Understanding the three and four-leg inverter Space Vector

Transcription

1 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Understndin the three nd four-le inverter Spe Vetor Llonh-Mshs M., Heredero-Peris D., Montesinos-Mirle D., Rull-Durn J. Centre d Innovió Tenolòi en Convertidors Estàtis i Aionments (CITCEA-UPC) Deprtment d Eninyeri Elètri, Universitt Politèni de Ctluny ETS d Eninyeri Industril de Brelon, Av. Dionl 647, 0808 Brelon, Spin Phone: Emil: mr.llonh@ite.up.edu, dniel.heredero@ite.up.edu, montesinos@ite.up.edu Aknowledments This work ws supported y the Ministerio de Eonomí y Competitividd under the projet ENE CE--R. Keywords Modultion Strtey, Spe Vetor, Three-phse system, Volte Soure Converter. Astrt This pper shows new point of view of the lssil volte spe vetors nd its implitions on three nd four-le onverters. It is esy to find in the literture, uthors usin i-dimensionl nd threedimensionl representtions of the onverter sttes. Nonetheless, the literture rrely speifies wht these spes represent. Therefore, this pper proposes wide nlysis of the stte voltes nd its referenes for three-le, three-le four-wire nd four-le inverters, in fvour of understndin the spe vetor ehviour under three nd four-wire senrios. Introdution Modultion tehniques llow to provide the required te sinls for power eletronis. For the ontrol of power onverters the most extended modultion tehnique is PWM (Pulse Width Modultion). The ontrol of three-phse inverters under SVPWM (Spe Vetor-PWM) [1 3] hs een proved to e more optiml thn other modultion strteies s SPWM (Sinusoidl PWM). Its mjor dvntes depend on the sequenin lorithm hosen nd n e summrised into: Low output volte hrmoni distortion Good utiliztion of the ville DC-link (up to % more thn SPWM) Low swithin losses Simple diitl implementtion in three-wire inverters However, SVPWM dvntes usility n depend on the inverter topoloy. In the prtiulr se of three-phse inverters it is possile to onsider: Three-wire inverters. Commonly used in se of renewle enery intertion where the onnetion point is supposed to e lned. This type of inverters re onstituted y three-le inverters (Fi. 1()). Four-wire inverters. Commonly used when the inverter needs to exhne enery with low volte rid, i.e. four-wire rid or even mirorid. This type of inverters n e lssified into: Three-le split pitor topoloy (Fi. 1()). Four-le topoloy (Fi. 1()). EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.1 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

2 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Uus o Uus o Uus n Uus n () Three-le three-phse inverter () Three-le split pitor Uus Uus o d n () Four-le three-phse inverter Fi. 1: Two-level three-phse inverter topoloies In this sense, the SVPWM hs een widely studied in the literture for three nd four-wire ses pyin prtiulr ttention in different strteies to optimize the omputtionl urden required to synthesize te sinls. This pper provides oneptul nlysis of how the SVPWM of four-wire inverter n e understood from three-wire senrio. To ondut this study it is importnt to remrk tht the referene onept is defined s the point from whih the voltes re omputed. Thus, when referene frme is required [4] (, αβγ, dq0), it will e only used frme to void onfusions. SVPWM fundmentls The spe vetor It is usul to depit three volte phsors in positive sequene to represent lned three-phse system in stedy-stte. They n result miuous if it is desired to use these sme phsors s xes to otin referene sis for n instntneous vetoril nlysis. This is due to the linel dependeny of the third omponent, i.e. there re only two deree of freedom. Nevertheless, in enerl unlned system where u n (t)+u n (t)+u n (t) 0 (1) it n e dedued from (1) tht, providin vetor movin in the spe, it is possile to onsider three derees of freedom. The spe vetor s n e defined s vetor tht represents eh volte t ny time instnt in the noni orthonorml C referene, ein C = {[100],[010],[001]}. This spe vetor n e nlysed from sttionry or αβγ frme, or from synhronous dq0 frme. These frmes re otined respetively, y the orthoonl Clrke s nd Prk s trnsform [4]. Then, it n e onluded tht the spe vetor represents the instntneous volte vlues, in sis whih dimension mthes with the numer of derees of freedom. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P. ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

3 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Three-le inverter sttes In this se, three-wire three-phse inverter is onsidered, s the one shown in Fi. 1(). The SVPWM tehnique for three-wire system, lso known s D-SVPWM, is minly sed on the strtion of onsiderin the onverter s stte mhine where the desired output volte is otined from the superposition of the eiht possile swithin sttes. A swithin vetor is defined y stte represented y three diits (one per le); if the diit is equl to one implies tht the top swith of the orrespondin le is losed nd if it is equl to zero tht it is opened. The possile sttes nd swithin vetors re olleted in Tle I. Tle I: D-SVPWM vetors nd sttes Vetor Stte Vetor Stte These eiht sttes re ommonly drwn in the well known SVPWM hexon of Fi.. This hexon is divided into six sextnts determined y to. It should e notied tht exists two Zero Swithin Vetors (ZSV) tht orresponds to nd. These vetors produe null phse-to-phse voltes nd re represented in the hexon entrl point. The other six SV re lso known s Non-ZSV (NZSV) [5]. Fi. : Clssi D representtion of the three le SVPWM. Thus, SVPWM modultion n e omputed s follows: Sextnt determintion. Seletion of the two djent vetors V djxy ordin with the lotion of s in one of the sextnts of the projeted hexon. Susripts x nd y represents the orrespondin djent vetors of the hexon t ny time. Projetion. Projetion of s onto the seleted V djxy in order to otin Proj( Vdjx s) nd Proj( Vdjy s). Duty rtios lultion nd seletion of one sequenin for the swithin vetors to otin the te sinls. Four-le inverter sttes In this se, four-wire three-phse inverter is onsidered, s the one shown in Fi. 1(). The SVPWM tehnique for four-wire system, lso known s 3D-SVPWM, is minly sed on the strtion of onsiderin the onverter s stte mhine where it is possile to otin sixteen different vetors. In this se, eh vetor is represented y four diits; the three first ones re relted with the tive phses {,,} nd the fourth with the neutrl wire {n}. The possile sttes nd swithin vetors re olleted in Tle II. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.3 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

4 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Tle II: 3D-SVPWM vetors nd sttes Vetor Stte Vetor Stte Vetor Stte Vetor Stte V V These sixteen sttes re sometimes drwn onformin the dodehedron of Fi. 3, whih is interted y the omintion of two ues onneted y ommon vertex onstituted y nd 6. It should e notied tht exists two Zero Swithin Vetors (ZSV) tht orresponds to nd 5. The other fourteen SV re lso known s Non-ZSV (NZSV) V9 0 V8 1 Fi. 3: 3D representtion of the four le SVPWM. Thus, SVPWM modultion n e omputed s follows: Tetrhedron determintion. Seletion of the three djent vetors V djxyz ordin with the lotion of s in one of the twenty-four tetrhedrons. Susripts x, y nd z represents the orrespondin djent vetors of the tetrhedron t ny time. Projetion. Projetion of s onto the seleted V djxyz in order to otin Proj( Vdjx s), Proj( Vdjy s) nd Proj( Vdjz s). Duty rtios lultion nd seletion of one sequenin for the swithin vetors to otin the te sinls. Spe vetor of three-le inverter As hs een forementioned, in order to understnd the dominion of spe vetor, it is neessry to determine how mny dimensions it hs. In ddition, this dominion lso depends on the referene of the spe vetor voltes. Thus, two different senrios n e extrted from the three-le inverter: the spe vetor onsiderin s referene the midpoint of the DC-link o or the AC neutrl point n, depited on Fi. 1(). It should e notied tht topis exposed immeditely fterwrds inlude the three-le split pitor topoloy. The voltes in this topoloy hve only one possile referene: the midpoint of the DC-link o. Then, it enertes the sme spe vetors s the three-le three-phse inverter. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.4 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

5 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Spe vetor dominion on DC-link midpoint referene Considerin the DC-link midpoint referene, it n e ssumed tht the spe vetor s R 3 due to its three derees of freedom. Then, the inverter sttes of Tle I onform the eiht verties of ue in the spe whih ede is equl to the volte pplied t the DC-link side. Fi. 4 shows these eiht sttes under the sttionry frme. Fi. 4: Three-phse inverter volte sttes referened to the DC-link midpoint, in frme. Notie tht the ue oundries re the physil limits of the mximum volte spe vetor tht ould e enerted y the inverter. Drwin the spe vetor onformed y the mximum volte lned system, the Fi. 5() is otined. Blned system spe vetors re lwys ontined in plne, nmed Π in this pper, whih norml vetor is n =(1,1,1). The speil hrteristi of Π is tht ll vetors ontined do not hve Zero Sequene omponent. Fi. 5() shows the null ZS prt y pplyin the Clrke s trnsformtion, hnin the frme to the αβγ frme. () In frme. () In αβγ frme. Fi. 5: Three-phse lned spe vetor referened to the DC-link midpoint. Spe vetor dominion on AC neutrl point referene Considerin the neutrl point n s referene, one deree of freedom is lost due to n is flotin in respet with o. It is widely known tht Zero Sequene omponents nnot e enerted from flotin neutrl point referene. Fi. 6 shows how the inverter volte sttes re moved, losin the homopolr dimension nd forin s R. This ft n e explined s follows. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.5 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

6 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Fi. 6: Three-phse inverter volte sttes referened to the AC neutrl point, in αβγ frme. Assumin the onverter sttes vetors referened to o s E o i =(u o,u o,u o ) () these n e referened to n y E n i = E o i u no (3) where u no = u o + u o + u o 3 (1,1,1) (4) In order to ive more informtion, SVPWM nottion hs een hned from V 0,V 1,V... to E r i where i is the vetor numer nd r represents the system referene: o for the DC-link midpoint nd n for the AC neutrl point. Spe vetor under different modultions nd referenes As it hs een introdued, SPWM nd SVPWM strteies re widely used modultions to ontrol threephse inverters. Tkin into ount the spe vetor dominions mentioned ove, the spe vetor trjetory plots n sinifintly inrese the strenths nd weknesses omprehension of these strteies. Fi. 5() shows the vere spe vetor trjetory usin SPWM, referened to the o point. It n e seen how the intersetion of Π plne with the ue determines the mximum volte voidin overmodultion. In tht se, the n view (entrl plot of Fi. 5()) lso n represent the sme trjetory, referened to the neutrl point n. Usin SVPWM, the three-dimensionl point of view results useful to understnd why it is possile to overtke in 15.47% the mximum volte. As it n e seen in Fi. 7, the spe vetor trjetory referened to the neutrl point n is the expeted lned system irle. However, referenin to the DC-link midpoint o, it n e seen how tkes more profit of the DC-link y usin the Zero Sequene omponent. Fi. 7: Mximum spe vetor trjetory referened to the DC-link midpoint, y usin SVPWM. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.6 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

7 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Spe vetor dominion fter phse-neutrl short-iruit The three-phse inverter spe vetor dominion fter sinle-phse short-iruit is prtil to understnd the four-phse inverter. After short-iruit etween the phse nd the neutrl point n, the onverter sttes referened to o of () eome referened to n s E n i = E o i u o (5) where u o = u o (1,1,1) (6) Then, the spe vetor dominion shown in Fi. 8 is otined. The onverter sttes suffer displement throuh the n diretion, to plne Π { = 0}. In other words, i-dimensionl spe ppers s onjuntion of two i-phse dominions (squres). One represents when the inverter onnets the shortiruited phse to the netive DC-link point nd the other when it is onneted to the positive one. Fi. 8: Three-phse inverter volte sttes fter mono-phse short-iruit. Spe vetor of four-le inverter Anlysin the four-le inverter showed in Fi. 1() in the sme wy s the three-le one, two senrios n lso e extrted: the spe vetor onsiderin s referene the midpoint of the DC-link o nd the spe vetor onsiderin s referene the AC neutrl point n. Spe vetor dominion on DC-link midpoint referene Considerin the DC-link midpoint referene, it n e ssumed tht the spe vetor s R 4 due to its four derees of freedom. Then the inverter sttes of Tle II onform the sixteen verties of hiperue or tessert in the tetr-dimensionl spe whih ede is equl to the volte pplied t the DC-link side. Fi. 9 shows projetion of these sixteen sttes under the sttionry d frme. 3 4 d 5 V8 V9 1 0 Fi. 9: Four-phse inverter volte sttes referened to the DC-link midpoint, in d frme. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.7 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

8 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Spe vetor dominion on AC neutrl point referene Considerin the neutrl point n s referene, one deree of freedom is lost. It this se, the reson is delierted short-iruit etween the d phse nd the AC neutrl point n. At this point, the nlysis of the phse to neutrl short-iruit forementioned eomes helpful. Mkin n nloy of wht hppens in the three-dimensionl dominion to the four dimensionl se, the four-le onverter sttes n e drwn in three-dimensionl spe. Assumin the onverter sttes vetors referened to o s E o i =(u o,u o,u o,u do ) (7) these n e referened to n s E n i = E o i u do (8) where u do = u do (1,1,1,1) (9) Then, the fourth dimension is nelled nd the spe vetor dominion of Fi. 10() is otined. Converter sttes suffer displement throuh the four-dimension homopolr vetor m =(1, 1, 1, 1) to volume Ω {d = 0}. In other words, three-dimensionl spe ppers s onjuntion of two threephse dominions (ues). One represents when the inverter onnets the short-iruited phse to the netive DC-link point, nd the other when it is onneted to the positive DC-link point V8 0 V9 V8 V9 3 4 () 3D view. 5 () (1,1,1) view. 4 Fi. 10: Four-phse inverter volte sttes referened to the AC neutrl point. As it n e seen in Fi. 10(), lso in Fi. 3, there exists two ZSV ( nd 5) whih hve null spe vetor referened to n. More over, there lso exists two NZSV ( nd V8) whih re only le to enerte homopolr omponent. Finlly, there exists twelve NZSV ple to enerte spe vetors projetions in the Π plne. As it n e seen in Fi. 10(), in order to enerte lned systems, the four-le inverter is similr to the three-le one. Nevertheless, four-le hve two SV for eh Π stte, one with positive homopolr nd the other in netive. Thus, four-le inverters wveforms will hve less hih frequeny swithin hrmonis, prt from hiher pility to produe homopolr ontent. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.8 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

9 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr Controllility reion One nlysed the spe vetor dominion, it is importnt to hihliht tht in terms of ontrollility, it is not 100% usle [6]. The onverter output voltes hve two omponents: one lre omponent tht mthes the output volte nd seond inrementl one used to mne the output urrent. Then, in order not to hve ontrollility hnes throuhout the volte phse, the spe vetor dominion is onstrined to symmetril reion in respet with the n diretion. Fi. 11() shows the ontrollility limit in lue, for three-le three-phse inverter (Fi. 1()). It is irle tht enlose the i-dimensionl spe vetor dominion referened to the AC neutrl point. Fi. 11() shows the ontrollility limit in lue, for three-le split pitor inverter (Fi. 1()). It is the union of two ones tht enlose the three-dimensionl spe vetor dominion referened to the AC neutrl point. Fi. 11() shows the ontrollility limit in lue, for four-le inverter (Fi. 1()). It is ylinder losed y two ones, tht enlose the three-dimensionl spe vetor dominion referened to the AC neutrl point. () Three-le threephse inverter. () Three-le split pitor inverter. () Four-le three-phse inverter. Fi. 11: Spe vetor ontrollility limits dependin on the topoloy. Overlyin the ontrollility reions on Fi. 1, some differenes of the prinipl three-phse inverter topoloies (Fi. 1) n e hihlihted. Fi. 1: Overlyin the three-phse spe vetor ontrollility limits. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.9 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)

10 Understndin the three nd four-le inverter Spe Vetor LLONCH-MASACHS Mr The three-le three-phse inverter n hve ood utiliztion of the ville DC-link due to the volte vetor projetions on the αβ plne. Therefore, it n enerte lrer output voltes (up to 15.47% more, if usin SVPWM), not ein le to otin homopolr omponent. The three-le split pitor inverter nnot use SVPWM, then it n enerte lower voltes thn the previous one. The fourth wire mkes possile the homopolr urrent, tht n unlne the DC-link. The four-le three-phse inverter hs the mjor ontrollility reion. It n synthesise lned voltes, in the αβ plne, s lrer s the three-le three-phse inverter. Furthermore, it n lso enerte unequl voltes with lrer homopolr omponent thn the three-le split pitor, without unlnin the DC-link. Conlusions This pper hs exposed the influenes of the volte referene nd the three nd four-le inverter topoloies on the spe vetor dominion. It hs iven wider point of view of the spe vetor trjetories throuh its n-dimensionl spes, useful to understnd the strenths nd weknesses of different modultion strteies. It hs een shown the inverter volte sttes referened to the DC-link nd to the AC neutrl point. Then it hs lso een presented the differenes etween SPWM nd SVPWM on its spe vetor trjetory. Finlly, the ontrollility limits hs een plotted nd ompred to ive rphil pereption of different inverter topoloy pilities. Referenes [1] H. Aki, Y. Tsukmoto, nd A. Ne, Anlysis nd desin of n tive power filter usin qudseries volte soure PWM onverters, Industry Applitions, IEEE Trnstions on, vol. 6, no. 1, pp , [] J. W. Kolr, E. R. T. L. Hns, nd C. Zh, Influene of the modultion method on the ondution nd swithin losses of pwm onverter system, vol. 1, no. 6, pp , [3] P. Enjeti nd B. Xie, A new rel time spe vetor PWM strtey for hih performne onverters, Conferene Reord of the 199 IEEE Industry Applitions Soiety Annul Meetin, no. i, pp , 199. [4] G. C. Pp, Symmetril Components in the Domin nd Their Applition to Power Network Clultions, IEEE Trnstions on power systems, vol. 15, no., 000. [5] R. Zhn, V. H. Prsd, D. Boroyevih, nd F. C. Lee, Three-dimensionl spe vetor modultion for four-le volte-soure onverters, IEEE Trnstions on Power Eletronis, vol. 17, no. 3, pp , 00. [6] D. Shen nd P. Lehn, Fixed-frequeny spe-vetor-modultion ontrol for three-phse four-le tive power filters, IEE Proeedins - Eletri Power Applitions, vol. 149, p. 68, 00. EPE'16 ECCE Europe ISBN: nd CFP16850-USB P.10 ssined jointly to the Europen Power Eletronis nd Drives Assoition & the Institute of Eletril nd Eletronis Enineers (IEEE)