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Analysis of Grid-connected Induction GeneratorsUnder Three-phaseBalanced ConditionsL. Wang, Member, IEEE, Ya-Feng Yang, and Sung-Chun Kuo

Akkuci-This paper analyzes both dynamic and steady-stateperformances of induction generators connecting to a utility grid.The studied systems with single induction generator underdifferent loading conditions are respectively examined. The rotorspeed parameters of the studied system under steady-stateconditions are explored. Dynamic characteristics of the studiedinduction generators under a severe torque disturbance andsudden disconnection from the utility grid are studied in detail..

Index Terms- grid-connected induction generator, parallel-operated, grid-connected.

I. INTRODUCTIONI T IS well known that an externally driven inductionmachine can maintain self-excitation when an appropriatevalue of a capacitor bank is appropriately connectedacross heterminals of the induction machine [l]. Such inductionmachine is ca lled a self-excited induction generator (SEIG).The primary advantages of a SEIG over conventionalsynchronousgeneratorare brushlessconstruction with squirrel-cage rotor, reduced size, without DC supply for excitation,reduced maintenancecost, and better transient characteristics.In recent years, SEIGs have received increasedattention andthey have been widely employed as suitable isolated powersources and grid-connected in small hydroelectric and windenergy applications.According to the analyzed results of available references,most of the researcheson a single induction generator orparallel operated induction generator focused on theautonomous or isolated operation, which supplied static ordynamic loads. These induction generator driven by theindividual prime movers employed excitation capacitor bankto buildup desired voltage via se lf-excited phenomena. Hencethe value of the excitation capacitor bank and the rotor speeddetermine the magnitude of the generated voltage and itsfrequency.Both voltage and frequency need o be controlled tofeed the power to the load. The grid-connected inductiongenerators an be divided into two types, i.e., single output [2-7] and double outputs [8-lo]. To supply the active power frominduction generator o the grid, the rotor speedof the inductiongenerator should be greater han the synchronousspeedof theresultant revolving magnetic field. The former sends the

generatedenergy from stator windings to the utility while thelatter feeds the generatedenergies obtained from both statorand rotor windings to the utility grid. The latter is also calledstatic Kramer, double-fed, or double outputs inductiongenerators. Since it generally employs a rectifier, a DC link,an inverter, and a step-up ransformer o transfer the rotor sideenergy o the utility grid and it will add ceiain complexities onstudying induction generator. This paper will focus on thegrid-connected induction generator feeding power only withsingle output.In this paper, an equivalent circuit of a three-phaseinduction machine basedd-q axis mode1 s used to derive thedynamic equations of an induction generator feeding to theutility grid. This paper is organized as follows. Section IIintroduces the derivation of dynamic equations of the studiedsystem. Section III describes he steady-stateanalyses esultsunder variation of rotor speed.Section IV shows he transientresponses due to the change of applied torque anddisconnected phenomena.Some specific conclusions of thispaper are drawn in the Section V.

II. MACHINE MODELFig. 1 showsa three-phase nduction generator IG) fed to

the utility grid with an excitation capacitor bank. The inductiongenerator is driven by a separately-excitedDC motor whosethe rotor speed s variable. A capacitor bank is connected othe stator terminal for supplying the reactive power to the IG.Fig. 2 shows the d-q axis equivalent-circuit of a three-phasesymmetrical induction machine connected to the utility gridincluding excitation capacitor bank based on synchronouslyreference rame model. The voltage equations of the studiedIG shown n Fig. 2 can be written as below.

Grid

L. Wang, Ya-Feng Yang, and Sung-Chun Kuo are with the Department ofElectrical Engineering National Cheng Kung University, Taman , Taiwan70101, R.O.C. (e-mail: [email protected])Fig. 1 Diagram of an induction generator fee&g to a utihty grid withexciting capacitor

4130-7803-7322-7/02/$17.00 2002 IEEE


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Fig. 2 D-q ax6 equivalent circuit of an induction generator connected tothe utility grid.

vqr =(-6 -~X,)I~. -Co&-XsS)ido +(p&)iqr +(sXm)ldr6b Ob (1)v& = (~x,,)ips +(-lo - pxs,)i,+ -(%&,)iqr + (PXm)ldr

wb Ob ub (2)vqr = -(c Xm)lps - (7 X,)I~ + (r, + 2 Xm )lqr + (y X,)i, (3)Y&=(-C - Or Xm)lqr - (-&X,>, - (DX,)i,, + (rr + t X,)i,

wb Ob (4)where X, is the mutual reactance between stator and rotor,while X,, and X, are the self-reactances f the stator windingand the rotor winding, respectively. The self-reactancesareexpressed s:

xs, = Xl, + Xand x,=x,,+x,where Xi, and Xi, are the leakage reactanceof the stator andthe rotor windings respectively.The stator flux linkages, h qsand h ds,and the rotor fluxlinkages, h qrand h dnare given by:

I,, = -X&, + %(i,, - iqs) (5)Ads = -Xl& + X,(id, -ids) (6)kqr = Xd,, + X,(i,, - &,I (7)k& = xl& + xrn (idr - ids) (8)

The torque and rotor speedof induction generator are relatedas:(2H)p(o,)=T, -Te -Do, (9)

where T, is the input mechanical orque which is supplied bythe prime mover. H is inertia constant and D is frictioncoefficient. The electromagnetic orque T, can be expressedby

T, = X, (i&i,, -i&,)The voltage-current equations of the excitation capacitorsshown in Fig. 2 can be exoressed s follows:

i,, = (c/@b h@,,) + (kcvdc&d =(c~~bh(vds)+~ecvqc

(10)(11)

where i,, and icd are the q and d-axis excitation capacitorcurrents, espectively.The voltage equations of the equivalent transmission ineare given:vqs = Jk3 COS@,f (0)) + R&L + w, /ab)p(iqL ) + %X&L (12Vd, =-fiV,sin(O,r(0))tRtidL +(X,/C~~)~(~~)+O~X&~ (13))where R1and X, are the equivalent resistanceand reactanceofthe transmission line, respectively. iqL and idL are theequivalent q and d-axis transmission ine currents. V, is therms value of the grid and C&f0) is its phasor respecting o q-axis. The employed induction generator has the followingspecifications: 1.1 kW, 127(6)/220(Y) V, 8.3 (A)/4.8(Y) A , 60Hz, 2 poles, 3600 rpm. The per unit baseare: Vb = 127 V, Ib =4.8 A, & = 26.462 Sz,Nb = 3600 rpm, and at, = 377 rad/s.

III. STEADY-STATE ANALYSISThe influences of the rotor speedof IG on the power flowof the studied systemare discussed n this section.Fig. 3(a) shows he active power of induction generatorversusits rotor speed. t is found that the induction machine operatedas motor mode when the rotor is driven below the synchronousspeed.The negative sign of active power means hat the powerabsorbedby the induction machine. Meanwhile, as the rotorspeedgets beyond the synchronousspeed, he active power issupplied from induction generator o the grid. Fig. 3(b) shows

that the reactive power always absorbed by the inductionmachine, despite its operating mode. Fig. 3(c) plots the activepower at the grid side, comparing with the active power at thestator side of IG, it is evident that the both are almost equal,except the lossesof the transmission ines. The reactive powerversus rotor speed at the grid is shown in Fig. 3(d). It isobserved hat the grid side absorbed he reactive power whenthe induction machine operated in motor mode, since thecapacitor bank provided amount of reactive power which theinduction motor can not adsorb completely. Fig. 3(e) showsthe efficiency of the induction machine versus he rotor speed.As can be seen, he motor mode has higher efficiency than themachine operated in generator mode, since the stator of themachine sinks more reactive power in the generatormode.

III. TRANSIENT ANALYSISSince the wind speed s stochastic variation and offers avariable torque to induction generator. Transient responses fan induction generatorsuffered a torque step change s studiedand illustrated in Fig. 4. Assume that a 0.1 pu torque stepdisturbance s added o the rotor at t=2.0 s and the disturbanceis ended at t=3.0 s. Fig. 4(a) shows the transient responseofthe stator voltage of induction generator under torquedisturbance. t is found that the voltage of the stator becomes

414


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0.8 -,

1720 1760 1800 1840 1880Rotor tpssd (RPM)(a) Active power of induction generator

.1.6

-2.4 I---.2.8 +,-I/

1720 1760 1800 1840 1880Rotor speed (RPM)(b) Reactive power of induction generator0.8 1

1720 1760 1800 1840 1880Rotor speed (RPM)(c) Active power at grid side1.0 -j

2 0.0 Y.-F .l.O8 1

.2.0 3

.3.0 &;-il1720 1760 1800 1840 1880Rotor speed (RPM)(d) Reactive power at grid side

1720 1760 1800 1840 1880Rotor sped (RPM)(e) Efiiciency of induction generator

Fig, 3 Steady-state cha racteristics versus rotor speed (RPM x 2) ofinduction generator

slightly small value after disturbance.The stator current of theinduction generator s also plotted in Fig. 4(b). It is found thatstator current has a step change ollowing the torque and thencarry the additional power to the grid. The change ofmagnetization eactanceof the induction generator s shown inFig. 4(c), one can be seen hat the induction generator s drivento deeper saturation region after the applied torque step

1.4152

141482 14144P

1.4140 H-l-1.4136 -,

0.0 1.0 2.0 3.0 4.0 5.0t (XC)(a) Terminal voltage of induction generato]1.72

1.68

9

C! 1.64

1.60

1.56 10.0 1.0 2.0 3.0 4.0 5 0t (set)(b) Stator current of induction generator

0 856

0 852

5 0.848 x

0.844

0.8400.0 1.0 2.0 3.0 40 5.0t (ret)(c) Magnetization reactance of inductlon generator

0 52 10 48

2

; 0.44b

0 40

0.36 c-l-_0.0 1.0 2.0 3.0 4.0 5.0

t (W(d) Active power of induction generator236 72.32

2 2.28f 2.24

2.20 c2 16 +r,

0.0 1.0 2.0 3.0 4.0 5.0t (SW3(e) Reactive power of induction generatorFig 4 Transient responses dumg torque disturbance

increase.Fig. 4(d) shows the transient responseof the activepower of the induction generator under torque disturbance.The active power suddenly ncreases rom 0.385 pu to 0.47 puand quickly recover to original value after disturbance. Thechangeof reactive power is shown in Fig. 4(e). It is observedthat the reactive power absorbed by the induction is alsoincreasing rapidly and cause he induction generator operatedin deepersaturation region.415


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0.0 1.0 2.0 3.0 4.0 5.0t (SK)(a) Termina l voltage of induction generator6.0 1

0010.0 1.0 2.0 3.0 4.0 5.0t (SC)(b) Stator current of induction generator10

0.85

0.6 r ---

0.0 1.0 2 0 3.0 4.0 5.0t(w)(c) Magnetization reactance of mduct ion generator

1.025

0.0

.2.00.0 1.0 2.0 3.0 40 50t (ICC)(d) Active power of induction generator

6.0

7

g 4.02.0

0.0 -;i

-

7-10.0 1.0 2.0 3.0 4.0 50t (ret)(e) Reactive power of induction generator

Fig. 5 Transient responses during disconnecting

In some casessuch as grid fault, the induction generatorhas o be disconnected rom the grid. The phenomena fter the I81induction generator disconnected rom the grid are shown inFig. 5. The transient response of stator voltages of the 191induction generator is shown in Fig. 5(a). Assume that theinduction generator is disconnectedat t=l s and re-closed att=3 s. It can be found that the stator voltage of the induction

generator ncreasesafter disconnected,since the stator voltageis no longer maintained at grid level during this time. Fig. 5(b)shows he stator current also has a step increasecausedby thecharging current of the excitation capacitor after thedisconnection, The change of magnetization reactanceof theinduction generator in this case is shown in Fig. 5(c), it isfound that the induction generator runs into deeper saturationregion after the induction generatordisconnected rom the grid.Fig. 5(d) shows the transient responseof the active power ofthe induction generator during disconnecting. The activepower supplied from induction generator decreaseswheninduction generator s disconnected rom the grid and quicklyrecover to original value after re-closed to the grid. Thechange of reactive power is also shown in Fig. 5(e). It isobserved hat the reactive power absorbedby the induction isalso increasing rapidly and cause the induction generatoroperated n deepersaturation egion during disconnecting.

V. CONCLUSIONSThis paper has presented steady-state and transientcharacteristicsof a three phase nduction generatorconnecting

to a utility grid. The d-q axis equivalent circuit of the inductionmachine based on synchronous reference frame has beenemployed to derive the dynamic equations of the studiedsystem. t is shown hat the rotor speedsignificantly influencesthe active power which is supplied by the induction generator.Even below the synchronousspeed, he induction machine willoperate in motor model. The capacity of the excitationcapacitor bank also affects the efficiency of the inductiongenerator and the voltage amplitude during transient. Largercapacitor makes ower efficiency and higher transient voltage.

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VI. REFERENCESE. D. Basset and F. M Potter, Capacitive excrtation of inductiongenerators, Trans. American Institu te Electrical Enginee ring, vol. 54,1935,pp. 540-545.B Singh, R. B Saxena, S S. Murthy, and B. P Singh, A smgle-phaseself-excited Induction generator for hghting loads in remote areas,International Journal on ElectrIci@ Engrneering Educatron, vol. 25,1988,pp. 269-275.C. S. Demoulias and P. S. Dokopoulos, Transient behaviour and self-excitation of wind-driven induction generator after its disconnection fromthe power grid, IEEE Trans. on Energy Converston, vol. 5, no. 2, 1990,pp. 272-278.A. Ouhrouche and X. D. Do, EMTP base simulation of a self-excitedinduction generator after its disconnection from the grtd, IEEE Transon Energy Conversion, vol. 13, no. I, 1998, pp. 7-13.L. Herbert and N. A. Abdul Melek, Power converter for wind turbineapplication, IEEE Power Engrneering Society Summer Meetmg, 2000,vol. 2, pp. 1275 -1276.A. Grauers, Efficiency of three wind energy generator systems, IEEETrans. on Energy Conversion, vol. II, no. 3, 1996, pp. 650-657.P. S. Nagendra and S. S. Murthy, Performance analysis of gridconnected induction generators driven by hydra/wind turbmes includinggrid abnormalities, Proceedmgs of the 24th Intersocrety on EnergyConversion Engmeering Conference, 1989, vol. 4, pp. 2045-2050I. Caddirci and M. Erm~s, Performance evaluation of wind driven DOIGusing a hybrid model, IEEE Trans. on Energy Conversron, vol 13, no 2,1998, pp 148-155.R. Pena, J. C. Glare and G. M. Asher, Doubly fed mductron generatorusing back-to-back PWM converters and its application to varrable-speedwind-energy generation, IEE, Proc B. Electr. Power A&., vol 143, noI, 1996, pp. 231-241.

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[ IOIL. Refouti, B. A. T. Al Zahawi, and A. G. Jack, Analysis and modelingof the steady state behavior of the static Kramer induction generator,IEEE Trans. on Energy Conversion, vol. 14, no. 3, 1999, pp. 333-339.

Li Wang (S87-M88) was born in Changhua,Taiwan, on December 20, 1963. He received a Ph. D.degree from Department of Electrical Engineer ing,National Taiwan University, Taipei, Taiwan, in June1988. He has been an associated professor and aprofessor at the Department of Electrical Engineer ing,National Cheng Kung University, Tainan, Taiwan in1988 and 1995, respectively. At present, his interestsinclude the science research of power engineeringsuch as power systems dynamics, power systemstability and AC machines analyses. He is an IEEE MemberSung-Chun Kuo was born on July 9,1957 in Tainan,Taiwan. He obtained his M. SC. degree fromDepartment of Electrical Engineering, NationalCheng Kung University. He is currently pursuing hisPh. D. degree at the Department of ElectricalEngineering, National Cheng Kung University,Tainan, Taiwan. His interest includes AC electricmachine analysis and power electronics.

Ya-Fang Yang was born in Kaohsiung, Taiwan, onApril 1977. He received the B. S. degree fromNational Ta ipei University of Technology, Taiwanin 1999 and M. S. degree from Department ofElectrical Engineering, National Cheng KungUniversity in June 2001. His interesting include theelectrical machine analysis and power electronicapplication.

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