Model Reference Current Control of a Unipolar Induction Motor Drive

Transcription

1 IEEE IAS Annual Meetng Page 1 of 7 Chcago, Illnos, September 3 October 4, 21 Model Reference Current Control of a Unpolar Inducton Motor Drve Bran A. Welchko Unversty of Wsconsn Madson 1415 Engneerng Drve Madson, WI 5376, USA Thomas A. Lpo Abstract A control algorthm to yeld the requred current shapng control of a three actve swtch, three-phase unpolar drve system for an nducton motor s derved n ths paper. The method utlzes termnal voltage control through PWM to properly shape the phase currents. Phase voltages are calculated based on both the fundamental frequency and zero sequence steady-state equvalent crcuts of an nducton machne to acheve the desred speed and load set pont. Snce ths method reles on characterzng the machne parameters, t does not requre feedback of the phase currents, and therefore, drve systems usng ths method for ths topology can elmnate three current sensors over tradtonal hysteretc current control methods. Both smulaton and expermental results are ncluded to verfy the proposed termnal voltage control method on ths potental low cost varable speed topology for ntegrated motornverter products. F I. INTRODUCTION OR MANY years, the low voltage varable speed nducton motor drve has been centered on the standard 6-swtch nverter (B6) topology. Whle ths crcut delvers unparalleled performance, ts hgh cost has been a hndrance for adopton of varable speed drves n the consumer marketplace. Snce the cost s a prncple drver n the fractonal to ntegral horsepower market, nverter topologes wth fewer than sx actve swtches can add sgnfcant value to applcaton specfc products where the cost of a standard nverter topology cannot be justfed [1]. Two such topologes that have receved the attenton of researchers are the B4 nverter topology wth four IGBT swtches [2 3], and the delta nverter [4], whch uses only three IGBT swtches. Whle the delta nverter s mpractcal snce t requres three solated dc busses, a new three actve swtch topology presented n [5] shows promse as a vable canddate for ths marketplace snce t delvers true varable speed performance wth a mnmum swtch count and uses a low cost dode voltage doubler rectfer front end. Ths paper develops a new control algorthm for ths topology n whch the requred current shapng control s acheved va termnal voltage control. Ths new control method s sgnfcant because t requres no current sensors, whle the control method demonstrated n [5] requred three current sensors as t employed a smple hysteress current controller. As a result, ths unpolar topology usng the proposed control method, could acheve sgnfcant cost reducton over the conventonal B6 or B4 nverters whle mantanng all the benefts of varable speed performance. II. INVERTER OPERATING PRINCIPLE The unpolar drve system for a three-phase nducton machne s shown n Fg. 1. Ths topology conssts of three phase legs each wth an IGBT type swtch and dode n a shoot-through free leg structure. The topology s asymmetrcal n nature as one of the actve swtches s connected to the postve dc ral and the other two are connected to the negatve dc bus. The dc lnk of ths system s obtaned va a voltage doubler type dode rectfer. Ths lnk arrangement represents the lowest cost soluton to provde the requred splt capactor dc bus. Ths topology requres a non-standard three-phase nducton machne. Whle dfferent, ths machne can be obtaned smply by externally rewrng the wndng connectons of a standard nducton machne wth a dual wound stator wndng. Machnes that are capable of operatng from two dfferent voltages are n ths category provded all twelve of the stator leads are avalable. The converter operates by controllng the machne phase currents to the shape of the currents shown n Fg. 2. These dc, or unpolar, currents consst of a fundamental component and a zero sequence component made up of a dc offset and trplen harmoncs as shown n Fg. 3. The addton of the zero sequence does not produce any useful torque, but makes the currents undrectonal, so the smpler nverter leg structure wth only one swtch per phase can be used. One of the phase legs (phase b n Fg. 1) must be reversed n ths topology n order to create a dscharge path for both of the lnk capactors. Ths reverses the drecton of current flow n ths leg, hence the reversal of the magnetc polarty of that motor phase n order to mantan the same rotatonal drecton of the motor flux. The current n ths reversed V s I s V c1 - n V c2 - N turns.5n turns N turns Asymmetrc IM wth Stator Neutral Access Fg. 1: Unpolar drve topology for an nducton machne. a b c

2 IEEE IAS Annual Meetng Page 2 of 7 Chcago, Illnos, September 3 October 4, b v v Z L Z L Ampltude (per unt).6.4 a c.2 I sw I sw Angular Poston (degrees) Fg 2: Requred shape and magntude of the motor phase currents for a unpolar nducton machne drve. (a) (b) Fg. 4: Current-voltage plane of a half-controlled phase leg (a) and a full controlled phase leg (b). R 1 L 1 v g L 2 R zs v 1 1 L m _ 2 R 2 S v z _ z L zs Fg. 3: Phase current harmonc spectrum for current wth ampltude 1. phase must also be double that of the other two phases n order to mantan an even dscharge of the lnk capactors. To create an equal contrbuton n ampltude to the motor flux, the number of turns n ths phase must be halved to mantan a constant number of ampere-turns n the motor. Essentally ths requres that the phase a and c wndngs be connected n seres whle the phase b wndngs are connected n parallel and reversed n magnetc orentaton. III. TERMINAL VOLTAGE CONTROL The phase leg structure of ths topology s half-controlled. Fg. 4(a) shows the current-voltage plane n whch each phase leg can operate whle mantanng control. Ths s n contrast to the fully controlled phase legs of a standard nverter as shown n Fg. 4(b). As a result, through approprate PWM technques, ths topology can mpress any voltage on the phase load, provded the current s greater than zero. The requred voltage to produce the desred phase currents can be obtaned from knowledge of the phase current harmonc spectrum and the steady state equvalent crcut (a) (b) Fg. 5: Inducton machne steady-state equvalent crcuts: (a) fundamental frequency, (b) zero sequence. model of the nducton machne shown n Fg. 5. Fg. 5(a) shows the fundamental equvalent crcut and 5(b) shows the zero sequence equvalent crcut where L zs s the zero sequence nductance and R zs s the zero sequence resstance. R zs s typcally taken to be equal to the stator resstance whle L zs s consdered to be some percentage (8 95%) of the per phase leakage nductance, L 1, due to saturaton effects. [8]. For purposes of ths paper, core losses n the machne have been neglected. Table I gves the phase current defntons n terms of a pecewse combnaton of sne waves. Table II gves the Fourer harmonc components of the phase a current defned n Table I and Fg. 2. Note that n ths table, the ampltude of the harmonc components has been normalzed to that of the fundamental. Snce the steady state per phase model of the nducton machne s a lnear tme nvarant system, the net requred appled termnal voltage can be obtaned by supermposng the ndvdual harmonc voltages requred to produce the desred harmonc current. TABLE I PHASE CURRENT DEFINITIONS OVER AN ELECTRICAL CYCLE Current Angular Poston < ωt < ωt < ωt 36 Phase a ( a) I maxsn(ωt) I maxsn(ωt π/3) Phase b ( b) 2I maxsn(ωt 2π/3) 2I maxsn(ωt) Phase c ( c) I maxsn(ωtπ/3) I maxsn(ωt 4π/3)

3 IEEE IAS Annual Meetng Page 3 of 7 Chcago, Illnos, September 3 October 4, 21 Table II PHASE a CURRENT FOURIER HARMONIC COMPONENTS Harmonc Number (n) Ampltude (per unt) Phase Angle Ψ n ( ) T em T R T em where the subscrpt pk ndcates a peak, as opposed to rms, quantty. For the gven load, (3) can be solved for the requred rotor current as 2pk = 2 3 ( Sω e ) Tem 1 (4) R 2 The requred ar-gap voltage s then calculated as v g-pk R 2 S jω e L 2 2pk (5) = where boldface font ndcates that the quantty contans both magntude and phase nformaton. Usng (4) and (5) along wth the fundamental frequency equvalent crcut, the fundamental frequency stator current s 1pk = 2pk v g-pk (6) jω e Lm ω R Sω er ω r Equatons (5) and (6) can then be used to gve the fundamental frequency phase voltage. Ths s Fg. 6: Steady-state torque and slp frequency relatonshp. A. Fundamental Voltage Calculatons For the target applcaton for ths drve of fan-type load where the load torque s proportonal to the square of the speed, ω r, the load n the steady state wll always be less than or equal to the rated motor torque, T R. Hence, t can be assumed that the developed motor torque, T em, wll vary lnearly wth slp frequency, Sω e, as shown n Fg. 6 [6 7]. For a gven load, T em, the requred slp frequency can be found va nterpolaton as T em Sω er ( Sω e ) = (1) T R The correspondng exctaton frequency s then ω e = ω r ( Sω e ) where ω r s the desred rotor speed. One expresson for the developed torque of an nducton machne s (2) pk R2 T em = (3) Sω e v 1pk = ( R 1 jω e L 1 ) 1pk v g-pk (7) Equaton (7) gves the fundamental frequency phase voltage requred to produce the desred load torque and speed. B. Zero Sequence Voltage Calculatons Once the ampltude and phase of the torque producng fundamental s solved usng the technques of the precedng secton, the zero sequence currents can be found from Table II as they are algebracally related to the fundamental from the Fourer analyss of the desred wave shape. The zero sequence voltage to produce the zero sequence currents can be calculated from the crcut of Fg. 5(b) as ( ) v z-pk = R zs jω e nl zs z(n)-pk (8) (n=,3,6, ) where n represents the harmonc number of the zero sequence current. The 18 th harmonc ampltude s only.5% of the fundamental, so, n practce, lttle beneft would result from ncludng more harmoncs n the zero sequence voltage calculaton. When usng (8), t s mportant to account for the phase dsplacement of the harmoncs to the fundamental (6 ) as shown n Table II n addton to the calculated fundamental phase angle n (6). The net requred appled phase voltage to produce the desred phase current ampltude and shape s obtaned by

4 IEEE IAS Annual Meetng Page 4 of 7 Chcago, Illnos, September 3 October 4, 21 superposton of the fundamental voltage (7) and the harmonc voltage (8) as v ph = v 1pk v z-pk. (9) Equaton (9) gves the requred appled phase voltage for the proposed control algorthm. However t does not account for the asymmetry of the nducton motor requred for ths topology. As a result, reversal of one phase polarty and change n ampltude for that phase must be accounted for when (9) s mplemented. For example, f (9) was calculated usng motor parameters of the hgh voltage phases (a and c), the phase b voltage must be reversed n polarty and halved n magntude to account for the connecton of the two phase b wndngs n parallel. IV. SIMULATION RESULTS To verfy the proposed algorthm a typcal fan load was smulated usng SIMULINK, wth data post-processng n MATLAB for a 1 hp nducton motor drven by an deal unpolar nverter topology. Parameters for the motor used for the smulaton are gven n the Appendx. Fg. 7 shows the control system block dagram that was used for the smulaton. Snce the proposed control algorthm was based on the steady state equvalent crcut model of an nducton machne, speed changes should be mplemented DC offset feedforward slowly so that the machne s n quas-electrcal steady state and the model s vald. For the target ar movng applcaton, ths poor transent performance s not detrmental snce the system wll change speeds nfrequently and a slow response wll hardly be notced. For a smooth transton, both jerk and acceleraton lmts were mposed on the system. Snce the phase leg structure of the unpolar nverter s only capable of controllng a postve current, an addtonal dc offset s added durng speed transents so that even wth parameter errors, the motor wll be able to draw the requred fundamental current to accelerate the load. Once steady state s reached, the dc offset s set back to that calculated n Secton III. Usng ths mnmum dc offset wll allow the topology to operate at ts maxmum effcency. Controllng the acceleraton of the system has an addtonal beneft; t provdes a smple means of controllng the rato of the peak transent current levels to that of steady state operaton. As a result, a better slcon utlzaton rato mght be feasble when compared to a more tradtonal V/f control. A smple speed estmator usng the mechancal equvalent crcut and the commanded torque (low pass fltered) s used to provde a feedback sgnal to the PI type speed controller snce the actual motor speed s unavalable for use n ths system. Inducton Machne speed setpont Jerk lmt Acceleraton lmt DC offset ω _ PI T em Equatons (1)-(9) v abc PWM gates Power Converter n ω Frst Order Speed Estmator 1 Fg. 7: Control system block dagram. 8 b Stator Currents (A) 6 4 c a Tme (seconds) Fg. 8: Phase currents obtaned usng the proposed voltage control algorthm durng acceleraton from to 12 rpm for a fan load. Current polartes as defned n Fg. 1.

5 IEEE IAS Annual Meetng Page 5 of 7 Chcago, Illnos, September 3 October 4, b 1 4 Shaft Speed (rpm) Stator Currents (A) c a Tme (seconds) Fg. 9: Smulated motor speed showng strartup Tme (seconds) Fg. 11: Expanded vew of the steady state phase currents. Motor Torque (Nm) Tme (seconds) Fg. 1: Smulated motor torque showng startup. The system was smulated for a speed profle from to 12rpm for a fan load. Results of ths smulaton are shown n Fgs Fgure 8 shows the motor phase currents durng acceleraton. These currents show evdence of the addtonal dc offset durng the speed transent as the currents are always above zero durng a porton of the acceleraton. Wave shape agreement durng the transent shows some dstorton due to errors n the feedback sgnal (estmate) and the steady state nature of the algorthm. Fgure 9 shows the shaft speed of the motor. The jerk lmt s evdent durng the frst 1.5 seconds at whch pont the control system s commandng a constant acceleraton. The reversal of ths takes place as the system slows nto constant speed mode at 12rpm. Fg. 1 gves the motor torque for ths smulated profle. Fgure 11 shows an expanded vew of the motor phase currents once the system has reached steady state. The currents show excellent agreement n wave shape to the theoretcal deal of Fg. 2. V. EXPERIMENTAL RESULTS The proposed control algorthm was also mplemented as a laboratory prototype to verfy the smulated results. A Motorola 6885EVM DSP control board was used to control the system wth a 1kHz swtchng frequency. Implementaton of the control algorthm presented n ths paper requres several practcal consderatons for any nondeal, real world system. The nducton machne fundamental equvalent crcut has a speed voltage term assocated wth t and ths back emf of the machne ncreases wth speed. The zero sequence crcut has no speed voltage assocated wth t. Hence, the zero sequence voltage necessary to nduce the desred currents becomes a small percentage when compared to the fundamental voltage as the speed ncreases. As a result, ths algorthm wll be more robust n machnes wth large zero sequence reactances. Also, as the phase b voltage of the machne s half that of phases a and c, phase b wll be more susceptble to non-lneartes n the nverter resultng from voltage drops n the devces. These devce drops (assumed constant) were measured n the expermental setup and compensated for n the commanded voltage profle. The machne avalable for testng purposes has a very small leakage reactance component, about 5%. Ths proved to be nsuffcent n order to control the phase currents wth the proposed algorthm. As a result, t was necessary to ncrease the zero sequence reactance of the test machne. Ths was accomplshed by placng a 5.5mH nductor n the neutral leg of the machne. Fgures show the measured phase currents and neutral current for the test machne operatng n an unloaded condton. The polartes of the currents n these fgures correspond to polartes as n ndcated n Fg. 1. The commanded machne speed was 12 rpm and the actual resultng speed was 1198 rpm. Ths speed was chosen for target ar handlng applcaton and not as an effort to de-rate the hgher speed machne whch otherwse met the qualfcatons needed for ths topology.

6 IEEE IAS Annual Meetng Page 6 of 7 Chcago, Illnos, September 3 October 4, 21 Fg. 12: No-load expermental phase currents. 2A/dv. Top trace: Ch. 1, Phase a. Bottom trace: Ch. 2, Phase c. Fg. 14: Expermental phase currents for half-rated torque operaton. 2A/dv. Top trace: Ch. 1, Phase a. Bottom trace: Ch. 2, Phase c. Fg. 13: No-load expermental phase currents. 2A/dv. Top trace: Ch. 1, Phase b. Bottom trace: Ch. 2, Neutral current. The three phase currents n Fgs show evdence that ths s an open loop control technque as the phase a and b currents show contan some asymmetry. As expected by the seres/parallel connected wndngs, the phase b currents contan a rpple component whch s twce as large as phases a and c. Furthermore, the neutral current s a snusodal quantty as expected Fgures show the measured phase and neutral currents for a commanded speed of 12rpm wth an appled load of ½rated torque. For ths machne, ths corresponds to a load of.7nm. Lke the unloaded case, the phase currents show the characterstc wave shape that s controlled by ths algorthm wth some asymmetry due to the non-deal wndngs of the machne and open loop nature of the algorthm In both the unloaded and loaded cases shown n Fgs , the currents show evdence of a thrd harmonc component whch s larger than what s needed to acheve the desred waveshape. It s the belef of the authors that the non-deal wndngs contan a thrd harmonc component that produces a rotatng flux component wth three tmes the number of poles of the fundamental component. Ths behavor s clearly not modeled n the zero sequence equvalent crcut shown n Fg. 5(b). For the machne tested, Fg. 15: Expermental phase currents for half-rated torque operaton. 5A/dv. Top trace: Ch. 1, Phase b. Bottom trace: Ch. 2, Neutral current. no nformaton about the wndng dstrbuton of the stator was avalable to calculate what ths affect would be, however, the expermental data ndcates that the conventonal zero sequence equvalent crcut may be ncomplete, especally for smaller machnes whch nherently have fewer numbers of stator slots. Ths aspect of the research s under further nvestgaton. V. CONCLUSIONS Ths paper proposes a new model based current shapng control for a three swtch unpolar nverter for an nducton machne. The new control method, based on the steady state equvalent crcut, s sgnfcant, as t requres zero current sensors, whle prevous control methods for ths topology requred three current sensors. Smulaton results were presented to verfy the feasblty of the proposed control algorthm. In addton, prototype hardware results ndcate that ths open loop control method can be used to control the speed and torque of nducton machne wth a unpolar drve topology. The hardware results presented n ths paper reled on artfcally ncreasng the zero sequence reactance of the machne by addng an external nductance n the machne neutral path. As a result, addtonal research needs to be done

7 IEEE IAS Annual Meetng Page 7 of 7 Chcago, Illnos, September 3 October 4, 21 to gan a better understandng of how zero sequence currents nfluence the fundamental torque producton of the machne before ths method s commercally vable. However, snce ths method only reles on commssoned motor parameters, t remans an attractve topology/control canddate for ntegrated motor drve products where varable speed s desrable, but the hgh cost of a standard three-phase motor drve s prohbtve. APPENDIX: MACHINE PARAMETERS The 115/23V, 3-phase, 1 hp, 2 pole, nducton machne wth a squrrel cage rotor and dual wound stator used for ths paper had the followng characterstcs when confgured for hgh voltage operaton. R 1 2. Ω R Ω R m 465 Ω L 1 L 2 5.6mH L m 218 mh f rated = 87 Hz ACKNOWLEDGEMENT Ths work was supported prmarly by the Center for Power Electroncs Systems. CPES s a Natonal Scence Foundaton ERC under Award Number EEC The authors would also lke to thank the Motorola Corporaton for donatng the DSP control board hardware and software used for the expermental results presented n ths paper. REFERENCES [1] K. Phllps, Power Electroncs: Wll Our Current Techncal Vson Take Us to the Next Level of AC Drve Product Performance?, Conf. Rec. 35 th IEEE IAS Annual Meetng, Rome, Italy, 2, vol. 1, pp. P1 P9. [2] J. F. Eastham, A. R. Danels, and R. T. Lpczynsk, A Novel Power Inverter Confguraton, Conf. Rec. IEEE IAS Annual Meetng, 198, vol. 2, pp [3] Henz W. Van Der Broeck, J.D. Van Wyk, "A Comparatve Investgaton of a Three-Phase Inducton Machne Drve wth a Component Mnmzed Voltage-Fed Inverter Under Dfferent Control Optons," IEEE Trans. on Ind. Applc., Vol. IA-2, No. 2, March/Aprl 1984, pp [4] P. D. Evans, R. C. Dodson, and J. F. Eastham, Delta Inverter, Proc. IEE, vol. 127, Pt. B, November 198, pp [5] B. A. Welchko, and T. A. Lpo, A Novel Varable Frequency Three- Phase Inducton Motor Drve System Usng Only Three Controlled Swtches, Conf. Rec. 35 th IEEE IAS Annual Meetng, Rome, Italy, 2, vol. 3, pp [6] K. Koga, R. Ueda, and T. Sonoda, Consttuton of V/f Control for Reducng the Steady State Speed Error to Zero n Inducton Motor Drve System, Conf. Rec. IEEE IAS Annual Meetng, 199, vol. 1, pp [7] A. Muñoz-García, T. A. Lpo, and D. W. Novotony, A New Inducton Motor Open-Loop Speed Control Capable of Low Frequency Operaton, Conf. Rec. 32nd IEEE IAS Annual Meetng, New Orleans, LA, 1997, vol. 1, pp [8] D. W. Novotony, and T. A. Lpo, Vector Control and Dynamcs of AC Drves, Oxford Unversty Press, 1996.