France



1. Introduction&lt;br/&gt;Ultra-high-speed (UHS) surface-mounted permanent magnet synchronous motor (SPMSM) is widely used for driving air compressor [1]. The electromagnetic losses generated by the UHS SPMSM inculde iron loss, copper loss, rotor eddy current loss, and etc. Especially, the UHS SPMSM can be have large stator iron loss and rotor eddy current loss due to its high rotational speed [2]. The stator iron loss is related to the magnetic properties of the stator iron core, and the rotor eddy current loss is related to the electrical properties of the rotor sleeve and permanent magnet (PM). In addition, the magnitude of these losses can be influenced by the armature magnetomotive force (MMF), which is the product of the number of turns and current. Accordingly, in order to determine the armature MMF, it is necessary to determine the appropriate number of turns and current magnitude in the motor design process. Since the magnetic flux density of stator iron core is different according to the armature MMF, the nonlinearity of the stator iron core must be considered in the motor design process.&lt;br/&gt;The contribution of this research is to propose the kriging surrogate model-based design process of UHS SPMSM considering stator iron loss and rotor eddy current loss. In the proposed design process, the nonlinearity of the stator iron loss and rotor eddy current loss according to the magnetic saturation is considered through the kriging surrogate model. The kriging surrogate model is suitable for use in electric motor design because it has high predicitive ability for reponses with nonlinear charateristics [3]. For the verification, a prototype is fabricated and the experiments wiil be conducted.&lt;br/&gt;&lt;br/&gt;2. Kriging surrogate model-based design process&lt;br/&gt;Using the constructed kriging surrogate models, the motor is designed through the motor design process shown in Fig. 1. The kriging surrogate model-based design process is divided into two stages: size determination and loss minimization. In both stages, optimization techniques are applied. First, the optimization problem is defined to minimize the objective function while satisfying the constraints. Next, the design of experiments for the selected design variables is performed, and a kriging surrogate model is created. Finally, the kriging surrogate models are used to determine the optimal model that satisfies the objective function and constraints. As a result, the model designed using the kriging surrogate model improves as follow compared to the model designed using the conventional design methodology: 1.4% reduction in stator outer diameter, 11.8% reduction in stack length, and 6.4% reduction in total losses.&lt;br/&gt;A. Size Determination&lt;br/&gt;The radial dimension of the rotor is determined in consideration of the mechanical stiffness and air gap magnetic flux density. Optimization technique is applied in the size determination. The objective function is set to minimize the stack length, and the constraints are defined considering the electrical specificatons. The tooth width, yoke thickness, and the number of turns are selected as design variables. Then, the respones to be predicted by the kriging surrogate models are the stator outer diameter, stack length and line to line voltage.&lt;br/&gt;When kriging surrogate models are used in the motor design process, the tendency according to design variables and the nonlinearity of the core can be considered. In particular, when the current is the same, the change in the armature MMF according to the number of turns affects the magnetic flux density of the stator core. Since saturation of core is an important parameter in determining the motor size, it is considered by using the kriging surrogate model.&lt;br/&gt;B. Loss Minimization&lt;br/&gt;In this paragraph, the loss of the motor is minimized by changing the stator shape. The considered losses are iron loss, rotor eddy current loss, alternation current (AC) copper loss, and windage loss. As mentioned in section 2. A&lt;i&gt;,&lt;/i&gt; optimization technique is applied to minimize motor losses. UHS SPMSM is designed through the kriging surrogate model for losses because the ratio of the stator core loss and the rotor eddy current loss due to the high rotational speed is large. Another major loss to consider in UHS SPMSMs is AC copper loss. As mentioned in section 1&lt;i&gt;,&lt;/i&gt; since the frequency of the input current is large in the UHS SPMSM, the AC copper loss is also large, which is considered through kriging surrogate model. The windage loss generated in the air gap and increases with increasing rotational speed. The windage loss is also considered through the kriging surrogate model. The constraints for motor loss minimization are electrical specifications and target torque. Design variables are selected as tooth tip and slot open. Using the kriging surrogate model, the optimal model is obtained that minimizes motor loss while satisfying the constraints.&lt;br/&gt;&lt;br/&gt;3. Result and Conclusion&lt;br/&gt;In this paper, a kriging surrogate model-based design process is proposed. Through the process, a motor that satisfies the required motor size and specifications is determined. As a result, the model designed using the kriging surrogate model reduced the stator iron loss by 7.6% and the rotor eddy current loss by 24.9% compared to the model designed using the conventional design methodology. As shown in Fig. 2, a prototype of the designed model is fabricated. Through the test, the validity of the designed model will be verified.

**References:**

[1] Z.Zhang, Z. Deng,and Q. Sun, IEEE Transactions on Magnetics., Vol. 55, p.1-11 (2019)&lt;br/&gt;[2] F. Zhou, J. Shen, and W. Fei, IEEE Transactions on Magnetics., Vol. 42, p. 3398-3400 (2006)&lt;br/&gt;[3] S. Kim, S.-Y. Lee, and J.-M. Kim, IEEE Transactions on Energy Conversion., Vol. 35, p.2056-2065 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e8038cd4fa9f73262d8420feee425528.jpg)
Fig. 1 Proposed kriging surrogate model-based design process

![](https://assets.underline.io/uploads/markdown_image/1/image/5df0db304ff9b96b9765d9cb3af52f65.jpg)
Fig. 2. Experimental setup for no-load test of prototype

INTERMAG 2021

 Kriging Surrogate Model-Based Design of Ultra-High-Speed Surface-mounted Permanent Magnet Synchronous Motor Considering Stator Iron Loss and Rotor Eddy Current Loss

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1. Introduction Ultra-high-speed (UHS) surface-mounted permanent magnet synchronous motor (SPMSM) is widely used for driving air compressor [1]. The electromagnetic losses generated by the UHS SPMSM inculde iron loss, copper loss, rotor eddy current loss, and etc. Especially, the UHS SPMSM can be have large stator iron loss and rotor eddy current loss due to its high rotational speed [2]. The stator iron loss is related to the magnetic properties of the stator iron core, and the rotor eddy current loss is related to the electrical properties of the rotor sleeve and permanent magnet (PM). In addition, the magnitude of these losses can be influenced by the armature magnetomotive force (MMF), which is the product of the number of turns and current. Accordingly, in order to determine the armature MMF, it is necessary to determine the appropriate number of turns and current magnitude in the motor design process. Since the magnetic flux density of stator iron core is different according to the armature MMF, the nonlinearity of the stator iron core must be considered in the motor design process. The contribution of this research is to propose the kriging surrogate model-based design process of UHS SPMSM considering stator iron loss and rotor eddy current loss. In the proposed design process, the nonlinearity of the stator iron loss and rotor eddy current loss according to the magnetic saturation is considered through the kriging surrogate model. The kriging surrogate model is suitable for use in electric motor design because it has high predicitive ability for reponses with nonlinear charateristics [3]. For the verification, a prototype is fabricated and the experiments wiil be conducted. 2. Kriging surrogate model-based design process Using the constructed kriging surrogate models, the motor is designed through the motor design process shown in Fig. 1. The kriging surrogate model-based design process is divided into two stages: size determination and loss minimization. In both stages, optimization techniques are applied. First, the optimization problem is defined to minimize the objective function while satisfying the constraints. Next, the design of experiments for the selected design variables is performed, and a kriging surrogate model is created. Finally, the kriging surrogate models are used to determine the optimal model that satisfies the objective function and constraints. As a result, the model designed using the kriging surrogate model improves as follow compared to the model designed using the conventional design methodology: 1.4% reduction in stator outer diameter, 11.8% reduction in stack length, and 6.4% reduction in total losses. A. Size Determination The radial dimension of the rotor is determined in consideration of the mechanical stiffness and air gap magnetic flux density. Optimization technique is applied in the size determination. The objective function is set to minimize the stack length, and the constraints are defined considering the electrical specificatons. The tooth width, yoke thickness, and the number of turns are selected as design variables. Then, the respones to be predicted by the kriging surrogate models are the stator outer diameter, stack length and line to line voltage. When kriging surrogate models are used in the motor design process, the tendency according to design variables and the nonlinearity of the core can be considered. In particular, when the current is the same, the change in the armature MMF according to the number of turns affects the magnetic flux density of the stator core. Since saturation of core is an important parameter in determining the motor size, it is considered by using the kriging surrogate model. B. Loss Minimization In this paragraph, the loss of the motor is minimized by changing the stator shape. The considered losses are iron loss, rotor eddy current loss, alternation current (AC) copper loss, and windage loss. As mentioned in section 2. A, optimization technique is applied to minimize motor losses. UHS SPMSM is designed through the kriging surrogate model for losses because the ratio of the stator core loss and the rotor eddy current loss due to the high rotational speed is large. Another major loss to consider in UHS SPMSMs is AC copper loss. As mentioned in section 1, since the frequency of the input current is large in the UHS SPMSM, the AC copper loss is also large, which is considered through kriging surrogate model. The windage loss generated in the air gap and increases with increasing rotational speed. The windage loss is also considered through the kriging surrogate model. The constraints for motor loss minimization are electrical specifications and target torque. Design variables are selected as tooth tip and slot open. Using the kriging surrogate model, the optimal model is obtained that minimizes motor loss while satisfying the constraints. 3. Result and Conclusion In this paper, a kriging surrogate model-based design process is proposed. Through the process, a motor that satisfies the required motor size and specifications is determined. As a result, the model designed using the kriging surrogate model reduced the stator iron loss by 7.6% and the rotor eddy current loss by 24.9% compared to the model designed using the conventional design methodology. As shown in Fig. 2, a prototype of the designed model is fabricated. Through the test, the validity of the designed model will be verified.

**References:**

[1] Z.Zhang, Z. Deng,and Q. Sun, IEEE Transactions on Magnetics., Vol. 55, p.1-11 (2019) [2] F. Zhou, J. Shen, and W. Fei, IEEE Transactions on Magnetics., Vol. 42, p. 3398-3400 (2006) [3] S. Kim, S.-Y. Lee, and J.-M. Kim, IEEE Transactions on Energy Conversion., Vol. 35, p.2056-2065 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e8038cd4fa9f73262d8420feee425528.jpg)
Fig. 1 Proposed kriging surrogate model-based design process

![](https://assets.underline.io/uploads/markdown_image/1/image/5df0db304ff9b96b9765d9cb3af52f65.jpg)
Fig. 2. Experimental setup for no-load test of prototype

poster

I Introduction Variable-flux permanent magnet synchronous machines (PMSMs) have gained a lot of attention for their ability to expand speed range and reduce copper loss by manipulating the magnetization state dynamically. Variable-flux PMSMs employ low coercive force magnets, whose magnetization states can be adjusted by d-axis current pulses [1-2]. The PM excitation field is adjustable and the need for continuous flux-weakening current is reduced. To maximize output torque and operation efficiency, the maximum torque per ampere (MTPA) control is widely used in interior PMSMs [3-4]. However, the parameters, like PM flux-linkage, d- and q-axis inductances, of variable-flux PMSMs are influenced by not only the load condition variations but also the magnetization state adjustments. The precise MTPA control for variable-flux PMSMs is highly affected by the nonlinear parameter properties. The operating principle of a novel variable-flux PMSM is analysed. The nonlinear load flux-linkage model is established to simplify the modelling of nonlinear parameter properties. The MTPA current trajectory search method based on Golden Selection method is proposed to obtain the current trajectory considering the influence of magnetization state adjustments and load condition variations. Moreover, the on-line MTPA control method based on neural-network algorithm is proposed to provide an effective way of on-line MTPA control for variable-flux PMSMs. II Operating Principle of Variable-flux PMSMs and Nonlinear Load Flux-Linkage Model A novel series-parallel-connected hybrid-PM variable-flux PMSM is proposed and shown in fig. 1. The magnetization state of this machine can be adjusted by manipulating the magnetization direction of AlNiCo near d-axis in V-shape magnets and the flux amplitude of all AlNiCo. The machine saturation degree varies significantly with magnetization state adjustments and load condition variations. Then the machine parameters, such as PM flux-linkage, d- and q-axis inductances, vary nonlinearly too. The nonlinear load flux-linkage model is established to simplify the modelling of nonlinear parameter properties. The amplitude-phase sequences of current working points are selected to calculate the corresponding d-, q-axis flux-linkage by FEA or experiment. And the permeability of any two adjacent selected points is nearly the same. The nonlinear load flux-linkage model is formed using the selected current working points and corresponding d-, q-axis flux-linkage. The separation of load PM flux-linkage and calculation of d-, q-axis inductances are no longer needed. The load flux-linkage model that presents the nonlinear parameter properties is used in the MTPA current trajectory search process. III MTPA Current Trajectory Search based on Golden Selection Method The proposed MTPA current trajectory search method includes two iterative loops which are both based on Golden Selection method. The current phase iterative loop is implemented firstly, and the optimization target is to minimize corresponding current amplitude at a given torque reference and a given magnetization state. The amplitude is optimized to the minimum value when the iteration interval of phase is within a given minuscule number. However, the corresponding amplitude of phase cannot be obtained directly due to nonlinear parameter properties. The current amplitude iterative loop is nested in the phase iterative loop to obtain corresponding amplitude of each phase. The target of amplitude iterative loop is to optimize the difference between present torque and torque reference to zero. During the amplitude iteration process, the value of present torque under different amplitudes and phases is calculated by the nonlinear load flux-linkage model. MTPA current trajectories of the proposed machine under 4 magnetization states are obtained by the proposed search method, and compared with the trajectories obtained by traditional method, as shown in fig. 2. The current trajectories are evaluated by FEA and experiments. The results prove that the proposed search method can find MTPA current trajectories precisely considering the influence of magnetization state adjustments and load condition variations. IV On-Line MTPA Control based on Neural-Network Algorithm The on-line generation of current commands by the proposed search method is time-consuming. The neural-network-based MTPA control method is proposed to implement MTPA control in real-time control system. The MTPA current trajectory generated by proposed search method under different magnetization states and torque references are selected as sample data. The on-line MTPA control neural-network model is trained, tested and validated using sample data. The model input is magnetization state and torque reference, and the output is current amplitude and phase. Once the train, test and validation process are finished, the knowledge about input-output relationship is acquired and the on-line MTPA control neural-network model is established. MTPA current trajectories at any magnetization state and torque reference can be predicted by this model. The mathematical expressions of established model are easily programmed and quickly executed by DSP for on-line MTPA control. The calculation speed and accuracy are evaluated by simulations and experiments. The results prove that the proposed neural-network model can realize on-line MTPA control for variable-flux PMSMs quickly and precisely.

**References:**

[1] V. Ostovic. "Memory Motors," IEEE Ind. Appl. Mag., 9(1): 52-61, 2003. [2] H. Hua, Z. Q. Zhu, A. Pride, et al. "Comparative Study on Variable Flux Memory Machines with Parallel or Series Hybrid Magnets," IEEE Trans. Ind. Appl., 55(2): 1408-1419, 2019. [3] S. Kim, Y. D. Yoon, S. K. Sul, et al. "Maximum Torque per Ampere (MTPA) Control of an IPM Machine Based on Signal Injection Considering Inductance Saturation," IEEE Trans. Power Electron., 28(1): 488–497, 2013. [4] J. H. Chen, J. Li and R. H. Qu. "Maximum-Torque-per-Ampere and Magnetization-State Control of a Variable-Flux Permanent Magnet Machine," IEEE Trans. Ind. Electron., 65(2): 1158–1169, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dfd2667da240b269f350b75ad5c8e9cf.jpg)
Fig.1 Structure of proposed machine.

![](https://assets.underline.io/uploads/markdown_image/1/image/a7ca35c45edd083408f18282dbf1d1bf.jpg)
Fig.2 Current trajectories obtained by proposed method and traditional method.

 Maximum Torque per Ampere Control for Variable-Flux PMSMs Considering the Influence of Magnetization State Adjustments and Load Condition Variations

I. Introduction Permanent magnet (PM) motors have been widely used in electric vehicles due to its high torque/power density and high efficiency. Yet, a relatively constant airgap magnetic field of PM motors may limit the speed range to large extent, which is still the shortfall for the further applications in EVs. In recent years, a type of variable-flux-leakage PM motor is emerged, which draws intense interest from academics of motor field because of the achievement of flux-controllable capability [1]. In this type of motors, the leakage flux can be varied by designing flux bridge and magnetic barrier, and it can be controllable through the change of q-axis current of winding. Compared with conventional PM motor, the variable flux is essentially derived from active design of flux leakage. So, the magnetic field distribution of leakage flux is sensitively linked to the flux controllability. Then, in [2], a variable-flux-leakage PM Motor is proposed, where a unique flux leakage path is purposely considered by arranging the PM position and magnetic barrier reasonably. The results indicate that the relatively obvious capability of flux regulation is achieved by effectively controlling the leakage flux. Yet, in flux-regulated process, the magnetoresistance characteristic of the motor is changed appreciably caused by the variation of leakage flux. It means that different flux-leakage operation modes of the motor will bring the characteristic differences of output torque. For instance, the varied main flux caused by leakage flux greatly leads to the change of PM torque, while the variation of inductance characteristics induced by magnetic saturation bring about the change of reluctance torque. Therefore, to the variable-flux-leakage PM motor, it is necessary and meaningful to comprehensively consider the torque characteristics at various flux-leakage operation modes. And, in this case, how to realize the optimal distribution of different torque components is full of challenge. In this paper, a flux-controllable permanent magnet (FC-PM) motor is proposed. The key of the study is to conduct torque characteristics analysis and optimization by combining with typical operation conditions. Then, based on different flux-leakage operation modes, a reasonable optimization strategy considering torque components is developed. The results reveal that, based on optimization, the comprehensive torque is effectively improved while maintaining a desirable flux regulation region. II. Motor Topology and Simulation Result Fig.1(a) shows the structure of the FC-PM motor with independent separated flux leakage branches. It can be seen that the q-axis is equipped with multi-layer arc and ellipse magnetic barriers to obtains good magnetic flux leakage controllable performance, which further broadens the motor speed regulation range. Fig.1(b) shows the magnetic density distributions of the FC-IPM motor under different flux-leakage operation modes, and the corresponding requirements of torque components distribution are listed. In Fig. 2(a) and (b), the sensitivity of each design variable to different design objectives is evaluated, and three variables with high sensitivity are selected for further optimization. Fig. 2(c) and (d) show the result of torque distribution under different flux-leakage Operation Modes, which can be seen that through the multi-objective optimization proposed in this paper, the torque quality is improved as expect. The torque performances and corresponding torque component distribution under different modes are shown in Fig.2 (d) and (f). The prototype of proposed FC-IPM motor and corresponding experiment result of back-EMF are shown in Fig. 2(g) and Fig. 2(h), respectively. In additional, III. Conclusion In this paper, a FC-PM motor is purposely designed, and a multi-objective optimization method is also newly proposed, where the optimal distribution of torque components under different flux-leakage operation modes is considered. Through optimization, the PM torque becomes the main component under less flux leakage, and the reluctance torque as the main component under more flux leakage. It means that the optimal proportion of different torque components of the FC-PM motor is realized. Both the simulation and experiment results not only verify the reasonability of the proposed motor but also confirm the effectiveness of the proposed optimization method. The more electromagnetic performance analysis and experimental results will be provided in the full paper.

**References:**

[1] X. Zhu, W. Wu, S. Yang, Z. Xiang and L. Quan, in IEEE Transactions on Energy Conversion, vol. 33, no. 4, pp. 2260-2269, Dec. 2018. [2] T. Kato, M. Minowa, H. Hijikata, K. Akatsu and R. D. Lorenz, in IEEE Transactions on Industry Applications, vol. 51, no. 5, pp. 3811-3821, Sept.-Oct. 2015.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/374892bf3a14e058bbeaa3286988bcda.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/4178320d508adb7f7bdb56859b57fb75.jpg)

 Torque Characteristics Investigation of A Flux-controllable Permanent Magnet Motor Considering Different Flux-leakage Operation Modes

I. INTRODUCTION The traditional three-phase PMSMs are confronted with severe challenge, and some researchers turn to investigate modular motor systems for better fault-tolerant capability [1]. The modular motor system is composed of several modules, and each module could be equivalent to an independent sub-motor. The better the independence of electric, magnetic, thermal, and physics between the modules, the better fault-tolerant performance of the motor is. The fractional slot concentrated winding (FSCW) has some advantages in non-overlapping end winding, large inductance and small coupling between phases, so it is very suitable for the application in modular fault-tolerant motors [2] However, the MMF of the motor with FSCW contains quantities of space harmonics which will cause PM eddy-current losses. The open-circuit fault is a typical fault in all kinds of motor faults [3], and the fault-tolerant capability of the motor is mostly determined by the output performance under open-circuit faults [4]. This paper investigates the influence of magneto motive force (MMF) space harmonic on permanent magnet (PM) eddy-current losses in a modular fault-tolerant in-wheel motor under various open-circuit faulty operations. First, reconfiguring maximum round MMF with constant amplitude of current is taken as the fault-tolerant (FT) strategy for the open-circuit of one phase. The fault-tolerant strategies for various faults are derived respectively based on this strategy. Second, the harmonic components of MMF under various faults and corresponding fault-tolerant control are analyzed respectively. Then, an analytical model based on multi-loop method for PM eddy current losses is proposed. The losses induced by each harmonic components of MMF can be obtained from the model. The analytical results agree well with the finite element method (FEM) results. The space harmonics are composed of slot harmonics and other harmonics. The proportions of eddy current losses caused by these two types of harmonics under various faults are derived. Finally, PM eddy-current losses induced by the fault-tolerant current under the overload condition are analyzed, and the results have a certain reference value for the fault-tolerant strategy which makes the faulty motor operates safer and more stable. II. MODULAR MOTOR SYSTEM WITH FAULT-TOLERANT CAPABILITY For design a better fault-tolerant motor, the entire fault-tolerant system needs to be considered comprehensively. Not only design the motor itself, but also should consider the topology of the controller and the fault-tolerant control strategy. The motor consists of 4 modules, as shown in Fig. 1. Each module is controlled by an independent drive with a three-phase four-wire control circuit, which ensures electrical isolation between the modules. III. ANSLYSIS OF CHARACTERISTICS OF MMF UNDER VARIOUS OPEN-CIRCUIT FAULTY OPERATIONS 1) Reconfiguring Maximum Round Fundamental MMF With Constant Current When A1 is in open-circuit condition, the performance of MMF will be declined. Quantities of sub-harmonics and high order harmonics closed to the working wave emerge, and the amplitude of working wave decreases, as shown in Fig. 2. Through the proposed fault-tolerant control, the performance of MMF is improved. 2) Spatial Harmonic Analysis of MMF under Various Faults The overall performance evaluation of the MMF is established by the two following aspects: 1 The amplitude of the working wave; 2 Total harmonic distortion (THD). The performance of MMF for the modular motor under various open-circuit faults can be effectively improved through the proposed fault-tolerant strategies. IV. ANSLYSIS OF PM EDDY-CURRENT LOSSES UNDER VARIOUS LOSSES UNDER VARIOUS OPEN-CIRCUIT FAULTY OPERATIONS 1) Analytical Model An analytical model based on multi-loop method for PM eddy current losses is proposed. 2) Verification by FEM The eddy-current losses of PMs by FEM consist of two parts. One is the slot ripple losses in PMs, which are the most important losses in PMs and generated by the fundamental frequency magnetic flux due to the stator slot openings. The other one is the losses in PMs induced by the space harmonics. The analytical results agree well with the FEM results. 3) Analysis of PM Eddy-Current Losses under Overload Fault-Tolerant Control When the overload FT controls are adopted, the motor can operate safely for a period of time rather than a long time. If we want the motor operates stably during the time, the PM losses should be considered. V. CONCLUSIONS An analytical model based on multi-loop method for calculating PM eddy-current losses is proposed. The analytical results agree well with the FEM result, which proves the correctness of the model. The proposed model is more accordant with the actual situation and the physical meaning is clearer. The eddy-current losses caused by high order slot harmonics are very small. Among the newly emerged harmonics, the sub-harmonics and high order harmonics closed to working wave will cause relatively large eddy-current losses. As the fault level increases, the proportion of eddy-current loss induced by slot harmonics decreases, while the proportion of eddy-current loss induced by other harmonics increases. If the overload fault-tolerant strategy is adopted, not only the copper losses but also the eddy-current losses of PMs should be considered.

**References:**

[1] Ifedi C. J., Mecrow B. C., Brockway S. T. M, “Fault-tolerant in-wheel motor topologies for high-performance electric vehicles”. IEEE Trans. Ind. Appl., 2013, 49, (3), pp. 1249-1257. [2] Heins G., Ionel D., Thiele M., “Winding factors and magnetic fields in permanent magnet brushless machines with concentrated windings and modular stator cores”. IEEE Trans. Ind. Appl., 2015, 51, (4), pp. 2924–2932. [3] Li Y. X., Zhu Z. Q., Thomas A. S., “Novel modular fractional slot permanent magnet machines with redundant teeth”. IEEE Trans. Magn., 2019, 55, (9), pp. 1-10. [4] Liang P. X., Pei Y. L., Chai F., “An improved method for armature-reaction magnetic field calculation of interior permanent magnet motors”. IEEE Trans. Magn., 2016, 52, (7), pp. 1-4.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b5f8d38fe4176b0605a175e03295d3aa.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/3dbccfaa57183c0d06276f162998ca2a.jpg)

 Influence of MMF Space Harmonic on PM Eddy-Current Losses in a Modular Fault-Tolerant In-Wheel Motor under Open-Circuit Faulty Operations

This paper presents a comparative study of the field modulation effects (FMEs) on consequent-pole permeant magnet (CPM) machines with different stator slot configurations, i.e., open-slot, semi-closed slot and close-slot. Due to the asymmetrical PM magneto-motive force (MMF) distributions and double-side slotting effect, the CPM machines exhibit more air-gap field harmonics for the torque production. In order to quantify the torque contributions of the various effective harmonics, the Maxwell stress tensor method (MSTD) is adopted. The torque proportions due to various air-gap field harmonics in the CPM machines with different stator slot configurations are subsequently investigated by finite element (FE) method, which confirms that the stator slot configurations have a great influence on FME. It can be found that the highest and the lowest torque proportion contributed by the modulated field harmonics can be observed in closed-slot and open-slot structures, respectively. Finally, some experimental measurements on a 12-slot/14-pole CPM machine prototype with a semi-closed slot configuration are carried out to validate the theoretical and FE analyses. I. Introduction In order to reduce permanent magnet (PM) consumption, consequent-pole PM (CPM) machines are widely investigated with hybrid excited [1], modular design [2] and multi-phase [3] in recent years. Besides, some interior CPM machines with different PM arrangements, i.e., V-shaped [4], U-shaped [5] and spoke-type [5]-[7] are studied. It demonstrates that the proposed designs exhibit comparable torque performance, high-efficiency region and relatively lower PM consumption than conventional counterparts. Moreover, the field modulation effect (FME) on CPM machine is comparatively studied with surfaced-mounted PM (SPM) machine, which shows that the CPM machine exhibits more pronounced FME than SPM case due to its double-side slotting effect [8] [9]. However, the influence of stator slot on FME of the CPM machines remain unexplained hitherto. Thus, this paper comparatively study of the FME on CPM machines with different stator slots, i.e., open-slot, semi-closed slot and closed-slot. II. Machine Topologies The illustrations of 12-slot stators with open-slot, semi-closed slot and closed-slot structures are given in Fig. 1(a), (b) and (c), respectively. In order to perform a fair comparison, the three CPM machines share the same 14-pole rotor, as shown in Fig. 1(d). Besides, in order to identify and compare the effective air-gap field harmonics for the torque production in a fair way, the same stator outer diameter, air-gap length, active stack length and current density are employed in the three CPM machine topologies. III. Comparison of Torque Contributons of Dominant Magnetic Field on CPM Machies The torque characteristics of the three CPM machines are illustrated in Fig. 1(e) and (f). It can be observed that the semi-closed slot structure exhibits the highest torque, as shown in Fig. 1(e), which is mainly due to its the lowest flux leakage. According to Maxwell stress tensor method, the instantaneous electromagnetic torque Te can be calculated by Τe=(lstkrg2/μ0)∫BrBtdθ=∑(πlstkrg2/μ0)BrkBtkcos[θrk(t)-θtk(t)]=∑Tk(t) (1) where rg is the air-gap radius. lstk is the active stack length. Tk is the instantaneous electromagnetic torque generated by the kth harmonics of radial and tangential air-gap flux densities, respectively. Thus, the contributions of the kth field harmonics to the total electromagnetic torque can be separated when the kth radial and tangential air-gap field harmonics are obtained, as illustrated in Figs. 1(f). It should be noted that, apart from the Zr order magnetic harmonic, various modulated field harmonics engage in the torque generation, which confirm that the pronounced FME in CPM machines. Besides, the Zr order harmonic contributes the highest and lowest torque proportion in open-slot and closed-slot, respectively. As a result, the highest and the lowest torque production contributed by the modulated field harmonics can be observed in closed-slot and open-slot structures, respectively. IV. Experimental Validation The stator and rotor assemblies of the CPM machine prototype with semi-closed slot configuration are shown in Figs. 2(a) and (b), respectively. The comparison of the FE predicted and measured back-EMF and average torque values are illustrated in Figs. 2(c) amd (d), respectively. Because the end flux leakage and mechanical tolerance are not considered in the FE analyses, the slight difference between the FE predicted and measured results can be observed in Figs. 2(c) and (d). Overall, a satisfactory agreement between the measured and FE predicted results confirms the theoretical analyses. The detailed analysis will be presented in the full paper.

**References:**

[1] J. A. Tapia, F. Leonardi and T. A. Lipo, IEEE Transactions on Industry Application, Vol. 39, p.1704-1709 (2003) [2] S. U. Chung, J. W. Kim and B. C. Woo IEEE Transactions on Magnetics, Vol. 47, p.4215-4218 (2011) [3] H. Dhulipati, E. Ghosh and S. Mukundan, IEEE Transactions on Energy Conversions, Vol. 34, p.2041-2051 (2019) [4] J. Li, K. Wang and H. Zhang, IEEE Transactions on Industrial Electronics, Vol. 67, p.3374-3385 (2020) [5] J. Li and K. Wang, IEEE/ASME T Transactions on Mechatronics, Vol. 24, p.2182-2192 (2019) [6] W. Liu and T, A. Lipo, IEEE Transactions on Industry Application, Vol. 54, p.5918-5929 (2018) [7] X. Ren, D. Li and R. Qu, IEEE Transactions on Energy Conversions, Vol. 33, p.2112-2121 (2018) [8] Y. Li, H. Yang and H. Lin, in Proc. XIII International Conference Electrical Machine (ICEM), pp. 65-71 (2018) [9] Y. Li, H. Yang and H. Lin, IEEE Transactions on Energy Conversions, accepted. (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7b6b32fc69a3721b8bce95d338aa550e.jpg)
Fig. 1. Machine Topologies of the CPM design with different stator slot configurations. (a) Open-slot. (b) Semi-closed slot. (c) Closed-slot. (d) CPM rotor. Torque characteristics of the CPM machines with different stator slot configurations. (e) Steady-state torque. (f) Torque proportion of the main working harmonics.

![](https://assets.underline.io/uploads/markdown_image/1/image/0b10a474aeab2a426720f5f07c6bab42.jpg)
 
Fig. 2. The CPM machine prototype with semi-closed slot. (a) Stator. (b) Rotor. Comparison of the measured and FE predicted back-EMF and average torque values. (c) Back-EMFs. (d) Average torque versus phase current.

 Comparative Study of Field Modulation Effects on Consequent-Pole PM Machines with Different Stator Slot Configurations

Recently, regulations on carbon dioxide emissions caused by environmental problems have been promoted worldwide. In the automotive industry, engine vehicles are being regulated and will disappear on the road in the next 10 years. As a result, the market for low-carbon Fuel Cell Electric Vehicles and electric vehicles is expanding, and much research on electrical components is underway. Compared to engine vehicles, electric vehicles have better efficiency of the drive unit itself without using a transmission. However, it has the disadvantages of the high vehicle price, low All-Electric Range(AER), and long charging time. These reasons are due to the high price of batteries that go into electric vehicles. To reduce the price of the vehicle, it is necessary to improve the performance of the battery and AER. In other ways, the efficiency of electric motors, inverters can affect the improvement of mileage when the same battery is used. Therefore, research to minimize the loss of both motors and inverters is also needed. Due to the characteristics of the electric motor, it does not come out efficiently in all operating ranges. Especially when the electric motor enters the high-speed region, the efficiency will be further reduced. The model is IPMSM used in electric vehicles, and the concept of electromagnetic multi-step transmission is introduced. The electromagnetic multi-step transmission is a method in which the parallel branch of the stator is changed at a constant speed by using the switch. Using this method, high torque and efficiency in the low-speed range, high efficiency in the high-speed range, and the operating range were expanded. The operating characteristics were analyzed using the finite element method (FEM). Additionally, phenomena occurring in the shifting process were analyzed. To proceed with the analysis, a 2D model was made by using a simulation tool. The model was analyzed into two models to select the parallel branch conversion point. The model's size is the same, and it is divided into two models of parallel branch 2 and 4. The base speed and maximum speed of parallel branch 2 are 3,000rpm and 8,000rpm, and the base and maximum speed of parallel branch 4 are 6,000rpm and 10,000rpm. The efficiency characteristics of both models were derived and analyzed for expanding the high-efficiency operating range. By combining the efficiency characteristics of both models, the conversion point of the parallel branch in which the high-efficiency section at the time of shifting is formed most widely was selected at 6,000 rpm. Fig. 1 shows a circuit diagram for electromagnetic multi-step shifting. The stator winding is Y-connected, and the dotted line is the circuit in the low-speed range, and the number of parallel circuits for each A, B, C phase is 2. The solid line shows the circuit when the number of parallel circuits of each phase is changed to 4 through a switch. Change the number of parallel branch The switch used for contact used a thyristor and consisted of 12 terminal terminals. The phenomenon that may be displayed when the number of parallel branch increases in the same model is that the torque decreases. And it is possible to operate up to a higher speed region than the model in which the number of parallel branch is small in voltage saturation. In addition, it was derived that the current density is reduced, which is advantageous in terms of heat. This motor operates with parallel branch 2 in the low-speed range, and changes the number of parallel branch of the stator to 4 through a switch at 6,000rpm. The electric motor used in the model is driven by parallel branch 2 in the low-speed section and changes the number of parallel branch of the stator to 4 by using the switch at 6,000rpm. The parallel branch 2 is called 1-step, and the voltage is saturated in the low-speed range. Therefore, it generates high torque at low speed, and the maximum efficiency point appears at low speed due to voltage saturation. After 6,000rpm, it is referred to as 2-step, driven by parallel branch 4. And the voltage is saturated at 6,000rpm. Therefore, in the case of parallel branch 4, the range of maximum efficiency point is displayed at around 6,000rpm. Fig. 2 shows the waveform of the current flowing through the stator winding in the process of shifting from 1-step to 2-step through FEM analysis. It was derived that the current waveform was unbalanced when shifting from 1-step to 2-step. In addition, a current unbalance phenomenon appeared in the process of shifting from 2-step to 1-step. current imbalance generates an impact during the shifting process, and is defined as a shift shock. It was analyzed that the shift shock was caused by a phenomenon in which the current was delayed by inductance in the process of changing the switch to shift. A study was conducted on the phenomena and characteristics of the electric motor when the electromagnetic transmission system was introduced into the IPMSM for electric vehicles. As a method of expanding the high-efficiency range of the motor, a method of changing the number of parallel branch through the shift process was used. However, it was confirmed that a shift shock was generated by an unbalanced current during the shifting process. In order to alleviate the shift shock, additional research was conducted to reduce the shock by selecting a parameter related to the stator.

**References:**

[1] Ho-Chang Jung, Gyeong-Jae Park, and Sang-Yong Jung, IEEE Trans. Magn, Vol. 53, No. 6 (2017) [2] Liang Fang, Jae-woo Jung, and Jung-Ho Lee, IEEE Trans. Magn, Vol. 44, No. 11, pp. 4393-4396 (2008) [3] Se-Young Oh, Su-Yeon Cho, and Ju Lee, IEEE Trans. Magn, Vol. 50, No. 2 (2014) [4] Ho-chang Jung, Deokjin Kim, and Sang-Yong Jung, IEEE Trans. Magn, Vol. 50, No. 2 (2014) [5] SangHyeok Seo, Gyeong-Jae Park, and Sang-Yong Jung, IEEE Trans. Magn, Vol. 53, No. 6 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/77518ee0e3bb22fe77956141eab380ec.jpg)
Circuit diagram for electromagnetic multi-step transmission

![](https://assets.underline.io/uploads/markdown_image/1/image/c6accf0acdac7081b6485cebeeec4332.jpg)
Current waveform from 1st to 2nd step

 A Study on The Electromagnetic Multi-Step Transmission Characteristics of Interior Permanent Magnet Synchronous Motor

1. In order to extending the operating speed range and increasing the maximum torque, two design methodologies of variable-flux machines (VFMs) are proposed, which make full utilizing of the material properties of the low coercive force (LCF) magnet. The inner relationship between the permanent-magnet (PM) flux variation range and speed-torque curves is comprehensively analyzed. The variation boundary of the PM flux for non-salient-pole with id=0 control method is investigated by analytic method. Due to the complexity of the transcendental equations, the per unit system is utilized for other types of machine and control method. Because the hysteresis loops of the LCF magnet employed in VFMs are quite different, which makes it difficult for machine designers to select suitable magnet. Therefore, an ideal determination model of hysteresis loop is established considering the remanent flux density, permeability of the recoil line, knee point and coercive force of the LCF magnet. A custom method is proposed to obtain the hysteresis loop calculated form the determination model. By using the proposed methodologies, the material prosperities of the magnet can be fully utilized and provide guidance to the scholars in the initial design stage of the VFM. 2. Introduction: Owing to the controllability of the permanent-magnet (PM) magnetic field, the variable-flux machine (VFM) become a good candidate for wide-speed operating demanding areas. By applying instantaneous demagnetizing current pulse, the PM flux of the VFM can be changed with negligible copper loss [1]. Compared with the conventional PMSMs, the negative d-axis current control (flux-weakening control) used under high speed condition is superseded by the instantaneous current pulse, so the overall efficiency of the VFM can be improved. Moreover, since the no-load back electromotive force proportional to the PM flux is reduced, the machine can operate under higher speed. There are many VFM topologies proposed by scholars, which has demonstrated the concepts and verified the merits of the VFM in detailed. In order to improve the torque output capability, the hybrid-PM variable flux machines (HPM-VFMs) are proposed [2-5]. The low coercive force (LCF) magnet employed in the above mentioned VFMs are AlNiCo, SmCo and Ferrite. However, there are little design methodologies to improve the machine performance in terms of the full utilizing of the material properties of the LCF magnet. In order to address the issues mentioned above, the design methodologies of the VFM are studied in this paper. 3. Design methodology of the boundary of the PM flux variation range: Conventionally, in order to obtain wider speed range, the minimum PM flux is designed to be low enough. However, during the deeply studying of the relationship between the torque-speed curves and PM flux variation ratio, the curves of several flux variation ratio is always lower than other ratios, as shown in Fig. 1 (a).The result shows that it is unnecessary to pursuit wider flux variation range. In order to investigate the inner relationship between the flux variation ratio and speed-torque curves and find the boundary of the PM flux variation range, the machine performance is comprehensively analyzed considering the PM flux linkage, machine inductance, saliency ratio, bus voltage and current limit. The operation equations of the non-salient-pole VFM with id=0 control method is deduced, and then the PM flux variation boundary is obtained. For the non-salient-pole VFM, if the PM flux linkage after saturation magnetization is larger than the product of the d-axis inductance and the current limit, all machine always possesses speed extension capability by demagnetization process. The comparison of the torque-speed areas of the VFM with and without adopting the proposed methodology is shown in Fig 1 (c). The torque-speed curves after adopting the proposed in Fig 1 (c) is composed of many PM variation ratios. It can be seen form Fig 1 that machine 1 can obtain extra speed region after adopting the proposed methodology. The then boundaries of other types of machines and control methods are investigated. Due to the complexity of the transcendental equation, the per unit system is used. For the other machines, we can conclude that the minimum PM flux should be larger than the product of the d-axis inductance and the current limit. 4. Design methodology of the Optimum PM hysteresis loop: By comparing the hysteresis loops of the AlNiCo, SmCo and Ferrite, the hysteresis loops are quite different from each other, and it is necessary to find the suitable loop. An ideal determination model of hysteresis loop is established considering the remanent flux density, permeability of the recoil line, knee point and coercive force of the LCF magnet. The overall performance of the VFM are also considered, including maximum torque, re/demagnetization difficulty and anti-passive demagnetization ability, and the ideal hysteresis loop can be obtained. By connecting the LCF and the high-coercive force magnet in series and adjusting the ratio of the two magnet, we can customize the hysteresis loop. Based on the proposed model and the custom method of the hysteresis loop, a VFM with optimum PM hysteresis loop is designed. The simulation result shows that the PM torque of the VFM can be increased. By using the proposed methodologies, the material properties of the LCF magnet can be fully utilized.

**References:**

[1] V. Ostovic, IEEE Ind. Appl. Mag. , Vol. 9, p. 52 (2003) [2] M. Ge, J. Li and R. Qu, IEEE Trans. on Appl. Sup. Vol.28(3), p. 1-5 (2018) [3] H. Yang, Z. Q. Zhu and H. Lin, IEEE Trans. on Mag. Vol.53(5), p. 1-4 (2017) [4] A. Athavale, K. Sasaki, and R. D. Lorenz, IEEE Trans. on Ind. Appl. Vol.53, p.4318-4326 (2017) [5] Z. Q. Zhu, H. Hua, A. Pride, IEEE Trans. on Mag. Vol.53(11), p. 1-4 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/12801efde0326c8f2103714289521f41.jpg)
Comparison of the torque-speed areas of the VFM with and without adopting the proposed methodology

 Design Methodologies for Variable-Flux Machines for Fully Utilizing the Material Properties of the Magnet

Recently, new energy electrical vehicles have a great development. To achieve longer driving range and higher acceleration performance at defined battery capacity and driving conditions, there is a demand of high efficiency and high torque-speed characteristics for electrical drive machines [1-2]. One of solutions is to use rectangular conductors, e.g. hair-pin winding. It can enhance the slot filling ratio to simultaneously decrease resistance and increase heat transfer ability. Furthermore, the tooth can be kept enough width and benefits for peak performance. The peak performance in new energy electrical vehicles generally require short duration (10-60 seconds) at each speed within an allowable temperature rise (Depend on the insulation level of winding and starting temperature). However, due to the strong skin effect, the current distribution in conductors become more and more uneven with speed rising. This will bring overheat risks at high speed because the temperature rising rate in short duration is closely related to the copper loss density. In this paper, a new peak torque-speed characteristics estimation method for these machines is proposed. Not only supplied maximal voltage and current limitation are considered, but also the skin effect of conductors and transient thermal issues are investigated. The copper loss density in the last conductor which has severest skin effect can be theoretically kept constant from some speed. Firstly, the supplied maximum voltage (Um) and current (Im) are defined according to the capability of battery and power electronic unit (PEU). The electromagnetic torque (Te), d-axis voltage (Ud), q-axis voltage (Uq) and terminal voltage (Us) are calculated under specified lead angle and current intervals. By scanning all points and based on MTPA and MTPV, the conventional peak torque-speed curve is acquired. Secondly, to apply the temperature rising limitation, an analytical equation on basis of the conductor size, position and frequency is used and the AC resistance of active parts of conductors is calculated [3]. rN/rdc=φ(ξ)+N(N-1)ψ(ξ) rN represents the AC resistance at some speed due to the skin effect and rdc represents the DC resistance. Both are only related to the conductors in stator lamination core. The functions φ(ξ) and ψ(ξ) are related to the frequency and conductor size because ξ is expressed by the ratio of conductor height and skin depth. To keep the highest copper loss density constant with speed rising, the current limitation Im shall be decreased with speed rising according to below question. Im=Ib/√(φ(ξ)+N(N-1)ψ(ξ)) where Ib is the current limitation at the base speed nb. At this base speed, the copper loss density reaches the maximum allowable value. It can be defined through thermal simulation or measurement. N represents the ID of conductors in stator slot which starts counting from slot bottom. φ(ξ)=ξ(sh(2ξ)+sin(2ξ))/(ch(2ξ)-cos(2ξ)) ψ(ξ)=2ξ(sh(ξ)-sin(ξ))/(ch(ξ)+cos(ξ)) In the end, the maximum torque at each speed with similar temperature rising level in short duration will be found out and improved peak torque and power curves are finally outputted. A typical PMSM with 8 poles and 48 slots are investigated. Figure 1 and 2 show the comparison results between the conventional and proposed methods. Based on CFD simulation or measurements, the maximum copper loss density can be defined under specified S2 work condition. The special prototype with 20 thermal couples in the stator is built. The simulated torque-speed curve and measured hotspots are compared. It verifies the good effectiveness of the proposed method.

**References:**

[1] Z.Q.Zhu and D. Howe, Proceedings of the IEEE, Vol:95, 2007. [2] L. Sepulchre, M. Fadel, IEEE Transactions on Industry Application, p6081-6089, Vol:54, 2018. [3] D. Lin and P. Zhou, ICEMS, p3810-3814. Nov. 2008. [4] J. Brauer, IEEE Transactions on Magnetics, Vol: 18, Mar 1982

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/06c8a22958201169c3cffedcfe1bea96.jpg)
Comparison of peak torque and power performance between conventional and proposed methods

![](https://assets.underline.io/uploads/markdown_image/1/image/e3d42ed2af385d786bd3ed8faff91a1e.jpg)
Comparison of copper loss densities in the last conductor of stator slot between conventional (dash line) and proposed (solid line) methods

 Torque-Speed Characteristics Evaluation for Permanent Magnet Synchronous Motors with Rectangular Conductors

Most mathematical torque models for the permanent magnet synchronous machines (PMSMs) are established based on neglecting the core reluctance. In order to analyze the torque of high power density PMSMs more effectively in the saturated state, this paper has considered the core reluctance in the torque analysis and a novel torque model is proposed to adapt magnetic saturation condition. It is demonstrated by simulation and experiment that the proposed torque model is closer to the actual torque. Index TermsTorque, permanent magnet synchronous machines (PMSMs), core reluctance, high power density. I. Introduction Various torque analysis studies have been presented for permanent magnet synchronous machines (PMSMs). For instance, when the machine is gradually saturated, it is considered with the variation of dq-axis self-inductances depending on operating conditions [1] and the cross-magnetization phenomenon in the electrical machine has been subjected to detailed scrutiny [2]. In order to deal with saturation and cross-saturation, an extension of the d-q model is proposed in [3]. However, those studies have not analyzed the effect of core reluctance on magnet torque. With the saturation level in PMSMs is getting severer, this will cause the magnetic conductivity of the core to decrease rapidly, in this case, the core reluctance cannot be ignored. Although some literatures have analyzed the influence of core reluctance on the magnetic circuit, there is no specific analysis of the influence on magnet torque [4]. This paper has considered the core reluctance on the magnetic circuit and analyzed the influence of the core magnetic motive force (mmf) generated by the core reluctance on the magnet torque, then a novel magnet torque model is proposed to adapt magnetic saturation condition. Finally, the validity of the proposed torque model is verified by experiment and simulation. II. Analysis of Magnet Torque A. Neglecting the Core Reluctance In the conventional analysis of magnet torque, core reluctance can often be made much smaller than that of the air gap, in this case, the reluctance of the core can be neglected, the dominant reluctance is that of the air gap. Therefore, the stator mmf Fs is equal to the air gap mmf Fsg provided by the stator and the rotor mmf Fr is equal to the air gap mmf Frg provided by the rotor. It can be known from the literature [5], the general expression for the magnet torque for the multi-pole non-salient-pole machines could be expressed as Te=-p(μ0πDl/2g)FsFrsinδsr (1) Where μ0 is the permeability of free space, p is the number of pole-pairs and g is the length of the air gap. D is the average diameter of the air gap; l is the axial length of the air gap and δsr is the angle between the mmf of the stator and the rotor. B. Considering the Core Reluctance When the machine is in the saturated state, this will cause the magnetic conductivity of the core to decrease rapidly, the core reluctance should be considered. In this case, the mmf includes the air gap mmf and the core mmf, the expression (1) could be rewritten as Te′=-p(μ0πDl/2g)(Fs-Fst)(Fr-Frt)sinδsr (2) Then, through a series of simplification, (2) could be expressed as Te′=Te(Fgd/(Fgd+Ftd))2 (3) Where Fg is the resultant air gap mmf and Ft is the resultant core mmf. Fgd and Ftd are the d-axis components of the Fg and Ft respectively. Further detailed derivation formula and calculation method will be reported in the full paper. III. Simulation and Experiment In order to verify the analysis, a 350kW high power density interior PMSM is studied as an example. The conventional id=0 control strategy is applied to eliminate the influence of reluctance torque. The air gap magnetic field intensity Hgd and the magnetic field intensity of stator teeth Htd in the d-axis direction are obtained by finite element software. The magnetic field intensity of the machine is illustrated in Fig. 1. Because most of the core mmf is in the stator teeth, the yoke mmf is ignored. Fgd=Hgd*g, Ftd=Htd*lt and lt is the calculated length of the magnetic circuit of the stator teeth. Then a 350kW high power density interior PMSM has been prototyped and tested for validation. As shown in Fig. 2, through comparison, the magnet torque Te obtained by conventional calculation has large error. The magnet torque Te` obtained by the modified torque model is very close to the actual torque and simulation torque, which verifies the validity of the torque analysis proposed in this paper.

**References:**

 [1] G. H. Kang, J. P. Hong, G. T. Kim, and J. W. Park, “Improved parameter modeling of interior permanent magnet synchronous motor based on finite element analysis,” IEEE Trans. Mag., vol. 36, pp. 1867–1870, July 2000. [2] E. Levi and V. A. Levi, “Impact of dynamic cross-saturation on accuracy of saturated synchronous machine models,” IEEE Trans. Energy Conversion, vol. 15, pp. 224–230, June 2000. [3] Stumberger, B.; Stumberger, G.; Dolinar, D.; Hamler, A.; Trlep, M.; “Evaluation of saturation and cross-magnetization effects in interior permanent-magnet synchronous motor,” IEEE Transactions on Industry Applications, vol.39, no.5, pp. 1264- 1271, Sept.-Oct. 2003 [4] Gabriel Forstner, Andreas Kugi, Wolfgang Kemmetmüller, “A Magnetic Equivalent Circuit Based Modeling Framework for Electric Motors Applied to a PMSM With Winding Short Circuit,” IEEE Transactions on Power Electronics, vol. 35, no. 11, pp. 12285–12295, Nov. 2020. [5] S. D. Umans, Fitzgeral & Kingslye’s Electric Machinery. New York, NY, USA: McGraw-Hill, Jan. 2013.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f74ac5e1ba446481d7b22ba84c9cfaa7.jpg)
Fig. 1. The machine model and magnetic field intensity distribution.

![](https://assets.underline.io/uploads/markdown_image/1/image/406d776507913d6aec801ff83098cd76.jpg)
Fig. 2. Comparison of the torque.

 Torque Analysis of High Power Density Permanent Magnet Synchronous Machines by Considering Core Reluctance

This paper proposes a rotor design method suitable for double-layer interior permanent magnet synchronous motor (BIPMSM), which can reduce electromagnetic torque ripple and at the same time reduce the electromagnetic noise of the motor. In previous studies, the inverse cosine function (ICF) has been used for torque ripple reduction by making the air gap flux density distribution sinusoidal under a no-load condition. However, ICF can only be used in a single-layer interior rotor structure. Therefore, this article proposes a piecewise inverse cosine function (PICF) based on ICF, which can be applied to BIPMSM. To verify the validity of the proposed design method, the characteristics of 8-pole, 36-slot motors that have different rotor shapes are analyzed using finite element analysis. 1.INTRODUCTION there are a number of advantages of shaping the salient pole shoes of interior permanent magnet (IPM) synchronous machines to produce a sinusoidal air-gap flux density distribution [1]. Firstly, the phase electromotive force (EMF) will be more sinusoidal which will reduce the electromagnetic torque ripple from the machine when using sinusoidal phase currents. Secondly, cogging torque will also be reduced. Thirdly, the magnitude of the radial force in the air-gap is proportional to the square of the radial component of the air-gap flux density. Therefore, the radial force space distribution in the air-gap will contain much reduced number of space harmonics which will lower the probability of exciting stator core resonances. All of these aspects will have a positive effect on the noise and vibration behavior of the machine. In [1], the application method of inverse cosine function in single-layer interior permanent magnet synchronous motor is demonstrated in detail. After optimizing the rotor structure through the inverse cosine function, a more sinusoidal air gap flux density can be obtained under no-load conditions. In [2], the author, through finite element analysis, found that ICF can reduce the torque ripple of the motor, but at the same time it can also cause the torque to drop. In this article, PICF makes the air gap magnetic density of BIPMSM more sinusoidal, thereby reducing torque ripple and electromagnetic noise, and improving the performance of the motor. 2.PRINCIPLES OF BICF The traditional ICF can be expressed by the following formula: Bmaxcosθ=μ0Fg/Ig(θ). where Bmax is the maximum value of the air gap flux density，Ig(θ) is the air gap length using，μ0 is the permeability of vacuum and Fg is the air gap magnetic potential by PM. In the traditional ICF, the magnetic potential generated by the permanent magnet can be regarded as a fixed value, but the magnetic potential generated by the permanent magnet in BIPMSM is not a fixed value, as shown in Fig.1. Therefore, it is necessary to calculate the magnetic potential in sections according to θ1 and θ2 , so that the air gap flux density generated by each section meets the same sinusoidal distribution. 3.FINITE ELEMENT SIMULATION VERIFICATION In order to verify that based on PICF, the rotor structure designed in this paper can reduce the torque ripple and electromagnetic noise of the motor, and the finite element simulation of the designed motor rotor is carried out. It can be seen from Fig.2(a) that after the use of PICF to improve the motor rotor structure, the electromagnetic torque ripple is well suppressed, but the torque amplitude is slightly reduced, which is consistent with the conclusion in [2]. Fig.2(b) shows the two-dimensional Fourier decomposition results of the radial force before and after the optimization. PICF greatly weakens the amplitude of most electromagnetic force components, which will effectively reduce the electromagnetic noise of the motor under different operating conditions. 4.DISCUSSION Through PICF, the torque ripple of BIPMSM can be significantly reduced and the motor control accuracy can be improved. As the air gap distance increases, the electromagnetic torque of the motor will inevitably be reduced. However, PICF can greatly reduce the electromagnetic noise of the motor, and it can effectively attenuate the noise of the motor at different operating speeds.

**References:**

[1] S. A. Evans, "Salient pole shoe shapes of interior permanent magnet synchronous machines," The XIX International Conference on Electrical Machines - ICEM 2010, Rome, 2010, pp. 1-6. [2] K. Wang, Z. Q. Zhu, G. Ombach and W. Chlebosz, "Optimal rotor shape with third harmonic for maximizing torque and minimizing torque ripple in IPM motors," 2012 XXth International Conference on Electrical Machines, Marseille, 2012, pp. 397-403.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/451f4fe7202c192a822ac896e7f41f42.jpg)
Fig.1

![](https://assets.underline.io/uploads/markdown_image/1/image/4ae432a93c1cfb5d1aa4bf0921920b57.jpg)
Fig.2

 Optimized Rotor Shape for Reducing Torque Ripple and Electromagnetic Noise

Comparing with the radial flux permanent magnet (RFPM) motor, axial flux permanent magnet (AFPM) motor has higher power density, higher torque density. Especially, if the AFPM motor is designed to work at a high speed, its size will be further reduced, leading to a more compact size and a significant volume saving. In addition, the AFPM motor has a superior cooling structure. The above features will boost the application of the high speed AFPM in many potential fields, such as flywheel energy storage system, man-portable power platforms, turbo-compressors, and machining spindles, and so forth [1-3]. A 3,2000r/min, 200W AFPM generator with a slotless stator core and toroidal coils was reported in literature [4]. Literature [5] designed a single-sided AFPM machine with 100W shaft output power at 50,000r/min, and stator core is slotless and made of powder composite material. Literature [6] developed a 15kW, 25,000 r/min AFPM motor, the stator core is slotted and used amorphous alloy. A 30kW, 16,000 r/min AFPM motor has been developed for the flywheel in which a slotted stator core and distributed winding are applied [7]. A 30kW, 30,000 r/min AFPM generator having 2 stators and 3 rotors was propounded [8]. It can be found that, in low power field such as hundreds of watts, high speed AFPM machines generally apply the slotless stator. Because the stator windings occupy the air gap, which leads to a wider air gap, then the air gap flux density is low, whereupon, the power can not be designed very large. However, for kilowatt power level field, a slotted stator is necessary. Moreover, the power can be further increased by the combination of multi-layer stator and rotor. It is well known that the slotless stator core also can eliminate the cogging torque. However, slotted stator will increase ripple torque. Relative to the AFPM motor with slotless stator, how much the motor power and the torque ripple can increase for the one with the slotted stator. It is an interesting, challenging question. However, rare researches about this are reported. Therefore, first, the paper will solve the electromagnetic field of the AFPM motor analytically. Then, electromagnetic torque will be obtained by Maxwell stress tensor method (MSTM). Thirdly, an example will be carried out for the cases in which both slotless and slotted stators are considered. Finally, results of torque comparison will be given and discussed. The analytical solution is verified by 3D finite element method (FEM) and experiment data.

**References:**

[1]S. Neethu, S. P. Nikam and S. Pal, et al. IEEE T Ind Electron.,vol. 67, no. 7, pp. 5269-5277 (2020) [2]M. G. Kesgin, P Han and N. Taran, et al. in Proc. Conf. (ICRERA), pp. 1026-1031 (2019). [3]WJ Cheng, ZK Deng and L Xiao, et al. Journal of Electrical and Computer Engineering, vol. 2019, pp. 1469637 (2019) [4]S. Kumar, T. A. Lipo and B. I. Kwon, et al. IEEE Trans. Magn.,vol. 52, no. 7, pp. 8205004 (2016) [5]L Zheng, TX Wu, K. B. Sundaram, et al. IEEE International Conference on Electric Machines and Drives (2005) [6]WM Tong, YP Ci. Electric Machines and Control, vol. 20, no. 6, pp. 68-76 (2016) [7]F. Sahin, A. M. Tuckey, and A. Vandenput. IEEE Industry Applications Conference (2001) [8]M. Sadeghierad, H. Lesani, and H. Monsef, et al. Journal of Applied Sciences, vol. 9, no. 10, pp. 1915-1921 (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fe375fb5c114165cee876cb4fa8e68a2.jpg)
Models of AFPM motor with slotless/slotted stator

![](https://assets.underline.io/uploads/markdown_image/1/image/17da96cf6decd8e991766ea2e804eb58.jpg)
Comparsion of results from analytical model and FE model

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