Chapter 13

Chapter 13 - 13-1 Chapter 13 Vector Control of...

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Unformatted text preview: 13-1 Chapter 13 Vector Control of InductionMotor Drives: A Qualitative Examination Exit 2001 by N. Mohan Print TOC " ! 13-2 DC Motor Drive Sa + N S Tem Na ia ia φf P P va U − φa La 0 Ra + ea t Tem = kT ia Tem − 0 t Tem = kT ia Exit 2001 by N. Mohan TOC " ! 13-3 Brushless DC Motor Drive !" is (t ) ˆ Is !!" Br (t ) 90 o S N 0 θm a − axis t ˆ Tem = kT I s Tem 0 t ˆ Tem = kT I S Exit 2001 by N. Mohan TOC " ! 13-4 Vector-Controlled Induction Motor Drive !! " Fr (t ) !! " vs (t ) θr θr !!" Br (t ) !!! " Blr (t ) !! " ir '(t ) a − axis !!! " Fr '(t ) !!!! " Bms (t ) IM P P U Tacho current feedback speed feedback " " " Br (t ) perpendicuar to Fr′(t ) and Fr (t ) ˆ Tem = kT I r' Exit 2001 by N. Mohan ˆ (keeping Br constant) TOC " ! 13-5 Analogy to a Current-Excited Transformer With a Shorted Secondary φm,i1 φm,i2 i2 i1 0 φl 2 i1 t R2 shown explicitly R2 v2 = 0 short net = 0 N:N λ2 (0+ ) = λ2 (0- ) = 0 φm,i (0+ ) = φm,i (0 + ) + φ# 2 (0+ ) Lm + i 2 (0 ) = i1 (0+ ) L2 1 Exit 2001 by N. Mohan 2 TOC " ! 13-6 d- and q- Axis Winding Representation isd = " 2 the projection of is (t) vector along the d-axis 3 isq = " 2 the projection of is (t) vector along the q-axis 3 b − axis at t ib b − axis isq ! " is ia a − axis Exit 2001 by N. Mohan at t ! " is b − axis c − axis q − axis at t ! " is d − axis isd a − axis isq ic c − axis q − axis projection 2 = projection × 3 d − axis a − axis projection isd = projection × 2 3 c − axis TOC " ! 13-7 Initial Flux Buildup Prior to t = 0 - q − axis isq = 0 t = 0− φm,isd !" is !!" Br d − axis isd isd −∞ 0 t 1ˆ ˆ i a (0 ) = I m,rated and i b (0 ) = i c (0 ) = - I m,rated 2 2ˆ 2 3ˆ 3ˆ isd (0 ) = Ims,rated = ( I m,rated ) = Im,rated 3 3 2 2 - isq = 0 Exit 2001 by N. Mohan TOC " ! 13-8 Step Change in Torque at t = 0 - ω slip isq isq ωm = 0 t = 0+ φm,isq φm,ir φlr !!" Br ω slip a − axis isd isd net = 0 −∞ 0 t ! ωm = 0 ! Isd unchanged ! Step-change in isq " Φq,net = 0 + + + " φm,i (0 ) = φm,i (0 ) + φ#r (0 ) sq Exit 2001 by N. Mohan r ˆ , Lm i " Tem α Br sq Lr TOC " ! 13-9 Flux Densities at t = 0 !!!! " Bms θ Exit 2001 by N. Mohan !!! " Blr !!" Br + t = 0+ a − axis TOC " ! Transformer Analogy – Voltage Needed to Prevent the Decay of Secondary Current R1 Ll′2 Ll1 ′ R2 ′ i2 t >0 − i1 ⋅ u (t ) Lm 13-10 im ′ ′ ′ v2 = R2 i2 (0 + ) u (t ) + Exit 2001 by N. Mohan TOC " ! Currents and Fluxes at Sometime Later t > 0, Blocked Rotor q − axis ωm = 0 ω slip isq 13-11 t >0 φm,isq isq φm,ir φlr !!" Br ω slip d − axis isd a − axis net = 0 ω slip R ′ , (L m /L r )isq α r ˆ B r Exit 2001 by N. Mohan TOC " ! Vector-Controlled Condition With a Rotor Speed ωm 13-12 q − axis ω syn t >0 isq isq φm,isq φ m,ir φlr ωm !!" Br ω syn d − axis isd a − axis net = 0 ωsyn = ωm + ωslip Exit 2001 by N. Mohan TOC " ! 13-13 Similarity Between Voltage-Fed and Vector-Controlled Induction Machines in Steady State !! " vs θr !!" isd !!! " ims θr !!" Br Exit 2001 by N. Mohan !!! " Blr !!!! " Bms !" is at t !! " ir ' !!" isq TOC " ! 13-14 Torque, Speed, and Position Control ω m (measured) motor mathematical model ˆ Br (calculated) Tem ˆ Br θ Br − ˆ Br ωm (measured) ωm ˆ* Br ∑ + PI calculations * isd * θm + ∑ − θm (measured) P * ωm + ∑ − PI * Tem + ωm (measured) * isq ∑ dq to abc * ia * ib * ic isd isq abc to dq current regulated PPU ia ib ic Motor PI − ωm d / dt (measured) Tem (calculated) θm encoder ωsyn (t) = ωm (t) + ωslip (t) t θ B (t) = 0 + 0∫ ωsyn (τ) ⋅ dτ r Exit 2001 by N. Mohan TOC " ! 13-15 Sensor-Less Drives ! DTC Reference 4: M. Depenbrock, “Direct Self Control (DSC) of Inverter-Fed Induction Machines,” IEEE Transactions on Power Electronics, Vol. 3, 1988, pp. 420-429 Reference 5: I. Takahashi and Y. Ohmori, “High Performance Direct Torque Control of an Induction Motor,” IEEE/IAS Annual Meeting, 1987, pp. 163169 Exit 2001 by N. Mohan TOC " ! 13-16 Summary/Review ! How is torque controlled in brush-type dc drives and brushless-dc drives? ! In a sentence, describe the vector control of induction-motor drives that emulates the performance of dc drives. Why is it more challenging? ! What does the Theorem of Constant Flux Linkage state? ! In words, what does the analogy of a transformer with the short-circuited secondary, and excited by a step-current conclude? ! What is the reason for introducing the d-axis and the q-axis windings? ! Without the details, state the reason for choosing 3/2 N s 2 as the number of turns in the d-axis and q-axis windings. Exit 2001 by N. Mohan TOC " ! 13-17 Summary/Review " ! How are isd and isq obtained from the is space vector? ! At the end of the initial flux build-up process at t = 0-, are there any currents in the rotor bar? ! How are the currents induced in the rotor bars at t = 0+ ? ! What needs to be done to maintain the torque produced at t = 0+ ? ! Why does the slip speed at which the d-axis and q-axis windings need to be rotated, to maintain the torque produced beyond t = 0+, depend on various quantities as given in Eq. 13-12? ! Describe the similarity between voltage-fed induction machines and vector-controlled induction machines. ! Describe the control block diagram of vector control. ! Describe DTC and its objectives. Exit TOC " ! 2001 by N. Mohan ...
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