THE main area of application of the switched reluctance motor

Transcription

1 44 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006 Asymmetrical Switched Reluctance Motor for a Wide Constant Power Range Vladan P. Vujic ić, Member, IEEE, Slobodan N. Vukosavić, Member, IEEE, and Milenko B. Jovanović Abstract In this paper the systematic approach to the design of a asymmetrical three-phase switched reluctance motor (SRM) with wide constant power range is described. It is shown that the SRM configuration with an unequal number of turns per phases may provide a wider constant power range than a corresponding symmetrical one. If the stator pole widths are unequal, the constant power range may be further extended. In these considerations, the maximal volt-ampere characteristics of the power converter are kept on the same level. The results are obtained using a suitable SRM model whose validity has been experimentally verified. The experimental results for the referent symmetrical SRM drive and asymmetrical one with an unequal number of turns per phase are also presented. Index Terms Computer-aided analysis, optimal control, optimization methods, reluctance motor drives. Methodology for determination the optimal motor configuration (i.e., optimal number of turns and pole widths) is described. The model suitable for performance prediction of the asymmetrical SRM is also proposed. As an example the design of the 500 W asymmetrical motor is included. Computer simulation is employed to predict the SRM drive performances and to determinate the optimal asymmetrical motor configurations. The results show that these configurations provide a significantly wider constant power region than the corresponding symmetrical one. Experimental results provided for the symmetrical drive and asymmetrical one with an unequal number of turns per phase refer to the reduced supply voltage and phase currents due to the setup limitations. I. INTRODUCTION THE main area of application of the switched reluctance motor (SRM) is electric traction and home appliances, where it is particularly important that the motor develops rated power in a wide speed range. The width of this range significantly depends on the motor geometry, topology of power converter, and skill of the applied control [1] [3]. Investigations described in [4] [6] give relation between motor geometry and its constant power region width. The results show that the wider constant power range is developed by SRM drives using motor with lower number of phases and poles with reduced pole width. An interesting idea to resolve the problem of low torque at high speed is the pole-changing method described in [7]. The 6/2 asymmetrical topology of SRM for a high-speed range is proposed in [8], where the low-speed pole winding is switched off as soon as the motor starts. A significant contribution to improve exploitation of the characteristics of the SRM in home appliances is also made in [9]. On the other hand, many new topologies of the power converter [8], [10], [11] and control techniques [12] [15] are proposed to improve the process of electromechanical conversion in the SRM, and, in such a way, to extend the constant power range. This paper proposes two asymmetrical configurations of the three-phase SRM drive that provide a wide constant power region. In one configuration, the SRM has an unequal number of turns per phase, and, in another, it also has unequal pole widths. Manuscript received April 9, 2002; revised April 22, Paper no. TEC V. P. Vujic ić is with the Department of Electrical Engineering, University of Montenegro, Podgorica, Serbia and Montenegro ( vladanv@cg.ac.yu). S. N. Vukosavić and M. B. Jovanović are with the Department of Electrical Engineering, University of Belgrade, Belgrade, Serbia and Montenegro ( boban@ieee.org; jmilenko@ieee.org). Digital Object Identifier /TEC II. BASIC CONSIDERATION The constant power regime of SRM is ensured by moving the turn-on (θ on ) and the turn-off (θ off ) angles in advance when rotor speed (ω) increases. At certain speed (ω c ), the turn-on angle cannot be further moved in advance, and, with further increasing of speed, the interval between θ on and θ off, is decreased. Thus, the flux (φ) decreases proportionally to 1/ω; consequently, the output torque (T ) and power (P ) decrease proportionally to 1/ω and 1/ω 2, respectively, as T is proportional to φ 2 and P = Tω [1]. One way to increase ω c (and thus the constant power range) is to ensure slower changes of θ on providing faster rise of φ. It requires an increase of voltage supply or a decrease in the number of turns per phase (N) and, thus, an increase in volt-ampere (VA) and speed requirements of switches in the power converter. Another way to increase ω c is to extend the range of θ on displacement. This can be achieved by decreasing a number of poles and their width, but, then, we face the problem of the motor starting because of the poor torque at some rotor positions. The investigation described in [5] shows that, when optimal control-maximizing output torque of the SRM drive is applied, the output power significantly varies inside the theoretically constant power range. Consequently, if we need to re-establish constant power regime applying adequate control, the maximum power of the SRM drive will be reduced. The basic idea of this work is to design the 6/4 SRM, which has two low-speed (LS) phases and one high-speed (HS) phase. LS phases have a larger number of turns and/or wider pole width than the HS phase. As a consequence, they will ensure lower VA requirements for same magnetomotive force (MMF), but the HS phase will have higher speed ω c and, thus, will provide dominant torque at high speed. Optimal combination of the phase s number of turns and/or pole widths should ensure a wide constant range of maximal output power /$ IEEE

2 VUJIC IĆ et al.: ASYMMETRICAL SWITCHED RELUCTANCE MOTOR FOR A WIDE CONSTANT POWER RANGE 45 To obtain valid results, the output characteristics of asymmetrical drives and referent symmetrical ones will be compared. Therefore, although the speed of switches in converters will be different, all drives will have approximately the same total VA requirements of power converters and the same motor volumes. Considerations are limited on drives with classic power converters [8]. Also, we assume the same slot-fill factor for any phase number of turns, i.e., any wire diameter. A. Asymmetrical Number of Turns Per Phase In the symmetrical SRM drive all phases have the same current waveforms. If the relative increase of the input filter capacitor voltage is neglected, the total VA requirements of power switches for three-phase SRM, fed by a classic converter, are [8]: 6 V I pm, where V is input dc voltage, and I pm is maximum of the phase current peak value (I p ).The same requirements for the asymmetrical three-phase SRM are: 2 V 1 I pm1 +4 V 2 I pm2, where subscript 1 refers to one phase (less number of turns) and subscript 2 to other two phases (larger number of turns). Thus, if we want to compare output characteristics of asymmetrical SRM drive with referent symmetrical one, (1) is to be satisfied: 6VI pm =2V 1 I pm1 +4V 2 I pm2. (1) If we assume the same values of phase input dc voltage, i.e., V = V 1 = V 2, then (1) becomes 6I pm =2I pm1 +4I pm2. (2) The same current density in the phase conductors and the same magnetic field structure may be achieved by the same values of the MMF in all phases, i.e., NI = N 1 I 1 = N 2 I 2 (3) where N,N 1, and N 2 are the number of turns of corresponding phases, and I,I 1, and I 2 are rms values of phase currents. In that case, the following expression is valid: I pm /I = I pm1 /I 1 = I pm2 /I 2 = k i (4) where k i is constant. Then, (2) can be written as 3I = I 1 +2I 2. (5) Combining (3) and (5), and defining coefficient k = N/N 1,we obtain the system N 1 = N/k N 2 =2N/(3 k) I 1 = ki I 2 =(3 k)i/2. (6) If N 1 <N<N 2 and 1 <k<3, the system (6) ensures the same VA requirements to power converters for symmetrical and asymmetrical SRM drive. Thus, changing the value of coefficient k, with given phase current (I) and number of turns (N) of the referent symmetrical SRM drive, we obtain currents and numbers of turns for different asymmetrical SRM drives. Note, the value of coefficient k =1refers to symmetric SRM drive Fig. 1. Illustration of 6/4 SRM torque. (a) Symmetrical motor. (b) Irregular asymmetrical motor. (c) Regular asymmetrical motor. (I 1 = I 2 = I,N 1 = N 2 = N), and the value k =3refers to the case: N 1 =3N,N 2,I 1 =3I,I 2 0. If the phase resistance R for symmetrical SRM is known, then the resistance of asymmetrical SRM phases can be obtained as R j =(N j /N ) 2 R, (j =1, 2). (7) Similarly, if L u value of unaligned inductance of the symmetrical SRM phases, then unaligned inductance L u1 and L u2 of asymmetrical SRM phases can be calculated as L uj =(N j /N ) 2 L u, (j =1, 2). (8) B. Asymmetrical Stator Pole Widths In this SRM configuration, one phase, besides a different number of turns, also has a pole width different from the other two phases. To ensure significant torque at all rotor positions, the reduction of pole width of the phase with N 1 number of turns must be accompanied by the enlargement of pole widths of the other two phases. Fig. 1(a) illustrates torque produced by symmetrical three-phase 6/4 SRM with stator pole arc β s = 30. Irregular and regular asymmetrical SRM configurations are illustrated in Fig. 1(a) and (b), respectively. For regular asymmetrical SRM, the following conditions must be satisfied: β r β s2 β s1 2β s2 + β s1 2π/N r (9)

3 46 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006 where β r is rotor pole arc, β s1 and β s2 are stator pole arcs for phase with narrow poles and for phases with wider poles, respectively, and N r is number of rotor poles. If we assume that asymmetrical SRM retains the same slot area as in the referent symmetrical one for all stator poles, then validity of (3) is also retained. However, (4) is not valid in general and, therefore, the condition (5) does not follow from (2). For this SRM configuration, the (4) can be written as TABLE I MOTOR PARAMETERS OF THE REFERENT SYMMETRICAL SRM DRIVE I pm /I = I pm1 /(c 1 I 1 )=I pm2 /(c 2 I 2 )=k i (10) where c 1 and c 2 are constants, that, for k = N/N 1 =1(i.e., N 1 = N 2 = N and I = I 1 = I 2 ), can be determined as c 1 = I pm1 /I pm and c 2 = I pm2 /I pm. Peak current values I pm,i pm1, and I pm2 can be determined only by measurement on physical drives or using proper simulation program for computer-aided design. Having in mind (10), (2), which is a condition for retaining invariable total VA requirements, can be written as 3I = c 1 I 1 +2c 2 I 2. (11) If we assume that, for k =1(i.e., N 1 = N 2 = N and I = I 1 = I 2 ), asymmetrical drive has the same total VA requirements as the referent symmetrical one, than, from (11), we have 3=c 1 +2c 2. (12) Combining (3), (11), and (12) we get equations for determining phase currents (I 1 and I 2 ) and the number of turns (N 1 and N 2 ) of various asymmetrical SRM drives N 1 = N/k N 2 =(3 c 1 )N/(3 c 1 k) I 1 = ki I 2 =(3 c 1 k)i/(3 c 1 ). (13) Equation (7) is also valid for this configuration. Unaligned inductances L u1 and L u2 can be also determined from (8), but here L u is to be replaced (by calculated or measured) values of L u1 and L u2, respectively, for k =1. III. DETERMINATION OF THE SRM DRIVE MAXIMAL OUTPUT POWER CHARACTERISTIC The main symmetrical and asymmetrical SRM drive comparison criterion used in this paper is maximal continuous output power characteristic, obtained for a given rated rms phase current. To provide the maximal output power the optimal control parameters turn-on angle (θ on ), turn-off angle (θ off ), and referent current (I ref ) must be precisely determined. The control parameters in asymmetrical SRM must be determined for LS and HS phases separately. For determination of the optimal control parameters and maximal drive performances, the computer simulation is used. The simulation is based on the appropriate SRM mathematical model described in [16]. The model provides torque and phase current waveforms, as well as the average torque, peak, and rms phase current values. Phase current (i) is defined as functions of flux Fig. 2. Magnetization curves of the symmetrical motor. linkage (Ψ) and rotor position (θ) i(θ, Ψ) = i o (θ, Ψ) + i fe (Ψ) (14) where [ ] i o = c o5 (1 c o1 )Ψ c o1 c o2 + c o1 (Ψ c o3 ) 2 + c 2 o4 (15) i fe = c fe1 Ψ+c fe2 Ψ α. (16) Coefficients c oj (j =1, 2,...,5) in (15) are functions of θ and coefficients α, c fe1 and c fe2 in (16) are constants. All of them are defined by motor geometry dimensions (such as pole widths), number of turns per phase, some magnetic properties of the iron and, for more reliable results, the value of unaligned inductance of the phases. Thus, computer simulation is well adapted for motor geometry and number of turns variations. IV. DESIGN EXAMPLES A. Referent Symmetrical Drive Parameters of the referent symmetrical motor are given in Table I. Magnetization curves of the referent motor for a

4 VUJIC IĆ et al.: ASYMMETRICAL SWITCHED RELUCTANCE MOTOR FOR A WIDE CONSTANT POWER RANGE 47 Fig. 3. Results for symmetrical SRM drive. (a) Optimal turn-on and turn-off angles and average output torque. (b) Values for currents I,I dc,andi p. number of rotor positions, obtained by computer simulation and by measurement, are shown in Fig. 2. Similarity of these results will provide the reliability of the simulation results in the time domain [1], [6], and [17]. Computer simulation for motor speed from n = 500 r/min to n = r/min, with step of 500 r/min is performed. For any of these speeds, the control parameters were varied, and the average output torque and rms phase current were observed. Optimal combination of control parameters ensures maximum level of output torque when rms phase current (I) does not exceed the rated value of 2 A. The main results are summarized in Fig. 3. The optimal control turn-on and turn-off angles together with developed average output torque are given in Fig. 3(a), while the rms phase current (I), average dc link current (I dc ) and phase current peak value (I p ) are shown in Fig. 3(b). From Fig. 3(b), it can be seen that maximum of I p is I pm = A. Thus, the VA requirements of the total power switches are: 6U d I pm = VA = KVA. Fig. 4. Output power characteristics of the asymmetrical SRM drives with various values of coefficient k. B. Asymmetrical Number of Turns Per Phase In the same way as for the symmetrical motor, but separately for LS and HS phases, the optimal control parameters for asymmetrical motor with an unequal number of turns per phases are obtained. Fig. 4 shows the output power characteristics for some values of coefficient k (1.9, 2, 2.5, and 3), together with the characteristic of the referent symmetrical drive (k =1). It is obvious from Fig. 4 that configuration with k =1.9 (i.e., N 1 305,N ) ensures approximately constant power range at the maximum output torque level. In this case, the motor output power is within W for motor speed from n nsmin = 2500 r/min to n nsmax = 9420 r/min (i.e., n nsmax /n nsmin =3.768). On the other hand, symmetrical motor can develop 470 W (or more) output power, only in the range: n smin = 1880 r/min to n smax = 6720 r/min (i.e., n smax /n smin =3.574). This means that, if the output power level is controlled to be 470 W, the optimal asymmetrical SRM drive will ensure 5.42% wider speed range. Note, the value k =3 refers to the case N 1 = N/3 and N 2, i.e., I 1 =3I,I 2 0. The purpose of two phases with N 2 number of turns is to enable the motor to start. The output power characteristic in this case is same as that in the Fig. 5. Stator cross section of the SRM with unequal stator pole widths. referent symmetrical drive, but with gear ratio 1:3 included. Theoretically, this motor is three times faster than the referent symmetrical one, but it has, except when n 0, three times lower average output torque.

5 48 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006 Fig. 6. Simulation results for SRM with unequal stator pole widths (case k =1). (a) Optimal control turn-on and turn-off angles. (b) Peak and rms currents of the phases. Investigation for 0 <k<1 (i.e., N 1 <N and N 2 >N)is also done, but the motor with optimal number of turns has the similar output power characterized as the referent symmetrical one. C. Asymmetrical Stator Pole Widths The stator cross sections, both for the asymmetrical SRM with unequal pole widths considered and the referent symmetrical SRM, are shown in Fig. 5. The stator pole arc of phase 1 (poles 1 and 1 ) is reduced to β s1 =26, while stator pole arcs of the other two phases are extended to β s2 =32. Rotor cross section of the asymmetrical motor is retained the same as for the referent symmetrical motor (β r =32 ). Chosen pole arcs β s1 and β s2 are limiting values following from (9). This means that further decreasing β s1 could be possible only if rotor pole arc β r is increased. The modification of the stator cross section shown in Fig. 5 ensures that slot areas, and consequently MMFs, are the same for all phases and equal to those of the referent symmetrical motor. Optimization of control parameters is primarily performed for the k =1, i.e., when all phases have the same number of turns. As the first step, by the three-dimensional finite-element method, the unaligned inductance for phase 1 (L u1 =44.9mH) and unaligned inductance for the other two phases (L u2 =49.6 mh) were determined. Except for these inductances and stator pole arcs (β s1 and β s2 ), all the other motor parameters are the same as for the referent symmetrical motor. Procedure for the optimal control parameters determination is similar to that for the asymmetrical motor with equal stator pole widths. Optimal control turn-on and turn-off angles for phase 1 (β s1 =26 ), and phases 2 and 3 (β s2 =32 ), versus motor speed, are given in Fig. 6(a). Corresponding peak and rms values of phase currents are given in Fig. 6(b). From Fig. 6, it can be seen that the maximum of peak value of phase 1 current is I pm1 = A, and the maximum of peak value of phases 2 and 3 is I pm2 = A. Consequently, the total VA requirements (6.921 KVA) are closed to the VA requirements of the referent symmetrical drive (6.972 KVA). The values for coefficients c 1 and c 2 in (10) are also calculated: c 1 = I pm1 /I pm =1.0257,c 2 = I pm2 /I pm = It can be Fig. 7. Output power characteristics of the asymmetrical (unequal pole widths) SRM drives with various values of coefficient k. shown that these values approximately satisfy (12). Thus, for this motor geometry, system (13) is valid. The output power characteristics for several asymmetrical motors (k =1,k =1.5,k =1.8,k =2,k =2.4,k = 3/c 1 ), with optimized control parameters, are shown in Fig. 7. It can be seen that the optimal asymmetrical drive (k =1.8, i.e., N 1 = 322,N 2 = 992) can produce output power higher than 440 W (maximum power, 465 W) in the speed range from n pwmin = 2200 r/min to n pwmax = r/min (i.e., n pwmax /n pwmin =5.227). The same level of output power the referent symmetrical drive can develop from: n smin = 1670 r/min to n smax = 7200 r/min (n smax /n smin =4.311), whereas the optimal asymmetrical drive, with equal stator pole widths, from n nsmin = 2230 r/min to n nsmax = r/min (n nsmax /n nsmin =4.543). This means that, if the output power is controlled to be 440 W, the optimal motor configuration produces constant power region 21.25% wider than the referent symmetrical one and 15.06% wider than the optimal asymmetrical configuration with equal pole widths. Note, for this configuration, the coefficient k can vary from 1to3/c 1.Thevaluek =3/c 1 means that N 1 = c 1 N/3 and N 2 0, and it is suitable for design of the very high speed SRM drive.

6 VUJIC IĆ et al.: ASYMMETRICAL SWITCHED RELUCTANCE MOTOR FOR A WIDE CONSTANT POWER RANGE 49 Fig. 8. Comparison of the symmetrical (S) and optimal asymmetrical drives with equal (AS1) and unequal (AS2) pole widths. (a) Efficiency and ER. (b) Dynamic responses for different loads. D. Efficiency, Energy Ratio, and Dynamic Response Efficiency of the referent symmetrical and two optimal asymmetrical drives are calculated and shown in Fig. 8(a), together with energy ratio (ER) of the motors. The copper, iron, and converter loses are included in calculation of efficiency. Except for the very high motor speed, the symmetrical drive has higher efficiency. ER is calculated for one energy cycle of all motor phases. Bellow approximately 6200 r/min, the symmetrical motor has higher ER, but for speeds above, it has lower ER than the optimal asymmetrical motors. Above 8500 r/min the optimal asymmetrical motor with unequal pole widths has significantly higher ER than the other two. The dynamic responses of these three drives, for various constant loads (T L ), are shown in Fig. 8(b). As expected, the symmetrical drive has the fastest response, but the optimal drive with unequal pole widths reaches the highest speed at lower T L. V. COMPARING EXPERIMENTAL AND SIMULATION RESULTS An experiment was performed on the motor with data in Table I to measure the output power characteristic of the referent symmetrical SRM drive. The motor windings then were replaced and arranged for an asymmetrical number of turns per phase SRM with k =2(i.e., N 1 = 2902 and N 2 = 1160), and Fig. 9. Output power characteristics of the symmetrical and the asymmetrical SRM drives. (a) Estimated. (b) Measured. measurements then were conducted on the asymmetrical drive as well. In both symmetrical and asymmetrical drives the supply voltage is reduced to 130 V. Also, the dwell angle in all phases is constantly kept at 36. Thus, the control optimization procedure is reduced on changing the turn-on angle only. The peak phase current of the symmetrical motor is limited to I pm =2.5 A, and the peak phase currents of the asymmetrical motor are limited to I pm1 =5A, and I pm2 =1.2 A. Equations (1) to (6) are, therefore, approximately satisfied. By using these conditions, the expected power versus speed characteristics of the two drives were estimated by simulation procedure. The turn-on angle was tuned to reach maximal power for each rotor speed from 500 r/min to r/min, with steps of 500 r/min. The same procedure was conducted for experimental measurements but up to 5000 r/min. Additionally, in the experiments the motors were started without load and then the load torque was gradually increased to attain the desired speed. Also, the starting turn-on angle was 54 (i.e., turn-off angle at the aligned position) and then it was gradually moved in advance. Thus, the maximal developed torque for every analyzed speed was remembered. The simulation results, presented in Fig. 9(a), show that the higher power of the asymmetrical drive is expected after 4500 r/min. However, the experimental results, presented in Fig. 9(b), show that its higher power can be expected only after

7 50 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006 VI. CONCLUSION This paper describes the systematic approach to the design of asymmetrical SRM drive. The basic equations that enable us to combine the number of turns and stator pole widths between different phases of the SRM, without changing the total VA requirements of power converter switches, are given. It is shown that, by such combining, to a certain extent, the maximal continuous output power speed characteristic can be shaped. The speed range, in which the drive develops the given power, was used as the main criterion for comparison of different configurations. This range, when the optimal asymmetrical motor has only unequal number of turns per phases is, in the analyzed example, more than 5% wider than the range of the referent symmetrical drive. When the asymmetrical motor has, also, unequal stator pole widths, this range can be further extended, and it is, in the analyzed example, 20% wider than corresponding range of the referent symmetrical drive. Symmetrical SRM drive, however, has better dynamic response and higher efficiency than asymmetrical drives. Besides, the experimentally tested configuration of the asymmetrical drive has worse power versus speed characteristic than it was estimated. Despite that, the proposed asymmetrical SRM configurations promise to be competitive in many applications, especially in those where wide constant power range is required (for example, home appliances). REFERENCES Fig. 10. Measured and computed phase current waveforms. (a) Symmetrical SRM at 3000 r/min. (b) Asymmetrical SRM (HS phase) at 3500 r/min r/min. The measured and the estimated phase current waveforms of the symmetrical motor at 3000 r/min are compared in Fig. 10(a), whereas the current waveforms in the HS phase of the asymmetrical motor at 3500 r/min are compared in Fig. 10(b). As it can be seen, better agreements of the experimental and the simulation results in Fig. 10 and 11 for the symmetrical motor are achieved. Worse agreements of the results of asymmetrical drive are mainly caused by increased coils volume after rewinding. The coils on the poles of HS phase consist of two subcoils (290 turns) connected into parallel. Although the same wire diameter as in the symmetrical motor is used, the resistance of HS phase is 20% higher than expected. Therefore, as the area of turns is increased, the leaking flux of asymmetrical motor is significantly increased, too. In addition, disagreement of the results is caused by voltage oscillations in the dc link capacitor. Effectively, the supply voltage of HS phase is lower and the supply voltage of LS phases is higher than in the case of symmetrical motor. [1] P. J. Lawrenson, J. M. Stephenson, P. T. Blenkinsop, J. c orda, and N. N. Fulton, Variable speed switched reluctance motors, Proc. Inst. Elect. Eng., vol. 127, pt. B, no. 4, pp , Jul [2] I. Obradović, Doubly Salient Reluctance Machines and Their Controllability, Belgrade, Serbia: Serbian Academy of Sciences and Arts, Monographs, vol. DLXVII, no. 26, May, [3] T. J. E. Miller, Switched Reluctance Motor and Their Control. Hillsboro, OH: Magna Physics Publishing; London: Oxford University Press, [4] J. Faiz and J. W. Finch, Aspects of design optimisation for switched reluctance motors, IEEE Trans. Energy Convers., vol. 8, no. 4, pp , Dec [5] K. M. Rahman, B. Fahimi, G. Suresh, A. V. Rajarathnam, and M. Ehsani, Advantages of switched reluctance motor applications to EV and HEV: Design and control issues, IEEE IAS Conf. Record: St. Louis, MO, [6] T. J. E. Miller, Optimal design of switched reluctance motor, IEEE Trans. Ind. Electron., vol. 49, no. 1, pp , Feb [7] G. Horst, Pole Changing Switched Reluctance Motor and Method, ESCD, Emerson Electric, St. Louis, MO, U.S. Patent , [8] S. Vukosavić and V. R. Stefanovic, SRM inverter topologies: A comparative evaluation, IEEE Trans. Ind. Appl., vol. 27, no. 6, pp , Nov./Dec [9] R. Furmanek, A. French, and G. E. Horst, Horizontal axis washers, Appliance Manufacturer, pp , Mar [10] S. Mir, I. Husain, and M. E. Elbuluk, Energy-efficient C-dump converters for switched reluctance motors, IEEE Trans. Power Electron., vol. 12, no. 5, pp , Sep [11] Y. Murai, J. Cheng, and M. Yoshida, New soft-switched/switchedreluctance motor drive circuit, IEEE Trans. Ind. Appl., vol. 35, no. 1, pp , Jan./Feb [12] B. K. Bose, T. J. E. Miller, P. M. Szczesny, and W. H. Bicknell, Microcomputer control of switched reluctance motor, IEEE Trans. Ind. Appl., vol. IA-22, no. 4, pp , Jul./Aug [13] P. Tandon and A. V. Rajarathnam, Self-tuning control of a switchedreluctance motor drive with shaft position sensor, IEEE Trans. Ind. Appl., vol. 33, no. 4, pp , Jul./Aug [14] A. V. Rajarathnam, B. Fahimi, and M. Ehsani, Neural network based selftuning control of a switched reluctance motor drive to maximize torque per ampere, in IEEE IAS Conf. Rec., New Orleans, LA, Oct

8 VUJIC IĆ et al.: ASYMMETRICAL SWITCHED RELUCTANCE MOTOR FOR A WIDE CONSTANT POWER RANGE 51 [15] K. M. Rahman, G. Suresh, B. Fahimi, A. V. Rajarathnam, and M. Ehsani, Optimized torque control of switched reluctance motor at all operational regimes using neural network, in IEEE IAS Conf. Record, St. Louis, MO, Oct [16] V. Vujic ić and S. N. Vukosavić, A simple nonlinear model of the switched reluctance motor, IEEE Trans. Energy Convers., vol. 15, no. 4, pp , Dec [17] T. J. E. Miller and M. McGilp, Nonlinear theory of the switched reluctance motor for rapid computer-aided design, Proc. Inst. Elect. Eng., vol. 137, no. 6, pp , Nov Slobodan N. Vukosavić (M 93) received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Belgrade, Belgrade, Yugoslavia, in 1985, 1987, and 1989, respectively. From 1986 to 1988, he was with Nikola Tesla Institute, Belgrade, leading research in the areas of power electronics and electrical drives. In 1988, he joined ESCD Laboratory of Emerson Electric, St. Louis, MO, under the Cooperative Research Program in the field of switched reluctance motor drives and speed sensorless AC drives. In 1991, he joined Vickers Electrics, Italy; he organized and led the R/D team developing products for process automation and industrial robots. He is currently an Associate Professor at the University of Belgrade. Vladan P. Vujic ić (M 05) received the B.S. and M.S. degrees in electrical engineering from the University of Montenegro, Podgorica, Yugoslavia, in 1993 and 1995, respectively, and the Ph.D. degree from the University of Belgrade, Belgrade, Yugoslavia, in He is currently an Assistant Professor at the University of Montenegro. His research interests include power electronic applications, variable-speed drives, and microprocessor control. Milenko B. Jovanović was born in Belgrade, Yugoslavia, in He received the B.S. degree in electrical engineering from the University of Belgrade in 2003, where he is currently pursuing the M.S. degree in the Department of Power Converters and Drives. Since January 2004, he has been with Circutor SA, Barcelona, Spain. His major areas of responsibility are specialized testing and resolving power quality problems for large industrial customers. His research interests have included power quality issues, real-time measurement, and modeling and control of electric drives.