SPACE VECTOR PULSE- WIDTH-MODULATED (SV-PWM) INVERTERS

Transcription

1 CHAPTER 7 SPACE VECTOR PULSE- WIDTH-MODULATED (SV-PWM) INVERTERS 7-1 INTRODUCTION In Chpter 5, we briefly icue current-regulte PWM inverter uing current-hyterei control, in which the witching frequency f oe not remin contnt. The eire current cn lo be upplie to the motor by clculting n then pplying pproprite voltge, which cn be generte be on the inuoil pule-with-moultion principle icue in bic coure in electric rive n power electronic [1]. However, the vilbility of igitl ignl proceor in control of electric rive provie n opportunity to improve upon thi inuoil pule-with moultion by proceure ecribe in thi chpter [, 3], which i terme pce vector pule-with moultion (SV-PWM). We will imulte uch n inverter uing Simulink for ue in c rive. 7- SYNTHESIS OF STATOR VOLTAGE SPACE VECTOR v In term of the intntneou ttor phe voltge, the ttor pce voltge vector i 7-1

2 v t v t e v t e v t e j j /3 j4 /3 ( ) n( ) bn( ) cn( ) (7-1) In the circuit of Fig. 7-1, in term of the inverter output voltge with repect to the negtive c bu n hypotheticlly uming the ttor neutrl reference groun v v v ; v v v ; v v v ; (7-) n N Nn bn bn Nn cn cn Nn Subtituting Eq. 7- into Eq. 7-1 n recognizing tht j j /3 j4 /3, (7-3) e e e the intntneou ttor voltge pce vector cn be written in term of the inverter output voltge v t v e v e v e j j /3 j4 /3 () N bn cn (7-4) A witch in n inverter pole of Fig. 7-1 i in the up poition if the pole i V b c i b i c v c v b v N q qb qc Figure 7-1 Switch-moe inverter. 7-

3 witching function q 1, otherwie in the own poition if q. In term of the witching function, the intntneou voltge pce vector cn be written v ( t) V ( q e q e q e ) j j /3 j4 /3 b c (7-5) With three pole, eight witch-ttu combintion re poible. In Eq. 7-5, the ttor voltge vector () t cn tke on one of the following even itinct intntneou vlue where in igitl repreenttion, phe "" repreent the let ignificnt igit n phe c the mot ignificnt igit (for exmple, the reulting voltge vector ue to the witch-ttu combintion 11 ( 3) v 3): i repreente () v j (1) v1 Ve (1) v Ve (11) v3 Ve (1) v4 Ve (11) v5 Ve j (11) v6 Ve v (111) v 7 j /3 j /3 j4 /3 j5 /3 (7-6) In Eq. 7-6, v n v 7 re the zero vector becue of their vlue. The reulting intntneou ttor voltge vector, which we will cll the bic vector, re plotte in Fig. 7-. The bic vector form ix ector hown in Fig. 7-. The objective of the PWM control of the inverter witche i to yntheize the eire reference ttor voltge pce vector in n optimum mnner with the following objective: A contnt witching frequency f 7-3

4 v (1) v 3(11) ector v 6(11) ector 3 v ector 1 v 1(1) -xi ector 4 ector 6 v ector 5 4(1) v 5(11) Figure 7- Bic voltge vector ( v n v not hown). 7 Smllet intntneou evition from it reference vlue Mximum utiliztion of the vilble c-bu voltge Lowet ripple in the motor current, n Minimum witching lo in the inverter. The bove conition re generlly met if the verge voltge vector i yntheize by men of the two intntneou bic non-zero voltge vector tht form the ector (in which the verge voltge vector to be yntheize lie) n both the zero voltge vector, uch tht ech trnition cue chnge of only one witch ttu to minimize the inverter witching lo. In the following nlyi, we will focu on the verge voltge vector in ector 1 with the im of generlizing the icuion to ll ector. To yntheize n verge voltge vector ( ˆ j v Ve ) over time perio T in Fig. 7-3, the joining bic vector v 1 n v 3 re pplie for intervl xt n yt repectively, n the zero vector v n v 7 re pplie for totl urtion of 7-4

5 v 3 j /3 V e yv 3 v ˆ j V e v 1 V e j zt. In term of the bic voltge vector, the verge voltge vector cn be expree xv 1 Figure 7-3 Voltge vector in ector 1. or where, 1 v [ xt v yt v zt ] 1 3 T v xv yv 1 3 (7-7) (7-8) x y z 1 (7-9) In Eq. 7-8, expreing voltge vector in term of their mplitue n phe ngle reult in ˆ j j j /3 (7-1) V e xv e yv e By equting rel n imginry term on both ie of Eq. 7-1, we cn olve for x n y (in term the given vlue of V ˆ, n V ) to yntheize the eire verge pce vector in ector 1 (ee Problem 7-1). Hving etermine the urtion for the joining bic vector n the two zero vector, the next tk i to relte the bove icuion to the ctul pole (, b n c). Note in Fig. 7- tht in ny ector, the joining bic vector iffer in one poition, for exmple in ector 1 with the bic vector v 1(1) n v 3(11), only 7-5

6 the pole b iffer in the witch poition. For ector 1, the witching pttern in Fig. 7-4 how tht pole- i in up poition uring the um of xt, yt, n zt 7 intervl, n hence for the longet intervl of the three pole. Next in the length of urtion in the up poition i pole-b for the um of yt, n zt 7 intervl. The mllet in the length of urtion i pole-c for only zt 7 intervl. Ech trnition require chnge in witch tte in only one of the pole, hown in Fig Similr witching pttern for the three pole cn be generte for ny other ector (ee Problem 7-). 7-3 COMPUTER SIMULATION OF SV-PWM INVERTER v v tri control, v control, b v control, c V v N V T v bn V v cn z x y z 7 y z x T 7-6 Figure 7-4 Wveform in Sector 1 ; z z z7 In computer imultion, for exmple uing Simulink, well in hrwre implementtion uing rpi prototyping tool uch from DSPACE [4], the bove ecribe pule-with moultion of the ttor voltge pce vector cn be crrie out by compring control voltge with tringulr wveform ignl t the

7 witching-frequency to generte witching function. It i imilr to the inuoil PWM pproch only to the extent of compring control voltge with tringulr wveform ignl. However, in SV-PWM, the control voltge o not hve purely inuoil nture thoe in the inuoil PWM. In n inuction mchine with n iolte neutrl, the three phe voltge um to zero (ee Problem 7-3) v ( t) v ( t) v ( t) (7-11) n bn cn To yntheize n verge pce vector v with phe component v, v b n v c (the c-bu voltge V i pecifie), the control voltge cn be written in term of the phe voltge follow, expree rtio of V ˆtri (the mplitue of the contnt witching-frequency tringulr ignl thee control voltge): v tri ue for comprion with vcontrol, vn vk 1 Vˆ V V tri vcontrol, b vbn vk 1 Vˆ V V tri vcontrol, c vcn vk 1 Vˆ V V tri (7-1) where, v k mx( vn, vbn, vcn ) min( vn, vbn, vcn ) (7-13) Deriving Eq. 7-1 n 7-13 i left homework problem (Problem 7-5). 7-7

8 7-4 LIMIT ON THE AMPLITUDE V ˆ OF THE STATOR VOLTAGE SPACE VECTOR v Firt we will etblih the bolute limit on the mplitue V ˆ of the verge ttor voltge pce vector t vriou ngle. The limit on the mplitue equl V (the c-bu voltge) if the verge voltge vector lie long non-zero bic voltge vector. In between the bic vector, the limit on the verge voltge vector mplitue i tht it tip cn lie on the tright line hown in Fig. 7-7 forming hexgon (ee Problem 7-6). However, the mximum mplitue of the output voltge v houl be limite to the circle within the hexgon in Fig. 7-7 to prevent itortion in the reulting current. Thi cn be eily conclue from the fct tht in blnce inuoil tey tte, the voltge vector v rotte t the ynchronou pee with it contnt mplitue. At it mximum mplitue, () ˆ j v t V e,mx,mx ynt (7-14) Therefore, the mximum vlue tht V ˆ cn ttin i 6 3,mx (7-15) Vˆ V co( ) V V 3 Vˆ,mx V 7-8 Figure 7-7 Limit on mplitue V ˆ.

9 From Eq. 7-15, the correponing limit on the phe voltge n the line-line voltge re follow: n Vˆ ˆ V 3 3 phe,mx V,mx (7-16) Vˆ V VLL,mx ( rm) 3.77 V phe,mx (7-17) The inuoil pule-with moultion in the liner rnge icue in the previou coure on electric rive n power electronic reult in mximum voltge 3 V rm V V LL,mx ( ).61 (inuoil PWM) (7-18) Comprion of Eq n 7-18 how tht the SV-PWM icue in thi chpter better utilize the c bu voltge n reult in higher limit on the vilble output voltge by fctor of (/ 3), or by pproximtely 15 percent higher, compre to the inuoil PWM. SUMMARY In thi chpter, n pproch clle SV-PWM i icue, which i better thn the inuoil PWM pproch in utilizing the vilble c-bu voltge. It moeling uing Simulink i ecribe. REFERENCES 1. N. Mohn, Electric Drive An Integrtive Approch, yer 1 eition, publihe by MNPERE ( 7-9

10 . H. W. vn er Broek et l, Anlyi n Reliztion of Pule With Moultor be on Voltge Spce Vector, IEEE Inutry Appliction Society Proceeing, pp , J. Holtz, Pule With Moultion for Electric Power Converter, Chpter 4 in book Power Electronic n Vrible Frequency Drive, eite by B. K. Boe, IEEE Pre, PROBLEMS 7-1 In converter V 7V. To yntheize n verge ttor voltge vector j e V, clculte x, y n z j.53 v Repet if e V. Plot reult imilr to thoe in Fig Show tht in n inuction mchine with iolte neutrl, t ny intnt of v ( ) ( ) ( ) time, t vb t vc t. j Given tht e V, clculte the phe voltge component. 7-5 Derive Eq n Derive tht the mximum limit on the mplitue of the pce vector form the hexgonl trjectory hown in Fig