Influence of PM- and Armature Winding-Stator Positions on Electromagnetic Performance of Novel Partitioned Stator Permanent Magnet Machines

Transcription

1 IEEE TRANSACTIONS ON MAGNETICS, VOL. 53, NO. 1, JANUARY Influence of PM- and Armature Winding-Stator Positions on Electromagnetic Performance of Novel Partitioned Stator Permanent Magnet Machines J. T. Shi 1,2,A.M.Wang 1, and Z. Q. Zhu 2, Fellow, IEEE 1 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Baoding, , China 2 Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, S1 3JD, U.K. Since the permanent magnets (PMs) and armature windings of partitioned stator (PS) PM machines are located in two separate inner and outer stators, their positions can be exchanged to optimize the space utilization, especially in radial field rotating machines. Therefore, in this paper, the influence of PM and armature winding stator positions on the electromagnetic performance of PS-PM machines is investigated based on the novel PS-PM machines (PS-PMMs) with surface-mounted PM (SPM) stator. Similar to the single-stator surface-mounted PMMs (SS-PMMs), flexible rotor pole number, bipolar phase flux linkage, and symmetrical phase back electromotive force (EMF) are also obtained in PS-PMMs. Based on the same 12/10 stator/rotor pole number combination, PS-PMM-I (PMs located in the inner stator) and PS-PMM-II (PMs located in the outer stator) exhibit 120% and 160% higher phase back EMFs as well as 120% and 139% larger average torques, respectively, than the SS-PMM together almost without scarifying the PM utilization efficiency under the same machine size and the same rated copper loss. Further, the proposed PS-PMM-IIs have both higher phase back EMFs and larger average torques than PS-PMM-Is among all the main stator/rotor pole number combinations. Meanwhile, for both PS-PMM-Is and PS-PMM-IIs with 12-pole stator, the machines with the 11-pole rotor exhibit the optimal torque capabilities. Moreover, the reluctance torque is also negligible in the proposed PS-PMMs due to very low saliency ratio. The analyses are validated by experiment results of the prototype machine. Index Terms Partitioned stator (PS), permanent magnet (PM), stator position. I. S INTRODUCTION TATOR permanent magnet (PM) machines have been extensively investigated over the last decades due to the inherent merits of high torque density and high efficiency together with the robust rotor structure, easy heat dissipation, and low risk of demagnetization [1]. Similar to the conventional rotor PM machines, the locations of PMs in the stator of stator PM machines are also flexible and can be sandwiched in the stator teeth, mounted on the surface of stator teeth, and inserted in the stator yoke [2], [3], which are corresponding to the switched flux PM machines (SFPMMs) [4] [9], flux reversal PM machines (FRPMMs) [10] [13], doubly salient PM machines (DSPMMs) [14] [17] and stator yoke/statorpole-mounted PM machines [18] [21]. However, since the PMs and armature windings of stator PM machines are both located in the stator, the stator is crowded and the available space for the PM and armature winding is limited compared with conventional rotor PM machines. Consequently, their potential torque capabilities are restricted. Theoretically, increasing the stator space within the fixed machine size will be an effective solution to release the potential torque capability of stator PM machines. Then, partitioned stator (PS) configuration, which can fully utilize the inner space by separating the PMs and armature Manuscript received April 1, 2016; revised June 25, 2016; accepted August 8, Date of publication August 24, 2016; date of current version December 20, Corresponding author: J. T. Shi ( j.t.shi.emd@gmail.com). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TMAG windings into inner and outer stators together with a sandwiched modular rotor, is proposed in [22]. According to the results shown in [22] and [23], the torque capabilities of SFPMMs and FRPMMs are both significantly enhanced by introducing the PS configuration. Further, based on the PS configuration, [24] proves that SFPMMs and FRPMMs intrinsically belong to the same machine type since they have the identical operating principle and machine topology except employing spoke interior PM (Spoke-IPM) stator and surfacemounted PM (SPM) stator, respectively. Meanwhile, [24] also proposes two alternate PM stator configurations, e.g., I-shaped and V-shaped IPM stators, to suit for different application requirements. Moreover, the PS configuration is also extended to DSPMMs and stator yoke-mounted PMMs as PS-DSPMMs and PS-PMM with Spoke-IPM stator, and the investigations are provided in [25]. Accordingly, the results further evidence that all the stator PM machines can benefit from the PS configuration. Since the PMs and armature windings of partitioned stator PM machines (PS-PMMs) are located in two separate inner and outer stators, the positions of two excitation sources can be exchanged to further optimize the space utilization for maximum torque capability, especially in the radial field machines. However, the previous investigations consider only the PMs located in the inner stator [22] [27]. Therefore, this paper will investigate the influence of PM and armature winding stator positions on the electromagnetic performance of PS-PMMs based on the novel PS-PMMs with SPM stator. First, the machine topologies and operation principle of PS-PMMs with different PM stator positions are illustrated IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 IEEE TRANSACTIONS ON MAGNETICS, VOL. 53, NO. 1, JANUARY 2017 Fig. 1. Schematics of the SS-PMM and the two proposed PS-PMMs at negative and positive d-axes (corresponding to the negative and positive maximum phase flux-linkage). (a) SS-PMM, maximum. (b) SS-PMM, minimum. (c) PS-PMM-I, maximum. (d) PS-PMM-I, minimum. (e) PS-PMM-II, maximum. (f) PS-PMM-II, minimum. Then, the single-stator surface-mounted PMM (SS-PMM) and two proposed SPM stator PS-PMMs are all globally optimized with the purpose of maximum average torque under the rated 30 W copper loss. Based on the 2-D finite element analysis (FEA), the electromagnetic performance in terms of phase flux linkage and back electromotive force (EMF), dq-axis inductances, self- and mutual inductances, unbalanced magnetic force (UMF), and torque capability of two proposed PS-PMMs considering the main stator and rotor pole number combinations are investigated and compared with the SS-PMMs under the 12/10 stator/rotor pole (12S/10R) combination and the same machine size. Finally, the prototype machine with the 12S/10R combination and PMs located in the inner stator is manufactured and measured to validate the analysis. II. TOPOLOGIES AND OPERATION PRINCIPLE OF PS-PMMs A. Topologies of PS-PMMs The basic model of original SS-PMMs is shown in Fig. 1(a). The PMs are mounted on the surface of adjacent stator poles with alternate polarities while concentrated armature windings are wound around the stator poles. The PS configuration [22], which can enhance the torque capability of stator PM machines by fully utilizing the inner space, can also be introduced in SS-PMMs as SPM stator PS-PMMs. As shown in Fig. 1(c), the PMs and armature windings of PS-PMMs are located in separate inner and outer stators, respectively, while a modular rotor is adopted. Meanwhile, the second air gap is introduced in PS-PMMs between the rotor and the PM stator to allow the rotor rotating. Further, since the PM stator and armature winding stator are independent, their relative positions can be Fig. 2. Coil EMF phasors for SS-PMMs and PS-PMMs with the 12S/10R number combination. (a) Stator coil-emf phasors (mechanical degree). (b) Coil EMF phasors (electrical degree). (c) Phase coils (electrical degree). exchanged to further optimize the space utilization, especially in radial field rotating machines, as shown in Fig. 1(c) and (e). B. Operation Principle and Characteristics of PS-PMMs When the rotor pole is aligned with stator pole, as shown in Fig. 1(c) and (e), maximum coil flux linkages are obtained in both two PS-PMMs. Then, when the rotor slot is aligned with stator pole (rotor rotates by half rotor pole pitch), as shown in Fig. 1(d) and (f), minimum coil flux linkages are achieved in both two PS-PMMs. Consequently, the back EMFs will be induced in the coils of two PS-PMMs by the periodical variation of flux linkages with rotor position. Further, according to the analyses shown in [21], [28], and [29] and the similar periodical variation trend of coil flux linkages in PS-PMMs and SS-PMMs, as shown in Fig. 1, the operational principle of PS-PMMs is consistent with that of SS-PMMs, although the flux paths of PS-PMMs and SS-PMMs are different when the rotor slot is close to the stator pole due to the influence of the introduced segment rotor in PS-PMMs. Therefore, the characteristics of electromagnetic performance existing in the SS-PMM will be inherited in PS-PMMs. First, the rotor pole number is flexible and can be any integers except the phase number and its multiples [21], [29]. Second, when the ratio of the stator pole number to the greatest common divisor of stator and rotor pole numbers is equal to even integers, bipolar phase flux linkage and symmetrical phase back EMF waveforms can be obtained, although the coil flux linkage and coil back EMF are unipolar and asymmetric due to the existence of even harmonics [21], [28]. Third, the reluctance torque is negligible [21], [28]. Moreover, due to the same operational principle, the coil EMF phasor method, which used to determine the winding configuration of SS-PMMs, can be extended to PS-PMMs, where the electrical degree between two adjacent coil EMF

3 SHI et al.: INFLUENCE OF PM- AND ARMATURE WINDING-STATOR POSITIONS ON ELECTROMAGNETIC PERFORMANCE TABLE I MAIN PARAMETERS OF SS-PMM AND PS-PMM-I Fig. 3. Topologies of the SS-PMM and the two proposed PS-PMMs with the 12S/10R number combination. (a) SS-PMM. (b) PS-PMM-I. (c) PS-PMM-II. phasors can be calculated from the mechanical degree and rotor pole number [28]. By way of example, for the 12S/10R SS-PMM, PS-PMM-I, and PS-PMM-II, as shown in Fig. 3, the corresponding coil EMF phasors are shown in Fig. 2. Accounting for the alternate magnetization directions in adjacent stator poles, coil n i and coil n i are referred as the coils with additional opposite polarities, such as coils 1 (A1) and 2(B4),asshowninFigs.2(b)and3. III. PERFORMANCE COMPARISON BETWEEN SS-PMMs AND PS-PMMs In this section, the electromagnetic performance of the proposed PS-PMM-I and PS-PMM-II will be analyzed and compared with the original SS-PMM under the same 12S/10R combination and the same machine size as well as the same rated copper loss. Then, the influence of stator and rotor pole number combinations on electromagnetic performance of PS-PMM-Is and PS-PMM-IIs will also be analyzed. All machines are globally optimized with the objective of maximum average torque under the same rated 30 W copper loss by the genetic algorithm (all the geometric parameters are considered in the global optimization). The main geometry parameters are detailed in Tables I and II. Further, to simplify the drawing in this section, the SS-PMM, PS-PMM-I, and PS-PMM-II are marked as SS, PS-I and PS-II, respectively, in Figs. 4 6, 8 11, and Tables I V. Moreover, the split ratios for SS-PMM, PS-PMM-I, and PS-PMM-II are defined as the ratios of stator inner radius to stator outer radius (including the PM), outer stator inner radius to outer stator outer radius, and inner stator outer radius to outer stator outer radius, respectively. A. Influence of PM Pole Arc and Thickness Based on the results of global optimization, the influence of PM pole arc and thickness on the average electromagnetic TABLE II MAIN PARAMETERS OF PS-PMM-II torque of the SS-PMM and two proposed PS-PMMs are investigated and shown in Figs. 4 and 5, respectively (split ratio and rotor geometric shape are kept consistent). Obviously, as shown in Fig. 4, the average torque would increase at first and then tend to decrease with the PM pole arc in both SS-PMM and PS-PMM-IIs, while that would only increase with the PM pole arc in PS-PMM-Is. Correspondingly, the optimal PM pole arcs for 12S/10R SS-PMM, and 12S/10R, 12S/11R, 12S/13R, and 12S/14R PS-SPMM-IIs are 18.6, 25.0, 26.4, 27.6, and 27.4 mechanical degrees respectively, while those for 12S/10R, 12S/11R, 12S/13R, and 12S/14R PS- SPMM-Is are all 30 mechanical degrees. Further, as shown in Fig. 5, the variation trend of average torque with PM thickness is similar to that of average torque

4 IEEE TRANSACTIONS ON MAGNETICS, VOL. 53, NO. 1, JANUARY 2017 Fig. 4. Variation of average torque with PM pole-arc in the SS-PMM and PS-PMMs, p c = 30 W. Fig. 6. Variation of minimum PM flux density with PM thickness in the SS-PMM and PS-PMMs, p c = 30 W, 120 C, B r = 1.08 T. 12S/13R, and 12S/14R PS-PMM-Is, the PM thicknesses are all chosen as 3.5 mm (yellow marks) when the tradeoff among the average torque, PM utilization efficiency, and demagnetization withstanding capability is considered. Furthermore, for PS-PMM-IIs, the PM thicknesses for 12S/10R, 12S/11R, 12S/13R, and 12S/14R stator/rotor pole number combinations are 2.5, 2.6, 2.6, and 2.7 mm (yellow marks), respectively, since they not only have the maximum average torques but also have the approximately optimal demagnetization withstanding capabilities. Fig. 5. Variation of average torque with PM thickness in the SS-PMM and PS-PMMs, p c = 30 W. with PM pole arc for the SS-PMM and all the PS-PMMs. The reason can be explained as follows. For the SS-PMM, the increased PM thickness would increase the average air gap flux density (magnetic loading) but also reduce the stator slot area (electric loading). Hence, there will be an optimal PM thickness for the SS-PMM. For the PS-PMMs, the increased PM thickness would also increase the magnetic loading but without influence on the stator slot area (electric loading) since the PMs and armature windings are located in two separate stators. However, different from PS-PMM-Is, the influence of increased PM thickness on the saturation of PM stator yoke in PS-PMM-IIs will be more sensitive and significant since their PM stator thickness is much thinner than PS-PMM-Is. Therefore, an optimal PM thickness will be obtained in PS-PMM-IIs. The risk of demagnetization should also be considered during the selection of PM thickness. To check the demagnetization withstanding capability under the rated on-load condition ( p c = 30 W), 120 C is set for the simulation models, while the corresponding magnetic remanence B r and knee point of demagnetization curve are 1.08 T and 0.22 T, respectively. Fig. 6 shows the variation of minimum PM flux density against the different PM thickness. Based on Figs. 5 and 6, the PM thickness of 12S/10R SS-PMM should be chosen as 2 mm (yellow mark) to avoid the demagnetization although the optimal value for maximum average torque is 1.4 mm (black mark). Then, for the 12S/10R, 12S/11R, B. Open-Circuit Field Distribution The open-circuit equipotential and flux density field distributions for all machines at aligned position (negative d-axis rotor position) are shown in Fig. 7. Obviously, for both PS-PMM-Is and PS-PMM-IIs, the flux loop of each coil belonging to the same phase is completely independent within 12S/10R and 12S/14R, while that is dependent within 12S/11R and 12S/13R, which is consistent with SS-PMM. Meanwhile, short flux path, which could result in lower MMF drop in the stator and thinner thickness of stator yoke, is also observed in all machines. Moreover, the saturation in PS-PMM-IIs is much heavier than those in the SS-PMM and PS-PMM-Is, especially in the regions of stator yoke that are close to the gaps between the adjacent PMs. Fig. 8 shows the open-circuit air-gap flux density waveforms for 12S/10R SS-PMM and two PS-PMMs at the aligned position. Since the PS-PMMs have two layers of air gap, the corresponding waveforms shown in Fig. 8 are based on the layers that are close to the stator wound with armature windings. It can be seen that the waveforms of two PS-PMMs are similar to those of the SS-PMM. C. Flux Linkage and Back-EMF Waveforms The open-circuit phase flux linkages of all machines are shown in Fig. 9. Obviously, symmetrical bipolar phase flux linkages are obtained in all machines since the even harmonics, which cause the biased value and asymmetric waveform in each coil, are completely canceled in the phase winding. Therefore, these four stator/rotor pole number combinations can be used to verify the second characteristic as summarized

5 SHI et al.: INFLUENCE OF PM- AND ARMATURE WINDING-STATOR POSITIONS ON ELECTROMAGNETIC PERFORMANCE Fig. 8. Open-circuit air-gap flux density at aligned position. Fig. 9. Open-circuit phase flux linkages of the SS-PMM and PS-PMMs. (a) Waveforms. (b) Spectra. Fig. 7. Open-circuit equipotential and flux density field distributions at aligned position. (a) SS-PMM_10R. (b) PS-PMM-I_10R. (c) PS- PMM-II_10R. (d) PS-PMM-I_11R. (e) PS-PMM-II_11R. (f) PS-PMM-I_13R. (g) PS-PMM-II_13R. (h) PS-PMM-I_14R. (i) PS-PMM-II_14R. in Section II-B. According to Tables III and IV, the magnitudes of fundamental phase flux linkages for the 12S/10R SS-PMM, 12S/10R PS-PMM-I, and 12S/10R PS-PMM-II are 3.84, 8.46, and 9.96 mwb, respectively. Compared with the 12S/10R SS-PMM, the fundamental phase flux linkages for 12S/10R PS-PMM-I and 12S/10R PS-PMM-II are enhanced by 120% and 160%, respectively. Moreover, as shown in Fig. 9, the fundamental phase flux linkages are enhanced in PS-PMM-IIs compared with PS-PMM-Is under the same stator/rotor pole number combinations. Further, for both PS-PMM-Is and PS-PMM-IIs, the highest fundamental phase flux linkages are all achieved in the 12S/10R number combination. Based on the same reason as the phase flux linkages, symmetrical phase back EMFs are also obtained in all machines as shown Fig. 10. Meanwhile, compared with the 12S/10R SS-PMM, the fundamental phase back EMFs for

6 IEEE TRANSACTIONS ON MAGNETICS, VOL. 53, NO. 1, JANUARY 2017 TABLE III ELECTROMAGNETIC PERFORMANCES OF SS-PMM AND PS-PMM-Is TABLE IV ELECTROMAGNETIC PERFORMANCES OF SS-PMM AND PS-PMM-IIs Fig. 11. Variation of dq-axis inductances with current angle under the rated currents, as given in Tables I and II, p c = 30 W. Fig. 12. Equipotential distribution at aligned position with injecting rated q-axis currents, PMs are replaced by air. (a) SS-PMM_10R. (b) PS-PMM-I_10R. (c) PS-PMM-II_10R. number combinations, which are 17.8%, 20.3%, 19.1%, and 20.7% corresponding to 12S/10R, 12S/11R, 12S/13R, and 12S/14R, as shown in Fig. 10. In addition, due to the influence of rated electrical frequency, the highest fundamental phase back EMFs for PS-PMM-Is and PS-PMM-IIs are both achieved in the 12/11 stator/rotor pole number combination. Fig. 10. Open-circuit phase back EMFs of the SS-PMM and PS-PMMs, 400 r/min. (a) Waveforms. (b) Spectra. 12S/10R PS-PMM-I and 12S/10R PS-PMM-II should also be enhanced by 120% and 160%, respectively, due to the same rated electrical frequencies (66.7 Hz at 400 r/min). It can be evidenced by the results shown in Tables III and IV, which are 1.61, 3.54, and 4.17 V, respectively. Further, PS-PMM-IIs always exhibit higher fundamental phase back EMFs than PS-PMM-Is under the same stator/rotor pole D. DQ-Axis Inductances Fig. 11 shows the dq-axis inductances of the SS-PMM and two proposed PS-PMMs with the same 12S/10R number combination against different current angles with the rated currents, as given in Tables I and II. Similar to the SS-PMM, the d-axis inductances are also quite close to q-axis inductances in both PS-PMM-I and PS-PMM-II. Consequently, the saliency ratios are all close to 1. Therefore, the potential reluctance torques can be negligible in both PS-PMM-I and PS-PMM-II. Moreover, both PS-PMM-I and PS-PPM-II exhibit higher dq-axis inductances than the SS-PMM due to the shorter equivalent air-gap length in the main magnetic flux path, as shown in Fig. 12. E. Self- and Mutual Inductances Fig. 13 shows the variation waveforms of self- and mutual inductances against with rotor position for all machines with

7 SHI et al.: INFLUENCE OF PM- AND ARMATURE WINDING-STATOR POSITIONS ON ELECTROMAGNETIC PERFORMANCE Fig. 13. Variation of self- and mutual inductances with rotor position in the SS-PMM and PS-PMMs, p a = 10 W. Fig. 15. UMFs for the SS-PMM and PS-PMMs at rated currents as given in Tables I and II, p c = 30 W and I d = 0 control. of cogging torque than the 12S/10R SS-PMM. Moreover, for both PS-PMM-Is and PS-PMM-IIs with a 12-pole stator, the machines with 11- and 13-pole rotors exhibit lower cogging torques than those with 10- and 14-pole rotors. As shown in Fig. 14, since the main harmonics of cogging torques in 12S/10R, 12S/11R, 12S/13R, and 12S/14R PS-PMMs are 6n, 12n, 12n, and6n times, the corresponding cogging torques exhibit 6, 12, 12, and 6 cycles, respectively, during one electrical period. Fig. 14. Open-circuit cogging torques of the SS-PMM and PS-PMMs. (a) Waveforms. (b) Spectra. the 12S/10R number combination. p a = 10 W is corresponding to the copper loss produced by the dc current, which is injected into the phase A winding. Obviously, both PS-PMM-I and PS-PMM-II exhibit higher self- and mutual inductances, which are both 2.7 and 3 times those for the SS-PMM, respectively. It is also due to the shorter equivalent air-gap length in the main magnetic flux path of PS-PMMs compared with that of the SS-PMM. F. Cogging Torque The cogging torque waveforms of all machines are shown in Fig. 14. It can be seen that both 12S/10R PS-PMM-I and 12S/10R PS-PMM-II exhibit slightly larger magnitudes G. Unbalanced Magnetic Force Fig. 15 compares the UMFs of all machines under the rated currents (p c = 30 W) and I d = 0 control. Obviously, different from machines with even rotor pole number, the machines with odd rotor pole number suffer from the significant UMF. Among the four stator/rotor pole number combinations, the largest UMFs of PS-PMM-Is and PS-PMM-IIs are observed in 12S/13R and 12S/11R, respectively. Meanwhile, compared with PS-PMM-IIs, PS-PMM-Is exhibits smaller UMF in 12S/11R, while it has larger UMF in 12S/13R. Moreover, the UMF may reduce the lifetime of bearing and also cause the vibration and noise. To eliminate the UMF of machines with odd rotor pole number, doubling the stator and rotor pole number simultaneously is one of the effective solutions for some applications, such as 24S/22R and 24S/26R. H. Electromagnetic Torque Characteristics Fig. 16 shows the waveforms of average torque against current angle at rated currents (p c = 30 W) for all machines. Obviously, the optimal current angles in both PS-PMM-Is and PS-PMM-IIs are all close to 0, which are the same as those in SS-PMMs. The results also indicate that the reluctance torques are negligible in both PS-PMM-I and PS-PMM-II, which is consistent with the conclusion mentioned in Section III-D. Meanwhile, it also can be used to verify the third characteristic as summarized in Section II-B. Fig. 17 shows the waveforms of torque against rotor position at rated currents (p c = 30 W) and I d = 0 control for all machines. Due to the combined influences of cogging

8 IEEE TRANSACTIONS ON MAGNETICS, VOL. 53, NO. 1, JANUARY 2017 Fig. 16. Variation of average torque with current angle under the rated currents for all machines as given in Tables I and II, p c = 30 W. Fig. 18. Torque density and torque per PM volume, p c = 30 W and I d = 0 control. Fig. 17. Variation of electromagnetic torque with rotor position in the SS-PMM and PS-PMMs at rated current as given in Tables I and II, p c = 30 W and I d = 0 control. (a) Waveforms. (b) Spectra. torque and back EMF harmonics (mainly in the fifth and seventh), all machines have six torque ripples over one electrical period. As shown in Tables III and IV, the torque ripples of the 12S/10R SS-PMM, 12S/10R PS-PMM-I, and 12S/10R PS-PMM-II are 11%, 14%, and 17.8%, respectively. Obviously, the torque ripple is increased in PS-PMMs compared with the SS-PMM, especially in PS-PMM-II. Moreover, for both PS-PMM-Is and PS-PMM-IIs with the 12-pole stator, the machines with 11- and 13-pole rotors exhibit a lower torque ripple than those with 10- and 14-pole rotors, as shown in Tables III and IV. As shown in Fig. 17, the average torque is enhanced significantly by employing the PS configuration. According to Tables III and IV, the average torques for the 12S/10R SS-PMM, 12S/10R PS-PMM-I, and 12S/10R PS-PMM-II under the rated copper loss are 1.29, 2.84, and 3.08 Nm, respectively. Compared with the 12S/10R SS-PMM, the average torque is enhanced by 120% and 139%, respectively, in 12S/10R PS-PMM-I and 12S/10R PS-PMM-II. Further, under the same stator/rotor pole number combinations, PS-PMM-IIs exhibit higher average torque than PS-PMM-Is, which are 8.5%, 7.9%, 10.8%, and 14.0% corresponding to 12S/10R, 12S/11R, 12S/13R, and 12S/14R, as shown in Fig. 17. Moreover, for both PS-PMM-Is and PS-PMM-IIs with the 12-pole stator, the machines with the 11-pole rotor exhibit the largest average, while the machines with 14-pole rotor have the smallest one, as shown in Fig. 17 and Tables III and IV. Fig. 18 compares the torque density and torque per PM volume of all machines at the rated currents (p c = 30 W) and I d = 0 control. Since all machines have the same machine size, the increase rates of torque density are consistent with the increase rates of average torque. As shown in Tables III and IV, the torque densities for 12S/10R SS-PMM, 12S/10R PS-PMM-I, and 12S/10R PS-PMM-II are 8.1, 17.9, and 19.4 knm/m 3, respectively. Similarly, for both PS-PMM-Is and PS-PMM-IIs with the 12-pole stator, the machine with the 11-pole rotor exhibits the largest torque density, while the machine with the 14-pole rotor has the smallest one, as shown in Fig. 18. Moreover, for the torque per PM volume (PM utilization efficiency), it is slightly decreased in 12S/10R PS-PMM-I (2.2%) but small increased in 12S/10R PS-PMM-II (3.1%) compared with the 12S/10R SS-PMM. Further, among the four stator/rotor pole number combinations, 12S/11R PS-PMM-I and 12S/10R PS-PMM-II have the highest PM utilization efficiency, respectively. Fig. 19 compares the torque performances of all machines under different copper losses. The vertical dashed and dotted line shows the rated copper loss, which is used for global optimization. Similar to the SS-PMMs, the increase rates of average torque in the two proposed PS-PMMs will be declined with the rising of copper loss (current) due to the aggravated magnetic saturation. Moreover, both 12S/10R PS-PMM-I and 12S/10R PS-PMM-II exhibit much larger average torques than 12S/10R SS-PMM under the same copper loss over the whole

9 SHI et al.: INFLUENCE OF PM- AND ARMATURE WINDING-STATOR POSITIONS ON ELECTROMAGNETIC PERFORMANCE Fig. 19. Variation of average torque with copper loss in the SS-PMM and PS-PMMs, I d = 0 control. TABLE V REOPTIMIZED PM PARAMETERS OF PS-PMMs HAVING THE IDENTICAL PM USAGE VOLUME OF SS-PMMs Fig. 20. Open-circuit phase back EMFs of the SS-PMM and PS-PMMs having the identical PM usage volume of SS-PMMs, 400 r/min. (a) Waveforms. (b) Spectra. copper loss range. Further, compared with PS-PMM-Is under the same stator/rotor pole number combinations, the torque capability of PS-PPM-IIs is further enhanced during the whole copper loss range. In addition, for both PS-PMM-Is and PS-PMM-IIs with the 12-pole stator, the machines with the 11-pole rotor have the optimal torque capability over the whole copper loss range. IV. COMPARISON BETWEEN SS-PMMs AND PS-PMMs HAVING IDENTICAL PM USAGE VOLUME OF SS-PMMs In Section III, the electromagnetic performance of proposed PS-PMM-Is and PS-PMM-IIs are comprehensively compared with that of the original SS-PMM based on the results of tradeoff between the globe optimization with the purpose of maximum average torque and PM demagnetization withstanding capability. However, since the PM usage volumes in these machines are significantly different, it is meaningful to further investigate the machines with an identical PM usage volume. Based on the identical PM usage volume of the 12S/10R SS-PMM, PS-PMM-Is and PS-PMM-IIs with all the stator/rotor pole number combinations are reoptimized (global optimization) with the purpose of maximum average torque under the rated 30 W copper loss without considering the PM demagnetization withstanding capability. The reoptimized Fig. 21. Torque waveforms of the SS-PMM and PS-PMMs having the identical PM usage volume of SS-PMMs at the rated currents, p c = 30 W, I d = 0 control. design parameters are listed in Table V, in which the identical PM usage volume can be observed. Obviously, for all PS-PMM-Is and PS-PMM-IIs, the PM pole arcs and the PM thicknesses are both reduced. Fig. 20 compares the phase back EMFs of all machines at rated speed 400 r/min. Obviously, 12S/10R PS-PMM-I and 12S/10R PS-PMM-II still exhibit higher fundamental phase back EMFs than the 12S/10R SS-PMM, which are 75% and 116%, respectively. The increase rates are lower than those shown in Section III due to the less PM usage volume. Further, compared with PS-PMM-Is under the same stator/rotor pole number combinations, PS-PMM-IIs still exhibit higher

10 IEEE TRANSACTIONS ON MAGNETICS, VOL. 53, NO. 1, JANUARY 2017 Fig. 22. Average torque with different copper losses of the SS-PMM and PS- PMMs having the identical PM usage volume of SS-PMMs, I d = 0 control. Fig. 24. Rotor lamination with bridge for 12S/10R PS-PMM-I. Fig. 23. Prototype of 12S/10R PS-PMM-I. (a) Outer stator with 12 stator poles. (b) Inner stator with 12 PMs. (c) Assembled stator. (d) Rotor with 10 rotor poles. Fig. 25. Measured and FE predicted phase back EMFs at 400 r/min. (a) Waveform. (b) Spectra. TABLE VI PARAMETERS OF PROTOTYPE MACHINE (12S/10R PS-PMM-I) fundamental phase back EMFs. Meanwhile, for both PS-PMM-Is and PS-PMM-IIs, their highest fundamental phase back EMFs are still achieved in the 12/11 stator/rotor pole number combination. The torque waveforms of all machines under the rated 30 W copper loss and I d = 0 control are presented in Fig. 21, while the waveforms of average torque against different copper losses are shown in Fig. 22. It can be seen that 12S/10R PS-PMM-I and 12S/10R PS-PMM-II still exhibit larger average torque than the 12S/10R SS-PMM under the same copper loss over the whole copper loss range. The increase rates of average torque under the rated 30 W copper loss are 91% and 117%, respectively, for 12S/10R PS-PMM-I and 12S/10R PS-PMM-II compared with the 12S/10R SS-PMM, which also are lower than those shown in Section III due to less PM usage volume. Moreover, based on the same stator/rotor pole number combination and the same copper loss, PS-PMM-IIs still exhibit larger average torque than PS-PMM-Is over the whole copper loss range. Further, among the four stator/rotor

11 SHI et al.: INFLUENCE OF PM- AND ARMATURE WINDING-STATOR POSITIONS ON ELECTROMAGNETIC PERFORMANCE Fig. 26. Measured and FE predicted open-circuit cogging torques. Fig. 28. Measured and FE predicted torque current characteristics waveforms when rotor position is 90. and shown in Fig. 28. With the increase of current, more severe end effect will be caused by the saturation. Correspondingly, the difference between the measured and predicted results will be bigger at high current. Overall, the measured results match well with the FE predictions. Fig. 27. Measured and FE predicted static torques, I DC = I A = 2I B = 2I C. pole number combinations, PS-PMM-Is and PS-PMM-IIs with the 11-pole rotor still have the optimal torque capability over the whole copper loss range. V. EXPERIMENTAL VERIFICATION The prototype machine of 12S/10R PS-PMM-I is made to validate the previous analyses, as shown in Fig. 23. To reduce the cost, this prototype machine is assembled by the existing inner stator (12 PMs), outer stator (12-pole), and modular rotor (10-pole). Hence, the parameters of prototype machine as shown in Table VI are different from the previous globally optimized parameters as shown in Table I. Moreover, for easing the fabrication, a ten-pole modular rotor is mechanically connected by the lamination bridges (T BRI = 0.5 mm) in the inner side, as shown in Figs. 23(d) and 24. Fig. 25 shows the predicted and measured phase back EMFs at rated speed (400 r/min). The measured fundamental value is 4% less than the prediction, which is mainly due to the end effect in 25 mm stack length machine. The predicted and measured open-circuit cogging torque waveforms are shown in Fig. 26. It can be seen that the measured peak-to-peak value is slightly larger than the finite element (FE) prediction. This difference is acceptable when considering the measurement error and assembling tolerance. Fig. 27 shows the waveforms of static torque against with rotor position at five different armature currents, i.e., 5, 10, 15, 20, and 25 A (I DC = I A = 2I B = 2I C ). Based on Fig. 27, the variation of the static torque at 90 rotor position with different currents is obtained VI. CONCLUSION Based on the novel PS-PMMs with the SPM stator, the influence of PM and armature winding stator positions on the electromagnetic performance of PS-PMMs is investigated. Similar to the SS-PMMs, PS-PMMs also have flexible rotor pole numbers, bipolar phase flux linkage, and symmetrical phase back EMF waveforms. Compared with the SS-PMM under the same 12S/10R number combinations and the same rated copper loss, the proposed PS-PMM-I and PS-PMM-II exhibit 120% and 160% higher phase back EMFs as well as 120% and 139% larger average torques, respectively, together almost without scarifying the PM utilization efficiency. Further, for all the 12/10, 12/11, 12/13, and 12/14 stator/rotor pole number combinations, PS-PMM-IIs exhibit both higher phase back EMFs and larger average torques than PS-PMM-Is, which are 17.8%, 20.3% 19.1%, and 20.7%, respectively, for the phase back EMF, while 8.5%, 7.9%, 10.8% and 14.0%, respectively, for the average torque under the rated copper loss. Meanwhile, the optimal torque capabilities for PS-PMM-Is and PS-PMM-IIs are both obtained in the 12/11 stator/rotor pole number combination. Moreover, the reluctance torque is negligible in PS-PMMs since the saliency ratio is quite close to 1, which is also consistent with the SS-PMMs. Finally, the analyses have been validated by both the FEA and the measurement. ACKNOWLEDGMENT This work was supported in part by State Key Laboratory of Alternate Electrical Power System through Renewable Energy Sources of China under Grant LAPS REFERENCES [1] Z. Q. Zhu and D. Howe, Electrical machines and drives for electric, hybrid, and fuel cell vehicles, Proc. IEEE, vol. 95, no. 4, pp , Apr

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