Demagnetization Characteristics of Permanent Magnet Synchronous Machines

Demagnetization Characteristics of Permanent Magnet Synchronous Machines Gilsu Choi T. M. Jahns Student Member, IEEE Fellow, IEEE Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC) Dept. of Electrical and Computer Engineering, University of Wisconsin-Madison Madison, WI 53706 USA gchoi4@wisc.edu jahns@engr.wisc.edu Abstract -- This paper presents the calculated demagnetization characteristics of different types of permanent magnet synchronous machines (PMSMs) under the influence of demagnetizing MMF contributed by the stator currents (i.e., armature reaction). The demagnetization of NdFeB magnets is quantified in terms of demagnetized magnet volume and loss of magnet remanence using finite element (FE) analysis. The impact of cross-coupled q-axis current and the rotor position are also investigated. The results comparing seven PM machine configurations show that burying the magnets inside the rotor using interior PM (IPM) rotor configurations generally improves the demagnetization performance. In addition, the machine configurations with distributed windings generally provides better demagnetization-withstand capabilities than the configurations with fractional-slot concentrated windings. Keywords -- Demagnetization, NdFeB magnets, permanent magnet, synchronous, concentrated, distributed, surface, interior, windings I. INTRODUCTION A. Background and Review of Past Work Permanent magnet synchronous machines (PMSMs) are widely used in many industry applications because of their high torque density and efficiency. In spite of the rapid price swings during recent years, neodymium-iron-boron (NdFeB) rare-earth magnets are still dominant for high-performance applications due to their high remanent flux density and coercive force. However, the large majority of PMSMs are inherently vulnerable to the risk of irreversible demagnetization that is generally due to external demagnetizing fields and temperature rise. This loss of magnet strength can cause serious performance degradation for this class of machines [1]. Demagnetization of PMSMs has been covered in many past work and its characteristics have typically been investigated by examining the consequences of Gauss's Law and Ampere's Law, often using magnetic equivalent circuits [2-4]. However, the analytical models used in several of the past studies are not sufficient to give accurate answers for many practical cases because of the ancillary effects that are typically ignored in order to make the analysis more tractable. These often include neglecting magnetic saturation, various leakage paths, and irreversible demagnetization, as well as over-simplifying the machine geometry in some cases. More attention has been devoted during the past several years to the demagnetization characteristics of ferrite magnet material because of the volatility of NdFeB magnet prices. Although the basic rules on demagnetization characteristics are the same for both types of magnets, the remanent flux density and coercivity are lower in ferrite magnet materials, requiring more attention to demagnetization in machines that use these magnets. Reference [5] presents the fraction of the total magnet material experiencing irreversible demagnetization for a PM-assisted synchronous reluctance machine using finite element (FE) analysis. More recent work presents interesting analytical results regarding design criteria for ferrite-assisted synchronous reluctance machines using a magnetic equivalent circuit model that is based on the assumption of an infinitely permeable core [6]. The estimated results from the analytical model match very well with FE results because of the use of low-energy-density magnet material. Several techniques have been introduced in the literature to evaluate the demagnetization state of PMSMs. Both semianalytic [7] and FE methods [1, 5, 6, 9-16] have been used to study the risk of demagnetization. One of the most widely used methods to indicate demagnetization state is to check the minimum PM flux density under the influence of demagnetizing MMF [8-12]. Some authors have used the reduction in the back-emf voltage amplitude after exposure to a demagnetizing current to represent the demagnetization state [1, 13]. The ratio of demagnetized magnet elements to the total number of magnet elements, and the reduction ratio of the phase a flux linkage have also been used [5, 16]. Vector plots of the magnetic flux density have been used to investigate the progression of localized demagnetization inside the magnets [14, 15]. Three-dimensional demagnetization analysis has also been carried out [16]. Unfortunately, experience has shown that it is not possible to incorporate all of the desired information to fully illustrate the machine s demagnetization state using any single representation. B. Paper Objectives The key objective of this paper is to investigate the demagnetization characteristics of seven different PMSMs under demagnetizing MMF, highlighting the impact of the winding type and rotor geometry on demagnetization. This topic has received very limited attention in the literature to date. Identifying PM machine configurations that have higher demagnetization resistance is very important because damaged magnets are difficult to re-magnetize. Generally, the loss can only be recovered by removing the rotor and magnets from the machine and re-magnetizing the rotor using a large external

Intrinsic Curve Normal Curve Figure 1: B-H characteristics of NMX-36EH sintered NdFeB magnets at 180 C [17]. field, a process that causes significant downtime and replacement/ repair cost. II. DEMAGNETIZATION CHARACTERISTICS Magnet demagnetization can generally be categorized into three different cases: (1) reversible loss due to the temperature and moderate stator current-induced demagnetizing MMF; (2) irreversible loss due to high temperature, age-related degradation, and large demagnetizing MMFs; and (3) irrecoverable loss due to changes in the material structure or composition by corrosion, heat, and/or shock. Of the three types of demagnetization, the irreversible demagnetization caused by heat, aging, and demagnetizing fields is the only one that can be recovered by re-magnetization. In many practical cases, the threshold condition for demagnetization depends on the combination of the temperature rise and demagnetizing MMF. The scope of this paper will be limited to irreversible demagnetization caused by demagnetizing MMF applied under an assumption of constant operating temperature. Figure 1 shows the intrinsic and normal demagnetization curves of the NdFeB magnets that are used for the baseline machines that will be shown in the following section. The knee point is in the second quadrant for NMX-36EH sintered NdFeB magnets at 180 C [17]. The intrinsic and normal demagnetization curves of this magnet material indicate that irreversible demagnetization at 180 C occurs when the magnetic flux density B inside the magnets is forced to approx. 0.14 T. The nonlinear B-H characteristics of the magnets in the 2 nd and 3 rd quadrant, especially in the knee area, is provided as a data table for the FE simulation to improve the accuracy of the demagnetization analysis. Load lines with permeance coefficient (P c ) values of 10, 2, and 0.2 are also included, indicating that magnets will start to demagnetize when the permeance coefficient is lower than ~ 0.2 without stator current. III. ANALYSIS METHOD AND BASELINE MODELS A. Approach Used in Demagnetization Analysis As introduced in Section I, several different technical approaches have been used to analyze demagnetization characteristics of PMSMs. A majority of the past investigations has used FE methods, while some others have used analytical methods, or a combination of analytical and FE methods. In practice, the sintered NdFeB magnets are composed of many domains that are in the size range of 3-5 microns. Each domain has a different operating point that will cause each domain to demagnetize individually. However, the magnets in a magnetic circuit model are typically lumped into just 1 or 2 pieces, making localized demagnetization analysis impractical [7]. In order to carry out a precise evaluation of local demagnetization, it is necessary to carry out detailed demagnetization analyses in each local area inside the magnets. FE analysis is one of the few analytical techniques that is appropriate for this task. One of the widely-used techniques is to find the minimum magnet flux density in a local area and to check whether the value is below the knee point or not [8-12]. However, this technique is not adequate to quantify the demagnetization state. Another technique used is vector plots of the magnetic flux density for the magnets and surrounding areas [14]. Although this technique is very useful to analyze the progression of demagnetization by examining the direction of flux density vector, demagnetization metrics such as the demagnetized volume and loss of magnet strength are still absent. For a complete picture of the health of every magnet segment, two representation techniques are used in this paper: (1) the ratio of magnet volume that is irreversibly demagnetized to the total magnet volume (in %), known as the demagnetization rate; and (2) a visual indication showing demagnetization state using a two-dimensional contour plot. B. Baseline PM Machines Seven different baseline 80 kw (pk) PM machines that were originally designed for a traction application are used to investigate the impact of different design configurations on demagnetization. Fractional-slot surface PM (SPM) and interior PM (IPM) machines that have a 12-slot/10-pole configuration were chosen for detailed examination due to the difference in rotor structure of the two designs. Demagnetization characteristics for fractional-slot concentrated winding (FSCW) and distributed winding (DW) topologies have been compared to highlight the impact of their different stator MMF harmonics. Five different magnet embedded positions inside the rotor are considered to show their impact on demagnetization; flat type (Flat 1), another flat type that is embedded closer to the airgap (Flat 2), spoke type, V-shape, and two-layer VU-shape. Each of the designs shown in Fig. 2 was optimized to constrain its characteristic current in the vicinity of 184 Apk ( 1.3 pu). With this constraint on the characteristic current, all of the designs have been designed for good flux-weakening performance, and the steady-state value of the three-phase symmetrical short-circuit fault current is limited to a similar value. The back-emf voltage amplitudes at the peak speed of 10,000 r/min are limited to line-to-line peak values of 880 V. The peak value of the rated current waveform, 145.7 A, is defined to be 1 pu current in this study. Another important constraint imposed on this optimization process is to maintain a constant magnet thickness of 8 mm for all of the designs, which has the effect of highlighting the different demagneti-

(a) FSCW-IPM with 12 slots & 10 poles (b) FSCW-SPM with 12 slots & 10 poles (c) DW-IPM with 48 slots & 8 poles: Spoke-type (d) DW-IPM with 48 slots & 8 poles: Flat 1 (e) DW-IPM with 48 slots & 8 poles: Flat 2 (closer to airgap) (f) DW-IPM with 48 slots & 8 poles: V-shape (g) DW-IPM with 48 slots & 8 poles: VU-shape Figure 2: Cross-section views of seven baseline 80 kw (pk) PM machines TABLE I: SUMMARY OF KEY DIMENSIONS AND METRICS OF THE BASELINE PM MACHINES Winding Type FSCW DW Rotor Type SPM IPM Flat 1 Flat 2 Spoke V-shape VU-shape Slots/Poles 12/10 12/10 48/8 48/8 48/8 48/8 48/8 Stator Diameter [mm] 275 261 273 291 260 291 291 Rotor Diameter [mm] 160 Stack Length [mm] 86 98 108 83 134 93 87 Series Turns/Phase 42 36 40 52 32 52 52 Magnet Remanence [T] 1.01 @ 180 degc Winding Factor 0.933 0.933 0.933 0.933 0.933 0.933 0.933 Unsat. Saliency 1 1.51 2.18 2.24 1.58 2.39 2.29 Magnet Mass [kg] 2.31 2.23 2.29 1.61 1.91 1.63 1.43 zation characteristics of the seven machines. More details on the machine design optimization process can be found in [18]. PM machines equipped with fractional-slot concentrated windings have received significant attention during the past decade due to their advantages including compact end windings and segmented stators that make it possible to increase their copper fill factor and power density values. FSCW machines with both SPM and IPM rotor types have been widely investigated. Rotor demagnetization due to threephase symmetrical short-circuit fault for an FSCW-IPM machine has been discussed in [19]. However, broader investigations into the demagnetization characteristics of FSCW-PM machines with both rotor configurations have received very limited attention to date. Some researchers have focused on spoke-type PM machines because of their potential for high torque density due to the flux concentration effect. The demagnetization characteristics for this type of PM machine have been reported [8, 10]. Generally, this type of rotor structure imposes several constraints on the rotor dimensions and number of poles. Flat rectangular-shaped magnets, V-shape magnets, or combinations of the two types of magnets have been the most popular rotor configurations in the automotive industry [20]. The VU-shape configuration is also included in the study as an example of a two-layer magnet configuration. Table I summarizes key dimensions and metrics for the seven baseline PM machines. As presented in Table I, the saliency ratio and magnet mass values vary among the different optimized machine configurations. For example, the saliency of the V- shape design is 10% higher than the Flat 1 design while utilizing only 70% of magnet mass. IV. FE SIMULATION RESULTS A. Demagnetization Rate: Negative d-axis Current Only Since negative d-axis stator current is generally recognized to be a primary source of demagnetizing MMF, 5 pu stator

Figure 3: Calculated demagnetization rate as a function of negative d-axis current for the baseline machines The SPM rotor experiences demagnetization at lower negative d-axis currents than the designs with IPM rotors as shown in Fig. 3. Considering that the peak transient value of three-phase symmetrical short-circuit fault current at no-load is approx. twice the machine's characteristic current ( 2.75 pu including saturation) [21], the magnets in the FSCW-SPM and DW-IPM Flat 2 machines will be partially demagnetized even for a symmetrical short-circuit fault at no-load. Since the demagnetizing MMF is a function of not only the applied current but also the number of turns, poles, and winding factor, the demagnetization rate as a function of fundamental MMF per pole is shown in Fig. 4. The armature MMF per pole is defined by [2] to be: F ph = N ph 2 4 π N t I m k wh CP h where N ph is number of phases, N t is number of series turns, I m is the peak current, C is number of parallel circuits, P is the number of poles, and k wh is the winding factor for the h th winding spatial harmonic component. The winding factor is a product of winding pitch factor k ph, winding distribution factor k dh, slot opening factor k xh, and skew factor k sh, as shown in (2): (1) k wh = k ph k dh k xh k sh (2) Figure 4: Calculated demagnetization rate as a function of fundamental MMF per pole for the baseline machines current aligned with the negative d-axis has been selected as the worst-case operating condition for this study. This current is applied suddenly using fixed-speed time-stepping FE analysis to investigate the demagnetization behavior in detail. Each individual element inside the magnets is programmed to follow the material s B-H curve based on the element's operating point at any time instant, and irreversible demagnetization is accounted for in the FE software. The demagnetization rate (expressed in %) as a function of the applied negative d-axis current one electrical cycle after the demagnetizing MMF excitation is applied is shown in Fig. 3 for the baseline machines. As noted earlier in Section III.A, the demagnetization rate is defined to be the ratio of demagnetized volume in the magnets to total magnet volume. Simulation results demonstrate that the magnets embedded deeper in the radial dimension (e.g., Flat 1 & V-shape) generally exhibit greater demagnetization resistance. However, it should be noted that the volume and mass of both a machine and its magnets typically increase as magnets are buried deeper. It is also shown that increasing the number of magnet layers while keeping the total magnet thickness the same (i.e., sum of the magnet layers) has a negative impact on the demagnetization in terms of the applied negative d-axis current. It is initially assumed that there is no skew, and the winding currents are approximated by an equivalent current sheet of infinitesimal thickness distributed over the stator slot opening, resulting in k sh and k xh equal to 1. Not surprisingly, the trend in the demagnetization rate is somewhat different from Fig. 3, mainly due to the different number of series turns for each design. The SPM machine is still the most vulnerable design to demagnetization. The FSCW-IPM and spoke-type machines follow in order, because these two designs have higher d-axis inductance than the other designs, resulting in a lower number of series turns that makes the fundamental MMF per pole lower for these machines. In contrast, the VU-shape machine shows good demagnetization characteristics based on the applied demagnetizing MMF because this machine requires a higher number of turns to achieve the target characteristic current value. The V-shape and Flat 1 designs show excellent resistance to demagnetization in both Figs. 3 and 4. The demagnetizing MMF due to the spatial subharmonics that are typical in FSCW-PM machines are not included in Fig. 4. Including them would increase the total demagnetizing MMF per pole for those machines. B. Impact of q-axis Current The demagnetization mitigation effects of q-axis current in IPM machines have been investigated for both the rare-earth and ferrite PM materials in [15]. To investigate whether this increased demagnetization-withstand capability holds true for the other machine configurations as well, the demagnetization state of the baseline machines with three different values of q- axis current has been investigated. Figure 5 shows a bar chart comparing the FE-calculated demagnetization rate for a large negative d-axis current (-5 pu) together with different values of q-axis current (0.5 pu, 1

Figure 5: Comparison of calculated demagnetization rate for the baseline machines with 3 different q-axis current values (i q = 0.5, 1, and 2 pu) in addition to -5 pu d-axis current (in all cases) shown in Fig. 6 along with the definition of peak-to-peak demagnetization rate. The pattern of the demagnetization rate curve in Fig. 6 displays a 60 elec. deg periodicity for this particular design, and its peak-to-peak value is 29.3%. The periodic change in demagnetization rate also appears in the other machine configurations with different peak-to-peak values. Table II provides a summary of the peak-to-peak demagnetization rate for the seven baseline machines, indicating that the demagnetization rate for the spoke-type machine varies widely by 91% depending on the rotor angular position when the demagnetizing MMF (i d = -5 pu) is applied. In contrast, the flat-type machines are much less sensitive to the rotor position. It should be noted that the final value of the demagnetization rate for each design will exhibit very little sensitivity to rotor position when the rotor is rotating and a constant demagnetizing MMF is applied for longer than one electrical period due to rotor s exposure to all angles during its rotation. TABLE II: PEAK-TO-PEAK DEMAGNETIZATION RATE [%] OF THE SEVEN BASELINE MACHINES FOR I D = -5 PU AND I Q = 0. FSCW-SPM 15.94 Spoke 91.73 FSCW-IPM 13.77 V-shape 21.96 Flat 1 0.45 VU-shape 29.27 Flat 2 3.74 Figure 6: Calculated demagnetization rate for VU-shaped PM machine vs. rotor position pu, and 2 pu). Although the effect of adding q-axis current depends on the degree of demagnetization state and machine configuration, the demagnetization rate generally decreases as the cross-coupled q-axis current increases. The spoke-type baseline model exhibits the highest sensitivity to the addition of q-axis current, resulting in a demagnetization rate reduction by 93% with i d = -5 pu and i q = 2 pu. Closer examination reveals that the demagnetization state of the spoke machine is highly sensitive to the change in d-axis current when the applied negative d-axis current falls between -4.5 and -5 pu. In contrast, the FSCW machines have the lowest sensitivity to the addition of q-axis current regardless of rotor type. C. Impact of Rotor Position In order to investigate the effect of rotor position on demagnetization, a series of magnetostatic FE analyses were run with different rotor positions for i d = -5 pu and i q = 0 pu. The rotor position was varied from its initial 0 elec. deg to 120 elec. deg in increments of 5 elec. deg. The rotor d-axis is aligned with the axis of stator phase a when the rotor position angle θ is equal to zero. The change of demagnetization rate as a function of rotor position for the DW-IPM machine with VU-shaped magnets is D. Remanence Ratio Contour Plots As discussed in Section III, further insights into the demagnetization characteristics for the baseline machines are provided by the color contour plots of the remanence ratio throughout the magnets presented in Fig. 7 for a repeating rotor pole-unit one electrical cycle after application of the negative d-axis current. The remanence ratio (in %) reflects the decrease in remanent magnetic flux density and is defined as: 1 - B r * 100 B ( ) ro % (3) where B ro is the initial remanent flux density and B r is the post-demagnetization value. Low values are desired. Consider first the results for the FSCW-SPM machine. The remanence ratio results in Fig. 7(a) indicate that the demagnetization is widespread, causing the remanent flux density of most of the magnet material to drop by approx. 45% of the pre-demagnetization value. Having the magnets directly exposed in the airgap region without being protected by core materials results in the worst demagnetization for the SPM machine among the seven baseline machines. The demagnetization rates presented earlier in Figs. 3 and 4 for the FSCW-IPM, Spoke, Flat 2, and VU-shape machines are as high or higher than the SPM machine values. However, the loss of magnet strength for these other machines in Fig. 7 is rather mild compared to the SPM machine, with remanence ratio values mostly in the range of 5 to 25% for these machines, except for the areas near the leakage flux paths. The rotor bridge and post provide magnetic shunts for the demagnetizing MMF that helps to reduce overall demagnetization risks. However, the flux flowing through these bypasses causes significant demagnetization in the adjacent magnets.

-61 % -22% (a) FSCW-SPM -9% -81% Figure 8: Magnet remanence ratio values for VU-shape machine after one elec. cycle with two q-axis current values: i d = -5 pu, i q = 0 pu (top); i d = -5 pu, i q = 2 pu (bottom) (b) FSCW-IPM (c) DW-IPM: Flat 1 (d) DW-IPM: Flat 2-21% -44% Figure 9: Magnet remanence ratio for FSCW-SPM machine after single-phase ASC fault (e) DW-IPM: Spoke (f) DW-IPM: V-shape Figure 7: Color contour plots of magnet remanence ratio values after one elec. cycle for 6 of the baseline machines (i d = -5 pu, i q = 0 pu) The Flat 1 and V-shape machines are the two most promising designs overall in terms of demagnetization resistance. However, the loss of flux density strength in the magnets for these two machines is significant in localized regions near the magnet corners where the peak remanence ratio values reach 100%. Despite the fact that the FSCW machines have a higher number of poles than the other baseline machines, it suffers similar or higher demagnetization when compared to the DW-IPM machines, as shown in Fig. 7. Figure 8 shows the calculated remanence ratio results for the VU-shape machine both with and without q-axis current. It can be clearly seen that both the demagnetized area and the loss of remanent flux density generally decrease with the addition of q-axis current. However, the remanence ratio value increases in some localized magnet areas near the airgap as the q-axis current is increased. A single-phase asymmetrical short-circuit (ASC) fault is generally considered to be one of the most dangerous faults in terms of peak current amplitudes and demagnetization risks [22]. Figure 9 shows remanence ratio results of the FSCW- SPM machine after the single-phase ASC fault condition. Figure 10: Demagnetization index showing normalized demagnetizing MMF per unit PM mass for the baseline machines Compared to Fig. 7(a), the demagnetization for the SPM machine after the ASC fault is relatively mild as reflected in both their magnet remanence ratios and demagnetization rates. This is a consequence of significant demagnetization during the initial fault transient, which, in turn, reduces the fault currents. A closer investigation reveals that both the FSCW-IPM and Flat 2 machines exhibit similar trends as the FSCW-SPM machine with some differences in the demagnetization state. In contrast, the rest of the machines (Flat 1, Spoke, V-shape, and VU-shape) exhibit demagnetization patterns that are very similar to their results in Fig. 7 for i d = -5 pu due to their relatively mild demagnetization during the fault.

E. Demagnetization Index The two demagnetization quantification methods that have been used so far provide meaningful numerical and graphical representations for the demagnetization state of the baseline machines. Unfortunately, these methods do not reflect the influence of each machine s magnet mass or volume on their demagnetization-withstand capabilities. A new demagnetization index metric has been defined that incorporates the total magnet mass into the calculation to reflect its impact on the demagnetization-withstand capability. More specifically, the demagnetization index is defined as: Normalized Demagnetization MMF Demagnetization index = (4) Magnet Mass [kg] The demagnetization MMF that appears in (4) is defined to be the stator MMF using negative d-axis current required to achieve a threshold demagnetization rate of 3% in each machine. This demagnetization MMF is normalized by the negative d-axis current MMF value required to achieve the 3% demagnetization ratio value for the SPM machine (= 1090 ampere-turns). The resulting demagnetization index value provides a metric for the maximum demagnetizing MMF that a machine can withstand per unit PM mass. Figure 10 presents the demagnetization index values for each of the baseline machines. The Flat 1 IPM machine which ranked highest in terms of demagnetization withstand capability without considering the magnet mass drops in ranking when the magnet mass is taken into account. Overall, the VU-shape machine has the highest demagnetization index value, followed by the V-shape machine. V. CONCLUSIONS This paper presents an investigation of the demagnetization characteristics of PM synchronous machines under the influence of demagnetization MMF with the impacts of both d- and q-axis currents included, as well as during the single-phase ASC fault. Since closed-form analytical solutions are very difficult for investigations of localized demagnetization, FE analysis has been used to explore the influence of PM machine type on the demagnetization characteristics. The results of this investigation show that adopting IPM rotors help to reduce demagnetization risks compared to SPM rotors. In general, magnets buried deeper into the rotor are shown to be helpful for reducing the demagnetization, but at the cost of increased volume and mass for both the machine and magnets. The machines with the distributed winding (DW) configurations show more resistance to demagnetization than the fractional-slot concentrated winding (FSCW) machines. Overall, two designs use a DW topology with a V-shape and VU-shape rotor configurations have been chosen as the two most attractive designs to mitigate demagnetization risks while minimizing magnet mass. 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