Permanent Magnets Aging in Variable Flux Permanent Magnet Synchronous Machines

— Permanent magnet synchronous machines (PMSMs) operation above base speed is typically achieved by injecting negative d -axis current to produce flux weakening. However, this mode of operation increases copper, stator/rotor core and permanent magnet (PM) losses, penalizing the efficiency and increasing the risk of demagnetization. Variable Flux PMSMs (VF-PMSM) in which PMs are magnetized/demagnetized during normal operation of the machine have been proposed to avoid the use of flux weakening current. However, PM aging due to magnetization/demagnetization cycles has not thoroughly studied yet. This paper analyzes the variation of NdFeB, SmCo and AlNiCo PMs properties, including magnetic, electric and thermal, resulting from magnetization/demagnetization cycles . 1


I. INTRODUCTION
Operation of electric drives using PMSM, both interior PMSMs (IPMSMs) and surface PMSMs (SPMSMs) machines, can be especially challenging for applications in which the machine must operate at high speed, due to the need to inject negative current in the d-axis, also known as field weakening current [1]. Flux weakening current reduces the stator flux linkage, matching the back electromotive force (back-EMF) with the available voltage in the DC link. However, flux weakening current also increases the airgap flux harmonic content [2], [3], and consequently, eddycurrents in PMs, stator and rotor cores. This increases the losses and consequently the temperature of all machine elements [3].
To avoid the injection of flux weakening current and its subsequent adverse effects, variable flux PMSMs (VF-PMSM, also called memory motors) have been developed. In this type of machines, the PMs magnetization state (MS) is dynamically changed during high speed operation to reduce the needs of flux weakening current [4], [5].
VF-PMSMs equipping AlNiCo magnets require relatively small magnetic fields to change the MS [4], [6], [7]; this limits machine torque capability as the magnetic field produced by the q-axis current could demagnetize the PMs [8], [10]. VF-PMSMs combining lowand high-Hc magnets reduce the risk of undesired demagnetization due to q-axis current. In this configuration high-Hc magnets provide the base rotor magnetic field, which is unaffected by the stator current, while d-axis current pulses are used to changes the MS of low-Hc magnets. In all cases, VF-PMSMs low-Hc magnets must be magnetized/demagnetized as required by the working condition of the machine. VF-PMSMs magnetization is achieved in-situ by injecting a short current pulse from the stator terminals, i.e. the machine does not have to be disassembled [10]- [11]. VF-PMSMs MS can be manipulated thousands of times all along their life [6]. However, PMs aging produced by this repetitive process has not been analyzed yet.
Available literature on PMs aging effects focuses on PM properties variation due to temperature of operation [12]- [17] thermal cycling [18], [19] and annealing temperature profile during the sintering process [12]. In all studies, PM magnetic aging is divided into structure aging and magnetic aging. Structure aging is produced due to metallurgical changes, which modifies the magnetic domains with the consequent irrecoverable magnetic field strength loss [13]- [14]. Magnetic aging is a recoverable loss of magnetization, caused by the thermal agitation of magnetic domain walls [13]- [14]. PM suffering from magnetic aging can be reverted to their initial MS using a magnetizer.
This paper analyzes aging effects on PM magnetic, electric and thermal properties, due to magnetization /demagnetization cycles for PMs used in VF-PMSMs (i.e. NdFeB, SmCo and AlNiCo) [15]. The paper is organized as follows: characterization of PMs is discussed in section II, the experimental setup designed to cycle and characterize PMs is analyzed in Section III, experimental results using magnet samples are provided in Section IV, the effects of PMs aging in VF-PMSM is discussed in section V and the conclusions are finally provided in Section VI.

II. CHARACTERIZATION OF PERMANENT MAGNETS
This section describes the main magnetic, electric and thermal properties that characterize PM materials and that will be considered therefore for the study of PM aging:  Magnetic properties. They can be obtained from the hysteresis loop, i.e. a plot of magnetic induction, B, and magnetic polarization, J, as a function of the magnetic field strength, H, (i.e. BH and JH curves) [20] as Fig. 1 shows. BH and JH curves provide the magnetic induction in the magnetic circuit and the flux density produced by the magnet alone vs. H respectively.  Thermal properties. Can be evaluated from the analysis of the hysteresis loop at different temperatures [20].  PM resistivity. This parameter will determine the magnet losses due to Eddy currents. PM resistivity can be estimated applying a time varying field to the PM [21]. Table I shows typical properties of four different PM types used in PMSMs: AlNiCo, ferrite, SmCo and NdFeB; where B r is the magnet remanence and accounts the flux density of the magnet in a closed magnetic circuit without externally applied field, H cJ is the intrinsic coercivity that measures the magnet's resistance to demagnetization, BH max is the maximum energy product, i.e. a metric of the energy available for interaction within a magnetic circuit, ρ is the electrical resistivity, T max is the maximum working temperature, α B is the reversible thermal coefficient of B r and α H is the reversible thermal coefficient of H cJ .  Table  I and the squareness factor. Table I, however, do not define the shape of the JH curve. A widely accepted metric to characterize the JH curve is the squareness factor (SF) in the second quadrant, also defined as squareness ratio (SR), (1), where 0 K H  is the knee field corresponding to a 10% magnetization loss, J, [22]. The squareness factor is representative of PM magnetic stability [22], i.e. the ability of the PM to preserve its magnetic properties irrespective of the applied external H.

Parameters listed in
PM magnetic properties in Table I will be measured as described in IEC60404-05:2015 standard for closed magnetic circuits.

III. EXPERIMENTAL SETUP
This section describes the experimental setup and further analysis used to study PMs aging effects and the methodology followed to emulate PM operating conditions in a VF-PMSM. An impulse magnetizer and a system to automatically change PM MS is proposed aiming to accelerate PM aging. PM magnetic properties variation due to aging are obtained using a hysteresisgraph. Fig. 2 shows the magnetizer yoke used for PM samples magnetization/ demagnetization, its main characteristics are given in Table II. The iron core is made of laminated soft magnetic material; its central column being movable to match PM sample size. Test samples have a cylindrical shape (see Fig. 3) with flat end faces. Fig. 4 shows the electric circuit used to control magnetic field strength applied. The capacitor bank "C" in Fig. 4 is first charged, and further discharged through coil "L" by turning on the IGBT (S 1 ) (see Fig. 4), the resulting field adjusted to modify the PM magnetization state as required. Contactor S 2 allows to reverse the field direction.   Repeated magnetization/demagnetization of the magnet sample using the setup represented in Fig. 4, accelerates aging process in the PM sample.

B. Hyestresisgraph
The setup and procedure to obtain the hysteresis loop (i.e. BH curve) described following are specified by IEC 60404-5 standard. Fig. 5 shows the schematic representation of the setup. Two search coils, see Figs. 5 and 6, are needed to measure the differential magnetic flux density (B), and the magnetic field strength (H). Initial magnetic remanence, Br, of each PM sample is obtained using a gauss meter. Coils are mounted on a plastic cylinder, its diameter being therefore constant and independent of PM samples diameter. PM test sample is surrounds by the "B" coil, its induced voltage being function of the flux passing through the PM test sample. "H" coil surrounds only support material (plastic). Since plastic is a paramagnetic material, it will not saturate, therefore the induced voltage in "H" coil will provide the information of the total magnetic field strength applied by the magnetizer. Fig. 7a and 7c shows the induced voltages in the two search coils during a remagnetization process; Fig. 7b and 7d showing the resulting magnetic flux obtained in each coil. Changes in the PM magnetic flux density, ΔB (2), are obtained by integrating the voltage induced in "B" coil, U B (see Fig. 7a and 7c), where B 2 and B 1 are the magnetic flux densities in the instant t 2 and t 1 respectively, A B is the cross-section area of the PM sample and N B is the number of turns of the "B" search coil. The total magnetic field strength, H (3), is obtained by integrating the voltage induced in "H" coil, U H , (see Fig. 7b and 7d), where H 2 and H 1 are the magnetic field strength in the instant t 2 and t 1 respectively, A H is the crosssection area of the plastic support and N H is the number of turns of the "H" coil. "H" coil must be placed within a homogeneous field in the airgap close to the PM sample, according to IEC60404-05 and the test sample and coil axes must be aligned. The dimensions of the region with homogeneous field are given by (4) and (5), where d 1 is the dimension of the smallest side of a rectangular pole piece, d 2 is the maximum diameter of the cylindrical volume with a homogeneous field and l' is the distance between the pole pieces, see Fig. 6b. Dimensions d 1 , d 2 and l' for the tapered poles and PM sample size are listed in Table II.    C. PM resistivity estimation PM resistivity can be also a metric of the PM aging. PM magnet resistance is estimated from the induced eddy currents in the magnet due to an externally applied time varying magnetic field [21], [23], the frequency must be chosen to avoid skin effect and full penetration of the high frequency magnetic field in the PM material. The system shown in Fig. 8 has been used for this purpose [21], [23] the signal injected is varied from 0.1 to 1kHz; the upper limit being chosen considering he skin depth of the PM.
It consists of an iron powder core, to minimize eddy current losses, a coil and an adjustable airgap to fit the PM size. The coil is fed from an H-bridge converter able to inject a high frequency signal of different frequencies and amplitudes into the coil, which will be used to induce a high frequency flux through the PM. The resulting high frequency Eddy currents in the PM will depend on its resistivity. The PM resistivity will be estimated from the coil voltages and currents [21], [23].  Table III) are from two different manufacturers and include high-Hc (NdFeB) PMs and low-Hc magnets (SmCo and AlNiCo). A. Test conditions MS changes occurring in actual VF-PMSMs will obviously depend on the road characteristics and the driving style and obviously it is not possible to reproduce them precisely. For the experimental results shown in this section a simplified driving profile has been defined, it is shown in Fig. 9a. PMs are initially fully magnetized starting BH curve begin measured under these conditions. MS is further varied repeatedly between 50% and 85% as shown in Figs. 9a and b. The power supply in Fig. 4 operates with variable voltage, the cadency of demagnetization/remagnetization pulses has been adjusted to keep the magnetizer coils at a safe temperature of 30ºC. The driving cycle is repeated several times, every driving cycle containing one thousand of magnetization/remagnetization cycles. Once the test is finished, the PM is fully magnetized, the BH curve being obtained as required by standard IEC60404-05:2015.    Table IV shows the changes in the main properties of the magnet with cycling, all of them are seen to get worse. Fig. 11 shows same results as Fig. 10 for sample NdFeB_2. This sample was supplied by a different manufacturer, it has a relatively higher cost and, and is expected to have superior characteristics. Variation of magnetic properties of NdFeB_2 samples are summarized in Table V. While the degradation is in general less relevant than for sample NdFeB_1, aging effects are still evident, the highest impact of being observed again in the maximum energy product, BHmax.   11. BH curve of sample NdFeB_2, same conditions as for Fig. 10. Fig. 12 and Table VI shown the results when SmCo samples are subjected to the cycling process. It can be observed that both B-H and J-H curves have been slightly affected, the most noticeable changes occurring in the maximum energy product; on the other hand, practically no effect is observed in the estimated high frequency resistance.     Fig. 14 shows a comparison of the relative PM remanence variation in a closed magnetic circuit vs. number of remagnetization cycles. It can be observed from the figure that PM remanence remains rather stable for all PM samples when the number of cycles is <500. For higher cycles counts all PM samples experiment a remanence drop, the effect begin more relevant in NdFeB PMs. On the contrary, SmCo sample shows the lowest sensitivity. In all cases a peak magnetization field of 3.34T is applied, which is the limit of the magnetizer. Following the pulse PM magnetic properties (i.e. BH and JH curves) stare measured. Aging in permanent magnets could be due to several reasons, e.g. magnetostriction and coating. Magnetostriction is the change in shape of crystal of ferromagnetic materials subject to an external magnetic field due to changes in the orientation (rotation) of the small magnetic domains. On the other hand, NdFeB magnets used in the experiments as well as AlNiCo magnets were coated using a NiCuNi structure. Coated magnets show a reduced magnetization capability [27], coating can also affect to PM magnet electromagnetic behavior [27], [28]. Precise understanding of this phenomena is a subject of ongoing research.

C. Effects of cycling on PM thermal coefficient of remanence B
 Effects of cycling on thermal coefficient of remanence is analyzed in this section. To perform this analysis, SmCo and AlNiCo magnets should be operated at a temperature of >250 ºC, and NdFeB magnets at a temperature 120 ºC. Unfortunately, the experimental setup currently available is unable to reach the temperatures required for the analysis of SmCo and AlNiCo magnets. Consequently, the analysis presented in this section has been restricted to NdFeB magnets. Fig. 15a shows the PM flux measured in an open magnetic circuit for different PM temperatures. PM flux is decreased with the number of cycles, which is consistent with the results shown in Fig. 10. It is also observed from Fig. 15a that the knee point, which corresponds to the maximum working temperature, does not change with cycling. Fig. 15b shows the flux density difference between the non-cycled and the cycled PM vs. magnet temperature; it is observed a slight increase in the reversible thermal coefficient of remanence, B  , due to the cycling process, i.e. 0 slope  , which means that PM flux temperature dependence change when the sample has been cycled.  Fig. 15a).
It is finally noted that upgrading the experimental setup to allow evaluation of the thermal behavior of SmCo and AlNiCo is currently being studied, but presents remarkable challenges.

D. Effects of cycling on PM high frequency resistance
Knowledge of the effect of cycling on the magnet resistance is relevant, as this will affect to the magnet losses due to Eddy currents [25]. Direct measurement of magnet resistance in NdFeB PMs is not reliable due the NiCuNi coating being applied. PM high frequency resistance has been estimated instead using the system shown in Fig. 8, the results for each type of magnet are included in Tables IV to VII. The increase of the estimated PM HF resistance is consistent with the results shown in Figs. 10 to 14, as PM high frequency resistance is a reliable indicator of the PM MS [23]. NdFeB magnets show the largest high frequency resistance variation with cycling, followed by AlNiCo magnets. On the contrary, SmCo magnets are barely affected.

E. Effects of cycling on PM flux distribution
Non-uniform flux distributions in the PM will result in airgap flux harmonic components due to the machine magnetomotive force (MMF), eventually increasing core losses and torque ripple, therefore penalizing machine efficiency and performance [4]. PM surface flux density distribution was measured for the case of uncycled and cycled PMs in an open magnetic circuit using a Gauss meter. Fig 16a shows the magnetic flux density measured all along the diameter (D) (see Fig. 17), of the PM sample NdFeB_2 before and after cycling, the adverse impact of cycling on PM magnetic flux density distribution being evident from the figure. Since the only difference between the PM samples used to obtain the results shown in Fig. 16a was the cycling process, PM flux density variation, see Fig. 16b, is expected to be due to the aging phenomena.   Table IV to Table VII. Fig. 18 shows a summarizes the results shown in this section. It is concluded that SmCo and AlNiCo magnets shows the lower sensitivity compared to NdFeB magnets.

V. EFFECTS OF PM AGING ON VF-PMSMS
All the previous analyses have focused on discrete magnets. Maximum torque reduction, losses increase, increased risk of PM irreversible demagnetization and efficiency reduction will be direct consequences of PM aging in VF-PMSMs.
Preliminary analysis of the effects of PM degradation on VF-PMSM due to cycling has been addressed by means of FEA for a VF-PMSM using NdFeB magnets. Main parameters are shown in Table VIII. VF-PMSM properties variation due to aging are shown Table IX. Total torque generated by a PMSM is (7) where p is the number of pole pairs of the machine, PM  is the PM flux linkage, ds i and qs i are the direct and quadrature axes currents respectively and L d and L q are the direct and quadrature axes inductances respectively; the first term of (7) is commonly known as electromagnetic torque (T e ) the second on as reluctance torque ( T  ).
When a PM has been cycled its flux density is weaker, affecting to both electromagnetic and reluctance torques. Fig. 19 shows the demagnetization curves before and after cycling the sample NdFeB_2 for the ideal load line, where the working point changes from operating point OP 1 to OP 2 . Taking into account that for a given load line there is a linear relationship between PM remanence B r and flux linkage PM  , the electromagnetic torque, e T (7), will be therefore reduced. On the other hand d L in IPMSMs tends to be particularly sensitive the magnetic saturation level of the machine [26]; therefore if B r decreases, d L will increase, resulting in a reduction of reluctance torque T  , see Table   IX. To maintain the torque level, it is possible to compensate the flux reduction by an increase of the current, but of course this will increase the risk of demagnetization and a lower limit of the machine overload capability. Variations of d L can also affect the controllability of the machine; d-axis current regulator is highly dependent on machine parameters and therefore, variations of d L can affect its dynamics, including time response or even compromising its stability. The consequences of a nonuniform magnetic flux density distribution in a VF-PMSM are additional harmonic components in the MMF waveform. This will lead to higher core losses and lower machine performance.

VI. CONCLUSIONS
Aging effects of the PM used in VF-PMSM (i.e. NdFeB, SmCo and AlNiCo) due to magnetization/demagnetization cycles have been analyzed in this paper. It has been shown that cycling has a direct impact on PM magnetic, electrical and thermal properties. Changes of B-H and J-H curves with cycling has been evaluated, it has been concluded that cycled magnets have lower magnetic energy, remanence and coercivity. It has also been shown that cycling increases the thermal remanence coefficient of the magnet. All these effects contribute to reduce the torque capability and efficiency of VF-PMSMs. The estimated PM high frequency resistance is seen to be also increased with cycling, which results in higher PM losses, higher demagnetization risk and in a reduction of the machine efficiency. Finally, it was shown that aging of PMs due to demagnetization/magnetization processes results in a nonuniform magnetic field distribution, which in PMSMs may make the MMF waveform to change, resulting therefore in a variation of the airgap flux harmonic content, which could have a negative impact on the machine losses.