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Comprehensive parameter identification and analysis are critical to develop accurate machine model. As reported in [1],[2], only two parameters can be estimated properly at the same time since the rank of the machine model is 2. However, in real-time application, machine parameters vary nonlinearly due to the change in operating conditions [3]–[5].Therefore, more accurate knowledge of motor parameters requires more undetermined coefficients in machine modelling, which results in severer rank deficiency problem.&lt;br/&gt;To overcome the rank deficiency and achieve a better estimation accuracy of dq-axis inductance modelling, this paper designs an experimentally testing pattern illustrated in Fig. 1 for PMSM and proposes a decoupled estimation scheme in (1) considering system uncertainties including magnetic saturation, core loss, temperature effect and voltage source inverter nonlinearity.&lt;br/&gt;(U&lt;sub&gt;q&lt;/sub&gt;I&lt;sub&gt;d&lt;/sub&gt;-U&lt;sub&gt;d&lt;/sub&gt;I&lt;sub&gt;q&lt;/sub&gt;)/ω&lt;sub&gt;e&lt;/sub&gt;+(D&lt;sub&gt;d&lt;/sub&gt;I&lt;sub&gt;s&lt;/sub&gt;cos(θ)+D&lt;sub&gt;q&lt;/sub&gt;I&lt;sub&gt;s&lt;/sub&gt;sin(θ))△V/ω&lt;sub&gt;e&lt;/sub&gt;=I&lt;sub&gt;q&lt;/sub&gt;I&lt;sub&gt;q&lt;/sub&gt;L&lt;sub&gt;q&lt;/sub&gt;+I&lt;sub&gt;d&lt;/sub&gt;(Λ+L&lt;sub&gt;d&lt;/sub&gt;I&lt;sub&gt;d&lt;/sub&gt;)+I&lt;sub&gt;q&lt;/sub&gt;I&lt;sub&gt;q&lt;/sub&gt;L&lt;sub&gt;q&lt;/sub&gt;Λ/R&lt;sub&gt;i&lt;/sub&gt; (1)&lt;br/&gt;where variables I, U, L, λ, D with subscript ‘d’ and ‘q’ are current, voltage, inductances, flux linkage and distorted coefficients on dq-axis frame accordingly. Λ and ΔV are PM flux linkage and distorted voltage drop due to dead time effect of voltage source inverter. R&lt;sub&gt;i&lt;/sub&gt; is the core loss resistance.&lt;br/&gt;As mentioned previously, the proposed estimation approach takes core loss effect into account. Therefore, given different speed conditions in (1), the differential model can be achieved by subtracting (1) at the first speed condition denoted as subscript 1 from the one at the second speed condition denoted as subscript 2, which contains the information of iron loss.&lt;br/&gt;In the full paper, an efficient least square method incorporating decoupled estimation scheme is employed to converge the undetermined coefficients in the proposed estimation model. The machine parameters including resistance, PM flux linkage and inductances will be estimated and reported. The estimated inductances illustrated in Fig. 2 will be validated through virtual signal injection based MTPA control and more experimental results will be presented to demonstrate the effectiveness of the proposed method.

![](https://assets.underline.io/uploads/markdown_image/1/image/49bc237555843438394366800f84a779.jpg)

Fig.1.Illustration of experimental data collection

![](https://assets.underline.io/uploads/markdown_image/1/image/2df751a5afa6d8760802b04a4e37dbbd.jpg)

Fig.2.Estimated inductance maps.(a)d-axis(b)q-axis

2022 Joint MMM-INTERMAG

Decoupled Estimation Scheme for PMSMs Towards Accurate Inductance Modelling

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INTERMAG 2021

Comprehensive parameter identification and analysis are critical to develop accurate machine model. As reported in [1],[2], only two parameters can be estimated properly at the same time since the rank of the machine model is 2. However, in real-time application, machine parameters vary nonlinearly due to the change in operating conditions [3]–[5].Therefore, more accurate knowledge of motor parameters requires more undetermined coefficients in machine modelling, which results in severer rank deficiency problem. To overcome the rank deficiency and achieve a better estimation accuracy of dq-axis inductance modelling, this paper designs an experimentally testing pattern illustrated in Fig. 1 for PMSM and proposes a decoupled estimation scheme in (1) considering system uncertainties including magnetic saturation, core loss, temperature effect and voltage source inverter nonlinearity. (UqId-UdIq)/ωe+(DdIscos(θ)+DqIssin(θ))△V/ωe=IqIqLq+Id(Λ+LdId)+IqIqLqΛ/Ri (1) where variables I, U, L, λ, D with subscript ‘d’ and ‘q’ are current, voltage, inductances, flux linkage and distorted coefficients on dq-axis frame accordingly. Λ and ΔV are PM flux linkage and distorted voltage drop due to dead time effect of voltage source inverter. Ri is the core loss resistance. As mentioned previously, the proposed estimation approach takes core loss effect into account. Therefore, given different speed conditions in (1), the differential model can be achieved by subtracting (1) at the first speed condition denoted as subscript 1 from the one at the second speed condition denoted as subscript 2, which contains the information of iron loss. In the full paper, an efficient least square method incorporating decoupled estimation scheme is employed to converge the undetermined coefficients in the proposed estimation model. The machine parameters including resistance, PM flux linkage and inductances will be estimated and reported. The estimated inductances illustrated in Fig. 2 will be validated through virtual signal injection based MTPA control and more experimental results will be presented to demonstrate the effectiveness of the proposed method.

![](https://assets.underline.io/uploads/markdown_image/1/image/49bc237555843438394366800f84a779.jpg)

Fig.1.Illustration of experimental data collection

![](https://assets.underline.io/uploads/markdown_image/1/image/2df751a5afa6d8760802b04a4e37dbbd.jpg)

Fig.2.Estimated inductance maps.(a)d-axis(b)q-axis

technical paper

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Recently an increasing demand emerges for high-speed permanent magnet motor (HSPMM) in fuel cell compressor application. Overheating is thought as one of the biggest causes for the failure of HSPMM. This paper presents a slotless Gramme-ring-winding HSPMM, so as to reduce the rotor eddy-current loss caused by stator slotting. Besides, it is convenient to fix the slotless windings. However, exposed to the alternating magnetic field of airgap, large AC loss will be generated in the slotless windings. Litz wire, with a high number of individually insulated, small gauge strands separated into bundles and continuously transposed, is employed to control the AC losses associated with high-frequency operation in this paper. Considering the influence of magnetic field of airgap, the analytical model for losses of the litz wire was built based on an external-rotor motor [1]. The components of the losses for litz wire was analyzed in an air-core pulsed alternator, and the diameter was optimized to minimize the loss[2]. Besides, the pitch of litz wire was thought has a great influence on the loss, and the design method of pitch was provided[3]. In addition, the impacts of the litz wire strand shape, such as circular, square and rectangular, were compared on AC copper loss of the HSPMM[4]. Due to the complex structure of litz wire, the calculation method of the equivalent thermal conductivity was given, based on the Gasar porous metal materials. This paper first analyzes the loss of the litz-wire gramme-ring winding based on the FEA methods, considering the different magnetic field of airgap and the outer slots of stator. Then the analytical model for the loss of litz-wire gramme-ring winding is established, and the diameter and shape are optimized to minimize the loss. After that, the thermal analysis model of the litz-wire gramme-ring winding is investigated, and the temperature rise is calculated. Moreover, the influence of diameter and shape of litz wire is also studied. Through the above studies, the design of litz wire is finally provided for the slotless gramme-ring-winding HSPMSM. Fig.1 shows the configuration of the studied motor, and Fig.2 is the distribution of current density in litz wires on different positions.

![](https://assets.underline.io/uploads/markdown_image/1/image/c26e4d7be8939286475fc381ce3c6820.jpg)

Design of Litz Wires for a Slotless High-speed Permanent Magnet Motor with Gramme-ring Windings

Internet of Things devices prompt a rising demand for autonomous and compact power supply generators to sustain low-power wireless sensor nodes. Due to the ubiquity of waste heat in buildings and urban environments, low-grade heat sources are very attractive for applications. Thermomagnetic generators (TMG) can be small and autonomous. Ahmim’s TMG [1] produces 4.2 μW (0.24 mW/cm3 over a 35°C temperature difference. While this device exploits direct thermal contact with both reservoirs, a key element of a thermal device [2], the output power is penalized by a sub-Hertz working frequency. Khol’s TMG [3] produces 118 mW/cm3 at 84 Hz but over a larger temperature difference of 138°C. Their use of 5 μm thick Heusler Alloy films, compared to a 250 μm thick plate of LaFeSi by Ahmim, is an important factor to explain the different in the working frequency. We aim to explore the possibility to use thin films in Ahmim’s TMG while keeping its low temperature difference capability. Ahmim’s TMG has specific characteristics. Firstly, it needs to have a freestanding magnetocaloric film of several micrometers. Our recent work on Gd film deposition has shown a 17 μm film with significant magnetocaloric effect [4]. Secondly, it needs to have a magnetic field source that gives a maximum field variation but also confines the magnetic field in order to reduce the film displacement. By combining Gd films and high performance NdFeB micro-magnets [5], [6] with our design experience on macro devices (Fig.1), we will discuss the key steps of the design, e.g., the spring characteristics to achieve self-oscillating micro-devices. Several parameters need to be optimized, such as the micro-magnet pattern, the air gap and Gd film thickness. 3D numerical simulations of the magnetic force as a function of the material position and temperature (Fig. 2), which are being used to optimize the system design, will be discussed in detail. With our proposed design, if we assume a 50 Hz working frequency, there is 5mW of mechanical energy available.

![](https://assets.underline.io/uploads/markdown_image/1/image/6c8def3c8eadc39bbbf231f211465813.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d44ec31fe73d8d8565d56c704b72f012.jpg)

Key steps in designing a micro thermomagnetic generator

Key steps in designing a micro thermomagnetic generator

I Introduction Due to the high-power density, simple structure and low cost, switched reluctance motors with amorphous alloy cores (SRMA) are widely applied in electric vehicles [1]. However, its development is limited by the vibration causing by the radial electromagnetic force. This paper proposes a new method to reduce the vibration of SRMA based on the inverse-magnetostriction effect. II Vibration reduction method based on inverse-magnetostriction effect The research in amorphous alloy motor is mainly about the evaluation of core loss and the literature involves vibration is rare [2]. The vibration mechanism of amorphous stator core was revealed through considering the Maxwell stress and magnetostriction stress [3]. However, the effective damping methods have not been involved and the inverse-magnetostriction effect was neglected. A method of vibration reduction for the SRMA is propose in this paper. First, compressive stress in the radial direction is applied to the stator teeth, because the magnetic permeability of the magnetic material will decrease under the action of compressive stress in the same direction. Then, the magnetic permeability is calculated by the nonlinear relationship with the stress. After the definition of the relative permeability of the stator core, the magnetic field distribution inside the motor is obtained. Second, the magneto-mechanical coupling model is established by combining the electromagnetic stiffness matrix and mechanical stiffness matrix to calculate the stress distribution of the stator core as shown in Fig.1(a-b). Third, the vibration reduction effect of the model is verified by the finite element simulation. III Results and discussion The simulation results of the sampling point of the stator teeth is calculated as shown in Fig.1(c-d). And the radial flux density of air gap (Bn) and radial electromagnetic force (Fn) is reduced by 13% and 20% respectively, which shows that the method can effectively reduce the radial electromagnetic force and has a certain damping effect.

![](https://assets.underline.io/uploads/markdown_image/1/image/b9b91cb059fef40d823d3087d758805e.jpg)

Research on vibration reduction method of switched reluctance motor with amorphous alloy cores based on inverse-magnetostriction effect

Research on vibration reduction method of switched reluctance motor with amorphous alloy cores based on inverse-magnetostriction effect

Permanent Magnet Linear Generators (PMLG) are currently studied as a main solution for the conversion of the energy contained in sea waves. Typically, a PMLG consists of an iron-made armature and a moving shaft. Magnets are usually installed on the shaft and the coils on the armature. The moving shaft generates an electromotive force in the coils. Such a machine suffers from a high level of cogging force due to the interfaces between air and iron impairing its overall performance. However, the function of iron in Permanent Magnet (PM) based machines is simply that of driving the flux along a predesigned path. No amplification of the magnetic flux is generated by iron because the flux is generated by the permanent magnet. As a result, a well-tailored design of a PM generator could avoid the use of iron avoiding any permeability difference along with its magnetic circuits and therefore cogging force is completely suppressed. Several questions remain open: how much is the performance of an ironless generator affected by the absence of iron? Which is the comparison between a traditional and an ironless generator? In this paper, we try to address experimentally these questions. We have built two prototypes of PM linear generators that share the same geometry: one of the two is a traditional generator the other is an ironless generator. At first, we have characterized the two machines by measuring the main electrical and mechanical parameters: resistance, reactance, mass, magnetic fields. Secondly, we have performed several open circuit measurements, by measuring cogging force, vibrations, electromotive force when the slider is moving at some given conditions. Finally, we have performed several load tests by measuring cogging force, vibrations, output voltage, current, and output power when the slider is moving at some given conditions. The comparison reported in the paper shows that the performance of the traditional machine is slightly superior in comparison with the ironless one, but an ironless machine does not present any cogging force and is lighter than the traditional one. These features can be a great advantage in the field of sea-wave energy conversion.

An Experimental Comparison Between an Ironless and a Traditional Permanent Magnet Linear Generator

Introduction - Flux-modulated type magnetic gears are expected to be applied as step-up gears for wind-power generation because of their advantages, including high torque density and maintenance-free operation [1]. Among them, an axial-flux magnetic gear (AFMG) has attracted great attention recently since it has a smaller axial length and is easy to assemble. In some cases, magnetic gears are required to have an integer gear ratio based on design requirements of the entire system, which results in larger cogging torque in the high-speed rotor that causes vibration and startup error. In addition, the conventional skew rotor structure is complicated and poor in assembling [2]. To solve the problems described above, this paper proposes two new types of pole-pieces, one is an unequal-width-type, another is an unequal-spacing-type. Two new types of pole-pieces – Fig. 1(a) shows the AFMG [3] investigated in this paper, while the (b) and (c) are the proposed unequal-width-type and unequal-spacing-type pole-pieces, respectively. The gear ratio of this AFMG is an integer of 10 given by the number of pole pairs of the high-speed and the low-speed rotors of 3 and 30, respectively. As shown in Fig. 1(b), pole-pieces with three different circumferential width ratios, which are 0.3, 0.8, and 0.7, are combined in the unequal-width-type, while as shown in Fig. 1(c), the relative position of the pole-pieces is adjusted which leads to an unequal interval structure. Both types are aimed at canceling the cogging torque. The cogging torque is calculated by the three-dimensional finite element method (3D-FEM). Fig. 2 shows the results of the high-speed rotor cogging torque of the two proposed new types, where (a) is of the unequal-width-type and (b) is of the unequal-spacing-type, respectively. As shown in the figure, it is clear that both proposed types can reduce the cogging torque significantly. This work was supported in part by the WISE Program for AI Electronics, Tohoku University.

![](https://assets.underline.io/uploads/markdown_image/1/image/eeec3ec6463607fb1bf5076d040b3ea8.jpg)

Fig. 1 The investigated AFMG and the proposed two types of pole-pieces; (b) unequal width, (c) unequal spacing.

![](https://assets.underline.io/uploads/markdown_image/1/image/9170e6aa71b8e0327dbcb0a6c124a106.jpg)

Fig. 2 The calculated high-speed rotor cogging torque of the two types of pole-pieces; (a) unequal width, (b) unequal spacing.

Cogging Torque Reduction of Integer Gear Ratio Axial-flux Magnetic Gear for Wind-Power Generation Application by Using Two New Types of Pole-Pieces

I. Introduction Stator-permanent magnet (PM) electrical machines are potential for developing as high-speed (HS) electrical machines, due to their advantages of high torque density and robust rotor structure. As one of the most promising stator-PM machines, flux-switching permanent magnet machine (FSPMM) has comparable torque density with the rotor-PM machines and easy thermal dissipation. However, the high fundamental frequency of conventional FSPMM is inevitable, making it difficult to be driven by the power electronics device. In this paper, a novel dual-step 2-phase 4/3 FSPMM is proposed and analyzed. Compared with the traditional FSPMM with the odd number of rotor poles, the proposed structure has good flux linkage waveform, non-UMF and high torque density. II. Design and Performance of the Proposed 4/3 FSPM Machine Fig. 1(a) shows the structure of the novel dual-step 4/3 FSPM machine. With using this structure, it can achieve the least number of rotor poles. The PMs have the same magnetization direction, whereas the winding directions are inverse, as shown in Fig. 1(b) and (c). The two set of windings can be connected in series, therefore it is convenient to drive the machine. The rear rotor is offset by 60° mechanically with respect to the corresponding front rotor. An appropriate gap distance between two stators is necessary to accommodate the end of inverse windings and avoid excessive magnet flux leakage. The flange and chamfering rotor is designed to reduce the cogging torque, as shown in Fig.2 (a). The performance of the novel 4/3 FSPM is obtained by using the finite element method and the parameters optimization method. Fig. 2(b) shows that the UMF of the proposed machine. It can be seen that the UMF of the proposed machine is relatively small. The peak-to-peak value of the cogging torque which varies with width of rotor flange is drawn in Fig.2 (c). The designed machine can obtain minimum cogging torque of 360.71 mNm.


![](https://assets.underline.io/uploads/markdown_image/1/image/cfeb923ad4dd15fdd6d408f889bdb4bb.jpg)

Design and Analysis of a Novel 2-Phase 4

![](https://assets.underline.io/uploads/markdown_image/1/image/c9e1a53d9fd13df6d0243077e46d6a55.jpg)

3 FSPMM with Chamfering and Flange Rotor Poles

Design and Analysis of a Novel 2-Phase 4/3 FSPMM with Chamfering and Flange Rotor Poles

Doubly salient brushless DC (DSBLDC) machine has been attracting much attention for aviation and vehicular applications, owing to its simple structure, adjustable flux, and reliability. Despite those merits, the torque ripple of DSBLDC machine limits its applications at medium-and-low speeds. The current harmonic injection (CHI) method has been proposed to reduce torque ripple, dealing with the subsequent issue, such as vibrations, acoustic noise, even starting failure. The traditional CHI choice of odd order harmonics to limit torque ripple is almost useless for the 3-phase 12/8-pole DSBLDC machine, due to the excitation and armature winding configurations, which generate its unique magnetic circuit and inductance characteristics. Firstly, A new instantaneous torque model from the perspective of harmonics has been derived. The main components of the excitation inductance are the 1st, 2nd and 4th harmonics. Only the armature current harmonics interact with the same-order inductance harmonics can contribute to the average torque, otherwise it will lead to torque harmonics. Thus, a harmonic injection algorithm based on the 2nd and 4th current harmonics is proposed to reduce the torque ripple. Fig.1(a) shows the topology of the DSBLDC machine, which is marked by the concentrated stator-field-winding and the absence of rotor excitation. Experiment platform is shown in Fig. 1(b). The instantaneous torque as shown in Fig. 1(c) can be divided into two parts: average torque and torque ripple, which is used to solve the current amplitude and phase parameters of injected current as shown in Fig.2(a). Fig.2 shows the solution based on the harmonic injection algorithm. Case I contains only the fundamental wave. The 2nd harmonic is added into Case II. Case III contains the 1st, 2nd and 4th harmonics, reducing the torque ripple from 54.84% to 44.28%. The torque waveform and its FFT results are shown in Fig. 2(b) and Fig. 2(c). Using the system diagram in Fig. 2(d) can experimentally validate the foregoing simulation, the partial result about Case I is given in Fig. 2(e).

![](https://assets.underline.io/uploads/markdown_image/1/image/06ff416686f82ddb1613b73f4d429ccc.png)

Fig.1 topology and torque model of the 12/8-pole DSBLDC machine.


![](https://assets.underline.io/uploads/markdown_image/1/image/9986831376a4f2901d749908e3201fc4.jpg)

Fig.2 simulation and experimental results based on the harmonic injection algorithm.

Torque Ripple Suppression of Doubly Salient Brushless DC Machine With Even-order Current Harmonic Injection

INTRODUCTION The structure of doubly salient laminations and concentrated windings as well as the operation with unipolar rectangle currents and pulsating torques result in the significant radial magnetic force (RMF) in switched reluctance machines (SRMs), which contributes to the vibration and acoustic noise [1][2]. The analysis of the RMF plays an essential role in SRMs, in which the analytical method (AM) featuring with fast calculation and low computing loading, is helpful in the initial design. However, due to the severe nonlinearity of SRMs, it is of challenge to analytically predict the RMF [3]. Based on magneto-motive force (MMF)-permeance model [4], an AM is developed in this paper, and the saturations are considered via a rotor-position-independent magnetic equivalent circuit (MEC). The AM predictions will be validated by the finite element (FE) results and a prototype SRM. ANALYTICAL MODEL and RMF RESULTS The overall flowchart is shown in Fig. 1. The MMF distribution along air-gap periphery originated from the winding function and excitation, together with the air-gap permeance considering both stator/rotor saliency, are employed to predict the air-gap radial flux density. Then the RMF is calculated with Maxwell stress tensor. The magnetic saturation effect is included via a simplified MEC. The calculated RMFs along the air-gap periphery at one rotor position with single-phase excited are shown in Fig. 2(a), where both the linear and saturated conditions are included, and FE results are presented for the validation. The AM calculations agree well with FE results. Moreover, the AM-RMF waveform along the half air-gap periphery during one electric period is shown in Fig. 2(b). CONCLUSION An AM has been developed for predicting the RMF of SRMs, considering doubly salient laminations, unipolar rectangle currents and magnetic saturations. The calculation results are validated by the FE predictions. In the coming full paper, the details of the method, the flux tube of MEC and saturation factor, the validations on various SRMs with different excitations including overlapped currents, will be presented. A prototype SRM is to be tested.

![](https://assets.underline.io/uploads/markdown_image/1/image/824cbe0d375218c8beaf462fb166234b.jpg)

Fig. 1 Flowchart of AM of RMF.

![](https://assets.underline.io/uploads/markdown_image/1/image/f94362f2599ed11e8d796db183624985.jpg)

Fig. 2 RMF results along air-gap periphery.

Analytical Model of Radial Magnetic Force in Switched Reluctance Machines with Consideration of Magnetic Saturations

I. INTRODUCTION Variable flux memory (VFM) machines were proposed to address the constant air-gap flux and thus sacrificed efficiency in high-speed operations of conventional permanent magnet (PM) machines [1]. The magnetization state (MS) of low coercive force (LCF) PMs can be intentional regulated by d-axis current pulses [2]. The properties and dimensions of LCF PMs are essential in VFM machines, which straightforwardly affect the intentional MS manipulation, torque density and unintentional demagnetization (UD) withstanding [3]. Two VFM machines with different LCF PMs, i.e. SmCo (Hc=335kA/m) and AlNiCo (Hc=112kA/m), are investigated and the guideline of PM design in VFM machines for EV tractions is proposed. II. MACHINE TOPOLOGY and PERFORMANCE Fig. 1 shows the VFM machine cross section, whose outline dimension is inherited from Prius2010 traction machine [4]. Two machine cases employing SmCo and AlNiCo as LCF PMs respectively, together with NdFeB PM to realize hybrid PM configuration for torque improvement, are presented. The NdFeB PM volumes are identical in the two cases while the LCF PM thickness is 4mm for the SmCo case but 12mm for the AlNiCo case, which guarantees an equal PM MMF. As magnetization characteristics shown in Fig. 2, the MS range is 55.11% in the AlNiCo case with the limitation of rated current (236A), which is much higher than 23.15% in the SmCo machine. However, with 2 p.u. current limitation, the MS range of the SmCo case increases to 54.07%, which is close to the AlNiCo case. In addition, the torque of the SmCo case is higher than the AlNiCo case by &gt;10%. III. CONCLUSION Although the identical initial PM MMFs are presented, the AlNiCo machine always requires lower de/re-magnetizing currents than the SmCo case. Nevertheless, the MS ranges are similar in both cases with 2 p.u. current limitation, while the SmCo machine exhibits a higher torque density. More details of the electromagnetic characteristics, LCF PM optimization, operation condition effects, and experimental validation will be demonstrated in the coming full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/9f796652d2ae704bf4bb7ae10908e29a.jpg)

Fig. 1 Cross section of VFM machine.

![](https://assets.underline.io/uploads/markdown_image/1/image/1dbcfb3ab8d3cad6ba3f64b3b37e48ff.jpg)

Fig. 2 Fundamental phase back-EMFs at 1500 r/min after different d-axis excitations.

Investigation on Low Coercive Force Magnets in Variable Flux Memory Machines for Traction Applications

Open-phase failure is typical in multiphase machines [1]. During the open-phase faults and to support the desired developed torque in a six-phase interior permanent magnet motor (IPMSM), various fault tolerant control (FTC) methods have been proposed [2]-[3]. Although the degraded torque of a faulty IPMSM can be compensated via FTC, the noise and vibration (NV) behavior of the machine may still be affected. NV characteristics of healthy and open-phase IPMSMs have been studied before [4]-[6]. However, these characteristics have not been studied in FTC mode for an open-phase IPMSM. This paper, thus, predicts the NV performance of a laboratory six-phase IPMSM in a single open-phase fault under a negative sequence current compensated FTC mode, and the results are compared with the ones under healthy condition. The IPMSM is analyzed using finite element analysis (FEA) software and the single phase fault is remedied by FTC algorithm [2]. Fig. 1(a) shows the IPMSM and its section cut. The currents in healthy and faulty conditions are shown in Fig. 1(b) while phase A is open in faulty condition. Torque comparison is shown in Fig. 1(c). As seen, an average torque of 12.5 Nm is produced under both conditions. However, as presented in Fig. 2(a), radial electromagnetic force density under faulty condition is larger than the one under healthy condition. The acceleration and deformation in Figs. 2(b) and (c) show that the largest difference between the accelerations under two conditions happens at 6,800 Hz causing the sound pressure level (SPL) of the faulty IPMSM to be 14.1% larger than the healthy IPMSM as in Fig. 2(d). Furthermore, the maximum deformation under fault is 11.8% larger than the one under healthy condition. As demonstrated, although the IPMSM under faulty condition with FTC can produce comparable torque as healthy IPMSM, machine NV aspects need attentions. Experimental results and detailed NV analysis including modal analysis will be provided in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/f696d21c3a89261ad880a06f12b0d39d.jpg)

Fig. 1. IPMSM characteristics. (a) The investigated IPMSM and its section cut. (b) Input six phase currents. (c) Torque under two conditions.

![](https://assets.underline.io/uploads/markdown_image/1/image/b8ef2fc43e78a009486f87b8deae8b66.jpg)

Fig. 2. NV performance. (a) Radial EM force density. (b) Radial acceleration. (c) Deformed housings. (d) SPL.

Noise and Vibration Prediction of a Six-Phase IPMSM in a Single Open-Phase Failure Under a Negative Sequence Current Compensated Fault Tolerant Control Mode

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