DIRECT TORQUE AND FLUX CONTROL OF ASYMMETRICAL SIX-PHASE INDUCTION MOTOR WITH ZERO SEQUENCE COMPONENTS ELIMINATION

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1 Rev. Roum. Sci. Techn. Électrotechn. et Énerg. Vol. 6,, pp. 36, Bucarest, 7 DIRECT TORQUE AND FLUX CONTROL OF ASYMMETRICAL SIX-PHASE INDUCTION MOTOR WITH ZERO SEQUENCE COMPONENTS ELIMINATION NAVID REZA ABJADI, DAVOUD GHANBARI, Key wors: Asymmetrical six-phase inuction motor, Zero sequence, Direct torque control (DTC). Direct torque an flux control (DTC) of inuction motor (IM) is one of the most effective methos in control of this electric machine. Using DTC the restrictions an complexities of vector control can be avoie. In this paper, the algorithm of DTC of an asymmetrical six-phase inuction motor (SPIM) with a two-level voltage source inverter (VSI) is improve. SPIM can be use in high power applications or fault tolerant systems such as traction systems with reuce torque pulsations. The machine is moele base on vector space ecomposition (VSD) theory. Selecting suitable switching vectors the torque an flux of the motor are controlle properly. Using the propose algorithm, the zero sequence current components are almost zero which is very important in SPIM control; since without them, the harmonics of phase currents are reuce an efficiency is improve consierably. The valiity an effectiveness of the propose metho are confirme by experimental results.. INTRODUCTION Multiphase motor rives are propose especially for high power applications such as traction, hybri vehicles aircraft an etc. The avantages of multiphase machines over conventional three-phase machines are: reuce torque pulsations, reuce c-link harmonics, higher torque ensity, greater fault tolerant, improvement of the rive noise characteristic, reuction in the require rating per inverter leg, an achieving a high power motor rive with a less angerous c-link voltage [ 3]. Among multi-phase schemes, five-phase an six-phase schemes are more common [, ]. This paper eals with an asymmetrical SPIM which is also calle quasi six-phase IM, split-phase IM or ual three-phase IM. The stator wining of an asymmetrical six-phase IM consists of two three-phase wining sets which have 3 egrees phase isplacement. IM rives controlle by fiel oriente control (FOC) have been still now employe in high performance inustrial applications []. Vector control implie inepenent control of the torque an flux by ecoupling the stator current into two components; however, FOC is very sensitive to flux, which is mainly affecte by parameter variation. To overcome this problem, nonlinear an intelligent methos are employe in IM control. Feeback linearization an moel following sliing moe control techniques are use to control SPIMs [6]. Chattering an high control efforts are the problems of the sliing moe controller. A rather complex backstepping control for SPIM is esigne in [7]. To enhance the performance of FOC for SPIM an emotional controller is employe in [8]. DTC of IM is an effective simple control strategy in the fiel of variable spee AC motor [9]. It provies a fast response with some robustness against machine parameter variations an uncertainties. In this metho, stator voltage vector is selecte accoring to the ifference between the reference an actual values of torque an stator flux consiering the position of stator flux vector. The main avantages of DTC are the absence of coorinate transformations an current proportional integral (PI) regulators. In aition, DTC has a sensorless nature. Using DTC, inverter is irectly controlle an there is no nee to any special pulse with moulation (PWM) techniques an finally it has a very fast ynamic response. The main isavantages of conventional DTC are high torque ripple an its variable switching frequency. In [, ], a conventional DTC is introuce for SPIM with a look-up table. The rawback of the DTC presente in [, ] is the generation of all voltage components which are epicte with α, β, x an y subscripts. These voltage components generate current components an even a small amount of (x, y) voltage components can cause large (x, y) current components which are calle zero sequence components. In SPIM, only α an β current components contribute in generate machine torque an air gap flux. Other components only increase machine power losses an they shoul be eliminate. In [], (x, y) components are cancele for a five-phase machine. In this paper, three look-up tables are propose to implement DTC for a SPIM an with the help of two aitional tables the zero sequence current components are suppresse. An asymmetrical machine is iscusse an experimental results are presente.. DESCRIPTION AND MODELING OF THE SPIM The SPIM consiere has two three-phase winings mutually isplace in space by 3 o as shown in Fig.. In some researches the moel of the machine is presente consiering each three-phase wining set an using the conventional Clarke s transformation for threephase case []; however, base on Clark's transformation escribe by the following matrix C, the (α β), (x y), an (zero sequence) equivalent circuits of motor in the stationary reference frame can be obtaine for a SPIM as shown in Fig. [3]. In this figure, ν αs, ν βs, ν xs, i αs, i βs, i xs, an i ys are stator voltage an current components respectively; i αr, i βr, I xr, an I yr are rotor current components; v ± s, i ± s an i ± r are voltage an current ( + ) components respectively; ω r is the rotor spee; λ αr an λ βr are rotor flux components. Shahrekor University, Faculty of Engineering, Shahrekor, Iran, naviabjai@yahoo.com Shahi Abbaspour Dam & Hyro Power Plant Operation & Generation Co., Masjesoleyman, Iran

2 Direct torque an flux control of six-phase inuction motor 37 Fig. Schematic representation of the SPIM stator winings. Fig. SPIM equivalent circuits. C = α cosφ cosφ cosφ cos8φ cos9φ β sin φ sin φ sinφ sin8φ sin 9φ,() x cosφ cos8φ cosφ cosφ cos9φ 6 y sinφ sin8φ sin φ sin φ sin 9φ + where the constant φ = π / 6 [3]. Using this transformation, the electromechanical components of currents, ( α - β ) components, can be separate. The stator voltage equations of the machine are vαs = Rsiαs + ( Lsi Lmi ) t αs + αr vβs = Rsiβs + ( Lsi Lmi ) t βs + βr v xs = Rsi xs + ( Llsi ) t xs, () v ys = Rsi ys + ( Llsi ) t ys where R s, L s, L ls an L m are stator resistance, stator inuctance, stator leakage inuctance an magnetizing inuctance respectively. The rotor voltage equations of the machine are = Rriαr + ωr( Lriβr + Lmiβs) + ( Lri Lmi ) t αr + αs,(3) = Rriβr ωr( Lriαr + Lmiαs) + ( Lri Lmi ) t βr + βs where R r, L r an L lr are rotor resistance, rotor inuctance an rotor leakage inuctance respectively. The torque equation of the machines is given as T e = P Lm ( iαr iβs iβr iαs ), () here T e is the torque, P is the number of pole pairs. From (), one can see that the torque generating current components are i αs, i βs. The (x y) components of the stator current only increase the motor power losses, thus one shoul force ν xs = ν ys =. The ( + ) components are equal to zero if the neutrals of the two three-phase wining sets are separate [3]; in fact, with separate neutrals there is no concern about ( + ) components. 3. THE SIX-PHASE VOLTAGE SOURCE INVERTER To fee the SPIM a six-phase VSI is neee. The sixphase VSI presente in Fig. 3 contains a switching network of power switches arrange to form 6 legs. Each leg supplies one phase of the motor. Base on the state of the upper or lower switches of the inverter, each phase switching function, which are calle Sa, Sb, Sc, S, Se, an Sf can take either or value. If the upper switch is on then the switching function becomes, otherwise it becomes ". The voltage equations of six-phase VSI are f vks = 6 vkn 6 vin i= a i k, () where k = a,b,, f an N is the lower point of the c link.. DTC WITHOUT ZERO SEQUENCE The block iagram of conventional DTC for a SPIM is represente in Fig.. In this figure, T * e an λ * s are references of torque an stator flux amplitue respectively; ˆT e an λˆ s are estimate values of torque an stator flux amplitue respectively. Fig. 3 Six-phase VSI connecte to stator winings.

3 38 Navi Reza Abjai, Davou Ghanbari 3 of Fig., with a proper combination of these vectors, zero sequence components of voltage can be omitte. These vectors are rerawn in Fig. 6. In this figure the resultant of v an v 3 is also rawn, which is in opposite irection of v. Assume the length of v an v 3 is equal to a then the length of the resultant of them can be expresse as Fig. Conventional DTC of SPIM. The iea of the DTC is to restrict the torque an stator flux errors within specifie limits of the torque an flux hysteresis bans by an appropriate selection of the inverter switching states. The evelope torque an stator flux variation of IM can be expresse as T e λs I s, (6) Δ λs = V st s, (7) where λs is stator flux amplitue; V s is voltage vector; I s is stator current vector an T s is sampling time. From (6), it can be seen that the torque is relate to the variation of the stator flux an torque angle. The stator flux variation of (7) can be irectly affecte by impressing the stator voltage. In six-phase VSI, there are 6 states for switching that each state generates a voltage vector. In other wors, there are 6 voltage vectors for the inverter. These voltage vectors can be shown in (α, β) an (x, y) planes. Projecting the 6 voltage vectors in (α, β) plane, vectors with ifferent lengths are appeare in this plane. In fact, the length of the switching vectors in (α, β) plane can be classifie in ifferent sizes [3]. To obtain larger voltage amplitue, only switching vectors with largest size are selecte in (α, β) plane. Figure shows the projection of these vectors in (α, β) an (x, y) planes. The numbers written near the vectors represent the state of the six-phase VSI, when these numbers are converte to binary, six bits are obtaine. Each zero/one in these binary numbers is correspone to a switch in the relate inverter leg. The number zero means the lower switch is on an the number one means the upper switch is on. These vectors have the smallest lengths among vectors in (x, y) plane which ecreases (x, y) voltage components; however, it is not enough. Referring to (x, y) equivalent circuit of Fig., a small amount of (x, y) voltage components can cause large (x, y) current components. The DTC strategy shoul enforce (x, y) voltage components to become almost zero. If the flux an torque errors are increase, a switching voltage vector shoul be selecte that increase the stator flux angle an magnitue. Tables, an 3 give the associate inverter switching states for conventional DTC approach. In these tables, TC = / means the torque shoul be increase/ecrease an FC = / means the stator flux shoul be increase/ecrease. From each of these tables one can select a proper switching vector epene on torque an flux error an position of stator flux. For example, if TC =, FC = an the stator flux vector is in sector then from Table,, 3, v /v 3 /v is selecte as switching voltage vector. Vectors v, v 3 an v are highlighte in Fig.. As can be seen from (x, y) plane b = + 3a. (8) To enforce the resultant of three vectors v, v an v 3 in (x, y) plane equal to zero averagely, the switching times of these vectors shoul satisfy the following conitions t t tv + v3+ v=, (9) t t t + + = TS, () t where t an are the switching times of the appropriate switching voltage vectors. From (9) an (), consiering (8), the switching times are obtaine as + 3 t = T.93 T, S S t = T. T S S Fig. The largest switching voltage vectors in (α, β) plane an their projection in (x, y) plane. () ()

4 Direct torque an flux control of six-phase inuction motor 39 In the propose DTC algorithm, in each perio T s three switching voltage vectors are use with the switching times t, t / an t / calculate above.. EXPERIMENTAL RESULTS Fig. 6 Representation of three switching vectors in (x, y) plane. Table Inverter voltage vector selection TC FC 3 6 v v3 v v v6 v7 v v6 v7 v8 v9 v v v v v v3 v v8 v9 v v v v TC FC v8 v9 v v v v v v v v v3 v v v6 v7 v8 v9 v v v3 v v v6 v7 Table Inverter voltage vector selection TC FC 3 6 v3 v v v6 v7 v8 v6 v7 v8 v9 v v v v v v3 v v v9 v v v v v TC FC v9 v v v v v v v v v3 v v v6 v7 v8 v9 v v v3 v v v6 v7 v8 Table 3 Inverter voltage vector selection 3 sector TC FC 3 6 v v v3 v v v6 v v v6 v7 v8 v9 v v v v v v3 v7 v8 v9 v v v sector TC FC v7 v8 v9 v v v v v v v v v3 v v v6 v7 v8 v9 v v v3 v v v6 To verify the theory of the propose DTC, practical results are obtaine for a SPIM with parameters given in Table. The experimental rig is illustrate in Fig. 7. The SPIM is obtaine by rewining the stator of a three-phase IM. A six-phase VSI is employe. The switching frequency of the six-phase insulate gate bipolar transistor (IGBT) inverter has been set at khz. The control software has been implemente on a PC. A Xilinx XC988 CPLD is use for real time implementation of switching patterns an to sen the ata from some analog to igital converters (A/Ds) use to measure currents an c link voltage. The CPLD boar communicates with PC via a igital Avantech PCI-7 I/O boar. A secon Xilinx XC98 CPLD is use to calculate an sen the spee ata from an encoer to computer through printer port. The currents are measure using LEM sensors. A c motor connecte to some rheostats use as mechanical loa. The control coe is written in C. It performs close-loop torque/spee control an stator flux control. The practical results for spee start up test using only one table (Table ) for DTC are shown in Fig. 8. In this test, the spee reference for SPIM is change from to 8 ra/s exponentially in about secon. The stator flux reference is.6 Wb. Fig. 7 Experimental rig: PC, CPLD boars an inverter (top), SPIM with c motor (bottom). Table SPIM Parameters poles R s 9 Ω R r 8.37 Ω L s 7 mh L r 7 mh L m 7 mh P n kw f n Hz

5 Navi Reza Abjai, Davou Ghanbari wr (ra/s) wr wr* wr (ra/s) wr wr* Te (Nm) Te (Nm) λs (Wb) λαs (Wb) λβs (Wb) iαs (A) iβs (A) Fig. 8 SPIM spee control response using one table: spee, torque, flux components an current components. λs (Wb) λαs (Wb) λβs (Wb) iαs (A) iβs (A) Fig. 9 SPIM spee control response using three tables an the propose DTC algorithm: spee, torque, flux amplitue, flux components an current components.

6 6 Direct torque an flux control of six-phase inuction motor The spee approaches its reference in a reasonable time. The stator flux components of the machine are shown in Fig. 8; both of the flux components are sinusoial an in quarature to each other. The stator flux amplitue of SPIM is shown in Fig. 8 which reaches its reference perfectly. One can observe from Fig. 8 that the stator flux amplitue of SPIM remains constant uring the spee start up. The (x, y) current components have large amplitues which cause high stator phase currents with a lot of harmonics. These harmonics increase the machine power losses an reuce efficiency significantly. Figure 9 shows the practical results for the same test using the propose DTC algorithm with three tables. The quality of the spee response an stator flux response are preserve. The (x, y) current components are reuce consierably compare to the results of Fig. 8. In fact, these components are near zero which shows the effectiveness of the propose DTC algorithm. The little amount of these components seen in Fig. 9 is arising from the switching effects an the measurement noise. With almost no (x, y) current components, the harmonics of stator phase currents are reuce significantly using one table using three tables - - Fig. SPIM (x, y) current components. In Fig., the (x, y) current components are rawn relative to each other using one/three tables methos respectively. It is seen using three tables metho, the obtaine figure is in origin neighborhoo. In theory, with infinite switching frequency an with no measurement noise, it can be coincient with origin. 6. CONCLUSION In this paper, an effective DTC algorithm for SPIM is propose. This algorithm uses three look up tables. The performance of the SPIM is teste by experimental results. The main improvements shown are: consierably reuction of (x, y) current components, no flux roppings cause by sector changes an fast stator flux an torque responses in transient state. The operation of the propose DTC is compare to the conventional DTC. Using the propose DTC, the (x, y) current components obtaine in practical results are near zero which reuces the harmonics in phase currents an machine power losses. The propose DTC has a simple structure which is very suitable an feasible for implementation. Receive on June, 6 REFERENCES. A. Azib, D. Ziane, T. Rekioua, A. Tounzi, Robustness of the irect torque control of ouble star inuction motor in falut conition, Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 6,, pp. 7 (6).. A. Taheri, A. Rahmati, S. Kaboli, Comparison of Efficiency for Different Switching Tables in Six-Phase Inuction Motor DTC Drive, Journal of Power Electronics,,, pp. 8 3 (). 3. E. Benyoussef, A. Meroufel, S. Barkat, Neural network an fuzzy logic irect torque control of sensorless ouble star synchronous machine, Rev. Roum. Sci. Techn. Électrotechn. Et Énerg., 6, 3, pp (6).. S.M.J. Rastegar Fatemi, J. Soltani, N.R. Abjai, G.R. Arab Markaeh, Space-vector pulse-with moulation of a Z-source six-phase inverter with neural network classification, IET Power Electronics,, 9, pp. ().. R. Bojoi, M. Lazzari, F. Profumo, A. Tenconi, Digital fiel oriente control for ual-three phase inuction motor rives, IEEE Transactions on Inustry Applications, 39, 3, pp (3). 6. N.R. Abjai, G.R. Arab Markaeh, J. Soltani, Moel following sliing-moe control of a six-phase inuction motor rive, Journal of Power Electronics,, 6, pp (). 7. S.M.J. Rastegar Fatemi, N.R. Abjai, J. Soltani, S. Abazari, Spee sensorless control of a six-phase inuction motor rive using backstepping control, IET Power Electronics, 7,, pp. 3 (). 8. E. Daryabeigi, N.R. Abjai, G.R. Arab Markaeh, Automatic spee control of an asymmetrical six-phase inuction motor using emotional controller (BELBIC), Journal of Intelligent & Fuzzy Systems, 6,, pp (3). 9. I. Takahashi, T. Naguchi, A new quick-response an highefficiency control strategy of an inuction motor, IEEE Trans. on Inustry Application,,, pp (986).. K. Marouani, F. Khoucha, A. Kheloui, L. Baghli L., D. Haiouche, Stuy an simulation of irect torque control of ouble-star inuction motor rive, EPE-PEMC 6, Portoroz, Slovenia, pp (6).. L. Zheng, J.E. Fletcher, B. Williams, X. He, A novel irect torque control scheme for a sensorless five phase inuction motor rive, IEEE Trans. on In. Electr., 8,, pp. 3 3 ().. R.H. Nelson, an P.C. Krause, Inuction machine analysis for arbitrary isplacement between multiple wining sets, IEEE Trans. on Power Apparatus an Systems, 93, 3, pp (97). 3. Y. Zhao, T.A. Lipo, Space vector PWM control of ual threephase inuction machine using vector space ecomposition, IEEE Trans. on In. Appl., 3,, pp. 9 (99).