n t \n ” , p e rc e nt a ge ) ;

34 printf ( ” \n b : The f i n a l f i e l d f l u x i s 1 . 1 ∗ 1 . 9 ∗

10 ˆ 6 l i n e s ” ) ;35 printf ( ” \n ( due t o th e 10 pe r c e n t i n c r e a s e i n

l o ad ) . The f i n a l t o rq u e i s \ n” ) ;

36 printf ( ” \n T f = %. 1 f l b −f t ” , T _ f ) ;

Scilab code Exa 4.15 calculate torque developed for varying flux and Ia

11 / / G iv en d a ta12 I _a _o ri g = 25 ; // O r i g i n al a rm at ur e c u r r e nt i n A13 I _ a_ fi na l = 3 0 ; // F i na l a rm at u re c u r r e nt i n A14 T _ or ig = 90 ; // O r i g i na l t or qu e d ev el op ed i n l b . f t15 p h i_ or ig = 1 .0 ; // O r i g i n al f l u x16 p hi _f in al = 1 .1 ; // F in a l f l u x

1718 / / C a l c u l a t i o n s19 T_a = T_orig * ( I _a _f in al / I _a_ or ig ) ^ 2 ; //

F i n a l t o r q ue d e v el o p ed i f f i e l d20 // i s u n sa t u r a t e d21 T_b = T_orig * ( I _a _f in al / I _a_ or ig ) * (

p hi _f in al / p hi _o ri g ) ;

22 / / F i na l t or qu e d ev el op ed when I a r i s e s t o 30 A andf l u x by 10%

26 printf ( ” \n a : T = %. 1 f l b− f t \n ” , T _ a ) ;

27 printf ( ” \n b : T = %. 1 f l b− f t ” , T _ b ) ;

Scilab code Exa 4.16 calculate speed at rated load and P and hp

11 / / G iv en d a ta12 V_a = 230 ; // Rated a rm at ur e v o l t a g e i n v o l t13 P = 1 0 ; // Ra ted p ower i n hp14 S = 1250 ; // Rat ed s p ee d i n rpm15 R _A = 0.25 ; // Armature r e s i s t a n c e i n ohm16 R _p = 0.25 ; // I n t e r p o l a r r e s i s t a n c e

17 BD = 5 ; // Brush v o l t ag e dro p i n v o l t18 R _s = 0.15 ; // S e r i e s f i e l d r e s i s t a n c e i n ohm19 R_sh = 230 ; / / Sh un t f i e l d r e s i s t a n c e i n ohm20

21 / / s hu nt c o n n ec t i on22 I_l = 54 ; // L i ne c u r r e n t i n A at r at ed l oa d23 I_ol = 4 ; / / No−l oa d l i n e c ur r e nt i n A24 S _o = 1810 ; / / No−l o ad s pe ed i n rpm25

26 / / C a l c u l a t i o n s27 R_a = R_A + R_p ; // E f f e c t i v e a r m a t u r e r e s i s t a n c e

i n ohm28 I_f = V_a / R_sh ; // F i e l d c u r r e n t i n A ( Shunt

c o n n ec t i o n )29 I_a = I_ol - I_f ; // Armature c u r r e n t i n A

31 E_c_o = V_a - ( I_a * R_a + BD ) ; / / No−l o a d BACKEMF i n v o l t32 E _c _f ul l_ lo ad = V_a - ( I_l * R_a + BD ) ; / / No−l o a d

BACK EMF i n v o l t a t f u l l − l o a d33

34 S_r = S_o * ( E _c _f ul l_ lo ad / E _c _o ) ; // S pe ed a tr a t ed l o ad

36 P _ d = E _c _f ul l_ lo ad * I _l ; // I n t e r n a l power i nw a t t s

37 h p = P_d / 746 ; // I n t e r n a l h o rs e power

41 printf ( ” \n a : S r = %d rpm\n ” , S _ r ) ;

42 printf ( ” \n b : P d = %d W ” , P _ d ) ;

43 printf ( ” \n hp = %. 1 f hp ” , hp ) ;

Scilab code Exa 4.17 calculate speed torque and horsepower

c o n s o l e .10

11 / / G iv en d a ta12 V_a = 230 ; // Rated a rm at ur e v o l t a g e i n v o l t13 P = 1 0 ; // Ra ted p ower i n hp

14 S = 1250 ; // Rat ed s p ee d i n rpm

15 R _A = 0.25 ; // Armature r e s i s t a n c e i n ohm16 R _p = 0.25 ; // I n t e r p o l a r r e s i s t a n c e17 BD = 5 ; // Brush v o l t ag e dro p i n v o l t18 R _s = 0.15 ; // S e r i e s f i e l d r e s i s t a n c e i n ohm19 R_sh = 230 ; / / Sh un t f i e l d r e s i s t a n c e i n ohm20 phi_1 = 1 ; // O r i g i n al f l u x p e r p ol e21

22 // Long−s hu nt c u m ul a t i ve c o n n e c t i o n23 I_l = 55 ; // L i ne c u r r e n t i n A at r at ed l oa d24 p hi _2 = 1. 25 ; // Fl ux i n c r e a s e d by 25% due t o l on g−

s h un t c u m u la t i v e c o n n e c t i o n

25 I_ol = 4 ; / / No−l oa d l i n e c ur r e nt i n A26 S _o = 1810 ; / / No−l o ad s pe ed i n rpm27

28 / / C a l c u l a t i o n s29 R_a = R_A + R_p ; // E f f e c t i v e a r m a t u r e r e s i s t a n c e

i n ohm30 I_f = V_a / R_sh ; // F i e l d c u r r e n t i n A i n s h u n t

w i n d i n g31 I_a = I_ol - I_f ; // Armature c u r r e n t i n A f o r

s h un t c o n n e c t i o n32 E_c_o = V_a - ( I_a * R_a + BD ) ;

/ / No−l o a d BACKEMF i n v o l t f o r s hu nt c o n n ec t i on33 E_c _o1 = V_a - ( I_a * R_a + I_a * R_s + BD ) ; / / No

−l o a d BACK EMF i n v o l t f o r34 / / l o ng s hu nt c u mu l at i ve c o n n ec t i o n35 S_n1 = S_o * ( E_c _o1 / E_c_o ) ; // Sp eed a t no l o ad36

37 I_f = V_a / R_sh ; // F i e l d c u r r e n t i n A i n s h u n tw i n d i n g

38 I _a_l sh = I_l - I_f ; // Armature c u r r e nt i n A39 E _c _f ul l_ lo ad = V_a - ( I _a _l sh * R_a + BD ) ; / / No−

l o a d BACK EMF i n v o l t a t40 // f u l l − l oa d f o r l o n g −s h un t c u m u la t i v e c o n n e c t i o n41

42 E _c _f ul l_ lo ad _l sh = V _a - ( I _a _l sh * R _a + I _a _l sh

* R_s + BD ) ; // BACK EMF in v o l t

43 / / a t f u l l − l oa d f o r l o n g −s h un t c u m u l a t i v e m ot or

4445 S_r = S_o * ( E _c _f ul l_ lo ad / E _c _o ) ; // S pe ed a t

r a te d l oa d f o r s hu nt c o nn e ct i on46 S _r _l sh = S_ n1 * ( E _c _f ul l_ lo ad _l sh / E _c _o 1 ) * (

p hi_ 1 / p hi _2 ) ;

47 / / S peed a t r a te d l oa d f o r s hu nt c o nn e ct i on48

49 P _d = E _c _f ul l_ lo ad * I _a _l sh ; // I n t e r n a l power i nw a t t s

50 h p = P_d / 746 ; // I n t e r n a l h o rs e power51

52 T _shu nt = ( hp * 5252 ) / S_r ; // I n t e r n a l t or qu e @f u l l − l o ad f o r s hu nt motor

54 I _ a1 = I _ a_ ls h ; // Arm at ure c u r r e n t f o r s hu nt mo to ri n A

55 I _ a2 = I _ a_ ls h ; // Armature c u r r e nt f o r l on g−s h u n tc u m ul a t i ve m oto r i n A

56 T_c omp = T_s hun t * ( phi_2 / phi_1 ) * ( I_a2 / I_a1

) ; // I n t e r n a l t or qu e57 / / a t f u l l − l oa d f o r l o n g −s hu nt c u m ul a t i ve m oto r i n A58

59 H or se po we r = ( E _c _f ul l_ lo ad _l sh * I _a _l sh ) / 7 46 ;

// I n t e r n a l h or se po we r o f 60 / / compound m oto r b as ed on f l u x i n c r e a s e61

64 printf ( ” \n a : S n 1 = %d rpm \n” , S_n1 ) ;

65 printf ( ” \n b : S r = %d rpm \n” , S _r _l sh ) ;

66 printf ( ” \n c : I n t e r n a l t or qu e o f s hu nt motor a tf u l l −l o a d : ” ) ;

67 printf ( ” \n T s hu nt = %. 2 f l b − f t ” , T _s hu nt ) ;68 printf ( ” \n T comp = %. 2 f l b − f t \n” , T _c om p ) ;

69 printf ( ” \n d : H o rs ep o we r = %. 1 f hp \n” , H o r s ep o w er

70 printf ( ” \n e : The i n t e r n a l h or se po we r e x ce e ds t he

r a t ed h or se po we r b ec a us e ” ) ;

71 printf ( ” \n t he power d ev el op ed i n t he motor musta l s o o ve rc om e t he i n t e r n a l ” ) ;

72 printf ( ” \n m e c h a n i c a l r o t a t i o n a l l o s s e s . ”) ;

Scilab code Exa 4.18 calculate speed with and without diverter

11 / / G iv en d a ta12 P = 2 5 ; // Power r a t i n g o f a s e r i e s motor i n hp

13 V_a = 250 ; // Rated v o l t a g e i n v o l t14 R_a = 0.1 ; // Armature c kt r e s i s t a n c e i n ohm15 BD = 3 ; // Brush v o l t ag e dro p i n v o l t16 R _s = 0.05 ; // S e r i e s f i e l d r e s i s t a n c e i n ohm17 I_a1 = 85 ; / / Armature c u r r e nt i n A ( c a s e a )18 I_a2 = 100 ; / / Armature c u r r e nt i n A ( c a s e b )19 I_a3 = 40 ; / / Ar ma tu re c u r r e n t i n A ( c a s e c )20 S_1 = 600 ; // Speed i n rpm a t c u r re n t I a 121 R _d = 0.05 ; // D i v e r t o r r e s i s t a n c e i n ohm22

23 / / C a l c u l a t i o n s24 E_c2 = V_a - I_a2 * ( R_a + R_s ) - BD ; // BACK EMFi n v o l t f o r I a 2

25 E_c1 = V_a - I_a1 * ( R_a + R_s ) - BD ; // BACK EMFi n v o l t f o r I a 1

27 S_2 = S_1 * ( E_c2 / E_c1 ) * ( I_a1 / I_a2 ) ; //Speed i n rpm a t c u r r e n t I a 228

29 E_c3 = V_a - I_a3 * ( R_a + R_s ) - BD ; // BACK EMFi n v o l t f o r I a 3

31 S_3 = S_1 * ( E_c3 / E_c1 ) * ( I_a1 / I_a3 ) ; //Speed i n rpm a t c u r r e n t I a 3

33 / / When d i v e r t o r i s c on ne ct ed i n p a r a l l e l t o R s34 R_sd = ( R_s * R_d ) / ( R_s + R_d ) ; // E f f e c t i v e

s e r i e s f i e l d r e s i s t a n c e i n ohm35

36 E _c 2_n ew = V_a - I_a2 * ( R_a + R_sd ) - BD ; //BACK EMF i n v o l t f o r I a 2

37 S _2_n ew = S_1 * ( E_ c2_ new / E_c1 ) * ( I_a1 / (

I_a2 / 2 ) ) ; // S pe ed i n rpm38 / / a t c ur r e n t I a 239

40 E _c 3_n ew = V_a - I_a3 * ( R_a + R_sd ) - BD ; //BACK EMF i n v o l t f o r I a 3

41 S _3_n ew = S_1 * ( E_ c3_ new / E_c1 ) * ( I_a1 / (

I_a3 / 2 ) ) ; // S pe ed i n rpm42 / / a t c ur r e n t I a 343

46 printf ( ” \n a : S 2 = %d rpm \n” , S _ 2 ) ;

47 printf ( ” \n b : S 3 = %d rpm \n” , S _ 3 ) ;

48 printf ( ” \n c : The e f f e c t o f t h e d i v e r t o r i s t or ed u ce t he s e r i e s f i e l d c u r r e n t ” ) ;

49 printf ( ” \n ( and f l u x ) t o h a l f t h e i r p r e v i o us

v a l u e s . ” ) ;50 printf ( ” \n S 2 = %d rpm ” , S _2 _n ew ) ;

51 printf ( ” \n S 3 = %d rpm \n” , S _3 _n ew ) ;

53 printf ( ” \n The r e s u l t s may be t a bu la te d as

f o l l o w s : \n ” ) ;

54 printf ( ” \n Case \ t I a i n A \ t S o i n rpm \ tS d i n rpm ” ) ;

55 printf ( ” \n

” ) ;

56 printf ( ” \n 1 \ t %d \ t %d\ t ” , I_a1 , S _1 ) ;

57 printf ( ” \n 2 . \ t %d \ t %d\ t %d ” , I_a2 , S_2 , S_2 _new ) ;

58 printf ( ” \n 3 . \ t %d \ t %d \ t%d ” , I_a3 , S_3 , S_ 3_ne w ) ;

Scilab code Exa 4.19 calculate percentage speed regulation

11 / / G iv en d a ta12 / / From t he c a l c u l a t i o n s o f Ex .4 −16 , Ex .4 −17 , Ex

.4 −18 we g e t no−l o a d and13 // f u l l − l oa d s pe ed s a s f o l l o w s

14 S _n1 = 18 10 ; / / No−l o a d s p ee d i n rpm ( Ex .4 −16)15 S _f1 = 16 03 ; // F u ll −l o a d s p ee d i n rpm ( Ex .4 −16)16

17 S _n2 = 18 06 ; / / No−l o a d s p ee d i n rpm ( Ex .4 −17)18 S _f2 = 12 31 ; // F u ll −l o a d s p ee d i n rpm ( Ex .4 −17)

20 S _n3 = 13 11 ; / / No−l o a d s p ee d i n rpm ( Ex .4 −18)21 S_f3 = 505 ; // F ul l −l o a d s p ee d i n rpm ( Ex .4 −18)22

23 / / C a l c u l a t i o n s24 SR_1 = ( S_n1 - S_f1 ) / S_f1 * 100 ; / / S p ee d

r e g u l a t i o n f o r s hu nt motor25

26 SR_2 = ( S_n2 - S_f2 ) / S_f2 * 100 ; / / S p ee dr e g u l a t i o n f o r compound mo to r

28 SR_3 = ( S_n3 - S_f3 ) / S_f3 * 100 ; / / S p ee d

r e g u l a t i o n f o r s e r i e s motor29

32 printf ( ” \n a : SR ( s h u n t ) = %. 1 f p e r c e n t \n ” , S R _ 1 )

33 printf ( ” \n b : SR ( c ompou nd ) = %. 1 f p e r c e n t \n ” ,

S R_ 2 ) ;

34 printf ( ” \n c : SR ( s e r i e s ) = %. 1 f p e r c e n t \n ” , S R_ 3

Scilab code Exa 4.20 calculate no load speed

11 / / G iv en d a ta12 S R = 0.1 ; // Given p e r ce n t s pe ed r e g u l a t i o n 10% o f a s h un t m ot or

13 o me ga_ f1 = 60 * %pi ; // F u ll −l oa d s pe ed i n r a d / s14

15 / / C a l c u l a t i o n s16 o me ga_ n1 = om ega _f 1 * ( 1 + SR ) ; / / No−l o ad s pe ed

i n r a d / s17

18 S = om eg a_n 1 * ( 1 / ( 2 * %pi ) ) * ( 60 / 1 ) ; //No−l o ad s pe ed i n rpm

22 printf ( ” \n a : o me ga n 1 = %. 2 f \n ” , o m eg a_ n 1 ) ;

23 printf ( ” \n b : S = %d rpm ” , S ) ;

Scilab code Exa 4.21 calculate internal and external torque

1011 / / G iv en d a ta12 S _i nt = 16 03 ; // I n t e r n a l r a te d s pe ed i n rpm ( Ex

. 4 −16)13 S _e xt = 12 50 ; // E x te r na l r a t ed s pe ed i n rpm ( Ex

. 4 −16)

14 h p_ in t = 1 4. 3 ; // I n t e r n a l h or se po we r15 h p _e xt = 10 ; // E x t e rn a l h o rs e po w er16

17 / / C a l c u l a t i o n s18 T_int = ( hp_ int * 5252 ) / S_int ; // I n t e r n a l

t or qu e i n l b − f t19

20 T_ext = ( hp_ ext * 5252 ) / S_ext ; // E x t e rn a lt or qu e i n l b − f t

23 disp ( ”E x ampl e 4−21 S o l u t i o n : ” ) ;24 printf ( ” \n a : T i n t = %. 2 f l b − f t \n ” , T _i nt ) ;

25 printf ( ” \n b : T e xt = %. 2 f l b− f t \n ” , T _e xt ) ;

26 printf ( ” \n c : I n t e r n a l h or se po we r i s d ev el op ed a s ar e s u l t o f e l e c t r o m a g ne t i c ” ) ;

27 printf ( ” \n t or qu e p r o d u c e d by e n er gy c o nv e r s i o n .Some o f t h e m e ch a n ic a l e n er g y ” ) ;

28 printf ( ” \n i s us e d i n t e r n a l l y to ov er co mem ec ha n ic a l l o s s e s o f t he motor , ” ) ;

29 printf ( ” \n r e d u c i n g th e to r q u e a v a i l a b l e at i t s

s h a f t t o p er f or m work . ”) ;

Scilab code Exa 4.22 calculate output torque in ounceinches

c o n s o l e .

1011 / / G iv en d a ta12 P = 5 0 ; // Power r a t i n g o f t he s er vo −m ot or i n W13 S = 3000 ; // F ul l −l oa d s pe ed o f t he s er vo −m ot or i n

15 / / C a l c u l a t i o n16 T_l bft = ( 7.04 * P ) / S ; // Output t o rq u e i n l b−

f t17 T _o un ce in ch = T _l bf t * 1 92 ; // Output t o r q ue i n

ounce−i n c h e s

1819 / / D is pl ay t h e r e s u l t20 disp ( ” E xa mp le 4−22 S o l u t i o n : ” ) ;

21 printf ( ” \n T = %. 1 f o z . i n ” , T _ ou n ce i nc h ) ;

Scilab code Exa 4.23 calculate speed and torque

11 / / G iv en d a ta12 P = 5 0 ; // Power r a t i n g o f t he s er vo −m ot or i n W13 S _r pm = 30 00 ; // F u ll −l oa d s pe ed o f t he s er vo −motor

i n rpm14

16 S _r ad _p er _s ec = S_rpm * 2 * %pi / 60 ; // F u ll −l o a ds pe ed o f t he s er vo −motor17 / / i n r ad / s18 o me ga = 3 14 .2 ; // A ng ul ar f r e qu e n cy i n r ad / s19 T_Nm = P / omega ; // Ou tpu t t o r q u e i n Nm20 T _o un ce in ch = T _Nm * ( 1 / 7 .0 61 2e -3 ) ; / / O ut pu t

t o r q ue i n o z . i n21

24 printf ( ” \n a : S peed i n r ad / s = %. 1 f r ad / s \n ” ,

S _ r a d_ p e r _s e c ) ;25 printf ( ” \n b : T = %. 4 f N−m \n ” , T_Nm ) ;

26 printf ( ” \n c : T = %. 1 f o z . i n \n ” , T _ ou n ce i nc h ) ;

27 printf ( ” \n d : Bo th a n s w er s a r e t h e same . ” ) ;

Chapter 5

ARMATURE REACTION

AND COMMUTATION IN

DYNAMOS

Scilab code Exa 5.1 calculate Zp

6 // Ch apt e r 5 : ARMATURE REACTION AND COMMUTATION INDYNAMOS

7 / / E xa mp le 5−18

11 / / G iv en d a ta12 c on du ct or s = 8 00 ; // No . o f c o nd u ct o r s13 I _a = 1000 ; // Rated a rm at ur e c u r r e n t i n A14 P = 1 0 ; // No . o f p o l es15 pitch = 0.7 ; // P ol e−f a c e c o v e r s 70% of t he p i t ch

16 a = P ; // No . o f p a r a l l e l p at hs ( S i m p l e x l a p −wound

18 / / C a l c u l a t i o n s19 / / U s in g Eq . ( 5 − 1 )20 Z = c on duc to rs / P ; // No . o f a rm at ur e c o nd u c to r s /

p at h u nd er e ac h p o l e21 Z_a = Z * pitch ; / / A c ti v e a rm at ur e c o n d u c to r s / p o l e22

23 // S ol vi ng f o r Z p u s in g Z p = Z a / a24 Z_p = Z_a / a ; // No . o f p o le f a c e c o nd uc t o r s / p o l e25

26 // D is pl ay t h e r e s u l t s27 disp ( ”E x ampl e 5−1 S o l u t i on : ” ) ;

28 printf ( ” \n No . o f p o l e f a c e c on du ct or s / p o l e t o g i vef u l l a rm at ur e r e a c t i o n ” ) ;

29 printf ( ” \n c om pe ns at io n , i f t he p o l e c o v e r s 70p er ce n t o f t h e p it ch i s : \n ” ) ;

30 printf ( ” \n Z p = %. 1 f c o n du c to r s / p o l e ” , Z _ p ) ;

Scilab code Exa 5.2 calculate cross and de magnetising ampereconduc-torsperpole and ampereturnsperpole

6 // Ch apt e r 5 : ARMATURE REACTION AND COMMUTATION INDYNAMOS

7 / / E xa mp le 5−28

12 c on du ct or s = 8 00 ; // No . o f c o nd u ct o r s13 I _a = 1000 ; // Rated a rm at ur e c u r r e n t i n A14 I_l = I_a ; // l oa d o r t o t a l c ur r e nt e n t e r i n g t h e

a rm at ur e i n A15 P = 1 0 ; // No . o f p o l es16 pitch = 0.7 ; // P ol e−f a c e c o v e r s 70% of t he p i t ch17 a = P ; // No . o f p a r a l l e l p at hs ( S i m p l e x l a p −wound

)18 alpha = 5 ; / / No . o f e l e c t r i c a l d e g r e s s t h a t t h e

b ru sh es a re s h i f t e d19

20 / / C a l c u l a t i o n s21 Z = c on duc to rs / P ; // No . o f a rm at ur e c o nd u c to r s /

p at h u nd er e ac h p o l e22 A_ Z _ pe r _p o l e = ( Z * I_l ) / ( P * a ) ; // C ro s s

m a g n e t i z i n g23 // ampe re−c o n d u c t o r s / p o l e24

25 At _ pe r _p o le = ( 1 / 2 ) * ( 8000 / 1 ) ; // Ampere−t u r n s / p o l e

27 f r ac _d em ag _A t_ pe r_ po le = ( 2* a lp ha ) / 1 80 * (

A t _ p e r _ p o l e ) ;

28 / / F r a c t i o n o f d e m a gn e t iz i n g ampere−t u r n s / p o l e29

30 funcprot ( 0 ) ; // t o a vo id r e d e f i n i n g f u nc t i o n : b et aw a r ni n g m e s sa g e

32 be ta = 180 - 2* a lp ha ; // c r o ss −m a g n e t i z i n ge l e c t r i c a l d e g r ee s

34 c r o s s _m a g _ A t_ p e r _ po l e = ( b e t a / 1 80 ) * ( A t _ p e r _p o l e ) ;

35 / / c r o ss −m a g n e t i z i n g a mp er e−t u r n s / p o l e36

39 printf ( ” \n a : With t h e b r u s h e s on t h e GNA, t h e

e n t i r e a rm at u re r e a c t i o n e f f e c t ” ) ;

40 printf ( ” \n i s c o m p l e t e l y c r o s s −m a g n e t i z i n g . Thec r o s s −m ag ne ti zi ng ” ) ;

41 printf ( ” \n ampere−c o nd u c to r s / p o l e a r e ” ) ;

42 printf ( ” \n = %d ampere−c o n d u c t o t s / p o l e \n” ,

A _ Z _ p e r _ p o l e ) ;

44 printf ( ” \n and s i n c e t he re a r e 2 c o nd uc t o rs / turn, t h e c ro ss −m a g n et i z i ng ” ) ;

45 printf ( ” \n ampere−t u r n s / p o l e a r e \n = %d At /p o l e \n\n” , A t _p e r_ p ol e ) ;

4748 printf ( ” \n b : L e t a l p h a = t h e n o . o f e l e c t r i c a l

d e g r e e s t ha t t he b ru sh es a re ” ) ;

49 printf ( ” \n s h i f t e d . Then t h e t o t a l no . o f d e m a g n e t i z i n g e l e c t r i c a l d e g r e e s ” ) ;

50 printf ( ” \n a r e 2∗ a lp ha , w h i l e t h e ( r e ma i n i ng )c r o s s −ma gn et iz in g e l e c t r i c a l ”) ;

51 printf ( ” \n d eg re e s , bet a , a re 180 − 2∗ a l p h a . Ther a t i o o f d em ag ne ti zi ng t o ” ) ;

52 printf ( ” \n c r o s s −m a g n e t i z i n g a mp er e−t ur ns i s

a l wa y s 2∗ a l p h a / b e t a . The ”) ;

53 printf ( ” \n f r a c t i o n o f d em ag ne ti zi ng ampere−t ur n s / p o le i s ” ) ;

54 printf ( ” \n = %. 1 f At / p ol e \n\n” ,

f r a c _ de m a g _ At _ p e r _p o l e ) ;

55 printf ( ” \n Note : S l i g h t c a l c u l a t i o n m is t a k e i nt h e t ex tb oo k f o r c as e b \n” )

58 printf ( ” \n c : S i n ce b et a = 180 −2∗ a l ph a = 1 7 0 , t h ec r o s s −m a g n e t i z i n g a mp er e−t u r n s / p o l e ” ) ;

59 printf ( ” \n a r e \n = %. 1 f At / p ol e ” ,c r o s s _m a g _ A t_ p e r _ po l e ) ;

Chapter 6

AC DYNAMO VOLTAGE

RELATIONS ALTERNATORS

Scilab code Exa 6.1 calculate Eg at unity PF and point75 lagging PF

6 // Ch apt e r 6 : AC DYNAMO VOLTAGE RELATIONS−ALTERNATORS

7 / / E xa mp le 6−18

11 / / G iv en d a ta12 k VA = 1000 ; // kVA r a t i n g o f t he 3−p ha se a l t e r n a t o r

13 V _L = 4600 ; // R ated l i n e v o l t a ge i n v o l t14 // 3−p h as e , Y−c on n ec te d a l t e r n a t o r15 R_a = 2 ; // Armature r e s i s t a n c e i n ohm p er p ha se16 X_s = 20 ; // S yn ch ro no us a rm at ur e r e a c t a n c e i n ohm

p e r p ha se

17 c os _t he ta _a = 1 ; // U ni ty power f a c t o r ( c a s e a )

18 c os _t he ta _b = 0 .7 5 ; // 0 . 7 5 power f a c t o r l a g gi n g (c a s e b )19 s i n _ t h et a _ b = sqrt ( 1 - ( c os _t he ta _b ) ^ 2 ) ;

21 / / C a l c u l a t i o n s22 V_P = V_L / sqrt (3) ; // Phase v o l t a g e i n v o l t23 I_P = ( kVA * 1000 ) / ( 3* V_P ) ; // P ha se c u r r e n t

i n A24 I_a = I_P ; // Arma tu re c u r r e n t i n A25

26 // a : At u ni ty PF

27 E_g_a = ( V_P + I_a * R_a ) + %i *( I_a * X_s );28 / / F u ll −l oa d g e ne r a t ed v o l t ag e per −p ha se ( c a s e a )29 E _ g _ a _ m = abs ( E _ g _ a ) ; // E g a m=m ag ni tu de o f E g a i n

v o l t30 E _ g _ a _ a = atan ( imag ( E _ g_ a ) / real ( E _ g _ a ) ) * 1 8 0 / % p i ; //

E g a a=p h a s e a n g l e o f E g a i n d e g r e e s31

32 // b : At 0 . 7 5 PF l a g g i n g33 E _g _b = ( V_ P* c os _t he ta _b + I_a * R_a ) + %i *( V_P *

s i n_ t he t a_ b + I _a * X _s ) ;

34 / / F u ll −l oa d g e ne r a t ed v o l t ag e per −p ha se ( c a se b )35 E _ g _ b _ m = abs ( E _ g _ b ) ; // E g b m=m ag ni tu de o f E g b i n

v o l t36 E _ g _ b _ a = atan ( imag ( E _ g_ b ) / real ( E _ g _ b ) ) * 1 8 0 / % p i ; //

E g b a=p h a s e a n g l e o f E g b i n d e g r e e s37

41 printf ( ” \n r o ot 3 v a l u e i s t a k e n a s %f , s o s l i g h tv a r i a t i o n s i n t he a ns we r . ” , sqrt ( 3 ) ) ;

42 printf ( ” \n\n a : At u n i ty PF , \n ” ) ;43 printf ( ” \n R e c t a n g u l a r form : \ n E g = ” ) ; disp

( E _ g _ a ) ;

44 printf ( ” \n P o l a r form : ” ) ;

45 printf ( ” \n E g = %d <%. 2 f V/ p h a s e ” , E _g _a _m ,

E _ g_ a _a ) ;

46 printf ( ” \n where %d i s mag ni t ude and %. 2 f i sp ha s e a n g l e \n” ,E_g_a_m ,E_g_ a_a) ;

48 printf ( ” \n b : At 0 . 7 5 PF l a g g i n g , \n ” ) ;

49 printf ( ” \n R e c t a n g u l a r form : \ n E g = ” ) ; disp

( E _ g _ b ) ;

51 printf ( ” \n E g = %d <%. 2 f V/ p h a s e ” , E _g _b _m ,

E _ g_ b _a ) ;

52 printf ( ” \n where %d i s mag ni t ude and %. 2 f i sp ha s e a n g l e \n” ,E_g_b_m ,E_g_ b_a) ;

Scilab code Exa 6.2 calculate Eg at point75 PF and point4 lead

7 / / E xa mp le 6−28

11 / / G iv en d a ta12 k VA = 1000 ; // kVA r a t i n g o f t he 3−p ha se a l t e r n a t o r13 V _L = 4600 ; // R ated l i n e v o l t a ge i n v o l t

14 // 3−p h as e , Y−c on n ec te d a l t e r n a t o r15 R_a = 2 ; // Armature r e s i s t a n c e i n ohm p er p ha se16 X_s = 20 ; // S yn ch ro no us a rm at ur e r e a c t a n c e i n ohm

p e r p ha se17 c os _t he ta _a = 0 .7 5 ; // 0 . 75 PF l e a d i ng ( c a se a )

18 c os _t he ta _b = 0 .4 0 ; / / 0 . 40 PF l e a d i ng ( c a se b )

19 s i n _ t h et a _ a = sqrt ( 1 - ( c os _t he ta _a ) ^ 2 ) ; / / ( c a s ea )20 s i n _ t h et a _ b = sqrt ( 1 - ( c os _t he ta _b ) ^ 2 ) ; / / ( c a s e

22 / / C a l c u l a t i o n s23 V_P = V_L / sqrt (3) ; // Phase v o l t a g e i n v o l t24 I_P = ( kVA * 1000 ) / ( 3* V_P ) ; // P ha se c u r r e n t

i n A25 I_a = I_P ; // Arma tu re c u r r e n t i n A26

27 // a : At 0 . 75 PF l e a d i ng28 E _g _a = ( V_ P* c os _t he ta _a + I_a * R_a ) + %i *( V_P *

s i n_ t he t a_ a - I _a * X _s ) ;

29 / / F u ll −l oa d g e ne r a t ed v o l t ag e per −p ha se ( c a s e a )30 E _ g _ a _ m = abs ( E _ g _ a ) ; // E g a m=m ag ni tu de o f E g a i n

v o l t31 E _ g _ a _ a = atan ( imag ( E _ g_ a ) / real ( E _ g _ a ) ) * 1 8 0 / % p i ; //

E g a a=p h a s e a n g l e o f E g a i n d e g r e e s32

33 // b : At 0 . 4 0 PF l e a d i n g34 E _g _b = ( V_ P* c os _t he ta _b + I_a * R_a ) + %i *( V_P *

s i n_ t he t a_ b - I _a * X _s ) ;

35 / / F u ll −l oa d g e ne r a t ed v o l t ag e per −p ha se ( c a se b )36 E _ g _ b _ m = abs ( E _ g _ b ) ; // E g b m=m ag ni tu de o f E g b i n

v o l t37 E _ g _ b _ a = atan ( imag ( E _ g_ b ) / real ( E _ g _ b ) ) * 1 8 0 / % p i ; //

E g b a=p h a s e a n g l e o f E g b i n d e g r e e s38

42 printf ( ” \n r o ot 3 v a l u e i s t a k e n a s %f , s o s l i g h tv a r i a t i o n s i n t he a ns we r . ” , sqrt ( 3 ) ) ;

43 printf ( ” \n\n a : 0 . 7 5 PF l e ad i n g , \n ” ) ;

( E _ g _ a ) ;

46 printf ( ” \n E g = %d <

%. 2 f V/ p h a s e ” , E _g _a _m ,E _ g_ a _a ) ;

47 printf ( ” \n where %d i s mag ni t ude and %. 2 f i sp ha s e a n g l e \n” ,E_g_a_m ,E_g_ a_a) ;

49 printf ( ” \n b : At 0 . 4 0 PF l e a d i n g , \n ” ) ;

( E _ g _ b ) ;

52 printf ( ” \n E g = %d <%. 2 f V/ p h a s e ” , E _g _b _m ,

E _ g_ b _a ) ;

53 printf ( ” \n where %d i s mag ni t ude and %. 2 f i sp ha s e a n g l e \n” ,E_g_b_m ,E_g_ b_a) ;

Scilab code Exa 6.3 calculate percent voltage regulation

4 / / 2 nd e d i t i om5

7 / / E xa mp le 6−38

12 // From Ex.6 −1 a nd Ex .6 −2 we ha ve V P and E g v a l u e sa s f o l l o w s13 / / Note : a pp ro xi ma te d v a l u e s a r e c o n s i d e r e d when

r oo t 3 v al ue i s t a k e n a s 1 . 7 314 // a s i n t ex tb oo k

15 V _P = 2660 ; // Pha se v o l t a g e

16 E _g _a 1 = 3 83 6 ; / / E g a t u n it y PF ( Ex.6 −1 c a s e a )17 E _g _b 1 = 4 81 4 ; // E g a t 0 . 75 PF l a g g i n g ( Ex.6 −1c a s e b )

19 E _g _a 2 = 2 36 4 ; // E g a t 0 . 75 PF l e a d i ng ( Ex.6 −2c a s e a )

20 E _g _b 2 = 1 31 5 ; // E g a t 0 . 40 PF l e a d i ng ( Ex.6 −2c a s e b )

22 / / C a l c u l a t i o n s23 VR_a = ( E_g_a1 - V_P ) /V_P * 100 ; // v o l t a g e

r e g u l a t i o n a t u ni t y PF ( Ex.6 −1 c a se a )24 VR_b = ( E_g_b1 - V_P ) /V_P * 100 ; // v o l t a g e

r e g u l a t i o n a t 0 . 75 PF l a g g i n g ( Ex.6 −1 c a s e b )25

26 VR_c = ( E_g_a2 - V_P ) /V_P * 100 ; // v o l t a g er e g u l a t i o n a t 0 . 75 PF l e a d i ng ( Ex.6 −2 c a se a )

27 VR_d = ( E_g_b2 - V_P ) /V_P * 100 ; // v o l t a g er e g u l a t i o n a t 0 . 40 PF l e a d i ng ( Ex.6 −2 c a s e b )

31 printf ( ” \n a : At u ni ty PF : ” ) ;

32 printf ( ” \n VR = %. 1 f p er ce nt \n ” , VR_a ) ;

34 printf ( ” \n b : At 0 . 7 5 PF l a g g i n g : ” ) ;

35 printf ( ” \n VR = %. 2 f p er ce nt \n ” , VR_b ) ;

37 printf ( ” \n c : At 0 . 7 5 PF l e a d i n g : ” ) ;

38 printf ( ” \n VR = %. 2 f p er ce nt \n ” , VR_c ) ;

40 printf ( ” \n d : At 0 . 4 0 PF l e a d i n g : ” ) ;

41 printf ( ” \n VR = %. 1 f p er ce nt \n ” , VR_d ) ;

Scilab code Exa 6.4 calculate Rdc Rac Zp Xs VR at point8 PF lag and

7 / / E xa mp le 6−48

11 / / G iv en d a ta12 kVA = 100 ; // kVA r a t i n g o f t he 3−p ha se a l t e r n a t o r13 V _L = 1100 ; // L i ne v o l t a ge o f t he 3−p h a s e

a l t e r n a t o r i n v o l t14

15 / / dc−r e s i s t a n c e t e s t d a t a16 E_gp1 = 6 ; // g e ne r a t ed p ha se v o l t a g e i n v o l t17 V_l = E_gp1 ;

// g en er at ed l i n e v o l t a g e i n v o l t18 I_a1 = 10 ; // f u l l −l oa d c u r r e n t p e r p h as e i n A19 c os _t he ta _b 1 = 0 .8 ; // 0 . 8 PF l a g g i n g ( c a se b )20 c os _t he ta _b 2 = 0 .8 ; // 0 . 8 PF l e a d i ng ( c a se b )21 s i n _ t h et a _ b 1 = sqrt ( 1 - ( c o s_ th et a_ b1 ) ^ 2 ) ; // (

c a s e b )22 s i n _ t h et a _ b 2 = sqrt ( 1 - ( c o s_ th et a_ b2 ) ^ 2 ) ; // (

c a s e b )23

24 / / o pe n− c i r c u i t t e s t d a t a25 E_gp2 = 420 ; // g e n e ra t ed p ha se v o l t ag e i n v o l t

26 I _f2 = 12 .5 ; // F i e l d c ur r e n t i n A27

28 / / s h or t − c i r c u i t t e s t d at a29 I _f3 = 12 .5 ; // F i e l d c ur r e n t i n A30 // L in e c u r r e n t I l = r a t e d v a l u e i n A

32 / / C a l c u l a t i o n s33 // Assuming t ha t t he a l t e r n a t o r i s Y−c o n n e c t e d34 / / c a s e a :35 I _ a _ r at e d = ( k V A * 1 0 00 ) / ( V _ L * sqrt ( 3 ) ) ; / / R at ed

c u r r e nt p er p ha se i n A36 I _a = sqrt ( 3 ) * I _ a _r a t ed ; // Rated L in e c u r r e nt i n A37

38 R _d c = V _l / ( 2* I _ a1 ) ; // e f f e c t i v e dc a r m a t u r er e s i s t a n c e i n ohm/ w in di ng

39 R_ac = R_dc * 1.5 ; // e f f e c t i v e ac a r m a t u r er e s i s t a n c e i n ohm . p ha se

40 R _a = R_ac ; // e f f e c t i v e ac a r m a t u r e r e s i s t a n c e i nohm . p ha se from dc r e s i s t a n c e t e s t

42 Z _p = E_gp2 / I_a ; / / S y nc h ro n ou s i mp ed an ce p e rp h a s e

43 X _s = sqrt ( Z_p ^2 - R_a ^2 ) ; // S y n c hr o n o u sr e a c t a nc e p er p ha se

45 / / c as e b :46 V_p = V_L / sqrt ( 3 ) ; // Phase v o l t a ge i n v o l t (Y−

c o n n e c t i o n )47

48 // At 0 . 8 PF l a g g i ng49 E _g p1 = ( V_ p* c os _t he ta _b 1 + I _a _r at ed * R_a ) + %i

* ( V _p * s i n _t h et a _b 1 + I _ a_ r at e d * X _s ) ;

50 E _ g p 1 _ m = abs ( E _ g p 1 ) ; / / E g p1 m=m a gn it ud e o f E gp 1 i nv o l t

51 E _ g p 1 _ a = atan ( imag ( E _ gp 1 ) / real ( E _ g p 1 ) ) * 1 8 0 / % p i ; //E gp 1 a=p ha se a n gl e o f E gp1 i n d e gr e e s

52 V _ n1 = E _g p1 _m ; / / No−l o ad v o l t a g e i n v o l t53 V_f1 = V_p ; // F ul l −l oa d v o l t a g e i n v o l t

54 VR1 = ( V_n1 - V_f1 ) / V_f1 * 100; // p e r ce n tv o l t a ge r e g u l a t i o n a t 0 . 8 PF l a g g i n g

57 // At 0 . 8 PF l e a d i n g

58 E _g p2 = ( V_ p* c os _t he ta _b 2 + I _a _r at ed * R_a ) + %i

* ( V _p * s i n _t h et a _b 2 - I _ a_ r at e d * X_ s ) ;59 E _ g p 2 _ m = abs ( E _ g p 2 ) ; / / E g p2 m=m a gn it ud e o f E gp 2 i nv o l t

61 V _ n2 = E _g p2 _m ; / / No−l o ad v o l t a g e i n v o l t62 V_f2 = V_p ; // F ul l −l oa d v o l t a g e i n v o l t63 VR2 = ( V_n2 - V_f2 ) /V_f2 * 100 ; // p e r ce n t

v o l t a ge r e g u l a t i o n a t 0 . 8 PF l e a d i ng64

66 disp ( ”E x ampl e 6−4 S o l u t i on : ” ) ;67 printf ( ” \n A ssuming t ha t t he a l t e r n a t o r i s Y−

c o n ne c te d ” ) ;

68 printf ( ” \n a : R dc = %. 1 f ohm/ w i n d i ng ” , R_dc ) ;

69 printf ( ” \n R ac = %. 2 f ohm/ p h a s e ” , R_ac ) ;

70 printf ( ” \n Z p = %. 2 f ohm/ ph a s e ” , Z _ p ) ;

71 printf ( ” \n X s = %. 2 f ohm/ p h a s e \n” , X _ s ) ;

73 printf ( ” \n b : At 0 . 8 PF l a g g i n g ” ) ;

74 printf ( ” \n P e r c e n t v o l t a ge r e g u l a t i o n = %. 1 f

p e r c e n t \n”, V R 1 ) ;

76 printf ( ” \n At 0 . 8 PF l e a d i n g ” ) ;

77 printf ( ” \n P e r c e n t v o l t a ge r e g u l a t i o n = %. 1 f p e rc e n t ” , V R 2 ) ;

Scilab code Exa 6.5 calculate prev eg values for delta connection

6 // Ch apt e r 6 : AC DYNAMO VOLTAGE RELATIONS−

ALTERNATORS7 / / E xa mp le 6−58

15 / / dc−r e s i s t a n c e t e s t d a t a16 E_gp1 = 6 ; // g e ne r a t ed p ha se v o l t a g e i n v o l t17 V_l = E_gp1 ; // g en er at ed l i n e v o l t a g e i n v o l t18 I_a1 = 10 ; // f u l l −l oa d c u r r e n t p e r p h as e i n A19 c os _t he ta _b 1 = 0 .8 ; // 0 . 8 PF l a g g i n g ( c a se b )20 c os _t he ta _b 2 = 0 .8 ; // 0 . 8 PF l e a d i ng ( c a se b )21 s i n _ t h et a _ b 1 = sqrt ( 1 - ( c o s_ th et a_ b1 ) ^ 2 ) ; // (

c a s e b )22 s i n _ t h et a _ b 2 = sqrt ( 1 - ( c o s_ th et a_ b2 ) ^ 2 ) ; // (

c a s e b )23

24 / / o pe n− c i r c u i t t e s t d a t a25 E_gp2 = 420 ; // g e n e ra t ed p ha se v o l t ag e i n v o l t26 I _f2 = 12 .5 ; // F i e l d c ur r e n t i n A27

28 / / s h or t − c i r c u i t t e s t d at a29 I _f3 = 12 .5 ; // F i e l d c ur r e n t i n A30 // L in e c u r r e n t I l = r a t e d v a l u e i n A31

32 / / C a l c u l a t i o n s33 // Assuming t ha t t he a l t e r n a t o r i s d el t a −c o n n e c t e d

34 / / c a s e a :35 I _ a _ r at e d = ( k V A * 1 0 00 ) / ( V _ L * sqrt ( 3 ) ) ; / / R at ed

c u r r e nt p er p ha se i n A36 I _ L = I _a _r at ed ; // L i ne c u rr e n t i n A37

38 V _p = E _g p2 ; // Phase v o l t a ge i n v o l t

39 V_l = V_p ; // L in e v o l t a ge i n v o l t ( from s h o r tc i r c u i t d at a )40

41 I_p = I_L / sqrt (3) ; / / Phase c u r re n t i n A ( d e l t ac o n n e c t i o n )

42 I_a = I_p ; // Rated c u r re n t i n A43

44 Z_s = V_l / I_p ; // S y nc h ro n ou s i mp ed an ce p e r p h a se45 R _d c = E _g p1 / ( 2* I _ a1 ) ; // e f f e c t i v e dc a r m a t ur e

r e s i s t a n c e i n ohm/ w in di ng46 R_ac = R_dc * 1.5 ; // e f f e c t i v e ac a r m a t u r e

r e s i s t a n c e i n ohm . p ha se47

48 / / R e f f i n d e l t a = 3 ∗ R e ff i n Y49 R_eff = 3 * R_ac ; // E f f e c t i v e a rm a t u r e r e s i s t a n c e

i n ohm50 R_a = R_eff ; // e f f e c t i v e a c a r m a t u r e r e s i s t a n c e i n

ohm . p ha se fro m dc r e s i s t a n c e t e s t51

52 X _s = sqrt ( Z_s ^2 - R_a ^2 ) ; // S y n c hr o n o u sr e a c t a nc e p er p ha se

54 V_p = V_L ; // Phase v o l t a g e i n v o l t ( d el t a −c o n n e c t i o n )

56 // At 0 . 8 PF l a g g i ng57 E _g p1 = ( V_ p* c os _t he ta _b 1 + I_a * R_ a ) + %i *( V_p *

s i n _t h e t a_ b 1 + I _a * X _ s ) ;

60 V _ n1 = E _g p1 _m ; / / No−l o ad v o l t a g e i n v o l t61 V_f1 = V_p ; // F ul l −l oa d v o l t a g e i n v o l t62 VR1 = ( V_n1 - V_f1 ) / V_f1 * 100; // p e r ce n t

v o l t a ge r e g u l a t i o n a t 0 . 8 PF l a g g i n g63

65 // At 0 . 8 PF l e a d i n g66 E _g p2 = ( V_ p* c os _t he ta _b 2 + I_a * R_ a ) + %i *( V_p *

s i n _t h e t a_ b 2 - I _a * X _ s ) ;

69 V _ n2 = E _g p2 _m ; / / No−l o ad v o l t a g e i n v o l t70 V_f2 = V_p ; // F ul l −l oa d v o l t a g e i n v o l t71 VR2 = ( V_n2 - V_f2 ) /V_f2 * 100 ; // p e r ce n t

v o l t a ge r e g u l a t i o n a t 0 . 8 PF l e a d i ng

75 printf ( ” \n Assuming t ha t t he a l t e r n a t o r i s d e l t a −c o n ne c te d : \n ” ) ;

76 printf ( ” \n a : I p = %. 3 f A ” , I _ p ) ;

77 printf ( ” \n Z s = %. 2 f ohm/ ph a s e ” , Z _ s ) ;

78 printf ( ” \n R e f f i n d e l t a = %. 2 f ohm/ ph a s e ” ,

R _e ff ) ;

79 printf ( ” \n X s = %. 1 f ohm/ p h a s e \n” , X _ s ) ;

80 printf (” \n R e ff , r e a c t a n c e a nd i mpe danc e p e rp h a s e i n d e l t a i s 3 t i me s ” )

81 printf ( ” \n t h e v al ue when c o nn ec t e d i n Y . \n” )

83 printf ( ” \n b : At 0 . 8 PF l a g g i n g ” ) ;

84 printf ( ” \n P e r c e n t v o l t a ge r e g u l a t i o n = %. 1 f p e r c e n t \n” , V R 1 ) ;

86 printf ( ” \n At 0 . 8 PF l e a d i n g ” ) ;

87 printf ( ” \n P e r c e n t v o l t a ge r e g u l a t i o n = %. 1 f p e r c e n t \n” , V R 2 ) ;

88 printf ( ” \n P er ce n ta ge v o l t a g e r e g u l a t i o n r e m a i n st he same b ot h i n Y a nd d e l t a c o n n ec t i o n . ” ) ;

Scilab code Exa 6.6 calculate Imax overload and Isteady

7 / / E xa mp le 6−68

11 / / G iv en d a ta12 // 3−p h a s e Y−c o nn e ct ed a l t e r n a t o r13 E_L = 11000 ; // L in e v o l t a ge g e n er at ed i n v o l t14 k VA = 1 65 00 0 ; // kVA r a t i n g o f t he a l t e r n a t o r15 R_p = 0.1 ; // Ar ma tu re r e s i s t a n c e i n ohm/ p e r p ha s e

16 Z_p = 1.0 ; / / S y nc h ro n o us r e a c t a n c e / p h a s e17 Z_r = 0.8 ; // R e ac t or r e a c t a n c e / p h as e18

19 / / C a l c u l a t i o n s20 E_p = E_L / sqrt ( 3 ) ; // Rated p ha se v o l t a g e i n v o l t21 I _p = ( k VA * 1 00 0) / (3 * E_ p ); // Rated c u r r e nt p er

p ha se i n A22

23 / / c as e a24 I _max _a = E_p / R_p ; // Maximum sh or t − c i r c u i t

c u r r e nt i n A ( c a se a )25 o ve rl oa d_ a = I _m ax _a / I _p ; / / O ve rl oa d ( c a s e a )26

27 / / c as e b28 I _ st ea dy = E_p / Z_p ; // S u s ta i n ed s h or t − c i r c u i t

c u r r e n t i n A

29 o ve rl oa d_ b = I _s te ad y / I _p ; / / O ve rl oa d ( c a s e b )30

31 / / c as e c32 Z_t = R_p + %i *Z_r ; // T ot al r e a ct a n ce p er p ha se33 I _max _c = E_p / Z_t ; // Maximum sh or t − c i r c u i t

c u r r e nt i n A ( c a se b )34 I _ m a x _ c _ m = abs ( I _ m a x _ c ) ; / / I m a x c m =m a gn i tu d e o f

I ma x c i n A35 I _ m a x _ c _ a = atan ( imag ( I _ ma x _c ) / real ( I _ m a x _ c ) ) * 1 8 0 / % p i

; // I m a x c a=p ha se a n gl e o f I m ax c i n d e g re e s36 o ve rl oa d_ c = I _m ax _c _m / I _p ; / / O ve rl oa d ( c a s e a )

40 printf ( ” \n r o ot 3 v a l u e i s t a k e n a s %f , s o s l i g h tv a r i a t i o n s i n t he a ns we r . \ n” , sqrt ( 3 ) ) ;

41 printf ( ” \n a : I m ax = %d A ” , I _m ax _a ) ;

42 printf ( ” \n o ve r l o a d = %. 1 f ∗ ra t e d c u r r e nt \n” ,

o v e r lo a d _ a ) ;

44 printf ( ” \n b : I s t e a d y = %d A ” , I _s te ad y ) ;

45 printf (” \n o ve r l o a d = %. 2 f ∗ ra t e d c u r r e nt \n”

o v e r lo a d _ b ) ;

47 printf ( ” \n c : R e ct a ng u la r for m : \ n I max = ” ) ;

disp ( I _ m a x _ c ) ;

49 printf ( ” \n I max = %d <%. 2 f A ” , I _m ax _c _m ,

I _ m ax _ c _a ) ;

50 printf ( ” \n wher e %d i s m agni t ude a nd %. 2 f i sp ha s e a n g l e \n” , I _ m a x _c _ m , I _ m a x _ c _ a ) ;

51 printf ( ” \n o ve r l o a d = %. 3 f ∗ ra t e d c u r r e nt \n” ,

o v e r lo a d _ c ) ;

Scilab code Exa 6.7 calculate P and Pperphase and Egp magnitude phase

angle and torque angle

7 / / E xa mp le 6−78

15 / / dc−r e s i s t a n c e t e s t d a t a16 E_gp1 = 6 ; // g e ne r a t ed p ha se v o l t a g e i n v o l t17 V_l = E_gp1 ;

// g en er at ed l i n e v o l t a g e i n v o l t18 I_a1 = 10 ; // f u l l −l oa d c u r r e n t p e r p h as e i n A19 c os _t he ta = 0 .8 ; // 0 . 8 PF l a g g i ng20 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ; //21

26 / / s h or t − c i r c u i t t e s t d at a27 I _f3 = 12 .5 ; // F i e l d c ur r e n t i n A

28 // L in e c u r r e n t I l = r a t e d v a l u e i n A29

30 / / C a l c u l a t e d d at a fr om Ex.6 −431 I _L = 52.5 ; // Rated l i n e c u r r e n t i n A32 I_a = I_L ; // Rated c u r re n t p er p ha se i n A

33 E_gp = 532 + %i *623 ; // G en er at ed v o l t a g e a t 0 . 8 PF

l a g g i n g34 X_s = 4.6 ; // S yn ch ro n ou s r e a c t a n c e p e r p ha se35 V_p = 635 ; // Phase v o l t a g e i n v o l t36

37 / / C a l c u l a t i o n s38 / / c as e a39 P _T = sqrt (3) * V_L * I_L * co s_ th et a ; // T o ta l

o u t p u t 3−p h a s e p ow er40

41 / / c as e b42 P_p_b = P_T / 3 ; // T ot al o ut pu t 3−p h as e p ow er p e r

p h a s e43

44 / / c as e c45 E _ g p _ m = abs ( E _ g p ) ; // E gp m=m ag ni tu de o f E gp i n v o l t46 E _ g p _ a = atan ( imag ( E _g p ) / real ( E _ g p ) ) * 1 8 0 / % p i ; // E g p a

=p ha se a n gl e o f E gp i n d e g re e s47

48 / / c as e d49 t h et a = acos ( 0 . 8 ) * 1 8 0 / % p i ; // p ha se a n gl e f o r PF i n

d e g r e e s50 t h et a _p l us _ de b a = E _ gp _a ;

// p h a s e a ng l e o f E gp i nd e g r e e s51 d eb a = t he ta _p lu s_ de ba - t he ta ; // Torque a n g l e i n

d e g r e e s52

53 / / c as e e54 P _ p _ e = ( E _ g p _m / X _ s ) * V _ p * s i nd ( d e b a ) ; / / A p p ro x i m at e

o u t p u t p ow er / p h a s e ( Eq . ( 6 − 10 ) )55

56 / / c as e f 57 P _ p _f = E _ gp _m * I _a * c os d ( t h et a _p l us _ de b a ) ; //

A p pr o xi m at e o u t p u t p ow er / p h a s e ( Eq . ( 6 − 9 ) )58

61 printf ( ” \n r o ot 3 v a l u e i s t a k e n a s %f , s o s l i g h t

v a r i a t i o n s i n t he a ns we r . \ n” , sqrt ( 3 ) ) ;

62 printf ( ” \n a : P T = %d W \n” , P _ T ) ;63 printf ( ” \n b : P p = %. 2 f W \n” , P _p _b ) ;

64 printf ( ” \n c : E gp = %d <%. 2 f V \n” , E _g p_ m , E _g p_ a

65 printf ( ” \n wher e %d i s m agni t ude i n V and %. 2 f i s p ha se a n gl e i n d e gr e e s . \ n” , E _ g p _ m , E _ g p _ a ) ;

66 printf ( ” \n d : T orq ue a n gl e , d eb a = %. 2 f d e g r e e s \n”, deba ) ;

67 printf ( ” \n e : P p = %d W \n” , P_ p_ e ) ;

68 printf ( ” \n f : P p = %d W ”, P _p _f ) ;

Scilab code Exa 6.8 calculate torqueperphase and total torque

6 // Ch apt e r 6 : AC DYNAMO VOLTAGE RELATIONS−

ALTERNATORS7 / / E xa mp le 6−88

11 / / G iv en d a ta12

13 kVA = 100 ; // kVA r a t i n g o f t he 3−p ha se a l t e r n a t o r14 V _L = 1100 ; // L i ne v o l t a ge o f t he 3−p h a s e

a l t e r n a t o r i n v o l t15 S = 1200 ; // S yn ch ro no us s p ee d i n rpm16

17 / / dc−r e s i s t a n c e t e s t d a t a18 E_gp1 = 6 ; // g e ne r a t ed p ha se v o l t a g e i n v o l t

19 V _l = E _g p1 ; // g en er at ed l i n e v o l t a g e i n v o l t

20 I_a1 = 10 ; // f u l l −l oa d c u r r e n t p e r p h as e i n A21 c os _t he ta = 0 .8 ; // 0 . 8 PF l a g g i ng22 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ; //23

28 / / s h or t − c i r c u i t t e s t d at a29 I _f3 = 12 .5 ; // F i e l d c ur r e n t i n A30 // L in e c u r r e n t I l = r a t e d v a l u e i n A

3132 / / C a l c u l a t e d d at a fr om Ex.6 −4 & E x . 6 −733 I _L = 52.5 ; // Rated l i n e c u r r e n t i n A34 I_a = I_L ; // Rated c u r re n t p er p ha se i n A35 E_gp = 532 + %i *623 ; // G en er at ed v o l t a g e a t 0 . 8 PF

l a g g i n g36 E_g = 819 ; // E g = mag ni t ude o f E gp i n v o l t37 X_s = 4.6 ; // S yn ch ro n ou s r e a c t a n c e p e r p ha se38 V_p = 635 ; // Phase v o l t a g e i n v o l t39 de ba = 1 2.6 3 ; // Torque a n g l e i n d e g r e es40

41 / / C a l c u l a t i o n s42 / / c as e a43 T _p_a = ( 7.04 * E_g * V_p * sind ( deba ) ) / ( S* X_s )

; / / Output t o rq u e p er p ha se i n l b . f t44 T _3 ph as e_ a = 3 * T _p_ a ; // Output t o rq u e f o r 3−

p ha se i n l b . f t45

46 / / c as e b47 o me ga = S * 2* %pi * (1 /6 0) ; // A ng ul ar f r e qu e n cy i n

r a d / s

48 T _p _b = ( E _g * V _p * s in d ( de ba ) ) /( o me ga * X _s ) ; //Output t o r q ue p e r p ha se i n l b . f t

49 T _3 ph as e_ b = 3 * T _p_ b ; // Output t o rq u e f o r 3−p ha se i n l b . f t

51 / / c as e c

52 T _p _c = T _p _a * 1 .3 56 ; // Output t o r q ue p e r p ha sei n N . m53 T _3 ph as e_ c = 3 * T _p_ c ; // Output t o rq u e f o r 3−

p ha s e i n N .m54

57 p i = %pi ;

58 printf ( ” \n S l i g h t v a r i a t i o n s i n th e a n s w e r s ar edue t o v al ue o f p i = %f ” , p i ) ;

59 printf ( ” \n and omega = %f , which a re s l i g h t l y

d i f f e r e n t a s i n t h e t ex tb oo k . \ n” , o m e g a ) ;60 printf ( ” \n a : T p = %d l b− f t ” , T _ p _ a ) ;

61 printf ( ” \n T 3 ph a s e = %d l b − f t \n” , T _ 3 ph a s e_ a ) ;

63 printf ( ” \n b : T p = %. 1 f N−m ” , T _ p _ b ) ;

64 printf ( ” \n T 3 ph a s e = %. 1 f N−m \n” , T _ 3 ph a s e_ b ) ;

66 printf ( ” \n c : T p = %. 1 f N−m ” , T _ p _ c ) ;

67 printf ( ” \n T 3 ph a s e = %. 1 f N−m \n” , T _ 3 ph a s e_ c ) ;

68 printf ( ” \n Answers from c a s e s b and c al m o s t

t a l l y e a c h o th er ”) ;

Chapter 7

PARALLEL OPERATION

Scilab code Exa 7.1 calculate I Ia and P

6 / / Ch apt e r 7 : PARALLEL OPERATION

7 / / E xa mp le 7−18

11 / / G iv en d a ta12 R_sh = 120 ; / / Sh un t f i e l d r e s i s t a n c e i n ohm13 R_a = 0.1 ; // Armature r e s i s t a n c e i n ohm14 V_L = 120 ; // L i n e v o l t a g e i n v o l t15 E_g1 = 125 ; / / G e ne r at e d v o l t a g e by dynamo A

16 E_g2 = 120 ; / / G e ne r at e d v o l t a g e by dynamo B17 E_g3 = 114 ; / / G e ne r at e d v o l t a g e by dynamo C18

19 / / C a l c u l a t i o n s20 / / c as e a

21 // 1 :

22 I_gA = ( E_g1 - V_L ) / R_a ; // C ur re nt i n t heg e n e r a t i n g s ou rc e A ( i n A)23 I_f = V_L / R_sh ; // S hu nt f i e l d c u r r e n t i n A24 I_a1 = I_gA + I_f ; // Armature c u r r e nt i n A f o r

g e n e r a t o r A25 I _L1 = I_ gA ; // C ur re nt d e l i v e r e d by dynamo A t o

t h e bus i n A26

27 // 2 :28 I _gB = ( E_g2 - V _L ) / R _a ; // C u rr en t i n t he

g e n e r a t i n g s ou rc e B ( i n A)

29 I_a2 = I_gB + I_f ; // Armature c u r r e nt i n A f o rg e n e r a t o r B

30 I _L2 = I_ gB ; // C ur re nt d e l i v e r e d by dynamo B t ot h e bus i n A

32 // 3 :33 I _gC = ( V _L - E _g3 ) / R _a ; // C u rr en t i n t he

g e n e r a t i n g s ou rc e C ( i n A)34 I _a3 = I_ gC ; // Armature c u r r e n t i n A f o r g e n e r a t or

C35 I_L3 = I_gC + I_f ;

// C ur re nt d e l i v e r e d by dynamo Ct o t h e bus i n A36

37 / / c as e b38 // 1 :39 P_LA = V_L * I_L1 ; // Power d e l i v e r e d t o t he bus by

dynamo A i n W40 P_gA = E_g1 * I_a1 ; / / P owe r g e n e r a t e d by dynamo A41

42 // 2 :43 P_LB = V_L * I_L2 ; // Power d e l i v e r e d t o t he bus by

dynamo B i n W44 P_gB = E_g2 * I_a2 ; / / P owe r g e n e r a t e d by dynamo B45

46 // 3 :47 P_LC = V_L * I_L3 ; // Power d e l i v e r e d t o t he bus by

dynamo C i n W

48 P_gC = E_g3 * I_a3 ; / / P owe r g e n e r a t e d by dynamo C49

52 printf ( ” \n a : 1 . I gA = %d A \ t I f = %d A ” , I _g A ,

I _f ) ;

53 printf ( ” \n Thus , dynamo A d e l i v e r s %d A t o t h eb us and h as an a rm at ur e ” , I _g A );

54 printf ( ” \n c u r r e n t o f %d A + %d A = %d \n” ,

I _g A , I _ f , I _ a 1 ) ;

56 printf ( ” \n 2 . I g B = %d A ” , I _g B ) ;57 printf ( ” \n Thus , dynamo B i s f l o a t i n g and ha s

a s a rm at ur e & f i e l d c u r r e n t o f %d A \n” , I _ f ) ;

59 printf ( ” \n 3 . I g C = %d A ” , I _ g C ) ;

60 printf ( ” \n Dynamo C r e c e i v e s %d A from t h ebus & h a s an a rm at ur e c u r r e nt o f %d A\n” , I _ L 3 ,

I _ a 3 ) ;

62 printf ( ” \n b : 1 . Power d e l i v e r e d t o t he bus by

dynamo A i s : ”) ;

63 printf ( ” \n P LA = %d W ” , P _ L A ) ;

64 printf ( ” \n Power g e n e r a t e d by dynamo A i s \nP gA = %d W \n” , P _ g A ) ;

66 printf ( ” \n 2 . S in ce dynamo B n e i t h e r d e l i v e r spower t o n or r e c e i v e s power fro m t he bus , ” ) ;

67 printf ( ” \n P B = %d W ” , P _ L B ) ;

68 printf ( ” \n Power g en er at ed by dynamo B , t oe x c i t e i t s f i e l d , i s ” ) ;

69 printf ( ” \n P gB = %d W \n ” , P _g B );

7071 printf ( ” \n 3 . Power d e l i v e r e d by th e bus t o

dynamo C i s ” ) ;

72 printf ( ” \n P LC = %d W ” , P _L C ) ;

73 printf ( ” \n w h i l e t h e i n t e r n a l power d e l i v e r e d

i n t h e d i r e c t i o n o f r o t a t i o n ” ) ;

74 printf ( ” \n o f i t s pr i m e mover t o a i d r o t a t i o ni s \n P gC = %d W” , P_gC ) ;

Scilab code Exa 7.2 calculate all currents and power of the generator

4 / / 2 nd e d i t i om5

6 / / Ch apt e r 7 : PARALLEL OPERATION7 / / E xa mp le 7−28

11 / / G iv en d a ta12 R_a = 0.1 ; // Armature r e s i s t a n c e i n ohm13 R_f = 100 ; // F i el d c kt r e s i s t a n c e i n ohm

14 V_L_b = 120 ; // Bus v o l t a ge i n v o l t15 V_L_a = 140 ; // V ol ta ge o f t h e g e n e ra t o r i n v o l t16 V _f = V _L _a ; // V ol ta ge a c r o s s t he f i e l d i n v o l t17

18 / / C a l c u l a t i o n s19 / / c as e a20 I _ f _ a = V _ f / R _ f ; // F i e l d c ur r e nt i n A21 I _a _a = I _f _a ; // Armature c u r r e nt i n A22 E_g_a = V_L_a + I_a_a * R_a ; / / G e n e r a t e d EMF i n

v o l t

23 P _g _a = E _g _a * I _a _a ; / / G en er at ed p ower i n W24

25 / / c as e b26 I_a_b = ( E_g_a - V_L_b ) / R_a ; // A r mat ur e

c u r r e n t i n A

27 I_f_b = V_L_b / R_f ; // F i e l d c u r r e nt i n A

28 I_ Lg = I _a_ b - I _f _b ; // G en er a te d l i n e c u r re n t i nA29 P_L = V_L_b * I_Lg ; // Power g e n er a t ed a c r o s s t he

l i n e s i n W30 E _g _b = V _L _a ;

31 P _g _b = E _g _b * I _a _b ; / / G en er at ed p ower i n W32

35 printf ( ” \n a : B ef o re i t i s c o nn ec t e d t o t h e bus ” ) ;

36 printf ( ” \n I a = I f = %. 1 f A \n E g = %. 2 f V

\n P g = %. 1 f W \n” , I _a _a , E _ g_ a , P _ g_ a ) ;37

38 printf ( ” \n b : A ft er i t i s c o nn ec t e d t o t h e bus ” ) ;

39 printf ( ” \n I a = %. 1 f A \n I f = %. 1 f A \nI L g = %. 1 f A \n” , I_ a_ b , I _f _b , I _L g ) ;

40 printf ( ” \n P L = %. f W \n P g = %. f W ” , P_L

, P_ g_ b ) ;

Scilab code Exa 7.3 calculate VL IL Pg and PL

11 / / G iv en d a ta12 R_a = 0.1 ; // Armature r e s i s t a n c e i n ohm o f 3 s hu nt

g e n e r a t o r s

13 R _ a1 = R _a ;14 R _ a2 = R _a ;

15 R _ a3 = R _a ;

16 R_L = 2 ; // Load r e s i s t a n c e i n ohm17 E_g1 = 127 ; // V ol ta ge g e n e ra t e d by g e n er a t o r 1 i n

v o l t18 E_g2 = 120 ; // V ol ta ge g e n e ra t e d by g e n er a t o r 2 i n

v o l t19 E_g3 = 119 ; // V ol ta ge g e n e ra t e d by g e n er a t o r 3 i n

v o l t20 / / N e g l e c t f i e l d c u r r e n t s

2122 / / C a l c u l a t i o n s23 / / c as e a24 / / T er mi na l bus v o l t a g e i n v o l t25 V_L = ( ( 12 7/ 0. 1) + ( 12 0/ 0. 1) + ( 11 9/ 0. 1) ) / (

( 1/ 0. 1) + ( 1/ 0. 1) + ( 1/ 0. 1) + 0 .5 ) ;

27 / / c as e b28 I_ L1 = ( E_g 1 - V_ L) / R_ a1 ; // C ur re nt d e l i v e r e d by

g e n e r a to r 1 i n A29 I_ L2 = ( E_g 2 - V_ L) / R_ a2 ;

// C ur re nt d e l i v e r e d byg e n e r a to r 2 i n A30 I_ L3 = ( E_g 3 - V_ L) / R_ a3 ; // C ur re nt d e l i v e r e d by

g e n e r a to r 3 i n A31 I _ L_ 2o hm = V_L / R_L ; // C ur re nt d e l i v e r e d by 2 ohm

l o ad i n A32

33 / / c as e c34 I _a1 = I_ L1 ; // Armature c u r r e n t i n A f o r g e n e r a t or

135 I _a2 = I_ L2 ; // Armature c u r r e n t i n A f o r g e n e r a t or

236 I _a3 = I_ L3 ; // Armature c u r r e n t i n A f o r g e n e r a t or

38 P_g1 = E_g1 * I_a1 ; // Power g e n e r a t ed by g e n e r a t o r

1 i n W

39 P_g2 = E_g2 * I_a2 ; // Power g e n e r a t ed by g e n e r a t o r2 i n W40 P_g3 = E_g3 * I_a3 ; // Power g e n e r a t ed by g e n e r a t o r

3 i n W41

42 / / c as e d43 P_L1 = V_L * I_L1 ; // Power d e l i v e r e d t o o r

r e c e i v e d from g e n er a t or 1 i n W44 P_L2 = V_L * I_L2 ; // Power d e l i v e r e d t o o r

r e c e i v e d from g e n er a t or 2 i n W45 P_L3 = V_L * I_L3 ; // Power d e l i v e r e d t o o r

r e c e i v e d from g e n er a t or 3 i n W46 P_L = V_L * - I_ L_ 2o hm ; // Power d e l i v e r e d t o o r

r e c e i v e d 2 ohm l oa d i n W47

50 printf ( ” \n a : C on ve rt in g e a ch v o l t a g e s o ur c e t o ac u r r e nt s o u r c e a nd a p p ly i n g ” ) ;

51 printf ( ” \n Millman ‘ s t heo r em y i e l d s ” )

52 printf ( ” \n V L = %d V \n ” , V _ L ) ;

54 printf ( ” \n b : I L 1 = %d A ( t o b us ) ” , I_L1 ) ;

55 printf ( ” \n I L 2 = %d A ” , I_L2 ) ;

56 printf ( ” \n I L3 = %d A ( from bus ) ” , I_L3 ) ;

57 printf ( ” \n I L 2o hm = −%d A ( f r om bus ) \n” ,

I _ L_ 2 oh m ) ;

59 printf ( ” \n c : P g 1 = %d W ” , P _g 1 ) ;

60 printf ( ” \n P g2 = %d W ( f l o a t i n g ) ” , P _g 2 ) ;

61 printf ( ” \n P g3 = %d W \n” , P _g 3 ) ;

63 printf ( ” \n d : P L1 = %d W ” , P _L 1 ) ;64 printf ( ” \n P L2 = %d W ” , P_L2 ) ;

65 printf ( ” \n P L3 = %d W ” , P_L3 ) ;

66 printf ( ” \n P L = %d W ” , P _ L ) ;

Scilab code Exa 7.4 calculate total load and kW output of each G

11 / / G iv en d a ta12 P 1 = 300 ; // Power r a t i n g o f g e n er a t o r 1 i n kW13 P 2 = 600 ; // Power r a t i n g o f g e n er a t o r 2 i n kW14 V = 220 ; // V ol ta ge r a t i n g o f g e ne r a t or 1 a nd 2 i n

v o l t15 V_o = 250 ; / / No−l oa d v o l t a ge a p pl i ed t o bot h t he

g e n e r a t o r s i n v o l t16 / / Assume l i n e a r c h a r a c t e r i s t i c s17 V_1 = 230 ; // T e r mi na l v o l t a g e i n v o l t ( c a se a )18 V_2 = 240 ; // T e r mi na l v o l t a g e i n v o l t ( c a se b )19

20 / / C a l c u l a t i o n s21 / / c as e a22 kW1_a = ( V_o - V_1 )/( V_o - V ) * P1 ; / / kW c a r r i e d

by g e n er a t o r 123 kW2_a = ( V_o - V_1 )/( V_o - V ) * P2 ; / / kW c a r r i e d

by g e n er a t o r 224

25 / / c as e b26 kW1_b = ( V_o - V_2 )/( V_o - V ) * P1 ; / / kW c a r r i e d

27 kW2_b = ( V_o - V_2 )/( V_o - V ) * P2 ; / / kW c a r r i e d

29 / / c as e c30 f ra c_ a = ( V_ o - V_1 ) /( V_o - V ); // F r a c t i o n o f r at ed

kW c a r r i e d by e ac h g e n e r a to r31 f ra c_ b = ( V_ o - V_2 ) /( V_o - V ); // F r a c t i o n o f r at ed

kW c a r r i e d by e ac h g e n e r a to r32

35 printf ( ” \n a : At 2 30 V, u s i ng Eq .( 7 − 3 ) be l o w : ” ) ;

36 printf ( ” \n G e n e r a t o r 1 c a r r i e s = %d kW ” , k W1 _a) ;

37 printf ( ” \n G e n e r a t o r 2 c a r r i e s = %d kW \n” ,

k W2 _a ) ;

39 printf ( ” \n b : At 2 40 V, u s i ng Eq .( 7 − 3 ) be l o w : ” ) ;

40 printf ( ” \n G e n e r a t o r 1 c a r r i e s = %d kW ” , k W1 _b

41 printf ( ” \n G e n e r a t o r 2 c a r r i e s = %d kW \n” ,

k W2 _b ) ;

43 printf ( ” \n c : Both g e n e ra t o r s c a rr y no−l oa d a t 250V ; ” ) ;

44 printf ( ” \n %f r a t e d l o a d a t %d V ; ” , f ra c_ b ,

V _2 ) ;

45 printf ( ” \n %f r a t e d l o a d a t %d V ; ” , f ra c_ a ,

V _1 ) ;

46 printf ( ” \n and r a t e d l oa d a t %d V . ” , V ) ;

Scilab code Exa 7.5 calculate max and min E and frequency and Epeakand n

2 / / I r v i n g L k osow

11 / / G iv en d a ta12 E_1 = 220 ; // T e r m i n a l v o l t a ge o f a l t e r n a t o r 1 i n

v o l t13 E_2 = 222 ; // T e r m i n a l v o l t a ge o f a l t e r n a t o r 2 i n

v o l t14 f_1 = 60 ; // F r e q ue n cy o f a l t e r n a t o r 1 i n Hz15 f _2 = 59.5 ; // F r e q u en cy o f a l t e r n a t o r 2 i n Hz16 // S wi tc h i s open17

18 / / C a l c u l a t i o n s19 / / c as e a20 E _m ax = ( E_1 + E_ 2) /2 ; // Maximum e f f e c t i v e v o l t a g e

a c r o s s e ac h lamp i n v o l t21 E _m in = ( E_2 - E_ 1) /2 ; // Minimum e f f e c t i v e v o l t a g ea c r o s s e ac h lamp i n v o l t

23 / / c as e b24 f = f_1 - f_2 ; // F r e q ue nc y i n Hz o f t he v o l t a g e

a c r o s s t he l am ps25

26 / / c as e c27 E _p ea k = E _m ax / 0 .7 07 1 ; // Peak v al u e o f t he

v o l t a ge i n v o l t a c r o s s e a c h lamp

2829 / / c as e d30 n = (1 /2 ) *f_1 ; / / Number o f maximum l i g h t

p u l s a t i o n s p er m in ute31

33 disp ( ”E x ampl e 7−5 S o l u t i on : ” ) ;34 printf ( ” \n a : E max / la mp = %d V ( r ms ) \n ” , E _m ax ) ;

35 printf ( ” \n E min /lamp = %d V \n ” , E _m in ) ;

36 printf ( ” \n b : f = %. 1 f Hz \n ” , f ) ;

37 printf ( ” \n c : E p ea k = %. f V \n ” , E _p ea k ) ;

38 printf ( ” \n d : n = %d p u l s a t i o n s / min ” , n ) ;

Scilab code Exa 7.6 calculate max and min E and f and phase relations

1011 / / G iv en d a ta12 E = 220 ; // V ol ta ge g e ne r a t ed i n v o l t13 E_1 = E ; // V ol ta ge g e n er at ed by a l t e r n a t o r 1 i n

v o l t14 E_2 = E ; // V ol ta ge g e n er at ed by a l t e r n a t o r 2 i n

v o l t15 f_1 = 60 ; // F r e q ue n cy i n Hz o f a l t e r n a t o r 116 f_2 = 58 ; // F r e q ue n cy i n Hz o f a l t e r n a t o r 217 // S wi tc h i s open

1819 / / C a l c u l a t i o n s20 / / c as e a21 E _m ax = ( E_1 + E_ 2) /2 ; // Maximum e f f e c t i v e v o l t a g e

a c r o s s e ac h lamp i n v o l t

22 f = f_1 - f_2 ; // F r e q ue nc y i n Hz o f t he v o l t a g e

a c r o s s t he l am ps23

24 / / c as e c25 E _m in = ( E_2 - E_ 1) /2 ; // Minimum e f f e c t i v e v o l t a g e

a c r o s s e ac h lamp i n v o l t26

29 printf ( ” \n a : E max / l am p = %d V \n f = %d Hz \n” , E _ m a x , f ) ;

30 printf ( ” \n b : The v o l t a g e s a re e qu al and o p p o si t e

i n t h e l o c a l c i r c u i t . \n ” ) ;31 printf ( ” \n c : E min / lamp = %d V a t z e r o f r e q u e n cy \

n ” , E _m in ) ;

32 printf ( ” \n d : The v o l t a g e s a re i n p h a s e i n t h el o c a l c i r c u i t . ” ) ;

Scilab code Exa 7.7 calculate Is in both alternators

1011 / / G ive n d at a a s p e r Ex . (7 − 5 )12 E 1 = 220 ; // T e r m i n a l v o l t a ge o f a l t e r n a t o r 1 i n

v o l t13 E 2 = 222 ; // T e r m i n a l v o l t a ge o f a l t e r n a t o r 2 i n

v o l t

14 f1 = 60 ; // F re q u en cy o f a l t e r n a t o r 1 i n Hz15 f 2 = 59.5 ; // F r eq u en cy o f a l t e r n a t o r 2 i n Hz16 // S wi tc h i s open17

18 / / G ive n d at a a s p e r Ex . (7 − 6 )19 E = 220 ; // V ol ta ge g e ne r a t ed i n v o l t20 E_1 = E ; // V ol ta ge g e n er at ed by a l t e r n a t o r 1 i n

v o l t21 E_2 = E ; // V ol ta ge g e n er at ed by a l t e r n a t o r 2 i n

v o l t22 f_1 = 60 ; // F r e q ue n cy i n Hz o f a l t e r n a t o r 1

23 f_2 = 58 ; // F r e q ue n cy i n Hz o f a l t e r n a t o r 224 // S wi tc h i s open25

26 / / G ive n d at a a s p e r Ex . (7 − 7 )27 R_a1 = 0.1 ; // a r m a t u r e r e s i s t a n c e o f a l t e r n a t o r 1

i n ohm28 R_a2 = 0.1 ; // a r m a t u r e r e s i s t a n c e o f a l t e r n a t o r 2

i n ohm29 X_a1 = 0.9 ; // a rm at u re r e a ct a n ce o f a l t e r n a t o r 1

i n ohm30 X_a2 = 0.9 ;

// a rm at u re r e a ct a n ce o f a l t e r n a t o r 2i n ohm31

32 Z_1 = R _a1 + %i *X_a1 ; // E f f e c t i v e i mpeda nce o f a l t e r n a t o r 1 i n ohm

33 Z_2 = R _a1 + %i *X_a2 ; // E f f e c t i v e i mpeda nce o f a l t e r n a t o r 2 i n ohm

34 // S wi tc he s a re c l o se d a t t h e p ro pe r i n s t a n t f o rp a r a l l e l i n g .

37 / / I n Ex .7 −5 ,38 E_r = E2 - E1 ; // E f f e c t i v e v o l t a ge g en e r at ed i n

v o l t39 I_s = E_r / ( Z_1 + Z_2 ); // S y nc hr o ni z in g c u r r e nt i n

t he a rm at ur e i n A

40 I _ s_ m = abs ( I _ s ) ; // I s m =m ag ni tu de o f I s i n A

41 I _ s_ a = atan ( imag ( I _s ) / real ( I _ s ) ) * 1 8 0 / % p i ; // I s a =p h a s e a ng le o f I s i n d e g r e es42

43 / / I n Ex .7 −6 ,44 Er = E_2 - E_1 ; // E f f e c t i v e v o l t a ge g en e r at ed i n

v o l t45 Is = Er / ( Z_1 + Z_2 ); // S y nc h ro n iz i ng c u r re n t i n

t he a rm at ur e i n A46

49 printf ( ” \n I n Ex .7 −5 , ” ) ;50 printf ( ” \n E r = %d V ” , E _r ) ;

51 printf ( ” \n I s = ” ) ; disp ( I _ s ) ;

52 printf ( ” \n I s = %. 3 f <%. 2 f A ” , I _s _m , I _ s_ a ) ;

53 printf ( ” \n where %. 3 f i s m ag ni tu de i n A a nd %. 2 f i sp ha se a n gl e i n d e g re e s \n” , I _ s _ m , I _ s _ a ) ;

55 printf ( ” \n I n Ex .7 −6 , ” ) ;

56 printf ( ” \n E r = %d V ” , Er ) ;

57 printf ( ” \n I s = %d A” , I s ) ;

Scilab code Exa 7.8 calculate generator and motor action and P loss andterminal V and phasor diagram

c o n s o l e .

1011 / / G iv en d a ta12 / / EMF’ s a r e o pp os ed e x a c t l y by 1 80 d e g r e e s13 E_gp1 = 200 ; // T e r mi n a l v o l t a ge o f a l t e r n a t o r 1 i n

v o l t14 E_gp2 = 220 ; // T e r mi n a l v o l t a ge o f a l t e r n a t o r 2 i n

v o l t15 R_a1 = 0.2 ; // a r m a t u r e r e s i s t a n c e o f a l t e r n a t o r 1

i n ohm16 R_a2 = 0.2 ; // a r m a t u r e r e s i s t a n c e o f a l t e r n a t o r 2

i n ohm

17 X_a1 = 2 ; // a r m a t u r e r e a c ta n ce o f a l t e r n a t o r 1 i nohm

18 X_a2 = 2 ; // a r m a t u r e r e a c ta n ce o f a l t e r n a t o r 2 i nohm

20 Z _p1 = R_a1 + %i *X_a1 ; // E f f e c t i v e i mpe danc e o f a l t e r n a t o r 1 i n ohm

21 Z _p2 = R_a1 + %i *X_a2 ; // E f f e c t i v e i mpe danc e o f a l t e r n a t o r 2 i n ohm

22 // S wi tc he s a re c l o se d a t t h e p ro pe r i n s t a n t f o r

p a r a l l e l i n g .23

24 / / C a l c u l a t i o n s25 / / c as e a26 E_r = ( E _gp 2 - E _g p1 ) ; // E f f e c t i v e v o l t a ge

g e n e ra t ed i n v o l t27 I_s = E_r / ( Z_p1 + Z_p2 ); // S y n ch r o ni z i ng c u r r e nt

i n t he a rm at u re i n A28 I _ s_ m = abs ( I _ s ) ; // I s m =m ag ni tu de o f I s i n A29 I _ s_ a = atan ( imag ( I _s ) / real ( I _ s ) ) * 1 8 0 / % p i ; // I s a =

p h a s e a ng le o f I s i n d e g r e es

3031 P _ 2 = E _g p2 * I _s _m * c os d ( I_ s_ a ); // G e n er a t o r

a c ti o n d ev el op ed by a l t e r n a t o r 2 i n W32

33 / / c as e b

34 t he ta = I _s _a ;

35 // P 1 = E gp1 ∗ I s m ∗ c o s d ( 1 8 0 − t h e t a )36 // P 1 = −E g p 1 ∗ I s m ∗ cos d ( th et a ) ,37 P _1 = - E _g p1 * I _s _m * c os d ( th et a ); // S y n c h r o n i zi n g

power r e c e i v e d by a l t e r n a t o r 1 i n W38

39 / / c as e c40 / / b ut c o n s i d e r +ve v l au e f o r P 1 f o r f i n d i n g l o s s e s

, s o41 P1 = abs ( P _ 1 ) ;

42 los ses = P_2 - P1 ; // Power l o s s e s i n bot ha r ma t ur e s i n W

43 c he ck = E _r * I _s _m * c os d ( I_ s_ a ); // V e r i f y i n gl o s s e s by Eq.7 −7

44 d ou bl e_ ch ec k = ( I _s _m ) ^2 * ( R _a 1 + R _a 2 ); //V e r i f y i n g l o s s e s by Eq.7 −7

46 / / c as e d47 V _p2 = E_gp2 - I _s * Z_p1 ; // G en er at or a c t i o n48 V _p1 = E_gp1 + I _s * Z_p1 ; // Motor a c t i o n49

52 printf ( ” \n a : E r = %d V ” , E _ r ) ;

53 printf ( ” \n I s = %. 2 f <%. 2 f A ” , I _s _m , I _s _a ) ;

54 printf ( ” \n P 2 = %. 1 f W ( t o t a l power d e l i v e r e dby a l t e r n a t o r 2 ) \n” , P _2 ) ;

56 printf ( ” \n b : P 1 = %f W ( s y n c h r o n i z i n g po we rr e c e i v e d by a l t e r n a t o r 1 ) ”, P _ 1 ) ;

57 printf ( ” \n Note : S c i l a b c o n s i d e r s p ha s e a ng le o f I s a s %f i n s t e ad ” , I _ s _ a ) ;

58 printf ( ” \n o f −84.3 d e gr e es , s o s l i g h t

v a r i a t i o n i n t he an swe r P 1 . \ n” ) ;59

60 printf ( ” \n c : C on si de r +ve v al ue o f P 1 f o rc a l c u l a t i n g l o s s e s ” ) ;

61 printf ( ” \n L o s s e s : P 2 − P 1 = %. 1 f W ” , l os se s )

62 printf ( ” \n Check : E a ∗ I s ∗ c o s ( t h e t a ) = % . 1 f W ” ,c he ck ) ;

63 printf ( ” \n Double c h e c k : ( I s ) ̂ 2 ∗ ( R a 1 + R a 2 ) =%. 1 f W a s g i v en i n Eq .( 7 − 1 ) ” , d o u b l e_ c h ec k ) ;

65 printf ( ” \n\n d : From F i g . 7 −1 4 , V p2 , t he t e rm i n alp h a se v o l t a ge o f ” ) ;

66 printf ( ” \n a l t e r n a t o r 2 , i s , from Eq . ( 7 − 1 ) ” ) ;

67 printf ( ” \n V p2 = %d V ( g e ne r a t or a c t i on ) \n\nFrom s e c t i o n 7 −2.1 ” , V _ p 2 ) ;

68 printf ( ” \n V p1 = %d V ( motor a c t i o n ) \n” , V _ p 1 ) ;

6970 printf ( ” \n e : The p ha so r d ia gr am i s shown i n F ig

. 7 − 1 4 . ” ) ;

Scilab code Exa 7.9 calculate synchronizing I and P and P losses

12 E _2 _m ag = 23 0 ; // Ma gn itud e o f v o l t a g e g e n er a t ed bya l t e r n a t o r 2 i n v o l t13 E _1 _m ag = 23 0 ; // Ma gn itud e o f v o l t a g e g e n er a t ed by

a l t e r n a t o r 1 i n v o l t14

15 t he ta _2 = 18 0 ; // Phase a n gl e o f g e n e ra t e d v o l t a g e

by a l t e r n a t o r 2 i n d e g r e es16 t he ta _1 = 20 ; // Phase a n gl e o f g e ne r a t ed v o l t a g eby a l t e r n a t o r 1 i n d e g r e es

18 R_a1 = 0.2 ; // a r m a t u r e r e s i s t a n c e o f a l t e r n a t o r 1i n ohm

19 R_a2 = 0.2 ; // a r m a t u r e r e s i s t a n c e o f a l t e r n a t o r 2i n ohm

21 / / w r i t i ng g i v en v o l t a ge i n e x po n e n t i a l form a sf o l l o w s

22 // %pi /180 f o r d e gr e e s t o r a d ia n s c o nv e r s i o n23 E_2 = E _2 _m ag * expm ( % i * t he t a_ 2 * ( %p i / 18 0) ) ; //

v o l t a ge g e n er at ed by a l t e r n a t o r 2 i n v o l t24 E_1 = E _1 _m ag * expm ( % i * t he t a_ 1 * ( %p i / 18 0) ) ; //

v o l t a ge g e n er at ed by a l t e r n a t o r 1 i n v o l t25

26 / / w r i t i n g g i v e n i mp ed an ce ( i n ohm ) i n e x p o n e n t i a lform a s f o l l o w s

27 Z _1 = 2.01 * expm ( %i * 8 4. 3* ( %p i /1 80 ) ) ; / / %pi / 1 8 0f o r d e g r ee s t o r a d i an s c o n v er s i o n

28 Z_2 = Z_1 ;

29 Z _ 1_ a = atan ( imag ( Z _1 ) / real ( Z _ 1 ) ) * 1 8 0 / % p i ; / / Z 1 a =p h a se a n g l e o f Z 1 i n d e g r e e s

31 / / C a l c u l a t i o n s32 E_r = E_2 + E_1 ; // T ot al v o l t a g e g e ne r a t ed by

A l t e r n at o r 1 and 2 i n v o l t33 E _ r_ m = abs ( E _ r ) ; // E r m=m ag ni tu de o f E r i n v o l t34 E _ r_ a = atan ( imag ( E _r ) / real ( E _ r ) ) * 1 8 0 / % p i ; / / E r a =

p h a s e a ng le o f E r i n d e g r e e s35

36 / / c as e a37 I_s = E_r / ( Z_1 + Z_2 ); // S yn ch ro n oz in g c u r r e nt i n

A38 I _ s_ m = abs ( I _ s ) ; // I s m =m ag ni tu de o f I s i n A39 I _ s_ a = atan ( imag ( I _s ) / real ( I _ s ) ) * 1 8 0 / % p i ; // I s a =

4041 / / c as e b42 E _ g p1 = E _1 _ ma g ;

43 P _ 1 = E _g p1 * I _s _m * c os d ( I_ s_ a - t he ta _1 ) ; //S yn ch ro no z in g power d e ve l op e d by a l t e r n a t o r 1 i n

45 / / c as e c46 E _ g p2 = E _2 _ ma g ;

49 / / c as e d50 / / b ut c o n s i d e r +ve v l au e f o r P 2 f o r f i n d i n g l o s s e s

, s o51 P2 = abs ( P _ 2 ) ;

52 los ses = P_1 - P2 ; // L o ss e s i n t he a rm at ur e i n W53

54 // E r a y i e l d s −80 d e g r e es which i s e q u i v al e n t t o10 0 d e gr e es , s o

55 theta = 100 - I_s_a ; // Pha se d i f f e r e n c e b et wee nE r and I a i n d e g r e e s

57 c he ck = E _r _m * I _s _m * c os d ( th et a ); // V e r i f y i n gl o s s e s by Eq.7 −7

58 R_aT = R_a1 + R_a2 ; // t o t a l a r m a t u r e r e s i s t a n c e o f a l t e r n a t o r 1 and 2 i n ohm

59 d o ub l e_ c he c k = ( I _ s_ m ) ^2 * ( R _a T ) ; // V e r i f y i n gl o s s e s by Eq.7 −7

62 disp ( ”E x ampl e 7−9 S o l u t i on : ” ) ;63 printf ( ” \n a : I s = ”) ; disp ( I _ s ) ;

64 printf ( ” \n I s = %. 2 f <%. 2 f A \n ” , I _s _m , I _ s_ a

66 printf ( ” \n b : P 1 = %. f W ( power d e l i v e r e d t o bus ) ”

, P _ 1 ) ;67 printf ( ” \n S l i g h t v a r i a t i o n i n P 1 i s due s l i g h tv a r i a t i o n s i n ” )

68 printf ( ” \n magni tud e o f I s ,& a ng l e btw ( E gp1 ,I s ) \n” )

69 printf ( ” \n P 2 = %. f W ( power r e c e i v e d from bus )\n” , P _ 2 ) ;

71 printf ( ” \n c : L o ss e s : P 1 − P 2 = %d” , l o s s e s ) ;

72 printf ( ” \n Check : E a ∗ I s ∗ c o s ( t h e t a ) = %d W ” ,

c he ck ) ;

73 printf ( ” \n Double c h e c k : ( I s ) ̂ 2 ∗ ( R a 1 + R a 2 ) =%d W ” , d o u b l e_ c h ec k ) ;

Scilab code Exa 7.10 calculate synchronizing I and P and P losses

4 / / 2 nd e d i t i om5

11 / / G iv en d a ta12 E _2 _m ag = 23 0 ; // Ma gn itud e o f v o l t a g e g e n er a t ed by

a l t e r n a t o r 2 i n v o l t13 E _1 _m ag = 23 0 ; // Ma gn itud e o f v o l t a g e g e n er a t ed bya l t e r n a t o r 1 i n v o l t

15 t he ta _2 = 18 0 ; // Phase a n gl e o f g e n e ra t e d v o l t a g e

by a l t e r n a t o r 2 i n d e g r e es

16 t he ta _1 = 20 ; // Phase a n gl e o f g e ne r a t ed v o l t a g eby a l t e r n a t o r 1 i n d e g r e es17

18 / / w r i t i ng g i v en v o l t a ge i n e x po n e n t i a l form a sf o l l o w s

19 // %pi /180 f o r d e gr e e s t o r a d ia n s c o nv e r s i o n20 E_2 = E _2 _m ag * expm ( % i * t he t a_ 2 * ( %p i / 18 0) ) ; //

v o l t a ge g e n er at ed by a l t e r n a t o r 2 i n v o l t21 E_1 = E _1 _m ag * expm ( % i * t he t a_ 1 * ( %p i / 18 0) ) ; //

v o l t a ge g e n er at ed by a l t e r n a t o r 1 i n v o l t22

23 / / w r i t i n g g i v e n i mp ed an ce ( i n ohm ) i n e x p o n e n t i a lform a s f o l l o w s

24 Z_1 = 6 * expm ( %i * 5 0* ( %p i /1 80 ) ) ; // %pi / 18 0 f o rd e gr e e s t o r a d ia n s c o n ve r s io n

25 Z_2 = Z_1 ;

26 Z _ 1_ a = atan ( imag ( Z _1 ) / real ( Z _ 1 ) ) * 1 8 0 / % p i ; / / Z 1 a =p h a se a n g l e o f Z 1 i n d e g r e e s

28 / / C a l c u l a t i o n s29 E_r = E_2 + E_1 ; // T ot al v o l t a g e g e ne r a t ed by

A l t e r n at o r 1 and 2 i n v o l t30 E _ r_ m = abs ( E _ r ) ; // E r m=m ag ni tu de o f E r i n v o l t31 E _ r_ a = atan ( imag ( E _r ) / real ( E _ r ) ) * 1 8 0 / % p i ; / / E r a =

33 / / c as e a34 I_s = E_r / ( Z_1 + Z_2 ); // S yn ch ro n oz in g c u r r e nt i n

A35 I _ s_ m = abs ( I _ s ) ; // I s m =m ag ni tu de o f I s i n A36 I _ s_ a = atan ( imag ( I _s ) / real ( I _ s ) ) * 1 8 0 / % p i ; // I s a =

3738 / / c as e b39 E _ g p1 = E _1 _ ma g ;

4142 / / c as e c43 E _ g p2 = E _2 _ ma g ;

46 / / c as e d47 / / b ut c o n s i d e r +ve v l au e f o r P 2 f o r f i n d i n g l o s s e s

, s o48 P2 = abs ( P _ 2 ) ;

49 los ses = P_1 - P2 ; // L o ss e s i n t he a rm at ur e i n W50

51 // E r a y i e l d s −80 d e g r e es which i s e q u i v al e n t t o10 0 d e gr e es , s o

52 theta = 100 - I_s_a ; // Pha se d i f f e r e n c e b et wee nE r and I s i n d eg re es

54 c he ck = E _r _m * I _s _m * c os d ( th et a ); // V e r i f y i n gl o s s e s by Eq.7 −7

55 R _a T = 1 2* c os d (5 0) ; // t o t a l a r m a t u r e r e s i s t a n c e o f

a l t e r n a t o r 1 and 2 i n ohm56 d o ub l e_ c he c k = ( I _ s_ m ) ^2 * ( R _a T ) ; // V e r i f y i n gl o s s e s by Eq.7 −7

60 printf ( ” \n a : I s = ”) ; disp ( I _ s ) ;

61 printf ( ” \n I s = %. 2 f <%. 2 f A \n ” , I _s _m , I _ s_ a

63 printf ( ” \n b : P 1 = %. f W ( power d e l i v e r e d t o bus ) ”

, P _ 1 ) ;64 printf ( ” \n Note : S l i g h t v a r i a t i o n i n P 1 i s due

s l i g h t v a r i a t i o n s i n ” )

65 printf ( ” \n p h a s e a n g l e o f I s ,& a n g l e btw (E g p1 , I s ) \n” )

66 printf ( ” \n P 2 = %. f W ( power r e c e i v e d from bus )

\n” , P _ 2 ) ;67

68 printf ( ” \n c : L o ss e s : P 1 − P 2 = %. f W” , l o s s e s ) ;

69 printf ( ” \n Check : E a ∗ I s ∗ c o s ( t h e t a ) = % . f W ” ,

c he ck ) ;

70 printf ( ” \n Double c h e c k : ( I s ) ̂ 2 ∗ ( R a 1 + R a 2 ) =% . f W ” , d o u b l e_ c h e ck ) ;

Scilab code Exa 7.11 calculate mesh currents line currents phase voltagesphasor diagram

11 / / G iv en d a ta12 / / w r i t i ng s up pl y v o l t a ge i n e x p o ne n ti a l form a s

f o l l o w s13 // %pi /180 f o r d e gr e e s t o r a d ia n s c o nv e r s i o n14 V_AB = 100 * expm ( %i * 0 *( % pi / 18 0) ) ; // v o l t a g e

s u pp l i e d a c r o s s A & B i n v o l t15 V_BC = 100 * expm ( % i * - 12 0* ( % pi / 1 8 0) ) ; // v o l t a g e

s u pp l i e d a c r o s s B & C i n v o l t16 V_CA = 100 * expm ( %i * 1 20 *( % pi / 18 0) ) ; // v o l t ag es u pp l i e d a c r o s s C & A i n v o l t

18 disp ( ”E x ampl e 7−11 : ” ) ;

19 printf ( ” \n W ri ti ng two mesh e q ua t i on s f o r I 1 and

I 2 i n f i g .7 −23 a y i e l d s f o l l o w i n g \n a r r ay : ” ) ;20 printf ( ” \n I 1 \ t \ t I 2 \ t \ t V ” ) ;

21 printf ( ” \n” ) ;

22 printf ( ” \n 6 + j 0 \ t −3 + j 0 \ t 100 + j 0 ” ) ;

23 printf ( ” \n −3 + j 0 \ t 3 − j 4 \ t −50 − j 8 6 . 6 ” ) ;

25 / / C a l c u l a t i o n s26 A = [ ( 6+ % i *0 ) ( - 3+ %i * 0) ; ( - 3+ %i * 0) (3 - %i * 4) ]; //

M at ri x c o n t a i n i n g a bo ve mesh e qn s a r r a y27 d e lt a = det ( A ) ; // D et er mi na nt o f A

2829 / / c as e a30 I _1 = det ( [ ( 10 0+ % i * 0) ( - 3+ % i * 0) ; ( - 50 - % i * 8 6. 6 0)

(3 - %i *4) ] ) / delta ;

31 // Mesh c u r r e n t I 1 i n A32 I _ 1_ m = abs ( I _ 1 ) ; // I 1 m=m ag ni tu de o f I 1 i n A33 I _ 1_ a = atan ( imag ( I _1 ) / real ( I _ 1 ) ) * 1 8 0 / % p i ; / / I 1 a =

p h a s e a ng le o f I 1 i n d e g r e e s34

35 I _2 = det ( [ ( 6+ % i *0 ) ( 10 0+ % i *0 ) ; ( -3 + %i * 0) ( -50 - %i

*86.6 ) ] ) / delta ;

36 // Mesh c u r r e n t I 2 i n A37 I _ 2_ m = abs ( I _ 2 ) ; // I 2 m=m ag ni tu de o f I 2 i n A38 I _ 2_ a = atan ( imag ( I _2 ) / real ( I _ 2 ) ) * 1 8 0 / % p i ; / / I 2 a =

40 / / c as e b41 I_A = I_1 ; // L i n e c ur r e n t I A i n A42 I _ A_ m = abs ( I _ A ) ; // I A m=m ag ni tu de o f I A i n A43 I _ A_ a = atan ( imag ( I _A ) / real ( I _ A ) ) * 1 8 0 / % p i ; / / I A a =

p h a se a n g l e o f I A i n d e gr e e s

4445 I_B = I_2 - I_1 ; // L i n e c ur re nt I B i n A46 I _ B_ m = abs ( I _ B ) ; // I B m=m ag ni tu de o f I B i n A47 I _ B_ a = atan ( imag ( I _B ) / real ( I _B ) ) * 18 0/ % p i - 1 80 ; //

I B a=p h a s e a ng l e o f I B i n d e g r e e s

49 I _C = - I_2 ; // L i n e c u r r en t I C i n A50 I _ C_ m = abs ( I _ C ) ; // I C m=m ag ni tu de o f I C i n A51 I_C_a = 180 + atan ( imag ( I _C ) / real ( I _ C ) ) * 1 8 0 / % p i ; //

I C a=p h a s e a ng l e o f I C i n d e g r e e s52

53 / / c as e c54 Z_A = 3 * expm ( %i * 0 *( % pi / 18 0) ) ; / / I mp ed an ce i n

l i n e A i n o h m55 Z_B = 3 * expm ( %i * 0 *( % pi / 18 0) ) ; / / I mp ed an ce i n

l i n e B i n o h m56 Z_C = 4 * expm ( % i * - 90 *( % p i / 18 0) ) ; // I mp ed an ce i n

l i n e C i n o h m57

58 V_AO = I_A * Z_A ; // Phas e v o l t a g e V AO i n v o l t59 V _ A O_ m = abs ( V _ A O ) ; //V AO m=magni t ude of V AO i n

v o l t60 V _ A O_ a = atan ( imag ( V _A O ) / real ( V _ A O ) ) * 1 8 0 / % p i ; //

V AO a=p ha s e a n g l e o f V AO i n d e g r e e s61

62 V_BO = I_B * Z_B ; // Phas e v o l t a g e V BO i n v o l t63 V _ B O_ m = abs ( V _ B O ) ; //V BO m=magni t ude of V BO i n

v o l t64 V _ B O_ a = atan ( imag ( V _B O ) / real ( V _B O ) ) * 18 0/ % p i - 1 80 ;

// V BO a=p ha se a n g l e o f V BO i n d e g r e e s65

66 V_CO = I_C * Z_C ; // Phas e v o l t a g e V CO i n v o l t67 V _ C O_ m = abs ( V _ C O ) ; //V CO m=magni t ude of V CO i n

v o l t68 V _ C O_ a = atan ( imag ( V _C O ) / real ( V _ C O ) ) * 1 8 0 / % p i ; //

V CO a=p ha s e a n g l e o f V CO i n d e g r e e s69

71 disp ( ” S o l u t i o n : ” ) ;72 printf ( ” \n a : I 1 i n A = ”) ; disp ( I _ 1 ) ;

73 printf ( ” \n I 1 = %. 2 f <%. 2 f A \n ” , I _1 _m , I _ 1_ a

74 printf ( ” \n I 2 i n A = ” ) ; disp ( I _ 2 ) ;

75 printf ( ” \n I 2 = %. 2 f <%. 2 f A\n ” , I_ 2_m , I _2 _a )

77 printf ( ” \n b : I A i n A = ” ) ; disp ( I _ 1 ) ;

78 printf ( ” \n I A = %. 2 f <%. 2 f A\n” , I _A _m , I _A _a ) ;

80 printf ( ” \n I B i n A = ” ) ; disp ( I _ B ) ;

81 printf ( ” \n I B = %. 2 f <%. 2 f A\n” , I _B _m , I _B _a ) ;

83 printf ( ” \n I C i n A = ” ) ; disp ( I _ C ) ;

84 printf ( ” \n I C = %. 2 f <%. 2 f A \n” , I_C_m , I _C _a

8586 printf ( ” \n c : V AO = % . 2 f <%. 2 f V” , V _A O_ m , V _A O_ a )

87 printf ( ” \n V BO = %. 2 f <%. 2 f V” , V _B O_ m , V _B O_ a )

88 printf ( ” \n V CO = %. 2 f <%. 2 f V\n” , V _ CO _m , V _ CO _ a

90 printf ( ” \n d : The p ha so r d ia gr am i s shown i n F ig.7 −23 b , w it h t he p ha se v o l t a g e s ” ) ;

91 printf (” \n i n s c r i b e d i n s i d e t he ( e q u i l a t e r a l )t r i a n g l e o f g iv e n l i n e v o l t a ge s ” ) ;

Chapter 8

AC DYNAMO TORQUE

RELATIONS

SYNCHRONOUS MOTORS

Scilab code Exa 8.1 calculate alpha Er Ia Pp Pt Power loss Pd

6 // Ch apt e r 8 : AC DYNAMO TORQUE RELATIONS −SYNCHRONOUS MOTORS

7 / / E xa mp le 8−18

11 / / G iv en d a ta12 // 3− p h a s e Y−c o n n e c te d s y n c h ro n o u s m ot or13 P = 2 0 ; // No . o f p o l es14 hp = 40 ; // power r a t i n g o f t he s yn ch ro no u s motor

i n hp

15 V_L = 660 ; // L i n e v o l t a g e i n v o l t

16 beta = 0.5 ; / / A t n o−l o a d , t h e r o t o r i s r e t a rd e d0 . 5 m e ch a ni c al d e gr e e from17 / / i t s s yn ch ro no us p o s i t i o n .18 X_s = 10 ; // S yn ch ro no us r e a c t a n c e i n ohm19 R_a = 1.0 ; // E f f e c t i v e a rm at ur e r e s i s t a n c e i n ohm20

21 / / C a l c u l a t i o n s22 / / c as e a23 funcprot ( 0 ) ; // To a v o id t h i s m es sa ge ” Warning :

r e d e f i n i n g f u n c t i o n : b et a ”24 a lp ha = P * ( be ta / 2) ; // The r o t o r s h i f t from t h e

s yn ch ro no us p o s i t i o n i n25 // e l e c t r i c a l d eg re es .26

27 / / c as e b28 V_p = V_L / sqrt ( 3 ) ; // Phase v o l t a ge i n v o l t29 E_gp = V_p ; / / G en er at ed v o l t a g e / p h a se a t no−l o a d

i n v o l t ( g i ve n )30 E _r = ( V _p - E _g p * c os d ( a lp ha ) ) + % i *( E _ gp * s i nd ( a l ph a

31 // R e s u lt an t emf a c r o s s t he a rm at u re p er p ha se i n V

/ p h a s e32 E _ r_ m = abs ( E _ r ) ; // E r m=m ag ni tu de o f E r i n v o l t33 E _ r_ a = atan ( imag ( E _r ) / real ( E _ r ) ) * 1 8 0 / % p i ; / / E r a =

35 / / c as e c36 Z_s = R_a + %i *X_s ; / / S y nc h ro n ou s i mp ed an ce i n ohm37 Z _ s_ m = abs ( Z _ s ) ; / / Z s m=m ag ni tu d e o f Z s i n ohm38 Z _ s_ a = atan ( imag ( Z _s ) / real ( Z _ s ) ) * 1 8 0 / % p i ; / / Z s a =

p h a s e a ng le o f Z s i n d e g r e e s39

40 I _a = E _r / Z _s ; / / A rm at ur e c u r r e n t / p h a s e i n A/p h a s e

41 I _ a_ m = abs ( I _ a ) ; // I a m=m ag ni tu de o f I a i n A42 I _ a_ a = atan ( imag ( I _a ) / real ( I _ a ) ) * 1 8 0 / % p i ; / / I a a =

p h a s e a ng le o f I a i n d e g r e e s

44 / / c as e d45 t he ta = I _a _a ; // Ph ase a n g l e b et we en V p and I ai n d e gr e e s

46 P _ p = V _p * I _a _m * c os d ( th et a ); // Power p e r p h as edrawn by t h e m oto r f ro m t h e b us

47 P_t = 3* P_p ; // T o t a l p ow er drawn by t h e m ot or f ro mt h e b us

49 / / c sa e e50 P _ a = 3 * ( I _ a _ m ) ^ 2 * R _ a ; // A rm at ur e p ow er l o s s

a t no−l oa d i n W

51 P_d = ( P_t - P _a ) /7 46 ; // I n t e r n a l d ev el op edh o rs e po w er a t no−l o a d

55 printf ( ” \n a : a l p h a = %d d e g r e e s ( e l e c t r i c a ld e g r e e s ) \n” , a lp ha ) ;

57 printf ( ” \n b : E gp = %d V a l so , a s g i ve n ” , E _ g p ) ;

58 printf ( ” \n E r i n V/ p h a s e = ” ) ; disp ( E _ r ) ;

59 printf (” \n E r = %. 1 f

% . 1 f V/ p h a s e \n”, E _ r _ m ,

E _r _a ) ;

61 printf ( ” \n c : Z s i n ohm/ p ha se = ” ) ; disp ( Z _ s ) ;

62 printf ( ” \n Z s = %. 2 f <%. 1 f ohm/pha se \n” , Z _ s _ m ,

Z _s _a ) ;

63 printf ( ” \n I a i n A/ p h a s e = ” ) ; disp ( I _ a ) ;

64 printf ( ” \n I a = %. 2 f <% . 2 f A/ p h a s e \n ” , I _ a _ m ,

I _ a _ a ) ;

66 printf ( ” \n d : P p = %. 2 f W/ p h a s e ” , P_ p ) ;

67 printf ( ” \n P t = %. 2 f W ” , P _ t ) ;68 printf ( ” \n Note : S l i g h t v a r i a t i o n s i n power

v al u e s i s due t o s l i g h t v a r i a t i o n s ” ) ;

69 printf ( ” \n i n V p , I a and t h e t a v a l u e sfrom t ho s e o f t he t ex tb oo k \n” ) ;

71 printf ( ” \n e : P a = %. f W ” , P_ a ) ;72 printf ( ” \n P d = %d hp ” , P _ d ) ;

Scilab code Exa 8.2 calculate alpha Er Ia Pp Pt Power loss Pd

4 / / 2 nd e d i t i om5

7 / / E xa mp le 8−28

11 / / G iv en d a ta12 // 3− p h a s e Y−c o n n e c te d s y n c h ro n o u s m ot or

13 P = 2 0 ; // No . o f p o l es14 hp = 40 ; // power r a t i n g o f t he s yn ch ro no u s motor

i n hp15 V_L = 660 ; // L i n e v o l t a g e i n v o l t16 beta = 5 ; / / At no−l o a d , t h e r o t o r i s r e t a r d e d 0 . 5

m e ch a n ic a l d e g r e e f ro m17 / / i t s s yn ch ro no us p o s i t i o n .18 X_s = 10 ; // S yn ch ro no us r e a c t a n c e i n ohm19 R_a = 1.0 ; // E f f e c t i v e a rm at ur e r e s i s t a n c e i n ohm20

21 / / C a l c u l a t i o n s22 / / c as e a23 funcprot ( 0 ) ; // To a v o id t h i s m es sa ge ” Warning :

r e d e f i n i n g f u n c t i o n : b et a ”24 a lp ha = P * ( be ta / 2) ; // The r o t o r s h i f t from t h e

s yn ch ro no us p o s i t i o n i n

25 // e l e c t r i c a l d eg re es .26

27 / / c as e b28 V_p = V_L / sqrt ( 3 ) ; // Phase v o l t a ge i n v o l t29 E_gp = V_p ; / / G en er at ed v o l t a g e / p h a se a t no−l o a d

i n v o l t ( g i ve n )30 E _r = ( V _p - E _g p * c os d ( a lp ha ) ) + % i *( E _ gp * s i nd ( a l ph a

31 E _ r_ m = abs ( E _ r ) ; // E r m=m ag ni tu de o f E r i n v o l t32 E _ r_ a = atan ( imag ( E _r ) / real ( E _ r ) ) * 1 8 0 / % p i ; / / E r a =

p h a s e a ng le o f E r i n d e g r e e s

3334 / / c as e c35 Z_s = R_a + %i *X_s ; / / S y nc h ro n ou s i mp ed an ce i n ohm36 Z _ s_ m = abs ( Z _ s ) ; / / Z s m=m ag ni tu d e o f Z s i n ohm37 Z _ s_ a = atan ( imag ( Z _s ) / real ( Z _ s ) ) * 1 8 0 / % p i ; / / Z s a =

p h a s e a ng le o f Z s i n d e g r e e s38

39 I _a = E _r / Z _s ; / / A rm at ur e c u r r e n t / p h a s e i n A/p h a s e

40 I _ a_ m = abs ( I _ a ) ; // I a m=m ag ni tu de o f I a i n A41 I _ a_ a = atan ( imag ( I _a ) / real ( I _ a ) ) * 1 8 0 / % p i ;

/ / I a a =p h a s e a ng le o f I a i n d e g r e e s42

43 / / c as e d44 t he ta = I _a _a ; // Ph ase a n g l e b et we en V p and I a

i n d e gr e e s45 P _ p = V _p * I _a _m * c os d ( th et a ); // Power p e r p h as e

drawn by t h e m oto r f ro m t h e b us46 P_t = 3* P_p ; // T o t a l p ow er drawn by t h e m ot or f ro m

t h e b us47

48 / / c sa e e49 P _ a = 3 * ( I _ a _ m ) ^ 2 * R _ a ; // A rm at ur e p ow er l o s s

a t no−l oa d i n W50 P_d = ( P_t - P _a ) /7 46 ; // I n t e r n a l d ev el op ed

h o rs e po w er a t no−l o a d

54 printf ( ” \n a : a l p h a = %d d e g r e e s ( e l e c t r i c a ld e g r e e s ) \n” , a lp ha ) ;

56 printf ( ” \n b : E gp = %d V a l so , a s g i ve n ” , E _ g p ) ;

57 printf ( ” \n E r i n V/ p h a s e = ” ) ; disp ( E _ r ) ;

58 printf ( ” \n E r = %d <% . 1 f V/ p h a s e \n” , E _ r _ m ,

E _r _a ) ;

60 printf ( ” \n c : Z s i n ohm/ p ha se = ” ) ; disp ( Z _ s ) ;

61 printf ( ” \n Z s = %. 2 f <%. 1 f ohm/pha se \n” , Z _ s _ m ,Z _s _a ) ;

62 printf ( ” \n I a i n A/ p h a s e = ” ) ; disp ( I _ a ) ;

63 printf ( ” \n I a = %. 2 f <% . 2 f A/ p h a s e \n ” , I _ a _ m ,

I _ a _ a ) ;

65 printf ( ” \n d : P p = %. 2 f W/ p h a s e ” , P_ p ) ;

66 printf ( ” \n P t = %. 2 f W ” , P _ t ) ;

67 printf ( ” \n Note : S l i g h t v a r i a t i o n s i n powerv al u e s i s due t o s l i g h t v a r i a t i o n s ” ) ;

68 printf (” \n i n V p , I a and t h e t a v a l u e sfrom t ho s e o f t he t ex tb oo k \n” ) ;

71 printf ( ” \n e : P a = %. f W ” , P_ a ) ;

72 printf ( ” \n P d = %. 1 f hp ” , P _ d ) ;

Scilab code Exa 8.3 calculate Ia PF hp

33 I _ap1 = E _ra / Z_s ; / / A rm at ur e c u r r e n t / p h a s e i n A

/ p h a s e34 I _ a p1 _ m = abs ( I _ a p 1 ) ; / / I ap 1 m=m ag ni tu de o f I a p 1 i nA

35 I _ a p1 _ a = atan ( imag ( I _ ap 1 ) / real ( I _ a p 1 ) ) * 1 8 0 / % p i ; //I a p 1 a=p h a s e a n g l e o f I a p 1 i n d e g r e e s

37 c o s _ t h et a _ a = c o sd ( I _ a p 1 _ a ) ; // Power f a c t o r38 I a _m 1 = abs ( I _ a p 1 _ m ) ; // A b so u l te v a l u e o f m ag ni tu de

o f I a p 139

40 P _d 1 = 3 * ( E _g p_ a * Ia _m 1 ) * c os d (1 60 - I _a p1 _a ) ; //

// I n t e r n a l d ev el op ed power i n W41 // 160 + I a p 1 a i s t he a ng l e be tw e en E g p a and

I a p 142 P d1 = abs ( P _ d 1 ) ; // C on si de r a b s o lu t e v al ue o f power

i n W f o r c a l c u l a t i n g hp43

44 H or se _p ow er 1 = Pd 1 / 746 ; // H o rs e po w er d e v e l o p e dby t he a rm at ur e i n hp

46 / / c as e b47 E _r b = ( V _p - E _g p_ b * c os d ( al ph a )) + %i * ( E_ gp _b *

s i n d ( a l p h a ) ) ;

48 E _ r b_ m = abs ( E _ r b ) ; / / E r b m=m ag n it ud e o f E rb i nv o l t

49 E _ r b_ a = atan ( imag ( E _r b ) / real ( E _ r b ) ) * 1 8 0 / % p i ; //E rb a=p ha se a n gl e o f E rb i n d e gr e e s

51 I _ap2 = E _rb / Z_s ; / / A rm at ur e c u r r e n t / p h a s e i n A/ p h a s e

52 I _ a p2 _ m = abs ( I _ a p 2 ) ; / / I ap 2 m=m ag ni tu de o f I a p 2 i nA

55 c o s _ t h et a _ b = c o sd ( I _ a p 2 _ a ) ; // Power f a c t o r56 I a _m 2 = abs ( I _ a p 2 _ m ) ; // A b so u l te v a l u e o f m ag ni tu de

o f I a p 2

5758 P _d 2 = 3 * ( E _g p_ b * Ia _m 2 ) * c os d (1 60 - I _a p2 _a ) ; //

// I n t e r n a l d ev el op ed power i n W59 / / 1 60 + I a p 2 a i s t he a ng l e be tw e en E g p b and

I a p 260 P d2 = abs ( P _ d 2 ) ; // C on si de r a b s o lu t e v al ue o f power

i n W f o r c a l c u l a t i n g hp61

62 H or se _p ow er 2 = Pd 2 / 746 ; // H o rs e po w er d e v e l o p e dby t he a rm at ur e i n hp

64 / / c as e c65 E _r c = ( V _p - E _g p_ c * c os d ( al ph a )) + %i * ( E_ gp _c *

s i n d ( a l p h a ) ) ;

66 E _ r c_ m = abs ( E _ r c ) ; // E rc m=m ag ni tu de o f E r c i nv o l t

67 E _ r c_ a = atan ( imag ( E _r c ) / real ( E _ r c ) ) * 1 8 0 / % p i ; //E r c a=p h a se a ng l e o f E rc i n d e g r e e s

69 I _ap3 = E _rc / Z_s ; / / A rm at ur e c u r r e n t / p h a s e i n A/ p h a s e

70 I _ a p3 _ m = abs ( I _ a p 3 ) ;/ / I ap 3 m=m ag ni tu de o f I a p 3 i nA

73 c o s _ t h et a _ c = c o sd ( I _ a p 3 _ a ) ; // Power f a c t o r74 I a _m 3 = abs ( I _ a p 3 _ m ) ; // A b so u l te v a l u e o f m ag ni tu de

o f I a p 375

76 P _d 3 = 3 * ( E _g p_ c * Ia _m 3 ) * c os d (1 60 - I _a p3 _a ) ; //// I n t e r n a l d ev el op ed power i n W

77 / / 1 60 + I a p 3 a i s t h e a ng le be tw e en E g p c andI a p 3

78 P d3 = abs ( P _ d 3 ) ; // C on si de r a b s o lu t e v al ue o f poweri n W f o r c a l c u l a t i n g hp

80 H or se _p ow er 3 = Pd 3 / 746 ; // H o rs e po w er d e v e l o p e d

by t he a rm at ur e i n hp81

84 disp ( ” S l i g h t v a r i a t i o n s i n power v a l ue s a re b ec au seo f non−a p p ro x i ma t i on o f I a & c o s ( E gp , I a )v a l u es d ur in g p ower c a l c u l a t i o n s i n s c i l a b ” )

85 printf ( ” \n a : V p = %. f <0 V \n ” , V _ p ) ;

86 printf ( ” \n E r i n V = ” ) ; disp ( E _ r a ) ;

87 printf ( ” \n E r = %. 2 f <%. 2 f V \n ” , E _ r a _ m , E _ r a _ a

88 printf ( ” \n I a p i n A = ” ) ; disp ( I _ a p 1 ) ;89 printf ( ” \n I a p = %. 2 f <%. 2 f A \n” , I _a p1 _m ,

I _ ap 1 _a ) ;

90 printf ( ” \n c os ( t he ta ) = %. 4 f l a g g i n g \n ” ,

c o s _t h e t a_ a ) ;

91 printf ( ” \n P d = %d W drawn f ro m b us ( mo to ro p e r a t i o n ) \n” , P_d1 ) ;

92 printf ( ” \n H o r s ep o we r = %. 1 f hp \n\n” ,

H o r se _ p o we r 1 ) ;

94 printf (” \n b : E r i n V = ”

) ; disp ( E _ r b ) ;

95 printf ( ” \n E r = %. 2 f <%. 2 f V \n ” , E _ r b _ m , E _ r b _ a

96 printf ( ” \n I a p i n A = ” ) ; disp ( I _ a p 2 ) ;

97 printf ( ” \n I a p = %. 2 f <%. 2 f A \n” , I _a p2 _m ,

I _ ap 2 _a ) ;

98 printf ( ” \n c o s ( t h e t a ) = %. 4 f = %. f ( u n i t y PF ) \n” , c o s_ t he t a_ b , c o s _ th e t a _b ) ;

H o r se _ p o we r 2 ) ;101

102 printf ( ” \n c : E r i n V = ”) ; disp ( E _ r c ) ;

103 printf ( ” \n E r = %. 2 f <%. 2 f V \n ” , E _ r c _ m , E _ r c _ a

104 printf ( ” \n I a p i n A = ” ) ; disp ( I _ a p 3 ) ;

105 printf ( ” \n I a p = %. 2 f <

%. 2 f A \n” , I _a p3 _m ,I _ ap 3 _a ) ;

106 printf ( ” \n c os ( t he ta ) = %. 4 f l e ad i n g \n ” ,

c o s _t h e t a_ c ) ;

H o r se _ p o we r 3 ) ;

Scilab code Exa 8.4 calculate IL Iap Zp IaZp theta deba Egp

7 / / E xa mp le 8−4

c o n s o l e .10

11 / / G iv en d a ta12 // Y−c o n n e c t e d s y n c h r o n o u s dynamo13 P = 2 ; // No . o f p o l e s14 h p = 1000 ; // power r a t i n g o f t he s yn ch ro no u s motor

i n hp15 V _L = 6000 ; // L i ne v o l t a ge i n v o l t

16 f = 6 0 ; // F re qu en cy i n Hz17 R _a = 0.52 ; // E f f e c t i v e a rm at u re r e s i s t a n c e i n ohm18 X_s = 4.2 ; // S yn ch ro n ou s r e a c t a n c e i n ohm19 P_t = 811 ; // I n p ut p ow er i n kW20 P F = 0.8 ; // Power f a c t o r l e a d i ng

22 / / C a l c u l a t i o n s23 V_p = V_L / sqrt ( 3 ) ; // Phase v o l t a ge i n v o l t24

25 / / c as e a26 c o s_ th et a = P F ; // Power f a c t o r l e a d i n g27 I_L = ( P_t * 10 00 ) / ( sqrt ( 3) * V _L * c os _t he ta ) ; //

L in e a rm at ur e c u r r e n t i n A28 I_ap = I_L ; // Pha se a rm at ur e c u r r e n t i n A29

30 / / c as e b31 Z_p = R_a + %i * X_s ; // I mp ed an ce p e r p h as e i n ohm

32 Z _ p_ m = abs ( Z _ p ) ; / / Z p m=m ag n it ud e o f Z p i n ohm33 Z _ p_ a = atan ( imag ( Z _p ) / real ( Z _ p ) ) * 1 8 0 / % p i ; / / Z p a =

p h a se a n g l e o f Z p i n d e gr e e s34

35 / / c as e c36 Ia_Zp = I_L * Z_p_m ;

37 E_r = Ia_Zp ;

39 / / c as e d40 t he ta = a co sd ( 0 . 8) ; // Power f a c t o r a n gl e i n d e g re e s41

42 / / c as e e43 funcprot ( 0 ) ; // U se t o a vo i d t h i s m es sa ge ” W arning

: r e d e f i n i n g f u n c t i o n : b e t a ” .44 be ta = Z _p_ a ; //45 de ba = be ta + th et a // D i f f e r e n c e a ng le a t 0 . 8

l e a d i ng PF i n d e g re e s46

47 / / c as e f 48 / / G en er a te d v o l t a g e / p ha se i n v o l t49 E _ g p_ f = sqrt ( ( E _r ) ^2 + ( V _p ) ^2 - 2* E _r * V _p * c os d (

d eb a ) ) ;50

51 / / c as e g52 / / G en er a te d v o l t a g e / p ha se i n v o l t53 E_g p_g = ( V_p + Ia_Zp * cosd (180 - deba ) ) + %i * (

I a_ Zp * s in d ( 18 0 - d e ba ) ) ;

54 E _ g p _g _ m = abs ( E _ g p _ g ) ; / / E g p g m=m a g ni t ud e o f E g p g i n v o l t55 E _ g p _g _ a = atan ( imag ( E _ gp _g ) / real ( E _ g p _ g ) ) * 1 8 0 / % p i ;

// E g p g a=p ha se a n gl e o f E gp g i n d e g re e s56

57 / / c as e h58 Ia Zp = I a_Z p * expm ( %i * Z _p _a * ( %pi / 18 0) ) ; //

v o l t a ge g e n er at ed by a l t e r n a t o r 1 i n v o l t59 I a Z p_ m = abs ( I a Z p ) ; / / Ia Zp m=m ag n it ud e o f I aZ p i n A60 I a Z p_ a = atan ( imag ( I aZ p ) / real ( I a Z p ) ) * 1 8 0 / % p i ; //

I a Zp a=p ha se a n g l e o f Ia Zp i n d e g r e es

61 I a R a = I a Zp _ m * c o sd ( I a Z p _ a ) ; // R e a l p ar t o f IaZp62 I a X s = I a Zp _ m * s i nd ( I a Z p _ a ) ; // I ma gi ne ry p ar t o f

IaZp63

64 c o s_ th et a = P F ; //65 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;

66 / / G en er a te d v o l t a g e / p ha se i n v o l t67 E_g p_h = ( V_p * c os _t he ta - IaRa ) + %i * ( V_p *

s i n_ t he t a + I aX s ) ;

68 E _ g p _h _ m = abs ( E _ g p _ h ) ; / / E g p h m=m a g ni t ud e o f

E gp h i n v o l t69 E _ g p _h _ a = atan ( imag ( E _ gp _h ) / real ( E _ g p _ h ) ) * 1 8 0 / % p i ;

// E g p h a=p ha se a n gl e o f E gp h i n d e g re e s70

73 printf ( ” \n a : I L = %. 2 f \n I a p = %. 2 f A \n” ,

I_L , I _a p ) ;

75 printf ( ” \n b : Z p i n ohm = ” ) ; disp ( Z _ p ) ;

76 printf ( ” \n Z p = %. 3 f <%.2 f ohm \n ” , Z_p_m ,

Z _p _a ) ;77

78 printf ( ” \n c : I aZ p = %. 1 f V \n E r = %. 1 f V \n ”, Ia _Z p , E_r ) ;

80 printf ( ” \n d : Power f a c t o r a ng le , \ n t h e t a = %. 2 f

d e g re e s l e a d i ng \n ” , t he ta ) ;81

82 printf ( ” \n e : D i f f e r e n c e a ng le , \ n deba = %. 2 f d e g r e e s \n ” , deba ) ;

84 printf ( ” \n f : E gp = %. f V \n ” , E _g p_ f ) ;

86 printf ( ” \n g : E gp i n V = ”) ; disp ( E _ gp _g ) ;

87 printf ( ” \n E gp = %d <%. 2 f V \n” , E _ gp _g _ m ,

E _ gp _ g_ a ) ;

89 printf ( ” \n h : E gp i n V = ” ) ; disp ( E _ g p _ h ) ;90 printf ( ” \n E gp = %. f <%. 2 f V” ,E_g p_h_m ,

E _ gp _ h_ a ) ;

Scilab code Exa 8.5 calculate torque angle

7 / / E xa mp le 8−58

11 / / G iv en d a ta12 // Y−c o n n e c t e d s y n c h r o n o u s dynamo13 P = 2 ; // No . o f p o l e s14 h p = 1000 ; // power r a t i n g o f t he s yn ch ro no u s motor

i n hp

15 V _L = 6000 ; // L i ne v o l t a ge i n v o l t

16 f = 6 0 ; // F re qu en cy i n Hz17 R _a = 0.52 ; // E f f e c t i v e a rm at u re r e s i s t a n c e i n ohm18 X_s = 4.2 ; // S yn ch ro n ou s r e a c t a n c e i n ohm19 P_t = 811 ; // I n p ut p ow er i n kW20 P F = 0.8 ; // Power f a c t o r l e a d i ng21

22 / / C a lc u la t ed v a l ue s23 E _gp = 36 87 ; / / G en er at ed v o l t a g e / p ha se i n v o l t24 V_p = V_L / sqrt ( 3 ) ; // Phase v o l t a ge i n v o l t25 E_r = 412.8 ; // R e s u l t a n t EMF a c r o s s a r ma t ur e / p h a s e

i n v o l t

26 de ba = 1 19 .8 1 ; // D i f f e r e n c e a ng l e a t 0 . 8 l e a d i n gPF i n d e g r e es

27 t he ta = 3 6. 87 ; // Power f a c t o r a n gl e i n d e g re e s28 Ia Xs = 4 09. 7 ; // V o lt ag e d ro p a c r o s s s yn ch ro no u s

r e a c t a nc e i n v o l t29 Ia Ra = 5 0.7 4 ; // V o lt ag e d ro p a c r o s s a rm at ur e

r e s i s t a n c e i n v o l t30

31 / / C a l c u l a t i o n s32

33 // Torque a n gl e a lp ha i n d e gr e e s c a l c u l a t e d byd i f f e r e n t Eqns

34 / / c as e a35 alp ha1 = acosd ( ( E_gp ^2 + V_p ^2 - E_r ^2 ) / ( 2*

E _g p * V_ p ) ) ; // Eq . 8 −1236

37 / / c as e b38 alp ha2 = asind ( ( E_r * sind ( deba ) ) / ( E_gp ) ) ;

// Eq . 8 −1339

40 / / c as e c

41 a lp ha 3 = t he ta - a ta nd ( ( V_ p * si nd ( t he ta ) + I aX s ) / (V _p * c o sd ( t h et a ) - I aR a ) ) ; / / Eq . 8−14

45 printf ( ” \n a : U si ng Eq . (8 − 1 2 ) \n a l p h a = %. 2 f

d e g r e e s \n ” , a lp ha 1 ) ;46

47 printf ( ” \n b : U s in g Eq . ( 8 − 1 3 ) \n a l p h a = %. 2 f d e g r e e s \n ” , a lp ha 2 ) ;

49 printf ( ” \n c : U si ng Eq . (8 − 1 4 ) \n a l p h a = %. 2 f d e g r e e s \n ” , a lp ha 3 ) ;

50 printf ( ” \n S l i g h t v a r i a t i o n i n c a s e c a l p h a i sdue t o t a n i n v e r s e v al ue ” ) ;

51 printf ( ” \n whi ch was c a l u l a t e d t o be 42 .4 45 60 4d e g r ee s , i n s t e a d o f 4 2 . 4 4 d e g r e e s ( t e xt b o ok ) . ” )

Scilab code Exa 8.6 calculate Pp Pt hp internal and external torque andmotor efficiency

56 // Ch apt e r 8 : AC DYNAMO TORQUE RELATIONS −

SYNCHRONOUS MOTORS7 / / E xa mp le 8−68

11 / / G ive n d at a a s p e r Example 8−412 // Y−c o n n e c t e d s y n c h r o n o u s dynamo

13 P = 2 ; // No . o f p o l e s14 h p = 1000 ; // power r a t i n g o f t he s yn ch ro no u s motori n hp

15 V _L = 6000 ; // L i ne v o l t a ge i n v o l t16 f = 6 0 ; // F re qu en cy i n Hz

17 R _a = 0.52 ; // E f f e c t i v e a rm at u re r e s i s t a n c e i n ohm

18 X_s = 4.2 ; // S yn ch ro n ou s r e a c t a n c e i n ohm19 P_t = 811 ; // I n p ut p ow er i n kW20 P F = 0.8 ; // Power f a c t o r l e a d i ng21

22 / / C a l c u l a t e d v a l u e s f ro m E xample 8−423 E _gp = 36 87 ; / / G en er at ed v o l t a g e / p ha se i n v o l t24

25 I_a = 97.55 ; // Phas e a rm at ur e c u r r e nt i n A26

27 p hi = ( 42 .4 5 - 0) ; // P ha se a n g l e b et we en E g p andI a i n d eg r e es

28 / / where 4 2 .4 5 and 0 a r e p ha se a n g l es o f E gp andI a i n d e g r e e s r e s p e c t i v e l y .

30 / / C a l c u l a t i o n s31 / / c as e a32 P_p = E _g p * I _a * c osd ( phi ) / 1 00 0; / / M e c ha n i c al

p ower d e v el o p e d p er p ha s e i n kW33

34 P_t_a = 3 * P_p ; // T o ta l m e ch a n ic a l po werd e v e l o p e d i n kW

36 / / c as e b37 P _t _b = P _t _a / 0 .7 46 ; // I n t e r n a l power d e ve l op e d

i n hp a t r at ed l oa d38

39 / / c as e c40 S = 120 * f / P ; // Sp eed o f t he motor i n rpm41 T_int = ( P_t_b * 5252 ) / S ; // I n t e r n a l t or qu e

d e ve l op e d i n l b− f t42

43 / / c as e d

44 T_ext = ( hp * 5252 ) / 3600 ; // E x te r na l t o rq u ed e ve l op e d i n l b− f t

45 eta = ( T_ext / T_int ) * 100 ; // Motor e f f i c i e n c y i np e r c e n t

12 P _o = 2000 ; // T ot al power consumed by a f a c t o r y i n

kW fr om t h e t r a n s f o r m e r13 c os _t he ta = 0 .6 ; // 0 . 6 l a g g i n g power f a c t o r a tw hi c h p ow er i s c on su me d −

14 // − fro m t he t r a n s f or m e r15 s i n _ th e t a = sqrt ( 1 - ( c o s _t h et a ) ^ 2) ;

16 t he ta = - a co sd ( 0 . 6) ; // power f a c t o r a n gl e a t whichp ow er i s c on su me d −

17 // − f rom t he t r an s f or m e r i n d e gr e e s18

19 V _L = 6000 ; // Pr imary l i n e v o l t a ge o f at r an s f o r me r i n v o l t

2021 P = 750 ; // kW e xp ec te d t o be d e l i v e r e d by t he dc

motor−g e n e r a t o r22

23 h p = 1000 ; / / hp r a t i n g o f t he motor ( i n d u c t i o n o rs y n c h r o n o u s )

24 V _L _m = 60 00 ; / / L in e v o l t a g e o f a s yn ch ro n ou s ( o ri n d u c t i on ) motor i n v o l t

25 c os _t he ta _s m = 0 .8 ; // 0 . 8 l e ad i n g power f a c t o r o f t h e s y n c h ro n o u s m ot or

26 t h et a_ s m = a co sd ( 0 . 8) ; // power f a c t o r a ng l e o f t h es y nc h ro n o us m ot or i n d e g r e e s

28 c os _t he ta _i m = 0 .8 ; // 0 . 8 l a g g i n g power f a c t o r o f t he i n d u c t i o n motor

29 t h et a_ i m = - a co sd ( 0 . 8) ; // power f a c t o r a ng l e o f t h ei n d u c t i o n motor i n d e g r e es

31 e ta = 0.92 ; // E f f i c i e n c y o f e a ch motor32

34 // c a s e a : u s i ng I n d u ct i o n Motor ( IM )35 P_m = ( hp * 746 ) / eta ; / / I n d u c t i o n ( o r

s y nc h ro n o us ) m oto r l o a d i n W36 I_1 = P_m / ( sqrt ( 3) * V _L _m * c os _t he ta _i m ) ; //

L ag g in g c u r r e n t drawn by IM i n A

38 I _1 _p ri me = P_o * 1 00 0 / ( sqrt ( 3) * V _L * c os _t he ta) ; // O r i g i n al l a g g i n g −39 // − f a c t o r y l oa d c u r r e n t i n A40

41 / / T ot al l oa d c u r r e nt i n A u si n g I n du c ti o n Motor :42 I _T M = I _1 * ( c os d ( t he t a_ i m ) + % i * si nd ( t h e ta _ im ) ) +

I _ 1 _p r i me * ( c o s d ( t h e ta ) + % i * s i nd ( t h e t a ) ) ;

43 I _ T M_ m = abs ( I _ T M ) ; / /I TM m = m ag ni tu d e o f I TM i n A44 I _ T M_ a = atan ( imag ( I _T M ) / real ( I _ T M ) ) * 1 8 0 / % p i ; //

I TM a=p ha se a n g l e o f I TM i n d e g r e es45

46 P F_ im = c os d ( I _T M_ a ) ; // O v e ra l l PF u s i n g i n d u c t i o nmotor

48 // c a s e b : u s i ng s yn ch ro n ou s motor49 I_s1 = P_m / ( sqrt ( 3) * V _L _m * c os _t he ta _s m ) ; //

L ag g in g c u r r e n t drawn by IM i n A50

51 / / T ot al l oa d c u r r e nt i n A u s i n g s yn ch ro no us motor :52 I _T SM = I _s 1 * ( co sd ( t h e ta _ sm ) + % i * si nd ( t h e ta _ sm ) ) +

I _ 1 _p r i me * ( c o s d ( t h e ta ) + % i * s i nd ( t h e t a ) ) ;

53 I _ T SM _ m = abs ( I _ T S M ) ;/ / I TSM m = m a g ni t ud e o f I TSMi n A

54 I _ T SM _ a = atan ( imag ( I _ TS M ) / real ( I _ T S M ) ) * 1 8 0 / % p i ; //I TSM a=p ha se a n g l e o f I TSM i n d e g r e e s

56 P F_ sm = c os d ( I _T S M_ a ) ; // O v e ra l l PF u s i ngS y n c hr o n o u s m ot or

58 / / c as e c59 p er ce nt _I _L = ( I _T M_ m - I _T SM _m ) / I _T M_ m * 100 ;

// P er ce nt r e du c t io n i n −

60 // − t o t a l l oa d c u rr e n t i n p e r c e nt61

62 // D is pl ay t h e r e s u l t s63 printf ( ” Note : c a se a , I 1 c a l c u l a t e d i s ar ound 9 7 .5 3

A i n s t e a d o f 4 7 . 5 3 A( t e x tb o o k ) . \ n” )

64 printf ( ” Note : c a se b , A ct ua l I s 1 i ma gi na ry p ar t i s

around 5 8. 5 2 i n s t e ad o f ” ) ;65 printf ( ” \n 5 2 . 5 2 ( t e x t b o o k ) s o s l i g h tv a r i a t i o n i n I TSM and p e rc e n t ” )

66 printf ( ” \n r e d u c t i o n i n t o t a l l o a d c u r r e n t . \n” )

68 disp ( ”E x ampl e 8−7 S o l u t i on : ” ) ;

69 printf ( ” \n a : I n d u c t i o n ( o r s u nc h ro n ou s ) mo to r l o a d ”) ;

70 printf ( ” \n P m = %. f W ” , P _ m ) ;

71 printf ( ” \n L a g gi ng c u r r e n t drawn by t he IM = I 1 ”

) ;72 printf ( ” \n I 1 = %. 2 f <−%. 2 f A \n” , I _ 1 , a c o s d (

c o s _ t h e t a _ s m ) ) ;

73 printf ( ” \n I 1 i n A = ” ) ; disp ( I _ 1 * c o s d ( - 3 6 . 8 7 ) +

% i * I _ 1 * s i n d ( - 3 6 . 8 7 ) ) ;

74 printf ( ” \n O r i g i n al l a g g i ng f a c t o r y l o a d c u r r e n t= I 1 p r i me ” ) ;

75 printf ( ” \n I 1 p r i m e i n A = ” ) ; disp ( I _ 1 _ p r i m e *

c o s d ( t h e t a ) + % i * I _ 1 _ p r i m e * s i n d ( t h e t a ) ) ;

76 printf ( ” \n I 1 p r i m e = %. 1 f <−%. 2 f A \n” ,

I _ 1 _ pr i m e , a c o s d ( c o s _ t h e t a ) ) ;

77 printf ( ” \n T o t a l l o a d c ur re nt = motor l oa d +f a c t o r y l oa d ”) ;

78 printf ( ” \n I TM = I 1 + I 1 p r i m e \n” ) ;

79 printf ( ” \n I TM i n A = ” ) ; disp ( I _ T M ) ;

80 printf ( ” \n I TM = %. 1 f <%. 1 f A \n ” , I _ TM _m ,

I _T M_ a ) ;

81 printf ( ” \n O ve ra l l sy s t e m PF = %. 4 f l a g g i n g \n ”, PF _i m ) ;

83 printf ( ” \n b : S y nc h ro n o us m ot or l o a d \n I s 1 = %

. 2 f <%. 2 f A\n” , I _ 1 , a c o s d ( c o s _ t h e t a _ s m ) ) ;84 printf ( ” \n I s 1 i n A = ” ) ; disp ( I _ s 1 * c o s d ( 3 6 . 8 7 ) +

% i * I _ s 1 * s i n d ( 3 6 . 8 7 ) ) ;

85 printf ( ” \n T o t a l l o a d c u rr e n t : I TSM = I s 1 +I 1 p r i m e \n” ) ;

86 printf ( ” \n I TSM i n A = ” ) ; disp ( I _ T S M ) ;

87 printf ( ” \n I TSM = %. 1 f <

%. 1 f A \n ” , I _T S M_ m ,I _ TS M _a ) ;

88 printf ( ” \n O ve ra l l sy s t e m PF = %. 1 f l a g g i n g \n ”, PF _s m ) ;

90 printf ( ” \n c : P er ce nt r e d u ct i o n i n t o t a l l oa dc u r r e n t = %. 1 f p e r c e n t \n” , p e r c e n t _ I _ L ) ;

92 printf ( ” \n d : PF i mp ro ve me nt : U s in g t h e s y n c h ro n o u smotor ( i n l i e u o f t he IM ) ” ) ;

93 printf ( ” \n r a i s e s t h e t o t a l s y s t e m PF from %. 4 f

l a g g i n g t o %. 1 f l a g g i n g . ” , P F _ i m , P F _ s m ) ;

Scilab code Exa 8.8 calculate Tp and hp

11 / / G iv en d a ta f ro m Ex .8 −3 a12 // 3− p h a s e Y−c o n n e c te d s y n c h ro n o u s m ot or

13 P = 6 ; // No . o f p o l e s14 hp = 50 ; // power r a t i n g o f t he s yn ch ro no u s motori n hp

15 V_L = 440 ; // L i n e v o l t a g e i n v o l t16 X_s = 2.4 ; // S yn ch ro n ou s r e a c t a n c e i n ohm

17 R_a = 0.1 ; // E f f e c t i v e a rm at ur e r e s i s t a n c e i n ohm

18 alpha = 20 ; // The r o t o r s h i f t from t he s yn ch ro no usp o s i t i o n i n19 // e l e c t r i c a l d eg re es .20 E_gp = 240 ; // G en er at ed v o l t a g e / p h a se i n v o l t when

t h e m o to r i s u nd er −e x c i t e d21 f = 6 0 ; // F re qu en cy i n Hz22

23 / / C a l c u l a t e d v a l u e s f ro m E xample 8−3a24 V_p = 254 ; // Phase v o l t a g e i n v o l t25

27 / / c as e a28 / / To rq ue d e v el o p ed p e r p ha s e U si ng Eq .( 8 −1 7 a )29 S = 120 * f / P ; // Sp eed o f t he motor i n rpm30 T_p = ( 7.04 * E_gp * V_p ) / ( S *X_s ) * sind ( alpha )

32 / / c as e b33 / / T ot al h or se po we r d e ve l op e d u s i ng p a rt a34 H o rs e po w er = ( 3 * T_ p * S ) / 52 52 ;

38 printf ( ” \n From g i v en and c a l c u l a t e d d at a o f Ex.8 −3a , \ n” ) ;

39 printf ( ” \n a : T p = %. 2 f l b−f t \n ” , T _ p ) ;

41 printf ( ” \n b : H o rs ep o we r = %. 1 f hp ” , H or se po we r ) ;

Scilab code Exa 8.9 calculate original kvar and kvar correction and kVAand Io and If and power triangle

4 / / 2 nd e d i t i om5

7 / / E xa mp le 8−98

11 / / G iv en d a ta12 P _o = 2000 ; // T ot al power consumed by a f a c t o r y i n

kW13 c os _t he ta = 0 .6 ; // 0 . 6 power f a c t o r a t w hi ch

p ow er i s c on su me d14 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;

15 V = 6000 ; // L i ne v o l t a ge i n v o l t16 / / S y n c h r o no u s c a p ac i t o r i s us e d t o r a i s e t he

o v e r a l l PF t o u ni t y17 P _l os s_ ca p = 2 75 ; // S yn ch ro no us c a p a c i t o r l o s s e s

in kW18

21 S _o _c on ju ga te = P _o / c os _t he ta ; // a p p a r en tc o mp l ex p ow er i n kW

22 j Q_ o = S _o _c on ju ga te * s in _t he ta ; // O r i g i na lk i l o v a r s o f l a g g i n g l oa d

24 / / c as e b25 jQ _c = - jQ_ o ; // K i lo v ar s o f c o r r e c t i o n ne e d e d t o

b r i ng t he PF t o u n it y26

27 / / c as e c28 R = P _l os s_ ca p ; // S yn ch ro no us c a p a c i t o r l o s s e s i n

kW29 S _c _c on ju ga te = R - %i * ( abs ( j Q _ c ) ) ; / / kVA r a t i n g

o f t he s yn ch ro no us c a p a c i t o r

30 S _ c _ c o n j ug a t e _ m = abs ( S _ c _ c o n j u g a t e ) ; //

S c c o nj u ga t e m = m agn itu de o f S c c o n j u ga t e i nkVA31 S _ c _ c o n j ug a t e _ a = atan ( imag ( S _ c _ c o nj u g a te ) / real (

S _ c _ c o n j u g a t e ) ) * 1 8 0 / % p i ;

32 // S c c o n j u g a t e a =p ha se a n gl e o f S c c o n j u g a t e i nd e g r e e s

33 P F = c o sd ( S _ c _ co n j u ga t e _ a ) ; // Power f a c t o r o f t hes y nc h ro n o us c a p a c i t o r

35 / / c as e d36 I_o = S _o _c on ju ga te * 1 000 / V ; // O r i g i na l c u r r e nt

drawn f ro m t h e m ai ns i n A37

39 / / c as e e40 P_f = P_o + P _l os s_ ca p ; // T o t a l p ow er i n kW41 S_f = P_f ; // T o ta l a p pa r en t p ower i n kW42 S _ f_ m = abs ( S _ f ) ; // S f m = magni t ude o f S f i n A43 S _ f_ a = atan ( imag ( S _f ) / real ( S _ f ) ) * 1 8 0 / % p i ; / / S f a =

p h a s e a ng le o f S f i n d e g r e es44

45 I_f = S_f * 1000 / V ; // F i n al c u r r e nt drawn fro mt h e mai ns a f t e r c o r r e c t i o n i n A

49 printf ( ” \n a : S∗ o = %d kVA \n” , S _ o_ c on j ug a te ) ;

50 printf ( ” \n +jQo i n k v a r = ” ) ; disp ( % i * j Q _ o ) ;

52 printf ( ” \n b : − jQc i n k v a r = ” ) ; disp ( % i * j Q _ c ) ;

54 printf ( ” \n c : S∗ c i n kVA = ”) ; disp ( S _ c _ c o n j u g a t e ) ;

55 printf ( ” \n S∗ c = %. f <%.1 f kVA \n” ,S _ c _ co n j u ga t e _ m , S _ c _ co n j u ga t e _ a ) ;

56 printf ( ” \n PF = %. 3 f l ea di ng \n” , PF ) ;

58 printf ( ” \n d : I o = %. 1 f A \n ” , I_ o ) ;

60 printf ( ” \n e : S f i n A = ”) ; disp ( S _ f ) ;61 printf ( ” \n S f = %d <%d kVA \n” , S _f _m , S_ f_ a

62 printf ( ” \n I f = %. 1 f A \n ” , I _f ) ;

64 printf ( ” \n f : S ee F ig . 8 − 2 5 . ” ) ;

Scilab code Exa 8.10 calculate cost of raising PF to unity and point85

lagging

7 / / E xa mp le 8−108

11 / / G iv en d a ta12 k VA = 1 00 00 ; // kVA r a t i n g o f a s ys te m13 c os _t he ta = 0 .6 5 ; // power f a c t o r o f t he s ys te m14 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;

15 c os _t he ta _b = 0 .8 5 ; / / R a i s ed PF16 s i n _ t h et a _ b = sqrt ( 1 - ( c os _t he ta _b ) ^ 2 ) ;

17 cost = 60 ; // c o st o f t h e s yn ch ro no us c a p a c i t o r t o

i m pr o ve t h e PF i n d o l l a r s /kVA18 // n e g l e c t t h e l o s s e s i n t he s yn ch ro no us c a p a c i t o r19

20 / / C a l c u l a t i o n s21 / / c as e a : For u ni ty PF

22 // a t t h e o r i g i n a l l oa d

23 kW _a = kVA * c os _t he ta ; //24 t he ta = a co sd ( c o s _t h et a ) ; // Power f a c t o r a n gl e o f t he s ys te m i n d e g re e s

25 kv ar = kVA * si nd ( th et a) ; // R e ac t iv e power i n k va r26 k VA _a = kv ar ;

27 c os t_ ca p_ a = kv ar * co st ; // C ost o f r a i s i n g t h e PFt o u ni ty PF i n d o l l a r s

29 / / c as e b30 t h et a _b = a co sd ( c o s _t h et a _b ) ; // Power f a c t o r a n g le

o f t he s ys te m i n d e gr e e s

31 k VA _b = k W_ a / c os _t he ta _b ; / / kVA v a l u e r e d u c t i o n32 k va r_ b = k VA _b * s in d ( th et a_ b ) ; // f i n a l k v a r v al ue

r e d u c e d33 k va r_ ad d = k va r - k va r_ b ; // k v a r o f c o r r e c t i o n

added34

35 c os t_ ca p_ b = k va r_ ad d * c os t ; // Cost o f r a i s i n gt h e PF t o 0 . 8 5 PF i n d o l l a r s

37 // D is pl ay t h e r e s u l t s38

39 disp ( ”E x ampl e 8−10 S o l u t i o n : ” ) ;

40 printf ( ” \n Note : S l i g h t v a r i a t i o n s i n t h e kv a rand c o s t v a l ue s a re d ue t o ” ) ;

41 printf ( ” \n non−a p pr o xi ma ti o n o f t h e ta v a l u e sw hi le c a l c u l a t i n g i n s c i l a b . \ n” ) ;

42 printf ( ” \n a : At t h e o r i g i n a l l o a d , \ n” ) ;

43 printf ( ” \n kW = %d kW a t t he t a = %. 1 f d e gr e e s \n” , kW_a , theta ) ;

44 printf ( ” \n k v a r = %. 3 f k v a r \n\n For u n i t y PF ,” , k v a r ) ;

45 printf ( ” \n kVA o f s yn ch ro no us c a p a c i t o r = %. 3 f kVA ( n e g l e c t i n g l o s s e s ) \n” , k V A _ a ) ;

46 printf ( ” \n C ost o f s y n c h r o n o us c a p a c i t or = $% . f \n\n” , c o s t _ ca p _ a ) ;

48 printf ( ” \n b : F or %. 2 f , PF = c o s (%. 1 f ) , t h e t o t a l

power , ” , c o s _ t h e ta _ b , t h e t a _ b ) ;49 printf ( ” \n %. f kW, r em ai ns t he same . T h er ef or e , \ n” , k W _ a ) ;

50 printf ( ” \n kVA o f f i n a l sy s t e m r e d u c e d t o = %. f kVA \n” , k V A _ b ) ;

51 printf ( ” \n k v a r o f f i n a l s y s t e m r e d u c e d t o = %. f k v a r \n T h e r e f o r e , ” , k v a r _ b ) ;

53 printf ( ” \n k v a r o f c o r r e c t i o n added = %. 3 f k v a r \n ” , k v a r _ a d d ) ;

54 printf ( ” \n kVA o f s yn ch ro no us c a p a c i t o r = %. 3 f

kVA ( n e g l e c t i n g l o s s e s ) \n” , k v a r _ a d d ) ;55 printf ( ” \n C ost o f s yn ch ro no us c a p ac i t or = $% . f ”

, c o s t _ ca p _ b ) ;

56 printf ( ” \n o r l e s s t han h a l f t h e c o s t i n p ar t ( a )” ) ;

Scilab code Exa 8.11 calculate Po jQo and power triangle

7 / / E xa mp le 8−118

c o n s o l e .10

11 / / G iv en d a ta12 S _c on ju ga te = 1 00 0 ; / / A pp ar en t c om pl ex p ow er i n

13 c os _t he ta = 0 .6 ; // l a g g i n g PF

14 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;15

16 / / C a l c u l a t i o n s17 / / c as e a18 P _o = S _c on ju ga te * c os _t he ta ; // A c t iv e p ower

d i s s i p a t e d by t he l oa d i n kW19

20 / / c as e b21 j Q_ o = S _c on ju ga te * s in _t he ta ; // I n d u c t i v e

r e a c t i v e q u ad r at u re power −22 // − drawn f ro m and r e t u r n e d t o t h e s u p pl y

27 printf ( ” \n a : A c t iv e p ower \n P o = %d kW \n ” ,

P _o ) ;

29 printf ( ” \n b : I n d uc t i v e r e a c t i v e q ua dr at ur e power \n +j Q o i n kv a r = \n” ) ; disp ( % i * j Q _ o ) ;

31 printf (” \n c : The o r i g i n a l power t r i a n g l e i s showni n F ig . 8 −26 a . ” ) ;

Scilab code Exa 8.12 calculate Pf jQf Pa jQa kVA and draw power tabu-lation grid

7 / / E xa mp le 8−12

c o n s o l e .10

11 / / G iv en d a ta12 S _c on ju ga te = 1 00 0 ; / / A pp ar en t c om pl ex p ow er i n

kVA13 c os _t he ta _f = 0 .8 ; // l a g g i n g PF14 s i n _ t h et a _ f = sqrt ( 1 - ( c os _t he ta _f ) ^ 2 ) ;

16 / / C a l c ul a t e d v a l u e s fro m Ex.8 −11

17 P_o = 600 ; // A ct iv e power d i s s i p a t e d by t he l oa din kW

18 Q_o = 800 ; // I n d u c t i ve r e a c t i v e q u ad r at u re power −19 // − drawn f ro m and r e t u r n e d t o t h e s u p pl y20

21 // C a l cu l a t i o n s :22

23 / / c as e a24 P _f = S _c on ju ga te * c os _t he ta _f ; // A c t i v e p ow er

26 / / c as e b27 Q _f = S _c on ju ga te * s in _t he ta _f ; // R e a c ti v e

q u a d r a t u r e p ow er d ra wn f ro m −28 // − and r e t ur n e d t o t he s u pp ly29

30 / / c as e c31 P_a = P_f - P_o ; // A d d i ti o n a l a c t i v e power i n kW

t h at may b e s u p p l i e d t o −32 // − new c u s t o m e r s33

34 / / c as e d35 jQ_a = %i * ( Q_f ) - %i * ( Q_o ) ; // C o r r e ct i o n

k v a r r e q u i r e d t o r a i s e PF −36 // −fr om 0 . 6 t o o . 8 l a g g i n g37

38 / / c as e e

39 S _c _c on ju ga te = 0 - jQ _a ; // R a ti ng o f c o r r e c t i o nc a p a c i t o r s n e e d ed f o r c as e d40

44 printf ( ” \n a : P f = %d kW \n ” , P _ f ) ;

45 printf ( ” \n b : +j Q f i n k v a r = ” ) ; disp ( % i * Q _ f ) ;

46 printf ( ” \n c : P a = %d kW \n ” , P _ a ) ;

47 printf ( ” \n d : j Q a i n k v a r = ” ) ; disp ( j Q _ a )

48 printf ( ” \n e : S c c o n j u g a t e = %d kVA \n ” , abs (

S _ c _ co n j u ga t e ) ) ;49 printf ( ” \n f : The power t a b u l at i o n g r i d i s shown i n

F i g . 8 −26 b . ” ) ;

Scilab code Exa 8.13 calculate Pf jQf Pa jQa kVA and power tabulationgrid

7 / / E xa mp le 8−138

1011 / / Ex . 8 −12 PF12 c os _t he ta = 0 .6 ; / / P F l a g g i n g13

15 S _c on ju ga te = 1 00 0 ; / / A pp ar en t c om pl ex p ow er i n

kVA16 c os _t he ta _f = 1 .0 ; // u n i t y PF17 s i n _ t h et a _ f = sqrt ( 1 - ( c os _t he ta _f ) ^ 2 ) ;

19 / / C a l c ul a t e d v a l u e s fro m Ex.8 −1120 P_o = 600 ; // A ct iv e power d i s s i p a t e d by t he l oa d

in kW21 Q_o = 800 ; // I n d u c t i ve r e a c t i v e q u ad r at u re power −22 // − drawn f ro m and r e t u r n e d t o t h e s u p pl y23

24 // C a l cu l a t i o n s :

2526 / / c as e a27 P _f = S _c on ju ga te * c os _t he ta _f ; // A c t i v e p ow er

29 / / c as e b30 Q _f = S _c on ju ga te * s in _t he ta _f ; // R e a c ti v e

q u a d r a t u r e p ow er d ra wn f ro m −31 // − and r e t ur n e d t o t he s u pp ly32

33 / / c as e c34 P_a = P_f - P_o ; // A d d i ti o n a l a c t i v e power i n kW

t h at may b e s u p p l i e d t o −35 // − new c u s t o m e r s36

37 / / c as e d38 jQ_a = %i * ( Q_f ) - %i * ( Q_o ) ; // C o r r e ct i o n

k v a r r e q u i r e d t o r a i s e PF −39 // −fr om 0 . 6 t o o . 8 l a g g i ng40 Q _a = - abs ( j Q _ a ) ; //41

42 / / c as e e43 S _c _c on ju ga te = 0 - jQ _a ; // R a ti ng o f c o r r e c t i o n

c a p a c i t o r s n e e d ed f o r c as e d44

47 disp ( ”E x ampl e 8−13 S o l u t i o n : ” ) ;48 printf ( ” \n a : P f = %d kW \n ” , P _ f ) ;

49 printf ( ” \n b : +j Q f i n k v a r = ” ) ; disp ( % i * Q _ f ) ;

50 printf ( ” \n c : P a = %d kW \n ” , P _ a ) ;

51 printf ( ” \n d : j Q a i n k v a r = ” ) ; disp ( j Q _ a )

52 printf ( ” \n e : S c c o n j u g a t e = %d kVA \n ” , abs (

S _ c _ co n j u ga t e ) ) ;

53 printf ( ” \n f : The power t a b u l at i o n g r i d i s shownbelow . \ n” ) ;

54 printf ( ” \n \ t \ t P \ t j Q \ t S∗ ” ) ;

55 printf ( ” \n \ t \ t (kW) \ t ( kv ar ) \ t (kVA) \ t c o s ” )

;56 printf ( ” \n

” ) ;

57 printf ( ” \n O r i g i n a l : \ t %d \ t +j%d \ t %d \ t % . 1f ” , P _o , Q _o , S _ c on j ug a te , c o s _ t he t a ) ;

58 printf ( ” \n Added : \ t %d \ t %dj \ t \ t ” ,P_a

, Q_ a ) ;

59 printf ( ” \n F i n a l : \ t %d \ t +j%d \ t %d \ t %. 1 f ” ,

P _f , Q _f , S _ c on j ug a te , c o s _ t h et a _ f ) ;

Scilab code Exa 8.14 calculate original and final kVA kvar P and correc-tion kvar Sa

6 // Ch apt e r 8 : AC DYNAMO TORQUE RELATIONS −SYNCHRONOUS MOTORS7 / / E xa mp le 8−148

c o n s o l e .

1011 / / G iv en d a ta12 P _o = 2000 ; / / l o ad i n kW drawn by a f a c t o r y13 c os _t he ta _o = 0 .6 ; / / P F l a g g i n g14 s i n _ t h et a _ o = sqrt ( 1 - ( c os _t he ta _o ) ^2 ) ;

15 c os _t he ta _f = 0 .8 5 ; // f i n a l PF l a g g i ng r e qu i r e d16 s i n _ t h et a _ f = sqrt ( 1 - ( c os _t he ta _f ) ^2 ) ;

17 P_a = 275 ; // L o ss e s i n t he s yn ch ro no us c a p a c i t o rin kW

20 / / c as e a21 S _ o _ co n ju g at e = P _o / c o s_ t he t a_ o ; / / O r i g i n a l kVA

drawn f r om t he u t i l i t y22

23 / / c as e b24 Q _o = S _o _c on ju ga te * s in _t he ta _o ; // O r i g i n al

l a g g i n g k va r25

26 / / c as e c27 P_f = P_o + P_a ; // F i n al s ys te m a c t i v e power

c on su m ed f r o m t h e u t i l i t y i n kW28

29 / / c as e d30 S _ f _ co n ju g at e = P _f / c o s_ t he t a_ f ; / / F i n a l kVA

drawn f r om t he u t i l i t y31 S _ f _ c o n j ug a t e _ a = a c os d ( c o s _ t h et a _ f ) ; // P ha se a n g l e

o f S f c o n j u g a t e i n d e g r e es32

33 / / c as e e34 j Q _f = S _ f_ c on j ug a te * s i n_ t he t a_ f ; // F i na l

l a g g i n g k va r

35 j Q_ a = % i *( j Q_ f ) - %i * ( Q_ o) ; // C o r r ec t i o n k va rp ro du ce d b y t h e s y nc h ro n o us c a p a c i t o r

36 Q _a = abs ( j Q _ a ) ; // Ma gni tude o f j Q a i n k va r37

38 / / c as e f

39 P = P_a ;

40 S _ a _ co n ju g at e = P - %i * ( abs ( j Q _ a ) ) ; // kVA r a t i n g o f t he s yn ch ro no u s c a p a c i t o r41 S _ a _ c o n j ug a t e _ m = abs ( S _ a _ c o n j u g a t e ) ; //

S a c o nj ug a te m = magn itud e o f S a c o n ju g a t e i nkVA

42 S _ a _ c o n j ug a t e _ a = atan ( imag ( S _ a _ c o nj u g a te ) / real (

S _ a _ c o n j u g a t e ) ) * 1 8 0 / % p i ;

43 // S a c o n j u ga t e a=p ha se a n gl e o f S a c o n ju g a t e i nd e g r e e s

44 P F _ f = c o sd ( S _ a _ co n j u ga t e _ a ) ; // PF45

48 printf ( ” \n a : S∗ o = %. 1 f kVA \n” , S _ o _ c on j u g at e ) ;

50 printf ( ” \n b : Q∗ o i n k v a r = ” ) ; disp ( % i * Q _ o ) ;

52 printf ( ” \n c : P∗ f = %. f kW \n” , P_ f ) ;

54 printf ( ” \n d : S∗ f = %. 1 f <%.1 f kVA\n ” ,

S _ f _ c o nj u g a t e , S _ f _ c o n j u g a t e _ a ) ;

56 printf ( ” \n e : j Q f i n k v a r = ”) ; disp ( % i * j Q _ f ) ;

57 printf ( ” \n − j Q a i n k v a r = ” ) ; disp ( j Q _ a ) ;

59 printf ( ” \n f : S∗ a = % . f <%. 2 f kVA ” ,

S _ a _ co n j u ga t e _ m , S _ a _ co n j u ga t e _ a ) ;

60 printf ( ” \n ( c o s (%. 2 f ) = %. 3 f l e a d i n g ) \n” ,

S_a_conjugate_a ,PF_f);

62 printf ( ” \n g : Power t a b u l a ti o n g r i d : \n ” ) ;

64 printf ( ” \n \ t \ t (kW) \ t ( kv ar ) \ t (kVA) \ t c o s ” );

65 printf ( ” \n” ) ;

66 printf ( ” \n O r i g i n a l : \ t %d \ t +j% . f %. 1 f %. 1 f

l a g ” , P _ o , Q _ o , S _ o _c o n ju g a te , c o s _ t h et a _ o ) ;

67 printf ( ” \n Added : \ t %d \ t −%. f j %. f \ t % . 3f l e a d ” , P _ a , Q _a , S _ a _ c o n j u g a t e _ m , c o s d (

S _ a _ co n j u ga t e _ a ) ) ;

68 printf ( ” \n F i n a l : \ t %d \ t +j% . f %. 1 f %. 2 f l a g ” , P _ f , j Q _f , S _ f _c o nj u g at e , c o s _ t h et a _ f ) ;

Scilab code Exa 8.15 calculate kVA added Pa and Qa and Pf Qf and PF

7 / / E xa mp le 8−158

1011 / / G iv en d a ta12 P _o = 2275 ; / / O r i g i n a l kVA13 Q _o = 1410 ; // O r i g i na l k va r14 S _ f _ co n ju g at e = 3 33 3. 3 ; // f i n a l kVA o f t h e l oa d15 S _o _c on ju ga te = P _o + % i* Q_ o ; // Load o f t he

a l t e r n a t o r i n kVA16 S _ o _ c o n j ug a t e _ m = abs ( S _ o _ c o n j u g a t e ) ; //

S o c o nj ug a te m = magn itud e o f S o c o n ju g a t e i nkVA

17 S _ o _ c o n j ug a t e _ a = atan ( imag ( S _ o _ c o nj u g a te ) / real (S _ o _ c o n j u g a t e ) ) * 1 8 0 / % p i ;

18 // S o c o n j u ga t e a=p ha se a n gl e o f S o c o n ju g a t e i nd e g r e e s

20 disp ( ”E x ampl e 8−15 ” ) ;

21 printf ( ” \n Power t a b u l a t i o n g r i d : \n ” ) ;22 printf ( ” \n \ t \ t P \ t \ t j Q \ t \ t S∗ ” ) ;

23 printf ( ” \n \ t \ t (kW) \ t \ t ( kv ar ) \ t \ t (kVA) \ t \ tc o s ” ) ;

24 printf ( ” \n

” ) ;

25 printf ( ” \n O r i g i n a l : \t%d \ t \ t j% . f \ t \ t %. 1 f \t%. 2 f l a g ” , real ( S _ o _ c o n ju g a t e ) , imag ( S _ o _ c o n j u g a t e )

, S _ o _ c o n j u g a te _ m , c o s d ( S _ o _ c o n j u g a t e _ a ) ) ;

26 printf ( ” \n Added : \ t0 . 8 x \ t \ t j 0 . 6 x \ t \ t x \ t \ t 0

. 8 0 l a g ” ) ;27 printf ( ” \n F i n a l : (%d + 0 . 8 x ) \ t j (%. f + 0 . 6 x )

%.1 f \ t 0 . 8 4 1 l a g \n” , real ( S _ o _ c o n ju g a t e ) , imag (

S _ o _ co n j u ga t e ) , S _ f _ c o n ju g a t e ) ;

29 / / C a l c u l a t i o n s30 / / c as e a31 // Assume x i s t he a d d i t i o n a l kVA l o ad . Then r e a l

and q u a dr a t ur e p ow er s a r e 0 . 8 x and j 0 . 6 x32 / / r e s p e c t i v e l y , a s sho wn . A dd in g e a ch c ol um n

v e r t i c a l l y and u s i ng t he P yt ha go re an theorem ,33 // we may w r i t e ( 22 75 + 0 . 8 x ) ˆ2 + ( 1 4 10 + 0 . 6 x ) ˆ2 =( 3 3 3 3 . 3 ) ̂ 2 , and s o l v i n g t h i s e q ut i on y i e l d s

34 / / t he q u a d r at i c x ˆ2 + 53 52 x −3 94 71 63 = 0 . A p p l yi n gt he q u a d r a ti c y i e l d s t he added kVA l o ad :

35 x = poly (0 , ’ x ’ ) ; // D e f in i n g a p o ly n om i al w it hv a r i a b l e ’ x ’ w i t h r o ot a t 0

36 p = -3 94 716 3 + 5 35 2* x + x ^2

37 a = 1 ; // c o e f f i c i e n t of xˆ238 b = 5332 ; // c o e f f i c i e n t o f x39 c = -3 94 716 3 ; // c o n st a n t

4041 / / R oots o f p42 x1 = ( - b + sqrt ( b^2 -4* a* c ) ) / (2 * a );

43 x 2 =( -b - sqrt ( b^2 -4* a* c ) ) / (2 * a );

45 / / c as e b

46 P _a = 0 .8 * x1 ; // Added a c t i v e power o f t hea d d i t i o n a l l oa d i n kW47 Q _a = 0 .6 * x1 ; // Added r e a c t i v e power o f t he

a d d i t i o n a l l oa d i n k v a r48

49 / / c as e c50 P_f = P_o + P_a ; // F in a l a c t i v e power o f t h e

a d d i t i o n a l l oa d i n kW51 Q_f = Q_o + Q_a ; // F in a l r e a c t i v e power o f t he

a d d i t i o n a l l oa d i n k v a r52

53 / / c as e d54 PF = P_ f / S _f _c on ju ga te ; // F i na l power f a c t o r55 / / V a l i d i t y c he ck56 S _c on ju ga te _f = P _f + % i* Q_ f ; // F i n al kVA o f t he

l o a d57 S _ c o n j u g at e _ f _ m = abs ( S _ c o n j u g a t e _ f ) ; //

S c o nj u g at e f m = magni tud e o f S c o n j u g a t e f i nkVA

58 S _ c o n j u g at e _ f _ a = atan ( imag ( S _ c o n j ug a t e _f ) / real (

S _ c o n j u g a t e _ f ) ) * 1 8 0 / % p i ;

59 / / S c o n j u g a t e f a=p ha se a n gl e o f S c o n j u g a t e f i nd e g r e e s

63 disp ( ” S ol ut i on : ” )

65 printf ( ” \n a : The g i ve n d at a i s shown i n t he a bo vep ow er t a b u l a t i o n g r i d . Assume ”) ;

66 printf ( ” \n x i s t h e a d d i t i o n a l kVA l oa d . Thenr e a l and q u ad r at u re p ow er s a r e ” ) ;

67 printf ( ” \n 0 . 8 x and j 0 . 6 x r e s p e c t i v e l y , a s shown .Ad ding e ac h col umn v e r t i c a l l y ” ) ;

68 printf ( ” \n and u s i ng t he P y t ha go re a n theorem , wemay w r i t e ” ) ;

69 printf ( ” \n ( 2 2 7 5 + 0 . 8 x ) ˆ2 + ( 1 4 1 0 + 0 . 6 x ) ˆ2 =

( 3 3 3 3 . 3 ) ̂ 2 , and s o l v i n g t h i s ” ) ;

70 printf ( ” \n e q u a t i o n y i e l d s th e qu a d r a ti c a sf o l l o w s : \n” ) ;

71 printf ( ” \n x ˆ2 + 5332 x −3 9 4 7 1 6 3 = 0 . \n ” )

72 printf ( ” \n A p p l y i n g t h e q u ad ra t i c y i e l d s th eadded kVA lo ad : ” ) ;

73 printf ( ” \n Roo ts o f q u ad ra ti c Eqn p a r e \n ” ) ;

74 printf ( ” \n x1 = %. 2 f \n x2 = %. 2 f ” , x1 , x2 )

75 printf ( ” \n C on si de r +ve v a l ue o f x f o r added kVAs o ” ) ;

76 printf ( ” \n x = S∗ a = %. 2 f kVA \n ” , x1 ) ;

7778 printf ( ” \n b : P a = %. 1 f kW \n ” , P _ a ) ;

79 printf ( ” \n Q a i n k v a r = \n” ) ; disp ( % i * Q _ a ) ;

81 printf ( ” \n c : P f = %. 1 f kW \n ” , P _ f ) ;

82 printf ( ” \n Q f i n k v a r = \n” ) ; disp ( % i * Q _ f ) ;

84 printf ( ” \n d : PF = c o s f = %. 3 f l a g g i n g \n ” , PF

85 printf ( ” \n V a l i d i t y c h e c k \n S∗ f = ” ) ; disp (

S _ c o n j u g a t e _ f ) ;

86 printf ( ” \n S∗ f = %. 1 f <%.2 f kVA \n” ,

S _ c o n j u g at e _ f _ m , S _ c o n j u g a t e _ f _ a ) ;

87 printf ( ” \n PF = c o s (%. 1 f ) = %. 3 f l a g g i n g ” ,

S _ c o nj u g a te _ f _ a , c o sd ( S _ c o nj u g a te _ f _ a ) ) ;

Scilab code Exa 8.16 Verify tellegens theorem for kVAs found in Ex 8 15

11 / / G iv en d a ta12 / / C a lc u la t ed v a l ue s a s p er Ex .8 −15 a re a s f o l l o w s13 S _ o _ c o nj u g a te = 2 6 7 6. 5 * exp ( % i * 3 1 . 7 9 * ( % p i / 1 8 0 ) ) ; //

O r i g i n a l k V A r a t i n g14 S _ o _ c o n j ug a t e _ m = abs ( S _ o _ c o n j u g a t e ) ; //

S o c o nj ug a te m = magn itud e o f S o c o n ju g a t e i nkVA

15 S _ o _ c o n j ug a t e _ a = atan ( imag ( S _ o _ c o nj u g a te ) / real (

S _ o _ c o n j u g a t e ) ) * 1 8 0 / % p i ;

16 // S o c o n j u ga t e a=p ha se a n gl e o f S o c o n ju g a t e i nd e g r e e s

18 S _ a _ c o nj u g a te = 6 5 8 .8 6 * exp ( % i * 3 6 . 8 7 * ( % p i / 1 8 0 ) ) ; //A dded kVA r a t i ng

19 S _ a _ c o n j ug a t e _ m = abs ( S _ a _ c o n j u g a t e ) ; //

S a c o nj ug a te m = magn itud e o f S a c o n ju g a t e i nkVA20 S _ a _ c o n j ug a t e _ a = atan ( imag ( S _ a _ c o nj u g a te ) / real (

S _ a _ c o n j u g a t e ) ) * 1 8 0 / % p i ;

21 // S a c o n j u ga t e a=p ha se a n gl e o f S a c o n ju g a t e i nd e g r e e s

23 S _ f _ c o nj u g a te = - 3 33 3 .3 * exp ( % i * 3 2 . 7 9 2 6 8 7 * ( % p i / 1 8 0 ) ) ;

/ / F i n a l kVA r a t i n g24 S _ f _ c o n j ug a t e _ m = abs ( S _ f _ c o n j u g a t e ) ; //

S f c o nj u g at e m = magni tud e o f S f c o n j u g a t e i n

kVA25 S _ f _ c o n j ug a t e _ a = atan ( imag ( S _ f _ c o nj u g a te ) / real (

S _ f _ c o n j u g a t e ) ) * 1 8 0 / % p i ;

26 / / S f c o n j u g a t e a=p ha se a n gl e o f S f c o n j u g a t e i nd e g r e e s

28 / / C a l c u l a t i o n s29 k V A_ t ot a l = S _ o_ c on j ug a te + S _ a_ c on j ug a te +

S _ f _ co n j u ga t e ; / / T e l l e g an ’ s t he or em30 k V A _ t o ta l _ m = abs ( k V A _ t o t a l ) ; / / k V A t o t a l m =

m a gn it ud e o f k V A t o t al i n kVA31 k V A _ t o ta l _ a = atan ( imag ( k V A _t o ta l ) / real ( k V A _ t o t a l ) )

* 1 8 0 / % p i ;

32 // k V A to t al a=p ha se a n g l e o f k VA to ta l i n d e g r e es33

36 printf ( ” \n From t he s o l u t i o n t o Ex .8 −1 5 , we h ave ” );

37 printf ( ” \n S∗ o = % . 1 f <%.2 f kVA \n ” ,

S _ o _ c o n j ug a t e _ m , S _ o _ c o n j u g a t e _ a ) ;

38 printf ( ” \n S∗ a = % . 1 f <%.2 f kVA \n ” ,

S _ a _ c o n j ug a t e _ m , S _ a _ c o n j u g a t e _ a ) ;

39 printf ( ” \n S∗ f = %. 1 f <%.2 f kVA \n ” ,

S _ f _ c o n j ug a t e _ m , S _ f _ c o n j u g a t e _ a ) ;

41 printf ( ” \n V a l i d i t y c h ec k ” ) ;

42 printf (” \n S∗ o + S∗ a + S∗ f = ”

43 disp ( S _ o _ c o n j u g a t e ) , printf ( ” +” ) , disp ( S _ a _ c o n j u g a t e

) , printf ( ” +”) , disp ( S _ f _ c o n j u g a t e ) ;

44 printf ( ” \n = %d ” , k V A _ to t a l ) ;

45 printf ( ” \n Hence , T e l le g e n ‘ s t he or em i s p ro ve d ” ) ;

Scilab code Exa 8.17 calculate overall PF using unity PF SM

11 / / G iv en d a ta12 k W = 40000 ; // Load on a f a c t o r y i n kW13 P F = 0.8 ; // power f a c t o r l a g gi n g o f t h e l oa d14 c o s _t h et a = P F ;

15 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;

16 h p = 7500 ; // power r a t i n g o f t he i n d uc t i o n motori n hp

17 P F_ IM = 0. 75 ; // power f a c t o r l a g g i n g o f t hei n d u c t i o n m oto r

18 c o s_ t he t a_ I M = P F_ IM ;

19 s i n _ t h et a _ I M = sqrt ( 1 - ( c o s_ th et a_ IM ) ^ 2 ) ;

20 e t a = 9 1* (1 /1 00 ) ; // E f f i c i e n c y o f IM21 PF_SM = 1 ; // power f a c t o r o f t he s yn ch ro no us

motor22

23 / / C a l c u l a t i o n s24 k VA _o ri gi na l = kW / PF ; / / O r i g i n a l kVA

25 k v ar _ or i gi n al = k V A_ o ri g in a l * s i n_ t he t a ; //O r i g i n a l k va r

27 kW_IM = ( hp * 746 ) / ( 1000 * eta ) ; // I n d u ct i o nmotor kW

28 k VA _I M = k W_ IM / P F_ IM ; / / I n d u c t i o n m ot or kVA29 k va r_ IM = k VA _I M * s in _t he ta _I M ; // I n d u c t i o n m oto r

k v a r30

31 k v a r _f i na l = k v ar _ or i gi n al - k v ar _I M ; // f i n a l k v a r32 k VA _f in al = k W + % i *( abs ( k v a r _ f i n a l ) ) ; // f i n a l kVA33 k V A _ f i na l _ m = abs ( k V A _ f i n a l ) ; // k V A f i n al m =

m ag ni tu de o f k V A f in a l i n kVA34 k V A _ f i na l _ a = atan ( imag ( k V A _f i na l ) / real ( k V A _ f i n a l ) )

* 1 8 0 / % p i ;

35 // k V A f in a l a=p ha se a n g l e o f k V A f i na l i n d e g r e es36

37 P F _ f in a l = c o sd ( k V A _ f i n al _ a ) ; // F i na l power f a c t o r38

41 printf ( ” \n The s yn ch ro no u s motor o p e r a t e s a t t hesame e f f i c i e n c y a s t he IM” ) ;

42 printf ( ” \n t ha t ha s bee n r e p l ac ed , and t h e r e f o r et he t o t a l power o f t he s ys te m ” ) ;

43 printf ( ” \n i s unchanged . The s o l u t i o n i n v o l v e s

c o n s t r uc t i o n o f t a b l e t ha t shows ” )44 printf ( ” \n t h e o r i g i n a l c o n d i t i o n o f t h e syst em ,

t he change , and t he f i n a l c o n d i t i o n . \ n” ) ;

45 printf ( ” \n O r i g i n a l kVA = %d kVA \n ” , k V A _ or i g i na l

46 printf ( ” \n O r i g i n al k v a r = \n” ) ; disp ( % i *

k v a r _ o r i g i n a l ) ;

48 printf ( ” \n I n d u c t i o n m o to r kW = %d kW \n ” , kW_IM )

49 printf (” \n I n d u c t i o n m ot or kVA = % . f kVA \n ”

k VA _I M ) ;

50 printf ( ” \n I n d u ct i o n motor k va r = ”) ; disp ( % i *

k v a r _ I M )

52 printf ( ” \n F i n a l k v a r = ”) ; disp ( % i * k v a r _ f i n a l ) ;

53 printf ( ” \n F i n a l kVA = ” ) ; disp ( k V A _ f i n a l ) ;

54 printf ( ” \n F i n a l kVA = %f <%.2 f kVA \n ” ,

k V A _ f in a l _ m , k V A _ f i n a l _ a ) ;

56 printf ( ” \n F i n a l PF = %. 3 f l a g g i n g \n ” , P F_ fi na l )

58 printf ( ” \n

” ) ;

59 printf ( ” \n Power t a b u l at i o n g r i d : \n ” ) ;

60 printf ( ” \n \ t \ t P \ t \ t j Q \ t \ t S∗ ” ) ;61 printf ( ” \n \ t \ t (kW) \ t \ t ( kv ar ) \ t \ t (kVA) \ t \ t c o s” ) ;

62 printf ( ” \n

” ) ;

63 printf ( ” \n O r i g i n a l : \t%d \ t \ tj% . f \ t \t % . 1 d \ t \ t %. 1 f l a g ” , k W , k v a r _ or i g i na l , k V A _o r ig i na l , P F ) ;

64 printf ( ” \n Removed : \ t−%. f \ t \ t −(+j% . f ) \t% . f \ t \t %. 2 f l a g ” , k W _I M , k v a r _ IM , k V A _ IM , P F _ I M ) ;

65 printf ( ” \n Added : \ t+%. f \ t \ t 0 \t% . 1 f \

t \ t 1 . 0 ” , k W _ I M , k W _ I M ) ;66 printf ( ” \n F i n a l : \t%d \ t \ tj% . f \ t \t% . 1 f \ t % . 3

f l a g ” , k W , k v a r _ fi n a l , k V A _f i na l _m , P F _ f i na l ) ;

67 printf ( ” \n

” ) ;

Scilab code Exa 8.18 calculate overall PF using point8 PF leading SM

7 / / E xa mp le 8−188

11 / / G iv en d a ta12 k W = 40000 ; // Load on a f a c t o r y i n kW

f i n a l k v a r

43 k VA _f in al = k W + % i *( abs ( k v a r _ f i n a l ) ) ; // f i n a l kVA44 k V A _ f i na l _ m = abs ( k V A _ f i n a l ) ; // k V A f i n al m =m ag ni tu de o f k V A f in a l i n kVA

45 k V A _ f i na l _ a = atan ( imag ( k V A _f i na l ) / real ( k V A _ f i n a l ) )

* 1 8 0 / % p i ;

46 // k V A f in a l a=p ha se a n g l e o f k V A f i na l i n d e g r e es47

48 P F _ f in a l = c o sd ( k V A _ f i n al _ a ) ; // F i na l power f a c t o r49

5253 printf ( ” \n O r i g i n a l kVA = %d kVA \n ” , k V A _ or i g i na l

54 printf ( ” \n O r i g i n al k v a r = \n” ) ; disp ( % i *

k v a r _ o r i g i n a l ) ;

55 printf ( ” \n a : ” ) ;

56 printf ( ” \n Sy nc hr o nous mot or kW = %d kW \n ” , k W_ SM

57 printf ( ” \n S y n c h r o n o u s m o to r kVA = %. f kVA \n ” ,

k VA _S M ) ;

58 printf (” \n S yn ch ro no u s m ot or k va r = ”

) ; disp ( - % i *

k v a r _ S M )

60 printf ( ” \n F i n a l k v a r = ”) ; disp ( % i * k v a r _ f i n a l ) ;

61 printf ( ” \n F i n a l kVA = ” ) ; disp ( k V A _ f i n a l ) ;

62 printf ( ” \n F i n a l kVA = %f <%.2 f kVA \n ” ,

k V A _ f in a l _ m , k V A _ f i n a l _ a ) ;

64 printf ( ” \n F i n a l PF = %. 3 f l a g g i n g \n ” , P F_ fi na l )

66 printf ( ” \n

” ) ;

67 printf ( ” \n Power t a b u l at i o n g r i d : \n ” ) ;

68 printf ( ” \n \ t \ t P \ t \ t j Q \ t \ t S∗ ” ) ;

69 printf ( ” \n \ t \ t (kW) \ t \ t ( kv ar ) \ t \ t (kVA) \ t \ t c o s

” ) ;70 printf ( ” \n

” ) ;

71 printf ( ” \n O r i g i n a l : \t%d \ t \ tj% . f \ t \t % . 1 d \ t \ t %. 1 f l a g ” , k W , k v a r _ or i g i na l , k V A _o r ig i na l , P F ) ;

72 printf ( ” \n Removed : \ t−%. f \ t \ t −(+j% . f ) \t% . f \ t \t %. 2 f l a g ” , k W _I M , k v a r _ IM , k V A _ IM , P F _ I M ) ;

73 printf ( ” \n Added : \ t+%. f \ t \ t− j% . 2 f \t% . 1 f \ t \ t %. 1 f l e a d ” , k W _ S M , abs ( k v a r _ S M ) , k V A _ S M , P F _ S M )

74 printf ( ” \n F i n a l : \t%d \ t \ tj% . 2 f \t% . 1 f \ t %. 3 f l a g ” , k W , k v a r _f i n a l , k V A _f i na l _m , P F _ f i na l ) ;

75 printf ( ” \n

\n\n” ) ;

77 printf ( ” \n b : ” ) ;

78 printf ( ” \n I n Ex .8 −1 7 , a 6 14 8 kVA , u n i t y PF , 7 50 0hp s y n c h ro n o u s m ot or i s n ee d ed . ” ) ;

79 printf ( ” \n I n Ex .8 −1 8 , a 7 68 5 kVA , 0 . 8 PF l e a d i n g ,

7 50 0 hp s y nc h ro n ou s m oto r i s n ee de d . \ n”) ;

80 printf ( ” \n \ t Ex . 8 −18 b s ho ws t h at a 0 . 8 PF l e a di n g, 7 5 0 0 hp s y nc h ro n o us m oto r ” ) ;

81 printf ( ” \n must be p h y s i c a l l y l a r g e r than a u ni tyPF , 7 5 0 0 hp s y n c h ro n o u s m ot or ” ) ;

82 printf ( ” \n b ec au se o f i t s h i g he r kVA r a t i n g . ” ) ;

Scilab code Exa 8.19 calculate kVA and PF of system and same for SM

6 // Ch apt e r 8 : AC DYNAMO TORQUE RELATIONS −SYNCHRONOUS MOTORS7 / / E xa mp le 8−198

11 / / G iv en d a ta12 k V A_ lo ad = 5 00 ; / / Load o f 5 00 kVA13 P F _l oa d = 0 .6 5 ; // Load o p e r a t e s a t t h i s PF l a g g i ng14 c o s_ t he t a_ l oa d = P F _l o ad ;

15 s i n _ t h e ta _ l o ad = sqrt ( 1 - ( c o s _t h et a _l o ad ) ^ 2 ) ;16 h p = 200 ; // power r a t i n g o f t he s ys te m i n hp17 e t a = 8 8 *( 1 /1 0 0) ; // E f f i c i e n c y o f t h e s y s t e m a f t e r

a dd in g t he l o ad18 P F _ fi na l = 0 .8 5 ; // F i n a l l a g g i n g PF a f t e r a dd in g

t he l o ad19

20 / / C a l c u l a t i o n s21 k W _o r ig i na l = k V A_ l oa d * c o s_ t he t a_ l oa d ; //

O r i g i n a l kW22 k v ar _ or i gi n al = k V A_ l oa d * s i n_ t he t a_ l oa d ;

//O r i g i n a l k va r23

24 kW_SM = ( hp * 746 ) / ( 1000 * eta ) ; //S y n c h r o n o u s m o to r kW

26 / / c as e a27 k W_ fi na l = k W_ or ig in al + k W_ SM ; // f i n a l kW o f t h e

s y st e m w i th t h e m ot or a dd ed28 k VA _f in al = k W_ fi na l / P F_ fi na l ; // f i n a l kVA o f

t h e s ys te m w it h t h e m oto r a dd ed

29 P F_ sy st em = k W_ fi na l / k VA _f in al ; // F i na l PF o f t h e s ys te m w it h t h e m oto r a dd ed

30 c o s_ t he t a_ s ys t em = P F _s y st e m ; // F i na l PF o f t hes y st e m w i th t h e m ot or a dd ed

31 s in _t he ta _s ys te m = sqrt ( 1 - ( c o s _t h et a _s y st e m ) ^ 2) ;

k V A _ S M ) ;

59 printf ( ” \n S yn ch ro no us motor kVA = %. f <

%.1 f kVA\n ” , k VA _S M_ m , k VA _S M_ a ) ;

60 printf ( ” \n S yn ch ro no u s m oto r PF = c o s (%. 1 f ) = %. 3 f l e a d i ng \n ” , k V A _ SM _ a , P F _ S M ) ;

62 printf ( ” \n”

63 printf ( ” \n Power t ab ul a t i o n g ri d : \n ” ) ;

65 printf ( ” \n \ t \ t (kW) \ t ( kv ar ) \ t (kVA) \ t c o s ” )

;66 printf ( ” \n

”) ;

67 printf ( ” \n O r i g i n a l : \ t %d \ t +j% . f %. 1 d \ t %. 2 f l a g ” ,kW_original ,kvar_ original ,kVA_load ,

P F _ l o a d ) ;

68 printf ( ” \n Added : \ t %. 1 f \ t −%. 1 f j %. f \ t%. 4 f l e a d ” , k W_ SM , abs ( k v a r _ S M ) , k V A _S M _ m , P F _ S M ) ;

69 printf ( ” \n F i n a l : \ t %. 1 f \ t +j% . f %. f

%. 2 f l a g ”,kW_final ,kvar_final ,kVA_final ,

P F _ f i n a l ) ;

70 printf ( ” \n”

Scilab code Exa 8.20 calulate speeds and poles for alternator and motor

11 / / G iv en d a ta12 f_a = 400 ; // F r eq u en cy o f t he a l t e r n a t o r i n Hz13 f_m = 60 ; // F re qu en cy o f t he motor i n Hz14

16 P ol e_ ra ti o = f _a / f_m ; // R a t i o o f no . o f p o l e s i na l t e r n a t o r t o t ha t o f motor

17 // S u b sc r i p t 1 be l o w i n d i c a t e s 1 s t c om bi na ti on18 P_a1 = 40 ; // f i r s t c o mb i na t io n must h av e 4 0 p o l e s

on t he a l t e r n a t o r19 P_m1 = 6 ; / / f i r s t c o mb i n at i on must h av e 6 p o l e s on

t he s yn ch ro n ou s motor a t a s pe ed20 S_ m1 = ( 120 * f_m ) / P _m 1 ; // Sp eed o f t he motor i n

22 // S u b sc r i p t 2 be l o w i n d i c a t e s 2 nd c om bi na ti on23 P_a2 = 80 ; // s e co n d c o mb i na t io n must h av e 40 p o l e s

on t h e a l t e r n a t o r24 P_m2 = 12 ; // s e co n d c o mb i na t io n must h av e 12 p o l e s

on t he s yn ch ro no u s motor a t a s pe ed25 S_ m2 = ( 120 * f_m ) / P _m 2 ; // Sp eed o f t he motor i n

27 // S u b sc r i p t 13 b el o w i n d i c a t e s 3 rd c om bi na ti on28 P_a3 = 120 ; // t h i r d c om bi na ti o n must ha ve 40 p o l e s

on t h e a l t e r n a t o r

29 P_m3 = 18 ; // t h i r d c om bi na ti on must h ave 18 p o l e son t he s yn ch ro n ou s motor a t a s pe ed

30 S_ m3 = ( 120 * f_m ) / P _m 3 ; // Sp eed o f t he motor i nrpm

33 disp ( ”E x ampl e 8−20 S o l u t i o n : ” ) ;34

35 printf ( ” \n S i n c e P a /P m = f a / f m = %d/%d , o r %d/%d, t he r a t i o o f ” , f _ a , f _ m , f _ a / 2 0 , f _ m / 2 0 ) ;

36 printf ( ” \n f a / f m d e t e r mi ne s t he c om bi na ti on s o f p o l e s and s p ee d . \ n” ) ;

37 printf ( ” \n Only e v en m u l t i p l es o f t he abov e r a t i oa re p o s si b l e , s i n c e p o l e s ” ) ;

38 printf ( ” \n a r e a lw ay s i n p a i rs , h en ce f i r s t t h r e ec om bi na t i on s a re a s f o l l o w s \n” ) ;

40 printf ( ” \n The f i r s t c o m b i na t i o n must h av e %d p o l e son t h e a l t e r n a t o r and ” , P _ a 1 ) ;

41 printf ( ” \n %d p o l e s on t he s y ch r on o us motor a t as p e e d = % d r p m . \ n” , P _ m 1 , S _ m 1 ) ;

43 printf ( ” \n The s e c o nd c o m b i na t i o n mus t h av e %dp o l es on t h e a l t e r n a t o r and ” , P _ a 2 ) ;

46 printf (” \n T he t h i r d c o mb i na t io n must h av e %d p o l e son t h e a l t e r n a t o r and ” , P _ a 3 ) ;

49 printf ( ” \n

” ) ;

50 printf ( ” \n C o m b i na t i o n \ t A l t e r na t o r P o le s \ tM ot or P o l e s \ t S pe ed ( rpm ) ” ) ;

51 printf ( ” \n \ t P a \ t

P m \ t S ” ) ;52 printf ( ” \n

” ) ;

53 printf ( ” \n F i r s t \ t \ t : \ t %d\ t \ t %d \ t %d”

, P _ a 1 , P _ m 1 , S _ m 1 ) ;

54 printf ( ” \n S e co n d \ t \ t : \ t %d\ t \ t %d \ t %d”, P _ a 2 , P _ m 2 , S _ m 2 ) ;

55 printf ( ” \n T hi rd \ t \ t : \ t %d\ t \ t %d \ t %d”, P _ a 3 , P _ m 3 , S _ m 3 ) ;

56 printf ( ” \n

” ) ;

Chapter 9

POLYPHASE INDUCTION

OR ASYNCHRONOUS

DYNAMOS

Scilab code Exa 9.1 calculate poles and synchronous speed

6 // Ch apt e r 9 : POLYPHASE INDUCTION (ASYNCHRONOUS)DYNAMOS

7 / / E xa mp le 9−18

11 / / G iv en d a ta12 phase = 3 ; // Number o f p h a s e s13 n = 3 ; // S l o t s p er p ol e p e r p h a s e14 f = 6 0 ; // L in e f r eq u en c y i n Hz15

17 / / c as e a18 P = 2 * n ; // Number o f p o l e s p r od u ce d19 To tal _sl ots = n * P * phase ; // T o t a l number o f

s l o t s on t h e s t a t o r20

21 / / c as e b22 S _ b = ( 12 0* f ) /P ; // Speed i n rpm o f t he r o t a t i n g

magn e t i c f i e l d23

24 / / c as e c25 f_c = 50 ; // Changed l i n e f r e qu e n cy i n Hz

26 S _c = ( 12 0* f _c ) /P ; // Speed i n rpm o f t he r o t a t i n gmagn e t i c f i e l d

30 printf ( ” \n a : P = %d p o l e s \n T o t a l s l o t s = %ds l o t s \n” , P , T ot al _s lo ts ) ;

32 printf ( ” \n b : S = %d rpm @ f = %d Hz \n ” , S_b , f

34 printf ( ” \n c : S = %d rpm @ f = %d Hz ” , S_c , f_c )

Scilab code Exa 9.2 calculate rotor speed

7 / / E xa mp le 9−2

c o n s o l e .10

11 / / G iv en d a ta12

13 s _ a = 5 * (1 / 10 0 ) ; // S l i p ( c as e a )14 s _ b = 7 * (1 / 10 0 ) ; // S l i p ( c as e b )15

16 / / Given d at a and c a l c u l a t e d v a l u e s fro m Ex.9 −117 f_a = 60 ; // L in e f r e q ue n cy i n Hz ( c a se a )

18 f_b = 50 ; / / L in e f r e q ue n cy i n Hz ( c a se b )19 S _a = 1200 ; // Speed i n rpm o f t he r o t a t i n g

m a g ne t i c f i e l d ( c a s e a )20 S _b = 1000 ; // Speed i n rpm o f t he r o t a t i n g

m a g ne t i c f i e l d ( c a s e b )21

22 / / C a l c u l a t i o n s23

24 / / c as e a25 S_r_a = S_a * ( 1 - s_a ) ; // R ot or s p ee d i n rpm

when s l i p i s 5% ( c a se a )26

27 / / c as e b28 S_r_b = S_b * ( 1 - s_b ) ; // R ot or s p ee d i n rpm

when s l i p i s 7% ( c a se b )29

33 printf ( ” \n a : S r = %. f rpm @ s = %. 2 f \n ” ,

S _r _a , s_ a ) ;

3435 printf ( ” \n b : S r = %. f rpm @ s = %. 2 f ” , S_r_b ,

s _b ) ;

Scilab code Exa 9.3 calculate rotor frequency

7 / / E xa mp le 9−38

11 / / G iv en d a ta12 P = 4 ; // Number o f p o l e s i n I n d u ct i o n motor13 f = 6 0 ; // F re qu en cy i n Hz14 s _ f = 5 *( 1/ 10 0) ; // F ul l −l oa d r o t o r s l i p15

16 / / C a l c u l a t i o n s17

18 / / c as e a19 // s l i p , s = ( S −S r ) / S ;20 / / wh ere S = Speed i n rpm o f t he r o t a t i n g m ag ne ti c

f i e l d and21 // S r = Speed i n rpm o f th e r o t o r22 s = 1 ; // S l i p = 1 , a t t h e i n s t a nt o f s t a r ti n g ,

s i n c e S r i s z e r o23 f_r_a = s * f ; // R ot or f r eq u en c y i n Hz a t t he

i n s t a n t o f s t a r t i n g24

25 / / c as e b26 f_r_b = s_f * f ; // F u ll −l oa d r o t o r f r e q ue n cy i n Hz27

29 disp ( ”E x ampl e 9−3 S o l u t i on : ” ) ;30

31 printf ( ” \n a : At t h e i n s t a n t o f s t a r t i n g , s l i p s =( S −S r ) /S ; ” ) ;

32 printf ( ” \n wher e S r i s t h e r o t o r s pe e d . S i n c et h e r o t o r s p e e d a t t h e ” ) ;

33 printf ( ” \n i n s t a n t o f s t a r t i n g i s z e r o , s = ( S −0 ) /S = 1 , o r u ni ty s l i p . ” ) ;

34 printf ( ” \n\n The r o t o r f r e q u e n c y i s \n f r =%d Hz \n\n ” , f _r _a ) ;

36 printf ( ” \n b : At f u l l −l oa d , t he s l i p i s 5 p e r ce n t ( a sg i v e n ) , and t h e r e f o r e ” ) ;

37 printf ( ” \n s = %. 2 f \n f r = %d Hz ” , s_f ,

f _ r _ b ) ;

Scilab code Exa 9.4 calculate starting torque and current

7 / / E xa mp le 9−48

1011 / / G iv en d a ta12 P = 4 ; // Number o f p o l e s i n t he IM13 hp = 50 ; // r a t i n g o f t h e IM i n hp14 V_o = 208 ; // V ol ta ge r a t i n g o f t h e IM i n v o l t

15 T _o ri g = 225 ; // S t a r t i n g t or qu e i n l b − f t

16 I _o ri g = 700 ; // I n s t a n t a n e o u s s t a r t i g n c u rr e n t i nA a t r at ed v o l t a ge17 V_s = 120 ; / / R ed uc ed 3−p ha se v o l t a g e s u p pl i e d i n

v o l t18

19 / / C a l c u l a t i o n s20 / / c as e a21 T _ s = T _o ri g * ( V _s / V_ o )^2 ; // S t a r t i n g t or qu e i n

l b − f t a f t e r a p p l i c a t i o n o f V s22

23 / / c as e b

24 I_s = I _o ri g * ( V_s / V_ o) ; // S t a r t i n g c u r r e n t i n Aa f t e r a p p l i c a t i o n o f V s

28 printf ( ” \n a : S t a r t i n g t or qu e : \ n T s = %. f l b −f t \n” , T_ s ) ;

30 printf ( ” \n b : S t a r t i n g c u r r e n t : \ n I s = %d A \n” , I_ s ) ;

Scilab code Exa 9.5 calculate s Xlr fr Sr

6 // Ch apt e r 9 : POLYPHASE INDUCTION (ASYNCHRONOUS)DYNAMOS7 / / E xa mp le 9−58

c o n s o l e .

1011 / / G iv en d a ta12 P = 8 ; // Number o f p o l e s i n t h e SCIM13 f = 6 0 ; // F re qu en cy i n Hz14 R_r = 0.3 ; // Ro to r r e s i s t a n c e p er p ha se i n ohm15 S_r = 650 ; / / S p ee d i n rpm a t w h ic h m ot or s t a l l s16

17 / / C a l c u l a t i o n s18 / / c as e a19 S = (1 20 * f) /P ; // Speed i n rpm o f t he r o t a t i n g

magn e t i c f i e l d

20 s_b = ( S - S_r )/ S ; // B re ak do wn S l i p21

22 / / c as e b23 X_lr = R_r / s_b ; // Lo cked r o t o r r e a c t a nc e i n ohm24

25 / / c as e c26 f_r = s_b * f ; // R ot or f r eq u en c y i n Hz , a t t he

maximum t o r q u e p o i n t27

28 / / c as e d29 s = 5 *( 1/ 10 0) ;

// Rated s l i p30 S_r = S * (1 - s ); // F u ll −l o ad i n rpm s pe ed a tr at ed s l i p

34 printf ( ” \n a : S = %d rpm \n s b = %. 3 f \n” , S ,

s _b ) ;

36 printf ( ” \n b : X b = %. 2 f ohm \n ” , X_lr ) ;

38 printf ( ” \n c : f r = %. 1 f Hz \n ” , f _ r ) ;39

40 printf ( ” \n d : S = %d rpm \n ” , S _ r ) ;

Scilab code Exa 9.6 calculate full load S and Tf

7 / / E xa mp le 9−68

11 / / G iv en d a ta12 P = 8 ; // Number o f p o l e s i n t h e SCIM13 f = 6 0 ; // F re qu en cy i n Hz14 R_r = 0.3 ; // r o t o r r e s i s t a n c e p er p ha se i n ohm/

p h a s e

15 R_x = 0.7 ; // Added r e s i s t a n c e i n ohm/ p h a se16 R _r _t ot al = R_r + R _x ; // T ot a l r e s i s t a n c e p er

p h a se i n ohm17 S_r = 875 ; // F u ll −l o a d S pe ed i n rpm18

20 / / C a l c ul a t e d v a l u e s fro m Ex.9 −621 S = 900 ; // Speed i n rpm o f t he r o t a t i n g m ag ne ti c

f i e l d22 X _lr = 1. 08 ; // Lo cked r o t o r r e a c t a nc e i n ohm23

24 / / C a l c u l a t i o n s25 / / c as e a26 s = ( S - S_r )/ S ; // F ul l −l oa d s l i p , s h or t c i r c u i t e d27 s_r = R _r_ to ta l / R_r * s ; // New f u l l −l oa d s l i p

w i th added r e s i s t a n c e

2829 S _ r_ n ew = S * (1 - s _ r ) ; / / New f u l l − l o ad s pe ed i n rpm30

31 / / c as e b32 // N e g le c t i n g c on s ta n t Kn t , s i n c e we a r e t a ki n g

t or qu e r a t i o s33 T_o = ( R _r / (( R_r ) ^2 + ( X_l r) ^2) ) ; // O r i g i na l

t o r q u e34 T _f = ( R_r + R_x ) / ( ( R_r + R_x )^2 + ( X_lr )^2 ) ;

// O r i g i na l t or qu e35

36 t or qu e_ ra ti o = T_ f / T_o ; // R a t i o o f f i n a l t o rq uet o o r i g i n a l t or qu e

37 T _ fi n al = 2 * t or q ue _ ra t io ;

41 printf ( ” \n a : The f u l l − l oa d s l i p , s h o rt c i r c u i t e d , i s” ) ;

42 printf ( ” \n s = %. 4 f \n” , s ) ;

43 printf ( ” \n S i n c e s l i p i s p r o p o r t i o n a l to r o t o r

r e s i s t a n c e and s i n c e t h e ”) ;

44 printf ( ” \n i n cr e a se d r o to r r e s i s t a n c e i s R r = %. 1 f + %. 1 f = %d , ” , R _ x , R _ r , R _ r _ t o t a l ) ;

45 printf ( ” \n t h e new f u l l − l oa d s l i p w i th addedr e s i s t a n c e i s : ” ) ;

46 printf ( ” \n s r = %. 4 f \n” , s _ r ) ;

47 printf ( ” \n The new f u l l − l o a d s pe e d i s : ” ) ;

48 printf ( ” \n S(1− s ) = %. f rpm \n” , S _r _ ne w ) ;

50 printf ( ” \n b : The o r i g i n a l s t a r t i n g t or qu e T o wast wi ce t h e f u l l −l o ad t o rq u e ” ) ;

51 printf ( ” \n w i t h a r o t o r r e s i s t a n c e o f %. 1 f ohmand a r o t o r r e a c t a nc e o f %. 2 f ohm” , R _ r , X _ l r ) ;

52 printf ( ” \n ( Ex . 9 −5 ) . The new s t a r t i n g t o r q u ec o n d i t i o n s may be s ummari zed by t h e ” ) ;

53 printf ( ” \n f o l l o w i n g t a b l e and compared from Eq

. ( 9 − 1 4 ) , w he r e T o ” ) ;

54 printf ( ” \n i s t h e o r i g i n a l t o r q u e and T f i s t h enew t o r q u e . ” ) ;

56 printf ( ” \n” ) ;

57 printf ( ” \n C o n d i t i o n \ t R r \ t X l r \ tT s t ar t i ng ” ) ;

58 printf ( ” \n \ t ohm \ t ohm \ t ” ) ;

59 printf ( ” \n” ) ;

60 printf ( ” \n O r i g i n a l : \ t %. 1 f \ t %. 2 f \ t 2∗ T n ”

, R _ r , X _ l r ) ;61 printf ( ” \n New : \ t %. 1 f \ t %. 2 f \ t ? ”

,R_r_total ,X_lr );

62 printf ( ” \n\n” ) ;

64 printf ( ” \n T o = %. 2 f ∗ K n t ” , T _ o ) ;

65 printf ( ” \n T f = %. 3 f ∗ K n t ” , T _ f ) ;

66 printf ( ” \n T f / T o = %. 2 f and T f = %. 2 f ∗ T o \n” , t o r q u e _ r at i o , t o r q u e _ r a t i o ) ;

67 printf (” \n T h e r e f o r e , \ n T f = %. 3 f ∗ T n ”

T _ f i n a l ) ;

Scilab code Exa 9.7 calculate rotor I and PF and same with added Rr

4 / / 2 nd e d i t i om5

7 / / E xa mp le 9−7

11 / / G iv en d a ta12 P = 8 ; // Number o f p o l e s i n t h e SCIM13 f = 6 0 ; // F re qu en cy i n Hz14 R_r = 0.3 ; // Ro to r r e s i s t a n c e p er p ha se i n ohm15 R_x = 0.7 ; // Added r e s i s t a n c e i n ohm/ p h a se16 R _r _t ot al = R_r + R _x ; // T ot a l r e s i s t a n c e p er

p h a se i n ohm17 X _lr = 1. 08 ; // Lo cked r o t o r r e a c t a nc e i n ohm

18 S_r = 650 ; / / S p ee d i n rpm a t w h ic h m ot or s t a l l s19 E_lr = 112 ; // I nd uc ed v o l t a g e p er p ha se20

21 / / C a l c u l a t i o n s22 / / c as e a23 Z_ lr = R_r + %i * X_l r ; // L oc ke d r o t o r i mp ed an ce p e r

p h a s e24 Z _ l r_ m = abs ( Z _ l r ) ; // Z l r m = magni tud e o f Z l r i n

ohm25 Z _ l r_ a = atan ( imag ( Z _l r ) / real ( Z _ l r ) ) * 1 8 0 / % p i ; //

Z l r a=p h a se a ng l e o f Z l r i n d e g r e e s26

27 I_r = E_lr / Z_ lr_m ; // Ro to r c u r r e n t p er p ha se28 c o s _ t h et a _ r = c o sd ( Z _ l r _ a ) ; // r o t o r power f a c t o r

w i th t he r o t o r s ho rt −c i r c u i t e d29 c o s_ th et a = R _r / Z _l r_ m ; // r o t o r power f a c t o r

w i th t he r o t o r s ho rt −c i r c u i t e d30

31 / / c as e b32 / / 1 a t t h e end o f Z l r 1 i s j u s t us e d f o r s h o w i n g

i t s d i f f e r e n t form Z l r

33 // and f o r e as e i n c a l c u l a t i o n s34 Z _l r1 = R _r _t ot al + % i* X _l r ; // L oc ke d r o t o r

i m pe da n ce p e r p h as e35 Z _ l r1 _ m = abs ( Z _ l r 1 ) ; // Z l r 1 m = m a gn it ud e o f Z l r 1

i n ohm

36 Z _ l r1 _ a = atan ( imag ( Z _ lr 1 ) / real ( Z _ l r 1 ) ) * 1 8 0 / % p i ; //

Z l r 1 a=p h a s e a n g l e o f Z l r 1 i n d e g r e e s37

38 I_ r1 = E_ lr / Z _l r1 _m ; // R ot or c u r r e n t p er p ha se39 c o s _ t h et a _ r 1 = c o sd ( Z _ l r 1 _ a ) ; // r o t o r power f a c t o r

w i th t he r o t o r s ho rt −c i r c u i t e d40 c os _t he ta 1 = R _r _t ot al / Z _l r1 _m ; // r o t o r power

f a c t o r w i t h t h e r o t o r s ho rt −c i r c u i t e d41

44 printf ( ” \n a : The l o ck e d −r o t o r i mp ed an ce p e r p ha s e

i s : ” ) ;45 printf ( ” \n Z l r i n ohm = ” ) , disp ( Z _ l r ) ;

46 printf ( ” \n Z l r = %. 2 f <%.1 f ohm \n” , Z _ l r _ m ,

Z _ l r _ a ) ;

47 printf ( ” \n I r = %. f A \n” , I _ r ) ;

48 printf ( ” \n c o s r = c os (%. 1 f ) = %. 3 f o r \nc o s = R r / Z l r = %. 3 f ” ,Z_lr_a,cos_theta_r ,

c o s _ t h e t a ) ;

50 printf ( ” \n\n\n b : The l o c k ed −r o t o r i mp ed an ce w it h

added r o t o r r e s i s t a n c e p e r p h a s e i s : ”) ;

51 printf ( ” \n Z l r i n ohm = ” ) , disp ( Z _ l r 1 ) ;

52 printf ( ” \n Z l r = %. 2 f <%.1 f ohm \n” ,Z_lr1_m ,

Z _ l r 1 _ a ) ;

53 printf ( ” \n I r = %. 1 f A \n” , I _ r 1 ) ;

54 printf ( ” \n c o s r = c os (%. 1 f ) = %. 3 f o r \nc o s = R r / Z l r = %. 3 f ” ,Z_lr1_a ,cos_theta_r1 ,

c o s _ t h e t a 1 ) ;

Scilab code Exa 9.8 calculate Rx and rotor PF and starting current

4 / / 2 nd e d i t i om5

7 / / E xa mp le 9−88

11 // G iven d a ta ( Exs .9 −5 t hr ou gh 9 −7)12 P = 8 ; // Number o f p o l e s i n t h e SCIM

13 f = 6 0 ; // F re qu en cy i n Hz14 R_r = 0.3 ; // Ro to r r e s i s t a n c e p er p ha se i n ohm15 X _lr = 1. 08 ; // Lo cked r o t o r r e a c t a nc e i n ohm16 S_r = 650 ; / / S p ee d i n rpm a t w h ic h m ot or s t a l l s17 E_lr = 112 ; // I nd uc ed v o l t a g e p er p ha se18

19 disp ( ”E x ampl e 9−8 : ” ) ;

20 printf ( ” \n The new and t he o r i g i n a l c o n d i t i o n s maybe summarized i n t he f o l l o w i n g t a b l e \n” ) ;

21 printf ( ” \n

” ) ;

22 printf ( ” \n C o n d i t i o n \ t R r \ t \ t X l r \ t \ tT s t ar t i ng ” ) ;

23 printf ( ” \n \ t ohm \ t \ t ohm \ t ” ) ;

24 printf ( ” \n

” ) ;

25 printf ( ” \n O r i g i n a l : \ t %. 1 f \ t \ t %. 2 f \ t \ t T o= 2∗ T n ” , R _ r , X _ l r ) ;

26 printf ( ” \n New : \ t (%. 1 f+R x ) \ t %. 2 f \ t \ t

T n = 2∗ T n ” , R _ r , X _ l r ) ;27 printf ( ” \n

\n” ) ;

29 / / C a l c u l a t i n g

30 / / c as e a31 // N e g le c t i n g c on s ta n t Kn t , s i n c e we a r e e qu a ti n gt o rq u e T o and T n

32 T_o = ( R _r / (( R_r ) ^2 + ( X_l r) ^2) ) ; // O r i g i na lt o r q u e

34 // T o = K n t ∗ ( 0 . 3 / ( ( 0 . 3 ) ̂ 2 + ( 1 . 0 8 ) ̂ 2) ) ;35 // T n = K n t ∗ ( 0 . 3 + R x ) / ( ( 0 . 3 + R x ) ˆ2 +

( 1 . 0 8 ) ̂ 2 ) ;36 // T n = T o37 // S i m pl y i f i n g y i e l d s

38 // 0 . 3 + R x = 0 . 2 4 [ ( 0 . 3 + R x ) ˆ 2 + ( 1 . 0 8 ) ̂ 2 ]39 / / E xp an di ng and c om bi ni n g t h e t er ms y i e l d s40 / / 0 . 24 ∗ ( R x ) ˆ 2 − 0 . 8 5 6 ∗ R x = 041 / / T hi s i s a q u ad r a ti c e q u a ti o n h av in g two r oo t s ,

w hi ch may b e f a c t o r e d a s42 // R x ∗ ( 0 . 2 4 ∗ R x − 0 . 8 5 6 ) = 0 , y i e l d i n g43 // R x = 0 and R x = 0 . 85 6 /0 , 2 4 = 3 . 5744 R _x = poly (0 , ’ R x ’ ) ; // D e f i ni n g a p o ly n om i al w it h

v a r i a b l e ’ R x ’ w i t h r o ot a t 045 a = 0.24 ; // c o e f f i c i e n t of xˆ246 b = -0.856 ;

// c o e f f i c i e n t o f x47 c = 0 ; // c o n st a n t48

49 / / R oots o f p50 R_x1 = ( -b + sqrt ( b ^2 -4* a* c ) ) /( 2* a );

51 R_ x2 =( - b - sqrt ( b^2 -4* a* c ) ) / (2 * a );

52 // C o ns i de r R x>0 v a l ue ,53 R _x = R _x 1 ;

55 R_T = R_r + R_x ; // T o ta l r o t o r r e s i s t a n c e i n ohm56

57 / / c as e b58 Z_T = R_T + %i * X_lr ; // T o t a l i mp ed an ce i n ohm59 Z _ T_ m = abs ( Z _ T ) ; // Z T m = m ag ni tu de o f Z T i n ohm60 Z _ T_ a = atan ( imag ( Z _T ) / real ( Z _ T ) ) * 1 8 0 / % p i ; / / Z T a =

p h a se a n g l e o f Z T i n d e g r e e s

62 c os _t he ta = R_T / Z _T _m ; // R ot or PF t h at w i l lp ro du ce t he same s t a r t i n g t o rq u e63

64 / / c as e c65 Z_r = Z_T_m ; / / I m pe da n ce i n ohm66 I_r = E_lr / Z_r ; // S t a r t i n g c u rr e n t i n A67

68 // D is pl ay t h e r e s u l t s69 disp ( ” S o l u t i o n : ” ) ;

71 printf ( ” \n a : T o = %. 2 f ∗ K n t ” , T_ o ) ;

72 printf ( ” \n T n = %. 2 f ∗ K n t \n” , T_ o ) ;73 printf ( ” \n S i m pl y i f i n g y i e l d s ” ) ;

74 printf ( ” \n 0 .3 + R x = 0 . 2 4 [ ( 0 . 3 + R x ) ˆ2 + ( 1 . 0 8 )ˆ2 ] ” ) ;

75 printf ( ” \n Expanding and co mb in in g th e te rm sy i e l d s ” ) ;

76 printf ( ” \n 0 . 2 4 ∗ ( R x ) ˆ 2 − 0 . 8 5 6 ∗ R x = 0 ”) ;

77 printf ( ” \n T hi s i s a q ua dr at i c e q u a t i on ha v i n gtwo r o o t s , w hi ch may be f a c t o r e d a s ” ) ;

78 printf ( ” \n R x ∗ ( 0 . 2 4 ∗ R x − 0 . 8 5 6 ) = 0 , y i e l d i n g ” )

79 printf ( ” \n R x = 0 ohm and R x = 0 . 8 56 / 0 . 2 4 =3 . 5 7 ohm\n\n T h i s p r o v e s t h a t ” ) ;

80 printf ( ” \n O r i g i n a l t o r q u e i s p r o d u c e d wi t h ane x t e r n a l r e s i s t a n c e o f e i t h e r ” ) ;

81 printf ( ” \n z e r o o r 12 ti m e s t h e o r i g i a n l r o t o rr e s i s t a n c e . T h e re f o re , \ n” ) ;

82 printf ( ” \n R T = R r + R x = %. 2 f ohm \n” , R _ T ) ;

84 printf ( ” \n b : Z T i n ohm = ” ) ; disp ( Z _ T ) ;

85 printf ( ” \n Z T = %. 2 f <% . 1 f ohm ” , Z _ T _ m , Z _ T _ a ) ;

86 printf ( ” \n c o s = R T / Z T = %. 3 f o r \nc o s = c o s d (%. 1 f ) = %. 3 f \n” ,cos_theta ,Z_T_a ,cosd

( Z _ T _ a ) ) ;

88 printf ( ” \n c : I r = E l r / Z r = %. f A \n\n T h i s

p r o v e s t h at , ” , I _ r ) ;

89 printf ( ” \n Ro to r c ur r en t at s t a r t i n g i s now o n l y28 p e r ce nt o f t he o r i g i n a l ” ) ;

90 printf ( ” \n s t a r t i n g c u rr e n t i n p a r t ( a ) o f Ex.9 −7” ) ;

Scilab code Exa 9.9 calculate Sr with added Rx

7 / / E xa mp le 9−98

11 / / G iv en d a ta12 P = 8 ; // Number o f p o l e s i n t h e SCIM13 f = 6 0 ; // F re qu en cy i n Hz14 S_r = 875 ; // F u ll −l o ad S peed i n rpm w it h r o t o r

s h o r t −c i r c u i t e d15 R_r = 0.3 ; // r o t o r r e s i s t a n c e p er p ha se i n ohm/

p h a s e16 R_x = 0.7 ; // Added r e s i s t a n c e i n ohm/ p h a se17 R_x_a = 1.7 ; / / Added r e s i s t a n c e i n ohm/ p h as e ( c a s e

18 R_x_b = 2.7 ; / / Added r e s i s t a n c e i n ohm/ p h as e ( c a s eb )19 R_x_c = 3.7 ; / / Added r e s i s t a n c e i n ohm/ p h as e ( c a s e

c )20 R_x_d = 4.7 ; / / Added r e s i s t a n c e i n ohm/ p h as e ( c a s e

2122 / / C a l c u l a t i o n s23 S = (1 20 * f) /P ; // Speed i n rpm o f t he r o t a t i n g

magn e t i c f i e l d24 s_o = ( S - S_r )/ S ; // S l i p a t r o to r s p e e d 875 rpm25

26 / / c as e a27 s _r _a = s _o * ( R_ r + R _x _a ) /R _r ; // Rated s l i p28 S_r_a = S * (1 - s_r_a ); // F u ll −l o ad s pe ed i n rpm

f o r added r e s i s t a n c e R x a29

30 / / c as e b31 s _r _b = s _o * ( R_ r + R _x _b ) /R _r ; // Rated s l i p32 S_r_b = S * (1 - s_r_b ); // F u ll −l o ad s pe ed i n rpm

f o r added r e s i s t a n c e R x b33

34 / / c as e c35 s _r _c = s _o * ( R_ r + R _x _c ) /R _r ; // Rated s l i p36 S_r_c = S * (1 - s_r_c ); // F u ll −l o ad s pe ed i n rpm

f o r added r e s i s t a n c e R x c37

38 / / c as e d39 s _r _d = s _o * ( R_ r + R _x _d ) /R _r ; // Rated s l i p

40 S_r_d = S * (1 - s_r_d ); // F u ll −l o ad s pe ed i n rpmf o r added r e s i s t a n c e R x d

45 printf ( ” \n S l i p s r = s o ∗ ( R r+R x ) / R r \n R ot ors p e e d S r = S o ∗(1 − s ) \n” ) ;

47 printf ( ” \n C a l c u l a t e d v al u e o f s o = %f ,i n s t e a d o f 0 . 0 2 7 8 ( t ex t bo o k ) ” , s _ o )

48 printf ( ” \n s o s l i g h t v a r i a t i o n s i n th e an s w e r sbelow . \ n” ) ;

50 printf ( ” \n a : When R x = % . 1 f ohm ” , R _ x _ a ) ;

51 printf ( ” \n s r = %. 3 f \n S r = %. 1 f rpm \n” ,s _r _a , S _ r _a ) ;

53 printf ( ” \n b : When R x = % . 1 f ohm ” , R _ x _ b ) ;

54 printf ( ” \n s r = %. 3 f \n S r = %. 1 f rpm \n” ,

s _r _b , S _ r _b ) ;

56 printf ( ” \n c : When R x = % . 1 f ohm ” , R _ x _ c ) ;

57 printf ( ” \n s r = %. 3 f \n S r = %. 1 f rpm \n” ,

s _r _c , S _ r _c ) ;

59 printf ( ” \n d : When R x = % . 1 f ohm ” , R _ x _ d ) ;60 printf ( ” \n s r = %. 3 f \n S r = %. 1 f rpm \n” ,

s _r _d , S _ r _d ) ;

62 printf ( ” \n T hi s example , v e r i f i e s t h at s l i p i sp r o po r t i o n a l t o r o t o r r e s i s t a n c e ” ) ;

63 printf ( ” \n a s s ummari zed be l ow . ” ) ;

65 printf ( ” \n

”) ;

66 printf ( ” \n R T (ohm ) = R r+R x \ t \ t S l i p \ t \ tF u l l −l o a d S p e ed ( rpm ) ” ) ;

67 printf ( ” \n

” ) ;

68 printf ( ” \n Given \ t \ t \ t G iv en \ t \ t G iv en \ t \ ”) ;

69 printf ( ” \n 0 . 3 \ t \ t \ t 0 . 0 27 8 \ t 875 ” ) ;

70 printf ( ” \n 0 . 3 + 0 . 1 = 1 . 0 \ t \ t 0 . 09 2 6 \ t 817 ” ) ;

71 printf ( ” \n

” ) ;

72 printf ( ” \n Given \ t \ t \ t C a l c ul a t e d \ tC a l c u l a t e d \ t \ ” ) ;

73 printf ( ” \n a . %. 1 f + %. 1 f = %. 1 f \ t \ t %. 3 f \ t \ t %

. 1 f ” , R _ r , R _ x _ a , R _ r + R _ x _ a , s _ r _ a , S _ r _ a ) ;

74 printf ( ” \n b . %. 1 f + %. 1 f = %. 1 f \ t \ t %. 3 f \ t \ t %. 1 f ” , R _ r , R _ x _ b , R _ r + R _ x _ b , s _ r _ b , S _ r _ b ) ;

75 printf ( ” \n c . %. 1 f + %. 1 f = %. 1 f \ t \ t %. 3 f \ t \ t %. 1 f ” , R _ r , R _ x _ c , R _ r + R _ x _ c , s _ r _ c , S _ r _ c ) ;

76 printf ( ” \n d . %. 1 f + %. 1 f = %. 1 f \ t \ t %. 3 f \ t \ t %. 1 f ” , R _ r , R _ x _ d , R _ r + R _ x _ d , s _ r _ d , S _ r _ d ) ;

77 printf ( ” \n

” ) ;

Scilab code Exa 9.10 calculate Elr Ir Pin RCL RPD torques

7 / / E xa mp le 9−108

11 / / G iv en d a ta12 P = 4 ; / / N umber o f p o l e s i n WRIM13 f = 6 0 ; // F re qu en cy i n Hz14 V = 220 ; // L i n e v o l t a g e i n v o l t15 V_p = 220 ; // Phase v o l t a g e i n v o l t ( d e l t a

c o n n e c t i o n )16 h p_WR IM = 1 ; / / Power r a t i n g o f WRIM i n hp17 S _r = 1740 ; // F ul l −l o ad r a t ed s pe ed i n rpm18 R_r = 0.3 ; // r o t o r r e s i s t a n c e p er p ha se i n ohm/

p h a s e

19 R_x = 0.7 ; // Added r e s i s t a n c e i n ohm/ p h a se

20 X _lr =1 ; // Lo cked r o t o r r e a c t a n ce i n ohm21

magn e t i c f i e l d24 / / c as e a25 E_lr = V_p / 4 ; / / L o ck ed−r o t o r v o l t a g e p er p ha se26

27 / / c as e b28 s = ( S - S_r ) / S ; // s l i p29 I _r = E_lr / sqrt ( ( R_ r /s ) ^2 + ( X _l r )^ 2 ) ; / / R ot or

c u r r e nt p er p ha se a t r a te d s pe ed30

31 / / c as e c32 P_ in = (( I_r ) ^2 * R_r ) /s ; // Ra ted r o t o r p ower

i n pu t p er p ha se33

34 / / c as e d35 P_ RL = ( I_r ) ^2 * R_r ; // Rated c op pe r l o s s p er

p h a s e36

37 / / c as e e38 P_d_W = P_in - P_RL ; // R ot or po we r d e v el o p ed p e r

p ha se i n W39 P _d _h p = P _d _W / 7 46 ; // R ot or p ower d e v el o p e d p e r

p ha se i n hp40

41 / / c as e f 42 h p = P_d _hp ; // R ot or power d e ve l op e d p er p ha se i n

hp43 T _d 1 = ( hp * 52 52 ) / S_ r ; // R ot or t o rq u e d e ve l op e d i n

l b − f t p er p ha se by method 1

44 T _d 2 = 7 .0 4* ( P _i n /S ) ; // R ot or t o rq u e d e ve l op e d i nl b − f t p er p ha se by method 2

46 T_ dm = 3* T _d 1 ; // T o ta l r o t o r t or qu e i n l b −f t47

DYNAMOS

7 / / E xa mp le 9−118

11 / / G iv en d a ta12 // 3−p h a s e WRIM13 V_L = 208 ; // V ol t ag e r a t i n g o f t he WRIM i n v o l t14 P = 6 ; / / N umber o f p o l e s i n WRIM15 f = 6 0 ; // F re qu en cy i n Hz16 P_o = 7.5 ; / / Power r a t i n g o f WRIM i n hp

17 S _r = 1125 ; // F ul l −l oa d r o t o r s pe ed i n rpm18 R _r = 0.08 ; // R ot or r e s i s t a n c e i n ohm/ p ha se19 X_lr = 0.4 ; // L ocked r o t o r r e s i s t a n c e i n ohm/ p ha se20

magn e t i c f i e l d23 / / c as e a24 E_lr = ( V_L / sqrt ( 3) ) / 2 ; // Lo cked r o t o r v o l t a g e

p e r p ha se25

26 / / c as e b27 s = ( S - S_r )/ S ; // F ul l −l oa d r at ed s l i p28 I _r = E_lr / sqrt ( ( R_ r /s ) ^2 + ( X _l r )^ 2 ) ; / / R ot or

c u r r e nt i n A pe r p ha se a t r a te d s pe ed29

30 / / c as e c31 P_in = ( ( I_r )^2 * R_r ) /s ; // Ra ted r o t o r p ower

i n p u t p e r p h a se i n (W/ p h a s e )32

33 / / c as e d

34 P_RL = ( ( I_r )^2 * R_r ) ; // Rated r o t o r c op pe r l o s sp e r p h a s e ( i n W/ p h a s e )

36 / / c as e e37 // S u b s c r i pt W i n P d i n d i c a t e s c a l c u l a t i n g P d i n W

38 P_d_W = P_in - P_RL ; // R ot or po we r d e v el o p ed p e r

p h a s e ( i n W/ p h a s e )39 / / S u b s c r i pt hp i n P d i n d i c a t e s c a l c u l a t i n g P d i nhp

40 P _d _h p = P _d _W / 7 46 ; // R ot or p ower d e v el o p e d p e rp h a s e ( i n hp / p h a s e )

42 / / c as e f 43 / / s u b s c r i p t 1 i n T d i n d i c a t e s method 1 f o r

c a l c u l a t i n g T d44 h p = P_d _hp ;

45 T _d 1 = ( hp * 52 52 ) / S_ r ; // R ot or t o rq u e d e ve l op e d p er

p ha se i n l b − f t46

47 / / s u b s c r i p t 2 i n T d i n d i c a t e s method 2 f o rc a l c u l a t i n g T d

48 T _d 2 = 7 .0 4* ( P _ in / S ) ; // Ro to r t o rq u e d ev e lo p ed p erp ha se i n l b −f t

50 / / c as e g51 T_ dm = 3* T _d 1 ; // T o ta l r o t o r t or qu e i n l b −f t52

53 / / c as e h54 T _ o = 7 .0 4* ( P _o * 7 4 6) / S _r ; // T ot al o ut pu t r o t o r

t or qu e i n l b − f t55

59 printf ( ” \n Note : S l i g h t v a r i a t i o n s i n t h ea n s w e r s I r , P i n , P RL , P d , T d ” ) ;

60 printf ( ” \n a r e b e c a u s e o f non−a p pr o x im a t io n o f E l r and ( R r / s ) ˆ 2 + ( X l r ) ˆ 2 ” ) ;

61 printf ( ” \n w h i l e c a l u l a t i n g i n s c i l a b . \ n” );

63 printf ( ” \n a : Locked r o t o r v o l t ag e p er p ha se : \ nE l r = %d V\n” , E _ l r ) ;

65 printf ( ” \n b : s l i p : \ n s = %. 4 f ”, s ) ;66 printf ( ” \n\n R ot o r c u rr en t pe r ph a s e at r a te ds pe ed : \ n I r = %. 2 f A/ ph a s e \n” , I _ r ) ;

68 printf ( ” \n c : Rated r o t o r power i np ut p er p ha se : \ nP i n = %. f W/ p h a s e \n” , P _ i n ) ;

70 printf ( ” \n d : Rated r o t o r c op pe r l o s s p er p h a s e : \ nP RL = %. 1 f W/ phase \n” , P _ R L ) ;

72 printf ( ” \n e : Ro to r power d e ve l op e d p er p ha se ” ) ;

73 printf ( ” \n P d = %. f W/ ph a s e \n P d = %. 2 f hp/ p h a s e \n” , P _ d _ W , P _ d _ h p ) ;

75 printf ( ” \n f : Ro to r t or qu e d ev el op ed p er p ha se : ” )

76 printf ( ” \n ( method 1 ) \n T d = %. 1 f l b − f t /p h a s e ” , T _ d 1 ) ;

77 printf ( ” \n\n ( method 2 ) \n T d = %. 1 f l b − f t /p h a s e \n” , T _ d 2 ) ;

79 printf (” \n g : T ot a l r o t o r t or qu e : \n T dm = %dl b − f t \ n” , T _ d m ) ;

81 printf ( ” \n h : T ot al o ut pu t r o t o r t or qu e : \n T o= % d l b − f t ” , T _ o ) ;

Scilab code Exa 9.12 calculate s and Sr for Tmax

6 // Ch apt e r 9 : POLYPHASE INDUCTION (ASYNCHRONOUS)

DYNAMOS7 / / E xa mp le 9−128

11 / / G ive n d at a a s p e r Ex .9 −1012 P = 4 ; / / N umber o f p o l e s i n WRIM13 f = 6 0 ; // F re qu en cy i n Hz14 V = 220 ; // L i n e v o l t a g e i n v o l t15 V_p = 220 ; // Phase v o l t a g e i n v o l t ( d e l t a

p h a s e19 R_x = 0.7 ; // Added r e s i s t a n c e i n ohm/ p h a se20 X_lr = 1 ; // Locked r o t o r r e a c t a nc e i n ohm21

22 / / C a l c u l a t i o n s fro m Ex.9 −1023 E_lr = V_p / 4 ; / / L o ck ed−r o t o r v o l t a g e p er p ha se24 S = (1 20 * f) /P ;

// Speed i n rpm o f t he r o t a t i n gmagn e t i c f i e l d25

26 // C a l c u l a t i o n s ( Ex .9 −12)27 P _i n = ( E _l r ) ^2 / ( 2* X _l r ); / / r o t o r p ow er i n p u t ( RPI

) i n W/ p h a s e28 P _i n_ to ta l = P_ in * 3 ; // T ot al 3−p ha se r o t o r p ower

i n p u t ( RPI ) i n W29

30 T _ m a x = 7 . 0 4* ( P _ i n _ t ot a l / S ) ; // Maximum to rq ued e ve l op e d i n l b− f t

3132 s_b = R_r / X_lr ; // S l i p33

34 s = s_b ;

35 S_r = S *(1 - s ); // Ro to r s pe ed i n rpm f o r T max

40 printf ( ” \n R ot o r p ower i np ut ( RPI ) p er p ha se i s : ”) ;

41 printf ( ” \n P i n = %. 1 f W/ p h a s e \n” , P _ i n ) ;

43 printf ( ” \n The t o t a l 3−p ha s e r o t o r po we r i n p u t ( RPI) i s : ” ) ;

44 printf ( ” \n P i n = %. 1 f W\n” , P _ i n _ t o t a l ) ;

46 printf ( ” \n S u b s t i t ut i n g i n Eq .( 9 − 19) , \ n T max = %. 2f l b − f t \ n” , T _ m a x ) ;

47 printf ( ” \n Then , s b = %. 1 f \n a nd S r = %d rpm ”,

s _ b , S _ r ) ;

Scilab code Exa 9.13 calculate starting torque

7 / / E xa mp le 9−138

1011 / / G ive n d at a a s p e r Ex .9 −1012 P = 4 ; / / N umber o f p o l e s i n WRIM13 f = 6 0 ; // F re qu en cy i n Hz14 V = 220 ; // L i n e v o l t a g e i n v o l t

15 V_p = 220 ; // Phase v o l t a g e i n v o l t ( d e l t a

p h a s e19 R_x = 0.7 ; // Added r e s i s t a n c e i n ohm/ p h a se20 X_lr = 1 ; // Locked r o t o r r e a c t a nc e i n ohm21

22 / / C a l c u l a t i o n s23 E_lr = V_p / 4 ; / / L o ck ed−r o t o r v o l t a g e p er p ha se24 S = (1 20 * f) /P ; // Speed i n rpm o f t he r o t a t i n g

26 / / T ot al 3−p ha se r o t o r p ower i n p u t ( RPI ) i n W27 P_in = 3 * ( ( E_lr ) ^2 ) / ( ( R_r ) ^2 + ( X_lr ) ^2 ) *

29 T _ s = 7 .0 4 * ( P _i n /S ); // S t a r t i n g t o rq u e d e ve l op e di n l b − f t

”E x ampl e 9−13 S o l u t i o n : ”) ;

34 printf ( ” \n P i n = %. f W \n” , P _ i n ) ;

35 printf ( ” \n From Eq . ( 9 − 1 9) , s t a r t i n g t or qu e i s : \nT s = %. 2 f l b− f t ” , T _ s ) ;

Scilab code Exa 9.14 calculate full load and starting torques

36 printf ( ” \n

” ) ;

37 printf ( ” \n I 1 (A) \ t \ t I 2 (A) \ t \ t V( v o l t ) ” ) ;

38 printf ( ” \n

” ) ;

39 printf ( ” \n ( 0 . 4 + j 1 6 . 35 ) \ t −(0 + j 1 6 ) \ t \ t ( 12 7+ j 0 ) ” ) ;

40 printf ( ” \n −(0 + j 1 6 ) \ t \ t ( 4 . 6 7 + j 16 . 3 5 ) \ t0 ” ) ;

41 printf ( ” \n

” ) ;

43 A = [ (0.4 + %i * 16.3 5) - %i *16 ; ( -%i *16) (4.67 + %i

* 1 6 .3 5 ) ] ; // M at ri x c o n t a i n i n g a bo ve mesh e qn sa r r a y

44 d e lt a = det ( A ) ; // D et er mi na nt o f A45

46 / / c as e a : S t a t o r a r m a t u r e c ur r e nt I p i n A47 I _p = det ( [ ( 12 7+ %i *0 ) ( -%i * 16 ) ; 0 ( 4. 67 + %i

*1 6.3 5) ] ) / delta ;

48 I _ p_ m = abs ( I _ p ) ; // I p m=m ag ni tu de o f I p i n A49 I _ p_ a = atan ( imag ( I _p ) / real ( I _ p ) ) * 1 8 0 / % p i ; / / I p a =

p h a s e a ng le o f I p i n d e g r e e s50 I_1 = I_p ; // S t at o r a rm at ur e c u r re n t i n A51

52 / / c as e b : R ot o r c ur r e nt I r p e r p h a s e i n A53 I _r = det ( [ ( 0. 4 + %i * 1 6. 35 ) ( 12 7+ % i *0 ) ; ( - %i * 16 )

0 ] ) / delta ;

54 I _ r_ m = abs ( I _ r ) ; // I r m =m ag ni tu de o f I r i n A55 I _ r_ a = atan ( imag ( I _r ) / real ( I _ r ) ) * 1 8 0 / % p i ; // I r a =

p h a s e a ng le o f I r i n d e g r e e s56

57 / / c as e c58 t he ta _1 = I _p _a ; // Motor PF a n g l e i n d e g r e es59 c o s _ t he t a 1 = c o sd ( t h e t a _1 ) ; / / M ot or PF

61 / / c as e d62 I _p = I _p _m ; // S t at o r a rm at u re c u r r e n t i n A63 S PI = V_p * I_p * c os _t he ta 1 ; // S t a t o r Power I n pu t

i n W64

65 / / c as e e66 SCL = ( I_p ) ^2 * R_a ; // S t a t or Copper L os s i n W67

68 / / c as e f 69 / / S u b s c r i p t s 1 and 2 f o r RPI i n d i c a t e s two methods

o f c a l c u l a t i n g RPI

70 RPI_1 = SPI - SCL ; / / R ot or Power I n pu t i n W71 R PI _2 = ( I _r _m ) ^2 * ( R _r / s) ; // R ot or Power I n pu t i n

W72 R P I = R PI _1 ;

74 / / c as e g75 / / S u b s c r i p t s 1 , 2 and 3 f o r RPD i n d i c a t e s t h r e e

m eth od s o f c a l c u l a t i n g RPD76 RPD_1 = RPI * ( 1 - s ) ; // R ot or Power D e ve l op e d i n

W77 R CL = s *( R PI ) ;

// R ot or c o pp er l o s s e s i n W78 RPD_2 = RPI - RCL ; / / R ot or Power D e ve l op e d i n W79 R PD _3 = ( I _r _m ) ^2 * R _r * (( 1 -s ) /s ) ; / / R o to r P ower

D e ve l op e d i n W80 RPD = RPD_1 ;

82 / / c as e h83 P_r = P _r_ to ta l / 3 ; // R o ta t i on a l L o ss e s p er p ha se

i n W84 P_o = RPD - P_r ; // R ot or power p er p ha se i n W85 P_ to = 3* P_o ; // T ot al r o t o r power i n W

8687 / / c as e i88 T = 7 .0 4 * ( P_ to / S_r ) ; // T ot al 3−p ha se t or q u e i n l b

− f t89

90 / / c as e j

91 P _t = P_to ;92 h p = P_t / 746 ; // O ut pu t h o r s e p o w e r93

94 / / c as e k95 P_in = SPI ; // I np ut power t o s t a t o r i n W96 eta = P_o / P_in * 100 ; // Motor e f f i c i e n c y a t

r a t ed l o ad97

100 printf ( ” \n P r e l i mi n a r y c a l c u l a t i o n s \ n” ) ;

101 printf ( ” \n S l i p : s = %. 2 f \n R r / s = %. 2 f ohm \n” ,s , R _ r / s ) ;

103 printf ( ” \n D e t e r m i n a n t = ” ) ; disp ( d e l t a ) ;

105 printf ( ” \n a : S t at o r a rm at ur e c u r re n t : \ n I p i nA = ” ) ; disp ( I _ 1 ) ;

106 printf ( ” \n I p = I 1 = %. 2 f <%. 2 f A \n ” , I _p _m ,

I _p _a ) ;

108 printf (” \n b : Ro to r c u r r e n t p er p ha se : \ n I r i nA = ” ) ; disp ( I _ r ) ;

109 printf ( ” \n I r = I 2 = %. 3 f <%. 2 f A \n ” , I _r _m ,

I _r _a ) ;

111 printf ( ” \n c : Mot or PF : \ n c o s 1 = %. 4 f \n” ,

c o s _ t h e t a 1 ) ;

113 printf ( ” \n d : S t a t or Power I np ut : \ n SPI = %d W\n” , S P I ) ;

115 printf ( ” \n e : S t at o r Copper L os s : \ n SCL = %. f W\n” , S C L ) ;

117 printf ( ” \n f : Ro to r Power I np ut : \ n RPI = %d W(m etho d 1 ) ” , R PI _1 ) ;

118 printf ( ” \n RPI = %. f W ( method 2 ) \n” , R P I _ 2 ) ;

119 printf ( ” \n Note : RPI c a l c u l a t e d by 2nd methods l i g h t l y v a r i e s from t ha t o f ” ) ;

120 printf ( ” \n t e x t b o o k v a l u e b e c a u s e o f non−a pp ro x im a ti on o f I r w h i le ” ) ;

121 printf ( ” \n c a l c u l a t i n g i n s c i l a b . \ n” )

123 printf ( ” \n g : R ot or Power D e ve l op e d : \ n RPD = %.f W \n” , R P D _ 1 ) ;

124 printf ( ” \n Ro to r c o p p e r l o s s : \ n RCL = %d W\n” , R C L ) ;

125 printf ( ” \n RPD = %. f W \n RPD = %d W \n ” ,

R P D _ 2 , R P D _ 3 ) ;126

127 printf ( ” \n h : Ro to r power p er p ha se : \ n P o / =%f W/ ” , P _ o ) ;

128 printf ( ” \n\n T o t a l r o t or power : \ n P t o = %f W\n” , P _ t o ) ;

129 printf ( ” \n Above P o / and P t o v a l u e s a re no ta pp ro xi ma te d w h il e c a l c u l a t i n g i n ” ) ;

130 printf ( ” \n SCILAB . So , t he y v ar y s l i g h t l y fromt e xt b o ok v a l u e s . \ n” ) ;

132 printf ( ” \n i : T o t a l 3−p ha se o ut pu t t o rq u e : \ n T= % . f l b− f t \ n” , T ) ;

134 printf ( ” \n j : Output h o rs e po w er : \n hp = %. 1 f hp \n” , h p ) ;

136 printf ( ” \n k : Motor e f f i c i e n c y a t r at ed l oa d : \ n= %. 1 f p e r c e n t \n” , e t a )

138 printf ( ” \n Power f l o w d ia g ra m ( p e r p h as e ) \n” ) ;

139 printf ( ” \n SPI−−−−−−−−−−> RPI−−−−−−−−−> RPD−−−−−−−−−−> P o ” ) ;

140 printf ( ” \n (%d W) | (%d W) | (%d W) | (%dW) ” , S P I , R P I _ 1 , R P D _ 3 , P _ o ) ;

141 printf ( ” \n | | |

” ) ;

142 printf ( ” \n SCL RCLP r ” ) ;

143 printf ( ” \n (%. f W) (%d W) (%dW) ” , S C L , R C L , P _ r ) ;

Scilab code Exa 9.16 calculate Ism IL Ts and percent IL and percent Ts

7 / / E xa mp le 9−168

11 / / G iv en d a ta12 / / t h r ee −pha se SCIM13 V = 208 ; // Rated v o l t a g e i n v o l t14 P_o = 15 ; // Rat ed p ower i n hp15 I = 4 2 ; // Rated c u r r e nt i n A16 I_st = 252 ; // S t a rt i n g c u r r e n t i n A17 T_st = 120 ; // F ul l −v o lt a g e s t a r t i n g t or qu e i n l b−

f t18 t a p = 6 0* (1 /1 00 ) ; / / T ap pi ng i n % e mp lo ye d by

c o m p e n s a t o r

1920 / / C a l c u l a t i o n s21 / / c as e a22 I_sm = tap * I_st ; // Motor s t a r t i n g c u r r e n t i n A

a t r ed uc ed v o l t a g e

24 / / c as e b25 I_L = tap * I_sm ; // Motor l i n e c u r r e nt i n A(n e g l e c t i n g t a r n s f o r m e r e x c i t i n g

26 // c u r r e nt and l o s s e s )27

28 / / c as e c29 T_s = ( tap ) ^2 * T_st ; // Motor s t a r t i n g t or qu e a t

r ed uc ed v o l t a g e i n l b −f t30

31 / / c as e d32 p er ce nt _I _L = I_L / I_ st * 100 ; // P er ce nt l i n e

c u r r e n t a t s t a r t i n g33

34 / / c as e e35 p er ce nt _T _s t = T_ s / T _s t * 1 00 ; // P e r c e nt m ot or

s t a r t i n g t or qu e36

40 printf ( ” \n a : Motor s t a r t i n g c u r r e nt a t r ed uc ed

v ol t a g e : ”) ;

41 printf ( ” \n I s m = %. 1 f A t o t h e motor . \ n” , I _ s m ) ;

43 printf ( ” \n b : Motor l i n e c u r re n t n e g l e c t i n gt a r n s f o r m e r e x c i t i n g c u r r e n t and l o s s e s : ” ) ;

44 printf ( ” \n I L = %. 2 f A drawn from t h e mai ns . \ n”, I _ L ) ;

46 printf ( ” \n c : Motor s t a r t i n g t or q u e a t r ed uc edv o l t a ge : \ n T s = %. 1 f l b − f t \ n” , T _ s ) ;

48 printf ( ” \n d : P e r c e n t l i n e c ur r e n t a t s t a r t i n g : ” );

49 printf ( ” \n = %. f p er c e n t o f l i n e c ur re nt a t f u l lv o l t a g e . \ n” , p e r c e n t _ I _ L ) ;

51 printf ( ” \n e : P er ce nt motor s t a r t i n g t or qu e : ” ) ;

52 printf ( ” \n = %d p e r c e n t o f s t a r t i n g t o r q u e a tf u l l v o l t a g e . \ n” , p e r c e n t _ T _ s t ) ;

Scilab code Exa 9.17 calculate T s Sr for different V

4 / / 2 nd e d i t i om5

7 / / E xa mp le 9−178

11 / / G iv en d a ta12 / / t h r ee −pha se SCIM

13 V_o = 220 ; // Rated v o l t a g e i n v o l t14 P = 4 ; // Number o f p o l e s i n SCIM15 P_o = 10 ; // Rat ed p ower i n hp16 f = 6 0 ; / / F r e qu e n cy i n Hz ( a ss um e , n o t g i v e n )17 T_o = 30 ; // Rated t o rq u e i n l b− f t18 S _r = 1710 ; // Rated r o t o r s pe ed i n rpm19 V_n1 = 242 ; // I mp re s se d s t a t o r v o l t a ge i n v o l t (

c a s e a )20 V_n2 = 198 ; // I mp re s se d s t a t o r v o l t a ge i n v o l t (

c a s e b )

magn e t i c f i e l d24 / / c as e a : I mp re ss ed s t a t o r v o l t a ge = 242 V

25 s _o = ( S - S_r )/ S ; // Rated s l i p

2627 T_ n1 = T_o * ( V_ n1 / V_o ) ^2 ; // New t o rq u e i n l b− f t28

29 s _n 1 = s _o * ( T _o / T _n 1 ); / / New s l i p30

31 S _r n1 = S *(1 - s_ n1 ) ;

33 / / c as e b : I mp re ss ed s t a t o r v o l t a ge = 198 V34 T_ n2 = T_o * ( V_ n2 / V_o ) ^2 ; // New t o rq u e i n l b− f t35

36 s _n 2 = s _o * ( T _o / T _n 2 ); / / New s l i p

3738 S _r n2 = S *(1 - s_ n2 ) ;

40 / / c as e c41 / / S u bs c r i pt a i n p e r c e n t s l i p and p e rc e n t s p ee d

i n d i c a t e s p ar t a42 p er ce nt _s li p_ a = ( s _o - s _n 1 )/ s_ o * 1 00 ; // P e rc e nt

c h a ng e i n s l i p i n p ar t ( a )43

44 p er ce nt _s pe ed _a = ( S _r n1 - S _r ) / S_ r * 1 00 ; //

P er ce nt c ha ng e i n s pe ed i n p a rt ( a )45

46 / / c as e d47 / / S u bs c r i pt b i n p e r c e n t s l i p and p e rc e n t sp e ed

i n d i c a t e s p ar t b48 p er ce nt _s li p_ b = ( s _n 2 - s _o ) / s_ o * 1 00 ; // P e rc e nt

c h a ng e i n s l i p i n p ar t ( b )49

50 p er ce nt _s pe ed _b = ( S _r - S _r n2 ) / S_ r * 1 00 ; //P er ce nt c ha ng e i n s pe ed i n p a rt ( b )

55 printf ( ” \n a : Rated s l i p : \ n s = %. 2 f \n” , s _ o ) ;

56 printf ( ” \n For i mp re ss ed s t a t o r v o l t a g e = %d V \

n ” , V _ n 1 ) ;

57 printf ( ” \n New t o r q u e : \ n T n = %. 1 f l b − f t \n” , T _ n 1 ) ;

58 printf ( ” \n New s l i p : \ n s n = %f \n ” , s _ n 1 ) ;

59 printf ( ” \n New r o t o r s p e e d : \ n S r = %f rpm \n” , S _ r n 1 ) ;

61 printf ( ” \n b : For i mp re ss ed s t a t o r v o l t a g e = %d V \n ” , V _ n 2 ) ;

66 printf ( ” \n c : P er ce nt c h a ng e i n s l i p i n p ar t ( a ) ” ) ;

67 printf ( ” \n = %. 1 f p er ce n t d e c re as e . \ n” ,

p e r c e n t _ s l i p _ a ) ;

68 printf ( ” \n P e r c e n t c h a ng e i n s pe e d i n p a rt ( a ) ”) ;

69 printf ( ” \n = %. 2 f p e r c e n t i n c r e a s e \n” ,

p e r c e n t _ s p e e d _ a ) ;

71 printf (” \n d : P er ce nt c h ang e i n s l i p i n p ar t ( b ) ”

72 printf ( ” \n = %. 2 f p er ce n t i n c r e a s e . \ n” ,

p e r c e n t _ s l i p _ b ) ;

73 printf ( ” \n P e r c e n t c ha ng e i n s pe e d i n p ar t ( b ) ” ) ;

74 printf ( ” \n = %. 2 f p er ce n t d e cr ea s e \n” ,

p e r c e n t _ s p e e d _ b ) ;

76 printf ( ” \n SLIGHT VARIATIONS IN PERCENT CHANGE INSLIP AND SPEED ARE DUE TO”) ;

77 printf ( ” \n NON−APPROXIMATION OF NEW SLIPS AND NEWSPEEDS CALCULATED IN SCILAB . ” )

Scilab code Exa 9.18 calculate T s Sr for different impressed stator V

31 s _o = ( S - S_r )/ S ; // Rated s l i p

3233 T_ n1 = T_o * ( V_ n1 / V_o ) ^2 ; // New t o rq u e i n l b− f t34

35 s _n 1 = s _o * ( T _o / T _n 1 ) * ( R _r n / R_ ro ) ; // New s l i p36

37 S _r n1 = S *(1 - s_ n1 ) ;

39 / / c as e b : I mp re ss ed s t a t o r v o l t a ge = 208 V40 T_ n2 = T_o * ( V_ n2 / V_o ) ^2 ; // New t o rq u e i n l b− f t41

42 s _n 2 = s _o * ( T _o / T _n 2 ) * ( R _r n / R_ ro ) ; // New s l i p

4344 S _r n2 = S *(1 - s_ n2 ) ;

46 / / c as e c : I mp re ss ed s t a t o r v o l t a ge = 110 V47 T_ n3 = T_o * ( V_ n3 / V_o ) ^2 ; // New t o rq u e i n l b− f t48

49 s _n 3 = s _o * ( T _o / T _n 3 ) * ( R _r n / R_ ro ) ; // New s l i p50

51 S _r n3 = S *(1 - s_ n3 ) ;

56 printf ( ” \n a : Rated s l i p : \ n s = %f \n” , s _ o ) ;

57 printf ( ” \n For i mp re ss ed s t a t o r v o l t a g e = %d V \n ” , V _ n 1 ) ;

6162 printf ( ” \n b : For i mp re ss ed s t a t o r v o l t a g e = %d V \

n ” , V _ n 2 ) ;

67 printf ( ” \n c : For i mp re ss ed s t a t o r v o l t a g e = %d V \n ” , V _ n 3 ) ;

Scilab code Exa 9.19 calculate fcon and Scon

6 // Ch apt e r 9 : POLYPHASE INDUCTION (ASYNCHRONOUS)

DYNAMOS7 / / E xa mp le 9−198

11 / / G iv en d a ta12 P = 8 ; / / N umber o f p o l e s i n WRIM13 f = 6 0 ; // O p e r at i n g f r e q u e n c y o f t h e WRIM i n Hz14 / / / WRIM i s d r i v e n by v a r i a b l e −s p e ed p ri m e m over a s

a f r eq u e nc y c ha ng er15 S _ c on _a 1 = 1 80 0 ; // Speed o f t he c o n ve r t o r i n rpm16 S _ co n_ a2 = 4 50 ; // Speed o f t he c o nv e rt o r i n rpm17

18 f _c on _b 1 = 25 ; // F re qu en cy o f an i n d u c t i o n

c o n v e r t e r i n Hz

19 f _ co n_ b2 = 4 00 ; // F re qu en cy o f an i n d u c t i o nc o n v e r t e r i n Hz20 f _ co n_ b3 = 1 20 ; // F re qu en cy o f an i n d u c t i o n

c o n v e r t e r i n Hz21

25 / / c as e a26 // S u b s c r i pt a1 i n f c o n i n d i c a t e s c as e a 1 s t

f r eq u e cy i n Hz27 f _ c on _ a1 = f * (1 + S _ co n _a 1 / S ) ; // F re qu en cy o f an

i n d uc t i on c o n v e r t er i n Hz28

29 / / S u b s c r i pt a2 i n f c o n i n d i c a t e s c as e a 2 ndf r e qu e n cy i n Hz

30 f _ c on _ a2 = f * (1 - S _ co n _a 2 / S ) ; // F re qu en cy o f ani n d uc t i on c o n v e r t er i n Hz

32 / / c as e b33

/ / S u bs c r i pt b1 i n S−con i n d i c a t e s c as e b 1 s t s pe e do f c o n v e r t er i n rpm34 S _c on_ b1 = ( -1 + f_ con _b 1/ f) * S ; // Speed o f t he

c o n v er t o r i n rpm35

36 / / S u bs c r i pt b2 i n S−con i n d i c a t e s c as e b 2 nd s pe e do f c o n v e r t er i n rpm

37 S _c on_ b2 = ( -1 + f_ con _b 2/ f) * S ; // Speed o f t hec o n v er t o r i n rpm

39 / / S u bs c r i pt b3 i n S−con i n d i c a t e s c as e b 3 rd s pe e d

o f c o n v e r t er i n rpm40 S _c on_ b3 = ( -1 + f_ con _b 3/ f) * S ; // Speed o f t he

c o n v er t o r i n rpm41

46 printf ( ” \n U s in g Eq . ( 9 − 26) , \ n” ) ;

48 printf ( ” \n a : f c o n = %d Hz f o r %d rpm i n o p p o s i t ed i r e c t i o n \ n” ,f_con_a1 ,S_con_a1);

49 printf ( ” \n f c o n = %d Hz f o r %d rpm i n samed i r e c t i o n \ n” ,f_con_a2 ,S_con_a2);

51 printf ( ” \n b : 1 . S c o n = %. f rpm , o r % . f rpm i nsame d i r e c t i o n . \ n” ,S_co n_b1 , abs ( S _ c o n _ b 1 ) ) ;

52 printf ( ” \n 2 . S c o n = %d rpm i n o p po s i t ed i r e c t i o n . \ n” , S _ c o n _ b 2 ) ;

53 printf ( ” \n 3 . S c o n = %d rpm i n o p po s i t ed i r e c t i o n t o r o t a t i n g s t a t o r f l ux . \ n” , S _ c o n _ b 3 ) ;

Chapter 10

SINGLE PHASE MOTORS

Scilab code Exa 10.1 calculate total starting current and PF and compo-nents of Is Ir and phase angle between Is Ir

6 / / C h a p t er 1 0 : SINGLE−PHASE MOTORS7 / / E xa mp le 10−18

11 / / G iv en d a ta12 h p = 0.25 ; // Power r a t i n g o f t he s i n g l e −p h a s e

m oto r i n hp13 V = 110 ; // V ol ta ge r a t i n g o f t h e s i n gl e −p h a s e

m oto r i n V14 I_sw = 4 ; // S t a r t i ng w in di ng c u r re n t15 p hi _I _s w = 15 ; // Ph ase a n g l e i n d e g r e es by wh ich

I sw l a g s b e h i n d V16 I_rw = 6 ; / / Run ning w in d in g c u r r e n t

17 p hi _I _r w = 40 ; // Ph ase a n g l e i n d e g r e es by wh ich

I rw l a g s b e h i n d V18

19 / / C a l c u l a t i o n s20 / / c as e a21 I _s = I_sw * exp ( %i * - p hi _I _s w *( % pi / 1 80 ) ) ; //

s t a r t i n g c ur r e nt i n A22 / / ( %pi / 18 0) f o r d e g r e e s t o r a di a ns c o nv e r s i o n o f

p ha s e a n g l e23 I _ s_ m = abs ( I _ s ) ; // I s m = m agni t ude o f I s i n A24 I _ s_ a = atan ( imag ( I _s ) / real ( I _ s ) ) * 1 8 0 / % p i ; // I s a =

2526 I _r = I_rw * exp ( %i * - p hi _I _r w *( % pi / 1 80 ) ) ; //

r un ni ng c u r r e nt i n A27 I _ r_ m = abs ( I _ r ) ; // I r m = m agni t ude o f I r i n A28 I _ r_ a = atan ( imag ( I _r ) / real ( I _ r ) ) * 1 8 0 / % p i ; // I r a =

30 I_t = I_s + I_r ; // T o t a l s t a r t i n g c u r r e nt i n A31 I _ t_ m = abs ( I _ t ) ; // I t m = m agni t ude o f I t i n A32 I _ t_ a = atan ( imag ( I _t ) / real ( I _ t ) ) * 1 8 0 / % p i ; // I t a =

p h a s e a ng le o f I t i n d e g r e e s33 P o w e r _ fa c t o r = c o sd ( I _ t _ a ) ; // Power f a c t o r34

35 / / c as e b36 I s _ c o s _t h e t a = real ( I _ s ) ; / / Co mpo nent o f t h e

s t a r t i n g w in di ng c u r r e nt i n p ha se37 // w i t h t h e s u p p ly v o l t a g e i n A38

39 / / c as e c40 I r _ s i n _t h e t a = imag ( I _ r ) ; / / Co mpo nent o f t h e

r un ni ng w in di ng c u r r e nt t ha t l a g s

41 / / t h e s up pl y v o l t a g e by 9 0 d e g re e s42

43 / / c as e d44 p ha se = ( p hi _I _r w - p hi _I _s w ) ; // P ha se a n g l e

b et wee n t he s t a r t i n g and r un ni ng

45 // c u r r e n t s i n d e g r e e s

4647 // D is pl ay t h e r e s u l t s48 disp ( ”Example 10−1 S ol u t i o n : ” ) ;

49 printf ( ” \n a : I s = %d <−%d A ” , I _sw , p hi _I _s w ) ;

50 printf ( ” \n I s i n A = ” ) ; disp ( I _ s ) ;

51 printf ( ” \n I r = %d <−%d A ” , I _rw , p hi _I _r w ) ;

52 printf ( ” \n I r i n A = ” ) ; disp ( I _ r ) ;

53 printf ( ” \n I t i n A = ” ) ; disp ( I _ t ) ;

54 printf ( ” \n I t = %. 2 f <% d A ” , I _t _m , I _t _a ) ;

55 printf ( ” \n\n Power f a c t o r = c o s (%d) = %. 3 f l a g g i n g \n” , I _t _a , P o we r _f a ct o r ) ;

5657 printf ( ” \n b : I s ∗ c o s = %. 2 f A ( from a ) \n ” ,

I s _ co s _ t he t a ) ;

59 printf ( ” \n c : ( f ro m a ) , \ n I r ∗ s i n i n A = ” ) ;

disp ( % i * I r _ s i n _ t h e t a ) ;

61 printf ( ” \n d : ( r − s ) = %d d e g r e e s ” , p ha se ) ;

Scilab code Exa 10.2 calculate Ps Pr Pt and motor efficiency

11 / / G ive n d at a a s p e r Ex .10 −1

12 h p = 0.25 ; // Power r a t i n g o f t he s i n g l e −p h a s e

m oto r i n hp13 V = 110 ; // V ol ta ge r a t i n g o f t h e s i n gl e −p h a s em oto r i n V

14 I_s = 4 ; // S t a r t i n g w i nd in g c u r r e nt15 p hi _I _s = 15 ; // Pha se a n g le i n d e g r e es by whi ch

I s l a g s b e h i n d V16 I_r = 6 ; / / Runni ng w i nd i ng c u r r e n t17 p hi _I _r = 40 ; // Pha se a n g le i n d e g r e es by whi ch

I r l a g s b e h i n d V18

20 / / c as e a21 P_s = V * I_ s * c os d( p hi _I _s ) ; // Power d i s s i p a t e d

i n t he s t a r t i n g w i n di ng i n W22

23 / / c as e b24 P_r = V * I_ r * c os d( p hi _I _r ) ; // Power d i s s i p a t e d

i n t he r un ni ng w in di ng i n W25

26 / / c as e c27 P_t = P_s + P_r ; // T ot al i n s t a n t a ne o u s power

d i s s i p a t e d d ur i ng s t a r t i n g i n W28

29 / / c as e d30 P_r_d = P_r ; // T o ta l s t ea d y−s t a t e power d i s s i p a t e d

d u ri n g r un ni ng i n W31

32 / / c as e e33 eta = ( hp * 746 ) / P_r * 100 ; // Motor e f f i c i e n c y

i n p e rc e n t34

36 disp ( ”Example 10−2 S ol u t i o n : ” ) ;37 printf ( ” \n a : Power d i s s i p a t e d i n t he s t a r t i n g

w i n d i n g \n P s = %d W \n” , P _ s ) ;

39 printf ( ” \n b : Power d i s s i p a t e d i n t he r un ni ng

w i n d i n g \n P r = %. 1 f W \n” , P _ r ) ;

4041 printf ( ” \n c : T ot al i n s t a n t an e o us power d i s s i p a t e d

d ur in g s t a r t i n g \ n P t = %. 1 f W \n” , P _ t ) ;

43 printf ( ” \n d : T ot al s te ad y −s t a t e power d i s s i p a t e dd u r in g r u nn i ng \n P r = %. 1 f W \n” , P _r _d ) ;

45 printf ( ” \n e : Motor e f f i c i e n c y \n = %. f p e r c e n t \n” , e t a ) ;

Scilab code Exa 10.3 calculate total starting current and sine of angle be-tween Is Ir

6 / / C h a p t er 1 0 : SINGLE−PHASE MOTORS

7 / / E xa mp le 10−38

11 / / G iv en d a ta12 h p = 0.25 ; // Power r a t i n g o f t he s i n g l e −p h a s e

m oto r i n hp13 V = 110 ; // V ol ta ge r a t i n g o f t h e s i n gl e −p h a s e

m oto r i n V

14 I_sw = 4 ; // S t a r t i ng w in di ng c u r re n t15 p hi _I _s w = 15 ; // Ph ase a n g l e i n d e g r e es by wh ichI sw l a g s b e h i n d V

16 I_rw = 6 ; / / Run ning w in d in g c u r r e n t17 p hi _I _r w = 40 ; // Ph ase a n g l e i n d e g r e es by wh ich

I rw l a g s b e h i n d V

18 / / when t he c a p a c i t o r i s added t o t h e a u x i l i a r ys t a r t i n g w in di ng o f t he motor19 / / o f Ex .1 0 −1 , I s l e a d s V by 42 d eg re es so ,20 p hi _I _s w_ ne w = 4 2 ; // I s l e a d s V by p hi I s w n e w

d e g r e e s21

22 / / C a l c u l a t i o n s23 / / c as e a24 I _s = I_sw * exp ( % i * p h i_ I _s w _n e w * ( %p i / 18 0) ) ; //

s t a r t i n g c ur r e nt i n A25 / / ( %pi / 18 0) f o r d e g r e e s t o r a di a ns c o nv e r s i o n o f

p ha s e a n g l e26 I _ s_ m = abs ( I _ s ) ; // I s m = m agni t ude o f I s i n A27 I _ s_ a = atan ( imag ( I _s ) / real ( I _ s ) ) * 1 8 0 / % p i ; // I s a =

p h a s e a ng le o f I s i n d e g r e es28

29 I _r = I_rw * exp ( %i * - p hi _I _r w *( % pi / 1 80 ) ) ; //r un ni ng c u r r e nt i n A

30 I _ r_ m = abs ( I _ r ) ; // I r m = m agni t ude o f I r i n A31 I _ r_ a = atan ( imag ( I _r ) / real ( I _ r ) ) * 1 8 0 / % p i ; // I r a =

33 I_t = I_s + I_r ; // T o t a l s t a r t i n g c u r r e nt i n A34 I _ t_ m = abs ( I _ t ) ; // I t m = m agni t ude o f I t i n A35 I _ t_ a = atan ( imag ( I _t ) / real ( I _ t ) ) * 1 8 0 / % p i ; // I t a =

p h a s e a ng le o f I t i n d e g r e e s36 P o w e r _ fa c t o r = c o sd ( I _ t _ a ) ; // Power f a c t o r37

38 / / c as e b39 t he ta = ( p hi _I _r w - ( - p hi _I _s w_ ne w ) ) ;

40 s i n _ th e t a = s i nd ( t h e t a ) ; // S i n e o f t he a n gl e be tw e ent h e

41 // s t a r t i n g and r un ni ng c u r r e n t s42 phase = 25 ; // Pha se a n g le b et we en t he s t a r t i n g and

r u n n i n g43 // c u r r e n t s i n d e g r e es ( fr om Ex .1 0 −1)44

45 / / c as e c

46 / / R at i o o f s t a r t i n g t o r q u e s ( c a p ac i t or t or e s i s t a n c e s t a r t )47 r a ti o _T = s in d ( t he ta ) / s in d ( p ha se ) ;

51 printf ( ” \n a : I s = %d <%d A ” , I _s w , p h i_ I _s w _n e w

52 printf ( ” \n I s i n A = ” ) ; disp ( I _ s ) ;

53 printf ( ” \n I r = %d <−%d A ” , I _rw , p hi _I _r w ) ;

54 printf ( ” \n I r i n A = ” ) ; disp ( I _ r ) ;

55 printf ( ” \n I t i n A = ” ) ; disp ( I _ t ) ;56 printf ( ” \n I t = %. 2 f <%. 1 f A ” , I_t_m , I_t_a )

57 printf ( ” \n\n Power f a c t o r = c o s (%. 1 f ) = %. 3 f l a g g i n g \n” , I _t _a , P o we r _f a ct o r ) ;

59 printf ( ” \n b : s i n ( %d − (−%d) ) = s i n ( %d) = %. 4 f \n” ,

phi_I_rw ,phi_I_sw_new ,theta,sin_theta);

61 printf ( ” \n c : The s te ad y s t a t e s t a r t i n g c u rr e n t ha s

b ee n r e d u ce d f ro m ”) ;

62 printf ( ” \n 9 . 7 7 <−30 A t o %. 2 f <%. 1 f A , ” ,I_t_m

, I _t _a ) ;

63 printf ( ” \n and th e power f a c t o r ha s r i s e n f rom0 . 8 6 6 l a g g i n g t o %. 3 f . ” , P o w e r _ f a c t o r ) ;

64 printf ( ” \n The motor d e v el o p s maximum s t a r t i n gt o r q u e ( T = K∗ I b ∗ ∗ c o s ) w i th ” ) ;

65 printf ( ” \n minimum s t a r t i n g c u r r e n t . The r a t i o o f s t a r t i n g t or qu e s ” ) ;

66 printf ( ” \n ( c a pa ci t o r t o r e s i s t a n c e s t a r t ) i s :\n” ) ;

67 printf ( ” \n T c s / T r s = s i n (%d) / s i n (%d) = %. 3 f ” ,t h e t a , p h a s e , r a t i o _ T )

Scilab code Exa 10.4 calculate ratios of T and efficiency and rated PFand hp

11 / / G iv en d a ta ( f ro m T ab l e 10 −2)12 T_r = 1 ; // Rated t or qu e i n l b− f t13 T_s = 4.5 ; // S t a r t i n g t or qu e i n l b − f t ( r fo m L oc ke d

−R o to r D at a )14 T_br = 2.5 ; // Breakdown t o r q ue i n l b−f t ( B re ak do wn

−T o rq u e D at a )15

16 / / R at ed L oa d D at a17 P = 400 ; // Ra ted i n p u t p ower i n W18 V = 115 ; // Rated i np ut v o l t a g e i n v o l t19 I _t = 5.35 ; // Rated i np ut c u r r e n t i n A20 S pe ed = 17 50 ; // Ra ted s p ee d i n rpm21

22 / / C a l c u l a t i o n s23 / / c as e a24 r at io _s _r _T = T_s / T_ r ; // R a t i o o f s t a r t i n g t o

r a t ed t o rq u e25

26 / / c as e b27 r at io _s _b r_ T = T _b r / T _r ; // R a ti o o f br ea kd own t o

r a t ed t o rq u e

2829 / / c as e c30 P_o _hp = 1 / 3 ; // Power o u tp ut i n hp31 P_o = P_o_hp * 746 ; / / Power o u tp ut i n W32 eta = P_o / P * 100 ; // Rated l oa d e f f i c i e n c y33

34 / / c as e d35 S = V * I_t ; // VA r a t i n g o f t he motor36 co s_ th et a = P / S ; / / Ra ted l o a d − power f a c t o r37

38 / / c as e e

39 T = 1 ; // Rated l oa d t or qu e i n l b − f t40 h p = ( T * Sp ee d ) /5 25 2 ; // Ra ted l o a d h o rs e po w er41

45 printf ( ” \n a : T s / T r = %. 1 f \n ” , r a t i o _s _ r _T ) ;

47 printf ( ” \n b : T b r / T r = %. 1 f \n ” , r a t i o _s _ b r_ T ) ;

49 printf (” \n c : Rated l oa d e f f i c i e n c y \n = %. 1 f p e r c e n t \n ” , et a ) ;

51 printf ( ” \n d : Rated l o ad power f a c t o r \n c o s =%.4 f \n ” , c o s _ th e t a ) ;

53 printf ( ” \n e : Ra ted l o a d h o rs e po w er \n hp = %. 4 f hp ” , h p ) ;

Chapter 11

SPECIALIZED DYNAMOS

Scilab code Exa 11.1 calculate S V P T A and B from torque speed rela-tions fig

6 // Ch ap te r 1 1 : SPECIALIZED DYNAMOS7 / / E xa mp le 11−18

11 / / G iv en d a ta12 / / T o rq u e − sp ee d r e l a t i o n s shown i n F ig . 11 −3 b f o r a

d c s e r v o mo t o r .13

14 / / C a l c u l a t i o n s15 / / c as e a16 / / E x t r a p ol a ti n g t o l oa d l i n e p oi nt x ,17 S = 800 ; // Motor s pe ed a t p o i n t x18 V = 6 0 ; // Armature v o l t a g e i n v o l t a t p o in t x

20 / / c as e b21 / / At s t a n d s t i l l , 60 V y i e l d s 4 . 5 l b − f t o f s t a r t i n gt o r q u e

22 T = 4.5 ;

24 / / c as e c25 P _ c = ( T *S ) /5 25 2 ; // Power d e l i v e r e d t o t he l oa d i n

hp ( from c a s e a c o n d i t i o n s )26 P _ c_ wa tt = P_c * 746 ; / / P c i n W27 / / c as e d28 // At p o i n t o :

29 T_d = 1.1 ; // S t a r t i n g t or qu e i n l b − f t ( s u b s c r i p t di n d i c a t e s c as e d ) and

30 S_d = 410 ; // Motor s pe ed a t p o in t a t p o in t o31

32 / / c as e e33 // At p o in t w :34 T_e = 2.4 ; // S t a r t i n g t or qu e i n l b − f t ( s u b s c r i p t e

i n d i c a t e s c a se e ) and35 S_e = 900 ; // Motor s pe ed a t p o in t a t p o in t w36

37 / / c as e f 38 P _d = ( T _d * S _d ) / 52 52 ; // Power d e l i v e r e d t o t he

l oa d i n hp ( from c a se d c o n d i t i o ns )39 P _ d_ wa tt = P_d * 746 ; / / P d i n W40

41 / / c as e g42 P _f = ( T _e * S _e ) / 52 52 ; // Power d e l i v e r e d t o t he

l oa d i n hp ( from c a se f c o n d i t i o n s )43 P _ f_ wa tt = P_f * 746 ; / / P f i n W44

45 / / c as e h

46 // Upper l i m i t o f power r a n ge s A a nd B a r e :47 A = 6 5 ; // Upper l i m i t o f power r an ge A i n W48 B = 305 ; // Upper l i m i t o f power r an ge B i n W49

51 disp ( ”Example 11−1 S ol u t i o n : ” ) ;

5253 printf ( ” \n a : E x t r a p ol a ti n g t o l oa d l i n e p oi nt x , \ n

S = %d rpm ” , S ) ;

54 printf ( ” \n Load l i n e v o l t a g e i s %d V \n” , V ) ;

56 printf ( ” \n b : At s t a n d s t i l l , %d V y i e l d s T = %. 1 f l b − f t o f s t a r t i n g t o rq ue \n” , V , T ) ;

58 printf ( ” \n c : Power d e l i v e r e d t o t h e l oa d i n hp (from c a se a c o n d i t i o n s ) ” ) ;

59 printf ( ” \n P = %. 4 f hp = %d W \n” , P _ c , P _ c _ w a t t ) ;

6061 printf ( ” \n d : At p o i n t o : \ n T = %. 1 f l b −f t and S

= %d rpm \n” , T _ d , S _ d ) ;

63 printf ( ” \n e : At p o in t w : \ n T = %. 1 f l b −f t and S= %d rpm \n” , T _ e , S _ e ) ;

65 printf ( ” \n f : P = %. 4 f hp = %. 1 f W \n ” , P _ d ,

P _ d _ w a t t ) ;

67 printf (” \n g : P = %. 4 f hp = % . f W \n”

, P _ f , P _ f _ w a t t

69 printf ( ” \n h : A = %d W and B = %d W ”, A , B ) ;

Scilab code Exa 11.2 calculate stepping angle

6 // Ch ap te r 1 1 : SPECIALIZED DYNAMOS

7 / / E xa mp le 11−2

c o n s o l e .10

11 / / G iv en d a ta12 / / VR s t e p p e r m ot or13 n = 3 ; // Number o f s t a c k s o r p ha s es14 P_a = 16 ; // Number o f r o t o r t e et h ( s u b s c r i p t a

i n d i c a t e s c as e a )15 / / PM s t e p p e r16 P_b = 24 ; // Number o f p o l e s ( s u b s c r i p t b i n d i c a t e s

c a s e b )17

18 / / C a l c u l a t i o n s19 / / c as e a20 a lp ha _a = 3 60 / ( n * P_ a ); // S te pp in g a n gl e i n

d e gr e e s p er s t ep21

22 a lp ha _b = 3 60 / ( n * P_ b ); // S te pp in g a n gl e i nd e gr e e s p er s t ep

26 printf ( ” \n a : a lp ha = %. 1 f d e g r ee s / s t e p \n ” ,

a l ph a _a ) ;

28 printf ( ” \n b : a lp h a = %. 1 f d e g r ee s / s t e p \n ” ,

a l ph a _b ) ;

Scilab code Exa 11.3 calculate stepping length

LIM i n m e te r

13 f = 6 0 ; // F re qu en cy a p p l i e d t o t h e p ri ma ry LIM i nHz14

15 / / C a l c u l a t i o n16 v_s = 2 * f * tou ; // S yn ch ro no us v e l o c i t y i n m et er

/ s e c o n d17

18 / / D is pl ay t h e r e s u l t19 disp ( ”Example 11−4 S ol u t i o n : ” ) ;

20 printf ( ” \n S y nc h ro no us v e l o c i t y : \n v s = %d m/ s ”, v _ s ) ;

Scilab code Exa 11.5 calculate slip of DSLIM

6 // Ch ap te r 1 1 : SPECIALIZED DYNAMOS7 / / E xa mp le 11−58

11 / / G iv en d a ta12 v_s = 12 ; // S yn ch ro no us v e l o c i t y i n m et er / s e co nd13 v = 1 0 ; // S ec on d ar y s h e e t i n Ex .11 −4 moves a t a

l i n e a r v e l o c i t y i n m/ s

1415 / / C a l c u l a t i o n16 s = ( v_s - v )/ v_s ; // S l i p o f t h e DSLIM17

19 disp ( ”Example 11−5 S ol u t i o n : ” ) ; disp ( ”From Eq

. ( 1 1 − 5 ) ” )20 printf ( ” \n S l i p o f t he DSLIM : \n s = %. 3 f ” , s ) ;

Chapter 12

POWER ENERGY AND

EFFICIENCY RELATIONS

OF DC AND AC DYNAMOS

Scilab code Exa 12.1 Pr Ia efficiency

6 // Ch apt e r 1 2 : POWER,ENERGY,AND EFFICIENCY RELATIONSOF DC AND AC DYNAMOS

7 / / E xa mp le 12−18

11 / / G iv en d a ta12 P = 10000 ; // Power r a t i n g o f t he s hu nt g e n er a t or

i n W13 V = 230 ; // V ol ta ge r a t i n g o f t he s h u n t g e n e ra t o r i n

v o l t

14 S = 1750 ; // Sp eed i n rpm o f t he s hu nt g e n e r a t or

15 / / S hu nt g e n e r a t o r was m ade t o r un a s a m oto r16 V_a = 245 ; // V ol ta ge a c r o s s a rm at ur e i n v o l t17 I_a = 2 ; // Armature c u r r e nt i n A18 R_f = 230 ; // F i el d r e s i s t a n c e i n ohm19 R_a = 0.2 ; // Armature r e s i s t a n c e20

21 / / C a l c u l a t i o n s22 / / c as e a23 R ot at io na l_ lo ss es = ( V _a * I _a ) - ( I_ a ^2 * R _a ) ; //

R o t a t i o n a l l o s s e s i n W a t f u l l l oa d24

25 / / c as e b26 V_t = V ;

27 / / At r a te d l oa d28 I_L = P / V_t ; // L i ne c u r r e n t i n A29 I_f = V / R_f ; // F i e l d c ur r e nt i n A30 I a = I_f + I_L ; // Armature c u r r e nt i n A31

32 a rm at ur e_ lo ss = ( Ia ^2 * R _a ) ; // F u ll −l o a d a r ma t ur el o s s i n W

33 V_f = V ; // F i e l d v o l t a g e i n v o l t34 f ie ld _l os s = V _f * I _f ;

// F u ll −l oa d f i e l d l o s s i n W35

36 / / c as e c37 //38 e ta = P / ( P + R ot at io na l_ lo ss es + ( a r ma tu re _l os s +

f ie ld _l os s ) ) * 100 ;

43 printf ( ” \n a : R o ta t i on a l l o s s e s a t f u l l l oa d = %. 1 f

W \n” , R o t a t i o n a l _ l o s s e s ) ;44

45 printf ( ” \n b : At t he r a t ed l oa d , \ n I L = %. 1 f A\n I a = %. 1 f A\n” , I _ L , I a ) ;

46 printf ( ” \n F u l l −l oa d a r m a t u r e l o s s : \ n ( I a

ˆ 2 ) ∗ R a = %. f W \n” , a r m a t u r e _ l o s s ) ;

47 printf ( ” \n F u l l −l oa d f i e l d l o s s : \ n V f ∗ I f =% . f W \n” , f i e l d _ l o s s ) ;

49 printf ( ” \n c : E f f i c i e n c y o f t h e g e n e r a t or a t r at edl o a d ( f u l l −l o a d i n t h i s Ex . ) : ” ) ;

50 printf ( ” \n = %. 1 f p e r c e n t ” , e t a ) ;

Scilab code Exa 12.2 efficiency at different LF

7 / / E xa mp le 12−28

c o n s o l e .10

11 / / G iv en d a ta12 / / d a ta f ro m Ex .1 2−113 P = 10000 ; // Power r a t i n g o f t he s hu nt g e n er a t or

v o l t15 S = 1750 ; // Sp eed i n rpm o f t he s hu nt g e n e r a t or16

17 / / ( S o l u t i o n s f ro m E xample 12−1 )18 R o t a t i o na l _ l o ss e s = 4 8 9. 2 // R ot at i o n a l l o s s e s a tf u l l l o a d i n W

19 a r m a tu r e_ l os s = 3 96 ; // F u ll −l oa d a rm at ur e l o s s i nW

20 f ie ld _l os s = 2 30 ; // F u ll −l oa d f i e l d l o s s i n W

2122 / / c as e a23 x 1 = ( 1/ 4) ; // F ra ct io n o f f u l l −l o a d24 // S u b s c r i pt a f o r e t a i n d i c a t e s c as e a25 e ta _a = ( P* x1 ) / ( ( P* x1 ) + R ot at io na l_ lo ss es + (

a r ma t ur e _l o ss * ( x 1 ^2 ) + f ie l d_ l os s ) ) * 1 00 ;

27 / / c as e b28 x 2 = ( 1/ 2) ; // F ra ct io n o f f u l l −l o a d29 // S u b s c r i pt b f o r e ta i n d i c a t e s c as e b30 e ta _b = ( P* x2 ) / ( ( P* x2 ) + R ot at io na l_ lo ss es + (

a r ma t ur e _l o ss * ( x 2 ^2 ) + f ie l d_ l os s ) ) * 1 00 ;31

32 / / c as e c33 x 3 = ( 3/ 4) ; // F ra ct io n o f f u l l −l o a d34 // S u b s c r i pt c f o r e ta i n d i c a t e s c as e c35 e ta _c = ( P* x3 ) / ( ( P* x3 ) + R ot at io na l_ lo ss es + (

37 / / c as e d38 x 4 = ( 5/ 4) ; // F ra ct io n o f f u l l −l o a d39

// S u b s c r i pt d f o r e ta i n d i c a t e s c as e d40 e ta _d = ( P* x4 ) / ( ( P* x4 ) + R ot at io na l_ lo ss es + (

45 printf ( ” \n I f x i s t h e f r a c t i o n o f f u l l −l o a d ,t h e n \n ” ) ;

46 printf ( ” \n a : E f f i c i e n c y o f g e ne r a to r when x = %. 2 f ” , x1 ) ;

47 printf ( ” \n = %. 1 f p e r c e n t \n ” , e t a _ a ) ;48

49 printf ( ” \n b : E f f i c i e n c y o f g e n er a t or when x = %. 2 f ” , x2 ) ;

50 printf ( ” \n = %. 1 f p e r c e n t \n ” , e t a _ b ) ;

52 printf ( ” \n c : E f f i c i e n c y o f g e n er a t or when x = %. 2 f ” , x3 ) ;

53 printf ( ” \n = %. 1 f p e r c e n t \n ” , e t a _ c ) ;

55 printf ( ” \n d : E f f i c i e n c y o f g e n er a t or when x = %. 2 f ” , x4 ) ;

56 printf ( ” \n = %. 1 f p e r c e n t \n ” , e t a _ d ) ;

Scilab code Exa 12.3 field current Ec Pf

7 / / E xa mp le 12−38

11 / / G iv en d a ta12 V = 240 ; // V ol ta ge r a t i n g o f t he dc s hu nt motor i n

v o l t13 P_hp = 25 ; // Power r a t i n g o f t he dc s hu nt motor i n

hp14 S = 1800 ; // Sp eed i n rpm o f t he s hu nt g e n e r a t or15 I_L = 89 ; // F ul l −l oa d l i n e c u r r e n t

16 R _a = 0.05 ; // Armature r e s i s t a n c e i n ohm17 R_f = 120 ; // F i el d r e s i s t a n c e i n ohm18

21 V_f = V ; // F i e l d v o l t a g e i n v o l t

22 I_f = V_f / R_f ; // F i e l d c ur r e nt i n A23 I _a = I _L - I _f ; // Armature c u r r e n t i n A24 V_a = V ;

25 E_c = V_a - I_a * R_a ; // Armature v o l t a g e t o bea p p l i e d t o t h e m oto r w hen m oto r

26 / / i s run l i g h t a t 180 0 rpm d ur in g s t ra y power t e s t27

28 / / c as e b29 I a = 4.2 ; // Arm at ure c u r r e n t i n A p ro d uc ed by E c30 V a = E_c ; // Armature v o l t a g e i n v o l t31 P_r = Va *Ia ; // S t ra y po wer i n W , when E c p r o du c e s

I a = 4 . 2 A a t s pe ed o f 18 00 rpm32

36 printf ( ” \n a : F i e l d c ur r e nt : \ n I f = %d A \n ” ,

I _f ) ;

37 printf ( ” \n Armature c u r r en t : \ n I a = %d A \n” , I_ a ) ;

38 printf ( ” \n Armature v ol t a g e t o be a pp l i e d t o th e

m ot or when m ot or i s r un ”) ;

39 printf ( ” \n l i g h t a t %d rpm du ri ng s t r a y p owert e s t : \ n ” , S ) ;

40 printf ( ” \n E c = %. 2 f V \n ” , E_ c ) ;

42 printf ( ” \n b : S tr a y power : \ n P r = %. 1 f W ” ,P_r

Scilab code Exa 12.4 Pr variable losses efficiency table

4 / / 2 nd e d i t i om

56 // Ch apt e r 1 2 : POWER,ENERGY,AND EFFICIENCY RELATIONS

OF DC AND AC DYNAMOS7 / / E xa mp le 12−48

11 / / G iv en d a ta12 V = 600 ; // V o lt ag e r a t i n g o f t he compound motor i n

v o l t

13 P_hp = 150 ; // Power r a t i n g o f t h e compound m ot ori n hp

14 I_L = 205 ; // F u ll −l oa d r at ed l i n e c u r r e nt i n A15 S = 1500 ; // F ul l −l o a d S pe ed i n rpm o f t h e compound

g e n e r a t o r16 R_sh = 300 ; / / Sh un t f i e l d r e s i s t a n c e i n ohm17 R _a = 0.05 ; // Armature r e s i s t a n c e i n ohm18 R_s = 0.1 ; // S e r i e s f i e l d r e s i s t a n c e i n ohm19 V_a = 570 ; // A p pl ie d v o l t a ge i n v o l t20 I_a = 6 ; // Armature c u r r e nt i n A21 S _o = 1800 ;

/ / No−l o a d S pe ed i n rpm o f t h e compoundg e n e r a t o r22

23 / / C a l c u l a t i o n s24 / / c as e a25 R o t _ lo s se s = V _a * I _a ; // R ot at i o na l l o s s e s i n W26 // I f x i s f r a c t i o n o f f u l l − l o a d27 x 1 = ( 1/ 4) ;

28 S_1 = S_o - 300* x1 ; // Sp eed a t 1 /4 l o ad29 R o t _ l o ss e s _ S _1 = ( S _ 1 / S ) * R o t_ l o s se s ; // R o t a t io n a l

l o s s e s i n W a t s p e e d S 1

3031 x 2 = ( 1/ 2) ;

32 S_2 = S_o - 300* x2 ; // Sp eed a t 1 /2 l o ad33 R o t _ l o ss e s _ S_ 2 = ( S _ 2 / S ) * R o t_ l o s se s ; // R o t a t io n a l

35 x 3 = ( 3/ 4) ;36 S_3 = S_o - 300* x3 ; // Sp eed a t 3 /4 l o ad37 R o t _ l o ss e s _ S_ 3 = ( S _ 3 / S ) * R o t_ l o s se s ; // R o t a t io n a l

39 x 4 = ( 5/ 4) ;

40 S_4 = S_o - 300* x4 ; // Sp eed a t 5 /4 l o ad41 R o t _ l o ss e s _ S_ 4 = ( S _ 4 / S ) * R o t_ l o s se s ; // R o t a t io n a l

43 / / c as e b

44 I_sh = V / R_sh ; // F ul l −l o a d s hu nt f i e l d c u r r e n ti n A

45 I a = I_L - I_sh ; // F ul l −l oa d a rm at u re c u r r e nt i n A46 F L _v a ri a bl e _l o ss = ( I a ^2 ) *( R _a + R _s ) ; // F u ll −l o a d

v a r i a b l e e l e c t r i c l o s s e s i n W47

48 x 1 _v a ri a bl e _l o ss = F L _v a ri a bl e _l o ss * ( x 1 ) ^2 ; //V a r i a b l e l o s s e s a t 1 /4 l oa d

53 / / c as e c54 // E f f i c i e n c y o f motor = ( I np ut − l o s s e s ) / I n pu t55 // wh ere I np ut = v o l t s ∗ ampe r e s ∗ l o a d f r a c t i o n56 // L o s s e s = f i e l d l o s s + r o t a t i o n a l l o s s e s +

v a r i a b l e e l e c t r i c l o s s e s57 / / I n pu t

58 I np ut_ FL = V * I_L ; // I np ut i n W at f u l l l o ad59 I np ut_ x1 = V * I_L * x1 ; // I np ut i n W a t 1/4 l oa d60 I np ut_ x2 = V * I_L * x2 ; // I np ut i n W a t 1/2 l oa d61 I np ut_ x3 = V * I_L * x3 ; // I np ut i n W a t 3/4 l oa d62 I np ut_ x4 = V * I_L * x4 ; // I np ut i n W a t 5/4 l oa d

64 F ie ld _l os s = V * I _s h // F i e l d l o s s f o r e a c h o f t h ec o n di t i o n s o f l oa d65

66 / / R ot at i o na l l o s s e s a re c a l c u l a t e d i n p ar t a w h il ev a r i a b l e e l e c t r i c l o s s e s i n p a rt b

68 // T o ta l l o s s e s69 L o s s es _ FL = F i el d _l o ss + R o t_ l os s es +

F L _ v ar i a b le _ l o s s ; / / T o ta l l o s s e s f o r f u l l l oa d70 L o s s es _ 1 = F i el d _l o ss + R o t_ l os s es _ S_ 1 +

x 1 _ v ar i a b le _ l o s s ; // T o t a l l o s s e s f o r 1/4 l oa d

71 L o s s es _ 2 = F i el d _l o ss + R o t_ l os s es _ S_ 2 +x 2 _ v ar i a b le _ l o s s ; // T o t a l l o s s e s f o r 1/2 l oa d

72 L o s s es _ 3 = F i el d _l o ss + R o t_ l os s es _ S_ 3 +

x 3 _ v ar i a b le _ l o s s ; // T o t a l l o s s e s f o r 3/4 l oa d73 L o s s es _ 4 = F i el d _l o ss + R o t_ l os s es _ S_ 4 +

x 4 _ v ar i a b le _ l o s s ; // T o t a l l o s s e s f o r 5/4 l oa d74

75 // E f f i c i e n c y76 e ta _F L = ( ( I np ut _F L - L os se s_ FL ) / I np ut _F L ) ; //

E f f i c i e n c y f o r 1/4 l oa d77 e ta _1 = ( ( I np ut _x 1 - L os se s_ 1 ) / I np ut _x 1 ) ;

//E f f i c i e n c y f o r 1/4 l oa d78 e ta _2 = ( ( I np ut _x 2 - L os se s_ 2 ) / I np ut _x 2 ) ; //

E f f i c i e n c y f o r 1/2 l oa d79 e ta _3 = ( ( I np ut _x 3 - L os se s_ 3 ) / I np ut _x 3 ) ; //

E f f i c i e n c y f o r 3/4 l oa d80 e ta _4 = ( ( I np ut _x 4 - L os se s_ 4 ) / I np ut _x 4 ) ; //

E f f i c i e n c y f o r 5/4 l oa d81

8485 printf ( ” \n a : R o t a t i o n a l l o s s = %d W a t %d rpm (

r a t e d l o a d ) \n” ,Rot_losses ,S);

86 printf ( ” \n Speed a t %. 2 f l o a d = %d rpm ” , x1 ,

S _1 ) ;

87 printf ( ” \n R ot at i o na l l o s s a t %d rpm = %d W \n ”

, S _1 , R ot _l os se s_ S_ 1 ) ;88

S _2 ) ;

90 printf ( ” \n R ot at i o na l l o s s a t %d rpm = %d W \n ”, S _2 , R ot _l os se s_ S_ 2 ) ;

S _3 ) ;

S _4 ) ;

98 printf ( ” \n b : F ul l −l oa d v a r i a b l e l o s s = %d W\n ” ,

F L _ v ar i a b le _ l o s s ) ;

99 printf ( ” \n V a r i a b l e l o s s e s , ” ) ;

100 printf ( ” \n a t %. 2 f l o a d = %. 2 f W ” , x1 ,

x 1 _ v ar i a b le _ l o s s ) ;

x 2 _ v ar i a b le _ l o s s ) ;

x 3 _ v ar i a b le _ l o s s ) ;

103 printf ( ” \n a t %. 2 f l o a d = %. 2 f W \n ” , x4 ,

x 4 _ v ar i a b le _ l o s s ) ;

105 printf ( ” \n c : E f f i c i e n c y o f motor = ( I np ut − l o s s e s) / I n pu t ” ) ;

106 printf ( ” \n wher e \n I n p u t = v o l t s ∗ ampe r e s ∗

l o a d f r a c t i o n ” ) ;107 printf ( ” \n L o s s e s = f i e l d l o s s + r o t a t i o n a l

l o s s e s + v a r i a b l e e l e c t r i c l o s s e s ” ) ;

108 printf ( ” \n Input , \ n a t %. 2 f l o a d = %d W ” , x1

, I np ut _x 1 ) ;

109 printf ( ” \n a t %. 2 f l o a d = %d W ” , x2 , I np ut _x 2 )

;110 printf ( ” \n a t %. 2 f l o a d = %d W ” , x3 , I np ut _x 3 )

111 printf ( ” \n a t f u l l l o a d = %d W ” , I np ut _F L ) ;

112 printf ( ” \n a t %. 2 f l o a d = %d W \n ” , x4 ,

I n pu t _x 4 ) ;

114 printf ( ” \n F i e l d l o s s f o r ea c h o f th e c o n di t i on so f l o a d = %d W \n” , F i e l d _ l o s s ) ;

115 printf ( ” \n R o t a t i o n a l l o s s e s a r e c a l c u l a t e d i np ar t a w hi le v a r i a b l e ” ) ;

116 printf ( ” \n e l e c t r i c l o s s e s i n p a r t b \n” ) ;117

118 printf ( ” \n E f f i c i e n c y a t %. 2 f l o a d = %f = %. 1 f p e rc e n t ” , x 1 , e t a _ 1 , e t a _ 1 * 1 0 0 ) ;

121 printf ( ” \n E f f i c i e n c y a t f u l l l oa d = %f = %. 1 f p e rc e n t ” , e t a _ F L , e t a _ F L * 1 0 0 ) ;

122 printf (” \n E f f i c i e n c y a t %. 2 f l o a d = %f = %. 1 f p e r c e n t \n” , x 4 , e t a _ 4 , e t a _ 4 * 1 0 0 ) ;

124 printf ( ” \n d :

” ) ;

125 printf ( ” \n Item \ t \ t \ t At 1/4 l oa d \ t A t 1 / 2l o a d \ t At 3/4 l oa d \ t A t F u l l −l o a d \ t A t 5 / 4

l o a d ” ) ;

126 printf ( ” \n

” ) ;127 printf ( ” \n I np ut ( w a tt s ) \ t \ t %d \ t \ t %d \ t \ t %d \

t \ t %d \ t % d ” ,Inpu t_x1 ,I nput_x2 ,Input_x3 ,

Input_FL ,In put_x4 );

128 printf ( ” \n\n F ie l d l o s s ( w a t t s ) \ t \ t %d \ t \ t %d \ t

\ t %d \ t \ t %d \ t \ t % d ” ,Field_loss ,Field_loss ,

Field_loss ,Field_loss ,F ield_loss );129 printf ( ” \n\n R o t a t i o n a l l o s s e s ” ) ;

130 printf ( ” \n from p ar t ( a ) ( w at ts ) \ t \ t %d \ t \ t %d \ t\ t %d \ t \ t %d \ t \ t % d ” ,Rot_losses _S_1 ,

Rot_losses_S_2 ,Rot_l osses_S_3 ,Rot_losses ,

R o t _ l o s s e s _ S _ 4 ) ;

131 printf ( ” \n\n V a ri a bl e e l e c t r i c l o s s e s ” ) ;

132 printf ( ” \n from p ar t ( b ) ( w at ts ) \ t \ t %. 2 f \ t %. 2 f \ t %. 2 f \ t %. 2 f \ t %. 2 f ” ,x1_va riable_loss ,

x2_variable_lo ss ,x 3_variable_loss ,

F L _ v a r i a b le _ l o s s , x 4 _ v a r i a b l e _ l o s s ) ;

133 printf ( ” \n\n T o t a l l o s s e s ( w a t t s ) \ t \ t %. 2 f \ t % . 2f \ t %. 2 f \ t %. 2 f \ t %. 2 f ” ,Los ses_1 ,L osses_2 ,

Losses_3 ,Losses_FL ,Losses_4 );

134 printf ( ” \n

” ) ;

135 printf ( ” \n E f f i c i e n c y ( p e r c e n t ) \ t %. 1 f \ t \ t %. 1 f \ t \ t %. 1 f \ t \ t %. 1 f \ t \ t %. 1 f ” , e t a _ 1 * 1 0 0 ,

e t a _ 2 * 1 0 0 , e t a _ 3 * 1 0 0 , e t a _ F L * 1 0 0 , e t a _ 4 * 1 0 0 ) ;

136 printf ( ” \n

” ) ;

Scilab code Exa 12.5 Ia LF max efficiency LF

4 / / 2 nd e d i t i om5

7 / / E xa mp le 12−5

11 / / G iv en d a ta12 P = 10000 ; // Power r a t i n g o f t he s hu nt g e n er a t or

v o l t14 S = 1750 ; // Sp eed i n rpm o f t he s hu nt g e n e r a t or15 R_a = 0.2 ; // Armature r e s i s t a n c e16 / / C a l c u l a t e d v a l u e s f ro m Ex .12 −1

17 P_r = 489.2 ; // Shunt g e ne r a t or r o t a t i o n a l l o s s e si n W

18 Vf_If = 230 ; // Shunt f i e l d c i r c u i t l o s s i n W19 I _a _r at ed = 4 4. 5 ; // Rated a rm at ur e c u r r e nt i n A20

21 / / C a l c u l a t i o n s22 / / c as e a23 I _a = sqrt ( ( Vf_If + P_r ) / R_a ) ; / / A r ma t ur e

c u r r e nt i n A f o r max . e f f i c i e n c y24

25 / / c as e b26 LF = I_a / I _a_ ra ted ; // Load f r a c t i o n

27 L F_ pe rc en t = LF * 10 0 ; // Load f r a c t i o n i n p e r c e nt28

29 / / c as e c30 P _k = Vf_If + P_r ;

31 e ta _m ax = ( P* LF ) /( ( P* LF ) + ( V f_ If + P_r ) + P_k ) *

100; / / Maximum e f f i c i e n c y32

33 / / c as e d34 / / s u b s c r i p t d f o r LF i n d i c a t e s c as e d

35 L F _d = sqrt ( P _ k / ( I _ a _r a t ed ^ 2* R _ a ) ) ; / / L oa df r a c t i o n from f i x e d l o s s e s and r at ed v a r i a b l el o s s e s

38 disp ( ”Example 12−5 S ol u t i o n : ” ) ;

3940 printf ( ” \n a : Armature c u r r e nt f o r max . e f f i c i e n c y

: \ n I a = %. f A \n” , I _ a ) ;

42 printf ( ” \n b : Load f r a c t i o n : \ n L . F . = %. 1 f p e r c e n t = %. 3 f ∗ r a t e d \n” ,LF_percent ,LF);

44 printf ( ” \n c : Maximum e f i i c i e n c y : \ n = %. 2 f p e r c e n t \n” , e t a _ m a x ) ;

46 printf ( ” \n d : Load f r a c t i o n fr om f i x e d l o s s e s and

r at ed v a r i a b l e l o s s e s : ” ) ;47 printf ( ” \n L . F . = %. 3 f ∗ r a t e d ” , L F _ d ) ;

Scilab code Exa 12.6 Pd Pr efficiency

4 / / 2 nd e d i t i om5

7 / / E xa mp le 12−68

12 V = 240 ; // V ol ta ge r a t i n g o f dc s hu nt motor i nv o l t13 P_hp = 5 ; // Power r a t i n g o f dc s hu nt motor i n hp14 S = 1100 ; // Sp eed i n rpm o f t he dc s hu nt motor15 R_a = 0.4 ; // Armture r e s i s t a n c e i n ohm

16 R_f = 240 ; // F i el d r e s i s t a n c e i n ohm

17 I_L = 20 ; // Rated l i n e c u r r e n t i n A18

19 / / C a l c u l a t i o n s20 / / P r e l i m i na r y c a l c u l a t i o n s21 V_f = V ; / / V o lt ag e a c r o s s f i e l d w in di ng i n v o l t22 I_f = V_f / R_f ; // F i e l d c ur r e nt i n A23 I_a = I_L - I_f ; // Arma tu re c u r r e n t i n A24 P_o = P_hp * 746 ; // Power r a t i n g o f dc s hu nt motor

i n W25 V_a = V ; // V ol ta ge a c r o s s a rm at u re i n v o l t26 E _c _f l = V_a - I_ a* R_a ; / / b ac k EMF i n v o l t

2728 / / c as e a29 E _c = E _c _f l ;

30 P_d = E_c * I_a ; / / Power d e v el o p ed by t h e a rm at ur ei n W

32 / / c as e b33 P_r = P_d - P_o ; // F ul l −l o a d r o t a t i o n a l l o s s e s i n

35 / / c as e c36 P_ in = V * I_L ; / / I np ut power i n W

37 e ta = ( P _o / P _i n ) *1 00 ; // F ul l −l oa d e f f i c i e n c y38

42 printf ( ” \n P r el i mi n ar y c a l c u l a t i o n s u s in g n am ep la ted a t a : ” ) ;

43 printf ( ” \n F i e l d c ur r e nt : I f = %d A \n ” , I _ f ) ;

44 printf ( ” \n Armature c u r r e n t : I a = %d A \n ” , I _ a ) ;

45 printf ( ” \n P o = %d W ” , P_ o ) ;46 printf ( ” \n E c ( f l ) = %. 1 f V \n” , E _ c _ f l ) ;

48 printf ( ” \n a : Power d e v el o p e d by t h e a rm at ur e : \ nP d = %. 1 f W \n” , P _ d ) ;

50 printf ( ” \n b : F ul l −l o a d r o t a t i o n a l l o s s e s : \ nP r = %. 1 f W \n” , P _ r ) ;

52 printf ( ” \n c : F ul l −l a o d e f f i c i e n c y : \ n = %. 1 f p e r ce n t ” , et a ) ;

Scilab code Exa 12.7 Pd Pr max and fl efficiency Pk Ia LF

7 / / E xa mp le 12−78

1011 / / G iv en d a ta12 V = 240 ; // V ol ta ge r a t i n g o f dc s hu nt motor i n

v o l t13 P_hp = 25 ; // Power r a t i n g o f dc s hu nt motor i n hp14 S = 1100 ; // Sp eed i n rpm o f t he dc s hu nt motor15 R _a = 0.15 ; // Armture r e s i s t a n c e i n ohm16 R_f = 80 ; // F i e l d r e s i s t a n c e i n ohm17 I_L = 89 ; // Rated l i n e c u r r e n t i n A18

19 / / C a l c u l a t i o n s20 / / P r e l i m i na r y c a l c u l a t i o n s21 V_f = V ; / / V o lt ag e a c r o s s f i e l d w in di ng i n v o l t22 I_f = V_f / R_f ; // F i e l d c ur r e nt i n A23 I_a = I_L - I_f ; // Arma tu re c u r r e n t i n A

56 printf ( ” \n Armature c u r r e n t : I a = %d A \n ” , I _ a ) ;

57 printf ( ” \n P o = %d W \n” , P_ o ) ;58 printf ( ” \n E c ( f l ) = %. 1 f V \n” , E _ c _ f l ) ;

60 printf ( ” \n a : Power d e v el o p e d by t h e a rm at ur e : \ nP d = %. 1 f W \n” , P _ d ) ;

62 printf ( ” \n b : F ul l −l o a d r o t a t i o n a l l o s s e s : \ nP r = %. 1 f W \n” , P _ r ) ;

64 printf ( ” \n c : F ul l −l a o d e f f i c i e n c y : \ n = %. 1 f p e r c e n t \n ” , e ta _f l ) ;

6566 printf ( ” \n d : T o t a l c o ns ta nt l o s s e s : \ n P k = %

. 1 f W \n” , P _ k ) ;

68 printf ( ” \n e : A r ma t ur e c u r r e n t f r o m maximume f f i c i e n c y : \ n I a = %. 1 f A\n ” , I a ) ;

70 printf ( ” \n f : L . F . = %. 1 f \n ” , L F ) ;

72 printf ( ” \n g : m a x = %. 1 f p e rc e nt ” , e t a _ m a x ) ;

Scilab code Exa 12.8 IL Ia Pd Pr Speed SR

6 // Ch apt e r 1 2 : POWER,ENERGY,AND EFFICIENCY RELATIONSOF DC AND AC DYNAMOS7 / / E xa mp le 12−88

c o n s o l e .

v o l t13 P_hp = 5 ; // Power r a t i n g o f dc s hu nt motor i n hp14 S _fl = 11 00 ; // Sp eed i n rpm o f t he dc s hu nt motor15 R_a = 0.4 ; // Armture r e s i s t a n c e i n ohm16 R_f = 240 ; // F i el d r e s i s t a n c e i n ohm17 e ta = 0.75 ; // F ul l −l oa d e f f i c i e n c y18

20 / / c as e a21 V_L = V ; // Load v o l t a g e22 P_o = P_hp * 746 ; // Power r a t i n g o f dc s hu nt motor

i n W23 I _ L = P _o / ( e ta * V_ L ); // Rated i np ut l i n e c u r r e n t

i n A24

25 V_f = V ; / / V o lt ag e a c r o s s f i e l d w in di ng i n v o l t26 I_f = V_f / R_f ; // F i e l d c ur r e nt i n A27 I_a = I_L - I_f ; // Rated a rm at ur e c u r r e n t i n A28

29 / / c as e b30 V_a = V ; // V ol ta ge a c r o s s a rm at u re i n v o l t31 E_c = V_a - I_a * R_a ; / / b ac k EMF i n v o l t32 P_d = E_c * I_a ; / / Power d e v el o p ed by t h e a rm at ur e

i n W33

34 / / c as e c35 P_r = P_d - P_o ; // R o t a t i o n a l l o s s e s i n W a t r at ed

l o a d36

37 / / c as e d38 / / A t n o−l o a d39 P_o _nl = 0 ;

40 P _r _n l = P_r ; // R o t a t i o n a l l o s s e s i n W a t n o l oa d41 P _d _n l = P _r _n l ;

43 / / c as e e44 I _a _n l = P _d _n l / V_a ; / / No−l o a d a rm at ur e c u r r e n ti n A

46 / / c as e f 47 E_c _nl = V ; / / No−l oa d v o l t a g e i n v o l t48 E _c _f l = E_c ; // F u ll −l o ad v o l t a g e i n v o l t49 S _n l = ( E _c _n l / E _c _f l ) * S_ fl ; / / No−l oa d s pe ed i n

51 / / c as e g

52 S R = ( S_n l - S_ fl ) /S _fl * 100 ; // S peed r e g u l a t i o n53

57 printf ( ” \n a : Rated i np ut l i n e c u r r e n t : \ n I L =%. 2 f A \n ” , I _ L ) ;

58 printf ( ” \n Rated a r ma t u r e cu rr en t : \ n I a = %. 2 f A \n ” , I_ a ) ;

60 printf (” \n b : E c = %. 1 f V \n ”

, E_ c ) ;

61 printf ( ” \n Power d e ve lo pe d by th e ar m a tu r e a tr at ed l oa d : \ n P d = %d W \n ” , P _ d ) ;

63 printf ( ” \n c : R ot at i o na l l o s s e s a t r at ed l oa d : \ nP r = %d W \n ” , P _ r ) ;

65 printf ( ” \n d : At no−l oa d , P o = %d W ; t h e r e f o r e \ n\t \ t P d = P r = %d W \n” , P _ o _ n l , P _ r ) ;

67 printf ( ” \n e : No−l o ad a rm at ur e c u r r e nt : \ n I a (

n l ) = %. 2 f A \n ” , I _a _ nl ) ;68

69 printf ( ” \n f : No−l oa d s pe ed : \ n S n l = %. f rpm \n ” , S _n l ) ;

71 printf ( ” \n g : Speed r e g u l a t i o n : \ n SR = %. 1 f

p e rc e n t ” , SR ) ;

Scilab code Exa 12.9 Ec Pd Po Pr To Ia efficiency speed SR

OF DC AND AC DYNAMOS7 / / E xa mp le 12−98

v o l t

13 I_L = 55 ; // Rated l i n e c u r r e n t i n A14 S = 1200 ; // Sp eed i n rpm o f t he dc s hu nt motor15 P_r = 406.4 ; // R o t a t i o n al l o s s e s i n W a t r at ed

l o a d16 R_f = 120 ; // F i el d r e s i s t a n c e i n ohm17 R_a = 0.4 ; // Armture r e s i s t a n c e i n ohm18

19 / / C a l c u l a t i o n s20 / / c as e a21

22 V_f = V ; / / V o lt ag e a c r o s s f i e l d w in di ng i n v o l t23 I_f = V_f / R_f ; // F i e l d c ur r e nt i n A24 I_a = I_L - I_f ; // Rated a rm at ur e c u r r e n t i n A25

26 V_a = V ; // V ol ta ge a c r o s s a rm at u re i n v o l t

27 E_c = V_a - I_a * R_a ; / / b ac k EMF i n v o l t

28 P_d = E_c * I_a ; / / Power d e v el o p ed by t h e a rm at ur ei n W29

30 / / c as e b31 P _o = P _d - P _r ; / / Ra ted o u tp ut p ower i n W32 P_o _hp = P_o / 746 ; // Ra ted o u tp u t p ower i n hp33

34 / / c as e c35 T_o = ( P _o _h p * 5 25 2) / S ; // C i n l b − f t36 T _o _N m = T _o * ( 1. 35 6) ; // Rated o ut pu t t o rq u e i n N−

3738 / / c as e d39 P_ in = V * I_L ; / / I np ut power i n W40 e ta = ( P _o / P _i n ) *1 00 ; // E f f i c i e n c y a t r at ed l oa d41

42 / / c as e e43 / / A t n o−l o a d44 P_o _nl = 0 ;

45 P _r _n l = P_r ; // R o t a t i o n a l l o s s e s i n W a t n o l oa d46 P _d _n l = P _r _n l ;

48 I _a _n l = P _d _n l / V_a ; / / No−l o a d a rm at ur e c u r r e n ti n A

50 E_c _nl = V ; / / No−l oa d v o l t a g e i n v o l t51 E _c _f l = E_c ; // F u ll −l o ad v o l t a g e i n v o l t52 S_fl = S ; // F ul l −l o ad s pe ed i n rpm53 S _n l = ( E _c _n l / E _c _f l ) * S_ fl ; / / No−l oa d s pe ed i n

55 / / c as e f

56 S R = ( S_n l - S_ fl ) /S _fl * 100 ; // S peed r e g u l a t i o n57

61 printf ( ” \n a : E c = %. 1 f V \n ” , E_ c ) ;

62 printf ( ” \n Power d e ve lo pe d by th e ar m a tu r e a tr at ed l oa d : \ n P d = %. 1 f W \n ” , P _ d ) ;

64 printf ( ” \n b : Ra ted o u tp ut p ower : \ n P o = %d W\n ” , P _ o ) ;

65 printf ( ” \n P o = %d hp \n ” , P _ o _ h p ) ;

67 printf ( ” \n c : Rated o ut pu t t o rq u e : \ n T o = %. 2 f l b − f t ” , T _ o ) ;

68 printf ( ” \n T o = %. f N−m \n ” , T _o _N m ) ;

70 printf ( ” \n d : E f f i c i e n c y a t r at ed l oa d : \ n =%. 1 f p e r c e n t \n ” , et a ) ;

72 printf ( ” \n e : At no−l oa d , P o = %d W ; t h e r e f o r e \ n\t \ t P d = P r = Ec I a VaIa = %. 1 f W \n” , P _ o _ n l ,

P _ r ) ;

73 printf ( ” \n No−l o ad a rm at ur e c u r r e nt : \ n I a (n l ) = %. 3 f A \n ” , I _a _ nl ) ;

74 printf ( ” \n No−l oa d s pe ed : \ n S n l = %f %.f rpm \n ” , S_ nl , S _n l ) ;

76 printf ( ” \n f : Speed r e g u l a t i o n : \ n SR = %. 1 f p e rc e n t ” , SR ) ;

78 printf ( ” \n V a r i a t i on i n SR i s due to non−a p pr o x im a t io n o f S n l = %f rpm ”, S _ n l ) ;

79 printf ( ” \n w h i l e c a l c u l a t i n g SR i n s c i l a b . ” )

Scilab code Exa 12.10 efficiency Pf Pd Pr Ia LF max efficiency

39 / / c as e d

40 P _d = P _d 1 ;41 P_r = P_in - P_d ; // R o t a t i o n al power l o s s e s i n W42

43 / / c as e e44 P_k = P_r + V_f * I_f ; // C o n s t a n t l o s s e s i n W45 Ia = sqrt ( P _ k / R _ a ) ; // A rma tu re c u r r e n t i n A f o r max

. e f f i c i e n c y46

47 / / c as e f 48 I _a _r at ed = I _a ; // Rated a rm at ur e c u r r e n t i n A49 LF = Ia / I_a ; // Load f r a c t i o n

5051 / / c as e g52 r a t e d_ o ut p ut = 1 25 00 ; / / R at ed o u tp u t i n kW53 / / Maximum e f f i c i e n c y54 e ta_m ax = ( LF * ra ted _o ut put ) / ( ( LF *

r at ed _o ut pu t ) + (2* P _k ) ) * 100 ;

59 printf (” \n a : E f f i c i e n c y : \ n = %f p e r c e n t%. 1 f p e r c e n t \n ” , e t a , e t a ) ;

61 printf ( ” \n b : Shunt f i e l d l o s s : \ n ( V f ) ̂ 2/ R f =%d W \n ” , P _ s h _ l o s s ) ;

63 printf ( ” \n c : L in e c u r r e n t : I L = %d A \n\nF i e l d c u r r e n t : I f = %d A” , I _ L , I _ f ) ;

64 printf ( ” \n\n Armature c ur r e n t : I a = %d A ” ,I_a

65 printf ( ” \n\n G e n e r a t e d EMF : E g = %. 1 f V ” , E _ g )

;66 printf ( ” \n\n G en er at ed e l e c t r i c power : ” ) ;

67 printf ( ” \n 1 . P d = %d W \n\n 2 . P d = %d W \n ” , P _ d 1 , P _ d 2 ) ;

69 printf ( ” \n d : R o t a t i o n a l power l o s s e s : \ n P r =

%f W %. f W \n” , P _ r , P _ r ) ;70

71 printf ( ” \n e : C o n s t a n t l o s s e s : P k = %f W %. f W \n ” , P _k , P_ k );

72 printf ( ” \n Armature c u r r e nt f o r max . e f f i c i e n c y :I a = %. 1 f A \n ” , I a ) ;

74 printf ( ” \n f : Load f r a c t i o n : L . F . = %. 2 f \n ” , L F ) ;

76 printf ( ” \n g : Maximum e f f i c i e n c y : = %f p e rc e n t%. 2 f p e r c e n t ” ,eta_max ,eta_ max) ;

Scilab code Exa 12.11 efficiency at different LF

7 / / E xa mp le 1 2−118

11 / / G iv en d a t a ( f ro m Ex . 1 2 −10)12 V = 125 ; // V ol ta ge r a t i n g o f g e n r a t o r i n v o l t13 P_o = 12500 ; // Power r a t i n g o f g e nr a t o r i n W

14 P_hp = 20 ; // Power r a t i n g o f motor i n hp15 R_a = 0.1 ; // Armture r e s i s t a n c e i n ohm16 R _f = 62.5 ; // F i el d r e s i s t a n c e i n ohm17 P _v ar = 10 40 ; / / Ra ted v a r i a b l e e l e c t r i c l o s s i n W18

19 / / C a l c u l a t e d d at a fr om Ex .1 2 −10

20 P _k = 1380 ; // C o n s t a n t l o s s e s i n W21

22 / / C a l c u l a t i o n s23 / / E f f i c i e n c y o f t he dc s h u n t g e n e ra t o r24 // = ( o u t p u t ∗L . F ) / ( ( o ut pu t ∗L . F) + P k + ( L . F)

ˆ2 ∗ P a r a t e d ) ∗ 10025 o ut pu t = P_o ;

26 P _a _r at ed = P _v ar ;

28 / / c as e a29 L F 1 = 2 5 *( 1 /1 0 0) ; / / At 25 % r a t e d o ut pu t

30 / / E f f i c i e n c y o f t he dc s h u n t g e n e ra t o r a t 2 5 %r a t e d o u tp ut

31 e ta _1 = ( o ut pu t * LF 1 ) / ( ( o ut pu t * LF 1) + P _k + ( LF 1 )

^2 * P _a _r at ed ) * 100 ;

33 / / c as e b34 L F 2 = 5 0 *( 1 /1 0 0) ; / / At 50 % r a t e d o ut pu t35 / / E f f i c i e n c y o f t he dc s h u n t g e n e ra t o r a t 5 0 %

r a t e d o u tp ut36 e ta _2 = ( o ut pu t * LF 2 ) / ( ( o ut pu t * LF 2) + P _k + ( LF 2 )

^2 * P _a _r at ed ) * 100 ;

38 / / c as e c39 L F 3 = 7 5 *( 1 /1 0 0) ; / / At 75 % r a t e d o ut pu t40 / / E f f i c i e n c y o f t he dc s h u n t g e n e ra t o r a t 7 5 %

r a t e d o u tp ut41 e ta _3 = ( o ut pu t * LF 3 ) / ( ( o ut pu t * LF 3) + P _k + ( LF 3 )

^2 * P _a _r at ed ) * 100 ;

43 / / c as e d44 L F 4 = 1 2 5* ( 1/ 1 00 ) ; / / At 1 25 % r a te d o ut pu t

45 / / E f f i c i e n c y o f t he dc s h u n t g e n e ra t o r a t 1 25 %r a t e d o u tp ut

46 e ta _4 = ( o ut pu t * LF 4 ) / ( ( o ut pu t * LF 4) + P _k + ( LF 4 )

^2 * P _a _r at ed ) * 100 ;

52 printf ( ” \n a : a t %. 2 f r at ed o u t p u t = %. 2 f p e r c e n t \n ” , L F 1 , e t a _ 1 ) ;

54 printf ( ” \n b : a t %. 2 f r at ed o u t p u t = %. 2 f p e r c e n t \n ” , L F 2 , e t a _ 2 ) ;

55 printf ( ” \n P l e a s e n o t e : C a l c u l a ti on e r r o r f o rc a s e b : i n t h e t e x t b o o k . \ n” ) ;

57 printf ( ” \n c : a t %. 2 f r at ed o u t p u t = %. 2 f p e r c e n t \n ” , L F 3 , e t a _ 3 ) ;

59 printf ( ” \n d : a t %. 2 f r at ed o u t p u t = %. 2 f p e r c e n t \n ” , L F 4 , e t a _ 4 ) ;

Scilab code Exa 12.12 Ia Ra Pf Pk Pcu efficiencies Pd

7 / / E xa mp le 1 2−128

c o n s o l e .10

11 / / G iv en d a ta12 // 3−p h a s e Y−c o nn e ct ed a l t e r n a t o r13 kVA = 100 ; // kVA r a t i n g o f t he a l t e r n a t o r

14 V = 1100 ; // Rated v o lt a g e o f t he a l t e r n a t o r i n

v o l t15 I_a _nl = 8 ; / / No−l oa d a rm at u re c u r r e n t i n A16 P _ in _n l = 6 00 0 ; / / No−l o ad Power i n pu t t o t he

a rm at ur e i n W17 V _oc = 13 50 ; // Open−c k t l i n e v ol t a g e i n v o l t18 I_f = 18 ; // F i e l d c ur r e nt i n A19 V_f = 125 ; // v o l t a g e a c r o s s f i e l d w in di ng i n v o l t20

21 / / C a l c u l a t i o n s22 // From Ex . 6 −4 ,23 R _a = 0.45 ; // Arma tu re r e s i s t a n c e i n ohm/ p h as e

24 I _a _r at ed = 5 2. 5 ; // Ra ted a rm at ur e c u r r e n t i n A/p h a s e

26 / / c as e a27 P_r = P_i n_nl - 3 * ( I_a_nl ) ^2 * R_a ; // R o t a ti o n a l

l o s s o f s y nc h ro n o us dynamo i n W28

29 / / c as e b30 P_f = V_f * I_ f ; // F i e l d c o p p e r l o s s i n W31

32 / / c as e c33 P_k = P_r + P_f ; // F i x e d l o s s e s i n W a t r at ed

s y n c hr o n o u s s p e ed34 Pk = P _k / 1 000 ; // F ix ed l o s s e s i n kW at r a te d

s y n c hr o n o u s s p e ed35

36 / / c as e d37 P_ cu = 3 * ( I _a _r at ed ) ^2 * R_a ; // Rated e l e c t r i c

a r m a t ur e cu− l o s s i n W38 P _c u_ kW = P_ cu / 10 00 ; // R at ed e l e c t r i c ar mat u r e

cu− l o s s i n kW

3940 LF1 = 1/4 ; // Load f r a c t i o n41 LF2 = 1/2 ; // Load f r a c t i o n42 LF3 = 3/4 ; // Load f r a c t i o n43 P _ c u_ LF 1 = P _c u * ( L F1 ) ^2 ; // E l e c t r i c a rm at ur e cu−

l o s s i n W a t 1/4 l oa d

44 P _ c u_ LF 2 = P _c u * ( L F2 ) ^2 ; // E l e c t r i c a rm at ur e cu−l o s s i n W a t 1/2 l oa d45 P _ c u_ LF 3 = P _c u * ( L F3 ) ^2 ; // E l e c t r i c a rm at ur e cu−

l o s s i n W a t 3/4 l oa d46

47 P _c u_ LF 1_ kW = P _c u_ LF 1 / 1 00 0 ; // E l e c t r i c a rm at u recu− l o s s i n kW at 1/4 l oa d

52 / / c as e e53 P F = 0.9 ; // Power f a c t o r l a g g i n g54 // E f f i c i e n c y55 // = LF ( r a te d kVA) ∗PF / ( LF ( r a t e d kVA ) ∗P F + P k

+ P cu ) ∗ 10056 eta_1 = ( LF1 * kVA * PF ) / ( ( LF1 * kVA * PF ) + Pk +

P _c u_ LF 1_ kW ) * 100 ; // E f f i c i e n c y a t 1/4 l oa d57 eta_2 = ( LF2 * kVA * PF ) / ( ( LF2 * kVA * PF ) + Pk +

P _c u_ LF 2_ kW ) * 100 ;// E f f i c i e n c y a t 1/2 l oa d58 eta_3 = ( LF3 * kVA * PF ) / ( ( LF3 * kVA * PF ) + Pk +

P _c u_ LF 3_ kW ) * 100 ; // E f f i c i e n c y a t 3/4 l oa d59 eta _fl = ( kVA * PF ) / ( ( kVA * PF ) + Pk + P _cu_ kW )

* 1 0 0 ; // E f f i c i e n c y a t f u l l l oa d60

61 / / c as e f 62 Ia = sqrt ( P _ k / ( 3 * R _ a ) ) ; // Armature c u r r e n t i n A f o r

max . e f f i c i e n c y a t 0 . 9 PF l a g g i ng63 LF = Ia / I_ a_ ra te d ; // Load f r a c t i o n f o r max .

e f f i c i e n c y

64 // a t max . e f f i c i e n c y P cu = P k65 e ta_m ax = ( LF * kVA * PF ) / ( ( LF * kVA * PF ) + 2* Pk

) * 100 ; // Max E f f i c i e n c y 0 . 9 PF l a g g i n g66

67 / / c as e g

68 P _o = kVA * PF ; // Output p ower a t 0 . 9 PF l a g g i n g

69 I _ a = I _a _r at ed ;70 P _d = P _o + ( 3* ( I_ a )^ 2* R _a / 1 00 0) + ( V _f * I_ f / 10 00 ) ;

/ / A rm at ur e p ow er d e v e l o p e d i n kW a t 0 . 9 PFl a gg i n g a t f u l l − l o a d

75 printf ( ” \n From Ex . 6 −4 , \ n R a = %. 2 f / ph a s e ” , R _ a )

76 printf ( ” \n I a ( r a t e d ) = %. 1 f A \n ” , I _ a _ r a t e d ) ;

7778 printf ( ” \n a : R o t a ti o n a l l o s s o f s yn ch ro n ou s dynamo

: \ n P r = %. f W \n” , P _ r ) ;

80 printf ( ” \n b : F i e l d c o p p e r l o s s : \ n P f = %d W \n ” , P _ f ) ;

82 printf ( ” \n c : F ix e d l o s s e s a t r at e d s yn ch ro no uss pe ed : \ n P k = %. f W\n” , P _ k ) ;

84 printf (” \n d : P cu a t r a te d l oa d = %. f W\n P cu, ” , P _ c u ) ;

85 printf ( ” \n a t %. 2 f r at ed l oa d = %. 1 f W” , LF1 ,

P _ c u _ L F 1 ) ;

86 printf ( ” \n a t %. 2 f r at ed l oa d = %. 1 f W” , LF2 ,

P _ c u _ L F 2 ) ;

87 printf ( ” \n a t %. 2 f r a te d l o a d = %. 1 f W \n” , LF3 ,

P _ c u _ L F 3 ) ;

90 printf ( ” \n e : E f f i c i e n c y : \ n a t %. 2 f l o a d = %

. 1 f p e r c e n t ” , L F 1 , e t a _ 1 ) ;91 printf ( ” \n a t %. 2 f l o a d = %. 1 f p e r c e n t ” , L F 2 ,

e t a _ 2 ) ;

92 printf ( ” \n a t %. 2 f l o a d = %. 1 f p e r c e n t ” , L F 3 ,

e t a _ 3 ) ;

93 printf ( ” \n a t f u l l − l o a d = %. 1 f p e r c e n t \n” ,

e t a _ f l ) ;94

95 printf ( ” \n f : Armature c u r r e nt f o r max . e f f i c i e n c ya t 0 . 9 PF l a g g i n g : ” ) ;

96 printf ( ” \n I a ( max ) = %f A %. 1 f A\n” , I a , I a ) ;

97 printf ( ” \n L . F . = %. 2 f \n” , L F ) ;

98 printf ( ” \n Maximum e f f i c i e n c y : \ n m a x = %. 1 f p e r ce n t \n ” , e t a _ m a x ) ;

100 printf ( ” \n g : Ar ma tu re p ower d e v el o p ed a t 0 . 9 PFl a gg i n g a t f u l l − l o ad : ” ) ;

101 printf ( ” \n P d = %. 2 f kW ” , P _ d ) ;

Scilab code Exa 12.13 Pf Pcu Zs VR efficiencies Pd

OF DC AND AC DYNAMOS7 / / E xa mp le 1 2−138

11 / / G iv en d a ta12 // 3−p h a s e Y−c o nn e ct ed a l t e r n a t o r

13 k VA = 1000 ; // kVA r a t i n g o f t he a l t e r n a t o r14 V = 2300 ; // Rated v o lt a g e o f t he a l t e r n a t o r i nv o l t

16 // DC MOTOR

51 c os _t he ta = 0 .8 ; / / P F l a g g i n g

52 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;53 V_p = V / sqrt ( 3 ) ; // Phase v o l t a ge i n v o l t54

55 / / Ge ne r at ed v o l t ag e p er p ha se i n v o l t56 I _a = I_sc ; // Arma tu re c u r r e n t i n A57

58 E _g p = ( V _p * c o s _t h et a + I _a * R _a ) + % i *( V _p * s i n _t h et a

+ I _a * X _s ) ;

59 E _ g p_ m = abs ( E _ g p ) ; / / E gp m=m ag n it ud e o f E gp i nv o l t

60 E _ g p_ a = atan ( imag ( E _g p ) / real ( E _ g p ) ) * 1 8 0 / % p i ; //

E gp a=p ha se a n gl e o f E gp i n d e gr e e s61

62 V_ nl = E _g p_ m ; / / No−l oa d v o l t a g e i n v o l t63 V_fl = V_p ; // F ul l −l oa d v o l t a g e i n v o l t64

65 V R = ( V_n l - V_ fl ) /V _fl * 100 ; // A l t e r n a to rv o l t a ge r e g u l a t i o n

67 / / c as e f 68 P F = 0.8 ; // l a g g i n g PF69 LF = 1 ;

// l oa d f r a c t i o n70 e ta _r at ed = ( LF * kV A *P F) /( ( LF * kV A *P F) + ( P _f + P _r )

+ P_cu ) * 100 ; // E f f i c i e n c y a t 0 . 8 l a g g i n g PF71

72 / / c as e g73 P_k = ( P_f + P_r ) ; // C o ns ta nt l o s s e s i n kW74 L _F = sqrt ( P _ k / P _ c u ) ; // Load f r a c t i o n f o r max .

e f f i c i e n c y75 // a t max . e f f i c i e n c y P k = P cu76 e ta _m ax = ( L _F * kV A *P F) /( ( L _F * kV A *P F) + 2* P _k ) *

100 ; / / Max . E f f i c i e n c y a t 0 . 8 l a g g i ng PF

79 / / c as e h80 P_o = kVA ; / / O ut pu t p o we r i n kVA81 P _d = P _o + (3 *( I _a ) ^2 * R_ a /1 00 0) + ( V fI f ) ; //

A rm at ur e p ow er d e v e l o p e d i n kW a t u n i t y PF a t

r a t e d −l o a d82

86 printf ( ” \n a : From T e st 2 , R o t a t i o n a l l o s s e s : \ nP r = %d kW \n” , P _ r ) ;

88 printf ( ” \n b : F ul l −l oa d a rm at ur e c op pe r l o s s : \ nP c u = %. 1 f kW \n” , P _ c u ) ;

90 printf ( ” \n c : S yn ch ro n ou s i mp ed an ce o f t h e a rm at ur e: \ n Z s = %f %. 2 f \n” , Z _ s , Z _ s ) ;

92 printf ( ” \n d : S yn ch ro no us r e a c t a nc e o f t he a rm at ur e: \ n j X s = %f %. 2 f \n” , X _ s , X _ s ) ;

94 printf ( ” \n e : E gp = ” ) ; disp ( E _ g p ) ;

95 printf ( ” \n E gp = %. f <%. 1 f V\n” , E _ g p _ m , E _ g p _ a ) ;

96 printf ( ” \n A l te r n a to r v o l t a ge r e g u l a t i o n : \ nVR = % . 2 f p e r c e n t \n” , V R ) ;

98 printf ( ” \n O bt a i ne d VR v al ue t h ro u gh s c i l a bc a l c u l a t i o n i s s l i g h t l y d i f f e r e n t from t e x t b oo k ”)

99 printf ( ” \n b e c a u s e o f non−a p pr ox im a ti o n o f Z s ,X s and E gp w hi l e c a l c u l a t i n g i n s c i l a b . \ n” ) ;

101 printf ( ” \n f : A l t e r na t o r e f f i c i e n c y a t 0 . 8 l a g g i n gPF : \ n r a t e d = %. 1 f p e r c e n t \n” , e t a _ r a t e d ) ;

103 printf ( ” \n g : L . F = %. 4 f \n” , L _ F ) ;

104 printf ( ” \n Max . E f f i c i e n c y a t 0 . 8 l a g g i n g PF : \m a x = %. 2 f p e r c e n t \n” , e ta _ ma x ) ;

106 printf ( ” \n h : Power d e ve l op e d by t he a l t e r n a t o ra rm at ur e a t r a t e d l oa d , u n i t y PF : ” ) ;

107 printf ( ” \n P d = %. f kW” , P _ d ) ;

Scilab code Exa 12.14 Pr Pcu efficiencies hp torque

6 // Ch apt e r 1 2 : POWER,ENERGY,AND EFFICIENCY RELATIONSOF DC AND AC DYNAMOS7 / / E xa mp le 1 2−148

11 / / G iv en d a ta12 P = 4 ; // Number o f p o l e s i n I n d u ct i o n motor13 f = 6 0 ; // F re qu en cy i n Hz14 V = 220 ; // Rated v o l t a g e o f IM i n v o l t

15 hp_IM = 5 ; // Power r a t i n g o f IM i n hp16 P F = 0.9 ; // Power f a c t o r17 I_L = 16 ; // L i ne c u r r e n t i n A18 S = 1750 ; // S pe ed o f IM i n rpm19

20 / / No−l oa d t e s t d a t a21 I_nl = 6.5 ; / / No−l oa d l i n e c ur r e nt i n A22 V_nl = 220 ; / / No−l oa d l i n e v o l t a g e i n v o l t23 P_nl = 300 ; / / No−l o ad power r e a d in g i n W24

25 // B lo ck ed r o t o r t e s t26 I_br = 16 ; // B l o ck e d r o t o r l i n e c u r r e n t i n A27 V_br = 50 ; // B l o ck e d r o t o r v o l t a ge i n v o l t28 P_br = 800 ; // B lo ck ed r o t o r power r e a di n g i n W29

31 / / c as e a32 P _cu = P_ br ; // F u ll −l oa d e q u i v al e n t cu− l o s s33 I _1 = I_br ; // Pr im ary c u r r e nt i n A34 R_ e1 = ( P_c u) / ( 3/ 2 * ( I_1 ) ^2 ) ; // E q u i v al e n t

t o t a l r e s i s t a n c e o f IM i n ohm35

36 / / c as e b37 P _in = P_ nl ; // I n pu t po wer t o IM38 I 1 = I_nl ; // I np ut c u r r en t i n A39 P _r = P _i n - ( 3/ 2 * ( I1 ) ^2 * R _e1 ) ; // R o t a t io n a l

l o s s e s i n W

4041 / / c as e c42 LF1 = 1/4 ; // Load f r a c t i o n43 LF2 = 1/2 ; // Load f r a c t i o n44 LF3 = 3/4 ; // Load f r a c t i o n45 LF4 = 5/4 ; // Load f r a c t i o n46 P _ c u_ LF 1 = ( L F1 ) ^2 * P _c u ; // E q u i v a le n t c o pp e r

l o s s a t 1/4 r a te d−l o a d47 P _ c u_ LF 2 = ( L F2 ) ^2 * P _c u ; // E q u i v a le n t c o pp e r

l o s s a t 1/2 r a te d−l o a d48 P _ c u_ LF 3 = ( L F3 ) ^2 * P _c u ;

// E q u i v a le n t c o pp e rl o s s a t 3/4 r a te d−l o a d49 P _ c u_ LF 4 = ( L F4 ) ^2 * P _c u ; // E q u i v a le n t c o pp e r

l o s s a t 5/4 r a te d−l o a d50

51 / / c as e d52 F u l l _ l o a d_ i n p u t = sqrt ( 3) * V * I _ L * P F ;

54 // E f f i c i e n c y55 // E f f i c i e n c y a t 1 /4 r at ed l oa d56 e ta _L F1 = ( F ul l_ lo ad _i np ut * L F1 - ( P_ r + P _c u_ LF 1 ) )

/ ( F u ll _l oa d_ in pu t * LF 1 ) * 1 00 ;57

58 // E f f i c i e n c y a t 1 /2 r at ed l oa d59 e ta _L F2 = ( F ul l_ lo ad _i np ut * L F2 - ( P_ r + P _c u_ LF 2 ) )

/ ( F u ll _l oa d_ in pu t * LF 2 ) * 1 00 ;

64 / / E f f i c i e n c y a t r at ed l o ad65 e ta _r at ed = ( F ul l_ lo ad _i np ut - ( P_r + P _cu ) ) / (

F u ll _ lo a d_ i np u t ) * 1 00 ;

6970 / / c as e e71 / / s i n c e e t a i s c a l c u l a t e d i n p er ce n t d i v i d e i t by

100 f o r hp c a l c u l a t i o n s72 P _ o _ L F1 = ( F u l l _ l o ad _ i n pu t * L F 1 * e t a _ LF 1 / 1 0 0 ) / 7 46 ; //

Output hp a t 1 /4 r a t ed l o ad73 P _ o _ L F2 = ( F u l l _ l o ad _ i n pu t * L F 2 * e t a _ LF 2 / 1 0 0 ) / 7 46 ; //

Output hp a t 1 /2 r a t ed l o ad74 P _ o _ L F3 = ( F u l l _ l o ad _ i n pu t * L F 3 * e t a _ LF 3 / 1 0 0 ) / 7 46 ; //

Output hp a t 3 /4 r a t ed l o ad75 P _ o = ( F u l l _ l o ad _ i n p ut * e t a _r a t ed / 1 00 ) / 7 4 6 ;

//Output hp a t 1 /4 r a t ed l o ad76 P _ o _ L F4 = ( F u l l _ l o ad _ i n pu t * L F 4 * e t a _ LF 4 / 1 0 0 ) / 7 46 ; //

Output hp a t 5 /4 r a t ed l o ad77

78 / / c as e f 79 h p = P_o ; // R at ed o u tp u t h o r s e po w e r80 T _o = ( P _o * 5 25 2) / S ; // Outpue t o rq u e a t f u l l − l o a d

i n l b − f t81 T _o _N m = T_o * 1 .3 56 ; // Outpue t o rq u e a t f u l l − l o a d

i n N−m

86 printf ( ” \n a : E qu iv al en t t o t a l r e s i s t a n c e o f IM : \ n

R e 1 = %. 3 f \n” , R _ e 1 ) ;

8788 printf ( ” \n b : R ot at i o na l l o s s e s : \ n P r = %. f W

\n ” , P _ r ) ;

90 printf ( ” \n c : At f u l l −l o a d , P c u = %d W \n” , P _ c u ) ;

91 printf ( ” \n P cu a t %. 2 f r at ed l oa d = %d W” , L F 1 ,

P _ c u _ L F 1 )

P _ c u _ L F 2 )

P _ c u _ L F 3 )

94 printf ( ” \n P cu a t %. 2 f r a te d l o a d = %d W \n” ,L F 4 , P _ c u _ L F 4 )

96 printf ( ” \n d : F ul l −l o a d i n p u t = %. f W \n” ,

F u l l _ l o a d _ i n p u t ) ;

97 printf ( ” \n E f f i c i e n c y : \ n a t %. 2 f r a t e dl o a d = %. 1 f p e r c e n t \n” , L F 1 , e t a _ L F 1 ) ;

98 printf ( ” \n a t %. 2 f r at e d l o a d = %. 1 f p e r c e n t\n” , L F 2 , e t a _ L F 2 ) ;

99 printf ( ” \n a t %. 2 f r at e d l o a d = %. 1 f p e r c e n t

\n”, L F 3 , e t a _ L F 3 ) ;

100 printf ( ” \n a t r a t e d l o a d = %. 1 f pe r c e n t \n” ,

e t a _ r a t e d ) ;

103 printf ( ” \n e : Output h o rs e po w er : \ n P o at %. 2 f r a t e d l o a d = %. 3 f hp \n” , L F 1 , P _ o _ L F 1 ) ;

104 printf ( ” \n P o a t %. 2 f r a te d l o a d = %. 3 f hp \n” ,

L F 2 , P _ o _ L F 2 ) ;

L F 3 , P _ o _ L F 3 ) ;106 printf ( ” \n P o a t r a t e d l o a d = %. 3 f hp \n” , P _ o ) ;

L F 4 , P _ o _ L F 4 ) ;

109 printf ( ” \n f : Output t or qu e a t f u l l −l oa d : \ n T o

= %. 1 f l b− f t ” , T _ o ) ;110 printf ( ” \n T o = %. 2 f N−m” , T _ o _ N m ) ;

Scilab code Exa 12.15 RPO efficiency hp torque compare

4 / / 2 nd e d i t i om5

7 / / E xa mp le 1 2−158

11 / / G i ve n d a t a ( f r om Ex . 1 2 −1 4)12 pole = 4 ; // Number o f p o l e s i n I n d u ct i o n motor

13 f = 6 0 ; // F re qu en cy i n Hz14 V = 220 ; // Rated v o l t a g e o f IM i n v o l t15 hp_IM = 5 ; // Power r a t i n g o f IM i n hp16 P F = 0.9 ; // Power f a c t o r17 I_L = 16 ; // L i ne c u r r e n t i n A18 S _r = 1750 ; // S pee d o f IM i n rpm19

20 / / No−l oa d t e s t d a t a21 I_nl = 6.5 ; / / No−l oa d l i n e c ur r e nt i n A22 V_nl = 220 ; / / No−l oa d l i n e v o l t a g e i n v o l t

23 P_nl = 300 ; / / No−l o ad power r e a d in g i n W24

25 // B lo ck ed r o t o r t e s t26 I_br = 16 ; // B l o ck e d r o t o r l i n e c u r r e n t i n A27 V_br = 50 ; // B l o ck e d r o t o r v o l t a ge i n v o l t

28 P_br = 800 ; // B lo ck ed r o t o r power r e a di n g i n W

29 R_dc = 1 ; // dc r e s i s t a n c e i n ohm b etw e en l i n e s30

31 / / g i ve n d at a from ex . 12 −1532 V = 220 ; // v o l t a g e r a t i n g i n v o l t33 P _ in pu t = 5 50 0 ; / / p ow er drawn i n W34

35 / / C a l c u l a t i o n s36 / / P r e l i m i na r y c a l c u l a t i o n s37 R _e 1 = 1 .2 5* R _ dc ; // E qu iv al en t t o t a l r e s i s t a n c e o f

IM i n ohm38 P _in = P_ nl ; // I np ut power t o IM i n W

39 I 1 = I_nl ; // I np ut c u r r en t i n A40 P _r = P _i n - ( 3/ 2 * ( I1 ) ^2 * R _e1 ) ; // R o t a t io n a l

l o s s e s i n W41

42 I_1 = I_L ;

43 SCL = (3/2 * ( I_1 ) ^2 * R_e1 ) ; // S t a t o r Co pper L o ssi n W a t f u l l − l o a d

44 SPI = P _i np ut ; // S t a t o r Power I np ut i n W45 RPI = SPI - SCL ; / / R ot or Power I n pu t i n W46

47 S = ( 12 0* f / p ol e ) ; // S pee d o f s y nc h ro n ou s m a gn et i cf i e l d i n rpm

48 s = ( S - S _ r ) / S ; // S l i p49

50 R P D = R PI * (1 - s ) ; // R ot or Power D e ve l op e d i n W51 RPO = RPD - P_r ; / / R ot or Power Out pu t i n W52

53 / / c as e a54 P_o = RPO ;

55 e ta _f l = ( P_ o / P _i np ut ) * 10 0 ; // F ul l −l o a de f f i c i e n c y

5657 / / c as e b58 h p = P_o / 746 ; // O ut pu t h o r s e p o w e r59 T _o = ( hp * 52 52 ) / S_ r ; // Output t o rq u e i n l b− f t60 T _o _N m = T_o * 1 .3 56 ; // Output t o rq u e i n N−m

65 printf ( ” \n P r e l i mi n a r y c a l c u l a t i o n s : ” ) ;

66 printf ( ” \n R e 1 = %. 2 f \n” , R _ e 1 ) ;

67 printf ( ” \n P r = %. 1 f W \n ” , P _ r ) ;

68 printf ( ” \n SCL( f l ) = %d W \n ” , S C L ) ;

69 printf ( ” \n RPI( f l ) = %d W \n ” , R P I ) ;

70 printf ( ” \n RPD( f l ) = %f W %. 1 f W \n ” , R P D , R P D ) ;

71 printf ( ” \n RPO( f l ) = %f W %. f W \n ” , R P O , R P O ) ;

73 printf ( ” \n a : F ul l −l o a d e f f i c i e n c y : \ n f l = %. 1 f p e r ce n t \n” , e t a _ f l ) ;

75 printf ( ” \n b : Output h o rs e po w er : \ n hp = %. 2 f hpa t f u l l − l o a d \n” , h p ) ;

76 printf ( ” \n Output t o r q u e a t f u l l −l oa d : \ n T o= %f l b− f t %. 1 f l b − f t ” , T _ o , T _ o ) ;

77 printf ( ” \n T o = %f l b − f t %. 2 f N−m \n ” ,

T _ o _ N m , T _ o _ N m ) ;

79 printf (” \n c : C o mp ar i si on o f r e s u l t s ”

80 printf ( ” \n

” ) ;

81 printf ( ” \n \ t \ t \ t \ t \ t Ex . 1 2 −14\ tEx.12 −15 ” ) ;

82 printf ( ” \n

” ) ;

83 printf ( ” \n \ t f l ( p er c e n t ) \ t \ t \ t 8 2. 4 \ t \ t %. 1 f ” , e t a _ f l ) ;

84 printf ( ” \n \ t R at ed o u t p u t ( h p ) \ t \ t 6 . 0 6 \ t \ t %. 2 f

” , h p ) ;85 printf ( ” \n \ t R at ed o u t pu t t o r q u e ( l b− f t ) \ t 1 8. 2 \ t

\ t %. 1 f ” , T _ o ) ;

86 printf ( ” \n

” ) ;

Scilab code Exa 12.16 Ip Ir PF SPI SCL RPI RCL RPD T hp efficiency

11 / / G iv en d a ta12 / / c o d e l e t t e r = J13 P = 6 ; // Number o f p o l e s14 S _r = 1176 ; // r o t o r s pe ed i n rpm

15 V = 220 ; // Rated v o l t a g e o f SCIM i n v o l t16 f = 6 0 ; // F re qu en cy i n Hz17 h p_ SC IM = 7. 5 ; // Power r a t i n g o f SCIM i n hp18

19 R_ap = 0.3 ; // a rm at ur e r e s i s t a n c e i n ohm/ p ha se20 R_r = 0.144 ; // r o t o r r e s i s t a n c e i n ohm/ p ha se21 j X_m = 13 .5 ; // r e a c t a n c e i n ohm/ p h a se22 jX_s = 0.5 ; // s y nc h ro n o us r e a c t a n c e i n ohm/ p h as e23 jX_lr = 0.2 ; // L ock ed r o t o r r e a c t a n c e i n ohm/ p h as e24 P_r = 300 ; // R ot at i o na l l o s s e s i n W

2526 disp ( ”E x ampl e 12−16 : ” ) ;

27 / / C a l c u l a t i o n s28 S = ( 12 0* f / P) ; // S pe ed o f s y nc h ro n o us m a gn e ti c

f i e l d i n rpm

29 / / c as e a

30 s = ( S - S _ r ) / S ; // S l i p31

32 R _r _by _s = R_r / s ;

34 / / c as e b35 printf ( ” \n From f i g . 12 −11 , u s i ng t he f or ma t method

o f mesh a n a l y s i s , we may w r i t e ” ) ;

36 printf ( ” \n t h e a rr ay by i n s p e c t i o n : \ n ” ) ;

37 printf ( ” \n ”

38 printf ( ” \n \ t I 1 \ t I 2 \ t \ t V ” ) ;39 printf ( ” \

n ”) ;

40 printf ( ” \n\ t ( 0 . 3 + j 1 4 ) −(0+ j 1 3 . 5 ) \ t ( 127+ j 0 ) ” ) ;

41 printf ( ” \n\ t −(0+ j 1 3 . 5 ) ( 7. 2+ j 1 3 . 7 ) \ t 0 ” ) ;

42 printf ( ” \n \

n” ) ;

44 A = [ (0.3 + %i *14) - %i *13.5 ; ( -%i *1 3.5) (7.2 + %i

* 13 .7 ) ] ; // M at ri x c o n t a i n i n g a bo ve mesh e qn sa r r a y

47 / / c as e b : S t a t o r a r m a t u r e c ur r e n t I p i n A48 I _p = det ( [ ( 12 7+ %i *0 ) ( -%i * 13 .5 ) ; 0 ( 7.2 + %i

*13.7 ) ] ) / delta ;

49 I _ p_ m = abs ( I _ p ) ; // I p m=m ag ni tu de o f I p i n A50 I _ p_ a = atan ( imag ( I _p ) / real ( I _ p ) ) * 1 8 0 / % p i ; / / I p a =

p h a s e a ng le o f I p i n d e g r e e s

51 I_1 = I_p ; // S t at o r a rm at ur e c u r re n t i n A52

53 / / c as e c : R ot o r c ur r e n t I r p e r p h a s e i n A54 I _r = det ( [ ( 0. 3 + %i * 14) ( 127 + %i *0) ; ( -%i * 13 .5 ) 0

] ) / delta ;

55 I _ r_ m = abs ( I _ r ) ; // I r m =m ag ni tu de o f I r i n A

56 I _ r_ a = atan ( imag ( I _r ) / real ( I _ r ) ) * 1 8 0 / % p i ; // I r a =p h a s e a ng le o f I r i n d e g r e e s57

58 / / c as e d59 t he ta = I _p _a ; // Motor PF a n g l e i n d e g r e es60 c o s _ th e t a = c o sd ( t h e t a ) ; / / M ot or PF61

62 / / c as e e63 I_p = I_p_m ; // S t at o r a rm at u re c u r r e n t i n A64 V_p = V / sqrt ( 3 ) ; // Phase v o l t a ge i n v o l t65 SPI = V_p * I_p * co s_ th et a ; // S t a t o r Power I n pu t

i n W66

67 / / c as e f 68 SCL = ( I_p ) ^2 * R_ap ; // S t a t o r Copper L os s i n W69

70 / / c as e g71 / / S u b s c r i p t s 1 and 2 f o r RPI i n d i c a t e s two methods

o f c a l c u l a t i n g RPI72 RPI_1 = SPI - SCL ; / / R ot or Power I n pu t i n W73 R PI _2 = ( I _r _m ) ^2 * ( R _r / s) ; // R ot or Power I n pu t i n

W74 R P I = R PI _1 ;

76 / / c as e h77 R CL = s *( R PI ) ; // R ot or c o pp er l o s s e s i n W78

79 / / c as e i80 / / S u b s c r i p t s 1 , 2 and 3 f o r RPD i n d i c a t e s t h r e e

m eth od s o f c a l c u l a t i n g RPD81 RPD_1 = RPI - RCL ; / / R ot or Power D e ve l op e d i n W82 RPD_2 = RPI * ( 1 - s ) ; // R ot or Power D e ve l op e d i n

W83 RPD = RPD_1 ;

85 / / c as e j86 R PO = 3* RPD - P_r ; / / R ot or Power D e ve l op e d i n W

88 / / c as e k89 P_to = RPO ; // T ot al r o t o r power i n W90 T _ o = ( 7. 04 * P _ to ) / S _r ; // T ot al 3−p ha se t o rq u e i n

l b − f t91

92 / / c as e l93 h p = P_to / 746 ; / / O ut pu t h o r s e p o w e r94

95 // c as e m96 P_ in = 3* SPI ; // I np ut power t o s t a t o r i n W97 P_o = RPO ; / / Ou tp ut p ow er i n W

98 eta = P_o / P_in * 100 ; // Motor e f f i c i e n c y a tr a t ed l o ad

102 printf ( ” \n a : s = %. 2 f \n R r / s = %. 1 f \n” ,s ,

R _ r_ b y_ s ) ;

104 printf ( ” \n De t e r m i n a n t = ” ) ; disp ( d e l t a ) ;

106 printf (” \n b : S t at o r a rm at ur e c u r re n t : \ n I p i nA = ” ) ; disp ( I _ 1 ) ;

107 printf ( ” \n I p = I 1 = %. 2 f <%. 2 f A \n ” , I _p _m ,

I _p _a ) ;

109 printf ( ” \n c : Ro to r c u r re n t p er p ha se : \ n I r i nA = ” ) ; disp ( I _ r ) ;

110 printf ( ” \n I r = I 2 = %. 3 f <%. 2 f A \n ” , I _r _m ,

I _r _a ) ;

112 printf ( ” \n d : Mot or PF : \ n c o s = %. 4 f \n” ,

c o s _ t h e t a ) ;113

114 printf ( ” \n e : S t a t or Power I np ut : \ n SPI = %d W\n” , S P I ) ;

116 printf ( ” \n f : S t at o r Copper L os s : \ n SCL = %. 1 f

W \n” , S C L ) ;117

118 printf ( ” \n g : R ot or Power I n pu t : \ n RPI = %. 1 f W( m eth od 1 ) ” , R PI _1 ) ;

119 printf ( ” \n RPI = %. 1 f W ( method 2 ) \n” , R P I _ 2 ) ;

121 printf ( ” \n h : Ro to r c o pp er l o s s : \ n RCL = %. 1 f W\n” , R C L ) ;

123 printf ( ” \n i : R ot or Power D ev el o pe d : \ n RPD = %. 1 f W \n” , R P D _ 1 ) ;

124125 printf ( ” \n RPD = %. 1 f W \n ” , R P D _ 2 ) ;

127 printf ( ” \n j : T ot a l 3−p h as e r o t o r p ow er : \ n RPO =%f W \n” , R P O ) ;

129 printf ( ” \n k : T ot al o ut pu t t o rq u e d e ve l op e d : \ nT o = %. 2 f l b− f t \ n” , T _ o ) ;

131 printf ( ” \n l : Output h o rs e po w er : \n hp = %. 2 f

hp ( r a t ed 7 . 5 hp ) \n”, h p ) ;

133 printf ( ” \n m: Motor e f f i c i e n c y a t r at ed l oa d : \ n= %. 2 f p e r c e n t \n” , e t a ) ;

135 printf ( ” \n n : S ee F ig . 12 −12 ” ) ;

Scilab code Exa 12.17 upper and lower limit Is

11 / / G iv en d a ta12 // c od e l e t t e r = J o f SCIM ( Ex .1 2 −16 )13

15 / / c as e a16 / / From A p pe n di x A−3 , T a b l e 4 30 −7 (b ) , t h e s t a r t i n g kVA

/ hp ( w it h r o t o r l o c ke d ) i s17 // l e s s th an 7 . 9 9 , which , when s u b s t i t u t e d i n t he

f o l l o w i n g e qu at io n , y i e l d s a18 / / maximum s t a r t i n g c u r r e nt o f :19

20 / / s u b s c r i p t u f o r I s i n d i c a t e s up pe r l i m i t o f s t a r t i n g c u r r en t

21 I _ s _ u = ( 7 . 9 9 *( 7 . 5 * 10 0 0 ) ) / ( sqrt ( 3) * 2 20 ) ;

23 / / c as e b24 / / The l o w er l i m i t , c od e l e t t e r J , i s 7 . 1 kVA/ hp . Thus

26 // s u b s c r i p t l f o r I s i n d i c a t e s l o w e r l i m i t o f s t a r t i n g c u r r en t

27 I _ s _ l = ( 7 . 1 *( 7 . 5 * 10 0 0 ) ) / ( sqrt ( 3) * 2 20 ) ;

3132 printf ( ” \n a : From A p pe n di x A−3 , T a b l e 4 30 −7(b) , the

s t a r t i n g kVA/ hp ” ) ;

33 printf ( ” \n ( w i t h r ot or l o c k e d ) i s l e s s than7 . 9 9 , wh ic h , when s u b s t i t u t e d ” ) ;

34 printf ( ” \n i n t h e f o l l o w i n g e qu a t i o n , y i e l d s a

maximum s t a r t i n g c u r r e n t o f : ” ) ;35 printf ( ” \n I s = %. 1 f A \n” , I _ s _ u ) ;

37 printf ( ” \n b : The l ow er l i m i t , c o de l e t t e r J , i s 7 . 1kVA/hp . \ n Thus : ” ) ;

38 printf ( ” \n I s = %. 1 f A ” , I _s _l ) ;

Scilab code Exa 12.18 starting I and PF

7 / / E xa mp le 1 2−188

c o n s o l e .10

11 / / G iv en d a ta ( Ex . 12 −16)12 / / c o d e l e t t e r = J13 P = 6 ; // Number o f p o l e s14 S _r = 1176 ; // r o t o r s pe ed i n rpm15 V = 220 ; // Rated v o l t a g e o f SCIM i n v o l t16 f = 6 0 ; // F re qu en cy i n Hz17 h p_ SC IM = 7. 5 ; // Power r a t i n g o f SCIM i n hp18

19 R_ap = 0.3 ; // a rm at ur e r e s i s t a n c e i n ohm/ p ha se20 R_r = 0.144 ; // r o t o r r e s i s t a n c e i n ohm/ p ha se21 j X_m = 13 .5 ; // r e a c t a n c e i n ohm/ p h a se22 jX_s = 0.5 ; // s y nc h ro n o us r e a c t a n c e i n ohm/ p h as e23 jX_lr = 0.2 ; // L ock ed r o t o r r e a c t a n c e i n ohm/ p h as e

24 P_r = 300 ; // R ot at i o na l l o s s e s i n W

25 s = 1 ; // u ni ty s l i p26

29 printf ( ” \n The r a t i o R r / s = %. 3 f ohm , i n f i g .12 −11, u s i ng t he f or ma t method ” , R _ r / s ) ;

30 printf ( ” \n o f mesh a n a l y s i s , we may w r i t e t he a r ra yby i n s p e c t i o n : \ n ” ) ;

31 printf ( ” \n ”

32 printf ( ” \n \ t I 1 \ t I 2 \ t \ t V ” ) ;33 printf ( ” \

n ”) ;

34 printf ( ” \n\ t ( 0 . 3 + j 1 4 ) −(0+ j 1 3 . 5 ) \ t ( 127+ j 0 ) ” ) ;

35 printf ( ” \n\ t −(0+ j 1 3 . 5 ) ( 0. 14 4+ j 1 3 . 7 ) \ t 0 ” ) ;

36 printf ( ” \n \

n” ) ;

38 / / C a l c u l a t i o n s39

40 A = [ ( 0. 3 + %i * 14) - %i * 13 .5 ; ( - %i * 13 .5 ) ( 0. 14 4 +

% i * 1 3 .7 ) ] ; // M at ri x c o n t a i n i n g a bo ve mesh e qn sa r r a y

43 / / c as e a : S t a r t i n g s t a t o r c ur re nt I s p e r p h a s e i nA

44 I _s = det ( [ ( 12 7+ %i *0 ) ( -%i * 13 .5 ) ; 0 ( 0. 14 4 + %i

*13.7 ) ] ) / delta ;

45 I _ s_ m = abs ( I _ s ) ; // I s m =m ag ni tu de o f I s i n A46 I _ s_ a = atan ( imag ( I _s ) / real ( I _ s ) ) * 1 8 0 / % p i ; // I s a =

p h a s e a ng le o f I s i n d e g r e es47

48 // c as e b : power f a c t o r o f t h e m otor a t s t a r t i n g

49 t he ta = I _s _a ; // Motor PF a n g l e i n d e g r e es

50 c o s _ th e t a = c o sd ( t h e t a ) ; / / M ot or PF51

54 printf ( ” \n a : S t a r t i n g s t a t o r c u r re n t o f SCIM : \ nI s = I 1 = ” ) ; disp ( I _ s ) ;

55 printf ( ” \n I s = I 1 = %. 2 f <%. 2 f A \n ” , I _s _m ,

I _s _a ) ;

57 printf ( ” \n b : Power f a c t o r o f t he motor a t s t a r t i n g: \ n c o s = %. 4 f %. 3 f \n” ,cos_theta ,

c o s _ t h e t a ) ;58

59 printf ( ” \n Note : I s = %. 2 f A c a l c u l a t e d i n Ex.12 −1 8 f a l l s b et we en t h e l i m i t s ” , I _ s _ m ) ;

60 printf ( ” \n f o u n d i n Ex . 1 2 − 1 7. T hi sv e r i f i e s t h e mesh a n a l y s i s t e c h n i q u e . ” ) ;

Scilab code Exa 12.19 Re1s slip Pcu and Pr at LFs hp T

7 / / E xa mp le 1 2−198

11 / / G iv en d a ta12 V = 220 ; // Rated v o l t a g e o f SCIM i n v o l t

13 f = 6 0 ; // F re qu en cy i n Hz

14 P = 4 ; // Number o f p o l e s15 P F = 0.85 ; // power f a c t o r o f c a p a c i t o r s t a r t IM16 // n am ep la te d e t a i l s17 hp_IM = 5 ; // power r a t i n g o f IM i n hp18 I_L = 28 ; // Rated l i n e c u r r e n t i n A19 S _r = 1620 ; // R ot or s pe ed o f IM i n rpm20

21 / / No−l oa d t e s t d a t a22 I_nl = 6.4 ; / / No−l oa d l i n e c ur r e nt i n A23 V_nl = 220 ; / / No−l oa d l i n e v o l t a g e i n v o l t24 P_nl = 239 ; / / No−l o ad power r e a d in g i n W

25 s _nl = 0. 01 ; / / No−l oa d s l i p26

27 // B lo ck ed r o t o r t e s t28 I_br = 62 ; // B l o ck e d r o t o r l i n e c u r r e n t i n A29 V_br = 64 ; // B l o ck e d r o t o r v o l t a ge i n v o l t30 P _br = 19 22 ; // B lo ck ed r o t o r power r e a d in g i n W31 s_br = 1 ; // b l oc k ed r o t o r s l i p ( u n it y )32

33 / / C a l c u l a t i o n s34 / / c as e a35 R _e 1s = P _b r / ( I _b r ^2 ) ;

// E q u i v a le nt t o t a lr e s i s t a n c e o f IM i n ohm36

37 / / c as e b38 P _in = P_ nl ; // I np ut power t o IM i n W39 I _1s = I_ nl ; // I np ut c u r r e n t i n A40 P _r o = P _i n - (( I _1 s ) ^2 * R _e 1s ) ; // R o t a ti o n a l

l o s s e s i n W41

42 / / c as e c43 S = ( 12 0* f / P) ; // S pe ed o f s y nc h ro n o us m a gn e ti c

f i e l d i n rpm44 S_fl = S_r ; // F ul l −l oa d r o t o r s pe ed o f IM i n rpm45 s_fl = ( S - S_fl )/ S ; // F u ll −l oa d S l i p46

47 LF1 = 1/4 ; // Load f r a c t i o n

48 LF2 = 1/2 ; // Load f r a c t i o n

49 LF3 = 3/4 ; // Load f r a c t i o n50 LF4 = 5/4 ; // Load f r a c t i o n51

52 s _L F1 = s _f l * LF 1 ; // s l i p a t 1/4 r at ed l oa d53 s _L F2 = s _f l * LF 2 ; // s l i p a t 1/2 r at ed l oa d54 s _L F3 = s _f l * LF 3 ; // s l i p a t 3/4 r at ed l oa d55 s _L F4 = s _f l * LF 4 ; // s l i p a t 5/4 r at ed l oa d56

57 / / c as e d58 s _o = s_nl ; / / No−l oa d s l i p59 P _r s_ LF 1 = P _r o * (1 - s _L F1 ) /(1 - s_ o) ; //

R o t a ti o na l l o s s e s i n W a t s LF 160 P _r s_ LF 2 = P _r o * (1 - s _L F2 ) /(1 - s_ o) ; //

R o t a ti o na l l o s s e s i n W a t s LF 261 P _r s_ LF 3 = P _r o * (1 - s _L F3 ) /(1 - s_ o) ; //

R o t a ti o na l l o s s e s i n W a t s LF 362 P _r s_ fl = P_ ro * (1 - s_ fl ) /(1 - s_o ) ; // R o t a ti o n a l

l o s s e s i n W a t f u l l − l o ad s l i p63 P _r s_ LF 4 = P _r o * (1 - s _L F4 ) /(1 - s_ o) ; //

R o t a ti o na l l o s s e s i n W a t s LF 464

65 / / c as e e66 I1s = I_L ; // L i n e c ur r e n t i n A

67 P _ c u_ f l = ( I 1s ) ^ 2* R _ e1 s ; // E q u i va l e nt c op pe r l o s sa t f u l l −l oa d s l i p

68 P _c u_ LF 1 = ( L F1 ) ^2 * P _c u_ fl ; // E q u i v a le n t c o pp e rl o s s a t s LF1

71 P _c u_ LF 4 = ( L F4 ) ^2 * P _c u_ fl ; // E q u i v a le n t c o pp e r

l o s s a t s LF472

73 / / c as e f 74 I np ut = V * I_ L *PF ; // I np ut t o s i n g l e p h a s e

c a p a c i t o r s t a r t IM

76 // E f f i c i e n c y a t 1 /4 r at ed l oa d77 e ta _L F1 = ( I np ut * LF1 - ( P _r s_ LF 1 + P _c u_ LF 1 ) ) / (

I np ut * L F1 ) * 1 00 ;

I np ut * L F2 ) * 1 00 ;

I np ut * L F3 ) * 1 00 ;

8485 / / E f f i c i e n c y a t r at ed l o ad86 e ta _f l = ( I np ut - ( P _r s_ fl + P _c u_ fl ) ) / ( I np ut ) *

1 00 ;

I np ut * L F4 ) * 1 00 ;

91 / / c as e g92

/ / s i n c e e t a i s c a l c u l a t e d i n p er ce n t d i v i d e i t by100 f o r hp c a l c u l a t i o n s93 P _ o _ LF 1 = ( I n p ut * L F 1 * e t a _ LF 1 / 1 0 0 ) / 7 46 ; / / O ut pu t hp

a t 1/4 r a te d l oa d94 P _ o _ LF 2 = ( I n p ut * L F 2 * e t a _ LF 2 / 1 0 0 ) / 7 46 ; / / O ut pu t hp

a t 1/2 r a te d l oa d95 P _ o _ LF 3 = ( I n p ut * L F 3 * e t a _ LF 3 / 1 0 0 ) / 7 46 ; / / O ut pu t hp

a t 3/4 r a te d l oa d96 P _o = ( I n pu t * e t a_ fl / 1 0 0) / 7 46 ; / / Output hp a t 1 /4

r a t ed l o ad97 P _ o _ LF 4 = ( I n p ut * L F 4 * e t a _ LF 4 / 1 0 0 ) / 7 46 ; / / O ut pu t hp

a t 5/4 r a te d l oa d98

99 / / c as e h100 h p = P_o ; // R at ed o u tp u t h o r s e po w e r101 S_fl = S_r ; // F ul l −l oa d r o t o r s pe ed i n rpm

102 T _ o = ( P _o * 5 2 52 ) / S _f l ; // Outpue t o rq u e a t f u l l −

l oa d i n l b − f t103 T _o _N m = T_o * 1 .3 56 ; // Outpue t o rq u e a t f u l l − l o a di n N−m

108 printf ( ” \n a : E qu iv al en t t o t a l r e s i s t a n c e o f IM : \ nR e 1 s = %. 1 f \n” , R _ e 1 s ) ;

110 printf ( ” \n b : R ot at i o na l l o s s e s : \ n P r o = %. 1 f

W \n ” , P _ r o ) ;111

112 printf ( ” \n c : S l i p a t r at ed l oa d : s = %. 1 f \nS l i p , ” , s _ f l ) ;

113 printf ( ” \n s a t %. 2 f r a te d l o a d = %. 3 f ” , L F 1 ,

s _ L F 1 ) ;

s _ L F 2 ) ;

s _ L F 3 ) ;

116 printf (” \n s a t %. 2 f r a t e d l o a d = %. 3 f \n ”

, L F 4 ,

s _ L F 4 ) ;

118 printf ( ” \n d : R ot at i o na l l o s s e s : \ n ” ) ;

119 printf ( ” \n P r a t a t %. 2 f r a te d l o a d = %. 1 f W ” ,

L F 1 , P _ r s _ L F 1 ) ;

L F 2 , P _ r s _ L F 2 ) ;

L F 3 , P _ r s _ L F 3 ) ;

122 printf ( ” \n P r a t a t f u l l l o a d = %. 1 f W ” ,

P _ r s _ f l ) ;123 printf ( ” \n P r a t a t %. 2 f r a te d l o a d = %. 1 f W \n

” , L F 4 , P _ r s _ L F 4 ) ;

125 printf ( ” \n e : At f u l l −l o a d , P c u = %d W \n” , P _ c u _ f l

126 printf ( ” \n P cu a t %. 2 f r at ed l oa d = %. 2 f W” ,LF1, P _ c u _ L F 1 )

127 printf ( ” \n P cu a t %. 2 f r at ed l oa d = %. 2 f W” ,LF2

, P _ c u _ L F 2 )

128 printf ( ” \n P cu a t %. 2 f r at ed l oa d = %. 2 f W” ,LF3

, P _ c u _ L F 3 )

129 printf ( ” \n P cu a t %. 2 f r a te d l o a d = %. 2 f W \n” ,

L F 4 , P _ c u _ L F 4 )

131 printf ( ” \n f : F ul l −l o a d i n p u t = %. f W \n” , I n p u t ) ;

132 printf ( ” \n E f f i c i e n c y : \ n a t %. 2 f r a t e d

l o a d = %. 1 f p e r c e n t \n” , L F 1 , e t a _ L F 1 ) ;133 printf ( ” \n a t %. 2 f r at e d l o a d = %. 1 f p e r c e n t

\n” , L F 2 , e t a _ L F 2 ) ;

135 printf ( ” \n a t r a t e d l o a d = f l = %. 1 f p e r c e n t \n” , e t a _ f l ) ;

137 printf ( ” \n P l e a s e n o t e : C a l c u l a ti on e r r o r f o r

f l i n t e xt bo o k . \ n”) ;

139 printf ( ” \n g : Output h o rs e po w er : \ n P o at %. 2 f r a t e d l o a d = %. 3 f hp \n” , L F 1 , P _ o _ L F 1 ) ;

L F 2 , P _ o _ L F 2 ) ;

L F 3 , P _ o _ L F 3 ) ;

142 printf ( ” \n P o a t r a t e d l o a d = %. 3 f hp \n” , P _ o ) ;

L F 4 , P _ o _ L F 4 ) ;

144145 printf ( ” \n h : Output t o rq u e a t f u l l −l oa d : \ n T o

= %. 1 f l b− f t ” , T _ o ) ;

146 printf ( ” \n T o = %. 2 f N−m %. 1 f N−m” , T _ o _ N m ,

T _ o _ N m ) ;

Chapter 13

RATINGS SELECTION AND

MAINTENANCE OF

ELECTRIC MACHINERY

Scilab code Exa 13.1 R and reduced life expectancy

6 // Ch apt e r 1 3 : RATINGS , SELECTION ,AND MAINTENANCE OFELECTRIC MACHINERY

7 / / E xa mp le 13−18

11 / / G iv en d a ta12 // MOTOR( c l a s s A i n s u l a t i o n ) i s o p er a te d f o r 6 h r s13 T = 125 ; // Te mper at ur e i n d e g r ee c e l s i u s r e co r de d

by t h e embedded d e t e c t o r s14 l i fe _o ri g = 1 0 ; // L i f e i n y ea r s o f t h e motor (

s t a n d a r d )

1516 / / C a l c u l a t i o n s17 d elta _T = T - 105 ; // P o s i t i v e t em p er at u re

d i f f e r e n c e be t we en t he g i v en18 / / max h o t t e s t s po t t em pe ra tu re o f i t s i n s u l a t i o n

and t h e a mb ie nt t e m pe r a tu r e r e c o r d e d .19 / / 1 05 i s c ho se n from t a b l e 13 −1( c l a s s A i n s u l a t i o n )20 R = 2 ^ ( d el ta _T / 10 ); // L i f e r e d u ct i o n f a c t o r21

22 L if e_ ca lc = l if e_ or ig / R ; // R e duc ed l i f ee xp ec ta n cy o f t he motor i n y e a rs

26 printf ( ” \n L i f e r e d u c ti o n f a c t o r : R = %d \n ” ,R )

27 printf ( ” \n Reduced l i f e e x p ec t a nc y o f t h e mo to r :L i f e c a l c = %. 1 f y e ar s ” , L i f e _ c a l c ) ;

Scilab code Exa 13.2 E and increased life expectancy

7 / / E xa mp le 13−2

12 // MOTOR( c l a s s A i n s u l a t i o n ) i s o p er a te d f o r 6 h r s

13 T = 7 5 ; // T empe r atu re i n d e g r e e c e l s i u s r e c o rd e dby t h e embedded d e t e c t o r s14 l i fe _o ri g = 1 0 ; // L i f e i n y ea r s o f t h e motor (

s t a n d a r d )15

16 / / C a l c u l a t i o n s17 d elta _T = 105 - T ; // P o s i t i v e t em p er at u re

d i f f e r e n c e be t we en t he g i v en18 / / max h o t t e s t s po t t em pe ra tu re o f i t s i n s u l a t i o n

and t h e a mb ie nt t e m pe r a tu r e r e c o r d e d .19 // 105 i s c ho se n from t a b l e 13−1 ( c l a s s A i n s u l a t i o n

)20 E = 2 ^ ( d el ta _T / 10 ); // L i f e e x t e n s i o n f a c t o r21

22 L if e_ ca lc = l if e_ or ig * E ; / / I n c r e a s e d l i f ee xp ec ta n cy o f t he motor i n y e a rs

26 printf ( ” \n L i f e e x t e n s i o n f a c t o r : E = %d \n ” , E ) ;

27 printf ( ” \n I n c r e a s e d l i f e e xp ec ta n cy o f t he motor :

L i f e c a l c = %d y ea r s ”, L i f e _ c a l c ) ;

Scilab code Exa 13.3 E and increased life expectancy classB

7 / / E xa mp le 13−38

c o n s o l e .10

11 / / G iv en d a ta12 / / C la ss A i n s u l a t i o n13 T_A = 105 ; // Te mp er at ure i n d e g re e c e l s i u s

r e c o r d e d by t h e embedded d e t e c t o r s14 l if e_ or ig = 5 ; // L i f e i n y ea rs o f t h e motor (

s t a n d a r d )15 / / C la ss B i n s u l a t i o n16 T_B = 130 ; // Te mp er at ure i n d e g re e c e l s i u s

r e c o r d e d by t h e embedded d e t e c t o r s

1718 / / C a l c u l a t i o n s19 d elta _T = T_B - T_A ; // P o s i t i v e t em pe ra t ur e

d i f f e r e n c e betw t he g i v en20 / / max h o t t e s t s po t t em pe ra tu re o f i t s i n s u l a t i o n

and t h e a mb ie nt t e m pe r a tu r e r e c o r d e d .21 // T A and T B a r e c ho se n fro m t a b l e 13−122 E = 2 ^ ( d el ta _T / 10 ); // L i f e e x t e n s i o n f a c t o r23

24 L if e_ ca lc = l if e_ or ig * E ; / / I n c r e a s e d l i f e

e xp ec ta n cy o f t he motor i n y e a rs25

28 printf ( ” \n L i f e e x t e n s i o n f a c t o r : E = %. 2 f \n ” ,E

29 printf ( ” \n I n c r e a s e d l i f e e xp ec ta n cy o f t he motor :L i f e c a l c = %. 1 f y e a r s ” , L i f e _ c a l c ) ;

Scilab code Exa 13.4 ClassB insulation SCIM details

4 / / 2 nd e d i t i om5

7 / / E xa mp le 13−48

11 / / G iv en d a ta12 P_o = 25 ; / / R at ed p ow er o f SCIM i n hp

13 / / c l a s s B i n s u l a t i o n14 T _ am bi en t = 4 0 ; // S t an d ar d a m bi en t t e m p e r at u r e

r e c o r d e d by t h e embedded h ot−s po t d e t e c t o r s i nd eg re e c e l s i u s

15 T _h ot te st = 1 15 ; / / H o tt e st −s p o t w in d in gt e m p e r at u r e r e c o r d e d by t h e em bed ded h ot−s p o td e t e c t o r s i n d eg re e c e l s i u s

17 / / C a l c u l a t i o n s18 / / c as e a19

/ / from t a b l e 13−1 a l l o w a b l e t em pe ra tu re r i s e i n 90d eg re e c e l s i u s20

21 / / c as e b22 T _r is e = T _h ot te st - T _a mb ie nt ; // A c tu a l

t em pe r at ur e r i s e f o r t h e i n s u l a t i o n t y p e u se d i nd eg re e c e l s i u s

24 / / c as e c25 P _f = P _o * ( 90 / T _r is e ); // A pp ro xi ma te p ow er t o t h e

motor t ha t can be d e l i v e r e d a t T r i s e

2627 / / c as e d28 / / same a s P f 29

30 / / c as e e

31 / / a ns we r fro m c a s e a

35 printf ( ” \n a : The a l l o w a b l e t em pe ra tu re r i s e f o rt h e ” ) ;

36 printf ( ” \n i n s u l a t i o n t y p e u se d = 90 d e g r e ec e l s i u s ( fro m t a b l e 13 −1) \n” ) ;

38 printf ( ” \n b : The a c t ua l t em pe ra tu re r i s e f o r t hei n s u l a t i o n t yp e us ed = %d d e g re e c e l s i u s \ n” ,

T _ r i s e ) ;

3940 printf ( ” \n c : The a p pr o xi m at e po we r t o t h e m oto r

t ha t can be d e l i v e r e d a t T r i s e ” ) ;

41 printf ( ” \n P f = %d hp\n” , P _ f ) ;

43 printf ( ” \n d : Power r a t i n g t h a t may be s ta mp ed ont he n am ep la te = %d hp ( s u b j e c t t o t e s t a t t h i sl o a d ) \n ” , P _ f ) ;

45 printf ( ” \n e : The t em pe ra t ur e r i s e t h at must be

stamped on t he n am ep la te = 90 d e gr e e c e l s i u s ”) ;

Scilab code Exa 13.5 final temperature

7 / / E xa mp le 13−58

c o n s o l e .10

11 / / G iv en d a ta12 P_o = 50 ; // Power r a t i n g o f t h e WRIM i n hp13 / / C la ss F i n s u l a t i o n14 T _h ot te st = 1 60 ; / / H o tt e st −s p o t w in d in g

t e m p e r at u r e r e c o r d e d by t h e em bed ded15 / / h ot−s po t d e t e c t o r s i n d eg re e c e l s i u s16 T _ am bi en t = 4 0 ; // S t an d ar d a m bi en t t e m p e r at u r e

r e c o r d e d by t h e embedded17 / / h ot−s po t d e t e c t o r s i n d eg re e c e l s i u s

18 P_f_a = 40 ; // Power r a t i n g o f l oa d a i n hp19 P_f_b = 55 ; // Power r a t i n g o f l oa d a i n hp20

21 / / C a l c u l a t i o n s22 / / c as e a23 d e l ta _ T_ o = T _ ho t te s t - T _ am b ie n t ; / / T e m p er a t u re

r i s e f o r t h e i n s u l a t i o n t y p e24 / / u s e d i n d eg re e c e l s i u s25

26 // s u b s c r i p t a i n d e l t a T f , P f a and T f i n d i c a t e s

c a s e a27 d e l t a _T _ f _a = ( P _ f _a / P _ o ) * d e l t a _T _ o ; // f i n a lt em pe r at ur e r i s e i n d eg re e c e l s i u s

28 T _f _a = d el ta _T _f _a + T _a mb ie nt ; / / A p p ro x i ma t ef i n a l hot−s po t t em pe ra tu re i n d e g r e e c e l s i u s

30 / / c as e b31 // s u b s c r i p t b i n d e l t a T f , P f and T f i n d i c a t e s

c a s e b32 d e l t a _T _ f _b = ( P _ f _b / P _ o ) * d e l t a _T _ o ; // f i n a l

t em pe r at ur e r i s e i n d eg re e c e l s i u s

33 T _f _b = d el ta _T _f _b + T _a mb ie nt ; / / A p p ro x i ma t ef i n a l hot−s po t t em pe ra tu re i n d e g r e e c e l s i u s

37 printf ( ” \n a : T o = %d d e g r e e c e l s i u s ” , d e l t a _ T _ o

) ;38 printf ( ” \n T f = %d d e g r e e c e l s i u s ” ,

d e l t a _ T _ f _ a ) ;

39 printf ( ” \n T f = %d d e g r e e c e l s i u s \n” , T _ f _ a ) ;

41 printf ( ” \n b : T f = %d d e g r e e c e l s i u s ” ,

d e l t a _ T _ f _ b ) ;

42 printf ( ” \n T f = %d d e g r e e c e l s i u s \n” , T _ f _ b ) ;

43 printf ( ” \n Yes , motor l i f e i s r e du ce d a t t h e 110p e r ce n t motor l o ad b e ca u se ” ) ;

44 printf ( ” \n t he a l l o wa b l e maximum hot−s p o t m ot or

t em p er a tu r e f o r C l a ss F ”) ;45 printf ( ” \n i n s u l a t i o n i s 155 d e g r e e c e l s i u s . ” ) ;

Scilab code Exa 13.6 Tf R decreased life expectancy

4 / / 2 nd e d i t i om5

7 / / E xa mp le 13−68

12 P_o = 55 ; // Power r a t i n g o f t h e WRIM i n hp13 T _ am bi en t = 4 0 ; // S t an d ar d a m bi en t t e m p e r at u r er e c o r d e d by t h e embedded

14 / / h ot−s po t d e t e c t o r s i n d eg re e c e l s i u s15 l i fe _o ri g = 1 0 ; // L i f e i n y ea r s o f t h e motor (

s t a n d a r d )

1617 / / C a l c u l a t e d d at a fr om Ex .13 −5 b18 T_f = 172 ; // A pp ro xi ma te f i n a l h ot−s p o t

t em pe ra tu re i n d e g r e e c e l s i u s19

20 / / C a l c u l a t i o n s21 d elta _T = T_f - 155 ; // P o s i t i v e t em pe ra t ur e

d i f f e r e n c e betw t he g i v en22 / / max h o t t e s t s po t t em pe ra tu re o f i t s i n s u l a t i o n

and t h e a mb ie nt t e m pe r a tu r e r e c o r d e d .23 / / 1 55 i s c ho se n from t a b l e 13 −1( c l a s s F i n s u l a t i o n )

2425 R = 2 ^ ( d el ta _T / 10 ); // L i f e r e d u ct i o n f a c t o r26

27 L if e_ ca lc = l if e_ or ig / R ; // R e duc ed l i f ee xp ec ta n cy o f t he motor i n y e a rs

31 printf ( ” \n From Ex.13 −5 b , T f = %d d e g re e c e l s i u s \ n”, T _ f ) ;

32 printf (” \n L i f e r e d u ct i on f a c t o r : R = %. 2 f \n ”

33 printf ( ” \n Reduced l i f e e x p ec t a nc y o f t h e mo to r :L i f e c a l c = %. 2 f y e ar s ” , L i f e _ c a l c ) ;

Scilab code Exa 13.7 rms hp

6 // Ch apt e r 1 3 : RATINGS , SELECTION ,AND MAINTENANCE OF

ELECTRIC MACHINERY

7 / / E xa mp le 13−78

11 / / G iv en d a ta12 P_o = 200 ; // Power r a t i n g o f t he t e s t motor i n hp13 t1 = 5 ; // t im e d u ra t io n i n m in ut es f o r which t e s t

motor i s o pe r a t e d a t 200 hp14 t2 = 5 ; // t im e d u ra t io n i n m in ut es f o r which t e s t

motor i s o pe r a t e d a t 20 hp

15 t3 = 10 ; // t i me d u ra t io n i n m in ut es f o r whi ch t e s tmotor i s o p er at ed a t 100 hp

17 / / C a l c u l a t i o n18 r m s _h p = sqrt ( ( ( 20 0^ 2) * t1 + ( 20 ^2 ) * t2 + ( 10 0^ 2) * t3

) / ( t 1 + t 2 + t 3 + 1 0 / 3 ) ) ;

19 / / H or s epo we r r e q ui r e d f o r i n t e r m i t t e n t v ar y i ng l oa d20

23 printf (” \n H o rse p ow e r r e q ui r e d f o r i n t e r m i t t e ntv a ry i ng l o a d i s : ” ) ;

24 printf ( ” \n rms hp = %. f hp \n ” , r m s _ h p ) ;

26 printf ( ” \n A 12 5 h p m otor would be s e l e c t e d b e ca u set ha t i s t h e n e ar e st l a r g e r ” ) ;

27 printf ( ” \n c o m me r ci a l s t a n d a r d r a t i n g . T h is meanst h at t he motor would o p e ra t e ” ) ;

28 printf ( ” \n w it h a 160 p e rc e n t o v er l oa d ( a t 200 hp )f o r 5 m in ute s , o r 1/ 6 th o f ” )

29 printf ( ” \n i t s t o t a l duty c y c l e . ” ) ;

Scilab code Exa 13.8 Vb Ib Rb Rpu

7 / / E xa mp le 13−88

11 / / G iv en d a ta12 V = 120 ; // Rated o ut pu t v o l t a g e i n v o l t o f

s e p a r a t e l y e x c i t ed dc g e n er a t or13 I = 100 ; // Rated o ut pu t c u r re n t i n A o f s e p a r a t e l y

e x c i t ed dc g e ne r a to r14 R = 0.1 ; // Armature r e s i s t a n c e i n ohm15

16 / / C a l c u l a t i o n s17 / / c as e a18 V_b = V ; // b a s e v o l t a g e i n v o l t19

20 / / c as e b21 I_b = I ; // b as e c u r r e n t i n A22

23 / / c as e c24 R_b = V_b / I_b ; // b a se r e s i s t a n c e i n ohm25

26 / / c as e d27 R_pu = R / R_b ; // p er −u n i t v a lu e o f a rm at ur e

r e s i s t a n c e i n p . u28

32 printf ( ” \n a : Base v o l t a g e \n V b = %d V \n ” ,

V _b ) ;

34 printf ( ” \n b : Bas e c u r r e nt \n I b = %d A \n ” ,I _b ) ;

36 printf ( ” \n c : Base r e s i s t a n c e \n R b = %. 1 f ohm\n ” , R _ b ) ;

38 printf ( ” \n d : Per−u n it v al u e o f a rm at ur e r e s i s t a n c e\n R p . u = %. 3 f p . u \n ” , R_pu ) ;

Scilab code Exa 13.9 Rpu jXpu Zpu

7 / / E xa mp le 13−9

c o n s o l e .10

11 / / G iv en d a ta12 // s i n g l e p h a s e a l t e r n a t o r13 V = 500 ; // R ated v o l t a ge o f t he a l t e r n a t o r i n v o l t14 P = 2 0 ; // Rated power o f t he a l t e r n a t o r i n kVA15 I = 4 0 ; // Rated c u r r e n t o f t h e a l t e r n a t o r i n A16 R = 2 ; // Armature r e s i s t a n c e i n ohm

17 X = 1 5 ; // A rm at ur e r e a c t a n c e i n ohm18

19 / / C a l c u l a t i o n s20 / / c as e a21 V_b = V ; // b a s e v o l t a g e i n v o l t

22 I_b = I ; // b as e c u r r e n t i n A

23 R _p u = ( R *I _b ) / V_ b ; / / p er −u n i t v a lu e o f a rm at ur er e s i s t a n c e i n p . u24

25 / / c as e b26 j X_ pu = ( X * I_ b )/ V _b ; // p er −u n i t v a lu e o f a rm at ur e

r e a c t a n c e i n p . u27

28 / / c as e c29 // s u b s c r i p t 1 i n d i c a t e s method 1 f o r f i n d i n g Z p . u30 Z _p u1 = R _p u + %i * ( jX _p u ); // p er −u n i t v al ue o f

a r m a t ur e i m pe d an c e i n p . u

31 Z _ p u1 _ m = abs ( Z _ p u 1 ) ; / / Z p u1 m = m ag n it ud e o f Z pu 1i n p . u

32 Z _ p u1 _ a = atan ( imag ( Z _ pu 1 ) / real ( Z _ p u 1 ) ) * 1 8 0 / % p i ; //Z pu 1 a=p ha se a n gl e o f Z pu1 i n d e gr e e s

34 // s u b s c r i p t 2 i n d i c a t e s method 2 f o r f i n d i n g Z p . u35 Z _p u2 = ( R + %i * X) *( I /V ) ; / / p er −u ni t v al ue o f

a r m a t ur e i m pe d an c e i n p . u36 Z _ p u2 _ m = abs ( Z _ p u 2 ) ; / / Z p u2 m = m ag n it ud e o f Z pu 2

i n p . u37 Z _ p u2 _ a = atan ( imag ( Z _ pu 2 ) / real ( Z _ p u 2 ) ) * 1 8 0 / % p i ;

//Z pu 2 a=p ha se a n gl e o f Z pu2 i n d e gr e e s38

42 printf ( ” \n a : Armature r e s i s t a n c e p er u n it v al u e \nR p . u = %. 2 f p . u \n” , R _ p u ) ;

44 printf ( ” \n b : Armature r e a c t a nc e p er u n i t v a lu e \n j X p . u i n p . u = ” ) ; disp ( % i * j X _ p u ) ;

4546 printf ( ” \n c : Ar ma tu re i mp ed an ce p e r u n i t v a l u e \n” )

47 printf ( ” \n ( method 1 ) \n Z p . u i n p . u = ” ) ;

disp ( Z _ p u 1 ) ;

48 printf ( ” \n Z p . u = %. 3 f <%. 1 f p . u \n” ,Z_pu1_ m ,

Z _ pu 1 _a ) ;49

50 printf ( ” \n ( method 2 ) \n Z p . u i n p . u = ” ) ;

disp ( Z _ p u 2 ) ;

51 printf ( ” \n Z p . u = %. 3 f <%. 1 f p . u \n” ,Z_pu2_ m ,

Z _ pu 2 _a ) ;

Scilab code Exa 13.10 new Zpu

7 / / E xa mp le 1 3−108

c o n s o l e .10

11 / / G iv en d a ta12 // s i n g l e p h a s e a l t e r n a t o r13 V _o ri g = 500 ; // Rated v o l t a ge o f t he a l t e r n a t o r i n

v o l t14 k VA _o ri g = 20 ; // Rated power o f t he a l t e r n a t o r i n

kVA15 I = 4 0 ; // Rated c u r r e n t o f t h e a l t e r n a t o r i n A16 R = 2 ; // Armature r e s i s t a n c e i n ohm

17 X = 1 5 ; // A rm at ur e r e a c t a n c e i n ohm18

19 V _n ew = 50 00 ; // New v o l t a ge o f t h e a l t e r n a t o r i nv o l t

20 k VA _n ew = 10 0 ; // New p ower o f t he a l t e r n a t o r i n

2122 / / C a l c u l a t e d a r ma t ur e i mp ed an ce f ro m Ex .1 3 −9 c23 Z _p u_ or ig = 1 .2 11 ; // o r i g i n a l per −u ni t v al ue o f

a r m a t ur e i m pe d an c e i n p . u24

25 / / C a l c u l a t i o n26 Z _ pu _n e w = Z _ pu _ or i g * ( k V A_ ne w / k V A_ or i g ) * ( V _ or ig /

V _n ew ) ^ 2 ;

27 / / new p e r−u n i t v a l u e o f a rm at ur e i mp ed an ce i n p . u28

30 disp ( ”E x ampl e 13−10 S o l u t i o n : ” ) ;31 printf ( ” \n New pe r−u n i t v a l u e o f a rm at ur e i mp ed an ce

\n Z p u ( n ew ) = %. 5 f p . u ” , Z _ p u _ n e w ) ;

Scilab code Exa 13.11 line and phase Vpu

7 / / E xa mp le 1 3−118

11 / / G iv en d a ta12 // 3−p ha se d i s t r i b u t i o n s ys te m13 V = 2300 ; // L i n e v o l t a g e o f 3−p h a se d i s t r i b u t i o n

s ys te m i n v o l t14 V _p = 1328 ; // Phase v o l t a g e o f 3−p h a s e

d i s t r i b u t i o n s y s t e m i n v o l t

1516 V _b = 6 90 00 ; // Common b a s e l i n e v o l t a g e i n v o l t17 V_ pb = 3 984 0 ; // Common b a se p ha se v o l t a g e i n v o l t18

19 / / C a l c u l a t i o n s20 / / c as e a21 V_ pu _l in e = V / V_b ; // D i s t r i b u t i o n s ys te m p . u

l i n e v o l t a g e22

23 / / c as e a24 V _p u_ ph as e = V _p / V _pb ; // D i s t r i b u t i o n s ys te m p . u

p ha se v o l t a g e25

28 printf ( ” \n a : D i s t r i b u t i o n sy st e m p . u l i n e v o l t a g e: \ n V pu = %. 2 f p . u\n” , V _ p u _ l i n e ) ;

30 printf ( ” \n b : D i s t r i b u t i o n s ys te m p . u p ha se v o l t a g e: \ n V pu = %. 2 f p . u\n” , V _ p u _ p h a s e ) ;

Scilab code Exa 13.12 Zb Xs Ra Zs P

6 // Ch apt e r 1 3 : RATINGS , SELECTION ,AND MAINTENANCE OF

ELECTRIC MACHINERY7 / / E xa mp le 1 3−128

11 / / G iv en d a ta12 VA_b = 50 ; // Base power r a t i n g o f t he 3−p h a s e Y−c o n ne c te d a l t e r n a t o r i n MVA

13 V_b = 25 ; // Base v o l t a ge o f t he 3−p h a s e Y−c on ne ct ed a l t e r n a t o r i n kV

14 X_pu = 1.3 ; // p er u n it v al ue o f s yn ch ro no usr e a c t a n c e

15 R_pu = 0.05 ; // p e r u ni t v al ue o f r e s i s t a n c e16

19 // s u b s c r i p t 1 f o r Z b i n d i c a t e s method 1 f o rf i n d i n g Z b

20 Z_ b1 = ( V_b ) ^2 / VA _b ; / / B as e i m pe da n ce i n ohm21

22 // s u b s c r i p t 2 f o r Z b i n d i c a t e s method 2 f o rf i n d i n g Z b

23 S _b = VA_b ; // Base power r a t i n g o f t he 3−p h a s e Y−c o n ne c te d a l t e r n a t o r i n MVA

24 I _ b = ( S _b ) / V_ b ; // Base c u r re n t i n kA25 Z_b2 = V_b / I_b ; / / B as e i m pe da n ce i n ohm26

27 / / c as e b28 Z_b = Z _b 1; / / B as e i mp ed a nc e i n ohm29 X_s = X_pu * Z_b ; // A ct ua l v a lu e o f s yn ch ro no u s

r e a c t a nc e p er p ha se i n ohm30

31 / / c as e c32 R_a = R_pu * Z_b ; // A ct ua l v a lu e o f a rm at ur e

s t a t o r r e s i s t a n c e p er p h a se i n ohm33

34 / / c as e d

35 / / s u b s c r i p t 1 f o r Z s i n d i c a t e s method 1 f o rf i n d i n g Z s

36 Z_s1 = R_a + %i * X_s ; // S y nc h ro n o us i m pe da n ce p e rp h a se i n ohm

37 Z _ s 1_ m = abs ( Z _ s 1 ) ; // Z s1 m = m ag ni tu de o f Z s 1 i n

38 Z _ s 1_ a = atan ( imag ( Z _s 1 ) / real ( Z _ s 1 ) ) * 1 8 0 / % p i ; //Z s 1 a=p h a se a ng l e o f Z s1 i n d e g r e e s39

40 / / s u b s c r i p t 2 f o r Z s i n d i c a t e s method 2 f o rf i n d i n g Z s

41 Z_ pu = R_ pu + %i * X_ pu ; // p e r u ni t v al ue o f i mpe danc e

42 Z_s2 = Z_pu * Z_b ; / / S y nc h ro n ou s i mp ed an ce p e rp h a se i n ohm

43 Z _ s 2_ m = abs ( Z _ s 2 ) ; // Z s2 m = m ag ni tu de o f Z s 2 i nohm

44 Z _ s 2_ a = atan ( imag ( Z _s 2 ) / real ( Z _ s 2 ) ) * 1 8 0 / % p i ; //Z s 2 a=p h a se a ng l e o f Z s2 i n d e g r e e s

46 / / c as e e47 S = S_b ; // Base power r a t i n g o f t he 3−p h a s e Y−

c o n ne c te d a l t e r n a t o r i n MVA48 P = S * R_pu ; // F u ll −l o a d c o p p e r l o s s e s f o r a l l

t h r e e p h a s es i n MW49

53 printf ( ” \n a : B as e i m pe d an c e ( m et ho d 1 ) : \n Z b =%.1 f ohm\n” , Z _ b 1 ) ;

54 printf ( ” \n Base i mpe danc e ( method 2 ) : ” ) ;

55 printf ( ” \n I b = %d kA \n Z b = %. 1 f ohm\n” ,

I _ b , Z _ b 2 ) ;

57 printf ( ” \n b : A ct ua l v a l ue o f s yn ch ro n ou s r e a c t a n cep e r p h a s e : ” ) ;

58 printf ( ” \n X s i n ohm = ” ) ; disp ( % i * X _ s ) ;

5960 printf ( ” \n c : A ct ua l v al u e o f a rm at u re s t a t o r

r e s i s t a n c e p e r p h a s e : ” ) ;

61 printf ( ” \n R a = %. 3 f ohm \n ” , R_ a ) ;

63 printf ( ” \n d : S yn ch ro no u s i mp ed an ce p e r p ha se (

m et ho d 1 ) : ” ) ;64 printf ( ” \n Z s i n ohm = ” ) ; disp ( Z _ s 1 ) ;

65 printf ( ” \n Z s = %. 2 f <%.1 f ohm\n” , Z _ s 1 _ m , Z _ s 1 _ a

66 printf ( ” \n S y n c h r o no us impeda nce p e r p h a s e (method 2 ) : ” ) ;

67 printf ( ” \n Z s i n ohm = ” ) ; disp ( Z _ s 2 ) ;

68 printf ( ” \n Z s = %. 2 f <%.1 f ohm\n” , Z _ s 2 _ m , Z _ s 2 _ a

70 printf ( ” \n e : F ul l −l o a d c o p p e r l o s s e s f o r a l l 3

p ha se s : \n P = %. 1 f MW” , P ) ;

Chapter 14

TRANSFORMERS

Scilab code Exa 14.1 stepup stepdown alpha I1

6 // Ch ap te r 1 4 : TRANSFORMERS

7 / / E xa mp le 14−18

11 / / G iven d at a f o r S te p −down t r a n s f o r m e r12 N_1 = 500 ; // Number o f t u r n s i n t h e p ri ma ry13 N_2 = 100 ; // Number o f t u r ns i n t he s ec o nd a ry14 I_2 = 12 ; / / Load ( S ec on d ar y ) c u r r e n t i n A15

16 / / C a l c u l a t i o n s17 / / c as e a18 a l p h a = N _ 1 / N _ 2 ; // T ra n sf o rm a ti o n r a t i o19

20 / / c as e b

21 I _1 = I_2 / alpha ; / / Load c om po ne nt o f p r im a ry

c u r r e n t i n A22

23 / / c as e c24 // s u n s c r i p t c f o r a l p h a i n d i c a t e s c as e c25 / / F or s t ep up t r an s f o r me r , u s in g above g i ve n d at a26 N 1 = 100 ; // Number o f t u r n s i n t h e p ri ma ry27 N 2 = 500 ; // Number o f t u rn s i n t he s e co n da r y28 a lpha _c = N1 / N2 ; // T ra n sf o rm a ti o n r a t i o29

3233 printf ( ” \n a : T r a ns f o rm a t io n r a t i o ( s te p −down

t r a n s fo r m e r ) : \ n = %d\n” , a l p h a ) ;

35 printf ( ” \n b : Load co mp on en t o f p ri ma ry c u r r e n t : \n I 1 = %. 1 f A \n” , I _ 1 ) ;

37 printf ( ” \n c : T r a ns f o rm a t io n r a t i o ( s te p −upt r a n s fo r m e r ) : \ n = %. 1 f ” , a l p h a _ c ) ;

Scilab code Exa 14.2 turns I1 I2 stepup stepdown alpha

7 / / E xa mp le 14−28

12 V _h = 2300 ; // h i g h v o l t a g e i n v o l t13 V_l = 115 ; // low v o l t a ge i n v o l t14 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t15 V_2 = 115 ; // S ec on da ry v o l t a g e i n v o l t16 f = 6 0 ; // F re qu en cy i n Hz17 S = 4.6 ; // kVA r a t i n g o f t he s te p −down t r a n s f o r m e r18 S_1 = S ;

19 S_2 = S ;

20 V _p er _t ur n = 2 .5 ; / / I n d uc e d EMF p e r t u r n i n V/ t u r n21 // I d e a l t r an s f or m e r22

23 / / C a l c u l a t i o n s24 / / c as e a25 N_h = V_h / V _p er _t ur n ; / / Number o f h i gh −s i d e

t u r n s26 N_l = V_l / V _p er _t ur n ; / / Number o f l ow−s i d e t ur ns27

28 N _1 = N_h ; / / Number o f t u r n s i n t h e p ri ma ry29 N _2 = N_l ; // Number o f t u r ns i n t he s e co n da r y30

31 / / c as e b32 I _1 = S_1 * 10 00 / V_1 ;

// Rated p ri ma ry c u r r e nt i n A33 I _2 = S_2 * 10 00 / V_2 ; // Rated s e co n da r y c u r r e nt i nA

35 I_h = 2 ; / / Rated c u r r en t i n A o n HV s i d e36 I_l = 40 ; // Rated c u r r e nt i n A on LV s i d e37

38 / / c as e c39 / / s u b s c r i p t c f o r a lp ha st ep do wn and a l ph a st e p u p

i n d i c a t e s c as e c40 a lp ha _s te pd ow n_ c = N _1 / N _2 ; // s t ep −down

t r a ns f o rm a t i o n r a t i o41 a lp ha _s te pu p_ c = N _l / N _h ; // s t ep −up

t r a ns f o rm a t i o n r a t i o42

43 / / c as e d

44 // s u b s c r i p t d f o r a lp ha st ep do wn and a l ph a st e p u p

i n d i c a t e s c as e d45 a lp ha _s te pd ow n_ d = I _2 / I _1 ; // s t ep −downt r a ns f o rm a t i o n r a t i o

46 a lp ha _s te pu p_ d = I _h / I _l ; // s t ep −upt r a ns f o rm a t i o n r a t i o

51 printf ( ” \n a : Number o f h i gh −s i d e t ur ns : \ n N h= %d t = N 1 \n” , N _ h ) ;

52 printf ( ” \n Number o f low−s i d e t ur ns : \ n N l =%d t = N 2 \n” , N _ l ) ;

54 printf ( ” \n b : Rated p ri ma ry c u r r e nt : \ n I h =I 1 = %d A \n” , I _ 1 ) ;

55 printf ( ” \n Rated s e c o n d a r y cu r r en t : \ n I l =I 2 = %d A\n” , I _ 2 ) ;

57 printf ( ” \n c : s te p−down t r a ns f o rm a t i o n r a t i o : \ n= N 1 / N 2 = %d\n” , a l p h a _ s t e p d o w n _ c ) ;

58 printf (” \n s t e p −up t r a n sf o rm a ti o n r a t i o : \ n= N l / N h = %. 2 f \n” , a l p h a _ s t e p u p _ c ) ;

60 printf ( ” \n d : s te p −down t r a ns f o rm a t i o n r a t i o : \ n= I 2 / I 1 = %d\n” , a l p h a _ s t e p d o w n _ d ) ;

61 printf ( ” \n s t e p −up t r a n sf o rm a ti o n r a t i o : \ n= I h / I l h = %. 2 f \n” , a l p h a _ s t e p u p _ d ) ;

Scilab code Exa 14.3 alpha Z1 I1

4 / / 2 nd e d i t i om

56 // Ch ap te r 1 4 : TRANSFORMERS7 / / E xa mp le 14−38

11 / / G iv en d a ta12 N_1 = 500 ; // Number o f p ri ma ry t u r ns i n t he a ud io

o ut p ut t r a n s f o r m e r13 N_2 = 25 ; // Number o f s e co n da r y t u rn s i n t he a ud io

o u tp ut t r a n s f o r m e r14 Z_L = 8 ; // S p e a ke r i mp ed an ce i n ohm15 V_1 = 10 ; // Output v o l t a g e o f t he a ud io o ut pu t

t r an s f o r me r i n v o l t16

17 / / C a l c u l a t i o n s18 / / c as e a19 a lp ha = N _1 / N_ 2 ; // s te p −down t r a n s f o r ma t i o n r a t i o20 Z_1 = ( a lph a )^2 * Z _L ; // Impedance r e f l e c t e d t o

t he t r a n s fo r m e r p ri ma ry21

/ / a t t he o ut p ut o f Tr i n ohm22

23 / / c as e b24 I_1 = V_1 / Z_1 ; // Pr im ary c u r r e nt i n A25

29 printf ( ” \n a : T ra ns fo rm at io n r a t i o : \ n = %d\n” , a l p h a ) ;

30 printf ( ” \n Impedance r e f l e c t e d to t h e

t r an s f o r me r p ri ma ry a t t he o ut pu t o f Tr : ” ) ;31 printf ( ” \n Z 1 = %d ohm \n ” , Z _ 1 ) ;

33 printf ( ” \n b : M at ch in g t r a n s f o r m e r p ri ma ry c u r r e n t: \ n I 1 = %f A” , I _ 1 ) ;

34 printf ( ” \n I 1 = %. 3 f mA ” , 10 00 * I _1 ) ;

Scilab code Exa 14.4 Z2prime Z3prime Z1 I1 Pt V2 P2 V3 P3 Pt

11 / / G iv en d a ta12 N_1 = 600 ; // Number o f p r im a ry t u r n s13 N_2 = 150 ; // Some number o f s e c o n d a r y t u r n s14 N_3 = 300 ; // Some number o f s e c o n d a r y t u r n s15 Z_2 = 30 ; // R e s i s t i v e l oa d i n ohm a c r o s s N 2

16 Z_3 = 15 ; // R e s i s t i v e l oa d i n ohm a c r o s s N 317 R_2 = 30 ;

18 R_3 = 15 ;

19 V_p = 16 ; // Pr imar y a p p li e d v o l t a g e i n v o l t20 c os _t he ta = 1 ; // u n i t y PF21

22 / / C a l c u l a t i o n s23 / / c as e a24 Z _2 _p ri me = Z _2 * ( N _1 / N _2 ) ^2 ; / / I m p ed a n ce

r e f l e c t e d t o t he p r i m a r y by l oa d Z 2 i n ohm

2526 / / c as e b27 Z _3 _p ri me = Z _3 * ( N _1 / N _3 ) ^2 ; / / I m p ed a n ce

r e f l e c t e d t o t he p r i m a r y by l oa d Z 3 i n ohm28

29 / / c as e c

30 / / T ot al i mp ed an ce r e f l e c t e d t o t he p ri ma ry i n ohm31 Z _1 = ( Z _2 _p ri me * Z _3 _p ri me ) / ( Z _2 _p ri me +

Z _ 3_ p ri m e ) ;

33 / / c as e d34 I_1 = V_p / Z_1 ; // T ot al c u r r e nt drawn fro m t he

s up pl y i n A35

36 / / c as e e37 P_t = V_p * I_1 * co s_ th et a ; / / T ot al power i n W

drwan f ro m t h e s u pp l y a t u n i t y PF

3839 / / c as e f 40 V_2 = V_p * ( N_2 / N_1 ) ; // V ol ta ge a c r o s s Z 2 i n

v o l t41 P_2 = ( V_2 ) ^2 / R_2 ; // Power d i s s i p a t e d i n l oa d

Z 2 i n W42

43 / / c as e g44 V_3 = V_p * ( N_3 / N_1 ) ; // V ol ta ge a c r o s s Z 3 i n

v o l t45 P_3 = ( V_3 ) ^2 / R_3 ;

// Power d i s s i p a t e d i n l oa dZ 3 i n W46

47 / / c as e h48 P _tot al = P_2 + P_3 ; // T ot al power d i s s i p a t e d i n

bot h l o a ds i n W49

53 printf ( ” \n a : Impedance r e f l e c t e d t o t he p ri ma ry by

l o a d Z 2 : ” ) ;54 printf ( ” \n Z 2 = %d ohm \n ” , Z _ 2_ p ri m e ) ;

56 printf ( ” \n b : Impedance r e f l e c t e d t o t he p ri ma ry byl o a d Z 3 : ” ) ;

57 printf ( ” \n Z 3 = %d ohm \n ” , Z _ 3_ p ri m e ) ;

5859 printf ( ” \n c : T ot al i mpe danc e r e f l e c t e d t o t he

p ri ma ry : ” ) ;

60 printf ( ” \n Z 1 = %. 1 f ohm \n ” , Z_ 1 ) ;

62 printf ( ” \n d : T ot al c u r r e n t drawn fro m t he s u pp l y :” ) ;

63 printf ( ” \n I 1 = %. 1 f A \n ” , I_ 1 ) ;

65 printf ( ” \n e : T o ta l po we r d rawn f ro m t h e s u pp l y a tu n it y PF : ” ) ;

66 printf ( ” \n P t = %. 1 f W \n ” , P_ t ) ;67

68 printf ( ” \n f : V o l t a g e a c r o s s Z 2 i n v o l t : \ n V 2= %d V \n ” , V_ 2 ) ;

69 printf ( ” \n Power d i s s i p a t e d i n l o a d Z 2 : \ nP 2 = %. 2 f W \n” , P_ 2 ) ;

71 printf ( ” \n g : V o l ta g e a c r o s s Z 3 i n v o l t : \ n V 3= %d V \n ” , V_ 3 ) ;

72 printf ( ” \n Power d i s s i p a t e d i n l o a d Z 3 : \ n

P 3 = %f W \n”, P_ 3 ) ;

74 printf ( ” \n h : T ot al power d i s s i p a t e d i n bot h l o a ds: \ n P t = %. 1 f W” , P _ t o t a l ) ;

Scilab code Exa 14.5 alpha N2 N1 ZL

7 / / E xa mp le 14−5

c o n s o l e .10

11 / / G iv en d a ta12 P = 100 ; // P ower r a t i n g o f t he s i n g l e c ha nn el

power a m p l i f i e r i n W13 Z _p = 3200 ; // Ou tp ut i mp ed an ce i n ohm o f t h e

s i n g l e c ha nn el power a m p l i f i e r14 N _p = 1500 ; // Number o f p ri ma ry t u r n s i n a t ap pe d

impedance −m at ch in g t r a n s f o r m e r

15 Z_L1 = 8 ; // A m p l i f i er o ut pu t i n ohm u s i ng a t ap pe dimpedance −m at ch in g t r a n s f o r m e r

16 Z_L2 = 4 ; // A m p l i f i er o ut pu t i n ohm u s i ng a t ap pe dimpedance −m at ch in g t r a n s f o r m e r

18 / / C a l c u l a t i o n s19 / / c as e a20 a l ph a = sqrt ( Z _p / Z _ L1 ) ; // T ra n sf o rm a ti o n r a t i o21 N _2 = N_p / alpha ; // T o ta l number o f s e c on d a ry

t u r n s t o match 8 ohm s p e a k e r22

23 / / c as e b24 // s u b s c r i p t b f o r a l p h a i n d i c a t e s c as e b25 a l p ha _ b = sqrt ( Z _p / Z _L 2 ) ; // T ra n sf o rm a ti o n r a t i o26 N_1 = N_p / al pha _b ; // Number o f p ri m ar y t u r n s t o

m at ch 4 ohm s p e a k e r27

28 / / c as e c29 t ur ns _d if fe re nc e = N _2 - N _1 ; // D i f f e r e n c e i n

s e c on d a r y and p ri ma ry t u r n s30 // s u b s c r i p t c f o r a l p h a i n d i c a t e s c as e c

31 a l ph a _c = ( 1 50 0 /2 2 ) ; // T ra n sf or m at io n r a t i o32 Z_L = Z_p / ( a lp ha _c ) ^2 ; // I mp ed an ce t h a t must b e

c o n n e c t e d b e tw e en 4 o hm a n d33 / / 8 ohm t e r m i n a l s t o r e f l e c t a p r im a ry i mp ed an ce o f

3 . 2 k i l o −ohm

38 printf ( ” \n a : T ra ns fo rm at io n r a t i o : \n = %d\n ” , a lp ha ) ;

39 printf ( ” \n T o t a l number o f s e c o nd ar y t u r ns t omatch 8 ohm s p e a k e r : ” ) ;

40 printf ( ” \n N 2 = %d t \n ” , N_ 2 ) ;

42 printf ( ” \n b : T ra ns fo rm at io n r a t i o : \n = %. 3f \n ” , a l ph a_ b ) ;

43 printf ( ” \n Number o f p ri ma r y t u r n s t o match 4ohm s p e a k e r : ” ) ;

44 printf ( ” \n N 1 = %d t \n ” , N_ 1 ) ;

46 printf ( ” \n c : D i f f e r e n c e i n s ec on da ry and p ri ma ryt u r n s : ” ) ;

47 printf ( ” \n N 2 − N 1 = %. f t \n ” ,

t u r n s_ d i f fe r e n c e ) ;

48 printf ( ” \n Impedance t h at must be co nn ec te db e tw e en 4 ohm a nd 8 ohm ” ) ;

49 printf (” \n t e r m i na l s t o r e f l e c t a p r i m a r yi mp ed an ce o f 3 . 2 k i l o −ohm : ” ) ;

50 printf ( ” \n Z L = %. 2 f ohm ”, Z_ L ) ;

Scilab code Exa 14.6 Z between terminals A B

11 / / G iv en d a ta12 P = 100 ; // P ower r a t i n g o f t he s i n g l e c ha nn el

power a m p l i f i e r i n W13 Z_L1 = 8 ; // A m p l i f i er o ut pu t i n ohm u s i ng a t ap pe d

impedance −m at ch in g t r a n s f o r m e r14 Z_L2 = 4 ; // A m p l i f i er o ut pu t i n ohm u s i ng a t ap pe d

impedance −m at ch in g t r a n s f o r m e r15 P _s er vo = 10 ; // Power r a t i n g o f t he s e rv o motor i n

W16 Z _s er vo = 0. 7 ; // Imp eda nce o f t he s e r vo motor i n

18 / / C a l c u l a t i o n s19 r o o t _Z _ A B = sqrt (8) - sqrt ( 4 ) ;

20 Z _A B = ( r o ot _ Z_ A B ) ^2 ;

22 / / D is pl ay t h e r e s u l t a23 disp ( ”Example 14−6 S ol u t i o n : ” ) ;

25 printf ( ” \n Z p = % d ∗ ( N p /N 1 ) ˆ2 = % d ∗ ( N p / N 2 )ˆ2\ n” , Z _ L 2 , Z _ L 1 ) ;

26 printf ( ” \n = Z AB ∗ ( N p / ( N 2 − N 1 ) ˆ2 ) \n” ) ;

27 printf ( ” \n D i vi d in g e a ch o f t he t h r e e n um er at or s byN p ˆ2 and t a ki n g t he ” ) ;

28 printf ( ” \n s q ua r e r o o t o f e ac h term , we h ave \n” ) ;

30 printf ( ” \n ( Z AB ) / ( N 2 − N 1 ) = ( 4 ) / N 1 =( 8 ) / N 2 \n” ) ;

31 printf ( ” \n ( Z AB ) / ( N 2 − N 1 ) = ( 4 ) / N 1 −

( 8 ) / N 2 \n” ) ;32 printf ( ” \n y i e l d i n g , ( Z AB ) = ( 8 ) − ( 4 ) =

%f \n” , r o o t _ Z _ A B ) ;

33 printf ( ” \n w hi ch Z AB = ( %f ) ˆ 2 = %. 2 f \n” ,

root_Z_AB ,Z_AB );

Scilab code Exa 14.7 alpha V1 V2 I2 I1 PL Ps PT efficiency

7 / / E xa mp le 14−78

11 / / G iv en d a ta12 V = 1 0 * exp ( %i * 0 * ( %pi / 18 0) ) ; // S up pl y v o l t a g e

o f t he s o u r c e 10<0 V13 R _s = 1000 ; // R e s is t a nc e o f t he s o ur c e i n ohm14 R_L = 10 ; // Load r e s i s t a n c e i n ohm15 Z_L = R_L ; // Load r e s i s t a n c e i n ohm16

17 / / C a l c u l a t i o n s18 / / c as e a19 a l ph a = sqrt ( R _s / R _L ) ; // T ra ns fo rm at io n r a t i o o f

t h e m a tc h in g t r a n s f o r m e r f o r MPT20

21 / / c as e b22 V_1 = V / 2 ; // T e r mi n a l v o l t a ge i n v o l t o f t he

s o u r c e a t MPT23

24 / / c as e c25 V _2 = V_1 / alpha ; // T e r mi na l v o l t a g e i n v o l t

a c r o s s t h e l o a d a t MPT26

27 / / c as e d

28 I_2 = V_2 / Z_L ; // S ec on da ry l oa d c u r re n t i n A (

m et ho d 1 )29 I 2 = V / (2* a lp ha * R_L ) ; // S ec on da ry l o ad c u r r e n ti n A ( m ethod 2 )

31 / / c as e e32 I _1 = I_2 / alpha ; // P ri ma ry l o a d c u r r e n t drawn

from t he s o u r ce i n A ( m ethod 1 )33 I1 = V / (2* R_s ) ; // P ri ma ry l o a d c u r r e n t drawn

from t he s o u r ce i n A ( m ethod 2 )34

35 / / c as e f

36 P_L = ( I_2 ) ^2 * R_L ; / / Maximum p ow er d i s s i p a t e d i nt h e l oa d i n W

38 / / c as e g39 P_s = ( I_1 ) ^2 * R_s ; // Power d i s s i p a t e d i n t e r n a l l y

w it hi n t he s o u r c e i n W40

41 / / c as e h42 P_T1 = V * I_1 * cosd (0) ; // T ot al power s u p p l i e d

by t h e s o u r c e i n W( m ethod 1 )43

44 P_T2 = P_L + P_s ; // T ot al power s u p p l i e d by t hes o u r c e i n W( m ethod 2 )

46 / / c as e i47 P _T = P_T1 ;

48 eta = P_L / P_T * 100 ; // Power t r a n s f e r e f f i c i e n c yi n p e rc e n t

5253 printf ( ” \n a : T ra n sf o rm a ti o n r a t i o o f t he m at ch in g

t r a n s f o r m e r f o r MPT : ” ) ;

54 printf ( ” \n = %d \n ” , a lp ha ) ;

56 printf ( ” \n b : T er mi na l v o l t a g e o f t he s o u r ce a t MPT

: \ n V 1 = %d V \n” , V _ 1 ) ;57

58 printf ( ” \n c : T e r m i n a l v o l t a ge a c r o s s t h e l oa d a tMPT : \ n V 2 = %. 1 f V \n” , V _ 2 ) ;

60 printf ( ” \n d : S ec on da ry l o ad c u r r e nt : ” ) ;

61 printf ( ” \n ( method 1 ) : \ n I 2 = %. 2 f A = %dmA \n ” , I _2 , 1 0 00 * I _ 2 ) ;

63 printf ( ” \n ( method 2 ) : \ n I 2 = %. 2 f A = %dmA \n ” , I2 , 1 0 00 * I 2 ) ;

6465 printf ( ” \n e : P ri ma ry l o a d c u r r e n t drawn f ro m t h e

s ou rc e : ” ) ;

66 printf ( ” \n ( method 1 ) : \ n I 1 = %f A = %d mA\n ” , I_ 1 , 1 00 0* I _1 ) ;

67 printf ( ” \n ( method 2 ) : \ n I 1 = %f A = %d mA\n ” , I1 , 1 00 0* I1 ) ;

69 printf ( ” \n f : Maximum p o wer d i s s i p a t e d i n t h e l o a d: ” ) ;

70 printf (” \n P L = %f W = %d mW \n”

, P _L , 1 00 0* P _ L

72 printf ( ” \n g : Power d i s s i p a t e d i n t e r n a l l y w it hi nt h e s ou rc e : ” ) ;

73 printf ( ” \n P s = %f W = %d mW \n” , P _s , 1 00 0* P _ s

75 printf ( ” \n h : T ot al power s u p p li e d by t he s o ur c e :” ) ;

76 printf ( ” \n ( method 1 ) : \ n P T = %f W = %d mW

\n ” , P _T 1 , 1 0 00 * P _ T 1 ) ;77 printf ( ” \n ( method 2 ) : \ n P T = %f W = %d mW

\n ” , P _T 2 , 1 0 00 * P _ T 2 ) ;

79 printf ( ” \n i : Power t r a n s f e r e f f i c i e n c y : \ n =

%d p e r c e n t ” , et a ) ;

Scilab code Exa 14.8 PL alpha maxPL

11 / / G iv en d a ta12 / / p ower t r a n s f o r m e r13 V = 2 0 ; / / No−l oa d v o l t a g e i n v o l t14 R_s = 18 ; // I n t e r n a l r e s i s t a n c e o f t he power

a m p l i f i e r i n ohm

15 R_L = 8 ; / / Load r e s i s t a n c e i n ohm ( S p ea k er )16

17 / / C a l c u l a t i o n s18 / / c as e a19 V_L = ( R_L / ( R_L + R_s ) ) * V ; // Load v o l t a g e i n

v o l t20 P_L = ( V_L ) ^2 / R_L ; // Power d e l i v e r e d i n W t o t he

s p e a k e r when c o n n e c t ed21 // d i r e c t l y t o t h e a m p l i f i e r22

23 / / c as e b24 a l ph a = sqrt ( R _ s / R _ L ) ; // Turns r a t i o o f t h et r a n s f o r m e r t o m ax im iz e s p e a k e r p ower

26 / / c as e c

27 V_2 = V / (2 * al ph a) ; // S ec o nd ar y v o l t a g e i n v o l t

28 P_ L2 = ( V_2 ) ^2 / R_L ; // Maximum p ow er d e l i v e r e d i nW t o t he s p e ak e r u s i ng m at ch in g29 / / t r a n s f o r m e r o f p ar t b30

34 printf ( ” \n a ; Load v o l t a g e : \ n V L = %. 2 f Va c r o s s t h e 8 s p e a k e r \n ” , V _ L ) ;

35 printf ( ” \n Power d e l i v e r e d i n W t o t h e s pe a ke rwhen c o nn ec te d d i r e c t l y t o t h e a m p l i f i e r : ” ) ;

36 printf ( ” \n P L = %. 2 f W \n ” , P _ L ) ;37

38 printf ( ” \n b : Turns r a t i o o f t he t r a n sf o r m e r t om ax im iz e s p e a k e r p ower : ” ) ;

39 printf ( ” \n = %. 1 f \n ” , al ph a ) ;

41 printf ( ” \n c : S ec on da ry v o l t a g e : \ n V 2 = %f V \n ” , V_ 2 ) ;

42 printf ( ” \n Maximum power d e l i v e r e d i n W t o t h es p e ak e r u s i ng m at ch in g ” ) ;

43 printf (” \n t r a n s f o r m e r o f pa r t b : \ n P L = %f W ” , P _L 2 ) ;

Scilab code Exa 14.9 Eh El Ih new kVA

4 / / 2 nd e d i t i om5

c o n s o l e .10

11 / / G iv en d a ta12 kVA = 1 ; // kVA r a t i n g o f t he t r a n s fo r m e r13 V_1 = 220 ; // P ri mary v o l t ag e i n v o l t14 V_2 = 110 ; // S ec on da ry v o l t a g e i n v o l t15 f_o = 400 ; / / F re qu en cy i n Hz ( o r i g i n a l f r e q u e n c y )16 f_f = 60 ; // F re qu en cy i n Hz f o r whi ch t he

t r a n sf o r m e r i s t o be us e d17

19 a l p h a = V _ 1 / V _ 2 ; // T ra n sf o rm a ti o n r a t i o20 / / c as e a21 E_h = V_1 * ( f_f / f_o ); / / Maximum rm s v o l t a g e i n

v o l t a p p l i e d t o HV s i d e22 E_1 = E_h ;

23 E _l = E_1 / alpha ; / / Maximum r ms v o l t a g e i n v o l ta p p l i e d t o HV s i d e

25 / / c as e b26 V_h = V_1 ; // High v o l t a ge i n v o l t27 I_h = kVA * 1000 / V_h ;

28 V h = E_h ;

29 k VA_n ew = Vh * I_h ;

34 printf ( ” \n a : To m ai nt ai n t he same p e r m i s s i b l e f l u xd e n s i t y i n Eqs . ( 14 − 1 5 ) ” ) ;

35 printf ( ” \n and (14 −16) , b ot h v o l t a g e s o f t he h ig hand lo w s i d e s must c ha ng e ” ) ;

36 printf ( ” \n i n t h e same pr o p o rt i on a s th ef r e q u e n c y : ” ) ;

37 printf ( ” \n E h = %d V \n and , \ n E l = %. 1 f V\n” , E_h , E_l ) ;

39 printf ( ” \n b : The o r i g i n a l c ur r e nt r a t i n g o f t h e

t r a n s fo r m e r i s u nch ang ed s i n c e ” ) ;40 printf ( ” \n t he c on du ct or s s t i l l have t h e samec u r r e nt c a r r y i n g c a p a c i ty . ” ) ;

41 printf ( ” \n Thus , \ n I h = %. 3 f A\n and t h enew kVA r a t i n g i s ” , I_ h ) ;

42 printf ( ” \n V h ∗ I h = V 1∗ I 1 = %d VA = %.2 f kVA”, k V A_ n ew , k VA _ ne w / 1 00 0) ;

Scilab code Exa 14.10 Piron

6 // Ch ap te r 1 4 : TRANSFORMERS7 / / E xa mp le 1 4−108

c o n s o l e .10

11 / / G i ve n d a t a ( f r om E xa mp le 1 4−9)12 kVA = 1 ; // kVA r a t i n g o f t he t r a n s fo r m e r13 V_1 = 220 ; // P ri mary v o l t ag e i n v o l t14 V_2 = 110 ; // S ec on da ry v o l t a g e i n v o l t15 f_o = 400 ; // F re qu en cy i n Hz16 f_f = 60 ; // F re qu en cy i n Hz f o r whi ch t he

t r a n sf o r m e r i s t o be us e d17 P _ or ig = 10 ; // O r i g i n a l i r o n l o s s e s o f t h e

t r an s f o r me r i n W18

19 / / C a l c u l a t i o n s20 // c o n s i d e r o n ly r a t i o o f f r e q u e n c i e s f o r

c a l c u l a t i n g B

21 B = f_o / f_f ; // f l u x d e n s i t y

2223 P _i r on = ( P _ or ig ) * ( B ^2 ) ; // I ro n l o s s e s i n W24

28 printf ( ” \n S i n ce E = k∗ f ∗B m and t h e same p r im a ryv o l t a g e i s a p p l i e d t o t h e ” ) ;

29 printf ( ” \n t r a n s fo r m e r a t r ed uc ed f re qu e nc y , t hef i n a l f l u x d e n s i t y B mf ” ) ;

30 printf ( ” \n i n c r e a s e d s i g n i f i c a n t l y abov e i t s

o r i g i n a l maximum p e r m i s s i b l e ” ) ;31 printf ( ” \n v al ue B mo t o : \ n B mf = B mo ∗ ( f o / f f

) = % . 2 f B m o \n ” , B ) ;

33 printf ( ” \n S i n ce t h e i r on l o s s e s v a r y a pp ro xi ma te lya s t h e s qu ar e o f t h e f l ux d e n s i t y : ” ) ;

34 printf ( ” \n P i r o n = %d W ”, P _ ir on ) ;

Scilab code Exa 14.11 I2 I1 Z2 Z1their loss E2 E1 alpha

11 / / G iv en d a ta12 kVA = 500 ; // kVA r a t i n g o f t he s te p −down

t r a n s f o r m e r

13 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t14 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t15 f = 6 0 ; // F re qu en cy i n Hz16 r_1 = 0.1 ; // P ri ma ry w in di ng r e s i s t a n c e i n ohm17 x_1 = 0.3 ; // P ri ma ry w in d in g r e a c t a n c e i n ohm18 r _2 = 0 .0 01 ; // S ec on da ry w in di ng r e s i s t a n c e i n ohm19 x _2 = 0 .0 03 ; // S ec on d ar y w in d in g r e a c t a n c e i n ohm20

21 / / C a l c u l a t i o n s22 a l p h a = V _ 1 / V _ 2 ; // T ra n sf o rm a ti o n r a t i o23 / / c as e a

24 I_2 = ( kVA * 10 00 ) / V_2 ; // S ec on da ry c u r r e n t i n A25 I _1 = I_2 / alpha ; // P ri ma ry c u r r e n t i n A26

27 / / c as e b28 Z_2 = r_2 + %i *( x _2 ) ; // S ec on da ry i n t e r n a l

i m p ed a n ce i n ohm29 Z _ 2_ m = abs ( Z _ 2 ) ; / / Z 2 m=m ag n it ud e o f Z 2 i n ohm30 Z _ 2_ a = atan ( imag ( Z _2 ) / real ( Z _ 2 ) ) * 1 8 0 / % p i ; / / Z 2 a =

p h a se a n g l e o f Z 2 i n d e g r e e s31

32 Z_1 = r_1 + %i *( x _1 ) ; // P ri ma ry i n t e r n a l i mp ed an cei n ohm

33 Z _ 1_ m = abs ( Z _ 1 ) ; / / Z 1 m=m ag n it ud e o f Z 1 i n ohm34 Z _ 1_ a = atan ( imag ( Z _1 ) / real ( Z _ 1 ) ) * 1 8 0 / % p i ; / / Z 1 a =

36 / / c as e c37 I _2 _Z _2 = I_ 2 * Z _2 _m ; // S ec on da ry i n t e r n a l

v o l t a ge dr op i n v o l t38 I _1 _Z _1 = I_ 1 * Z _1 _m ; // P ri mar y i n t e r n a l v o l t a g e

dr op i n v o l t

3940 / / c as e d41 E_2 = V_2 + I_ 2_Z _2 ; // S ec on d ar y i n du c ed v o l t a g e

i n v o l t42 E_1 = V_1 - I_ 1_Z _1 ; // P ri ma ry i nd uc ed v o l t a g e i n

v o l t

4344 / / c as e e45 r atio _E = E_1 / E_2 ; // r a t i o o f p r i m a ry t o

s e co n da r y i nd uc ed v o l t a g e46 r atio _V = V_1 / V_2 ; // r a t i o o f p r i m a ry t o

s e co n da r y t e r m i na l v o l t a g e47

51 printf ( ” \n a : S ec on da ry c u r r e nt : \ n I 2 = %. f A

\n ” , I_ 2 ) ;52 printf ( ” \n P ri mary c u r r e n t : \ n I 1 = %. 1 f A \

n ” , I_ 1 ) ;

54 printf ( ” \n b : S ec on da ry i n t e r n a l i mp ed an ce : \nZ 2 i n ohm = ”) ; disp ( Z _ 2 ) ;

55 printf ( ” \n Z 2 = %f <%.2 f ohm \n ” , Z _2 _m , Z _2 _a

56 printf ( ” \n P ri mary i n t e r n a l i mpeda nce : \nZ 1 i n ohm = ”) ; disp ( Z _ 1 ) ;

57 printf (” \n Z 1 = %f

%.2 f ohm \n ”, Z _1 _m , Z _1 _a

59 printf ( ” \n c : S ec on da ry i n t e r n a l v o l t a g e dr op : \ nI 2 ∗ Z 2 = %. 2 f V \n ” , I _ 2 _ Z _ 2 ) ;

60 printf ( ” \n P ri mary i n t e r n a l v o l t a g e drop : \ nI 1 ∗ Z 1 = %. 2 f V \n ” , I _ 1 _ Z _ 1 ) ;

62 printf ( ” \n d : S ec on da ry i nd uc ed v o l t a g e : \ n E 2= %. 2 f V \n” , E_ 2 ) ;

63 printf ( ” \n P ri mary i n d u c e d vo l t ag e : \ n E 1 =

%. 2 f V \n” , E_ 1 ) ;64

65 printf ( ” \n e : R a t i o o f E 1 /E 2 = %. 2 f = = N 1 /N 2 \n” , r a ti o _E ) ;

66 printf ( ” \n But V 1 / V 2 = %d ” , r a ti o_ V ) ;

Scilab code Exa 14.12 ZL ZP difference

7 / / E xa mp le 1 4−128

11 / / G i ve n d a t a ( f r om E xa mp le 1 4−11)12 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t13 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t14 I _2 = 2174 ; // S ec on da ry c u r re n t i n A15 I_1 = 217.4 ; // P ri ma ry c u r r e nt i n A16 / / c a l c u l a t e d v a l u e s fro m E xample 14−1117 Z_2 = 0 .0 03 16 ; // S ec on da ry i n t e r n a l i mp ed an ce i n

ohm18 Z_1 = 0.316 ; // P ri ma ry i n t e r n a l i mp ed an ce i n ohm19

21 / / C a l c u l a t i o n s22 a l p h a = V _ 1 / V _ 2 ; // T ra n sf o rm a ti o n r a t i o23 / / c as e a24 Z_L = V_2 / I_2 ; / / L oa d i m pe d an c e i n ohm25

26 / / c as e b27 Z_p = V_1 / I_1 ; // P ri ma ry i n p u t i mp ed an ce i n ohm28

29 Zp = ( alpha ) ^2 * Z_L ; // P ri ma ry i n p u t i mp ed an ce i nohm

34 printf ( ” \n a : Load i mp ed an ce : \ n Z L = %. 4 f ohm\n ” , Z _ L ) ;

36 printf ( ” \n b : P ri ma ry i n pu t i mp ed an ce : ” ) ;

37 printf ( ” \n ( method 1 ) : \ n Z p = %. 2 f ohm \n ”, Z_ p ) ;

38 printf ( ” \n ( method 2 ) : \ n Z p = %. 2 f ohm \n ”, Zp ) ;

3940 printf ( ” \n c : The i mp ed an ce o f t he l o ad Z L = %. 4 f

, wh ich i s much g r e a t e r ” , Z _ L ) ;

41 printf ( ” \n t han th e i n t e r n a l s e c o nd ar y impe danc eZ 2 = %. 5 f . \ n ” , Z _ 2 ) ;

42 printf ( ” \n The p ri ma ry i np ut i mpe danc e Z p = %. 2f , whi ch i s much g r e at e r ” , Z _ p ) ;

43 printf ( ” \n t han th e i n t e r n a l p ri m a r y impe dan ceZ 1 = %. 3 f . \ n” , Z _ 1 ) ;

45 printf (” \n d : I t i s e s s e n t i a l f o r Z L t o be muchg r e a t e r t han Z 2 s o t ha t t h e ” ) ;

46 printf ( ” \n maj or p a rt o f t h e v o lt a g e pr o d uc e d byE 2 i s dr opp ed a c r o s s t he ” ) ;

47 printf ( ” \n l oa d i mped anc e Z L . As Z L i s r e d u c e di n p r o p or t i o n t o Z 2 , t he ” ) ;

48 printf ( ” \n l o a d c u rr en t i n c r e a s e s and morev o l t a ge i s dr op ped i n t e r n a l l y ” ) ;

49 printf ( ” \n a c r o s s Z 2 . ” ) ;

Scilab code Exa 14.13 Re1 Xe1 Ze1 ZLprime I1

t r a n s f o r m e r13 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t14 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t15 f = 6 0 ; // F re qu en cy i n Hz16 r_1 = 0.1 ; // P ri ma ry w in di ng r e s i s t a n c e i n ohm17 x_1 = 0.3 ; // P ri ma ry w in d in g r e a c t a n c e i n ohm18 r_2 = 0.001 ; // S ec on da ry w in di ng r e s i s t a n c e i n ohm19 x_2 = 0.003 ; // S ec on d ar y w in d in g r e a c t a n c e i n ohm20 / / c a l c u l a t e d d at a fr om Example 1 4−1221 Z _L = 0 .1 05 8 ; / / Lo ad i m pe d an c e i n ohm22

23 / / C a l c u l a t i o n s24 a l p h a = V _ 1 / V _ 2 ; // T ra n sf o rm a ti o n r a t i o25

26 / / c as e a27 R_e1 = r_1 + ( alpha ) ^2 * r_2 ; // E q u i v a le n t

i n t e r n a l r e s i s t a n c e r e f e r r e d t o t h e28 / / p ri ma ry s i d e i n ohm29

30 / / c as e b31 X_e1 = x_1 + ( alpha ) ^2 * x_2 ; // E q u i v a le n t

i n t e r n a l r e a c t an c e r e f e r r e d t o t h e32 / / p ri ma ry s i d e i n ohm33

34 / / c as e c35 Z_ e1 = R_ e1 + %i *( X _e 1) ; // E q u i va l e nt i n t e r n a l

i mp ed an ce r e f e r r e d t o t he

36 / / p ri ma ry s i d e i n ohm37 Z _ e 1_ m = abs ( Z _ e 1 ) ; / / Z e 1 m=m ag n it ud e o f Z e 1 i n ohm38 Z _ e 1_ a = atan ( imag ( Z _e 1 ) / real ( Z _ e 1 ) ) * 1 8 0 / % p i ; //

Z e1 a=p ha se a n gl e o f Z e 1 i n d e gr e e s39

40 / / c as e d41 Z _ L _ pr i me = ( a l ph a ) ^2 * ( Z _L ) ; // E q u i v a le n t

s e co n da r y l o ad i mp ed an ce r e f e r r e d42 // t o t h e p ri m a r y s i d e i n ohm43

44 / / c as e e

45 R_L = Z_L ; // Load r e s i s t a n c e i n ohm46 X_L = 0 ; // Load r e a c t a n c e i n ohm47

48 // P ri mary l oa d c u r r e n t i n A , when V 1 = 2 300 V49 I_1 = V_1 / ( ( R_ e1 + a lp ha ^ 2* R _L ) + %i *( X _e 1 +

a l ph a ^ 2 * X _ L ) ) ;

54 printf (” \n a : E qu iv al en t i n t e r n a l r e s i s t a n c er e f e r r e d t o t h e p r i m a r y s i d e : ” ) ;

55 printf ( ” \n R c1 = %. 2 f ohm \n ” , R _e 1 ) ;

57 printf ( ” \n b : E q u i v al e n t i n t e r n a l r e a ct a n cer e f e r r e d t o t h e p r i m a r y s i d e : ” ) ;

58 printf ( ” \n X c1 = %. 2 f ohm \n ” , X _e 1 ) ;

60 printf ( ” \n c : E q ui v al e n t i n t e r n a l i mp ed an cer e f e r r e d t o t h e p r i m a r y s i de : ” ) ;

61 printf ( ” \n Z c 1 i n ohm = ” ) ; disp ( Z _ e 1 ) ;

62 printf ( ” \n Z c 1 = %. 3 f <%.2 f ohm \n ” , Z _e 1_ m ,Z _e 1_ a ) ;

64 printf ( ” \n d : E q u i v al e n t s e c on d a ry l o a d i mp ed an cer e f e r r e d t o t h e p r i m a r y s i d e : ” ) ;

65 printf ( ” \n ( a l p h a ) ˆ2 ∗ Z L = %. 2 f ohm = ( a l p h a )

ˆ2 ∗ R L \n” , Z _ L _ p r i m e ) ;66

67 printf ( ” \n e : P ri mary l oa d c u r r e n t : \ n I 1 = %f A %. f A ” , I_1 , I _1 ) ;

Scilab code Exa 14.14 I2 ohmdrops E2 VR

12 kVA = 500 ; // kVA r a t i n g o f t he s te p −downt r a n s f o r m e r

13 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t14 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t15 R_e2 = 2 ; // E qu i v al en t r e s i s t a n c e r e f e r r e d t o t h e16 / / p r i m a r y s i de i n m17 X_e2 = 6 ; // E qu i v al en t r e a c t a nc e r e f e r r e d t o t he18 / / p r i m a r y s i de i n m19

21 / / c as e a22 I_2 = ( kVA ) / V_2 ; // Rated s e co n da r y c u r r e nt i nkA

24 / / c as e b

25 R _e 2_ dr op = I_2 * R _e 2 ; // F u ll −l oa d e q u i v a l e n t

r e s i s t a n c e v o l t a g e dro p i n v o l t26

27 / / c as e c28 X _e 2_ dr op = I_2 * X _e 2 ; // F u ll −l oa d e q u i v a l e n t

r e a c t a nc e v o l t a ge dr op i n v o l t29

30 / / c as e d31 / / u n i t y PF32 c o s _ th e ta 2 = 1 ;

33 s i n _ t he t a 2 = sqrt ( 1 - ( c o s _t h et a 2 ) ^2 ) ;

35 / / I n du ce d v o l t a g e when t he t r a n s fo r m e r i sd e l i v e r i n g r at ed c u r r e n t t o u ni ty PF l o ad

36 E _2 = ( V _2 * c os _t he ta 2 + I _2 * R _e 2 ) + %i * ( V_ 2 *

s i n_ t he t a2 + I _2 * X _ e2 ) ;

37 E _ 2_ m = abs ( E _ 2 ) ; // E 2 m=m ag ni tu de o f E 2 i n v o l t38 E _ 2_ a = atan ( imag ( E _2 ) / real ( E _ 2 ) ) * 1 8 0 / % p i ; // E 2 a=

p h a se a n g l e o f E 2 i n d e g r e e s39

40 / / c as e e41 VR = ( ( E_2_m - V_2 ) / V_2 ) * 100 ; // P e rc e nt

v o l t a ge r e g u l a t i o n a t u ni ty PF42

46 printf ( ” \n a : Rated s e co n da r y c u r r e n t : \ n I 2 =% . 3 f kA \n ” , I _ 2 ) ;

48 printf ( ” \n b : F ul l −l oa d e q ui v a l e n t r e s i s t a n c ev o l t a ge dr op : ” ) ;

49 printf ( ” \n I 2 ∗ R c 2 = %. 2 f V \n” , R _e 2_ dr op ) ;

5051 printf ( ” \n c : F ul l −l oa d e q u i v a l e n t r e a ct a n ce

v o l t a ge dr op : ” ) ;

52 printf ( ” \n I 2 ∗ X c 2 = %. 2 f V \n” , X _e 2_ dr op ) ;

54 printf ( ” \n d : I nd uc ed v o l t a g e when t he t r a n s fo r m e r

i s d e l i v e r i n g r at ed c ur r e nt ” ) ;55 printf ( ” \n t o un i t y PF l o a d : \ n E 2 i n v o l t =” ) ; disp ( E _ 2 ) ;

56 printf ( ” \n E 2 = %. 2 f <%. 2 f V \n ” , E _2 _m , E _2 _a

58 printf ( ” \n e : V ol ta ge r e g u l a t i o n a t u ni ty PF : \ nVR = %. 2 f p e r c e n t ” , VR ) ;

Scilab code Exa 14.15 E2 VR

t r a n s f o r m e r13 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t14 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t15 R_e2 = 2 ; // E qu i v al en t r e s i s t a n c e r e f e r r e d t o t h e16 / / p r i m a r y s i de i n m

17 X_e2 = 6 ; // E qu i v al en t r e a c t a nc e r e f e r r e d t o t he18 / / p r i m a r y s i de i n m19 I_2 = 2.174 ; // Rated s ec on da ry c u r r e nt i n kA20

21 c os _t he ta 2 = 0 .8 ; // l a g g i n g PF

2324 / / C a l c u l a t i o n s25

26 / / c as e d27 / / I n du ce d v o l t a g e when t he t r a n s fo r m e r i s

d e l i v e r i n g r at ed c u r r e n t t o 0 . 8 l a g gi n g PF l oa d28 E _2 = ( V _2 * c os _t he ta 2 + I _2 * R _e 2 ) + %i * ( V_ 2 *

s i n_ t he t a2 + I _2 * X _ e2 ) ;

p h a se a n g l e o f E 2 i n d e g r e e s

v o l t a ge r e g u l a t i o n a t 0 . 8 PF l a g34

38 printf ( ” \n d : I nd uc ed v o l t a g e when t he t r a n s fo r m e ri s d e l i v e r i n g r at ed c ur r e nt ” ) ;

39 printf (” \n t o 0 . 8 l a g g i n g PF l o a d : \ n E 2 i nv o l t = ” ) ; disp ( E _ 2 ) ;

42 printf ( ” \n e : V ol ta ge r e g u l a t i o n a t 0 . 8 l a g g i n g PF: \ n VR = %. 2 f p er c en t ” , VR ) ;

Scilab code Exa 14.16 E2 VR

4 / / 2 nd e d i t i om

t r a n s f o r m e r13 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t

14 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t15 R_e2 = 2 ; // E qu i v al en t r e s i s t a n c e r e f e r r e d t o t h e16 / / p r i m a r y s i de i n m17 X_e2 = 6 ; // E qu i v al en t r e a c t a nc e r e f e r r e d t o t he18 / / p r i m a r y s i de i n m19 I_2 = 2.174 ; // Rated s ec on da ry c u r r e nt i n kA20

21 c os _t he ta 2 = 0 .6 ; // l e a d i n g PF22 s i n _ t he t a 2 = sqrt ( 1 - ( c o s _t h et a 2 ) ^2 ) ;

24 / / C a l c u l a t i o n s25

26 / / c as e d27 / / I n du ce d v o l t a g e when t he t r a n s fo r m e r i s

d e l i v e r i n g r at ed c u r r e n t t o u ni ty PF l o ad28 E _2 = ( V _2 * c os _t he ta 2 + I _2 * R _e 2 ) + %i * ( V_ 2 *

s i n_ t he t a2 - I _2 * X _ e2 ) ;

v o l t a ge r e g u l a t i o n a t 0 . 8 l e ad i n g PF34

3738 printf ( ” \n d : I nd uc ed v o l t a g e when t he t r a n s fo r m e r

i s d e l i v e r i n g r at ed c ur r e nt ” ) ;

39 printf ( ” \n t o 0 . 6 l e a d i n g PF l o a d : \ n E 2 i nv o l t = ” ) ; disp ( E _ 2 ) ;

42 printf ( ” \n e : V ol ta ge r e g u l a t i o n a t 0 . 8 l e a d i n g PF: \ n VR = %. 2 f p er c en t ” , VR ) ;

Scilab code Exa 14.17 Ze1 Re1 Xe1 Ze2 Re2 Xe2their drops VR

7 / / E xa mp le 1 4−178

t r a n s f o r m e r13 S = 20000 ; // power r a t i n g o f t he s te p−down

t r a n s f o r m e r i n VA

14 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t15 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t16

17 // w . r . t HV s i d e f o l l o w i n g i s SC−t e s t d at a18 P 1 = 250 ; // w at tm et er r e a di n g i n W

19 I 1 = 8.7 ; // I n pu t c u r r e n t i n A

20 V1 = 50 ; // I np u t v o l t a ge i n V21

22 / / C a l c u l a t i o n s23 a l p h a = V _ 1 / V _ 2 ; // T ra n sf o rm a ti o n r a t i o24 / / c as e a25 Z_e1 = V1 / I1 ; / / E q u i v a l e n t i m pe d an c e w . r . t HV

s i d e i n ohm26

27 R_e1 = P1 / ( I1 )^2 ; // E q ui v a le n t r e s i s t a n c e w . r . tHV s i d e i n ohm

29 t he ta = a co sd ( R _ e1 / Z _ e1 ) ; // PF a n gl e i n d e gr e e s30

31 X _ e1 = Z _ e1 * s i n d ( t h e ta ) ; / / E q ui v a le n t r e a c t a nc e w . r. t HV s i d e i n ohm

33 / / c as e b34 Z_ e2 = Z_ e1 / ( al ph a) ^2 ; / / E q u i v a le n t i mp ed an ce w .

r . t LV s i d e i n ohm35

36 R_ e2 = R_ e1 / ( al ph a) ^2 ; // E qu i v al en t r e s i s t a n c e w

. r . t LV s i d e i n ohm37

38 X _ e2 = Z _ e2 * s i n d ( t h e ta ) ; / / E q ui v a le n t r e a c t a nc e w . r. t LV s i d e i n ohm

40 / / c as e c41 I_2 = S / V_2 ; // Rated s ec on da ry l oa d c u r r e nt i n A42

43 R _e 2_ dr op = I_2 * R _e 2 ; // F u ll −l oa d e q u i v a l e n tr e s i s t a n c e v o l t a g e dro p i n v o l t

44 X _e 2_ dr op = I_2 * X _e 2 ; // F u ll −l oa d e q u i v a l e n t

r e a c t a nc e v o l t a ge dr op i n v o l t45

46 / / At u n i t y PF47 c o s _ th e ta 2 = 1 ;

50 / / I n du ce d v o l t a g e when t he t r a n s fo r m e r i sd e l i v e r i n g r at ed c u r r e n t t o u ni ty PF l o ad51 E _2 = ( V _2 * c os _t he ta 2 + I _2 * R _e 2 ) + %i * ( V_ 2 *

s i n_ t he t a2 + I _2 * X _ e2 ) ;

55 VR _un ity _PF = ( ( E_2_m - V_2 ) / V_2 ) * 100 ; //T ra ns fo rm er v o l t a g e r e g u l a t i o n

57 / / c as e d58 / / a t 0 . 7 l a g gi n g PF59 c os _t he ta _2 = 0 .7 ; // l a g g i n g PF60 s i n _ t h et a _ 2 = sqrt ( 1 - ( c o s _t h et a _2 ) ^ 2 ) ;

63 E 2 = ( V _2 * c os _t he ta _2 + I _2 * R _e 2 ) + %i * ( V_ 2*

s i n _t h e t a_ 2 + I _2 * X _ e 2 ) ;

64 E 2 _m = abs ( E 2 ) ; / /E2 m=m a gn it ud e o f E2 i n v o l t65 E 2 _a = atan ( imag ( E 2 ) / real ( E 2 ) ) * 1 8 0 / % p i ;

//E 2 a= phasea ng l e o f E2 i n d e g r ee s66

67 VR _l ag _P F = ( ( E2_m - V_2 ) / V_2 ) * 100 ; //T ra ns fo rm er v o l t a g e r e g u l a t i o n

72 printf ( ” \n a : E q u i v al e n t i mp ed an ce w . r . t HV s i d e : \n Z e 1 = %. 2 f \n” , Z _ e 1 ) ;

73 printf ( ” \n E qu iv al en t r e s i s t a n c e w . r . t HV s i d e: \ n R e1 = %. 1 f \n” , R _ e 1 ) ;

74 printf ( ” \n = %. f d e g r e e s \n” , t he ta ) ;

75 printf ( ” \n E qu iv al en t r e a c ta n ce w . r . t HV s i d e : \n X e1 = %. 2 f \n” , X _ e 1 ) ;

77 printf ( ” \n b : E q u i v al e n t i mp ed an ce w . r . t LV s i d e : ”) ;

78 printf ( ” \n Z e 2 = %f = %. 2 f m \n” , Z _e 2 ,

Z _ e 2 * 1 0 0 0 ) ;

79 printf ( ” \n E qu iv al en t r e s i s t a n c e w . r . t LV s i d e: \ n R e2 = %f \n” , R _ e 2 ) ;

80 printf ( ” \n R e2 = %f = %. 2 f m \n” , R _ e 2 , R _ e 2

* 1 0 0 0 ) ;

81 printf ( ” \n E qu iv al en t r e a c t an c e w . r . t LV s i d e : \n X e2 = %f \n” , X _ e 2 ) ;

82 printf ( ” \n X e2 = %f = %. 2 f m \n” , X _ e 2 , X _ e 2

* 1 0 0 0 ) ;83

84 printf ( ” \n c : Rated s ec on da ry l oa d c u r re n t : \ nI 2 = %. f A\n” , I _ 2 ) ;

85 printf ( ” \n I 2 ∗ R c 2 = %. 2 f V \n” , R _e 2_ dr op ) ;

86 printf ( ” \n I 2 ∗ X c 2 = %. 2 f V \n” , X _e 2_ dr op ) ;

87 printf ( ” \n At u n i t y PF , \ n E 2 i n v o l t = ” ) ;

disp ( E _ 2 ) ;

89 printf (” \n V o l t a g e r e g u l a t i o n a t un i t y PF : \ nVR = %. 2 f p e r c e n t ” , V R _ u n it y _ PF ) ;

91 printf ( ” \n\n d : At 0 . 7 l a g g i n g PF , \n E 2 i nv o l t = ” ) ; disp ( E 2 ) ;

92 printf ( ” \n E 2 = %. 2 f <%. 2 f V \n ” , E2 _m , E 2_ a );

93 printf ( ” \n V o l t a g e r e g u l a t i o n a t 0 .7 l a gg i n g PF: \ n VR = %. 2 f p er c en t ” , V R _ l ag _ P F ) ;

Scilab code Exa 14.18 Pcsc

4 / / 2 nd e d i t i om5

11 / / G iv en d a ta12 V_sc = 50 ; // S h o r t c i r c u i t v o l t a g e i n v o l t13 V _1 = 2300 ; // Rated p ri ma ry v o l t a g e i n v o l t

1415 / / C a l c u l a t i o n s16 P _c = poly (0 , ’ P c ’ ) ; // Making P c a s a v a r i a b l e j u s t

f o r d i s p l a y i n g a n sw e r a s p e r17 / / t e xt b o o k18

19 P _c _s c = ( V_ sc / V_1 ) ^2 * P_c ; // F r a c t i o n o f P cm ea su re d by t h e w a tt m et e r

24 printf ( ” \n S in ce P c i s p r o p o r t i o na l t o t h e s qu ar eo f t he p ri ma ry v o l t a g e V sc , ” ) ;

25 printf ( ” \n t he n und er s h o rt c i r c u i t c o nd i t io n s , t hef r a c t i o n o f r a te d −c o r e l o s s i s : ” ) ;

26 printf ( ” \n P c ( s c ) = ” ) ; disp ( P _ c _ s c ) ;

Scilab code Exa 14.19 Ze1drop Re1drop Xe1drop VR

4 / / 2 nd e d i t i om

11 / / G iv en d a ta12

13 kVA = 20 ; // kVA r a t i n g o f t he s te p −downt r a n s f o r m e r

14 S = 20000 ; // power r a t i n g o f t he s te p−downt r a n s f o r m e r i n VA

15 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t16 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t17 Z _e1 = 5. 75 ; / / E q u i v a l e n t i mp ed an ce w . r . t HV s i d e

i n ohm18 R_e1 = 3.3 ; // E q ui v a le n t r e s i s t a n c e w . r . t HV s i d e

i n ohm19 X _e1 = 4. 71 ; // E q u i v al e n t r e a c t a n c e w . r . t HV s i d e

i n ohm20

21 // w . r . t HV s i d e f o l l o w i n g i s SC−t e s t d at a22 P 1 = 250 ; // w at tm et er r e a di n g i n W23 I 1 = 8.7 ; // I n pu t c u r r e n t i n A24 V1 = 50 ; // I np u t v o l t a ge i n V25

26 / / C a l c u l a t i o n s27 / / c as e a28 Z _ e1 _d ro p = V 1 ; // Hi gh v o l t a g e i mp ed an ce d ro p i n

v o l t29

30 / / c as e b31 t he ta = a co sd ( R _ e1 / Z _ e1 ) ; // PF a n gl e i n d e gr e e s32

33 R _ e1 _ dr o p = I 1 * Z_ e1 * c o sd ( t h et a ) ; //HV−s i d ee q u i v a l e n t r e s i s t a n c e v o l t a ge dr op i n v o l t

35 / / c as e c36 X _ e1 _ dr o p = I 1 * Z_ e1 * s i nd ( t h et a ) ; //HV−s i d ee q u i v a l e n t r e a c ta n ce v o l t a ge dro p i n v o l t

38 / / c as e d39 / / At u n i t y PF40 c o s _ th e ta 1 = 1 ;

44 E _1 = ( V _1 * c os _t he ta 1 + I1 * R _e 1 ) + %i * ( V_ 1 *s i n_ t he t a1 + I 1 * X_ e1 ) ;

48 VR _un ity _PF = ( ( E_1_m - V_1 ) / V_1 ) * 100 ; //T ra ns fo rm er v o l t a g e r e g u l a t i o n

50 / / c as e e51

/ / a t 0 . 7 l a g gi n g PF52 c os _t he ta _1 = 0 .7 ; // l a g g i n g PF53 s i n _ t h et a _ 1 = sqrt ( 1 - ( c o s _t h et a _1 ) ^ 2 ) ;

56 E 1 = ( V _1 * c os _t he ta _1 + I 1* R _e 1 ) + %i * ( V_ 1 *

s i n_ t he t a_ 1 + I 1 * X_ e1 ) ;

57 E 1 _m = abs ( E 1 ) ; / /E1 m=m a gn it ud e o f E1 i n v o l t58 E 1 _a = atan ( imag ( E 1 ) / real ( E 1 ) ) * 1 8 0 / % p i ; //E 1 a= phase

a ng l e o f E1 i n d e g r ee s

5960 VR _l ag _P F = ( ( E1_m - V_1 ) / V_1 ) * 100 ; //

T ra ns fo rm er v o l t a g e r e g u l a t i o n61

6465 printf ( ” \n a : High v o l t a g e i mp ed an ce d ro p : \ n

I 1 ∗ Z e 1 = V 1 = %d\n” , Z _ e 1 _ d r o p ) ;

67 printf ( ” \n b : = %. f d e g r e e s \n” , t he ta ) ;

68 printf ( ” \n High v ol ta ge r e s i s t a n c e dr op : \ nI 1 ∗ R e 1 = %. 2 f \n” , R _ e 1 _ d r o p ) ;

70 printf ( ” \n c : High v o l t a g e r e a ct a n ce drop : \ nI 1 ∗ X e 1 = %. 2 f \n” , X _ e 1 _ d r o p ) ;

72 printf ( ” \n d : At u n i t y PF , \ n E 2 i n v o l t = ” ) ;disp ( E _ 1 ) ;

74 printf ( ” \n V o l t a g e r e g u l a t i o n a t un i t y PF : \ nVR = %. 2 f p e r c e n t ” , V R _ u n it y _ PF ) ;

76 printf ( ” \n\n e : At 0 . 7 l a g g i n g PF , \n E 2 i nv o l t = ” ) ; disp ( E 1 ) ;

77 printf ( ” \n E 2 = %. 2 f <%. 2 f V \n ” , E1 _m , E 1_ a );

78 printf (” \n V o l t a g e r e g u l a t i o n a t 0 .7 l a gg i n g PF: \ n VR = %. 2 f p er c en t ” , V R _ l ag _ P F ) ;

Scilab code Exa 14.20 Re1 Re1 r2 its drop Pc

4 / / 2 nd e d i t i om5

c o n s o l e .10

t r a n s f o r m e r13 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t14 V_2 = 208 ; // S ec on da ry v o l t a g e i n v o l t15 f = 6 0 ; // F re qu en cy i n Hz16

17 / / SC−t e s t d at a18 P _sc = 82 00 ; // w at tm et er r e a di n g i n W

19 I_ sc = 2 17. 4 ; // S h o rt c i r c u i t c ur r e nt i n A20 V_sc = 95 ; // S h o r t c i r c u i t v o l t a g e i n V21

22 // OC−t e s t d at a23 P _oc = 18 00 ; // w at tm et er r e a di n g i n W24 I_oc = 85 ; // Open c i r c u i t c u r r e n t i n A25 V_oc = 208 ; // Open c i r c u i t v o l t a ge i n V26

27 / / C a l c u l a t i o n s28 a l p h a = V _ 1 / V _ 2 ; // T ra n sf o rm a ti o n r a t i o29

/ / c as e a30 P = P_sc ; // w at tm et er r e a di n g i n W31 I 1 = I_sc ; // S h o r t c i r c u i t c ur r e nt i n A32 R_e1 = P / ( I1 )^2 ; // E q ui v a le n t r e s i s t a n c e w . r . t

HV s i d e i n ohm33 R _e 2 = R _e 1 / ( a lp ha ) ^2 // E qu i va l en t r e s i s t a n c e

r e f e r r e d t o LV s i d e i n ohm34

35 / / c as e b36 r_2 = R_e2 / 2 ; // R e s is t a nc e o f low−v o l t a ge s i d e

i n ohm

3738 / / c as e c39 I _m = I_oc ; // Open c i r c u i t c u r r e n t i n A40 P_ cu = ( I_m ) ^2 * r_2 ; // T ra ns fo rm er c op pe r l o s s o f

t h e LV s i d e wdg d u r i n g OC−t e s t i n W

42 / / c as e d43 P _c = P_oc - P_cu ; // T ra ns fo rm er c o re l o s s i n W44

48 printf ( ” \n a : E q ui v al e n t r e s i s t a n c e w . r . t HV s i d e: \ n R e1 = %. 4 f \n” , R _ e 1 ) ;

49 printf ( ” \n E qu iv al en t r e s i s t a n c e w . r . t LV s i d e: \ n R e2 = %f = %. 3 f m \n” , R _ e 2 , R _ e 2

* 1 0 0 0 ) ;

5051 printf ( ” \n b : R e s i st a n c e o f LV s i d e : \ n r 2 = %f

= %. 2 f m \n” , r _ 2 , r _ 2 * 1 0 0 0 ) ;

53 printf ( ” \n c : T ra ns fo rm er c op pe r l o s s o f t he LVs i d e wdg d u r i n g OC−t e s t : ” ) ;

54 printf ( ” \n ( I m ) ˆ2 ∗ r 2 = %f W \n” , P _ c u ) ;

56 printf ( ” \n d : T ra ns fo rm er c or e l o s s : \ n P c = %f W \n ” , P _ c ) ;

58 printf ( ” \n e : Yes . The e r r o r i s a p p r ox i m a te l y 5 /%d =0 . 2 7 8 p e r c e n t , w hi ch i s ” , P _ o c ) ;

59 printf ( ” \n w i t h i n th e e r r o r pr o d u c e d by t h ei n s tr u m en t s u se d i n t he t e s t . ” ) ;

60 printf ( ” \n We may assume t ha t t h e c or e l o s s i s%d W. ” , P _ o c ) ;

Scilab code Exa 14.21 tabulate I2 efficiencies

4 / / 2 nd e d i t i om

11 / / G i ve n d a t a ( f r om Ex . 1 4 −1 8)12 V_sc = 50 ; // S h o r t c i r c u i t v o l t a g e i n v o l t13 V _1 = 2300 ; // Rated p ri ma ry v o l t a g e i n v o l t14

1516 // P r el i mi n ar y d at a b e f o re t a b u l at i n g17

18 / / f ro m e x . 14 −2019 P_c = 1.8 ; // c o r e l o s s e s i n kW20 P_k = 1.8 ; // f i x e d l o s s e s i n kW21 P _c u_ ra te d = 8 .2 ; // Rated c op pe r l o s s i n kW22

23 / / g iv en r a t i n g24 kVA = 500 ; // Power r a t i n g i n kVA25 PF = 1 ;

// power f a c t o r26 P_o = kVA * PF ; // f u l l −l o ad o ut pu t a t u n it y PF i nkW

28 / / C a l c u l a t i o n s29 / / c as e a30 LF1 = 1/4 ; // Load f r a c t i o n31 LF2 = 1/2 ; // Load f r a c t i o n32 LF3 = 3/4 ; // Load f r a c t i o n33 LF4 = 5/4 ; // Load f r a c t i o n34 P _c u_ fl = 8. 2 ; // E qu i v al en t c op pe r l o s s a t f u l l −

l oa d s l i p35 P _c u_ LF 1 = ( L F1 ) ^2 * P _c u_ fl ; // E q u i v a le n t c o pp e r

l o s s a t 1 /4 r at ed l oa d36 P _c u_ LF 2 = ( L F2 ) ^2 * P _c u_ fl ; // E q u i v a le n t c o pp e r

l o s s a t 1 /2 r at ed l oa d

37 P _c u_ LF 3 = ( L F3 ) ^2 * P _c u_ fl ; // E q u i v a le n t c o pp e r

l o s s a t 3 /4 r at ed l oa d38 P _c u_ LF 4 = ( L F4 ) ^2 * P _c u_ fl ; // E q u i v a le n t c o pp e rl o s s a t 5 /4 r at ed l oa d

40 P _L _1 = P _c + P _c u_ LF 1 ; // T o ta l l o s s e s i n kW at1/4 r a te d l oa d

43 P _L _f l = P_c + P _c u_ fl ; // T o ta l l o s s e s i n kW at

r a t ed l o ad44 P _L _4 = P _c + P _c u_ LF 4 ; // T o ta l l o s s e s i n kW at

5/4 r a te d l oa d45

46 P _o _1 = P _o * LF 1 ; // T ot al o ut pu t i n kW a t 1 /4 r a t edl o a d

49 P _o _f l = P_o ; // T ot al o ut pu t i n kW at r a t ed l o ad50 P _o _4 = P _o * LF 4 ; // T ot al o ut pu t i n kW a t 5 /4 r a t ed

l o a d51

52 P _i n_ 1 = P _L _1 + P _o _1 ; // T ot al i n pu t i n kW a t 1/ 4r a te d l oa d

55 P _i n_ fl = P _L _f l + P _o _f l ; // T ot al i n pu t i n kW a t

r a t ed l o ad56 P _i n_ 4 = P _L _4 + P _o _4 ; // T ot al i n pu t i n kW a t 5/ 4

r a te d l oa d57

58 e ta _1 = ( P _ o_ 1 / P _i n _1 ) * 1 00 ; // E f f i c i e n c y a t 1/4

r a t ed l o ad

59 e ta _2 = ( P _ o_ 2 / P _i n _2 ) * 1 00 ; // E f f i c i e n c y a t 1/2r a t ed l o ad60 e ta _3 = ( P _ o_ 3 / P _i n _3 ) * 1 00 ; // E f f i c i e n c y a t 3/4

r a t ed l o ad61 e ta _ fl = ( P _ o_ fl / P _ i n_ f l ) *1 00 ; // E f f i c i e n c y a t

r a t ed l o ad62 e ta _4 = ( P _ o_ 4 / P _i n _4 ) * 1 00 ; // E f f i c i e n c y a t 5/4

r a t ed l o ad63

65 / / c as e b

66 PF_b = 0.8 ; // 0 . 8 PF l a g g i ng67 P o_ 1 = P _o * L F1 * P F_ b ; // T ot al o ut pu t i n kW a t 1/ 4

r a t ed l o ad68 P o_ 2 = P _o * L F2 * P F_ b ; // T ot al o ut pu t i n kW a t 1/ 2

r a t ed l o ad69 P o_ 3 = P _o * L F3 * P F_ b ; // T ot al o ut pu t i n kW a t 3/ 4

r a t ed l o ad70 P o_ fl = P _o * P F_ b ; // T ot al o ut pu t i n kW a t r a t ed

l o a d71 P o_ 4 = P _o * L F4 * P F_ b ; // T ot al o ut pu t i n kW a t 5/ 4

r a t ed l o ad72

73 P in _1 = P _L _1 + P o_ 1 ; // T ot al i n pu t i n kW a t 1/ 4r a t ed l o ad

76 P in _f l = P _L _f l + P o_ fl ; // T ot al i n pu t i n kW a tr a t ed l o ad

77 P in _4 = P _L _4 + P o_ 4 ; // T ot al i n pu t i n kW a t 5/ 4

r a t ed l o ad78

79 e t a1 = ( P o_ 1 / P in _1 ) * 1 00 ; // E f f i c i e n c y a t 1 /4 r at edl o a d

80 e t a2 = ( P o_ 2 / P in _2 ) * 1 00 ; // E f f i c i e n c y a t 1 /2 r at ed

l o a d

81 e t a3 = ( P o_ 3 / P in _3 ) * 1 00 ; // E f f i c i e n c y a t 3 /4 r at edl o a d82 e ta fl = ( P o _f l / P in _ fl ) * 1 00 ; // E f f i c i e n c y a t r at ed

l o a d83 e t a4 = ( P o_ 4 / P in _4 ) * 1 00 ; // E f f i c i e n c y a t 5 /4 r at ed

l o a d84

85 / / c as e c86 R _e 2 = 1 .4 17 e -3 ; // E q u i va l en t r e s i s t a n c e i n ohm

r e f e r r e d t o LV s i d e87 P c = 1800 ; // Core l o s s e s i n W

88 I _2 = sqrt ( P c / R _ e 2 ) ; // Load c u r r e nt i n A f o r max .e f f i c i e n c y i n v a r i a n t o f LF

90 / / c as e d91 V = 208 ; // V ol ta ge r a t i n g i n v o l t92 I _2 _r at ed = ( k VA * 1 00 0) / V ; // R at ed s e c o n d a r y

c u r r e n t i n A93 L F _m ax = I _2 / I _2 _r at ed ; // Load f r a c t i o n f o r max .

e f f i c i e n c y94

95 / / c as e e96 / / s u b s c r i p t e f o r e t a max i n d i c a t e s c as e e

97 c o s _t h et a = 1 ;

98 V_2 = V ; // s ec on da ry v o l t a ge i n v o l t99 P c = 1800 ; // c or e l o s s i n W

100 // max . e f f i c i e n c y f o r u n it y PF101 e t a_ m ax _ e = ( V _2 * I _2 * c o s _t h et a ) / ( ( V_ 2 * I_ 2 *

c os _t he ta ) + ( Pc + I _2 ^ 2* R _e 2 )) * 1 00

103 / / c as e f 104 / / s u b s c r i p t f f o r e t a max i n d i c a t e s c as e e

105 c o s_ t he t a2 = 0 .8 ;106 // max . e f f i c i e n c y f o r 0 . 8 l a g g i n g PF107 e t a_ m ax _ f = ( V _2 * I _2 * c o s _t h et a 2 ) / ( ( V_ 2 * I_ 2 *

c os _t he ta 2 ) + ( Pc + I _2 ^ 2* R _e 2 )) * 1 00

112 printf ( ” \n a : T ab ul at io n a t u n it y PF : ” ) ;

113 printf ( ” \n

” ) ;

114 printf ( ” \n L . F \ t Core l o s s \ t Copper l o s s \t To t a l l o s s \ t T o t a l Out pu t \ t T ot al I np ut \ tE f f i c i e n c y ” ) ;

115 printf ( ” \n \ t (kW) \ t (kW) \ tP L (kW) \ t P o (kW) \ t P L+P o (kW) \ t P o /

P i n ( p e r c e n t ) ” ) ;116 printf ( ” \n

” ) ;

117 printf ( ” \n %. 2 f \ t %. 1 f \ t \ t %. 3 f \ t%.3 f \ t \ t %. 1 f \ t %. 2 f \ t %. 2 f ” , L F 1 , P _ c ,

P _ c u_ L F 1 , P _L _ 1 , P _ o_ 1 , P _ i n _1 , e t a _ 1 ) ;

119 printf (” \n %. 2 f \ t %. 1 f \ t \ t %. 3 f \ t%.3 f \ t \ t %. 1 f \ t %. 2 f \ t %. 2 f ” , L F 3 , P _ c ,

120 printf ( ” \n 1 \ t \ t %. 1 f \ t \ t %. 3 f \ t %. 3 f \ t %. 1 f \ t %. 2 f \ t %. 2 f ” ,P_c, P_cu_fl ,

P _ L_ f l , P _ o _ fl , P _ i n _ fl , e t a _ f l ) ;

121 printf ( ” \n %. 2 f \ t %. 1 f \ t \ t %. 3 f \ t %. 3 f \ t %. 1 f \ t %. 2 f \ t %. 2 f ” ,LF4, P_c, P_cu_LF4 ,

P _ L _ 4 , P _ o _ 4 , P _ i n _ 4 , e t a _ 4 ) ;

122 printf ( ” \n

\n\n” ) ;123

124 printf ( ” \n b : T ab ul at io n a t 0 . 8 PF l a g g i n g : ” ) ;

125 printf ( ” \n

” ) ;

126 printf ( ” \n L . F \ t Core l o s s \ t Copper l o s s \t To t a l l o s s \ t T o t a l Out pu t \ t T ot al I np ut \ tE f f i c i e n c y ” ) ;

127 printf ( ” \n \ t (kW) \ t (kW) \ tP L (kW) \ t P o (kW) \ t P L+P o (kW) \ t P o /P i n ( p e r c e n t ) ” ) ;

128 printf ( ” \n

” ) ;

P _ c u_ L F 1 , P _ L_ 1 , P o _ 1 , P i n _ 1 , e t a 1 ) ;130 printf ( ” \n %. 2 f \ t %. 1 f \ t \ t %. 3 f \ t

%.3 f \ t \ t %. 1 f \ t %. 2 f \ t %. 2 f ” , L F 2 , P _ c ,

P _ c u_ L F 2 , P _ L_ 2 , P o _ 2 , P i n _ 2 , e t a 2 ) ;

P _ c u_ L F 3 , P _ L_ 3 , P o _ 3 , P i n _ 3 , e t a 3 ) ;

132 printf ( ” \n 1 \ t \ t %. 1 f \ t \ t %. 3 f \ t %. 3 f \ t %. 1 f \ t %. 2 f \ t %. 2 f ” ,P_c, P_cu_fl ,

P _ L _ f l , P o _ f l , P i n _ f l , e t a f l ) ;

133 printf (” \n %. 2 f \ t %. 1 f \ t \ t %. 3 f \ t %. 3 f \ t %. 1 f \ t %. 2 f \ t %. 2 f ” ,LF4, P_c, P_cu_LF4 ,

P _ L _ 4 , P o _ 4 , P i n _ 4 , e t a 4 ) ;

134 printf ( ” \n

\n\n” ) ;

136 printf ( ” \n c : Load c u r r e nt a t wh ich max . e f f i c i e n c yo c c ur s : \ n I 2 = %. 1 f A \n” , I _ 2 ) ;

138 printf ( ” \n d : Rated l oa d c u r re n t : \ n I 2 ( r a t e d )

= %. 1 f A \n” , I _ 2 _ r a t e d ) ;139 printf ( ” \n Load f r a c t i o n f o r m a x = %. 3 f (

h a l f r a t e d l o a d ) \n ” , L F _ m a x ) ;

141 printf ( ” \n e : Max . e f f i c i e n c y f o r u n it y PF : \ n

m a x = %. 2 f p e r c e n t \n” , e t a _ m a x _ e ) ;

142143 printf ( ” \n f : Max . e f f i c i e n c y f o r 0 . 8 l a g g i n g PF : \ n

m a x = %. 2 f p e r c e n t ” , e t a _ m a x _ f ) ;

Scilab code Exa 14.22 Zeqpu V1pu VR

11 / / G iv en d a ta12 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t

13 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t14 P = 2 0 ; // Power r a t i n g o f t he t r a n s fo r m e r i n kVA15 // S h o rt c i r c u i t t e s t d a t a16 P_sc = 250 ; / / Power m ea su re d i n W17 V_sc = 50 ; // S h o r t c i r c u i t v o l t a g e i n v o l t18 I_sc = 8.7 ; // S h o r t c i r c u i t c ur r e nt i n A19

20 / / C a l c u l a t i o n s21 / / c as e a22 V_1b = V_1 ; // b a se v o l t a ge i n v o l t

23 Z _e q_ pu = V_ sc / V_1 ;24

25 funcprot ( 0) ; // Use t h i s t o a vo id t he me ss ag e ”Warning : r e d e f i n i n g f u n c t i o n : b et a ”

26 b e t a = a c os d ( P _ s c / ( V _ sc * I _ s c ) ) ; // a ng l e i n d e g r e e s

2728 Z e q _p u = Z _e q _p u * exp ( % i * ( b e t a ) * ( % p i / 1 8 0 ) ) ;

29 Z e q _ pu _ m = abs ( Z e q _ p u ) ; / / Z e q pu m=m a g n i t ud e o f Z eq p u i n p . u

30 Z e q _ pu _ a = atan ( imag ( Z e q_ pu ) / real ( Z e q _ p u ) ) * 1 8 0 / % p i ;

// Z eq p u a=p ha se a n g le o f Ze q p u i n d e g r e es31

32 / / c as e b33 / / a t u ni t y PF34 V _ 1_ pu = 1* exp ( % i *( 0) * ( % pi / 1 80 ) ) + 1 *exp ( % i * ( 0 ) * ( % p i

/ 1 8 0 ) ) * Z _ e q _ p u * exp ( % i * ( b e t a ) * ( % p i / 1 8 0 ) ) ;

35 / / RHS i s w r i t t en i n e x p o n e n t i a l co mp lex fo rm and (%pi / 18 0) i s r a d i an s t o d e g r e e s c o nv e r s i o n f a c t o r

36 V _ 1 _ pu _ m = abs ( V _ 1 _ p u ) ; / / V 1 p u m=m a g ni t ud e o f V 1 pu i n v o l t

37 V _ 1 _ pu _ a = atan ( imag ( V _ 1_ pu ) / real ( V _ 1 _ p u ) ) * 1 8 0 / % p i ;

// V 1 pu a=p ha se a n gl e o f V 1 pu i n d e g re e s38

39 / / c as e c40 // a t 0 . 7 PF l a g g i n g41 t he ta = a co sd ( 0 . 7) ; // Power f a c t o r a n gl e i n d e g re e s42 V 1_ pu = 1* exp ( % i * (0 ) * ( %p i / 18 0) ) + 1 * exp ( % i * ( - t h e t a )

* ( % p i / 1 8 0 ) ) * Z _ e q _ p u * exp ( % i * ( b e t a ) * ( % p i / 1 8 0 ) ) ;

43 V 1 _ pu _ m = abs ( V 1 _ p u ) ; / / V1 pu m=m a g ni t ud e o f V 1 p u i nv o l t

44 V 1 _ pu _ a = atan ( imag ( V 1 _p u ) / real ( V 1 _ p u ) ) * 1 8 0 / % p i ; //V 1 p u a=p ha se a n g l e o f V1 pu i n d e g r e es

46 / / c as e d47 V R_ un it y_ PF = V _1 _p u_ m - 1 ; // v o l t a ge r e g u l a t i o n

a t u n it y PF48

49 / / c as e e50 V R_ la g_ PF = V 1_ pu _m - 1 ; // v o l t a ge r e g u l a t i o n a t

0 . 7 l a g g i ng PF51

5455 printf ( ” \n a : Z e q ( p u ) = %. 5 f p . u \n” , Z _ e q _ p u ) ;

56 printf ( ” \n = %. f d e g r e e s \n” , b e t a ) ;

57 printf ( ” \n Z e q ( pu ) < = ” ) ; disp ( Z e q _ p u ) ;

58 printf ( ” \n Z e q ( pu ) < = %. 5 f <%. f p . u \n ” ,

Zeq_pu_m ,Ze q_pu_a );

60 printf ( ” \n b : | V 1 ( p u ) | = ” ) ; disp ( V _ 1 _ p u ) ;

61 printf ( ” \n | V 1 ( p u ) | = %. 4 f <%. 2 f V \n ” ,

V _ 1_ p u_ m , V _ 1_ p u_ a ) ;

63 printf ( ” \n c : | V 1 ( p u ) | = ” ) ; disp ( V 1 _ p u ) ;64 printf ( ” \n | V 1 ( p u ) | = %. 4 f <%. 2 f V \n ” , V 1 _ p u _ m

, V 1_ pu _a ) ;

66 printf ( ” \n d : V ol ta ge r e g u l a t i o n a t u ni ty PF : \ nVR = %f ” , V R _ u n i t y _ P F ) ;

67 printf ( ” \n VR = %. 3 f p er ce nt \n ” ,100*

V R _ u n i t y _ P F ) ;

69 printf ( ” \n e : V ol ta ge r e g u l a t i o n a t 0 . 7 l a g g i n g PF

: \ n VR = %f ”, V R _ l a g _ P F ) ;

70 printf ( ” \n VR = %. 2 f p er ce nt \n ” , 1 0 0 * V R _ l a g _ P F )

72 printf ( ” \n f : VRs a s f o un d by p . u metho d a r ee s s e n t i a l l y t h e s ame a s t ho se f o u n d ” ) ;

73 printf ( ” \n i n Exs .14 −1 7 and 14−19 u s i ng t he sameda ta , f o r t he same t r an s fo r me r , ” ) ;

74 printf ( ” \n but w i t h much l e s s e f f o r t . ” ) ;

Scilab code Exa 14.23 Pcu LF efficiencies

11 / / G iv en d a ta12 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t

13 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t14 S = 500 ; // Power r a t i n g o f t he t r a n s fo r m e r i n kVA15 f = 6 0 ; // F re qu en cy i n Hz16

17 / / Open c i r c u i t t e s t d a t a18 V_oc = 208 ; // Open c i r c u i t v o l t a ge i n v o l t19 I_oc = 85 ; // Open c i r c u i t c u r r e n t i n A20 P _oc = 18 00 ; / / Power m ea su re d i n W21

22 // S h o rt c i r c u i t t e s t d a t a23 V_sc = 95 ;

// S h o r t c i r c u i t v o l t a g e i n v o l t24 I_ sc = 2 17. 4 ; // S h o rt c i r c u i t c ur r e nt i n A25 P _sc = 82 00 ; / / Power m ea su re d i n W26

27 / / C a l c u l a t i o n s28 / / c as e a29 S_b = S ; // B as e v o l t a g e i n kVA30 Psc = 8.2 ; / / P ow er m e as u re d i n kW d u r i n g SC−t e s t31 P _Cu_ pu = Psc / S_b ; // p er u n i t v al ue o f P Cu a t

r a t ed l o ad32

33 / / c as e b34 Poc = 1.8 ; / / P ow er m e as u re d i n kW d u r i n g OC−t e s t35 P _CL_ pu = Poc / S_b ; // p er u n i t v al ue o f P CL a t

r a t ed l o ad36

37 / / c as e c

38 PF = 1 ; // u n i ty Power f a c t o r39 eta _pu = PF / ( PF + P _CL _pu + P _Cu _pu ) * 100 ; //E f f i c i e n c y a t r a te d l oa d , u n it y PF

41 / / c as e d42 // s u b s c r i p t d f o r PF and e t a p u i n d i c a t e s c as e d43 PF_d = 0.8 ; // 0 . 8 l a g g i n g Power f a c t o r44 e ta _p u_ d = P F_ d / ( PF_ d + P _C L_ pu + P _C u_ pu ) * 100

; / / E f f i c i e n c y a t r at e d l oa d , u ni t y PF45

46 / / c as e e

47 LF = sqrt ( P _ CL _ pu / P _ Cu _ pu ) ; // Load f r a c t i o np ro d uc i ng max . e f f i c i e n c y

49 / / c as e f 50 e ta _p u_ ma x = ( LF * PF ) / ( ( LF * PF ) + 2* ( P_ CL _p u ) ) *

100 ; // Maximum e f f i c i e n c y a t u n i t y PF l o a d51

52 / / c as e g53 e ta _p u_ ma x_ g = ( LF * P F_ d ) / ( ( LF * P F_ d ) + 2 *( P _ CL _p u )

) * 100 ; // Maximum e f f i c i e n c y a t 0 . 8 l a g g i n g

P F l o a d54

59 printf ( ” \n a : Per u ni t c o pp er l o s s a t r at ed l oa d : ”) ;

60 printf ( ” \n P Cu ( pu ) = %. 4 f p . u = R eq ( pu ) \n” ,

P _ C u _ p u ) ;

62 printf ( ” \n a : Per u ni t c or e l o s s a t r at ed l oa d : ” ) ;63 printf ( ” \n P CL ( pu ) = %. 4 f p . u \n” , P _ C L _ p u ) ;

65 printf ( ” \n c : E f f i c i e n c y a t r a te d l oa d , u ni t y PF : \ np u = %. 2 f p e r c e n t \n” , e t a _ p u ) ;

67 printf ( ” \n c : E f f i c i e n c y a t r at ed l o a d , 0 . 8 l a g gi n gPF : \ n p u = %. 2 f p e r c e n t \n” , e t a _ p u _ d ) ;

69 printf ( ” \n e : Load f r a c t i o n p ro d uc i ng max .e f f i c i e n c y : \ n L . F = %. 3 f \n ” , LF ) ;

71 printf ( ” \n f : Maximum e f f i c i e n c y a t u n it y PF l o ad: \ n p u ( max ) = %. 2 f p e r c e n t \n” , e t a _ p u _ m a x ) ;

73 printf ( ” \n g : Maximum e f f i c i e n c y a t 0 . 8 l a g g i n g PFl oa d : \ n p u ( max ) = %. 2 f p e r c e n t \n” ,

e t a _ p u _ m a x _ g ) ;74

75 printf ( ” \n h : A l l e f f i c i e n c y v al ue s a re i d e n t i c a lt o t h o se computed i n s o l u t i o n t o Ex .1 4 − 2 1 . \n” ) ;

77 printf ( ” \n i : Per−u n i t method i s much s i m p l e r andl e s s s u b j e c t t o e r r o r t ha n c o n v e n ti o n a l method . ” )

Scilab code Exa 14.24 efficiencies at differnt LFs

11 / / G i ve n d a t a ( From Ex . 1 4 −2 3)

12 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t

13 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t14 S = 500 ; // Power r a t i n g o f t he t r a n s fo r m e r i n kVA15 f = 6 0 ; // F re qu en cy i n Hz16

17 / / Open c i r c u i t t e s t d a t a18 V_oc = 208 ; // Open c i r c u i t v o l t a ge i n v o l t19 I_oc = 85 ; // Open c i r c u i t c u r r e n t i n A20 P _oc = 18 00 ; / / Power m ea su re d i n W21

22 // S h o rt c i r c u i t t e s t d a t a23 V_sc = 95 ; // S h o r t c i r c u i t v o l t a g e i n v o l t

24 I_ sc = 2 17. 4 ; // S h o rt c i r c u i t c ur r e nt i n A25 P _sc = 82 00 ; / / Power m ea su re d i n W26

27 / / C a l c u l a t i o n s28 / / P r e l i m i na r y c a l c u l a t i o n s29 S_b = S ; // B as e v o l t a g e i n kVA30 Psc = 8.2 ; / / P ow er m e as u re d i n kW d u r i n g SC−t e s t31 P _Cu_ pu = Psc / S_b ; // p er u n i t v al ue o f P Cu a t

r a t ed l o ad32

33 Poc = 1.8 ; / / P ow er m e as u re d i n kW d u r i n g OC−t e s t34 P _CL_ pu = Poc / S_b ; // p er u n i t v al ue o f P CL a t

r a t ed l o ad35

36 / / c as e a37 LF1 = 3/4 ; // Load f r a c t i o n o f r at ed l oa d38 PF1 = 1 ; // u n it y Power f a c t o r39 e ta _p u_ LF 1 = ( L F1 * P F1 ) / (( L F1 * P F1 ) + P _C L_ pu + ( L F1

) ^2* P _C u_ pu ) * 1 00 ; // E f f i c i e n c y a t r at ed l o a d, u n i t y PF

41 / / c as e b42 LF2 = 1/4 ; // Load f r a c t i o n o f r at ed l oa d43 PF2 = 0.8 ; // 0 . 8 l a g g i n g PF44 e ta _p u_ LF 2 = ( L F2 * P F2 ) / (( L F2 * P F2 ) + P _C L_ pu + ( L F2

) ^2* P _C u_ pu ) * 1 00 ; // E f f i c i e n c y a t 1 /4 r at ed

l oa d , 0 . 8 l a g g i n g PF

4546 / / c as e c47 LF3 = 5/4 ; // Load f r a c t i o n o f r at ed l oa d48 PF3 = 0.8 ; // 0 . 8 l e a d i ng PF49 e ta _p u_ LF 3 = ( L F3 * P F3 ) / (( L F3 * P F3 ) + P _C L_ pu + ( L F3

) ^2* P _C u_ pu ) * 1 00 ; // E f f i c i e n c y a t r 1 / 4 r at edl oa d , 0 . 8 l e a d i n g PF

5455 printf ( ” \n E f f i c i e n c y ( pu ) : \ n ” ) ;

56 printf ( ” \n a : p u a t %. 2 f r a t e d −l o a d = %. 2 f p e r c e n t \n” , L F 1 , e t a _ p u _ L F 1 ) ;

58 printf ( ” \n b : p u a t %. 2 f r a t e d −l o a d = %. 2 f p e r c e n t \n” , L F 2 , e t a _ p u _ L F 2 ) ;

60 printf ( ” \n c : p u a t %. 2 f r a t e d −l o a d = %. 2 f p e r c e n t \n” , L F 3 , e t a _ p u _ L F 3 ) ;

Scilab code Exa 14.25 Zpu2 St S2 S1 LF

11 / / G iv en d a ta12 kVA_1 = 500 ; // Power r a t i n g o f t he t r an s f o r me r 1in kVA

13 R _1 _p u = 0 .0 1 ; / / p er −u ni t v al ue o f r e s i s t a n c e o f t he t r an s f o r m er 1

14 X _1 _p u = 0 .0 5 ; / / p er −u ni t v al ue o f r e a c t a nc e o f t he t r an s f o r m er 1

15 Z _1 _p u = R _1 _p u + %i * X _1 _p u ; / / p e r −u ni t v al ue o f i mp ed an ce o f t he t r a n s f or m e r 1

17 P F = 0.8 ; // l a g g i n g power f a c t o r

18 V_2 = 400 ; // S ec on da ry v o l t a g e i n v o l t19 S _l oa d = 750 ; // I n c r e a s e d s ys te m l o ad i n kVA20

21 kVA_2 = 250 ; // Power r a t i n g o f t h e t r a n sf o r m e r 2in kVA

22 R _ pu _2 = 0 .0 15 ; // p er −u ni t v a lu e o f r e s i s t a n c e o f t he t r an s f o r m er 2

23 X _p u_ 2 = 0 .0 4 ; / / p er −u ni t v al ue o f r e a c t a nc e o f t he t r an s f o r m er 2

25 // s m a l l er t r an s f o r m er s ec on da ry v o l t a g e i s same a sl a r g e r t r an s f or m e r

27 / / C a l c u l a t i o n s28 / / P r e l i m i na r y c a l c u l a t i o n s29 Z _p u_ 1 = R _p u_ 2 + %i * X _p u_ 2 ; / / New t r a n s f o r m e r p . u

. i m p ed a n ce30

31 / / C a l c u l a t i o n s32 / / c as e a33 V_b1 = 400 ; // b a se v o l t a ge i n v o l t

34 V_b2 = 400 ; // b a se v o l t a ge i n v o l t35 Z _p u _2 = ( k V A_ 1 / k VA _2 ) * ( V _b 1 / V _b 2 ) ^2 * ( Z _ pu _1 ) ; //

New t r a n s f o r m e r p . u i m pe d an c e36 Z _2 _p u = Z _p u_ 2 ; / /New t r a n s f o r m e r p . u i m pe d an c e37

38 / / c as e b

39 c o s_ th et a = P F ; // Power f a c t o r40 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;

41 S _ t_ c on j ug a te = ( k V A_ 1 + k VA _2 ) * ( c o s_ t he t a + % i *

s i n _ t h e t a ) ; // kVA o f t o t a l l oa d42

43 / / c as e c44 S _ 2 _ co n ju g at e = S _ t_ c on j ug a te * ( Z _1 _p u / ( Z _1 _p u +

Z _2 _p u ) ) ; // P or ti on o f l oa d c a r r i e d by t h es m a l l e r t r a n s fo r m e r i n kVA

45 S _ 2 _ c o n j ug a t e _ m = abs ( S _ 2 _ c o n j u g a t e ) ; //S 2 c o n j u g a t e m=m ag ni tu de o f S 2 c o n j u g a t e i n kVA

46 S _ 2 _ c o n j ug a t e _ a = atan ( imag ( S _ 2 _ c o nj u g a te ) / real (S _ 2 _ c o n j u g a t e ) ) * 1 8 0 / % p i ; / / S 2 c o n j u g a t e a =p h a sea ng l e o f S 2 c o nj u ga t e i n d e g r ee s

48 / / c as e d49 S _ 1_ c on j ug a te = S _ t_ c on j ug a te * ( Z _2 _p u / ( Z _1 _ pu +

Z _2 _p u ) ) ; // P or ti on o f l oa d c a r r i e d by t h eo r i g i n a l t r an s f o r m er i n kVA

50 S _ 1 _ c o n j ug a t e _ m = abs ( S _ 1 _ c o n j u g a t e ) ; //S 1 c o n j u g a t e m=m ag ni tu de o f S 1 c o n j u g a t e i n kVA

51 S _ 1 _ c o n j ug a t e _ a = atan ( imag ( S _ 1 _ c o nj u g a te ) / real (

S _ 1 _ c o n j u g a t e ) ) * 1 8 0 / % p i ; / / S 1 c o n j u g a t e a =p h a sea ng l e o f S 1 c o nj u ga t e i n d e g r ee s

53 / / c as e e54 S _ 1 = S _ 1_ c on j ug a te _ m ;

55 S_ b1 = k VA_ 1 ; // b as e power i n kVA o f t r a n c s fo r m e r1

56 LF1 = ( S_1 / S _b 1) *1 00 ; // Load f r a c t i o n o f t heo r i g i n a l t r a n s f o r me r i n p e r ce nt

58 / / c as e f 59 S _ 2 = S _ 2_ c on j ug a te _ m ;

60 S_ b2 = k VA_ 2 ; // b as e power i n kVA o f t r a n c s fo r m e r2

61 LF2 = ( S_2 / S _b 2) *1 00 ; // Load f r a c t i o n o f t he

o r i g i n a l t r a n s f o r me r i n p e r ce nt

66 printf ( ” \n a : New t r a n s f o r m e r p . u i mp ed an ce : \ nZ p . u . 2 i n p . u = ” ) ; disp ( Z _ p u _ 2 ) ;

68 printf ( ” \n b : kVA o f t o t a l l oa d : \ n S∗ t i n kVA= ” ) ; disp ( S _ t _ c o n j u g a t e ) ;

70 printf ( ” \n c : P or ti on o f l oa d c a r r i e d by t he

s m a l l e r t r a n s fo r m e r i n kVA : ” ) ;71 printf ( ” \n S∗ 2 i n kVA = ” ) ; disp ( S _ 2 _ c o n j u g a t e )

72 printf ( ” \n S∗ 2 = %. 1 f <%. 2 f kVA ( i n d u c t i v e l o a d) \n” , S _ 2 _ c o n j u g a te _ m , S _ 2 _ c o n j u g a t e _ a ) ;

74 printf ( ” \n d : P or ti on o f l oa d c a r r i e d by t heo r i g i n a l t r an s f o r m er i n kVA : ” ) ;

75 printf ( ” \n S∗ 2 i n kVA = ” ) ; disp ( S _ 1 _ c o n j u g a t e ) ;

76 printf ( ” \n S∗ 2 = %. 1 f <%. 2 f kVA ( i n d u c t i v e l o a d

) \n”, S _ 1 _ c o n j u g a te _ m , S _ 1 _ c o n j u g a t e _ a ) ;

78 printf ( ” \n e : Load f r a c t i o n o f t h e o r i g i n a lt r an s f o r me r : \ n L . F . 1 = %. 1 f p e r c e n t \n” , L F 1 ) ;

80 printf ( ” \n f : Load f r a c t i o n o f t h e o r i g i n a lt r an s f o r me r : \ n L . F . 2 = %. 1 f p e r c e n t \n” , L F 2 ) ;

82 printf ( ” \n g : Yes . R ed uc e t h e no−l oa d v o l t a ge o f t he new t r a n s fo r m e r t o some v a lu e ” ) ;

83 printf ( ” \n be l o w th a t o f i t s p r e s e n t v a l u e s o

t ha t i t s s ha r e o f t he l oa d i s r ed uc ed . ” ) ;

Scilab code Exa 14.26 Vb Ib Zb Z1 Z2 I1 I2 E1 E2

1011 / / G i ve n d a t a ( From Ex . 1 4 −2 5)12 kVA_1 = 500 ; // Power r a t i n g o f t he t r an s f o r me r 1

in kVA13 R _1 _p u = 0 .0 1 ; / / p er −u ni t v al ue o f r e s i s t a n c e o f

t he t r an s f o r m er 114 X _1 _p u = 0 .0 5 ; / / p er −u ni t v al ue o f r e a c t a nc e o f

t he t r an s f o r m er 115 Z _1 _p u = R _1 _p u + %i * X _1 _p u ; / / p e r −u ni t v al ue o f

i mp ed an ce o f t he t r a n s f or m e r 116

17 P F = 0.8 ; // l a g g i n g power f a c t o r18 V = 400 ; // S ec on da ry v o l t ag e i n v o l t19 S _l oa d = 750 ; // I n c r e a s e d s ys te m l o ad i n kVA20

21 kVA_2 = 250 ; // Power r a t i n g o f t h e t r a n sf o r m e r 2in kVA

22 R _ pu _2 = 0 .0 15 ; // p er −u ni t v a lu e o f r e s i s t a n c e o f t he t r an s f o r m er 2

23 X _p u_ 2 = 0 .0 4 ; / / p er −u ni t v al ue o f r e a c t a nc e o f t he t r an s f o r m er 2

2425 // s m a l l er t r an s f o r m er s ec on da ry v o l t a g e i s same a s

l a r g e r t r an s f or m e r26

28 / / P r e l i m i na r y c a l c u l a t i o n s

29 Z _p u_ 1 = R _p u_ 2 + %i * X _p u_ 2 ; / / New t r a n s f o r m e r p . u. i m p ed a n ce30

31 / / c as e a32 V_b = V ; / / ( g i v e n )33

34 / / c a s e b35 S _ b = 5 00 * 10 0 0 ; // b a se p ower i n VA36 I_b = S_b / V_b ; // b a se c u rr e n t i n A37

38 / / c as e c

39 Z_b = V ^2/ S _b ; / / B as e i m pe da n ce i n ohm40

41 / / c as e d42 Z_1 = Z_b * Z_1_p u * 1000 ; // A ct u al i mp ed an ce o f

l a r g e r t r a n sf o r m e r i n m i l l i −ohm43 Z _ 1_ m = abs ( Z _ 1 ) ; / / Z 1 m=m ag n it ud e o f Z 1 i n ohm44 Z _ 1_ a = atan ( imag ( Z _1 ) / real ( Z _ 1 ) ) * 1 8 0 / % p i ; / / Z 1 a =

46 / / c as e e47 V_b1 = V_b ;

// b a se v o l t a ge i n v o l t48 V_b2 = V_b ; // b a se v o l t a ge i n v o l t49 Z _p u _2 = ( k V A_ 1 / k VA _2 ) * ( V _b 1 / V _b 2 ) ^2 * ( Z _ pu _1 ) ; //

New t r a n s f o r m e r p . u i m pe d an c e50 Z _2 _p u = Z _p u_ 2 ; / /New t r a n s f o r m e r p . u i m pe d an c e51

52 Z_2 = Z_b * Z _2 _p u *1 00 0 ; // A ct u al i mp ed an ce o f s m a l l e r t r a n sf o r m e r i n m i l l i −ohm

53 Z _ 2_ m = abs ( Z _ 2 ) ; / / Z 2 m=m ag n it ud e o f Z 2 i n ohm54 Z _ 2_ a = atan ( imag ( Z _2 ) / real ( Z _ 2 ) ) * 1 8 0 / % p i ; / / Z 2 a =

p h a se a n g l e o f Z 2 i n d e g r e e s

5556 / / c as e f 57 c os _t he ta = 0 .8 ; // Power f a c t o r58 s i n _ th e t a = sqrt ( 1 - ( c os _t he ta ) ^2 ) ;

59 S _ T = ( k V A_ 1 + k VA _2 ) * ( c o s_ t he t a - % i * si n _t h et a ) ; //

kVA o f t o t a l l oa d

6061 I _T = S_T * 10 00 / V_b ; // T o ta l c u r r e n t i n A62

63 I _1 = I _T * ( Z_ 2 /( Z _1 + Z _2 ) ) ; // A ct ua l c u r r e ntd e l i v e r e d by l a r g e r t r a n sf o r m e r i n A

64 I _ 1_ m = abs ( I _ 1 ) ; // I 1 m=m ag ni tu de o f I 1 i n A65 I _ 1_ a = atan ( imag ( I _1 ) / real ( I _ 1 ) ) * 1 8 0 / % p i ; / / I 1 a =

67 / / c as e g68 I _2 = I _T * ( Z_ 1 /( Z _1 + Z _2 ) ) ; // A ct ua l c u r r e nt

d e l i v e r e d by l a r g e r t r a n sf o r m e r i n A69 I _ 2_ m = abs ( I _ 2 ) ; // I 2 m=m ag ni tu de o f I 2 i n A70 I _ 2_ a = atan ( imag ( I _2 ) / real ( I _ 2 ) ) * 1 8 0 / % p i ; / / I 2 a =

72 / / c as e h73 Z 1 = Z_ 1 /1 00 0 ; // Z 1 i n ohm74 E_1 = I_1 * Z1 + V_b ; / / No−l oa d v o l t a g e o f l a r g e r Tr

. i n v o l t75 E _ 1_ m = abs ( E _ 1 ) ; // E 1 m=m ag ni tu de o f E 1 i n v o l t76 E _ 1_ a = atan ( imag ( E _1 ) / real ( E _ 1 ) ) * 1 8 0 / % p i ;

// E 1 a=p h a se a n g l e o f E 1 i n d e g r e e s77

79 / / c as e i80 Z 2 = Z_ 2 /1 00 0 ; // Z 2 i n ohm81 E_2 = I_2 * Z2 + V_b ; / / No−l oa d v o l t a ge o f s m a l l e r

Tr . i n v o l t82 E _ 2_ m = abs ( E _ 2 ) ; // E 2 m=m ag ni tu de o f E 2 i n v o l t83 E _ 2_ a = atan ( imag ( E _2 ) / real ( E _ 2 ) ) * 1 8 0 / % p i ; // E 2 a=

p h a se a n g l e o f E 2 i n d e g r e e s

88 printf ( ” \n a : Base v o l t a ge : \ n V b = %d <0 V (

g i v e n ) \n” , V _ b ) ;

8990 printf ( ” \n b : Base c u r r e nt : \ n I b = %. 2 f A \n” ,

I _ b ) ;

92 printf ( ” \n c : B as e i mp ed an ce : \ n Z b = %. 2 f ohm\n” , Z _ b ) ;

94 printf ( ” \n d : A ct ua l i mp ed an ce o f l a r g e rt r an s f o r me r : \ n Z 1 i n m = \n” ) ; disp ( Z _ 1 ) ;

95 printf ( ” \n Z 1 = %. 2 f <%. 2 f m \n ” , Z _ 1 _ m , Z _ 1 _ a

9697 printf ( ” \n e : A ct ua l i mp ed an ce o f s m a l l e r

t r an s f o r me r : \ n Z 1 i n m = \n” ) ; disp ( Z _ 2 ) ;

98 printf ( ” \n Z 1 = %. 2 f <%. 2 f m \n ” , Z _ 2 _ m , Z _ 2 _ a

100 printf ( ” \n f : A c tu a l c u r r e n t d e l i v e r e d by l a r g e rt r an s f o r me r : \ n I 1 in A = ” ) ; disp ( I _ 1 ) ;

101 printf ( ” \n I 1 = %. 2 f <%. 2 f A \n ” , I _ 1 _ m , I _ 1 _ a ) ;

103 printf (” \n g : A ct ua l c u r r e nt d e l i v e r e d by s m a l l ert r an s f o r me r : \ n I 2 in A = ” ) ; disp ( I _ 2 ) ;

104 printf ( ” \n I 1 = %. 2 f <%. 2 f A \n ” , I _ 2 _ m , I _ 2 _ a ) ;

106 printf ( ” \n h : No−l o ad v o l t a g e o f l a r g e r Tr : \ nE 1 i n v o l t = ” ) ; disp ( E _ 1 ) ;

107 printf ( ” \n E 1 = %. 2 f <%. 2 f V \n ” , E _ 1 _ m , E _ 1 _ a ) ;

109 printf ( ” \n i : No−l o ad v o l t a g e o f s m a l l e r Tr : \ nE 2 i n v o l t = ” ) ; disp ( E _ 2 ) ;

110 printf ( ” \n E 1 = %. 2 f <%. 2 f V \n ” , E _ 2 _ m , E _ 2 _ a ) ;

Scilab code Exa 14.27 RL ZbL ZLpu Z2pu Z1pu IbL ILpu VRpu VSpu

VS VxVxpu

c o n s o l e .10

11 / / G iv en d a ta12 / / From d ia g ra m i n f i g . 14 −23 a13 P_L = 14400 ; / / Load o ut p ut p ower i n W14 V_L = 120 ; // Load v o l t a ge i n v o l t15 V_b1 = 120 ; // b a s e v o l t a g e a t p oi nt 1 i n v o l t16 V_b2 = 600 ; // b a s e v o l t a g e a t p oi nt 2 i n v o l t17 V_b3 = 120 ; // b a s e v o l t a g e a t p oi nt 3 i n v o l t18 S _b3 = 14 .4 ; // b a s e p ow er i n kVA19 X_2 = %i * 0. 25 ;

// r e a c t a nc e i n p . u20 X _1 = %i * 0. 2 ; // r e a c t a n ce i n p . u21 I_L = 120 ; // Load c u r r e nt i n A22

23 / / C a l c u l a t i o n s24 / / c as e a25 R_L = P_L / ( V_L ^ 2) ; // R e s i st a nc e o f t h e l oa d i n

27 / / c as e b28 Z _ b L = ( V _ b 3 ^ 2) / ( S _ b 3 * 1 0 00 ) ; // B as e i m pe da nc e i n

30 / / c as e c31 Z_L _pu = R_L / Z_bL ; // p er u n i t l o ad i mp ed an ce32

33 / / c as e d

34 Z _2 _p u = X_2 ; // p er u n i t i mp ed an ce o f Tr . 235

36 / / c as e e37 Z _1 _p u = X_1 ; // p er u n i t i mp ed an ce o f Tr . 138

39 / / c as e g40 I _ bL = ( S _b 3 * 1 00 0 ) / V_ b3 ; // Base c u r r e n t i n l oa d i n

42 / / c as e h43 I_L _pu = I_L / I_bL ; // p er u n i t l oa d c u r r e n t

4445 / / c as e i46 V _R _p u = I _L _p u * Z _L _p u ; // p er u n i t v o l t a ge

a c r o s s l oa d47

48 / / c as e j49 I _S _p u = I _L _p u ; // p er u n it c u r r e nt o f s o ur c e50 Z _T _p u = Z _L _p u + Z _1 _p u + Z _2 _p u ; / / T o t a l p . u

i mpe danc e51 V _S _p u = I _S _p u * Z _T _p u ; // p e r u ni t v o l t a g e o f

s o u r c e52 V _ S _ pu _ m = abs ( V _ S _ p u ) ; / / V S p u m=m a g n i t ud e o f V S p u i n p . u

53 V _ S _ pu _ a = atan ( imag ( V _ S_ pu ) / real ( V _ S _ p u ) ) * 1 8 0 / % p i ;

// V S pu a=p ha se a n gl e o f V S pu i n d e g re e s54

55 / / c as e k56 V_S = V_S_pu * V_b1 ; // A ct ua l v o l t a g e a c r o s s

s o u r c e i n v o l t57 V _ S_ m = abs ( V _ S ) ; // V S m=m ag ni tu de o f V S i n v o l t58 V _ S_ a = atan ( imag ( V _S ) / real ( V _ S ) ) * 1 8 0 / % p i ; / / V S a=

p h a se a n g l e o f V S i n d e g r e e s59

61 / / c as e l62 I _x _p u = I _L _p u ; / / p . u c u r r e nt a t p o in t x

63 Z _x _p u = Z _L _p u + Z _2 _p u ; / / p . u i m pe da n ce a t p o i n t

x64 V _x _p u = I _x _p u * Z _x _p u ; / / p . u v o l t a g e a t p o in t x65

66 // c as e m67 V_x = V_x_pu * V_b2 ; // A ct u a l v o l t a ge a t p o i nt x

i n v o l t68 V _ x_ m = abs ( V _ x ) ; // V x m=m ag ni tu de o f V x i n v o l t69 V _ x_ a = atan ( imag ( V _x ) / real ( V _ x ) ) * 1 8 0 / % p i ; / / V x a =

p h a se a n g l e o f V x i n d e gr e e s70

75 printf ( ” \n a : R e s i s t a n c e o f t h e l o ad : \ n R L =%d \n” , R _ L ) ;

77 printf ( ” \n b : B as e i mp ed an ce : \ n Z bL = %d \n” , Z _ b L ) ;

79 printf ( ” \n c : p er u n it l oa d i mp eda nce : \ n Z L ( pu

) = ”) ; disp ( Z _ L _ p u ) ;

81 printf ( ” \n d : p er u n i t i mp ed an ce o f Tr . 2 : \ n Z 2( p u ) = ” ) ; disp ( Z _ 2 _ p u ) ;

83 printf ( ” \n e : p er u n it i mp eda nce o f Tr . 1 : \ n Z 1( pu ) = ” ) ; disp ( Z _ 1 _ p u ) ;

85 printf ( ” \n f : S ee F i g .14 −23 b \n” ) ;

87 printf ( ” \n g : Base c u r r e n t i n l oa d : \ n I b L = %d

A ( r e s i s t i v e ) \n” , I _ b L ) ;88

89 printf ( ” \n h : p e r u ni t l oa d c ur r e nt : \ n I L p u =” ) ; disp ( I _ L _ p u ) ;

91 printf ( ” \n i : p e r u ni t v o l t a g e a c r o s s l oa d : \ n

V R p u ” ) ; disp ( V _ R _ p u ) ;92

93 printf ( ” \n j : p e r u ni t v o l t a g e o f s ou rc e : \ nV S pu = ” ) ; disp ( V _ S _ p u ) ;

94 printf ( ” \n V S pu = %. 3 f <%.2 f p . u \n” ,V_S _pu_m ,

V _ S _ p u _ a ) ;

96 printf ( ” \n k : A ct u a l v o l t a ge a c r o s s s o u r c e : \ nV S i n v o l t = ”) ; disp ( V _ S ) ;

97 printf ( ” \n V S = %. 1 f <%. 2 f V \n” , V _ S _ m , V _ S _ a ) ;

99 printf ( ” \n l : p . u v o l t a ge a t p oi nt x : \ n V x ( pu )= ” ) ; disp ( V _ x _ p u ) ;

101 printf ( ” \n m: A c t u a l v o l t a g e a t p oi nt x : \ n V xi n v o l t = ” ) ; disp ( V _ x ) ;

102 printf ( ” \n V S = %. 1 f <%. 2 f V \n” , V _ x _ m , V _ x _ a ) ;

Scilab code Exa 14.28 ZT1 ZT2 Zbline3 Zlinepu VLpu IbL IL ILpu VSpu

11 / / G iv en d a ta12 / / From d ia g ra m i n f i g . 14 −24 a

13 V_1 = 11 ; / / Tr . 1 v o l t a g e i n kV

14 V_b1 = 11 ; // Bas e Tr . 1 v o l t a g e i n kV15 S_1 = 50 ; / / KVA r a t i n g o f po wer f o r Tr . 116 S_2 = 100 ; / / KVA r a t i n g o f p ower f o r Tr . 217 Z _1 _p u = %i * 0. 1 ; // p e r u n i t i mp ed an ce o f Tr . 118 Z _2 _p u = %i * 0. 1 ; // p e r u n i t i mp ed an ce o f Tr . 219 V_b2 = 55 ; // Base Tr . 2 v o l t a g e i n kV20 S_b = 100 ; // b a s e p ow er i n kVA21 P F = 0.8 ; / / power f a c t o r o f t he Tr . s22

23 Z _l in e = %i * 20 0 ; // l i n e i mp ed an ce i n ohm24

25 V_L = 10 ; // Load v o l t a g e i n kV26 V_Lb3 = 11 ; // b a s e l i n e v o l t a g e a t p oi nt 327

28 V_b3 = 11 ; // l i n e v ol t a g e a t p o in t 329

30 P_L = 50 ; / / Power r a t i n g o f e ac h Tr . s i n kW31 c os _t het a_L = 0 .8 ; / / PF o p e r a t i o n o f e ac h Tr . s32

33 / / C a l c u l a t i o n s34 / / c as e a35 Z _T 1 = Z _1 _p u * ( V _1 / V _b 1 ) ^2 * ( S _2 / S _1 ) ;

// p . ui m p ed a n ce o f Tr . 136

37 / / c as e b38 Z _T 2 = Z _2 _p u * ( V _1 / V _b 3 ) ^2 * ( S _2 / S _1 ) ; // p . u

i m p ed a n ce o f Tr . 139

40 / / c as e c41 V_b = 55 ; // b as e v o l t a ge i n v o l t42 Z _b _l in e = ( V _b ^ 2) / S_ b * 1 00 0 ; // b a s e l i n e

i m p ed a n ce i n ohm

43 Z _l in e_ pu = Z _l in e / Z _b _l in e ; / / p . u i m p ed a n ce o f t h e t r an s m i s s i o n l i n e

45 / / c as e d46 V _L _p u = V_L / V _L b3 ; / / p . u v o l t a g e a c r o s s l oa d

48 / / c as e e49 / / S e e F i g . 14 −24 b50

51 / / c as e f 52 I_bL = S_b / V_b3 ; // b a s e c ur r e n t i n l oa d i n A53

54 / / c as e g55 VL = 11 ; // l oa d v o l t a ge i n kV56 c os _t he ta _L = 0 .8 ; // power f a c t o r57 I _L = P _L / ( VL * c os _t he ta _L ) ;

58 I_L _pu = I_L / I_bL ; // p . u l o a d c u r r e n t

59 t he ta = a co sd ( 0 . 8) ;60 I _L pu = I _ L_ pu * ( c os d ( t he ta ) - % i * si nd ( t h et a ) ) ; / / p .

u c u r r e nt i n c om ple x fo rm61

62 / / c as e h63 Z _s er ie s_ pu = Z _T 1 + Z _l in e_ pu + Z _T 2 ; // p . u

s e r i e s i mp eda nce o s t he t r an s m i s s i o n l i n e64 V _S _p u = I _L pu * Z _s er ie s_ pu + V _L _p u ; // p . u

s o ur c e v o l t a g e65 V _ S _ pu _ m = abs ( V _ S _ p u ) ; / / V S p u m=m a g n i t ud e o f

V S p u i n p . u66 V _ S _ pu _ a = atan ( imag ( V _ S_ pu ) / real ( V _ S _ p u ) ) * 1 8 0 / % p i ;

// V S pu a=p ha se a n gl e o f V S pu i n d e g re e s67

68 / / c as e i69 V_S = V _S _p u_ m * V_ b1 ; // A ct ua l v al u e o f s o ur c e

v o l t a g e i n kV70 V _ s ou r ce = V _S * exp ( % i * ( V _ S _ p u _ a ) * ( % p i / 1 8 0 ) ) ; / / V S

i n e x p on e n t i a l form71 V _ s o u rc e _ m = abs ( V _ s o u r c e ) ; / / V s o u r ce m =m a gn i tu d e o f

V s o u rc e i n p . u

72 V _ s o u rc e _ a = atan ( imag ( V _ so u rc e ) / real ( V _ s o u r c e ) )* 1 8 0 / % p i ; // V s o u r c e a=p ha se a n g l e o f V s o ur ce i nd e g r e e s

78 printf ( ” \n a : p . u i mp ed an ce o f Tr . 1 : \ n Z T1 = ”) ; disp ( Z _ T 1 ) ;

80 printf ( ” \n b : p . u i mp ed an ce o f Tr . 2 : \ n Z T2 = ”) ; disp ( Z _ T 2 ) ;

82 printf ( ” \n c : b as e l i n e i mpe danc e i n ohm : \ n Z b( l i n e ) = %d ohm \n” , Z _ b _ l i n e ) ;

83 printf ( ” \n p . u i mp eda nce o f t he t r an s m i s s i o n

l i n e : \ n Z ( l i n e ) pu = ” ) ; disp ( Z _ l i n e _ p u ) ;84

85 printf ( ” \n d : p . u v o l t a ge a c r o s s l oa d : \ n V L pu= ” ) ; disp ( V _ L _ p u ) ;

87 printf ( ” \n e : S ee F ig . 14 −24 b \n” ) ;

89 printf ( ” \n f : b a s e c ur r e nt i n l oa d : \ n I b L = %. 3 f A \n” , I _ b L ) ;

91 printf (” \n g : Load c u r r e nt : \ n I L = %f A \n”

I _ L ) ;

92 printf ( ” \n p . u l o a d c u rr e n t : \ n I L p u = %. 3 f a t % . 1 f PF l a g g i n g \n” , I _ L _ p u , P F ) ;

93 printf ( ” \n p . u c u r r e n t i n c ompl ex f orm : \ nI L p u = ” ) ; disp ( I _ L p u ) ;

95 printf ( ” \n h : p e r u ni t v o l t a g e o f s ou rc e : \ nV S pu = ” ) ; disp ( V _ S _ p u ) ;

96 printf ( ” \n V S pu = %. 3 f <%.2 f p . u \n” ,V_S _pu_m ,

V _ S _ p u _ a ) ;

9798 printf ( ” \n i : A c tu a l v o l t a ge a c r o s s s o ur c e : \ n

V S i n kV = ”) ; disp ( V _ s o u r c e ) ;

99 printf ( ” \n V S = %. 1 f <% . 2 f kV \n” ,V_source_m ,

V _ s o u r c e _ a ) ;

Scilab code Exa 14.29 Z1pu Z2pu Vbline Zlinepu ZMs

7 / / E xa mp le 1 4−298

11 / / G iv en d a ta12 / / From d ia g ra m i n f i g . 14 −25 a13 Z _p u_ 1 = %i * 0. 1 ; / / p . u i mp ed an ce14 MVA_2 = 80 ; / / MVA r a t i n g o s s y st em 215 MVA_1 = 100 ; / / MVA r a t i n g o f Tr . s 1 and 216 V_2 = 30 ; // v o l t a g e i n KV17 V_1 = 32 ; // v o l t a g e i n KV18

19 Z _p u_ 2 = %i * 0. 15 ; / / p . u i m pe da n ce20

21 V_b1 = 100 ; // b as e v o l t a g e o f Tr . 122

23 Z _ li ne = %i * 60 ; // L i n e i mp ed an ce24

25 M V A_ M1 = 20 ; // MVA r a t i n g o f mo to r l o a d 126 Z _p u_ M1 = %i * 0. 15 ; / / p . u i m pe da n ce o f m ot or l o a d

28 M V A_ M2 = 35 ; // MVA r a t i n g o f mo to r l o a d 229 Z _p u_ M2 = %i * 0. 25 ; / / p . u i m pe da n ce o f m ot or l o a d

31 M V A_ M3 = 25 ; // MVA r a t i n g o f mo to r l o a d 332 Z _p u_ M3 = %i * 0. 2 ; / / p . u i mp ed an ce o f m ot or l o a d M333

34 V_M = 28 ; // v o l t a g e a c r o s s m oto r l o a d s M1 , M2 ,M3 i nkV

36 / / C a l c u l a t i o n s37 / / c as e a38 Z _ 1 _ pu = Z _ pu _ 1 * ( M V A_ 2 / M V A _ 1 ) *( V _ 2 / V _ 1 ) ^ 2 ; // p . u

i m ep e da n ce o f T139

40 / / c as e b41 Z _ 2 _ pu = Z _ pu _ 2 * ( M V A_ 2 / M V A _ 1 ) *( V _ 2 / V _ 1 ) ^ 2 ; // p . u

i m ep e da n ce o f T242

43 / / c as e c44 V _ b_ li n e = V _b 1 * ( V_ 1 / V_ 2 ) ; // b as e v o l t a ge o f t he

l o n g −t r an s m i s s i o n l i n e i n kV45

46 / / c as e d47 MVA_b = 80 ; // MVA r a t i ng48 V _b = V _b _l in e ;

49 Z _ l i n e _p u = Z _ li n e * ( M V A _b / ( V _ b ) ^ 2 ) ; / / p . u i m p e d an c eo f t h e t r a n s m i s s i o n l i n e

51 / / c as e e52 Z _ M1 _ pu = Z _ pu _ M1 * ( M V A_ 2 / M VA _ M1 ) * ( V _M / V _1 ) ^ 2 ; //

p . u i mp ed an ce o f m ot or l o a d M153 Z _ M2 _ pu = Z _ pu _ M2 * ( M V A_ 2 / M VA _ M2 ) * ( V _M / V _1 ) ^ 2 ; //

p . u i mp ed an ce o f m ot or l o a d M254 Z _ M3 _ pu = Z _ pu _ M3 * ( M V A_ 2 / M VA _ M3 ) * ( V _M / V _1 ) ^ 2 ; //

p . u i mp ed an ce o f m ot or l o a d M3

59 printf ( ” \n a : p . u i me pe da nc e o f T1 : \ n Z 1 ( pu ) =

” ) ; disp ( Z _ 1 _ p u ) ;

6061 printf ( ” \n b : p . u i me pe da nc e o f T2 : \ n Z 2 ( pu ) =

” ) ; disp ( Z _ 2 _ p u ) ;

63 printf ( ” \n c : b as e v o l t a ge o f t h e l o n g −t r a n s m i s s i o nl i n e : \ n V b ( l i n e ) = %. 1 f kV \n” , V _ b _ l i n e ) ;

65 printf ( ” \n d : p . u i mp ed an ce o f t he t r a n s m i s s i o nl i n e : \ n Z ( l i n e ) pu = ” ) ; disp ( Z _ l i n e _ p u ) ;

67 printf ( ” \n e : p . u i mp ed an ce o f m oto r l o a d M1 : \ n

Z M1 ( p u ) = ” ) ; disp ( Z _ M 1 _ p u ) ;68

69 printf ( ” \n f : p . u i mp ed an ce o f m oto r l o a d M1 : \ nZ M2 ( p u ) = ” ) ; disp ( Z _ M 2 _ p u ) ;

71 printf ( ” \n g : p . u i mp ed an ce o f m oto r l o a d M1 : \ nZ M3 ( p u ) = ” ) ; disp ( Z _ M 3 _ p u ) ;

73 printf ( ” \n h : S ee F ig . 14 −25 b . ”) ;

Scilab code Exa 14.30 ST ST Sxformer

7 / / E xa mp le 1 4−308

12 // s u b s c r i p t s a , b , c f o r t he c ur re nt , v o l t a g e si n d i c a t e s r e s p e c t i v e c a s e s a , b , c .13 / / f ro m f i g .1 4 −27 a14 V _pa = 10 00 ; // Phase v o l t a ge i n v o l t15 I_1a = 1 ; // l i n e c u r r e n t i n p r i ma r y i n A16 V_2a = 100 ; // v o lt a g e a c r o s s s ec on da ry i n V17 Ic_a = 10 ; // c u r r e n t i n l ow er h a l f o f auto −

t r an s f o r me r i n A18

19 / / f ro m f i g .1 4 −26 b20 V_s = 100 ; // v o l t a g e i n s ec on da ry wdg i n V

21 I_2b = 10 ; // c u r r e n t i n s ec on da ry i n A22 V _1b = 10 00 ; // v o l t a ge a c r o s s p ri m a ry i n V23 Ic_b = 1 ; // c u r r e n t i n l ow er h a l f o f auto −

t r an s f o r me r i n A24

25 / / C a l c u l a t i o n s26 / / c as e a27 S _ T1 = ( V _p a * I _1 a + V _2 a * I _1 a ) / 10 00 ; / / T o t a l kVA

t r a n s f e r i n s t e p −down mode28

29 / / c as e b30 S _T 2 = ( V _s * I _2 b + V _1 b * I_ 2b ) / 10 00 ; / / T o t a l kVA

t r a n s f e r i n s t e p −up mode31

32 / / c as e c33 S _ x_ f or m er _ c = V _p a * I _1 a / 10 00 ; // kVA r a t i n g o f t h

a u t o t r a n sf o rm e r i n Fi g . 14 −27 a34

35 / / c as e d36 V _1 = V_pa ;

37 S _x _f or me r_ d = V _1 * I c_ b / 10 00 ; // kVA r a t i n g o f t h

a u t o t r a n sf o rm e r i n Fi g . 14 −26 b38

43 printf ( ” \n a : T ot al kVA t r a n s f e r i n s te p−down mode: \ n S T = %. 1 f kVA t r a n s f e r r e d \n” , S _ T 1 ) ;

45 printf ( ” \n b : T ot al kVA t r a n s f e r i n s te p−up mode : \n S T = %. 1 f kVA t r a n s f e r r e d \n” , S _ T 2 ) ;

47 printf ( ” \n c : kVA r a t i n g o f t h a u t o t r a n sf o rm e r i nF i g . 1 4 −27 a : \ n S x−fo rm er = %d kVA \n ” ,

S _ x _ f o r m e r _ c ) ;

49 printf ( ” \n d : kVA r a t i n g o f t h a u t o t r a n sf o rm e r i n

F i g . 1 4 −2 6 b : \ n S x−fo rm er = %d kVA \n ” ,S _ x _ f o r m e r _ d ) ;

51 printf ( ” \n e : Both t r a n s f o r m e r s h av e t h e same kVAr a t i n g o f 1 kVA s i n c e t he same ” ) ;

52 printf ( ” \n a ut o tr an sf or m er i s u s e d i n bot h p a rt s. Both t r a n s f o r m e r s t r an s fo r m ” ) ;

53 printf ( ” \n a t o t a l o f 1 KVA. But th e s te p −downt r an s f o r me r i n p ar t ( a ) c on du ct s ” ) ;

54 printf ( ” \n o n l y 0 . 1 kVA w h il e th e s t e p −up

t r a n s fo r m e r i n t he p a rt ( b ) c on d uc ts 10 ”) ;

55 printf ( ” \n kVA from t he p r i m a r y t o t h e s ec on da ry. ” ) ;

Scilab code Exa 14.31 Wc tabulate allday efficiency

11 / / G iv en d a ta12 S = 500 ; // kVA r a t i n g o f d i s t r i b u t i o n t r an s f o r m er13 / / g i ve n d at a from ex . 14 −2014 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t15 V_2 = 208 ; // S ec on da ry v o l t a g e i n v o l t16 f = 6 0 ; // F re qu en cy i n Hz17

18 / / SC−t e s t d at a

19 P _sc = 82 00 ; // w at tm et er r e a di n g i n W20 I_ sc = 2 17. 4 ; // S h o rt c i r c u i t c ur r e nt i n A21 V_sc = 95 ; // S h o r t c i r c u i t v o l t a g e i n V22

23 // OC−t e s t d at a24 P _oc = 18 00 ; // w at tm et er r e a di n g i n W25 I_oc = 85 ; // Open c i r c u i t c u r r e n t i n A26 V_oc = 208 ; // Open c i r c u i t v o l t a ge i n V27

28 LF_1 = 20 ; // Load f r a c t i o n i n p e r c e nt29 LF_2 = 40 ;

// Load f r a c t i o n i n p e r c e nt30 LF_3 = 80 ; // Load f r a c t i o n i n p e r c e nt31 LF_fl = 100 ; // r at ed l oa d i n p e r ce nt32 LF_4 = 125 ; // Load f r a c t i o n i n p e r ce nt33

34 LF1 = 0.2 ; // Load f r a c t i o n35 LF2 = 0.4 ; // Load f r a c t i o n36 LF3 = 0.8 ; // Load f r a c t i o n37 L F4 = 1.25 ; // Load f r a c t i o n38

39 PF1 = 0.7 ; // power f a c t o r

40 PF2 = 0.8 ; // power f a c t o r41 PF3 = 0.9 ; // power f a c t o r42 PF_fl = 1 ; // power f a c t o r43 P F4 = 0.85 ; // power f a c t o r44

45 t1 = 4 ; // p e r i o d o f o p er a t i on i n h ou rs

46 t2 = 4 ; // p e r i o d o f o p er a t i on i n h ou rs47 t3 = 6 ; // p e r i o d o f o p er a t i on i n h ou rs48 t_fl = 6 ; // p e r i o d o f o p er a ti o n i n h ou rs49 t4 = 2 ; // p e r i o d o f o p er a t i on i n h ou rs50

51 / / C a l c u l a t i o n s52 / / c as e a53 t = 2 4 ; // h rs i n a day54 P_c = P_oc ; / / w at tm et er r e a d i n g i n W (OC t e s t )55 W_c = ( P_c * t )/1000 ; // COre l o s s o v er 24 h ou r

p e r i o d

5657 / / c as e b58 P s c = P _s c / 10 00 ; / / w at tm et er r e a di n g i n W ( SC t e s t

)59 P _ l os s _1 = ( L F1 ^ 2 ) * Ps c ; // Power l o s s i n kW f o r 20%

Load60 P _ l os s _2 = ( L F2 ^ 2 ) * Ps c ; // Power l o s s i n kW f o r 40%

Load61 P _ l os s _3 = ( L F3 ^ 2 ) * Ps c ; // Power l o s s i n kW f o r 80%

Load62 P _l os s_ fl = P sc ;

/ / Power l o s s i n kW f o r 1 00% Load63 P _ l os s _4 = ( L F4 ^ 2 ) * Ps c ; // Power l o s s i n kW f o r 12 5% Load

65 / / e ne rg y l o s s i n kWh66 e ne rg y_ lo ss 1 = P _l os s_ 1 * t1 ; // E ne gr y l o s s i n kWh

f o r 2 0% L oa d67 e ne rg y_ lo ss 2 = P _l os s_ 2 * t2 ; // E ne gr y l o s s i n kWh

f o r 4 0% L oa d68 e ne rg y_ lo ss 3 = P _l os s_ 3 * t3 ; // E ne gr y l o s s i n kWh

f o r 8 0% L oa d

69 e n e r gy _ lo s s_ f l = P _ lo s s_ f l * t _f l ; // Eneg ry l o s si n kWh f o r 1 0 0% L oa d

70 e ne rg y_ lo ss 4 = P _l os s_ 4 * t4 ; // E ne gr y l o s s i n kWhf o r 1 2 5% Lo ad

72 / / T ot al e ne rg y l o s s e s i n 24 h rs

73 W _ lo s s_ t ot a l = e n er g y_ l os s 1 + e n er g y_ l os s 2 +e n er g y_ l os s 3 + e n er g y_ l os s _f l + e n er g y_ l os s 4 ;

75 / / c as e c76 P _ 1 = L F1 * S* P F1 ; // Power o ut p ut f o r 2 0% l o a d77 P _ 2 = L F2 * S* P F2 ; // Power o ut p ut f o r 4 0% l o a d78 P _ 3 = L F3 * S* P F3 ; // Power o ut p ut f o r 8 0% l o a d79 P_ fl = S * PF_ fl ; // Power o u tp ut f o r 1 00% l o a d80 P _ 4 = L F4 * S* P F4 ; // Power o ut p ut f o r 1 25% l o a d81

82 E ne rg y_ 1 = P _1 * t1 ; // En erg y d e l i v e r e d i n kWh f o r

20%load83 E ne rg y_ 2 = P _2 * t2 ; // En erg y d e l i v e r e d i n kWh f o r

40%load84 E ne rg y_ 3 = P _3 * t3 ; // En erg y d e l i v e r e d i n kWh f o r

80%load85 E n e r gy _ fl = P _f l * t _f l ; // E ne rg y d e l i v e r e d i n kWh

f o r 1 00 % lo ad86 E ne rg y_ 4 = P _4 * t4 ; // En erg y d e l i v e r e d i n kWh f o r

125%l oad87

88 // T ot al e ne rg y d e l i v e r e d i n 24 h rs89 W _o ut _t ot al = E ne rg y_ 1 + E ne rg y_ 2 + E ne rg y_ 3 +

E n er g y_ f l + E n er g y_ 4 ;

91 / / c as e d92 e t a = W _o ut _t ot al / ( W _o ut _t ot al + W _c +

W _l os s_ to ta l ) * 1 00 ; // A ll −day e f f i c i e n c y93

97 printf ( ” \n a : T ot a l e ne rg y c or e l o s s f o r 24 h rs ,i n c l u d i ng 2 h ou rs a t no−loa d , ” ) ;

98 printf ( ” \n W c = %. 1 f kWh \n ” , W _ c ) ;

100 printf ( ” \n b : From SC t e s t , e q u i v a l e n t c op pe r l o s s

a t r a te d l oa d = %. 1 f kW, ” , P s c ) ;

101 printf ( ” \n and t h e v a r i ou s en e r g y l o s s e s d u r i n gt h e 2 4 h r p e r i o d a re t ab u l a te d a s : \ n” ) ;

103 printf ( ” \n

” ) ;

104 printf ( ” \n P e r c e n t Rated l o a d \ t P ow er l o s s (kW)\ t Tim e p e r i o d ( h o u r s ) \ t E ne rg y l o s s (kWh ) ” ) ;

105 printf ( ” \n

” ) ;

106 printf ( ” \n\ t \t%d \ t %f \ t \ t \ t %d \ t \ t \ t %. 2 f \n ” ,L F _1 , P _ l o s s _1 , t 1 , e n e r g y _ l o s s 1 ) ;

107 printf ( ” \n\ t \t%d \ t %f \ t \ t \ t %d \ t \ t \ t %. 2 f \n ” ,

L F _2 , P _ l o s s _2 , t 2 , e n e r g y _ l o s s 2 ) ;

L F _f l , P _ l o s s _f l , t _ fl , e n e r g y _ l o s s _ f l ) ;

111 printf (” \n

” ) ;

112 printf ( ” \n T o t a l e n e r g y l o a d l o s s e s o ve r 24 hourp e ri o d ( e x cl u di n g 2 h r s a t no−l o a d ) = %. 2 f ” ,

W _ l o s s _ t o t a l ) ;

113 printf ( ” \n

\n\n” ) ;

115 printf ( ” \n c : T ot al e ne rg y o ut pu t o ve r t he 24 hour

p e r io d i s t ab ul at ed a s : \n” ) ;116

117 printf ( ” \n

” ) ;

118 printf ( ” \n P e r c e n t Rated l o a d \ t PF \ t kW \ t

Time p e r i o d ( h o u r s ) \ t E ne rg y d e l i v e r e d (kWh ) ” ) ;119 printf ( ” \n

” ) ;

120 printf ( ” \n\ t \t%d \ t %. 1 f \ t % . f \ t \ t %d \ t \ t \ t % d ”, L F _ 1 , P F 1 , P _ 1 , t 1 , E n e r g y _ 1 ) ;

123 printf ( ” \n\ t \t%d \ t %. 1 f \ t % . f \ t \ t %d \ t \ t \ t % d ”

, L F _ f l , P F 1 , P _ f l , t _ f l , E n e r g y _ f l ) ;124 printf ( ” \n\ t \t%d \ t %. 1 f \ t % . f \ t \ t %d \ t \ t \ t % d ”

, L F _ 4 , P F 4 , P _ 4 , t 4 , E n e r g y _ 4 ) ;

125 printf ( ” \n

” ) ;

126 printf ( ” \n T o t a l e n e r g y r e q ui r e d by l o a d f o r 24hour p e ri o d ( e x cl u di n g 2 h r s a t no−l o a d ) = %d ” ,

W _ o u t _ t o t a l ) ;

127 printf ( ” \n

\n\n” ) ;

129 printf ( ” \n d : A ll −day e f f i c i e n c y = %. 1 f p e r ce n t ” ,

e t a ) ;

Scilab code Exa 14.32 I2 Ic

7 / / E xa mp le 1 4−328

11 / / G iv en d a ta12 S_1 = 10 ; // VA r a t i n g o f s m al l t r an s f o r m er13 V = 115 ; // v o l t a g e r a t i ng o f t ra n s f o r m e r i n v o l t14 V_2_1 = 6.3 ; // v o l t a g e r a t i n g o f one p ar t o f

s e co n da r y w in di ng i n v o l t15 V_2_2 = 5.0 ; // v o l t a g e r a t i n g o f o th er p ar t o f

s e co n da r y w in di ng i n v o l t16 Z_2_1 = 0.2 ; // i mp ed an ce o f on e p a rt o f s e co n da r y

w i nd i n g i n ohm17 Z _2 _2 = 0. 15 ; // i mpe danc e o f o t he r p ar t o f

s e c on d a r y w in d in g i n ohm18

20 / / C a l c u l a t i o n s21 / / c as e a22 V_2 = V_2_1 + V_2_2 ; // v o l t a g e a c r o s s s ec on da ry

w in di ng i n v o l t23 I_2 = S_1 / V_2 ; // Rated s e co n da r y c u r r e nt i n Awhen t he LV s e c o n d a r i e s a r e

24 // c on ne ct ed i n s e r i e s −a i d i n g25

26 / / c as e b27 I_c = ( V _2_ 1 - V _2 _2 ) / ( Z_ 2_ 1 + Z _2 _2 ) ; //

C i r c u l a t i n g c u r r e nt when LV w i nd i ng s a r e p a r a l l e d28 p er ce nt _o ve rl oa d = ( I_ c / I _2 ) * 10 0 ; // p e r ce n t

o v e r l o a d p r od u ce d29

33 printf ( ” \n a : Both c o i l s must be s e r i e s −c o n n e c t e dand u se d t o a cc ou nt f o r t he ” ) ;

34 printf ( ” \n f u l l VA r a t i n g o f t h e t ra n s f o r m e r .

Hence , t he r a t ed c u r r e n t i n 5 V ” ) ;35 printf ( ” \n and 6 . 3 V w i n d i n g i s : \n” ) ;

36 printf ( ” \n I 2 = %. 3 f A \n\n” , I _2 ) ;

38 printf ( ” \n b : When t he w in d in g s a r e p a r a l l e l e d , t hen e t c i r c u l a t i n g c u r r en t i s ” ) ;

39 printf ( ” \n t h e ne t v o lt ag e ap p li ed a c r o s s t h et o t a l i n t e r n a l i mpeda nce o f ” ) ;

40 printf ( ” \n t h e w i n d i n g s , o r : \ n” ) ;

41 printf ( ” \n I c = %. 2 f A \n ” , I _ c ) ;

43 printf ( ” \n The p er c en t o v e r lo ad i s = %f p er c en t%. f p e rc e n t ” ,perce nt_overload ,

p e r c e n t _ o v e r l o a d ) ;

Scilab code Exa 14.33 Zeh Zel I2rated I2sc overload

12 S = 2 0 ; // kVA r a t i n g o f t r a n s fo r m e r13 N_1 = 230 ; // Number o f p r im a ry t u r n s14 N_2 = 20 ; // Number o f s e c o n d a r y t u r n s15

16 V_1 = 230 ; // P ri mary v o l t ag e i n v o l t

17 V_2 = 20 ; // S ec o nd ar y v o l t a g e i n v o l t

1819 / / f ro m F ig . 14 −31 a20 / / HV s i d e SC t e s t d at a21 V_sc = 4.5 ; // s ho rt c i r c u i t v ol t a g e i n v o l t22 I_sc = 87 ; // s ho r t c i r c u i t c ur r e nt i n A23 P_sc = 250 ; / / Power m ea su re d i n W24

25 / / C a l c u l a t i o n s26 / / c as e a27 V _h = V_sc ; // s ho r t c i r c u i t v o l t a g e i n v o l t on HV

s i d e

28 I _h = I_sc ; // s h o r t c i r c u i t c u r r e n t i n A on HV s i d e29 Z_eh = V_h / I_h ; // E q u i v a le n t immpedance r e f f e r e d

t o t he h ig h s i d e when c o i l s a re s e r i e s c o nn ec te d30

31 / / c as e b32 Z _e l = Z _e h * ( N_ 2 / N_ 1 )^2 ; / / E q u i v a l e n t i mm pe da nc e

r e f f e r e d t o t h e l ow s i d e33 / / when c o i l s a re s e r i e s c on ne ct ed34

35 / / c as e c36 I _ 2_ r at e d = ( S * 10 00 ) / V _2 ;

// R at ed s e c o n d a r yc u r r e n t when c o i l s a re s e r i e s c on ne ct ed37

38 / / c as e d39 I_2 _sc = S / Z_el ; // S ec on d ar y c u r r e n t when t h e

c o i l s i n F i g .14 −31 a a r e40 / / s h or t −c i r c u i t e d w i t h r at ed v o l t a ge a p pl i ed t o t h e

HV s i d e41

42 p e r c e n t _o v e r lo a d = ( I _ 2 _ sc / I _ 2 _ r a t ed ) * 1 00 ; //p e r ce n t o v e r lo a d

48 printf ( ” \n S l i g h t v a r i a t i o n s i n an s w e r s ar e due

t o non−a p pr ox im at ed c a l c u l a t i o n s ” ) ;49 printf ( ” \n i n s c i l a b \ n\n” ) ;

50 printf ( ” \n a : E q ui v al e n t immpedance r e f f e r e d t o t heh i gh s i d e when c o i l s a re s e r i e s c on ne ct ed : ” ) ;

51 printf ( ” \n Z e h = %f ohm \n ” , Z _ e h ) ;

53 printf ( ” \n b : E q ui v al e n t immpedance r e f f e r e d t o t hel ow s i d e when c o i l s a re s e r i e s c on ne ct ed : ” ) ;

54 printf ( ” \n Z e l = %f ohm \n ” , Z _ e l ) ;

56 printf ( ” \n c : Rated s e co n da r y c u r r e n t when c o i l s

a re s e r i e s c on ne ct ed : ” ) ;57 printf ( ” \n I 2 ( r a te d ) = %d A \n” , I _ 2 _ r a t e d ) ;

59 printf ( ” \n d : S ec on da ry c u r r e nt when t he c o i l s i nF i g . 1 4 −31 a a r e s ho rt −c i r c u i t e d : ” ) ;

60 printf ( ” \n w i t h r at e d v ol t a g e a pp l i e d t o th e HVs i d e : ” ) ;

61 printf ( ” \n I 2 ( s c ) = %d A \n” , I _ 2 _ s c ) ;

62 printf ( ” \n The p e rc e n t o v e r l o a d i s = %d pe rc e n t ”, p e r c e n t _ o v e r l o a d ) ;

Scilab code Exa 14.34 PT kVA phase and line currents kVAtransformers

11 / / G iv en d a ta12 I_L = 100 ; // Load c u r r e nt i n A13 c os _t he ta = 0 .7 ; // power f a c t o r l a g g i n g14

15 // Y− d i s t r i b u t i o n t r a ns f o rm e r16 S = 6 0 ; // kVA r a t i n g o f t r a n s fo r m e r17 V _1 = 2300 ; // p ri ma ry v o l t a g e i n v o l t18 V_2 = 230 ; // s ec on da ry v o l t a ge i n v o l t19

22 V_L = 230 ; // v o l t a g e a c r o s s l oa d i n v o l t23 P_T = ( sqrt ( 3) * V _ L * I _ L * c o s _t h e ta ) / 1 0 0 0 ; / / p ow er

co ns um ed by t h e p l a n t i n kW24 k V A _T = P _T / c o s _t h et a ; // a p p a r en t p ow er i n kVA25

26 / / c as e b27 kVA = S ; // kVA r a t i n g o f t r a n s fo r m e r28 V_p = V_2 ; // p ha se v o l t a g e i n v o l t ( d el t a −

c on n e ct i o n on l oa d s i d e )29 I _ P 2 _ r at e d = ( k V A * 1 0 00 ) / ( 3 * V _ p ) ; // R at ed s e c o n d a r y

p ha se c u r r e nt i n A30 I _ L 2 _ ra t e d = sqrt ( 3) * I _ P 2 _ r a te d ; // R at ed s e c o n d a r yl i n e c ur r e nt i n A

32 / / c as e c33 // p e r ce n t l o ad on e ac h t r a n s fo r m e r = ( l o ad c u r r e n t

p er l i n e ) / ( r at ed c u rr e n t p er l i n e )34 p er ce nt _l oa d = I _L / I _L 2_ ra te d * 1 00 ;

36 / / c as e d37 / / s u b s c r i p t d f o r V L i n d i c a t e s c as e d , V L

38 V _L _d = 23 00 ;39 I _P 1 = ( k V A_ T * 1 00 0) / ( sqrt ( 3 ) * V _ L _ d ) ; // p r im a ry

p ha se c u r r e nt i n A40 I _L1 = I_ P1 ; // p ri ma ry l i n e c u r r e nt i n A(Y−

c o n n e c t i o n )

42 / / c as e e43 k VA _t ra ns fo rm er = k VA / 3 ; // kVA r a t i n g o f e ac ht r a n s f o r m e r

48 printf ( ” \n a : p ower cons umed by t h e p l a n t : \ nP T = %. 1 f kW \n ” , P _ T ) ;

49 printf ( ” \n a p p a r e n t power : \ n kVA T = %. 1 f kVA \n” , k V A _ T ) ;

5051 printf ( ” \n b : Rated s e co n da r y p ha se c u r r e nt : \ n

I P2 ( r at ed ) = %f A %. f A \n” ,I_P2_rated ,

I _ P 2 _ r a t e d ) ;

52 printf ( ” \n Rated s e c o n d a r y l i n e c ur re n t : \ nI L2 ( r at ed ) = %f A %. 1 f A \n” ,I_L2_rated ,

I _ L 2 _ r a t e d ) ;

54 printf ( ” \n c : p e rc e n t l oa d on e a ch t r an s f o r m er = %. 1 f p e r ce n t \n ” , p e r c e n t _ l o a d ) ;

56 printf ( ” \n d : p ri ma ry p ha se c u r r e nt : \ n I P 1 = %. f A \n” , I _ P 1 ) ;

57 printf ( ” \n p r i m a r y l i n e c u r r e n t : \ n I L 1 = %.f A \n” , I _ L 1 ) ;

59 printf ( ” \n e : kVA r a t i n g o f e ac h t r a n s f or m e r = %dkVA” , k V A _ t r a n s f o r m e r ) ;

Scilab code Exa 14.35 PT ST phase and line currents kVAtransformers

4 / / 2 nd e d i t i om5

11 / / G iv en d a ta12 I_L = 100 ; // Load c u r r e nt i n A13 c os _t he ta = 0 .7 ; // power f a c t o r l a g g i n g

1415 // − d i s t r i b u t i o n t r a n s f o r m e r16 S = 6 0 ; // kVA r a t i n g o f t r a n s fo r m e r17 V _1 = 2300 ; // p ri ma ry v o l t a g e i n v o l t18 V_2 = 230 ; // s ec on da ry v o l t a ge i n v o l t19

20 / / C a l c u l a t i o n s21 / / c as e a22 V_L = 230 ; // v o l t a g e a c r o s s l oa d i n v o l t23 P_T = ( sqrt ( 3) * V _ L * I _ L * c o s _t h e ta ) / 1 0 0 0 ; / / p ow er

co ns um ed by t h e p l a n t i n kW24 k V A _T = P _T / c o s _t h et a ; // a p p a r en t p ow er i n kVA25

26 / / c as e b27 kVA = S ; // kVA r a t i n g o f t r a n s fo r m e r28 V_p = V_2 ; // p h a s e v o lt a g e i n v o l t29 I _ P 2 _ r at e d = ( k V A * 1 0 00 ) / ( 3 * V _ p ) ; // R at ed s e c o n d a r y

p ha se c u r r e nt i n A30 I _ L 2 _ ra t e d = sqrt ( 3) * I _ P 2 _ r a te d ; // R at ed s e c o n d a r y

l i n e c ur r e nt i n A31

32 / / c as e c33 // p e r ce n t l o ad on e ac h t r a n s fo r m e r = ( l o ad c u r r e n t

p er l i n e ) / ( r at ed c u rr e n t p er l i n e )34 p er ce nt _l oa d = I _L / I _L 2_ ra te d * 1 00 ;

36 / / c as e d

37 / / s u b s c r i p t d f o r V L i n d i c a t e s c as e d , V L38 V _L _d = 23 00 ;

39 I _P 1 = ( k V A_ T * 1 00 0) / ( sqrt ( 3 ) * V _ L _ d ) ; // p r im a ryp ha se c u r r e nt i n A

40 I _ L1 = sqrt ( 3) * I _ P1 ; // p r i ma r y l i n e c u r r e n t i n A41

42 / / c as e e43 k VA _t ra ns fo rm er = k VA / 3 ; // kVA r a t i n g o f e ac h

t r a n s f o r m e r44

48 printf ( ” \n a : p ower cons umed by t h e p l a n t : \ nP T = %. 1 f kW \n ” , P _ T ) ;

49 printf ( ” \n a p p a r e n t power : \ n kVA T = %. 1 f kVA \n” , k V A _ T ) ;

51 printf ( ” \n b : Rated s e co n da r y p ha se c u r r e nt : \ nI P2 ( r at ed ) = %f A %. f A \n” ,I_P2_rated ,

I _ P 2 _ r a t e d ) ;

52 printf (” \n Rated s e c o n d a r y l i n e c ur re n t : \ nI L2 ( r at ed ) = %f A %. 1 f A \n” ,I_L2_rated ,

I _ L 2 _ r a t e d ) ;

54 printf ( ” \n c : p e rc e n t l oa d on e a ch t r an s f o r m er = %. 1 f p e r ce n t \n ” , p e r c e n t _ l o a d ) ;

56 printf ( ” \n d : p ri ma ry p ha se c u r r e nt : \ n I P 1 = %. f A \n” , I _ P 1 ) ;

57 printf ( ” \n p r i m a r y l i n e c u r r e n t : \ n I L 1 = %f A %. 1 f A \n” , I _ L 1 , I _ L 1 ) ;

58 printf ( ” \n The pr i m a r y l i n e c ur r e nt drawn by a− bank i s 3 t i m e s t h e ” ) ;

59 printf ( ” \n l i n e c u r r e n t drawn by a Y− bank . \ n”) ;

61 printf ( ” \n e : kVA r a t i n g o f e ac h t r a n s f or m e r = %d

kVA” , k V A _ t r a n s f o r m e r ) ;

Scilab code Exa 14.36 find line currents and their sum

11 / / G iv en d a ta12 // 3−phas e ,3 − w i r e −c o nn ec te d t r a n s f o r m e r shown i n

F i g . 1 4 −4213 V_L = 33 ; // l i n e v o l t a g e i n kV

1415 f = 6 0 ; // f r e q ue n cy i n Hz16

17 / / p ower f a c t o r18 P F1 = 1; // u ni ty power f a c t o r f o r I AB19 P F2 = 0 .7 ; // 0 . 7 l a g g i n g power f a c t o r f o r I BC20 P F3 = 0 .9 ; // 0 . 9 l a g g i n g power f a c t o r f o r I CA21

22 / / C a l c u l a t i o n s23 V _ AB = V _L * exp ( % i * ( 0) * ( % p i / 1 8 0) ) ; // l i n e v o l t a g e

i n kV t a k e n a s r e f e r e n c e v o l t a ge24

25 V _ BC = V _L * exp ( % i * ( - 1 20 ) * ( % p i / 1 80 ) ) ; // l i n ev o l t a g e i n kV

26 V _ B C_ m = abs ( V _ B C ) ; / / V BC m=m a g n i t ud e o f V BC i n kV

27 V _ B C_ a = atan ( imag ( V _B C ) / real ( V _B C ) ) * 18 0/ % p i - 1 80

; / /V BC a=p ha s e a n g l e o f V BC i n d e g r e e s28 / / 180 i s s u b t r a c t e d from I BC a t o make i t s i m i l a rt o t ex t bo o k a n g le

30 V _ CA = V _L * exp ( % i * ( - 2 40 ) * ( % p i / 1 80 ) ) ; // l i n ev o l t a g e i n kV

31 V _ C A_ m = abs ( V _ C A ) ; //V CA m=magni t ude of V CA i n kV32 V _ C A_ a = atan ( imag ( V _C A ) / real ( V _C A ) ) * 18 0/ % p i - 1 80

; / /V CA a=p ha s e a n g l e o f V CA i n d e g r e e s33 / / 180 i s s u b t r a c t e d from I BC a t o make i t s i m i l a r

t o t ex t bo o k a n g le

3435 t h et a _1 = a co sd ( P F1 ) ; / / PF1 a n g l e36 t h et a _2 = a co sd ( P F2 ) ; / / PF2 a n g l e37 t h et a _3 = a co sd ( P F3 ) ; / / PF3 a n g l e38

40 I _ AB = 1 0* exp ( % i * ( t h e ta _ 1 ) * ( % pi / 1 8 0 ) ) ; / / I ABc u r r e nt i n kA

41 I _ A B_ m = abs ( I _ A B ) ; / / I AB m=m a g ni t ud e o f I AB i n kA42 I _ A B_ a = atan ( imag ( I _A B ) / real ( I _ A B ) ) * 1 8 0 / % p i ; //

I AB a=p ha se a n gl e o f I AB i n d e gr e e s43

44 I _ BC = 1 5* exp ( % i *( - 1 20 - t h et a _2 ) * ( % pi / 1 80 ) ) ; //I BC c u r r e nt i n kA

45 I _ B C_ m = abs ( I _ B C ) ; / / I BC m=m ag n it ud e o f I BC i n kA46 I _ B C_ a = atan ( imag ( I _B C ) / real ( I _B C ) ) * 18 0/ % p i - 1 80 ;

// I BC a=p ha se a n g le o f I BC i n d e g r e es47 / / 180 i s s u b t r a c t e d from I BC a t o make i t s i m i l a r

t o t ex t bo o k a n g le48

49 I _ CA = 1 2* exp ( % i *( - 2 40 + t h et a _3 ) * ( % pi / 1 80 ) ) ; //

I CA c u r r e nt i n kA50 I _ C A_ m = abs ( I _ C A ) ; / / I CA m=m a g ni t ud e o f I CA i n kA51 I _C A_ a = 180 + atan ( imag ( I _C A ) / real ( I _ C A ) ) * 1 8 0 / % p i ;

// I CA a=p ha se a n g le o f I CA i n d e g r e es52 / / 1 80 i s added t o I BC a t o make i t s i m i l a r t o

t e xt b o ok a n g l e

5354 / / c as e a55 I_ AC = - I_C A ;

56 I _A = I_AB + I_AC ; // p ha se c u r r e nt i n kA57 I _ A_ m = abs ( I _ A ) ; // I A m=m ag ni tu de o f I A i n kA58 I _ A_ a = atan ( imag ( I _A ) / real ( I _ A ) ) * 1 8 0 / % p i ; / / I A a =

p h a se a n g l e o f I A i n d e gr e e s59

60 / / c as e b61 I_ BA = - I_A B ;

62 I _B = I_BC + I_BA ; // p ha se c u r r e nt i n kA

63 I _ B_ m = abs ( I _ B ) ; // I B m=m ag ni tu de o f I B i n kA64 I _ B_ a = atan ( imag ( I _B ) / real ( I _ B ) ) * 1 8 0 / % p i ; / / I B a =

p h a s e a ng le o f I B i n d e g r e e s65

66 / / c as e c67 I_ CB = - I_B C ;

68 I _C = I_CA + I_CB ; // p ha se c u r r e nt i n kA69 I _ C_ m = abs ( I _ C ) ; // I C m=m ag ni tu de o f I C i n kA70 I _ C_ a = atan ( imag ( I _C ) / real ( I _ C ) ) * 1 8 0 / % p i ; / / I C a =

p h a se a n g l e o f I C i n d e g r e e s71

72 / / c as e d73 ph as or_ su m = I_A + I_B + I_C ;

79 printf ( ” \n We m ust f i r s t w r i t e e ac h o f t h e p ha s ec u r r e nt s i n p o l a r form . ” ) ;

80 printf ( ” \n S i n ce r e f e r e n c e v o lt a g e , V AB i s assumed

a s 33 <0 kV , we may w r i t e \n” ) ;81

82 printf ( ” \n I AB = %d <%d kA ( un i t y PF ) , \ n” , I _ A B _ m ,

I _ A B _ a ) ;

83 printf ( ” \n But I BC l a g s V BC , whi ch i s %. f <%d kV”

, V _ B C _ m , V _ B C _ a ) ;

84 printf ( ” \n by = a co sd (%. 1 f ) = −%. 2 f l a g , andc o n s e q u e n t l y ” , P F 2 , t h e t a _ 2 ) ;

85 printf ( ” \n I B C = %. f <% . 2 f kA \n” , I _ B C _ m , I _ B C _ a ) ;

87 printf ( ” \n S i m i l a r l y , I CA l e a d s V CA = %. f <%. f kV”, V _ C A _ m , V _ C A _ a ) ;

88 printf ( ” \n by = a c o sd (%. 1 f ) = %. 2 f l ea d , andc o n s e q u e n t l y ” , P F 3 , t h e t a _ 3 ) ;

89 printf ( ” \n I C A = % d <%. 2 f kA \n” , I _ C A _ m , I _ C A _ a ) ;

91 printf ( ” \n W ri ti ng t h r e e p ha se c u r r en t s i n c o mp le s

form y i e l d s . \ n” ) ;92 printf ( ” \n I AB i n kA = ”) ; disp ( I _ A B ) ;

93 printf ( ” \n I BC i n kA = ” ) ; disp ( I _ B C ) ;

94 printf ( ” \n I CA i n kA = ”) ; disp ( I _ C A ) ;

96 printf ( ” \n From c o n v e n ti o n a l t h r e e p ha se t h eo r y f o ru n b a l a n c e d −c o n n e c te d l o a d s ” ) ;

97 printf ( ” \n a nd f ro m F i g . 1 4 −4 2 , we h a ve \n” ) ;

99 printf ( ” \n a : I A i n kA = ” ) ; disp ( I _ A ) ;

100 printf (” \n I A = %. 2 f

% . 2 f kA \n”, I _ A _ m , I _ A _ a ) ;

102 printf ( ” \n b : I B i n kA = ” ) ; disp ( I _ B ) ;

103 printf ( ” \n I B = %. 2 f <% . 2 f kA \n” , I _ B _ m , I _ B _ a ) ;

105 printf ( ” \n c : I C i n kA = ” ) ; disp ( I _ C ) ;

106 printf ( ” \n I C = %. 2 f <% . 2 f kA \n” , I _ C _ m , I _ C _ a ) ;

108 printf ( ” \n d : P ha so r sum o f t he l i n e c u r r e n t s : ” ) ;

109 printf ( ” \n I L in kA = ” ) ; disp ( p h a s o r _ s u m ) ;

Scilab code Exa 14.37 kVAcarry loadtransformer VVkVA ratiokVA in-creaseload

12 // − t r a n s f o r m e r s i n Ex . 3 513 kVA_1 = 20 ; // kVA r a t i n g o f t r an s f o r m er 114 kVA_2 = 20 ; // kVA r a t i n g o f t r an s f o r m er 215 kVA_3 = 20 ; // kVA r a t i n g o f t r an s f o r m er 316

17 V _1 = 2300 ; // Pr imary v o l t a g e i n v o l t18 V_2 = 230 ; // S ec on da ry v o l t a g e i n v o l t19

20 kVA = 40 ; / / kVA s u p p l i e d by t h e bank21 P F = 0.7 ; // l a g g i n g power f a c t o r a t which bank

s u p p l i e s kVA22

23 // one d e f e c t i v e t r an s f o r me r i s removed24

25 / / C a l c u l a t i o n s26 / / c as e a27 k V A _ tr a ns f or m er = k VA / sqrt ( 3 ) ; // kVA l o a d c a r r i e d

by e ac h t r a n s fo r m e r28

29 / / c as e b30 p e rc e nt _ ra t ed l oa d _T r = k V A_ t ra n sf o rm e r / k VA _1 * 1 00

; // p e rc e n t l oa d c a r r i e d by e ac h t r an s f o r me r31

32 / / c as e c33 k V A _V _ V = sqrt ( 3) * k V A_ 1 ; // T ot al kVA r a t i n g o f t he

t r a n s fo r m e r bank i n V−V

35 / / c as e d36 r at io _b an ks = k VA _V _V / ( k VA _1 + k VA _2 + k VA _3 ) *

100; // r a t i o o f V−V b ank t o − bank Trr a t i n g s

38 / / c as e e39 kVA _Tr = kVA / 3 ;

40 p e rc e nt _ in c re a se _ lo a d = k V A_ t ra n sf o rm e r / k VA _ Tr *

100 ; // p e r ce nt i n c r e a s e i n l oa d on e a cht r a n s f o r m e r when o ne Tr i s rem oved

46 printf ( ” \n a : kVA l o ad c a r r i e d by e ac h t r a n s fo r m e r= % . 1 f kVA/ t r a n s f o r m e r \n” , k V A _ t r a n s f o r m e r ) ;

48 printf ( ” \n b : p e r c e nt r at ed l oa d c a r r i e d by e a c ht r a n s f o r m e r = %. 1 f p e r c e n t \n” ,

p e r c e n t _ r a t e d l o a d _ T r ) ;

50 printf ( ” \n c : T ot al kVA r a t i n g o f t he t r an s f or m e rbank i n V−V = %. 2 f kVA \n” , k V A _ V _ V ) ;

52 printf ( ” \n d : r a t i o o f V−V b ank t o − bank Trr a t i n g s = %. 1 f p e r ce n t \n” , r a t i o _ b a n k s ) ;

54 printf ( ” \n e : kVA l o ad c a r r i e d by e ac h t r a n s fo r m e r (V−V ) = %. 2 f kVA/ t r a n s f o r m e r \n” , k V A _ T r ) ;

55 printf ( ” \n p e r c e n t i n c r e a s e i n l o a d on e a c ht r a n s f o r m e r when o ne Tr i s rem oved : ” ) ;

56 printf ( ” \n = %. 1 f p e r c e n t ” ,p e r c e n t _ i n c r e a s e _ l o a d ) ;

Scilab code Exa 14.38 IL alpha Ia kVA

11 / / G iv en d a ta12 // 3−pha se SCIM13 V = 440 ; // r a te d v o l t a g e i n v o l t o f SCIM14 h p = 100 ; // r a t e d p ower i n hp o f SCIM15 P F = 0.8 ; // power f a c t o r16 V_1 = 155 ; // p r i ma r y v o l t a ge i n v o l t o f Tr

17 V_2 = 110 ; // s ec on da ry v o l t a ge i n v o l t o f T r18

19 V_a = 110 ; // a rm at ur e v o l t a g e i n v o l t20 V_L = 440 ; // Load v o l t a ge i n v o l t21 eta = .98 ; // e f f i c i e n c y o f t h e Tr .22

23 / / C a l c u l a t i o n s24 / / c as e a25 / / r e f e r r i n g t o a pp e n d i x A−3 , T a b l e 4 30 −150 f o o t n o t e s26 I _L = 1 24 *1 .2 5 ; // Motor l i n e c u rr e n t i n A27

28 / / c as e b29 a lp ha = V _a / V_ L ; // T ra n sf o rm a ti o n r a t i o30

31 / / c as e c

32 I_a = ( sqrt ( 3) / 2) * ( I _L / ( a lp ha * e ta ) ) ; / / C u rr e nt

i n t he p r i m a ry o f t he s c o t t t r an s f o r me r s33

34 / / c as e d35 k V A = ( V _a * I _a ) / (( sqrt ( 3 ) / 2 ) * 1 0 0 0 ) ; / / kVA r a t i n g o f

t he main a nd t e a s e r t r a n s f o r m e r s36

40 printf ( ” \n a : Motor l i n e c u rr e n t : \ n I L = %d A\n ” , I _ L ) ;

4142 printf ( ” \n b : T ra ns fo rm at io n r a t i o : \ n a l p h a =

N 1 / N 2 = V a / V L = %. 2 f \n” , a l p h a ) ;

44 printf ( ” \n c : C ur re nt i n t he p ri ma ry o f t he s c o t tt r a n sf o r m er s : \ n I a = %. f A \n” , I _ a ) ;

46 printf ( ” \n d : kVA r a t i n g o f t he main and t e a s e rt r a n sf o r m er s : \ n kVA = %. 1 f kVA” , k V A ) ;

Scilab code Exa 14.39 VL ST Idc Sac Sdc per line

7 / / E xa mp le 1 4−398

12 I_L = 1 ; // Load c u r r e n t i n kA13 V_m = 750 ; // Peak v o l t a g e i n kV14

15 / / C a l c u l a t i o n s16 / / c as e a17 V _ L = ( V _m ) / sqrt ( 2 ) ; / / Max . a l l o w a b l e Vrms i n kV

t ha t may be a p p l i e d t o t he l i n e s u si ng ac18

19 / / c as e b20 S _ T _a c = sqrt ( 3 ) * V _L * I _ L ; // T ot al 3−p h as e a p p a r en t

power i n MVA

2122 / / c as e c23 I_rms = I_L ; // rms v al ue o f l oa d c u r r e n t i n kA24 I _ dc = I _ r ms * sqrt ( 2 ) ; / / Max . a l l o w a b l e c u r r e n t i n kA

t ha t can be d e l i v e r e d by d c t r a n s mi s s i o n25

26 / / c as e d27 V_dc = V_m ; // dc v o l t a ge i n kV28 S _T _d c = V _d c * I_ dc ; // T o ta l dc a p pa r en t p ower

d e l i v e r e d by two l i n e s i n MVA29

30 / / c as e e31 S _a c_ li ne = S _T _a c / 3 ; // Power p er ac l i n e32

33 / / c as e f 34 S _d c_ li ne = S _T _d c / 2 ; // Power p er dc l i n e35

Electric Machinery and Transformers_I. L. Kosow

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