ch12 - 12-1 Chapter 12 Induction Motor Drives Speed Control...

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Unformatted text preview: 12-1 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 12-2 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 " ! 12-3 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 (ωsyn-ωm) = Tem ωslip Therefore, to minimize rotor losses, ωslip should be small Exit 2001 by N. Mohan TOC " ! 12-4 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 12-5 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 12-6 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…) 12-7 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 first-order 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 12-8 TOC " ! 12-9 Start-up 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 12-10 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 12-11 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 12-12 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 12-13 Pulse-Width-Modulated 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 12-14 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 12-15 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 12-16 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 ! 12-17 Summary/Review ! What are the applications of adjustable-speed drives? ! Why are the thyristor-based, voltage reduction circuits for controlling induction-motor speed so inefficient? ! In operating below the rated speed (and not considering the core losses), why is it most efficient to keep the flux-density 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 " ! 12-18 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 start-up, why should small-frequency 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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