A Dual Three-Phase Drive System with a Reduced Switch Count

Transcription

1 Page of 8 A Dual ThreePhase Drve System wth a Reduced Swtch Count E. Ledezma A. MuñozGarca T. A. Lpo Department of Electrcal and Computer Engneerng Unversty of Wsconsn Madson 45 Engneerng Drve Madson, WI USA AbstractA dual CRPWM VSI based on multple twophase PWM nverters, also called a B4 topology, requrng a dual threephase drve system wth reduced swtch count s proposed. The drve utlzes a total of only eght swtches to produce two sets of threephase snusodal output currents. Ths new scheme mnmzes the snglephase current flow through the DClnk capactors, whch s a common problem n reduced swtch count topologes. By controllng the phase and magntude of the currents generated by each nverter t s possble to cancel out the snglephase current flow through the DClnk capactors. The paper presents a mathematcal model of the proposed dual motor drve system ncludng a control strategy that mnmzes the capactor s voltage varatons and the snglephase current flow through the DClnk capactors. In order to verfy the performance of the proposed drve system, an applcaton on tracton of an electrc vehcle s carred out. The smulaton results show that the snglephase current flow through the DClnk can be elmnated or mnmzed when the vehcle moves n a straghtlne regme, turnng regme, or slppage condton. I. INTRODUCTION Due to the advances n power electronc technology, varable frequency AC drves are presently beng broadly appled. Tradtonal AC drves are based on a threephase nverter that s used to feed an nducton motor; thus, a total of sx swtches are requred. Reducng the number of actve swtches s desrable n applcatons where low cost, mproved relablty and less conducton loss s of mportance. Due to ts many advantages, a number of studes have been conducted utlzng a reducedswtch count structure. For nstance, a twophase topology usng a splt DClnk capactor and requrng only four swtches was ntroduced n []. In addton, n [] a B4 nverter employng only four swtches s proposed as a vable alternatve compared to the conventonal sxswtch converter. A detaled analyss of the harmonc losses and torque pulsatons produced by a fourswtch voltage controlled topology was carred out by Van Der Broeck et.al. [,3]. Ths analyss showed that both copper losses and torque pulsatons could be greatly reduced by nstantaneously controllng the tme shft between the two voltage pulses durng the pulse perod. A threephase to threephase VSI PWM rectfernverter scheme wth eght swtches was proposed n [4]. Ths topology had the capablty of delverng snusodal nput currents wth unty power factor and bdrectonal power flow. The problem of voltage fluctuaton n the DClnk, however, s a potental lmtaton for ths eghtswtch structure. Drawbacks of the reducedswtch topologes also nclude ncreased voltage stress on both the power devces and the nducton motor, ncreased swtchng losses due to a hgher DClnk voltage, and snglephase crculatng currents through the DClnk capactors [5]. The problem of snglephase crculatng currents through the DClnk capactors s also addressed n [6]. A comparatve study of a reducedswtch drve structure was conducted and appled to moble robot motorzaton n [7]. However, the problem of the snglephase currents was not addressed, whch s a common lmtaton of reducedswtch count topologes. In addton, the exstence of large DClnk voltage varatons due to, among other causes, the crculaton of snglephase currents through the DClnk capactor was dscussed n [8], although a soluton was not gven. In ths paper a new dual AC drve system that mnmzes the snglephase current flow through the DClnk capactors, thus elmnatng ther voltage varaton and extra losses, s ntroduced. The proposed drve system uses two fourswtch nverters connected back to back whch share a sngle splt DClnk capactor. The nverters are used to feed two nducton motors that operate at the same fundamental frequency wth a smlar current level. To verfy the performance of the proposed drve system, an applcaton on tracton of an electrc vehcle s carred out. A mathematcal model of the proposed AC drve s derved and appled through smulaton. II. SYSTEM CONFIGURATION AND PRINCIPLE OF OPERATION The proposed drve system s schematcally shown n Fg.. The drve conssts of dual twophase nverters connected back to back wth a common DC bus, thus requrng only eght swtches nstead of the conventonal twelve. The load corresponds to two nducton machnes that are fed from each nverter. It s assumed that the phase and magntude of the load currents can be ndependently adjusted and that each nverter s operated under current control usng hysteress regulators. It s also assumed that the DC bus voltage s suppled by a rectfer (not shown for smplcty) /98/$0.00 (c) 998 IEEE

2 Page of 8 In a twophase nverter topology two of the machne s phases are connected to two poles of the nverter and the thrd phase s connected to the center pont of the DClnk. Because there s no neutral connecton and two of the lne currents are regulated, the current through the thrd lne s also regulated (snusodal). Ths confguraton creates a snglephase current flow through the capactors n the DClnk. By connectng a second twophase nverter to the same DC bus t s possble to compensate for the snglephase current n the capactors. Ths s acheved by adjustng the relatve phase angle of the currents n the two nverters. In order to elmnate the snglephase current, the relatve phase of the currents n each nverter must be 80 degrees out of phase. The current through C n Fg. s gven by cap = cs zs cap () where cs and zs are the lne currents and cap s the current through C. From () t can be noted that f cs has the negatve value zs, then cap wll be equal to cap. Therefore, they wll total zero. As a consequence, the effectve crculatng current through the DClnk capactors wll be deally zero. To develop actvely ths control strategy, the space complex vector dqo approach s utlzed. III. CONTROL STRATEGY TO MINIMIZE THE DC LINK SINGLEPHASE CURRENT CAPACITORS In (), to mnmze the snglephase crculatng current through the DClnk capactors, the lne currents cs and zs must be 80 degrees out of phase. Ths s accomplshed by choosng the current references for nverter as follows: as = cos θ q rf d sn θrf () bs = cos( θ q rf 0 ) d sn θrf, (3) where s the torque command, and s the flux q d command n the synchronous reference frame. In the same fashon, the current references for nverter are chosen as xs = qrot cos θrf _ drot sn θrf (4) ys qrot rf drot rf = (cos θ 0 ) (sn θ 0 ). (5) In (4) and (5), qrot and drot are chosen such that qrot = cos φ sn φ q d drot = sn φ sn φ, (7) q d where q (6) and are the torque and flux commands for e d nducton machne. In (6) and (7), the angle φ s determned as ndcated n the block dagram of Fg.. Here, qs, ds, qs and ds are the nputs measured stator currents n the statonary reference frame. The currents are transform to the synchronous reference frame utlzng the flux rotor poston θ rf n both transformatons n order to have the currents referred to a common frame of reference. After the transformatons, the new currents e e q, d, e d and e q referred to the rotor flux frame of nducton machne are obtaned. The poston of the complex current vector for nducton machne, φ, and nducton machne, φ, are calculated utlzng the complex current components. Angles φ and φ become e q φ = a tan e (8) d θrf Inducton M otor ac bs cs C cap zs cap C y s xs Inducton Motor qs ds Coordnate Transformaton/ Angle Calculaton PI φ as bs Current Fg.. Reduced swtch count threephase dual drve. xs y s qs φ φ ds Coordnate Transformaton/ Angle Calculaton θrf φ Fg.. Actve calculaton of the rotaton angle φ /98/$0.00 (c) 998 IEEE

3 Page 3 of 8 e q φ = a tan e. (9) d q q Fg. shows the actve calculaton process of the rotaton angle φ. The error φ φ = φ s calculated and compared to π and further processed through a PItype controller. The actual angle φ s found as φ I I d d φ = t K p φ ( π φ) K φ ( π φ) dt. (0) 0 d rot I rot Angle φ, when used n (6) and (7), has the property of rotatng the complex current vector I to be 80 degrees out of phase wth respect to the complex current vector I. Ths rotaton process s shown graphcally n Fg. 3. Here, the new poston of the complex current vector of nducton machne, I rot, s accomplshed by rotatng the complex vector I by φ degrees. The reference frame of nducton machne remans fxed because the rotor flux angle θ rf was selected as the reference. In Fg. 3 there are three dfferent reference systems: q d, whch defnes the poston of nducton machne, q d, whch defnes the poston of nducton machne, and q rot d rot, whch defnes the new poston of the machne. Thus, t can be noted that n ths new poston, the complex current vectors I and I are 80 degrees out of phase. Ths an mportant result because f I and I have smlar magntudes, whch s possble durng normal drve operaton, the elmnaton of the snglephase current through the DClnk capactors can be acheved accordng to (). Once φ s calculated by the PItype controller n (0), t s utlzed to generate the proper sets of reference currents n (4) and (5) for nducton motor. q rot Fg. 3.Rotaton of the reference frame of motor by φ degrees wth respect to the reference frame of motor. IV. TRACTION APPLICATION OF THE PROPOSED DUAL DRIVE SYSTEM Fg. 4 llustrates the general block dagram for the controls of the proposed drve system. The controls for nducton motors and are developed utlzng Indrect Feld Orented (IFO) control n the synchronous reference frame [9]. For an electrc vehcle tracton applcaton, three drvng stuatons are of nterest: ) the straght lne regme, where both motors operate at the same speed, ) the turnng regme, where each machne operates at dfferent speeds, and 3) slppage, where one of the nducton motors holds almost zero load torque [0]. θ rf PI q Indrect Feld Orented as bs cs CRPWM IM Velocty Command Gear Rato φ d θ rf ω r ω r PI q j e φ qrot drot Indrect Feld Orented xs ys zs CRPWM IM ω r d Fg. 4. General block dagram for the control of the proposed drve system /98/$0.00 (c) 998 IEEE

4 Page 4 of 8 A. Angular veloctes of the two nducton motors In the block dagram of Fg.4, t s assumed that the vehcle total velocty (v) s mantaned constant durng each manuever. Then, the torque commands for the IFO control are produced by selectng the desred speed for the vehcle. Each nducton motor of the proposed drve s utlzed to drve one of the wheels of the tracton axle. The angular speed for each motor depends on the type of drvng regme selected. For the straght lne regme, the angular speeds for each motor become v ω r = ω r =. () Rw For the turnng regme, the angular speeds for each motor are dfferent and expressed as ω ω r r v = W R Rw W R v =. W R Rw W R () (3) Note that from (3) that the angular speed of nducton motor wll be larger than the angular speed of nducton motor. B. Speed control of motor drve The torque command for nducton motor s generated by a PI controller, whch mantans constant speed under any load torque. The flux command becomes q K ( ) w ( ) = K pw r r r. (4) r p A constrant n the operaton of the drve s that both motors must operate at the same frequency n order to mnmze the ac current n the lnk capactors. Fg. 5 shows the block dagram to determne the flux command for nducton motor. To mantan the same frequences n both nducton motors, the necessary amount of flux d s determned by the followng expresson: d = Kpf K ( ) f ω ω ( ω ω ) (5) e e e e p ωe ωe PI I qnom q Fg. 5.Block dagram for generaton of the flux command for nducton motor, to mantan the same frequency n both machnes. Then, the dfferental flux d s added to the nomnal flux of nducton motor. The fnal expresson for the flux command becomes d d Idnom = (6) where ωe s the frequency of nducton motor and ω e s the frequency of nducton motor. C. Speed control of motor drve The speed control for nducton motor nvolves the generaton of the torque command to mantan constant velocty. Its expresson n the synchronous reference frame s K = Kp ( ) ω r ωr ( ω r ωr). (7) q p The flux command,, s mantaned constant n ts d nomnal value, 6 A. Both the flux and torque commands must be appled wth negatve sgns. Ths wll accomplsh an outofphase angle of 80 degrees between the respectve stator currents of both nverters. The strategy of elmnatng the snglephase current through the DClnk capactor s also contaned n the control of nducton motor, as seen n Fg. 4. V. SIMULATION RESULTS The proposed drve system has been smulated assumng two dentcal nducton motors operatng at the same fundamental frequency. In all smulatons except the slppage condton, the nducton motors operate under smlar loads. The focus of ths study s the analyss of the behavor of the DClnk crculatng current through the /98/$0.00 (c) 998 IEEE

5 Page 5 of 8 capactors as the vehcle performs basc maneuvers. Therefore, for smplcty, the necessary torque to accelerate the vehcle and the torque to overcome the road load are modeled by a step torque. Three basc drvng stuatons are smulated: straghtlne, turnng, and slppage. Prmarly, the proposed drve system s smulated wthout control to mnmze the DClnk capactor currents. A. Operaton of the proposed drve wthout capactor current control Fg. 6 shows the current and voltage through DClnk capactor when the system s operatng wthout any control. The crculaton of snglephase currents s clearly seen. The current rses as hgh as the current of phase c (.4 Apeak). In addton, due to ths large capactor current, large voltage oscllatons can be seen through capactor (60 Vpeak). The same effect s produced n capactor. Wthout utlzng any control method to reduce the voltage and current varatons, the sze of the DClnk capactors would ncrease. Due to the ncrease n loss and larger capactors, ths would have a drect mpact n the weght and cost of the drve. Therefore, the snglephase current flow n the DClnk must be elmnated or mnmzed for a practcal applcaton of the drve. Fg. 6.Operaton of the proposed drve system wthout control. B. Straghtlne Regme Durng straghtlne drvng operaton, each nductor motor operates wth dentcal speeds as gven by (). Fg. 7 llustrates the current through capactor. The smulaton s carred out wth a load of 4 N.m on each nducton motor and a total vehcle velocty of 0 mph. It can be seen that at less than seconds, the current reaches ts steady state value. At ths pont, the current and voltage varatons of the capactor have been fully elmnated. Fg. 8 demonstrates that f the load torque (rated torque) appled to each machne s ncreased, the mnmzaton technque contnues to be vald. Here, also, the current and the voltage through the capactor are free of oscllatons n the steady state. Accordng to (), to elmnate the currents through the DC capactors, cs and zs must total zero. In addton, these currents must have smlar magntudes. Fg. 9 exhbts the currents of phase c and phase z. It can be seen that the current zs ncreases ts phase untl t becomes 80 degrees out of phase wth respect to the current n phase c. Ths rotaton s actvely accomplshed by feedng the angle gven by (0) nto the general block dagram of Fg 4. Because an electrc vehcle wll perform prmarly n the straghtlne regme, n whch there s complete elmnaton of the DClnk capactor currents, the proposed drve system s attractve for ths tracton applcaton. Fg. 7.Straghtlne regme: DClnk capactor current wth the same load (4 N.m) and same speed (36 rad/sec) n both motors /98/$0.00 (c) 998 IEEE

6 Page 6 of 8 Fg. 8.Straghtlne regme: DClnk capactor voltage and current ( N.m, 36 rad/sec for both motors). (a) Fg. 9. Straghtlne regme: current of phase c and z, 80 out of phase C. Turnng Regme It s clear that the speeds of the motors are dfferent for the turnng condton. Gven the total speed of the vehcle, the angular veloctes of the motors are determned by () and (3). Fg. 0(a) shows that the proposed drve s capable of operatng at dfferent speeds and elmnatng the snglephase current flow, as shown n 0(b). For ths case, each nducton motor operates wth the same load torque (rated torque), and due to the restrcton of equal frequency, each nducton motor must operate wth dfferent slp and speed. In sum, the turnng regme smulatons demonstrate that when both motor drves are operated approxmately wth the same current level, the problem of snglephase crculatng current through the DClnk and voltage fluctuatons can stll be elmnated. It was found that asde from the dfference n phase, the correspondng lne current phases (e.g., c and z) reman nearly the same ( A dfference) for ths condton. Ths represents a reducton of approxmately 9% of the current through the capactors wthout any control. (b) Fg. 0. Performance of the proposed drve system when operatng under dfferent speeds and same load torque ( N.m): (a) the two motor speeds, (b) current and voltage capactors. D. Wheel Slppage One specal operatonal condton for the drve s when one of the wheels has full tracton and the other has lost almost all tracton capablty. Ths operatonal condton, though a rare drvng stuaton, s mportant to analyze n order to determne the lmtatons of the drve. The smulaton of wheel slppage s accomplshed by applyng N.m on motor and N.m on motor. Durng the slppage condton, t s assumed that the vehcle s turnng wth a curve radus of 4.8 meters at a constant speed of 0 mph. Fg. llustrates the capactor /98/$0.00 (c) 998 IEEE

7 Page 7 of 8 APPENDIX A Fg.. Response of capactor and phase currents a and x durng wheel slppage. current and voltage durng the slppage operaton. The currents of phase a and phase x are also shown. Due to the dfferent load torques, t was found that the current n phase x becomes 3 A larger than the current of phase a. As a result, the dfference n phase currents appears n the DClnk, whch represents approxmately 5% of the current of the DClnk wthout control. Thus, the voltage oscllatons are approxmately 50% of the actual value wthout control. Although the elmnaton of the crculatng current through the DC capactor s not complete, 75% of the current s elmnated, compared to the case wthout control. Ths drvng stuaton also would be a worst case scenaro for the operaton of the proposed drve system. VI. CONCLUSIONS A dual threephase motor drve system based on multple twophase PWM nverters has been proposed. The proposed drve system s capable of elmnatng the snglephase crculaton current through the DClnk capactors. It has been shown that the elmnaton of the snglephase current, when appled to electrc vehcle tracton n the normal drvng regmes, can be acheved by controllng the phase angle of the commanded currents to each nverter. Ths s accomplshed wthout any addtonal hardware to that requred for normal operaton. The elmnaton of the crculatng current reduces the overall losses, elmnates DC voltage varatons and has relevant mpact n reducng the cost and weght of the drve. An approprate control model for vehcle tracton applcaton has been developed and smulated, demonstratng that the proposed drve system s a sutable alternatve to conventonal sx swtch nverter drves. as reference current phase a bs reference current phase b xs reference current phase x ys reference current phase y q torque command, motor q torque command, motor d flux command, motor d flux command, motor I magntude current, motor I magntude current, motor I qnom nomnal value of q θ rf rotor flux poston, motor θ rf rotor flux poston, motor p dfferental operator d/dt angular speed, motor ω r angular speed, motor angular speed reference, motor ω r angular speed reference, motor Machne Parameters 3 Hp, 3φ L m =0.070 H 0 V L r =0.07 H 8.08 A L s =0.07 H 4poles r r =0.8 Ω I qnom =6 A r s =0.50 Ω Parameters K p φ=3.0 K p φ=8.0 K pw =5.0 K w =.8 K pf =0.0 K f =.5 K p =.0 K =.5 R=4.8 m v=0 mph W=.5 m R w =0.3 m APPENDIX B APPENDIX C /98/$0.00 (c) 998 IEEE

8 Page 8 of 8 REFERENCES [] J. F. Eastham, A. R. Danels, and R. T. Lpcynsk, A novel power nverter confguraton, n Conference Records IEEE/IAS Annual Meetng, pp , 980. [] H. W. Van Der Broeck and J. D. Van Wyk, A comparatve nvestgaton of a threephase nducton machne wth a component mnmzed voltagefed nverter under dfferent control optons, IEEE Transactons on Industry Applcatons, vol. IA0, no., pp , March/Aprl 984. [3] H. W. Van Der Broeck and H. C. Skudelny, Analytcal analyss of the harmonc effects of a PWM ac drve, IEEE Transactons on Power Electroncs, vol. PE3, no., pp. 63, Aprl 988. [4] G. T. Km and T. A. Lpo, VSIPWM rectfer/nverter system wth a reduced swtch count, IEEE Transactons on Industry Applcatons, vol. IA3, no. 6, pp , Nov./Dec [5] F. Blaabjerg, S. Freysson, H.H. Hansen, and S. Hansen, A new optmzed space vector modulaton strategy for a component mnmzed voltage source nverter, Appled Power Electroncs Conference and Exposton, vol., pp , 995. [6] F. B. Blaabjerg, D. Neacsu, and J. K. Pedersen, Adaptve SVM to compensate dclnk voltage rpple for component mnmzed voltage source nverter," Proceedngs on IEEE PESC, pp , 997. [7] A. Bouscayrol, M. PetrzakDavd, and B. de Fornel, Comparatve studes of nverter structures for a moble robot asynchronous motorsaton, IEEE Internatonal Symposum on ndustral Electroncs, pp , 996. [8] G. T. Km and T. A. Lpo, DC Lnk voltage control of reduced swtch VSIPWM rectfer/nverter system, Proceedngs of the IECON 97, vol., pp , 997. [9] D. W. Novotny and T. A. Lpo, Vector Control and Dynamcs of AC Drves, Oxford: New York, 997. [0] P. M. Kelecy, Control methodologes for sngle nverter, dual nducton motor drves for electrc vehcles, Ph.D. Dssertaton, Unversty of WsconsnMadson, /98/$0.00 (c) 998 IEEE