IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010
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Optimization of a Switched Reluctance Motor Made of Permendur Yu Hasegawa, Kenji Nakamura, and Osamu Ichinokura School of Engineering, Tohoku University, Sendai 980-8579, Japan A switched reluctance (SR) motor has a doubly salient pole structure. A stator has concentrated windings on each pole, while a rotor is only made of iron core. Therefore, the SR motor is expected as a low cost, extremely robust, variable speed motor. The performance of the SR motor greatly depends on magnetic properties of core material since it consists of only laminated-core and windings. This paper investigates the performance of an SR motor made of permendur which has extremely high saturation flux density and very low core loss. Motor torque, iron loss, and efficiency of the SR motor are estimated by finite element method (FEM). Furthermore, a suitable structure for the SR motor made of permendur is examined based on the design of experiments. Index Terms—Design of experiments, finite element method (FEM), permendur, switched reluctance (SR) motor.
I. INTRODUCTION HE DEMAND FOR electric motors keeps on increasing in various fields such as living, industry, and transportation. Therefore, the improvement of size and weight, torque, and efficiency of the motors is strongly required. Following the advancement of the power electronics technology, an AC motor has achieved the same controllability as a conventional DC motor. As a result, an induction motor and a permanent magnet synchronous motor have received practical application due to a simple and robust structure, and maintenance-free. In addition, a switched reluctance (SR) motor is also expected as a low cost, extremely robust, variable speed motor [1], and its application to the electric vehicle (EV) and the hybrid EV (HEV) is anticipated. The SR motor has a doubly salient pole structure, and consists of only laminated-core and windings. The concentrated windings are coiled around each stator pole, while the rotor is only made of laminated-core. Hence, its performance greatly depends on magnetic properties of core material. In previous papers, we have examined the SR motors with divided-core [2] and with C-shapedcore [3], respectively, in order to utilize grain-oriented silicon (Si) steel. These SR motors exhibit the high power and efficiency, but the productivity is low due to a complicated structure. This paper investigates the performance of an SR motor made of permendur by finite element method (FEM). The permendur, which is the isotropic material, has extremely high saturation flux density and very low core loss [4].
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II. COMPARISON OF SR MOTORS MADE OF NON-ORIENTED SILICON STEEL AND PERMENDUR A. Basic Configuration and Operating Principle of the 6/4-Pole SR Motor Fig. 1 shows the specifications of the present three-phase 6/4-pole SR motor. The core material is non-oriented Si steel (35A300) with a thickness of 0.35 mm. The rated power is about 300 W. In this section, the characteristics of the present SR motor and that made of permendur are compared. Fig. 2 shows a general configuration of the SR motor drive circuit, which is called asymmetric half bridge converter. Every phase winding is connected to a couple of transistors and freeManuscript received October 20, 2009; revised January 04, 2010; accepted January 19, 2010. Current version published May 19, 2010. Corresponding author: Y. Hasegawa (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2010.2041903
Fig. 1. Specifications of the present 6/4-pole SR motor.
Fig. 2. Asymmetric half bridge converter.
wheeling diodes. In the motoring mode, electric power from DC battery is supplied to the windings through the transistors. Contrary to this, in the regenerating mode, stored energy of the SR motor is back to DC buttery through the free-wheeling diodes. Fig. 3 illustrates the rotating principle of the SR motor. If the B-phase winding is excited when the A-phase stator pole and the rotor pole of are aligned as shown in the figure, the rotor pole of is attracted to the B-phase stator pole by the electromagnetic force, and the rotor rotates to the position where the B-phase stator pole and the rotor pole of are aligned. After that, by switching the excitation phase to the C-phase, the rotor rotates continuously to the position where the C-phase stator pole and the rotor pole of are aligned. A continuous rotation can be obtained by switching the excitation phase with the appropriate order described above. Now, let the rotor position angle be , which is 0 deg. when a rotor pole is in aligned position relative to the A-phase stator pole as shown in Fig. 4(a), while deg. in the case of unaligned position. Fig. 4(b) illustrates the A-phase inductance , exciting voltage , and current , respectively. In the figure, the excitation beginning angle and the excitation width are and , respectively. If the magnetic nonlinearity is ignored, the A-phase torque of the SR motor is given by
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Fig. 3. Rotating principle of the SR motor.
Fig. 5. Analytical model of the 6/4-pole SR motor. (a) Two-dimensional FEM model of the 6/4-pole SR motor. (b) Drive circuit model. (c) Switching pattern of the transistors. Fig. 4. Schematic diagram of waveforms of A-phase inductance L , exciting . (b) Waveforms of voltage v and current i . (a) Rotor position angle L ; v , and i .
=0
It is understood from (1) that the positive torque can be obtained when the A-phase winding is excited in Region I of Fig. 4(b). On the other hand, the negative torque is generated when the A-phase winding is excited in Region II. Therefore, the SR motor requires the position detection by a rotary encoder or a hole sensor. B. FEM Model of the 6/4-Pole SR Motor
Fig. 6. Comparison of B-H curves.
Fig. 5(a) shows a two-dimensional FEM model of the 6/4-pole SR motor, and (b) indicates an electric circuit model of the drive circuit, which is coupled with the FEM model. In the figure, transistors are approximately expressed as ideal switches. Fig. 5(c) illustrates the switching pattern of each deg., phase transistor. As shown in the figure, deg. Fig. 6 shows the - curves of core material. The figure indicates that the saturation flux density of permendur is larger than that of conventional non-oriented Si steel by 40% or more. C. Comparison of the SR Motors Made of Non-Oriented Si Steel and Permendur
Fig. 7. Current density versus torque characteristics.
Fig. 7 shows the current density versus torque characteristics of the SR motors made of non-oriented Si steel and permendur. In the figure, the symbols denote the measured values of the non-oriented Si steel. This figure reveals that the calculated and measured values of non-oriented Si steel are in good agreement. The maximum torque of the SR motor made of permendur at a current density of 15 A/mm is larger than that of nonoriented Si steel by over 40%. (Nowadays, in the EV and HEV, the current density is rising up to 15 A/mm or more on the assumption that the windings are well cooled.) Fig. 8 indicates the rotational speed versus torque characteristics. From the figure, it is clear that the controllable speed
range of the SR motor made of permendur is wider than that of non-oriented Si steel if the generation torque is limited by the maximum current density of 15 A/mm . The iron loss of the SR motor is calculated from Steinmetz’s equation shown below (2) where, the first term shows hysteresis loss and the second term indicates eddy current loss. The coefficients are and , which are obtained from the intercept and the gradient of core loss curves of core materials shown in Fig. 9. Therefore, the -th
HASEGAWA et al.: OPTIMIZATION OF A SWITCHED RELUCTANCE MOTOR MADE OF PERMENDUR
Fig. 8. Rotational speed versus torque characteristics.
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Fig. 11. Efficiency characteristics of the SR motors.
Fig. 9. Core loss curves of core material.
Fig. 12. Flow chart of the design of experiments.
Fig. 10. Torque versus iron loss characteristics.
harmonic iron loss can be obtained from frequency and the amplitude of the -th harmonic flux density . The total iron loss of the SR more is given as the sum of every harmonic iron loss shown below
Fig. 13. Controllable factors for the design of experiments. TABLE I LEVEL VALUES OF THE CONTROLLABLE FACTORS
(3) where, the mass density is and the volume is , respectively. In this paper, the terms up to 20th order harmonic were considered. Fig. 10 indicates the torque versus iron loss characteristics. The iron loss of the SR motor made of permendur is halved as compared to that of non-oriented Si steel. Fig. 11 shows the efficiency characteristics. This figure clearly indicates that the efficiency of the SR motor made of permendur is higher than that of non-oriented Si steel over all the operating range. III. OPTIMUM DESIGN OF THE SR MOTOR MADE OF PERMENDUR In the previous section, it was indicated that the maximum torque and efficiency are improved by employing permendur, but torque under continuous operating region (less than 10 A/mm ) was not improved enough. In this section, by noticing
the high saturation flux density of permendur, the balance of iron core and windings of the SR motor is adjusted for further improvement. The design of experiments is employed for the optimization of the SR motor made of permendur. Fig. 12 shows the flow chart. At the beginning, the target function is determined, which is the maximization of torque at a current density of 10 A/mm in this paper. Next, four controllable factors A, B, C and D shown in Fig. 13 are chosen from the standpoint of the high saturation flux density of permendur, and then the three level values of these controllable factors are selected as shown in Table I. Based on the combinations of the level of these controllable factors, Table II is prepared, which is called “the orthogonal table L9” because the number of calculations for finding the
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TABLE II ORTHOGONAL TABLE L9
Fig. 15. Current density versus torque characteristics.
Fig. 14. Factor effect diagram corresponding to torque. Fig. 16. Copper and iron loss characteristics.
TABLE III MAIN SPECIFICATIONS OF THE SR MOTORS
best combination of the controllable factors is reduced to nine, while it takes generally times without the design of experiments. According to “the orthogonal table L9,” torque about nine combinations of the controllable factors are calculated by FEM. The results are shown in Table II. In the table, torque sensitivity is defined by dB
(4)
where, the average torque at 10 A/mm is . Finally, by calculating the average values of the torque sensitivities, the factor effect diagram shown in Fig. 14 is obtained. The figure indicates that every controllable factor A, B, C and D has the peak value at the second level, namely, this is the best combination. In the same manner described above, the SR motor made of non-oriented Si steel was also optimized. Table III shows the main specifications of the SR motors. Model A and B have initial dimensions, while Model C and D have the optimal dimensions. Fig. 15 shows current density versus torque characteristics of these four SR motors. The figure clearly reveals that the torque of the optimized SR motor made of permendur is further improved, and the rated torque at 10 A/mm is greater than that of non-oriented Si steel by 50%. Fig. 16 shows the copper and iron loss characteristics. The copper loss of the optimized SR motor is decreased greatly although the iron loss is increased slightly. Fig. 17 shows the efficiency characteristics. It is understood that the efficiency of the optimized SR motor made of perme-
Fig. 17. Efficiency characteristics of the SR motors.
ndur is improved from the initial one, especially under heavy load condition. IV. CONCLUSION This paper investigated the optimization of the SR motor made of permendur. The balance of iron core and windings of the SR motor was optimized by noticing the high saturation flux density of permendur. As a result, stator core was decreased, while winding region was increased. The optimized SR motor made of permendur exhibits large rated torque as compared to that made of non-oriented Si steel by 50%, and high efficiency of almost 85%, especially it is remarkably improved under heavy load condition. REFERENCES [1] R. C. Becerra, M. Ehsani, and T. J. E. Miller, “Commutation of SR motors,” IEEE Trans. Power Electron., vol. 8, pp. 257–263, 1993. [2] K. Nakamura, T. Ono, H. Goto, T. Watanabe, and O. Ichinokura, “A novel switched reluctance motor with wound-cores put on stator and rotor poles,” IEEE Trans. Magn., vol. 41, no. 10, pp. 3919–3921, Oct. 2005. [3] K. Murota, K. Nakamura, and O. Ichinokura, “Calculation of characteristics of an SR motor with divided stator core made of grain-oriented silicon steel,” in Proc. 17th ICEM Conf., 2006, OTA2-2. [4] J. Ish-Shalom, “Composite magnetic structure for planar motors,” IEEE Trans. Magn., vol. 31, no. 6, pp. 4077–4079, Nov. 1995.
