VERNIER permanent magnet motors (VPMM) are essentially

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1 2088 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 53, NO. 3, MAY/JUNE 2017 Torque Performance Comparison Between a Ferrite Magnet Vernier Motor and an Industrial Interior Permanent Magnet Machine Zhentao S. Du, Student Member, IEEE, and Thomas A. Lipo, Life Fellow, IEEE Abstract This paper proposes a low-speed dual-stator spoketype vernier permanent magnet motor (DSSVPMM) using ferrite permanent magnets (PMs). The machine is designed and verified by finite element (FE) analysis. The final design is compared against a commercial industrial interior permanent magnet machine (IPMM) using rare earth PMs and a single air gap vernier spoke-type PM machine. The final design demonstrates higher torque density, lower torque ripple, and higher efficiency than those of the IPMM and the single air gap vernier spoke-type PM machine. A PM demagnetization analysis is provided for different fault currents and temperatures. The analysis concludes that the ferrite PMs are able to withstand the fault current without evidence of severe irreversible demagnetization. The proposed design also shows balanced net radial force. Index Terms Demagnetization, efficiency, fault currents, finite element (FE) modeling, harmonics, permanent magnet (PM) machines, radial force analysis, torque density, torque ripple ratio. I. INTRODUCTION VERNIER permanent magnet motors (VPMM) are essentially machines embedded with electrical gears. Although the reluctance vernier motor (VM) was developed 50 years ago, not much attention has been paid to VMs during the intervening years [1]. This type of motor is particularly suitable for low-speed motoring/generating applications because it produces high torque at low speed, analogous to the mechanical gear-down operation. Adding permanent magnets (PMs) onto the rotor improves the torque and power density [2], but still produces undesirable low power factor at the stator terminal due to the harmonic leakage in the air gap [3]. The power factor is inversely proportional to the slot per pole per phase (SPP) of the VM stator, providing a key to improving the VM power factor [4]. Manuscript received September 2, 2016; revised December 23, 2016; accepted February 12, Date of publication February 23, 2017; date of current version May 18, Paper no EMC R1, presented at the 2015 Energy Conversion Congress and Exposition, Montreal, QC, Canada, Sep , and approved for publication in the IEEE TRANSACTIONS ON INDUS- TRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. The authors are with the Wisconsin Electric Machines and Power Electronics Consortium, Department of Electrical and Computer Engineering, University of Wisconsin Madison, Madison, WI USA ( zdu4@wisc.edu; lipo@engr.wisc.edu). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TIA Adapting a dual-excitation and dual-rotor structure can further increase torque density by effectively utilizing the unused space within a machine structure [5] [8]. The dual-stator structure can improve the torque density by nearly 50% compared to a single stator [9] and also elevates the power factor [5] [7]. While recent development of dual-stator spoke-type vernier permanent magnet motors (DSSVPMMs) has improved torque density, the choice of ferrite magnets has not yet been considered with the aim of lowering the material cost of the machine. In addition, the issue of demagnetization for the PMs in VPMMs under fault condition has not yet been addressed. Furthermore, the net radial force of the dual-stator structure for VPMM has not yet been studied. Unbalanced radial force can cause rotor eccentricity, shorter bearing life, vibration, and noise [10]. The objective of the paper is to develop a DSSVPMM using ferrite magnets which can directly replace a commercial interior permanent magnet machine (IPMM) using rare-earth PMs for a low-speed industrial fan application. The susceptibility of the ferrite PMs to demagnetization is studied under various fault currents and temperatures. Based on this study, the ferrite PMs are proven to be capable of withstanding a fault current up to three times the rated current. The performance of the DSSVPMM is compared to that of an existing IPMM. Based on the comparisons, the proposed DSSVPMM using ferrite magnets demonstrates 33% higher torque density, 4% higher efficiency, and 13% less copper usage than those of the existing IPMM using rare-earth PMs. II. PRINCIPLE OF OPERATION VPMMs operate based on the principle of electrical gears that allows the torque production to occur at a stator excitation frequency that is different from the rotor rotating frequency. Because of the slot effect, the rotor magnetic loading can be modulated to different frequencies which couple with the harmonics of the stator electric loading. Wide slot openings are used deliberately to enhance the slot effect. For the purpose of illustrating the operating principle, a simple single stator surface PM (SPM) VM is shown in Fig. 1. The rotor position angle is defined as θ rm = θ s θ r. (1) IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See standards/publications/rights/index.html for more information.

2 DU AND LIPO: TORQUE PERFORMANCE COMPARISON BETWEEN A FERRITE MAGNET VERNIER MOTOR 2089 Fig. 1. Definitions of key axes and angles: Stator reference axis: defines the origin of the stator MMF and the spatial air gap permeance function, rotor MMF reference axis: defines the origin of the spatial rotor MMF; and the key angles: θ s : the stator angle in stator reference axis, θ r : the rotor angle in the rotor reference axis, and θ rm : the rotor position angle. The air gap permeance (P g ) per unit area to the radial direction [3] with the stator slot effect is P g = P 0 + P h cos(hs s θ s ) (2) h=1 and the rotor PM magnetomotive force (MMF) is [ ( ) ] Pr F pmg = F pmgh cos h θ r 2 h=1,5,7,11... where S s and P r are the number of stator slots and rotor poles, respectively. Then, the flux density (the product of the fundamental components of P g and F pmg )inthegapis B rg = (F pmg1 P 1 /2) cos [((P r /2) S s )θ s (P r /2)ω rm t] + F pmg1 P 0 cos [(P r /2)θ s (P r /2)ω rm t] +(F pmg1 P 1 /2) cos [((P r /2) + S s )θ s (P r /2)ω rm t] (4) where ω rm is the rotor mechanical frequency, θ r was substituted using (1) and θ rm = ω rm t. The stator MMF in the gap is F sg = F sgpkh cos [h(p s /2)θ s ( 1) n (ω e t + φ)] h=1,5,7,... (5) where F sgpkh is the MMF peak, h is the harmonic order, P s is the stator pole number, ω e is the stator frequency, φ is the phase shift angle, and the order of corresponds to the positive sequence and the negative sequence, respectively, n =2 for h =1, 7, 13,..., and n =1for h =5, 11,... In order to match the frequencies in space and time of the three terms expressed in B rg with these three harmonics expressed in F sg, the following three criteria must be imposed: ±P s /2=P r /2 S s (6) S s =(h 1)(P s /2) (7) ω e = ±(P r /2)ω rm (8) (3) Fig. 2. Proposed 12-slots 20-poles ferrite DSSVPMM: (a) overall structure; and (b) quarter model with stator winding sequence. where the order of + and must match the sequence of excitation expressed in (5). For a SPM VM, the torque produced by the magnetic couplings can be approximated using T e D isl i 2 2π 0 ( θ rm B rg ) F sgh dθ s (9) where D is is the inner stator diameter and l i is the active stack length. Note that the MMF spatial distribution can be expressed in terms of the surface current density spatial distribution (K sgh )as 2π F sgh (θ s )= D is K sgh (θ s )dθ s. (10) 2 0 Using (4) (10), the resultant torque components at maximum torque per amp (MTPA) corresponding to the three magnetic couplings are T e = (π/4)disl 2 i (P r /P s )K sgpk1 (F pmg1 P 1 /2) +(π/4)disl 2 i [P r /(h 1 P s )]K sgpkh1 (F pmg1 P 0 ) +(π/4)disl 2 i [P r /(h 2 P s )]K sgpkh2 (F pmg1 P 1 /2)(11) where h 2 is the higher harmonic order than that of h 1. When (6) and (7) are satisfied: P r is greater than P s and the factor P r /P s can be interpreted as a gear down effect, P r is equal to h 1 P s and the factor [P r /(h 1 P s )] corresponds to a unity gear effect, P r is less than h 2 P s and the factor [P r /(h 2 P s )] is a gear up effect. As shown in (11), the torque of the VM has three magnetic couplings compared to the single magnetic coupling featured in normal machines. Because of the gear down effect and the additional magnetic couplings, VMs generally have a large amount of torque. III. PROPOSED DESIGN A four-stator-pole ferrite DSSVPMM is proposed here with the aim of increasing the torque density and reducing the material cost of the machine. The proposed design is shown in Fig. 2(a). The stator pole number is chosen to match the commercial IPMM so that a direct comparison can be drawn. The SPP is selected to be unity for both stators, which increases the torque density and improves the power factor. The resultant

3 2090 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 53, NO. 3, MAY/JUNE 2017 Fig. 3. Key design parameters and geometric definitions. number of stator slots matches (7) so that all three harmonic terms of (4) are coupled. The winding sequences for both stators are also shown in Fig. 2(b). The outer and inner stator coils are connected in series so that only a single drive system is required. Based on the stator pole number and the unity SPP, the rotor pole number can be obtained using (6). The spoke-type rotor structure is used to strengthen the air gap flux. The ferrite magnets are thickened to avoid being permanently demagnetized by the fault current. The inner stator is shifted from the outer stator by a half slot pitch to obtain the maximum torque produced by this dual-stator structure. The slot area of the inner stator is somewhat larger than that of the outer stator so that a lower current density can be achieved to reduce the inner winding temperature. IV. DESIGN CONSIDERATIONS The key design variables are shown in Fig. 3. The outer stator outer diameter (D oso ) and the active stack length (l i ) are fixed to be the same as those of the commercial IPMM so that a fair comparison can be achieved. The main design objective is to achieve a design with high torque density and small torque ripple using about the same or even smaller amount of copper than that of the IPMM. A fast and simple optimization routine is used to determine the key variables of the design, which consists of an analytical suboptimization routine and many FE analyses. A brief design procedure is outlined in Fig. 4. The optimization routine begins with arbitrary assignments of the PM thickness (d pm ) and the rotor inner diameter (D ir ). Within the space bounded by D oso and D ir, the suboptimization analytically maximizes the total PM flux per pole and the outer stator electric loading. Then, the inner stator design is inserted in the remaining space within the boundary of D ir. Next, the overall model is simulated using FE analysis. If the PMs are not demagnetized, the routine starts the next iteration for a different D ir. A final D ir is selected at the end so that the design achieves maximum torque density. Finally, all the variables of the best design are fine-tuned using further FE analysis to improve the torque density and minimize torque ripple. The objective function of the suboptimization can be expressed as max (φ pmt K s1o ). (12) D cso,d iso,w pm,t so,τ so Fig. 4. Brief design procedure for the proposed DSSVPMM. The total amount of PM flux can be expressed as φ pmt =2Bpmw nl pm l i φ bg (13) where Bpm nl is the no load PM flux density that is approximately equal to the remanence when a large PM thickness d pm is used, and φ bg is the leakage flux passing through the magnetic bridges, which are assumed to be saturated. According to (13), the total PM flux is proportional to the width of each PM (w pm ). Thus, the PMs should be made as wide as possible to increase the total PM flux (φ pmt ). The surface current density can be expressed as K s1o =(K cu A sloto S s J so ) / (πd iso ) (14) where K cu, A sloto, S s, J so, and D iso denote the copper fill factor, outer slot area, number of stator slots, outer stator current density, and outer stator inner diameter, respectively. The current density is fixed to be the same as that of the existing IPMM. The slot area can be roughly estimated using the outer stator outer diameter D oso, the outer stator inner diameter D iso, D cso, t so, and τ so. When designing the inner stator, it is necessary to use a larger amount of copper to lower the current density, since the heat is difficult to remove in the inner stator. D ir needs to be reassigned if the space is not enough to accommodate the inner stator. The yoke thickness (D cso and D csi ) of both stators should be adjusted to ensure the iron is used efficiently. The design procedures also ensure the ferrite PMs are not demagnetized when a fault current is applied in the FE model. If the ferrite PMs are demagnetized, then a larger d pm must be used. However, excessively increasing d pm reduces the thickness of the iron channel

4 DU AND LIPO: TORQUE PERFORMANCE COMPARISON BETWEEN A FERRITE MAGNET VERNIER MOTOR 2091 Fig. 5. Torque (T eavg ) at MTPA and Torque ripple ratio (T err ) against PM thickness (d pm ): the square indicates the oversized d pm and the triangle indicates the d pm used in the final design; d pm is inversely proportional to τ pmi and τ pmo : τ pmi is 38 elec. and τ pmo is 72 elec. when d pm is 26 mm, and τ pmi is 82 elec. and τ pmo is 105 elec. when d pm is 18 mm. between two adjacent PMs, resulting in saturation even at no load. The saturation in the iron channel reduces the torque performance because it increases the reluctance along the armature reaction path when the current loading is applied. V. FE PARAMETRIC STUDY All the key parameters were fine-tuned in the final design step. This section mainly shows how the torque is impacted by a few critical key parameters. The depth of the PM (d pm ) is initially studied since it determines the susceptibility of the ferrite PMs to the demagnetization field and the torque production. Fig. 5 shows the torque production and torque ripple studies as the d pm changes at the final rotor inner and outer diameters. The torque ripple ratio (T err ) is defined as T err = T eripple /T eavg (15) where T eripple is the peak-to-peak torque ripple and T eavg is the average torque. A feasible d pm is selected for the final design, which can handle the fault current and achieve high torque performance with low torque ripple. The d pm will be proven to withstand the fault current up to three times the rated current (defined as the marginal fault current) in a later section. The next parametrization studied the influence of the thicknesses of the two air gaps on torque. Fig. 6 shows that the torque is inversely proportional to both air gaps. In other words, achieving small air gaps is an effective way to improve torque density. Although IPMMs or switch reluctance machines can possibly adopt as small as 0.6 mm air gap, a larger air gap needs be chosen in this case to reduce the difficulty in the rotor alignment. Especially for the cup rotor used in this design with one end bearing, larger air gaps are essential to prevent possible rotor stator contact. The medium 1 mm air gaps were chosen in this analysis to achieve reasonable torque production. The torque of the proposed design could be further reduced if larger air gaps are required, as indicated in Fig. 6. Fig. 6. Torque versus the inner air gap and the outer air gap: the cross indicates the air gap used in the final design. Fig. 7. Torque versus rotor bridge thickness; the triangle indicates the bridge thickness used in the final design. Rotor bridges are employed in the rotor in order to keep the rotor laminations as a single piece. Having thin rotor bridges can reduce the PM leakage flux and hence improve the torque production. In other words, torque is inversely proportional to the bridge thickness d bg, as shown in Fig. 7. Moreover, the rotor bridge must be thick enough to withstand the stress imposed by the PMs when the rotor is rotating. The maximum mechanical stress (MMS) acting on a rotor bridge at a rotating speed can be estimated using the equivalent ring method, which transfers the centrifugal stress imposed by the PM and the rotor iron covering the PM to an equivalent ring with a thickness equal to the minimum bridge thickness and an artificial increased mass density ρ equiv [11]. The MMS inside the ring must stay below the iron yield strength, which is 450 N/mm 2 for typical sheet laminations [11]. The choice of the bridge thickness indicated in Fig. 7 ensures that the bridge can withstand the MMS without experiencing deformation while leaving enough margin for cutting. The MMS of the chosen bridge at rated speed was determined to be only 17.6 N/mm 2. This MMS is significantly lower than the typical iron yield strength.

5 2092 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 53, NO. 3, MAY/JUNE 2017 TABLE I KEY DIMENSIONS OF THE PROPOSED FERRITE DSSVPMM M1 M2 Outer stator ID, D iso [mm] Inner stator OD/ID, D osi /D isi [mm] 208.8/100 - D cso /D csi [mm] 22.8/ /- τ so /τ si [ ] 30/30 30/- t so /t si [mm] 44.1/ /- w pm /d pm [mm] 30/18 40/18 Minimum d bg [mm] Fill factor, K cu In. stat. cur. den. J si [A/mm 2 ] Out./in. surf. cur. den. K so /K si [A/mm] 12.6/ /- Turns per in./out. slot 10/10 20/- Peak rated phase current I rated [A] Current angle at MTPA, γ [ ] Phase resistance, R s [Ω] d and q Inductance, L d /L q [mh] 4.3/ /1.7 PM flux, λ pm [wb] Ferrite PM material [12] NMF-12G NMF-12G Lamination steel M19-26G M19-26G Fig. 8. No-load flux density distribution: (a) M1; and (b) M2. TABLE II PERFORMANCE COMPARISON BETWEEN THE IPM AND THE DSSVPMM IPMM M1 M2 Machine type IPM VPM VPM Magnet type NdFeB Ferrite Ferrite Rotor speed, ω rm [RPM] J s or J so [A/mm 2 ] Cu vol. (incl. end wind.), V cu [L] PM mass, m pm [kg] Stator/rotor poles, P s /P r 4/4 4/20 4/20 SPP, q Excitation frequency, f e [Hz] Stator slots, S s D os or D oso [mm] Active Stack length, l i [mm] Air gap, g [mm] 1 1/1 1 Nominal/Overload temperature [ C] 60/100 60/100 60/100 Torque [Nm] Torque Density [Nm/L] Power factor [lagging] Efficiency about 92% 96% 94% Fig. 9. Interaction between stator air gap MMF and the rotor air gap PM field in M1: (a) MMF, the outer and inner air gaps no load flux density normal components B gon and B gin against the spatial angle; and (b) the corresponding spectra: the fundamental is the 4-pole field, the 5th harmonic is the 20-pole field, and the 11th harmonic is the 44-pole field. VI. PERFORMANCE COMPARISON For comparison purposes, a single air gap VPMM was also developed by simply removing the inner stator of the proposed design. The rotor OD (D or ) of the single air gap design is exactly the same as that of the proposed design. The amount of copper in the inner stator was moved to the outer stator by making the stator slots wider. The magnet width (w pm ) can be increased inward due to the absence of the inner stator core. The key dimensions of the final proposed design (M1) and the single air gap design (M2) are shown in Table I. Additional key dimensions are given in Table II. The performance of M1 and M2 are compared against the performance of the commercial IPMM in Table II. The no-load magnetic flux density is shown in Fig. 8. Though M2 has a larger amount of PMs, the PM flux in the outer stator of M1 is higher than that in the stator of M2. The reason is because the inner stator in M1 provides extra iron paths for extra PM flux to flow between both stators. The extra PM flux will produce extra flux linkage in both stator windings when the rotor rotates. In contrast, some of the PM flux in M2 can only circulate in the air gap without linking the stator windings. When M1 is loaded, the armature reaction flux has the same advantage, that of having the inner stator to assist its flux paths between both stators. The normal or the radial component of the M1 no-load PM flux density in both gaps are shown in Fig. 9(a) as well as the air gap MMF due to the stator excitation. Referring to their spectra in Fig. 9(b), although many harmonics are spatially in common, only the fundamental, the 5th harmonic, and the 11th harmonic of the magnetic loading share the same frequency (i.e., (P r /2)ω rm ) in time with the stator excitation. As a result, these

6 DU AND LIPO: TORQUE PERFORMANCE COMPARISON BETWEEN A FERRITE MAGNET VERNIER MOTOR 2093 Fig. 10. Back-EMF of design: (a) M1; and (b) M2. Fig. 12. Instantaneous torque at rated load MTPA: (a) M1 (T err =3%); and (b) M2 (T err = 53%). Fig. 11. Flux density distribution at rated load MTPA: (a) M1; and (b) M2. three harmonics couple with the stator MMF to produce torque, as illustrated in (11). These three harmonics correspond to the three terms in (4). The no load back-electromotive force (EMF) of both designs are shown in Fig. 10, which shows that the negative sequence excitation must be applied to produce torque as suggested in (8). The magnitude of the M2 back-emf is much smaller than that of the M1 design, even with the same number of turns. This suggests that M2 has a larger amount of PM flux that cannot link the stator windings, which will become leakage flux when M2 is loaded. Both back-emfs indicate harmonics in the flux linkage which normally result in ripple torque. However, the ripple torque can still be further minimized by phase-shifting the inner stator in the M1 design. Both machines were driven by the rated current at MTPA to evaluate the performance at the rated operating point. The flux density distribution is illustrated in Fig. 11. Both the outer stator yoke and the inner stator yoke of M1 are not saturated and the iron is fully utilized. The flux density in the stator yoke of M2 is much lower even when the same excitation is applied. Without the inner stator, the strength of the armature reaction in M2 is greatly reduced since it needs to travel across many PMs, slots, and air gaps to return to the stator. Fig. 12 shows the torque performance of M1 and M2. The ripple ratio of M2 is large because of the unity SPP used in its windings. Furthermore, M2 cannot rely on the inner stator to cancel its ripple torque. In contrast, the torque of M1 is much higher and the ripple torque is very small compared to the M2 design. Fig. 13. Torque capability comparison for various loads at two operating temperatures: 1 p.u. current equals to the rated current of each machine design. The torque capabilities of design M1, M2, and the IPMM are shown in Fig. 13 at the nominal temperature and the overloading temperature. The torque capability of the proposed machine is lower at 100 C than that at 60 C, since the strength of ferrite PMs is inversely proportional to the temperature. Referring to Table II, M1 achieves higher torque and efficiency than the IPMM using ferrite PMs and less amount of copper. The torque density of M2 is 73% of the IPMM. The results also illustrate that adding the inner stator and splitting the copper into two stators can significantly improve the torque density of single

7 2094 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 53, NO. 3, MAY/JUNE 2017 Fig. 14. Key labels and postfault current trajectory: (a) PM labels and line labels for the demagnetization study; and (b) the postfault current trajectory with the starting point indicated by the red circle. air gap VPMMs. Therefore, adding the inner stator is necessary in VPMM designs if torque density is the primary concern. The power factor of M1 is lower than that of the existing IPMM but higher than M2. Thus, a reduction in power factor is another tradeoff for higher torque production. The proposed design M1 uses less copper even while using two stators because of the unity SPP and the smaller inner stator, which save copper in the end winding portions. Fig. 15. Flux density distributions when the marginal fault current was applied at 60 C: (a) γ = 0 (Iq s = 3Ir a t e d ; Id s = 0); (b) γ = 30 (Iq s = 2.6Ir a t e d ; Id s = 1.5Ir a t e d ); (c) γ = 60 (Iq s = 1.5Ir a t e d ; Id s = 2.6Ir a t e d ); and (d) γ = 90 (Iq s = 0; Id s = 3Ir a t e d ). VII. DEMAGNETIZATION ANALYSIS This section examines the demagnetization of the ferrite PMs in M1 for different fault currents at different temperatures. Since ferrite PMs become more resistive to demagnetization as the temperature increases, low temperature, as low as 60 C, is used as well as the nominal temperature in the study. The severity of demagnetization will be investigated when the marginal fault current is applied (i.e., three times the magnitude of the rated current). The flux density in the direction of the PM magnetization, defined as BM, was investigated across the three lines labeled in Fig. 14(a) for each PM. The actual postfault current for a three-phase symmetrical fault can be simulated using the numerical integration of the flux state equations [13]. The inductances and the PM flux linkage are shown in Table I. The machine was initially running at rated speed and rated load MTPA and all the terminals were shorted at the occurrence of the fault. The trajectory of the actual postfault current is plotted in Fig. 14(b). It can be seen that the largest magnitude of the actual postfault current is 238 A (i.e., 1.8Ir ated ) pointed in the d direction, which is smaller than the marginal fault current. This actual postfault current is also investigated during the demagnetization study. The demagnetization of the PMs was studied for different combinations of Iq s and Ids. The flux density distributions are illustrated in Fig. 15 for each current angle denoted as γ. It can be seen that the armature reaction path varies as different current angles are applied. The worst case is shown in Fig. 15(d) since the armature field must pass the PMs to reach the outer stator. Instead of having all the armature fields penetrating across the PMs, some armature MMFs cross the outer stator slot to reach the outer stator and the remaining demagnetization field strikes across the PMs to reach the outer stator via the tooth, especially at the corners of the PMs. Fig. 16 shows the BM along the lines labeled in Fig. 14(a) when different fault currents and current angles are applied. Based on Figs. 15 and 16, it can be seen that the PMs close to the armature reaction switch positions among the six PMs as the current angle changes. The PMs that are not in the vicinity of the armature reaction show very little demagnetization. The magnetization of the ferrite PMs is stronger at 60 C; however, the demagnetization threshold is higher than that of the case at 60 C. That is why the BM for 60 C is generally higher than the BM for 60 C. Fig. 16 also demonstrates that the demagnetization always occurs on both sides of the PMs, especially at the corners, but that the center part of the PMs shows much less demagnetization. Fig. 16 suggests that many fewer armature fields travel across the PMs, most of the armature fields are concentrated at the corners instead. Because of the dual-stator spoke-type structure, the armature fields travel through the rotor iron and strike through the corners to reach the stator, since passing through the corners is the shortest path. The middle part of the PMs shows no permanent demagnetization even at 60 C. The BM for the actual postfault current is generally higher in the demagnetized areas since the magnitude of the postfault current is smaller than that of the marginal current. The worst case scenario in Fig. 16 is the case at γ = 90 (i.e., the fault current is pointed in the d direction), since the BM of PMs close to the armature reaction shows the lowest values compared to those of the rest of the cases. The demagnetization proximity plots are provided in Fig. 17 only for the worst case

8 DU AND LIPO: TORQUE PERFORMANCE COMPARISON BETWEEN A FERRITE MAGNET VERNIER MOTOR 2095 Fig. 16. B M for each PM when different fault currents applied at different current angles. PF stands for postfault and MF stands for marginal fault. Demag. thres. stands for permanent demagnetization threshold. (a) PM1/6 (γ =0). (b) PM2 (γ =0). (c) PM3 (γ =0). (d) PM4 (γ =0). (e) PM5 (γ =0). (f) PM1/6 (γ =30 ). (g) PM2 (γ =30 ). (h) PM3 (γ =30 ). (i) PM4 (γ =30 ). (j) PM5 (γ =30 ). (k) PM1/6 (γ =60 ). (l) PM2 (γ =60 ). (m) PM3 (γ =60 ). (n) PM4 (γ =60 ). (o) PM5 (γ =60 ). (p) PM1/6 (γ =90 ). (q) PM2 (γ =90 ). (r) PM3 (γ =90 ). (s) PM4 (γ =90 ). (t) PM5 (γ =90 ). Fig. 17. Demagnetization proximity when the demagnetizing currents are present: (a) actual postfault current at 60 Candγ =90 ; (b) marginal fault current at 60 Candγ =90 ;and(c)b M color bar. at 60 C since this is the nominal operating temperature. In the case shown in Fig. 17(b), the magnetic domains are permanently flipped to the opposite magnetization at the corners of the PMs since the values of their B M are lower than the permanently demagnetized threshold. These portions of the PMs are permanently demagnetized. The permanently demagnetized portions at the corners are insignificant in the case shown in Fig. 17(a) since the actual postfault current is lower than the marginal fault current. The remaining portion of the PM is not demagnetized but its B M has been lowered by the armature reaction flux. In both cases, the B M of the center portion of the PMs is much higher than that at the corners. This reinforces the point that the dual-stator spoke-type structure offers some protection for the center portion of the PMs, and is the main reason why the thickness of the ferrite PMs need not be oversized. The torque capability of the machine after the occurrence of the fault is given in Fig. 18 at the nominal temperature and the overloading temperature. The postfault FE model of M1 is a slight modification of the original model in which all the permanently demagnetized portions of the PMs are replaced by

9 2096 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 53, NO. 3, MAY/JUNE 2017 Fig. 18. Torque capability before and after faults at: (a) 60 C; and (b) 100 C. Fig. 20. Surface force density distributions for two stators and lumped tooth force under rated load MTPA at initial rotor position (The small red circles indicate the strength of the lumped force acting toward each tooth and the dash lines connect the small red circles): (a) due to the flux density in the outer gap; and (b) due to the flux density in the inner gap. Fig. 19. Radial force density spatial distribution under rated load MTPA at initial rotor position. air. The postfault FE model is driven by the same loads again. Fig. 18 shows that the permanently demagnetized portions of the PMs penalize the torque capability of the machine. However, the torque reduction is not very significant since the majority portion of the PMs remain intact. The torque performance of the proposed design remains higher than that of the rare earth IPMM after the occurrence of the fault. VIII. RADIAL FORCE ANALYSIS The net radial force of the proposed design M1 should be zero since the GCD(S s,p r )=4, which is an even number, indicating that the rotor should experience a radially symmetric magnetic field around the air gap. The radial force density acting on the rotor due to the magnetic field in the air gap can be obtained by the Maxwell stress tensor [14] f n (θ) = 1 [ B 2 2μ n (θ) Bt 2 (θ) ] (16) 0 where θ is the spatial angle, and B n and B t are the normal and tangential components of the air gap flux density taken at the center line of the air gap [14] from the FE solution. The radial force density at the rated load for the initial rotor position is shown in Fig. 19. The radial force density due to the magnetic field at both air gaps clearly shows radial symmetry in Fig. 19. Therefore, the resultant net radial force is zero, since the radial force diametrically cancels out around the periphery of the rotor. The radial force density shows similar radial symmetry for all other rotor positions. Furthermore, the radial force acting on both stators can also be obtained by the FE solution. The surface force density distribution acting on the teeth is shown in Fig. 20. Similarly, the surface force density also shows radial symmetry. The lumped force [15] acting on each tooth can be calculated by taking the surface integral of the normal component of the surface force density distributed on the surface of each tooth. The lumped force acting on each tooth is also provided at the centers of both stators, as shown in Fig. 20. It clearly shows that the lumped force acting on the stator teeth is also radially balanced so that the net radial force also cancels. The surface force density distributions for any other rotor positions also show similar radial symmetry. IX. CONCLUSION A ferrite DSSVPMM has been proposed and its torque performance compared against a single air gap VPMM and a commercial IPMM using rare-earth PMs. The proposed design was developed using a fast and simple optimization routine in conjunction with many FE analyses. Throughout the demagnetization analysis, the dual-stator spoke-type structure was shown to be able to protect the majority of the ferrite PMs from permanent demagnetization caused by the fault current (i.e., up to 3I rated ), while the PMs are only required to have reasonable thickness. The permanently demagnetized corners have very little impact on the torque capability of the machine. The inner stator plays an essential role in VPMM designs since it can effectively improve on the torque density of single air gap VPMMs. The proposed design also demonstrates 33% higher torque production using ferrite PMs at the nominal temperature compared to that of the commercial IPMM using rare-earth PMs. The torque ripple ratio of the proposed design is also very small, that is 3%. The proposed design also achieves higher efficiency and uses a smaller amount of copper. A somewhat smaller power factor is the tradeoff to obtain all of these improvements. The proposed design was also proven to have zero net radial force due to the radial field symmetry. Overall, the ferrite DSSVPMM promises lower material cost and excellent performance for low-speed applications.

10 DU AND LIPO: TORQUE PERFORMANCE COMPARISON BETWEEN A FERRITE MAGNET VERNIER MOTOR 2097 ACKNOWLEDGMENT The authors would like to thank ABB for the support provided throughout this project and Infolytica for making their MagNet FE software available. REFERENCES [1] C. H. Lee, Vernier motor and its design, IEEE Trans. Power App. Syst., vol. 82, no. 66, pp , Apr [2] A. Ishizaki, T. Tanaka, K. Takahashi, and S. Nishikata, Theory and optimum design of PM vernier motor in Proc. 7th Int. Conf. Elect. Mach. Drives, Durham, U.K., 1995, pp [3] A. Toba and T. A. Lipo, Generic torque-maximizing design methodology of surface permanent-magnet vernier machine, IEEE Trans. Ind. Appl., vol. 36, no. 6, pp , Nov./Dec [4] B. Kim and T. A. Lipo, Operation and design principles of a PM vernier motor, IEEE Trans. Ind. Appl., vol. 50, no. 6, pp , Nov./Dec [5] B. Kim and T. A. Lipo, Analysis of a PM vernier motor with spoke structure, IEEE Trans. Ind. Appl., vol. 52, no. 1, pp , Jan./Feb [6] D. Li, R. Qu, and T. A. Lipo, High-power-factor vernier permanentmagnet machines, IEEE Trans. Ind. Appl., vol.50,no.6,pp , Nov./Dec [7] D. Li, R. Qu, W. Xu, J. Li, and T. A. Lipo, Design procedure of dualstator spoke-array vernier permanent-magnet machines, IEEE Trans. Ind. Appl., vol. 51, no. 4, pp , Jul./Aug [8] Z. S. Du and T. A. Lipo, High torque density ferrite permanent magnet vernier motor analysis and design with demagnetization consideration, in Proc. IEEE Energy Convers. Congr. Expo., Montreal, Canada, 2015, pp [9] S. Niu, S. L. Ho, W. N. Fu, and L. L. Wang, Quantitative comparison of novel vernier permanent magnet machines, IEEE Trans. Magn., vol. 46, no. 6, pp , Jun [10] Z. Q. Zhu, M. L. Mohd Jamil, and L. J. Wu, Influence of slot and pole number combinations on unbalanced magnetic force in PM machines with diametrically asymmetric windings, IEEE Trans. Ind. Appl.,vol.49, no. 1, pp , Jan./Feb [11] A. Binder, T. Schneider, and M. Klohr, Fixation of buried and surface-mounted magnets in high-speed permanent-magnet synchronous machines, IEEE Trans. Ind. Appl., vol. 42, no. 4, pp , Jul./Aug [12] Hitachi Metals, Ltd. Ferrite Magnet NMF Demagnetization Curves. Dec. 18, [Online]. Available: products/auto/el/pdf/nmf_a.pdf [13] J. D. McFarland and T. M. Jahns, Investigation of the rotor demagnetization characteristics of interior PM synchronous machines during fault conditions, IEEE Trans. Ind. Appl., vol. 50, no. 4, pp , Jul./Aug [14] Z. Q. Zhu, Z. P. Xia, L. J. Wu, and G. W. Jewell, Analytical modeling and finite-element computation of radial vibration force in fractional-slot permanent-magnet brushless machines, IEEE Trans. Ind. Appl., vol. 46, no. 5, pp , Sep./Oct [15] G. Y. Sizov, P. Zhang, D. M. Ionel, N. A. O. Demerdash, I. P. Brown, and M. G. Solveson, Modeling and analysis of effects of skew on torque ripple and stator tooth forces in permanent magnet AC machines in Proc. IEEE Energy Convers. Congr. Expo., Raleigh, NC, USA, 2012, pp Zhentao S. Du (S 16) received the B.E. degree in electrical engineering (first class hon.) from the University of Technology, Sydney, Australia, in 2008 and the M.S. degree in electrical engineering from the University of Wisconsin Madison, Madison, WI, USA, in 2013, where he is currently working toward the Ph.D. degree in electrical engineering in the Department of Electrical and Computer Engineering. From 2009 to 2011, he was an Electrical Engineer in the Power and Energy Division, AECOM, Sydney. Since 2012, he has been a Research Assistant with the Wisconsin Electric Machines and Power Electronics Consortium, University of Wisconsin Madison. His research interests include the analysis and design of electric machines and drives. He has several journal and conference publications, and has a pending U.S. patent. Thomas A. Lipo (M 64 SM 71 F 87 LF 00) was born in Milwaukee, WI, USA. He received the B.E.E. and M.S.E.E. degrees from Marquette University, Milwaukee, in 1962 and 1964, respectively, and the Ph.D. degree in electrical engineering from the University of Wisconsin, Madison, WI, in From 1969 to 1979, he was an Electrical Engineer in the Power Electronics Laboratory, Corporate Research and Development, General Electric Company, Schenectady, NY, USA. He became a Professor of electrical engineering at Purdue University, West Lafayette, IN, USA, in 1979, and in 1981, he joined the University of Wisconsin, Madison, WI, where he served for 28 years as the W. W. Grainger Professor for power electronics and electrical machines. He is currently an Emeritus Professor with the University of Wisconsin and a Research Professor with Florida State University, Tallahassee, FL, USA. Dr. Lipo has received the Outstanding Achievement Award from the IEEE Industry Applications Society, the William E. Newell Award from the IEEE Power Electronics Society, and the 1995 Nicola Tesla IEEE Field Award from the IEEE Power Engineering Society. In 2002, he was elected a Member of the Royal Academy of Engineering, U.K.; in 2008, a member of the National Academy of Engineering, USA; and in 2013, a member of the National Academy of Inventors, USA. In 2014, he was selected to receive the IEEE Medal for Power Engineering. For the past 50 years, he has served the IEEE in numerous capacities, including as President of the IEEE Industry Applications Society in 1994.

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