25741 Energy Conversion 23

ENERGY CONVERSION ONE (Course 25741)

CHAPTER NINE ….continuedDC MOTORS AND GENERATORS

SPEED CONTROL of SHUNT DC MOTOR

• Effect of Armature motor’s resistance speed control on a shunt motor’s torque-speed

• Only used in applications in which: - motor spends almost all its time operating at full speed or - inexpensive to justify a better form of speed control


• In field resistance control, lower IF higher its speed, & higher IF causes a decrease in speed

• there is always a minimum achievable speed by IF control

• Minimum speed occurs when IF has maximum permissible value

• if motor operate at its rated terminal voltage, power, & IF then it will be running at rated speed

• this is known also as : “base speed”• to achieve a reduction in this speed by IF control,

require excessive IF that may burn up field windings


• In armature voltage control, lower armature voltage on separately excited motor, reduce its speed & higher armature voltage increase its speed

• There is a maximum achievable speed, in maximum permissible armature voltage level

• Armature voltage control would require excessive armature voltage, which may damage armature circuit

• Armature voltage control works well for speeds below base speed & field current control works well for speeds above base speed

• By combining two speed-control techniques in same motor, it is possible to get a range of speed variations of up to 40 to 1 or more

• Shunt & S.E. motors have excellent speed control characteristics


• There is significant difference in torque & power limits on machine under two types of speed control

• Limiting factor in either case is heating of armature conductors, which places an upper limit on magnitude of IA

• For armature voltage control, flux in motor is constant, so maximum torque in motor is:

Tmax=KφIA,max • maximum torque is constant, regardless of

speed


• power o/p, P=T.ω maximum power of motor at any speed under armature voltage control is: Pmax=Tmax ω

• Thus maximum power out of motor is directly proportional to its operating speed under armature voltage control

• on the other hand, while RF control used flux changes

& speed increase by decrease in flux• In order that IA do not exceed its limit, Tind must

decrease as speed of motor increases


• since P=T.ω, & torque limit decreases as speed of motor increases:

- max. power out of dc motor under field current control is constant, while max. torque varies as reciprocal of motor’s speed

• These shunt dc motor power & torque limitations for safe operation as a function of speed shown next


• Power & Torque limits as a function of speed for a shunt motor under VA & RF control


• Example 3:• figure, shows a 100 hp, 250 V,

1200 r/min shunt dc motor with an armature resistance of 0.03 Ω & a field resistance of 41.67 Ω

• Motor has compensating windings, so armature reaction can be ignored

• Mechanical & core losses may be ignored

• assumed to be driving a load with a line current of 126 A & an initial speed of 1103 r/min,

• to simplify the problem assume armature current drawn by motor remains constant

SPEED CONTROL of SHUNT DC MOTOR-Example 3

(a) machine magnetization curve shown in next slide, what is motor’s speed if RF raised to 50 Ω

(b) calculate & plot speed of motor as a function

of RF assuming a constant-current load • SOLUTION(a) Initial IA1= IL1-IF1=126- 250/41.67=120 A EA1=VT-IA1RA=250-120 x 0.03=246.4 VRF increased to 50 Ω, IF2=VT/RF=250/50=5 A


• Magnetization curve


• EA2/EA1=[K’φ2n2]/[K’φ1n1], and since IA assumed constant EA1 = EA2 1=[φ2n2]/[φ1n1]

or n2= [φ1 / φ2] n1

• Last Plot is EA versus IF , for a given speed• EA directly proportional to flux on this curve: EA2/EA1 =φ2/φ1 • At IF=5 A, EA0=250 V, while at IF=6 A, EA0=268 V φ2/φ1= 268/250 =1.076 • New speed of motor: n2= φ1/φ2 n1=(1.076)(1103)=1187 r/min


• A MATLAB M-file can be made to calculate speed of motor as a function of RF

• plot of its speed versus RF shown below:


• Note: assumption of constant IA not a good assumption for real loads

• IA vary with speed in a fashion dependent on torque required by type of load attached to motor

• these differences cause a motor’s speed –versus-RF curve slightly different than shown in last figure.


• Motor in Example-3 now connected separately excited, as shown below:


• Motor is initially running with VA=250 V, IA=120 A, and n=1103 r/min, while supplying a constant torque load.

• What will the speed of this motor be if VA is reduced to 200 V?

• SOLUTION:EA=VT-IARA=250-120x0.03=246.4 V• Since flux is constant: EA2/EA1=[K’φ2n2]/[K’φ1n1]=n2/n1 n2= EA2/EA1 n1 • Since torque is constant & flux is constant IA is

constant: EA2=200-120x0.03=196.4 V n2= EA2/EA1 x n1=196.4/246.4 x 1103=879 r/min

SPEED CONTROL of SHUNT DCEffect of an Open Field Circuit

• As shown speed increase as RF increased, what would happen if field circuit open while motor is running? The flux in machine would drop drastically, and reach φres & EA=Kφω would drop with it

• cause an enormous increase in IA & resulting Tind would be quite a bit higher than load torque on motor. Therefore motor’s speed starts to rise & just keeps going up

• Author Experience of undergraduate lab. • Where field cct. fused by mistake (instead of 3-A by a 0.3-A

fuse) and when started after 3 s, suddenly a flash from fuse & motor’s speed skyrocketed. Someone turned main cct. Breaker off within a few seconds, but by that time tachometer pegged 4000 r/min, while motor rated 800 r/min needless to say every one present very badly scared

• And learned to be most careful about field cct protection• A field loss relay normally included to disconnect motor from

line in event of loss of field current

SPEED CONTROL of SHUNT DCEffect of an Open Field Circuit

• Two other causes of field weakening: (a) in shunt motors operating with light fields if A.R. effects

severe enough, in case of an increase in load can weaken its flux and cause rise of speed until motor over-speed known as runaway

(b) motors operating with severe load changes & duty cycles, this flux weakening problem solved by installing compensating windings

• Unfortunately compensating windings too expensive for use on ordinary run-of-the-mill motors

• Solution: to use a turn or 2 turns of cumulative compounding to motor’s poles

• As load increases mmf from series turns increases, which counteracts demagnetizing mmf of A.R.

• A shunt motor equipped with just few series turns like this is called: stabilized shunt motor

PERMANENT-MAGNET DC MOTOR

• A permanent magnet dc motor (PMDC) is a dc motor whose poles are made of permanent magnets.

• PMDC motor offer a number of benefits compared with shunt dc motors in some applications

• Advantage: Since these motors do not require an external field circuit, they do not have the field circuit copper losses. Because no field windings are required, they can be smaller than corresponding shunt dc motors


• Disadvantages: (a) Permanent magnets cannot produce as high flux density as

an externally supplied shunt field so a PMDC motor will have a lower induced torque per ampere

of armature current than a shunt motor of the same size. (b) PMDC motors run risk of demagnetization due to A.R. effect which reduces overall net flux, also if IA become very large there is a risk that its mmf demagnetize poles, permanently reducing & reorienting residual flux (c) A PMDC motor is basically the same machine as a shunt dc

motor, except that flux of a PMDC motor is fixed. Therefore, it is not possible to control the speed of the PMDC motor by varying the field current or flux. The only methods of speed control available for a PMDC motor are armature voltage control and armature resistance control.


• The magnetization curve of typical ferromagnetic material

• Note: after a large magnetizing intensity H applied to core & removed, a residual flux Bres remains behind in core

• Flux can be brought to zero if a coercive magnetizing intensity Hc is applied to core with opposite polarity

• in this case, a relatively small value of it will demagnetize the core


• (a)Typical ferromagnetic material & its Bres (b) suitable for P.M. (c) second quadrant rare earth magnets combine High residual flux and high coercive magnetizing intensity

SERIES DC MOTOR• A series DC motor is a dc motor whose field

windings consist of relatively few turns connected in series with the armature circuit KVL for this motor is VT = EA + IA (RA + RS)

SERIES DC MOTOR• The Tind=KφIA while flux in this machine directly

proportional to IA (at least until metal saturates) • Flux in machine can be given by: φ=c IA • Where c is constant of proportionality. Tind=KφIA = K c IA^2 (1)• Torque in motor proportional to square of IA • As a result of this relationship, series motor gives

more torque per ampere than any other dc motor• Therefore it is used in applications requiring very high

torques• Examples: starter motors in cars, elevator motors, and

tractor motors locomotives

TERMINAL CHARCATERISTIC SERIES DC MOTOR

• As seen before an increase in flux cause a decrease in speed.

• in series motor a sharply drooping torque-speed characteristic exist (since IA pass field winding)

• Analysis is based on assumption of linear magnetization curve, & then effects of saturation considered in a graphical analysis

• therefore: φ=c IA (2) VT = EA + IA (RA + RS) (3)• From (1) IA=√Tind /Kc & EA=Kφω VT = Kφω + √Tind /Kc (RA + RS) (4)


• To eliminate flux from equation (4): IA=φ/c and Tind=K/c φ^2 φ=√c/K √Tind (5)• Substituting equation (5) in (4) and solving for

speed: VT=K √c/K √Tind ω + √Tind /Kc (RA + RS) √c/K √Tind ω= VT - (RA + RS) / [Kc] x √Tind ω= VT / [Kc] x 1/√Tind - (RA + RS) / [Kc] (6)• Note: for unsaturated series motor; speed of

motor varies as reciprocal of square root of Tind & its torque-speed characteristic shown next


• Torque-speed characteristic of a series motor

• One disadvantage can be seen from Eq.(6) - when Tind goes to zero speed goes to infinity - in practice torque can never go zero due to

mechanical, core & stray losses that must be overcome,

however if no other load exist, can turn fast enough to seriously damage itself


• Therefore; Never completely unload a series motor & never connect one to a load by a belt or other mechanism that could break

• nonlinear analysis of a series dc motor with magnetic saturation effects, ignoring A.R. illustrated in EXAMPLE-5

• Example 5: consider the equivalent cct. of a series dc motor with a

250 V series dc motor having compensating windings, and atotal series resistance RA+RS of 0.08 Ω. The series field consists of 25 turns per pole, with magnetization curve shown next

SERIES DC MOTOREXAMPLE-5

• Magnetization Curve

SERIES DC MOTOR(a) find speed & induced torque of this motor for when its armature current is 50 A(b) calculate & plot torque-speed characteristic

for this motorSOLUTION :(a) Pick points along operating curve & find

torque & speed for each point for IA=50 A EA=VT-IA(RA+RS) =250 – 50 x 0.08 =246 V since IA=IF=50 A, mmf=25 x 50=1250 A.turns

SERIES DC MOTORFrom magnetization curve at mmf =1250 A.turns

EA0=80 VSpeed can be found: n= EA/EA0 x n0=246/80 x 1200= 3690 r/minPconv=EAIA=Tind ω Tind=EAIA/ω=[246 x50]/[3690x1/60x2π]=31.8 N.m. (b) to calculate complete torque-speed

characteristic, the same steps of (a) should be repeated for may values of IA, this can be done using a M-file of MATLAB

SERIES DC MOTORSPEED CONTROL

• Unlike shunt dc motor, there is only one efficient way to change speed of a series dc motor

• Method is to change terminal voltage of motor• If terminal voltage is increased, first term in Eq. (6)

increased, result in a higher speed for any given torque

• speed of series dc motors can be controlled by insertion of a series resistor however is very wasteful of power & only used for very short time during start-up

• Now with introduction of solid-state control, techniques available for variable terminal voltages

COMPOUND DC MOTOR• A compound dc motor is a motor with both a

shunt & a series field • Such a motor shown below: (a) long-shunt connection

COMPOUND DC MOTOR(b) Compound dc motor with short-shunt

connection

COMPOUND DC MOTOR• Current flowing into dot produces a positive mmf

(same as in transformer)• If current flows into dots on both field coils, resulting

mmfs add to produce a larger total mmf• This situation is known as cumulative compounding• If current flows into dot on one field coil & out of dot on

other field coil resulting mmfs subtract• In previous (a)&(b) figures round dots correspond to

cumulative compounding & squares corresponds to differential compounding

COMPOUND DC MOTOR• KVl for the compound motor: VT=EA+IA(RA+RS) • Currents in compound motor are related by: IA=IL-IF IF=VT/RF

- Net mmf & effective shunt field currnt in compound motor:

Fnet =FF(+,-) FSE-FAR

IF*=IF(+,-) NSE/NF IA – FAR/NF (+) in equations associated with cumulatively

compounded (-) associated with differentially compound motor

COMPOUND DC MOTORTorque-Speed Characteristic

• In cumulatively compound dc motor, a component of flux is constant & another one which is ~ to IA (& thus to its load)

cumulatively compound motor has a higher starting torque than a shunt motor (whose φ constant) but lower than a series motor (whose entire φ ~ to IA )

• Cumulatively compound motor combines best features of both shunt & series motors:

Like a series motor has extra torque for starting; Like a shunt motor it does not overspeed at no load


• At light load, series field has very small effect, so motor behaves approximately as a shunt dc motor

• As load gets very large series flux becomes quite important & torque-speed curve begins to look like a series motor’s characteristic

• A comparison of torque-speed characteristics of each of these types of machines shown next


(a) T-ω curve of cumulatively compound, compared to series & shunt motors with same full-load rating

(b) T-ω curve of cumulatively compound, compared to shunt motor with same no-load speed


• Torque-Speed of Differentially Compound dc motor

• In a differentially compounded dc motor, the shunt mmf and series mmf subtract from each other. This means that as the load on the motor increases, IA increases and the flux in the motor decreases.

• But as the flux decreases, the speed of the motor increases. This speed increase causes another increase in load, which further increases IA, further decreasing the flux, and increasing the speed again


• The result is that a differentially compounded motor is unstable and tends to runaway

• This instability is much worse than that of a shunt motor with armature reaction. It is so bad that a differentially compounded motor is unsuitable for any application.


• Differentially compounded motor is also impossible to start

• At starting conditions, the armature current and the series field current are very high

• Since the series flux subtracts from the shunt flux, the series field can actually reverse the magnetic polarity of the machine’s poles

• The motor will typically remain still or turn slowly in the wrong direction while burning up, because of the excessive armature current


• When this type of motor is to be started, its series field must be short-circuited, so that it behaves as an ordinary shunt motor during the starting period

• Nonlinear Analysis of Compound dc Motors• Example 6: a 100 hp, 250 V compounded dc motor

with compensating windings has an internal resistance, including series winding, of 0.04 Ω. There are 1000 turns per pole on shunt field & 3 turns per pole on series windings

• The machine shown in next figure, & its magnetization curve shown also. At no load field resistor has been adjusted to make motor run at 1200 r/min. core, mechanical & stray losses negligible


(a) what is the shunt current in this machine at no load?

(b) if motor is cumulatively compounded, find its speed when IA=200 A

(c) if motor is differentially compounded, find its speed when IA=200 A

SOLUTION:(a) At no load, IA=0, so internal generated voltage

equal VT =250 V. & from Mag. Curve a IF=5 A EA=250 V at 1200 r/min (& IF=5 A )


• Compound dc motor of example 6:


(b) when IA=200 A flows in motor, machine’s internal voltage:

EA=VT-IA(RA+RS)=250-200x0.04=242 V effective field current of cumulatively compounded

motor is: IF*=IF+NSE/NF IA- FAR/NF =5 +3/1000 x 200=5.6A From mag. Curve, EA0=262 V at n0=1200 r/min therefore motor’s speed will be: n =EA/EA0xn0=242/262 x 1200 = 1108 r/min (c) If machine is differentially compounded, IF*=IF-NSE/NF IA- FAR/NF=5 – 3/1000 x 200=4.4 A


from mag. Curve EA0=236 V at n0=1200 r/min n=EA/EA0 x n0=242/236 x 1200 = 1230 r/minNote: speed of cumulatively compounded motor

decreases with load, while speed of differentially compounded motor increases with load


• Speed Control in Cumulatively Compounded DC Motor

• Techniques available for control of speed in a cumulatively compounded dc motor are the same as those available for a shunt motor

1- change in field resistance 2- change armature voltage 3- change armature resistance Differentially compounded dc motor could be

controlled in a similar manner. Since differentially compounded motor almost never used, that fact hardly matters

DC MOTOR STARTERS• Equipments used for protection of dc motors,

for the following reasons:1- protect motor against damage due to short

circuits in equipment2- protect motor against damage from long-term

overloads3-protect motor against damage from excessive

starting currents4- provide a convenient manner in which to

control the operating speed of motor

DC MOTOR PROBLEMS on STARTING• In order for a dc motor to function properly, it must be

protected from physical damage during starting period• At starting conditions, motor is not turning & so EA=0 V• since internal resistance of a normal dc motor is very

low compared to its size (3 to 6 percent per unit for Medium size motors) a very high current flows

• Consider for example, 50 hp, 250 V motor of EXAMPLE 1, RA is 0.06 Ω, & full-load current less than 200 A, but current on starting is:

IA=[VT-EA]/RA=[250-0]/0.06=4167 A This current is over 20 times motor’s rated full-load

current It is possible a motor severely damaged by such current

25741 Energy Conversion 23

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