Unformatted text preview: 121 Chapter 12
Induction Motor Drives:
Speed Control Exit 2001 by N. Mohan Print TOC " ! Induction Motor Drives :
Speed Control
PPU Speed
control input Induction
motor Sensors Load Controller 122 ωm ! Efficient speed control over a wide range
 Reduced voltage control (inefficient)
 Frequency control (efficient) Exit ! PPU drives induction motor with variable frequency to
maintain low slip
! As frequency decreases, voltage must also decrease to
avoid magnetic saturation 2001 by N. Mohan TOC " ! 123 Rotor Losses
Power crossing air gap to rotor:
Pr = Tem ωsyn
Power delivered through rotor to load:
Pem = Tem ωm
Power lost in rotor:
Pr,loss = Pr – Pem = Tem (ωsynωm) = Tem ωslip
Therefore, to minimize rotor losses, ωslip should be small Exit 2001 by N. Mohan TOC " ! 124 Minimizing ωslip For A Given TL
and ωm
ω
ωsyn1 ωslip1
ωslip2 ωsyn2
ωsyn3 ωslip3 ˆ
Bms increasing ωm TL Tem ! Large flux density allows low slip
ˆ
ˆ
! Keep Bms as large as possible – maintain at Bms,rated
Exit 2001 by N. Mohan TOC " ! Operating Characteristics with
ˆ
ˆ
Bms = ( Bms ) rated 125 ωm ω syn , rated ω slip , rated frated ω syn ,1 ω slip ,2 f2
(a) Exit 2001 by N. Mohan k ω syn ,1
ω slip,1 { f1 ω slip,1 0 Load Torque
(Constant) ωm k ω m , rated f1 ω m1 f2 ω m2
(b) f3
Tem 0 frated f3
Tem ! If flux is kept constant, slope will be the same at
every frequency
! Load torque and speed are met by adjusting
frequency
TOC " ! ˆ
Maintaining B Over Operating
Frequencies and Current Levels by
Adjusting Voltage
126 ms,rated Rs ′
jω Llr j ω Lls + ′
I ra + Ia Va − − ω R′
rω I ma Ema Rs jω L
m j ω Lls + Ia syn − − ω R′
rω I ma Ema Va slip ′
I ra + jωL
m syn slip ˆ′
ω Lsl I ra ˆ
Rs I ma , rated Va
I ma Exit 2001 by N. Mohan ′
I ra Ema !! reference
ˆ
ˆ′
ω Lls I ma , rated Rs I ra TOC " ! ˆ
Maintaining B Over Operating
Frequencies and Current Levels by
Adjusting Voltage (cont…)
127 ms,rated ˆ
! Maintaining constant Bms is equivalent to maintaining a
constant ˆ ma (magnetizing current)
I
ˆ
ˆ
ˆ
E ma
E ma
E ma
ˆ =
! Since I ma
,
or
should be kept constant
ωL m
ω
f
Va
is a constant.
! Ignoring Rs and Lls, this means that
f
As f decreases, so should Va. Constant volts per hertz.
! This is a good firstorder approximation
Exit 2001 by N. Mohan TOC " ! Adjusting Voltage – Stator
Resistance Included
! Approximation: ˆ
Va = k;⋅ f k= ˆ
Va,rated ! Including voltage drop across Rs:
ˆ
Va = k ⋅ f + R s ˆ′
I ra
ˆ
Va,rated
ˆ
Va at rated torque ˆ′
Rs I ra,rated { 0 Exit f rated ˆ
(Va,rated  R s ˆ′ra,rated )
I
k=
f rated ˆ
Va voltage
boost ˆ
ˆ
Va,rated
Va
= constant =
f
frated V at zeroTem
slope a
frated f ( Hz) ! For large torques, considerable voltage boost is
I ra
needed at low frequencies. This is the R s ˆ′ term. 2001 by N. Mohan 128 TOC " ! 129 Startup Considerations
f ωm ˆ
Bms = constant, rated
f steadystate ωsyn,start
ωslip,start f start = f slip,rated { fstart 0 50%
Tem
Tem ,rated Exit 2001 by N. Mohan inertia t 100% ˆ
I 'ra
,
(%)
′
I ra ,rated
TOC " ! Capability Below and Above
Rated Speed 1210 ωm ω m , rated
Rated power
capability
1 .0
Rated torque
capability 0 1 .0 Tem
Tem , rated Exit ˆ
! Voltages limited to rated values, therefore Bms must be
reduced at higher speeds (Flux Weakening)
! Currents limited to rated values, therefore torque
ˆ
limited when Bms is limited 2001 by N. Mohan TOC " ! Braking in Induction Motor Drives
1211 speed of airgap
field ωsyn P
P
U ωm ωm > ωsyn
ωslip = negative
Tem Tem ˆ
Bms = constant
f0 Motoring
mod e R′
r Tem0 f1 ωm Generation
mod e 0 ωsyn1 ωm ωsyn 0 ωm Tem1 < 0 f1 < f0 ! To initiate braking, lower ωsyn to some value less than ωm
! Braking torque can be adjusted by setting the negative slip
frequency
Exit
TOC
"
2001 by N. Mohan ! Speed Control of Induction
Motor Drives 1212 ac input Rectifier Slip
compensation Voltage
boost id
ˆ
V ω m, ref
*
ωm ∑ +
− ω syn PWM
controller ω slip ; this is an estimate Vd limiter Vd + Inverter Current
limiter
circuit ω syn = ω m, ref + Tem / KωT
" $#
# % − Motor Measured Vd Va = k f f + kvT Tem ! ωm,ref is passed through a rate limiter to avoid over driving the
motor
! This method does not give precise speed control
Exit
TOC
" !
2001 by N. Mohan 1213 PulseWidthModulated Power
Processing Unit
a
+ b Vd
− c a
b + vcontrol,a (t) qa (t) qb (t) qc (t) c "# #
$ %
acmotor Vd
− vcontrol,b (t) vcontrol,c (t) da (t) db (t) dc (t) vtri (t) Exit 2001 by N. Mohan TOC " ! Harmonics in PPU
vtri vcontrol ,a vcontrol ,b 1214 vcontrol ,c va
f1 2fs − f1 2fs + f1 vb
fs − f1 (a)
vab = va − vb fundamental, vab1 3fs − f1 fs + f1 fs 3fs − 2f1
2fs 3fs + f1
3fs + 2f1 3fs t ! PPU with switching frequency of 800 Hz generating a fundamental
sine wave of 50 Hz
! Frequency spectrum shows large 50 Hz component and smaller
components at higher frequencies due to switching
! These higher frequency components add to the losses in the motor
Exit
TOC
" !
2001 by N. Mohan PPU – Supplied Induction Motor
1215 Ia1 R s jω1L ls + Va1 ′
Ira,1 Ima,1
jω1Lm −
Fundamental Frequency Model Exit Iah jω1L′
lr R s jhωL ls jhωL′
lr + R ′r
R ′r ωm
ωslip Vah jhωL m R′
r ωsyn,h
ωslip,h −
Harmonic Frequency Model ! At harmonic frequencies R e q & Rr′
Magnetizing inductance can be ignored
Harmonic currents controlled by leakage inductance
ˆ
Vah
ˆ &
Iah
(X ls,h + X′r,h )
l 2001 by N. Mohan & R′
r TOC " ! PPU – Supplied Induction Motor
Model
1216 ia,1 (t ) R
s Lls ′
ira,1 (t ) Llr
′ + R′
r im,1 (t ) va,1 (t ) + ′
′
var ,1 (t ) = Rr Lm
− ωm
′
ira ,1
ω slip − ia (t ) Rs Lls ′
ira (t ) ′
Rr L′
lr ′
var ,1 (t ) + − Lm
ib (t ) Rs Lls ′
irb (t ) L′
lr ′
vbr ,1 (t ) R′
r + R′
r + − Lm
ic (t ) R
s Lls ′
irc (t ) ′
Llr ′
vcr ,1 (t ) − Lm ! Fundamental frequency drop across resistor replaced with
AC voltage source
! Harmonic currents produce voltage across R ′
r
Exit
TOC
"
2001 by N. Mohan ! 1217 Summary/Review ! What are the applications of adjustablespeed drives?
! Why are the thyristorbased, voltage reduction circuits for
controlling inductionmotor speed so inefficient?
! In operating below the rated speed (and not considering the core
losses), why is it most efficient to keep the fluxdensity peak in
the air gap at the rated value?
! Since an induction motor is operated at different values of
frequency, hence different values of synchronous speed, how is
the slip speed defined?
! Supplying a load that demands a constant torque independent of
speed, what is the slip speed at various values of the frequency f
of the applied voltages?
Exit 2001 by N. Mohan TOC " ! 1218 Summary/Review ! To keep the flux density peak in the air gap at the rated value,
why do the voltage magnitudes, at a given frequency of
operation, depend on the torque supplied by the motor?
! At startup, why should smallfrequency voltages be applied
initially? What determines the rate at which the frequency can
be ramped up?
! At speeds below the rated value, what is the limit on the torque
that can be delivered, and why?
! At speeds above the rated values, what is the limit on the power
that can be delivered, and why? What does it mean for the
torque that can be delivered above the rated speed? Exit 2001 by N. Mohan TOC " ! ...
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 Fall '06
 Scalzo

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