France



This paper presents an optimization method considering both electromagnetic and thermal performance, and a novel strategy to construct an approximate model considering multi-fidelity finite element models (FEMs) is proposed. The electromagnetic and thermal FEMs are established in ANSYS/Maxwell and Fluent, respectively. Finally, both simulation and experimental results are given and discussed. Compared with the initial design, the optimal solution exhibits lower housing temperature, higher torque, lower torque ripple and less loss.&lt;br/&gt;1. Introduction&lt;br/&gt;Tradition optimization mainly considers electromagnetic performance and the approximate model is constructed only with the 2D FEMs [1]. In the optimization, the multiphysics performance is considered, and the 3D FEMs are predicted by 2D FEMs and the errors between 2D and 3D FEMs. The temperature of the housing, output torque, torque ripple and total loss are taken into consideration. The objective function and constraints can be defined as&lt;br/&gt;Function: min &lt;i&gt;f&lt;sub&gt;1&lt;/sub&gt;(TEM&lt;sub&gt;housing&lt;/sub&gt;)&lt;/i&gt;, &lt;i&gt;f&lt;sub&gt;2&lt;/sub&gt;(-T&lt;sub&gt;out&lt;/sub&gt;)&lt;/i&gt;, &lt;i&gt;f&lt;sub&gt;3&lt;/sub&gt;(T&lt;sub&gt;ripple&lt;/sub&gt;)&lt;/i&gt;, &lt;i&gt;f&lt;sub&gt;4&lt;/sub&gt;(P&lt;sub&gt;loss&lt;/sub&gt;) &lt;/i&gt;&lt;br/&gt;Constraints:1.10-&lt;i&gt;T&lt;sub&gt;out&lt;/sub&gt;&lt;/i&gt;≤0, &lt;i&gt;J&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt;-5≤0 (1)&lt;br/&gt;where &lt;i&gt;TEM&lt;sub&gt;hoursing&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;T&lt;sub&gt;out&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;T&lt;sub&gt;ripple&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;P&lt;sub&gt;loss&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;J&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt; are housing temperature, output torque, torque ripple, loss, and allowable current density.&lt;br/&gt;2. Electromagnetic and thermal FEA&lt;br/&gt;The 2D and 3D electromagnetic FEMs are established in Maxwell, and the 2D and 3D thermal FEMs are established in Fluent. The 2D housing thermal model in Fluent for the initial design is shown in Fig.1.&lt;br/&gt;3. Two-step multi-fidelity strategy&lt;br/&gt;The flowchart of this optimization process is presented in Fig.1. In the first step, the initial sample points are generated by the design of experiment (DoE) and the errors between 2D and 3D FEMs are utilized to create response surface (RES). In the second step, additional sample points are generated and radial basis function (RBF) is constructed by 2D models. Then, the result of 3D FEM is predicted by the errors between 2D and 3D FEMs and the results of 2D FEMs. The &lt;i&gt;β&lt;sub&gt;j&lt;/sub&gt;&lt;sup&gt;RES&lt;/sup&gt;&lt;/i&gt;(x) and &lt;i&gt;δ&lt;sub&gt;j&lt;/sub&gt;&lt;sup&gt;RES&lt;/sup&gt;&lt;/i&gt; is the ratio and variance between 2D and 3D FEMs&lt;br/&gt;4. Results&lt;br/&gt;The proposed method can reduce the computational burden and improve the performance of the motor. The number of 3D and 2D FEMs are 96 and 512, respectively. The computational time duration is about 149h, which is much shorter than only use 3D FEMs. The accuracy of the approximate model in the proposed method is 1.70% and 1.06% for the 3D electromagnetic and thermal FEA, which is much more accurate than the approximate model only constructed by 2D FEMs. For the initial design, the &lt;i&gt;TEM&lt;sub&gt;housing&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;T&lt;sub&gt;out&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;T&lt;sub&gt;ripple&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;P&lt;sub&gt;loss&lt;/sub&gt;&lt;/i&gt; is 371.53°C, 0.96 Nm，0.31 and 227.18W, respectively. After the optimization, the &lt;i&gt;TEM&lt;sub&gt;housing&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;T&lt;sub&gt;out&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;T&lt;sub&gt;ripple&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;P&lt;sub&gt;loss&lt;/sub&gt;&lt;/i&gt; is 337.51°C, 1.18 Nm, 0.23 and 207.83 W.&lt;br/&gt;5. Conclusion&lt;br/&gt;In this paper, a multiphysics optimization method, which can improve the performance of the switched reluctance motor, is proposed. At the same time, the two-step multi-fidelity strategy can greatly improve the accuracy of the approximate model and reduce the computational cost.

**References:**

[1] G. Y. Sizov, P. Zhang, D. M. Ionel, N. A. O. Demerdash, and M. Rosu, “Automated Multi-Objective Design Optimization of PM AC Machines Using Computationally Efficient FEA and Differential Evolution,” &lt;i&gt;IEEE Trans. Ind. Appl., &lt;/i&gt;vol. 49, no. 5, pp. 2086-2096, 2013.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2cecec84f943298f55bf45248d022757.jpg)
Fig. 1. Flowchart of this optimization.

![](https://assets.underline.io/uploads/markdown_image/1/image/8bdd2e77ffbfec8d72dc3e18cfc53cf4.jpg)
Fig. 2. 2D housing thermal model in fluent for the initial design.

INTERMAG 2021

 Multiphysics and Two-step Multi-fidelity Optimization for a Switched Reluctance Motor

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This paper presents an optimization method considering both electromagnetic and thermal performance, and a novel strategy to construct an approximate model considering multi-fidelity finite element models (FEMs) is proposed. The electromagnetic and thermal FEMs are established in ANSYS/Maxwell and Fluent, respectively. Finally, both simulation and experimental results are given and discussed. Compared with the initial design, the optimal solution exhibits lower housing temperature, higher torque, lower torque ripple and less loss. 1. Introduction Tradition optimization mainly considers electromagnetic performance and the approximate model is constructed only with the 2D FEMs [1]. In the optimization, the multiphysics performance is considered, and the 3D FEMs are predicted by 2D FEMs and the errors between 2D and 3D FEMs. The temperature of the housing, output torque, torque ripple and total loss are taken into consideration. The objective function and constraints can be defined as Function: min f1(TEMhousing), f2(-Tout), f3(Tripple), f4(Ploss) Constraints:1.10-Tout≤0, Jc-5≤0 (1) where TEMhoursing, Tout, Tripple, Ploss and Jc are housing temperature, output torque, torque ripple, loss, and allowable current density. 2. Electromagnetic and thermal FEA The 2D and 3D electromagnetic FEMs are established in Maxwell, and the 2D and 3D thermal FEMs are established in Fluent. The 2D housing thermal model in Fluent for the initial design is shown in Fig.1. 3. Two-step multi-fidelity strategy The flowchart of this optimization process is presented in Fig.1. In the first step, the initial sample points are generated by the design of experiment (DoE) and the errors between 2D and 3D FEMs are utilized to create response surface (RES). In the second step, additional sample points are generated and radial basis function (RBF) is constructed by 2D models. Then, the result of 3D FEM is predicted by the errors between 2D and 3D FEMs and the results of 2D FEMs. The βjRES(x) and δjRES is the ratio and variance between 2D and 3D FEMs 4. Results The proposed method can reduce the computational burden and improve the performance of the motor. The number of 3D and 2D FEMs are 96 and 512, respectively. The computational time duration is about 149h, which is much shorter than only use 3D FEMs. The accuracy of the approximate model in the proposed method is 1.70% and 1.06% for the 3D electromagnetic and thermal FEA, which is much more accurate than the approximate model only constructed by 2D FEMs. For the initial design, the TEMhousing, Tout, Tripple and Ploss is 371.53°C, 0.96 Nm，0.31 and 227.18W, respectively. After the optimization, the TEMhousing, Tout, Tripple and Ploss is 337.51°C, 1.18 Nm, 0.23 and 207.83 W. 5. Conclusion In this paper, a multiphysics optimization method, which can improve the performance of the switched reluctance motor, is proposed. At the same time, the two-step multi-fidelity strategy can greatly improve the accuracy of the approximate model and reduce the computational cost.

**References:**

[1] G. Y. Sizov, P. Zhang, D. M. Ionel, N. A. O. Demerdash, and M. Rosu, “Automated Multi-Objective Design Optimization of PM AC Machines Using Computationally Efficient FEA and Differential Evolution,” IEEE Trans. Ind. Appl., vol. 49, no. 5, pp. 2086-2096, 2013.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2cecec84f943298f55bf45248d022757.jpg)
Fig. 1. Flowchart of this optimization.

![](https://assets.underline.io/uploads/markdown_image/1/image/8bdd2e77ffbfec8d72dc3e18cfc53cf4.jpg)
Fig. 2. 2D housing thermal model in fluent for the initial design.

poster

I. Introduction Direct drive wave energy conversion (DDWEC) device using permanent magnet linear generator (PMLG) eliminates the inefficient transmission device and achieves simpler mechanical structure. However, due to the direct connection between buoy and translator, the low-speed linear reciprocating wave motion will be directly transmitted to the translator. So PMLG needs to adopt a low-speed design [1]. It is necessary to increase the number of pole pairs of the generator or use power electronic devices to increase the output voltage and power density. But this will increase the loss and reduce the efficiency of the whole system. The linear-rotating axial flux permanent magnet generator (AFPMG) is proposed to improve the output voltage and power density of the DDWEC. By employing the magnet screw (MS) and AFPMG, it combines the merits of MS and AFPMG and realizes the soft connection between the buoy and generator rotor. The nut and screw of MS are directly connected to the buoy and generator rotor, respectively. When approximately 0.5m/s reciprocating wave motion comes, the movement can be accelerated by MS and magnetic field modulation and finally the speed of the rotor will reach 1200 rpm/min, which can improve the output voltage and power density consequently. While this structure brings advantages, at the same time, due to the use of a large number of rare-earth PMs, it will increase power generation costs and reduce practical competitiveness. Therefore, a hybrid excitation axial flux permanent magnet generator (HE-AFPMG) is proposed to reduce the amount of PMs and become a candidate for DDWEC. Not only that, because the wave conditions (typically 3-20s) are constantly changing, the corresponding wave excitation forces of the same buoy vary widely. By using hybrid excitation, the excitation current can easily adjusted to regulate the magnetic field of the air gap [2], which make generator suitable for different working conditions in wave energy conversion. II. Machine Configuration and Operation Principle In the proposed topology, as shown in Fig. 1, the armature winding and field winding are placed in upper stator and lower stator of AFPMG, respectively. PMs are placed at the slots of the upper stator and work as parallel excitation source. There is no risk of irreversible demagnetization in PMs with this configuration, meanwhile, it can reduce flux linkage and back electromotive force (EMF) harmonics. The operation principle of AFPMG based on modulation effect is similar to a magnetic gear and a magnetically geared machine when the rotor is consists of modulation teeth. The magnetic field will be accelerated due to the magnetic gear effect, when the excitation magnetic field passes through the air gap and modulation teeth. Eventually, potentials are induced in the armature windings. The number of pole pairs and speed of armature magnetic field are expressed as follow: paw = | pfw ± pmt | Ωaw = ( pfwΩfw ± pmtΩmt ) / ( pfw ± pmt ) where paw, Ωaw, pfw, Ωfw are the number of pole pairs and rotational speed of magnetic field in armature winding and field winding, respectively. pmt and Ωmt are the number and rotational speed of modulation teeth, respectively. In proposed AFPMG, the upper stator pole number Nus = 12, hence the number of pole pairs of magnetic field in armature winding paw = 2 or paw = 1 when the number of modulation teeth satisfies pmt = Nus ±2 or pmt = Nus ±1. Fig.1 III. Results Fig.2 The output power versus excitation current in proposed HE-AFPMG with armature winding having different load current is shown in Fig.2. IV. Conclusion The application of hybrid excitation in AFPMG used in DDWEC can eliminate risk of irreversible demagnetization in PMs and reduce flux linkage and back electromotive force harmonics. Meanwhile, it can adjust the air gap magnetic field to suit different sea conditions.

**References:**

[1] W. Li, K. T. Chau and J. Z. Jiang, "Application of Linear Magnetic Gears for Pseudo-Direct-Drive Oceanic Wave Energy Harvesting," in IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 2624-2627, Oct. 2011. [2] C. Ye, Y. Du, J. Yang, X. Liang, F. Xiong and W. Xu, "Research of an Axial Flux Stator Partition Hybrid Excitation Brushless Synchronous Generator," in IEEE Transactions on Magnetics, vol. 54, no. 11, pp. 1-4, Nov. 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/951d474bb6205f855448b547badaaa7c.jpg)
Fig. 1

![](https://assets.underline.io/uploads/markdown_image/1/image/53fb22268e717a1e38e511372a0a531b.jpg)
Fig. 2

 A Hybrid Excitation Axial Flux Permanent Magnet Generator for Direct Drive Wave Energy Conversion

Due to the widespread concern of the greenhouse effect, people's requirements for energy saving and emission reduction of drive systems are becoming higher. The electrification of drive systems seems to be an irresistible trend. As the core of electric drive system, electric motor has been widely mentioned. The Permanent Magnet Synchronous Machine (PMSM) proved to be better in energy conversion which efficiency is higher than conventional Induction Machines [1-2]. In the application field of commercial logistics vehicles, the trend of electrification is increasing and the space occupied by the electric drive system is limited. As a result, a higher demand for density is required. Conventional electric motors applied in this platform are mainly Radial Flux Permanent Machines (RFPM). In particular, the application of the logistics EV traction motor requires low maximum speed but high output torque. The conventional design developed on this platform is a PMSM using traditional round copper wire as winding part and the rotor adopts “delta” shape topology. The “flux barrier” structure was added to increase the reluctance torque ratio, which was aimed to increase torque density of the whole system. However, due to the further reduction in already limited space, it will be difficult to meet the requirements using RFPM. Since the topological structure of the disc motor was proposed in last 70s [3-4], many researches have been done, especially on AFPM’s topological structures. Among them, some classic structures are: the TORUS (double-rotor-one-stator) structure, whose stator part is composed of copper winding and iron core, and the rotor part is composed of the surface mounted PMs and back iron; the AFIR (double-stator-one-rotor) structure, whose stator part is the same, but rotor part is composed only of the fan-shaped PMs [5-6]. As there is no back iron structure in the rotor part for AFIR, its rotational inertia is quite low and resulting the starting torque is low [7-8]. This advantage attracts us because the size requirements are more stringent for our platform. Based on this consideration, the optimal structure of the traction motor is selected as the AFIR structure with two stators and one rotor. In AFPM design, the rotor Permanent Magnets (PM) are directly in contact with the air gap, and the complex magnetic field has rich harmonic content, resulting in a higher proportion of eddy current losses in rotor PMs. Which can cause higher temperature rise in the rotor of an AFIR structure AFPM. Reducing PM eddy current loss is significantly important to the PM topology design, rotor temperature rise and overall performance. The AFPM in this paper adopts an AFIR 24s/20p design. The rotor PMs are segmented with identical radial distance, in order to reduce the length of the eddy current path in each PM and reduce the eddy-current loss, thereby reducing the risk of PM demagnetization caused by high temperature. In this paper the main body is divided in three parts, in part II, the design problems will be presented, which mainly includes: 1) Stator and rotor design, 2) The influence of the rotor support material on the motor, 3) The magnetic field measurement on the surface of the segmented magnet, 4) difference analysis between simulation and test. Part III will mainly introduce the problems encountered and the corresponding solutions during the manufacturing process, which includes: 1) assembly problem due to strong magnetic force, 2) air-gap width balance before and after test and in part IV we conclude. This application research is aimed to have a positive guiding significance for the AFPM production. We hope that our description of prototype developing process and the solutions we took to deal with the manufacturing problems can have a positive influence for future research.

**References:**

 [1] Edward, Iman, Said Wahsh, and M. A. Badr. "Analysis of PMSM drives for electric vehicles." Proceedings of the 37th SICE Annual Conference. International Session Papers. IEEE, 1998. [2] Situ, Lixin. "Electric vehicle development: the past, present & future." 2009 3rd International Conference on Power Electronics Systems and Applications (PESA). IEEE, 2009. [3] P. Campbell, "Principles of a permanent-magnet axial-field d.c. machine," in Proceedings of the Institution of Electrical Engineers, vol. 121, no. 12, pp. 1489-1494, December 1974. [4] P. Campbell, “The magnetic circuit of an axial-field DC electrical machine”, IEEE Transactions on Magnetics, Vol.Mag11, No.5, Sept. 1975, pp.1541-1543. [5] E. Spooner and B. J. Chalmers, “TORUS, a slotless, toroidal stator, permanent magnet generator”, Proc. IEE, Part-B, Vol.139, No. 6, Nov. 1992, pp. 497-506. [6] F. Caricchi, F. Crescimbini and E. Santini, “Basic principles and design criteria of axial-flux PM machines having counterrotating rotors”, IEEE Transactions on Industry Applications, Vol.31, No. 5, Sept/Oct 1995, pp.1062-1068. [7] Aydin. M, Huang. S and Lipo, T.A. (2004). Axial flux permanent magnet disc machines: A review. Conf. Record of SPEEDAM. [8] Akatsu, K. and Wakui, S. , “A comparison between axial and radial flux PM motor by optimum design method from the required output NT characteristics”, in international journal for computation and mathematics in electrical and electronic engineering, Vol. 25 No. 2, pp. 496-509.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8d70807489b42e8db65cc0ef3398b370.jpg)
Impact of PM Segment Number on Rotor PM Eddy Current Loss

![](https://assets.underline.io/uploads/markdown_image/1/image/d5d466e7ccd06071dfca97e53692f578.jpg)
Rotor magnetic flux density distribution

 Axial-flux Permanent Magnet Machine Application Research with Strap-wire Technique and Difference Analysis of Rotor Eddy-current Loss between Simulation and Test

I. INTRODUCTION With the increasingly serious problems of energy shortage and environmental pollution, the development of electric vehicles has become the focus of the world. Electric motors and their drive systems are one of the largest electrical energy consumptions, consuming more than twice as much as lighting, the next largest end-use, accounting for about between 43% and 46% of all global electricity consumption [1]. Therefore, it is necessary to further improve the overall efficiency of electric motors, especially for New European Driving Cycle (NEDC). More and more scholars improve motor efficiency by changing motor materials [2-6]. Grain-Oriented electrical steel materials (GO materials) are mainly used in the core manufacturing of transformers, reactors and large generators. In recent years, GO materials are gradually introduced into motors. Compared with the non-oriented electrical steel materials (NO materials) commonly used in motors, the GO material has the advantages of lower core loss characteristic and higher saturation magnetic flux density. However, the GO material has different permeability and core loss in different directions, so it is difficult to design an axial-flux permanent magnet (AFPM) motor with yoke to take advantage of the GO material. The main flux of the AFPM motor with yokeless stator studied in this paper only passes through the stator in one direction, eliminating the disadvantages of AFPM motor with stator yoke. This paper discusses the application of GO materials in AFPM motors with yokeless stator, compares the basic characteristics of the GO material and NO material used in AFPM motor, analyses the difference between two axial-flux topologies in the use of materials and verifies through finite-element analysis (FEA). II. DESCRIPTION OF THE AFPM MACHINE AND GRAIN-ORIENTED ELECTRICAL STEEL SHEET The GO material has electromagnetic anisotropy: the electromagnetic properties in different directions are different, as is shown in Fig.1(a). In the easy magnetization direction of GO material, it can be seen from Fig.1(b-e) that it is easier to magnetize than NO material, with higher saturation point and lower core loss. However, in the direction of hard magnetization, the GO material is harder to magnetize and has higher core loss. So reasonable use of the easy magnetization direction can provide better torque output ability and less core loss for motors. The explosive view of the AFPM machine investigated in the paper with 48-slot /8-pole is shown in Fig.2, which belongs to the axial-flux topology with a single-stator double-rotor. Main parameters of the motor are shown in Tab. I. Due to the arrangement of the PMs, the main magnetic flux paths only pass through the stator in one direction, which can be set as easy magnetization direction, without passing through the stator yoke tangentially, as shown in Fig.3. III. FEA AND PERFORMANCE Due to AFPM machine’s particular 3-D configuration, 3-D FEA is carried out. Fig.4 shows the stator flux distributions and flux density under no load, showing that the main flux paths go through the easy magnetization direction. It should be noted that even if the GO material is easier to magnetize, the air-gap flux density and back-EMF are not greatly improved under no-load condition due to the large air-gap and PM reluctance. With the increase of armature current, the advantages of GO material are gradually manifested. The torque output capacity of the AFPM machine with GO material and NO material obtained by 3-D FEA is shown in Fig.5, reflecting that the motor with GO material has better torque output capacity than that of NO material. Taking Irms=530A as an example, the torque of GO material is about 15 N.m higher than that of NO material, increased by about 3%. Fig.6 shows the efficiency map of the motor with different materials. The GO material not only improves the torque, but also improves the efficiency. Tab. II compares torque, core loss and efficiency of motors with yokeless stator using different materials under typical working conditions. Similarly, this paper also tried the application of GO material in AFPM machine with stator yoke. As is shown in Fig.7, since a tangential magnetic circuit passes the stator yoke, it is hard to avoid the different magnetization direction when using the easy magnetization direction. Tab. III compares the torque and efficiency of the AFPM machine with yoke under several working conditions. With the stator using GO material, the torque output capacity is lower than that with NO material, and core loss is also increased. Hence, it is not recommended to use GO material in this AFPM topology. IV. CONCLUSION By introducing GO material to yokeless stator, an attempt is made in this paper to use its electromagnetic anisotropy to make the main magnetic flux paths of the motor passing through its easy magnetization direction, without crossing hard magnetization direction, so as to improve torque performance and reduce core loss as well as efficiency. Base on the 3-D FEA model of 48-slot /8-pole AFPM machine, the field distributions, flux density, torque output capacity and efficiency map have been compared between GO and NO material. Benefitting from GO material and yokeless structure, the torque output capacity of AFPM machine is increased by about 5%, the core loss is also reduced by 10%, and the efficiency is improved by 2%. Furthermore, the inapplicability of GO material in the AFPM with stator yoke is also discussed and verified in this paper.

**References:**

[1] P. Waide and C. U. Brunner, “Energy-efficiency policy opportunities for electric motor-driven systems,” International Energy Agency (IEA), 2011. [2] W. Geng, Z. Zhang and Q. Li, "High Torque Density Fractional-Slot Concentrated-Winding Axial-Flux Permanent-Magnet Machine With Modular SMC Stator," IEEE Transactions on Industry Applications, vol. 56, no. 4, pp. 3691-3699, July-Aug. 2020. [3] D. Kowal, P. Sergeant, L. Dupre and A. Van den Bossche, "Comparison of Nonoriented and Grain-Oriented Material in an Axial Flux Permanent-Magnet Machine," IEEE Transactions on Magnetics, vol. 46, no. 2, pp. 279-285, Feb. 2010. [4] J. Ma et al., "Optimal Design of an Axial-Flux Switched Reluctance Motor With Grain-Oriented Electrical Steel," IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5327-5337, Nov.-Dec. 2017. [5] Y. Tsuchiya and K. Akatsu, "A Study of the Switched Reluctance Motor using Grain-Oriented Electrical Steel Sheets," 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, MI, USA, 2020, pp. 3623-3628. [6] S. Javadi, M. Mirsalim and J. Sabzivand, "3-D FEM analysis of a novel structure for axial-flux homopolar generators using a grain-oriented silicon steel stator core," 2008 International Conference on Electrical Machines and Systems, Wuhan, 2008, pp. 3640-3643.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2e470724e420eb5e24f1d276f4bcb0de.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/9c74136a3b306c49ec4636f896a67e57.jpg)

 Electromagnetic Analysis and Efficiency Improvement of Axial-Flux Permanent Magnet Motor with Yokeless Stator by using Grain-oriented Silicon Steel Material

I. INTRODUCTION Due to the absence of neither permanent magnets (PMs) nor windings on the rotor, stator wound-field synchronous (SWFS) machines [1]-[5] were presented for potential applications to domestic appliances and more-electric aircraft, and renewable energy, etc. SWFS machines have the advantages of the eliminations of brushes and slip rings, low cost, fault tolerance, simple as well as a robust double salient structure similar to switched reluctance machines (SRMs) [6], which are suitable for critical-safety applications. Besides, the demerits of high torque ripple, acoustic noise, and vibration in SRM are alleviated with the SWFS machines which can be fed by a standard three-phase full-bridge inverter. Nevertheless, the existence of additional DC windings makes SWFS machines suffer from restricted torque density and redundant DC power source. Thus, the variable flux reluctance machines (VFRMs) [5] [7] with integrated DC bias and AC current excitations were developed by using an open-winding winding configuration to offer DC excitations. However, the inherently unipolar coil flux linkage in VFRMs still results in a relatively low torque density. Therefore, this paper attempts to propose a novel wound field switched flux (WFSF) machine with a zero-sequence field current excitation. An open-winding circuit is employed to generate a zero-sequence current to offer DC excitation. Moreover, the SF working principle will be employed to improve the torque capability compared to the VFRM. In this paper, the machine topology, operating principle, and design considerations will be described, respectively. Then the major electromagnetic performance will be analyzed and compared with the conventional WFSF counterpart, which confirms the superiority of the proposed design. II. MACHINE TOPOLOGIES AND OPERATING PRINCIPLE Figs. 1 (a) and (b) show the WFSF machines with conventional separate and integrated DC and AC excitations. It demonstrates that the two machines are with identical stator/rotor doubly salient structure and single-layer overlapping winding layout. The main difference lies in the winding functions of the two sets of windings in the two WFSF machines. In the conventional WFSF machine [2]-[4], one set of winding serves as continuous DC excitation while another works as the armature winding. On the other hand, two sets of windings are both injected with integrated AC plus DC bias currents in the WFSF machine with zero-sequence field current excitation. As a result, more copper area is available for the armature windings in the proposed WFSF machine with integrated “AC+DC” current excitations. The control circuit is illustrated in Fig. 1(c), in which the open-winding-based dual three-phase inverter with a single voltage source is utilized [7], and the output terminals of two inverters are connected to both ends of the stator windings. This method is the utilization of the constant zero-sequence current acting as the field current, while two three-phase currents are controlled by two inverters. The operating principle of the proposed WFSF machine is shown in Fig. 1(d). For each group armature windings, such as A1 and B2, when A1 is injected with continuous DC current, and the sinusoidal flux linkage will be induced in B2, and vice versa. As a result, when an AC sinusoidal current with a DC bias is applied to both two coils A1 and B2, the effective electromagnetic energy conversion will be achieved similar to those conventional WFSF counterparts [2]-[4]. III. ELECTROMAGNETIC PERFORMANCE AND COMPARISON Fig. 2(a) shows the open-circuit coil and phase flux linkage waveforms, it can be the DC biases in two individual coils are canceled, and a bipolar and sinusoidal phase flux linkage can be obtained. Besides, the open-circuit phase back-EMF waveforms at 400 r/min are shown in Fig. 2(b). It can be observed that the back-EMF is symmetric and sinusoidal in the WSFC machine with zero-sequence field excitation, while asymmetric non-sinusoidal for the conventional case. This is mainly attributed to the fact that the dual three-phase winding arrangement in the proposed machine allows the even-order harmonic cancellation within one phase. Besides, the steady torque and torque versus current characteristics of the two machines are compared as shown in Figs. (c) and (d), respectively. It should be noted that the winding turns of the two machines are designed as the same for a fair comparison. As a result, it demonstrates the WSFC machine with zero-sequence field excitation exhibits 68% higher magnitudes of steady torque, together with 30.4% lower torque ripple than the conventional case. Meanwhile, it demonstrates that the average torques of the proposed machine exceed that of the conventional counterpart regardless of the armature current excitations. Thus, better electromagnetic performance can be obtained with the proposed design with zero sequence field excitation. The detailed characteristics analysis, comparison results, and experimental verification will be presented in the full paper.

**References:**

[1] Z. Q. Zhu, Y. J. Zhou, J. T. Chen and J. E. Green, “Investigation of nonoverlapping stator wound-field synchronous machines.” IEEE Trans. Energy Convers., vol. 30 no. 4, pp. 1420-1427, May. 2015. [2] H. Pollock, C. Pollock, R. T. Walter, and B. V. Gorti, “Low cost, high power density, flux switching machines, and drives for power tools,” in Conf. Rec. 38th IEEE IAS Annu. Meeting, Oct. 2003, vol. 3, pp. 1451–1457. [3] Y. Tang, J. J. H. Paulides, T. E. Motoasca, and E. A. Lomonova, “Flux switching machine with DC excitation,” IEEE Trans. Magn., vol. 48, no. 11, pp. 3583-3585, Nov. 2012. [4] B. Gaussens, E. Hoang, O. Barriere, J. Saint-Michel, and M. Gabsi, “Analytical approach for air-gap modeling of field-excited flux-switching machine: No-load operation,” IEEE Trans. Magn., vol. 48, no. 9, pp. 2505–2517, Sep. 2012. [5] X. Liu and Z. Q. Zhu, “Electromagnetic performance of novel variable flux reluctance machines with dc-field coil in stator,” IEEE Trans. Magn., vol. 49, no. 6, pp. 3020-3028, Jun. 2013. [6] K. Vijayakumar, R. Karthikeyan, S. Paramasivam, R. Arumugam, and K. N. Srinivas, “Switched reluctance motor modeling, design, simulation, and analysis: a comprehensive review,” IEEE Trans. Magn., vol. 44, no. 12, pp. 4605-4617, Dec. 2008. [7] Z. Q. Zhu, B. Lee, and X. Liu, “Integrated field and armature current control strategy for variable flux reluctance machine using open winding,” IEEE Trans. Ind. Appl., vol. 52, no. 2, pp. 1519-1529, Mar./Apr. 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/16bc6a2168fbe73c6a5b2b933b4fc140.jpg)
Fig. 1. Topologies of the WFSF machines (a) with zero-sequence field current excitation and (b) conventional separate AC and DC windings. (c) Control circuit. (d) Operating principle.

![](https://assets.underline.io/uploads/markdown_image/1/image/ac8f544001c98b644d34bbc569f7b5d0.jpg)
Fig. 2. Electromagnetic characteristics comparison. (a) Flux linkages in the proposed machine. (b) Back-EMFs. (c) Steady-state torque. (d). Torque versus current characteristics.

 A Novel Wound Field Switched Flux Machine with Zero-Sequence Field Current Excitation

Wound rotor synchronous machines are widely used because of their advantages, such as simple control, cost efficiency, and stable operation [1]. Because of these advantages, the wound rotor synchronous generator (WRSG) is used in large factories, aircraft, ships, and hydroelectric power generation that require a large power supply [2]. The WRSG does not have a rare earth magnet, and it forms a magnetic field through the rotor winding, as shown in Fig. 1(a). A magnetic field is formed by applying current to the rotor windings through an exciter, and the magnetic flux density can be controlled using the exciter to increase the power density. The core of many electrical machines is made of electrical steel with nonlinear characteristics, and the magnetic flux density must be adjusted to a level where the core is unsaturated to satisfy the user’s desired output power, efficiency, and voltage. Therefore, it is necessary to evaluate the electromagnetic characteristics through electromagnetic analysis during the initial design. Finite element analysis (FEA) software is commercially available because it can obtain accurate analysis results that reflect nonlinearity. However, FEA consumes significant analysis time in the initial design, in which the design parameters change frequently [3]. Therefore, in this study, we propose a nonlinear magnetic equivalent circuit (MEC) to predict the electromagnetic and power generation characteristics of the WRSG. The magnetic equivalent area was divided according to the magnetic path of the WRSM (Fig. 1(b)). The paths through which the magnetic flux passes are divided into stator, rotor, air-gap, and interpolar regions. The magnetic flux inside the circuit could be calculated using the magnetomotive force(MMF) and reluctance, and the flux density in air gap could be calculated using the magnetic flux. Fig. 2(a) shows a comparison of the air gap flux density derived through the MEC and FEA when a field current is applied. The air flux density derived for the MEC represented the flux density waveform when the rotor position rotated, which could be used to derive the stator flux linkage waveform according to the rotor position. The derived flux linkage induced a back electromotive force (EMF) at no load (Fig. 2(b)). In the initial position, the rotor was positioned such that the flux linkage to the windings of one phase was maximized, and the back EMF through the flux that varied according to the rotation of one slot pitch was derived. The back EMF was influenced by the MMF of the rotor winding, and beyond the linearly increasing region, it became saturated because of the nonlinearity of the core material. The back EMF derived from the nonlinear MEC increased linearly and then nonlinearly, owing to saturation beyond a certain field current (Fig. 2(c)). The back EMF obtained using the nonlinear MEC was compared with those obtained through FEA and experimental measurements; the comparison validates the nonlinear MEC proposed in this study. It is necessary to determine the values of the back EMF, inductance, and phase resistance, which are equivalent circuit parameters, to predict the power generation characteristics of a WRSG. A MEC based on the rotor position must be constructed to reflect the inductance that varies with the rotor position, owing to the salient structure of the WRSG. Fig. 2(d) shows the prediction results of power generation characteristics using the inductance derived through the MEC, back EMF, and phase resistance. The FEA results indicated the power generation characteristics in the low-voltage regulation rate region, and the MEC results were in good agreement with the FEA results. Even when the rotational speed of the WRSG changed, the MEC results were in good agreement with the FEA results. By predicting power generation characteristics, the speed and power required by the designer can be predicted, which is useful in the initial design. The nonlinear MEC and analysis results of the WRSG will be presented in further detail in the main paper.

**References:**

[1] S. Nuzzo, M. Degano, M. Galea, et al, IEEE Trans. Ind. Electron., vol. 64, no. 3, pp. 1958–1970, Mar. 2017. [2] A. Griffo, D. Drury, T. Sawata, et al, IEEE Trans. Ind. Electron, vol. 59, no. 9, pp. 3579–3587, Sep. 2012. [3] H.W. derbas, J.M. Williams, A.C. Koenig, et al, IEEE Trans. Energy Convers., vol. 24, no. 2, pp. 388–396, Jun. 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/30110081fcfd5756909893a64d2ecd83.jpg)
Fig 1. (a) WRSG analysis model and rotor core experimental model; (b) Construction of nonlinear MEC

![](https://assets.underline.io/uploads/markdown_image/1/image/0abfb2acf0d58abdf081b148aaeb8928.jpg)
Fig 2. Comparison of electromagnetic characteristics obtained using the FEA, MEC, and experimental methods: (a) Comparison of air-gap flux density obtained using FEA and MEC methods; (b) Waveform of back EMF at rated speed of 900 rpm; (c) Variation of back EMF with field current; (d) Power-voltage curve

 Prediction of power generation performance of wound rotor synchronous generator using nonlinear magnetic equivalent circuit method

Compared with the conventional motors used on the ground, the DC starter-generators (DCSGs) for aero-engines have higher electrical, thermal, magnetic and mechanical loads. Excessive electrical loads will increase the armature response of the (DCSGs) and worsen the commutation, thus shortening the lifetime and reducing the reliability of the (DCSGs). In order to improve the lifetime and reliability of the (DCSGs), this paper studied the effects of commutator structure, compensation windings, commutating poles and brush sizes on commutation effect of DCSGs based theory analysis combined with numerical analysis. Then effective measures to improve the commutation performance of this type of DCSGs are proposed, and the commutation spark observation test of a certain type of DCSGs verifies the effectiveness of the optimization design measures proposed in this paper. Index Terms：DC starter-generators (DCSGs); Brush; Commutation; Optimal design. I. Introduction The DC starter-generators (DCSGs) used in aero-engine is installed on the engine accessory box. When the aero-engine starts, it acts as a starter motor to drive the engine to ignite. After the engine ignites, it acts as a generator to supply power to the aircraft network. Due to the special application environment of the DCSG, it has the characteristics of low voltage and high current compared with the motor used on the ground. The commutation process is extremely bad, and it may produce larger commutation sparks or even ring fire, shortening the lifetime of the brush and reducing the operational reliability of DCSGs[1][2][3][4]. This paper optimizes the design of parameters such as commutator structure, commutating pole winding and brush size, and studies the influence of parameter changes on the commutation performance of DCSGs under the conditions of low voltage and high current, and discusses the effectiveness of improving the commutation performance of this type of DCSGs The method provides a reference for commutation spark suppression in commutation of the same type of DCSGs. II. Large Current Commutation Modeling The electromotive force and current in the armature winding of the DCSG form an AC-DC voltage and current conversion through the cooperation of the commutator and the brush. This conversion process is called commutation. There is a complicated electromagnetic process in the commutation process, and reactance electromotive force is generated in the commutation element. By reducing the armature reaction and adjusting the brush width to reduce the reactive electromotive force, the commutation spark can be reduced and the commutation performance can be improved. III. Optimal Design Take a 9kW, 6250rpm～12000rpm DCSG as an example to study the influence of commutator structure selection, compensation winding, commutating pole and brush size on DCSG commutation performance. Finite element analysis model of the DCSG is shown in Fig.1. IV. Experimental Verification A start-up test was carried out on the simulated engine load characteristics of a 9kW a DCSG. The test bench is shown in Fig.2. No visible commutation sparks were observed in the test, which verified that the effectiveness of the commutation performance optimization design method proposed in this paper. V. Conclusion This paper studies the optimization design of DCSG to improve its commutation performance. Based theory analysis combined with numerical analysis, the influence of different commutator types, compensation windings, commutating pole windings and brush parameters on the commutation performance of the DCSG is analyzed. The prototype is tested for starting and generating performance. The experimental results verify the effectiveness of the optimized design method in improving the commutation performance, which can provide a reference for improving the commutation performance of the same type of DCSG, and is useful for improving the operating reliability and lifetime of the DCSGs.

**References:**

[1] Takashi, Fukutsuka and Yasunobu. “Arc discharge during commutation process in DC motor immersed in ethanol: approach to contact state of brush on commutator segment”, IEEJ Transactions on Power and Energy, Vol. 139, pp.293-301,2019. [2] H. Kim, H. Kim and W. Moon. “Design optimization of brush permanent magnet DC motors using response surface method”, Journal of Magnetics, vol. 25, pp. 355-362, 2020. [3] K. Sawa, M. Isato and T. Ueno. "Commutation characteristics and brush wear of DC motor at high rotation speed," 2017 IEEE Holm Conference on Electrical Contacts, pp. 176-181, 2017. [4] Z. Qingliang, Takahiro and Ueno. “The new commutation theory to the optimization technique of the large DC machine commutation design”, IEEJ Transactions on Industry Applications, Vol. 131, pp. 654-666, 2011.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/246f78fbf529af15431c6c92f934689e.jpg)
Fig.1. Finite element analysis model of the DCSG.

![](https://assets.underline.io/uploads/markdown_image/1/image/acbe807bc1de68577c1c67ffac5a574f.jpg)
Fig.2. Test bench of DCSG.

 Research on Optimal Design of Commutation Performance of Starter-Generator Used in Aero-Engine

I.Introduction Permanent magnet synchronous machine (PMSM) is widely recognized as a competent candidate for automotive propulsion [1], which offer the merits of high power density and high efficiency. Nevertheless, due to the inverter voltage and current limitations, the air-gap flux of the conventional PMSM is difficult to adjust even though a continuous negative d-axis current is injected for flux-weakening under high-speed operation [2]. As a result, how to realize effective air-gap flux adjustment, and further extend the speed range as well as high efficiency operation is regarded as a major challenge for the conventional PMSMs. Fortunately, the concept of variable flux memory machine (VFMM) is proposed to address the above issues [3]-[4]. The low coercive force (LCF) PM can be varied via a magnetizing or demagnetizing current pulse, in which the air-gap flux density can be flexibly adjusted. Generally, high coercive force (HCF) and LCF PMs are simultaneously employed in VFMM to realize high torque density and excellent flux adjustability [5]-[6]. Due to the magnetization state (MS) stabilization effect of HCF PMs on LCF PMs in series magnetic circuit VFMM, the unintentional on-load demagnetization issue can be avoided. Nevertheless, it also brings the problems of limited flux regulation range and higher required current pulse level for full remagnetization, which are undesirable for practical applications [7]. Therefore, this paper proposes a novel asymmetric-PM VFMM (APM-VFMM) with anti-demagnetization barrier design to realize wide flux regulation range and excellent on-load demagnetization withstand capability. The topology and features of the proposed APM-VFMM are introduced, respectively. The electromagnetic characteristics under different MSs are evaluated and compared. The efficiency maps are investigated to verify the advantages of the proposed design in terms of excellent flux regulation range and high efficiency operation over a wide speed range. II.Machine Configuration The topology evolution of the proposed APM-VFMM is shown in Fig. 1, in which the magnetic barrier is designed to resist the on-load unintentional demagnetization of the LCF magnet. The “U”-shaped magnetic barrier is added to the conventional series magnetic circuit VFMM, thereby forming into the anti-demagnetization barrier design. Then, the LCF magnet can be a substituted for the HCF magnet on one sided portion of the barrier design to form an asymmetric-PM configuration. The corresponding cross section of the proposed machine is shown in Fig. 2, which are characterized by a dual-layer PM structure [7]. The “U”-shaped magnetic barrier of the first PM layer can be employed to protect the working point stability of LCF PMs. For the second PM layer, asymmetric spoke-type hybrid PM arrangement is located on the d-axis, which can reduce magnetic saturation and enlarge flux regulation range. Each LCF magnet has an adjacent spoke-type HCF magnet to form a series magnetic circuit, achieving excellent demagnetization withstand capability. III.Electromagnetic Performance The open-circuit air-gap flux density waveforms of the proposed APM-VFMM under different MSs are plotted in Fig. 2(a) and (b), in which the flux-enhanced and flux-weakened states refer to the cases that the LCF magnets forward or reverse magnetized by twice the rated current considering inverter capacity, respectively. It demonstrates that the magnetic field in the flux-weakened state is significantly lower than flux-enhanced state, which implies that an expected flux-weakening effect can be achieved. Furthermore, the torque characteristics of the proposed machine are plotted in Fig. 2(c) and (d). It can be observed that the proposed machine in flux-enhanced state provides higher output torque than that of the flux-weakened state. Finally, the efficiency maps of the proposed machine under different MSs are shown in Fig. 2(e) and (f), which confirm that the proposed machine can achieve high efficiency maintaining by selecting appropriate MS under different operating regions.

**References:**

[1] I. Boldea, L. N. Tutelea, L. Parsa, and D. Dorrell, IEEE Trans. Ind. Electron., vol. 61, no. 10,pp. 5696-5711, Oct.2014. [2] W. L. Soong and T. J. E. Miller, IEE Proc. Electr. Power Appl., vol. 141, no. 6, pp. 331-340, Nov. 1994. [3] V. Ostovic, IEEE Ind. Appl. Mag., vol. 9, no. 1, pp. 52-61, Jan./Feb. 2003. [4] H. Hua, Z. .Q. Zhu, A. Pride, R. P. Deodhar, and T. Sasaki, IEEE Trans. Ind. Appl., vol. 53, no. 5, pp. 4396-4405, Sept./Oct. 2017. [5] A. Athavale, K. Sasaki, B. S. Gagas, T. Kato, and R. D. Lorenz, IEEE Trans. Ind. Appl., vol. 53, no. 5, pp. 4318- 4326, Sep./Oct. 2017. [6] H. Yang, S. Lyu, H. Lin, Z. Q. Zhu, H. Zheng, and T. Wang, IEEE Trans. Ind. Electron., vol. 67, no. 7, pp. 5258-5268, July 2020. [7] H. Yang, H. Lin, Z. Q. Zhu, S. Lyu, and H. Wang, in Proc. Energy Convers. Congre. Expo (ECCE 2018), Portland, OR, Sept. 23-27, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/de9377d8916ba31d300acd96c34980c4.jpg)
Fig. 1. Machine topology. (a) Topology evolution. (b) Cross section of the proposed APM-VFMM.

![](https://assets.underline.io/uploads/markdown_image/1/image/bf10326bea48e5d7b69487091f164d07.jpg)
Fig. 2. Electromagnetic characteristics. (a) Open-circuit air-gap radial flux densities. (b) Harmonic spectra. (c) Steady-state torque waveforms. (d) Torque-angle waveforms. (e) Efficiency maps under flux-enhanced state. (b) Efficiency maps under Flux-weakened state.

 A Novel Asymmetric-PM Variable Flux Memory Machine with Anti-Demagnetization Barrier Design

Introduction: The torque ripple can hardly be avoided for synchronous reluctance motors (SynRMs) in load conditions. It is generated by the interaction of the stator and rotor electromagnetic field harmonics, which have the same number of pole pairs but different rotating angular frequencies. In the air gap, the flux density is equal to the magnetomotive force (MMF) times the permeance. In [1], the air-gap field was analyzed, and a method for designing low-torque-ripple SynRMs was proposed. However, it did not consider the rotor permeance distribution and was limited to a relatively symmetrical rotor topology. In [2], it was verified that the torque ripple is highly affected by the position of the flux-barrier ends. The introduction of non-uniform flux barriers is capable of reducing the torque ripple. Based on the recent air-gap field modulation theory [3], the SynRM rotor with multi-layer flux guides, or flux barriers, can modulate extra harmonics in the air gap, whose frequencies are different from the primitive MMF. It is considered that the topology of the SynRM rotor is usually asymmetric, especially when a rotor with non-uniform flux barriers is adopted, and a series of permeance harmonics are produced. However, it is quite difficult to calculate the rotor permeance by analytical methods when the flux-barrier ends distribute along the rotor surface non-uniformly. This study proposes a method to analyze the effects that the rotor topology has on the rotor permeance harmonics by a virtual permanent magnet harmonic machine (VPMHM). By adjusting the rotor topology, certain permeance harmonics resulting in tremendous torque ripple can be avoided. Instead of simulating the output torque waveform directly, the proposed method can accelerate the optimization process and save much time. Analysis model: In [4], the concept of a VPMHM was introduced to generate harmonics with sinusoidal magnetization. Fig. 1(a) shows the model of the VPMHM, and Fig. 1(b) shows the implementation of the VPMHM in the optimization process for SynRMs in this study. The VPMHM has two parts, an ideal stator yoke whose permeability is infinite and an annular permanent magnet (PM) with the sinusoidal magnetization. The VPMHM is capable of generating sinusoidal distributed flux density in the air gap. Once an actual rotor is put in, the flux density waveform is no longer the pure sinusoid because of the modulation of the flux guides. The harmonics can be regarded as the effects of the rotor permeance. In this article, a 36-slot, 4-pole SynRM model is taken as an example to investigate the effects of the rotor permeance and perform the finite-element based optimization. The rated phase current is 130 Arms, and the motor is controlled by the maximum torque per ampere (MTPA) strategy. Results: An initial rotor was fast established based on some specific rules. The rotor permeance is mainly determined by the positions of the flux-barrier ends. With the help of the VPMHM, there is no need to analyze the entire dynamic process. A large-scale enumeration calculation is carried out for the air-gap electromagnetic field under different positions of the flux-barrier ends. The rotor that can create the minimum harmonics, whose orders are the same as the stator harmonics is preferred. Compared with the absolute values, per unit values are used to describe the magnitude which makes the comparison easier and more straightforward during the optimization process. Fig. 2(a) shows the fast Fourier transform (FFT) results of the air-gap flux density harmonics before and after the optimization. Though both of them contain considerable 21st and 23rd order harmonics, the effects on torque ripple are minor because the magnitudes of the corresponding stator harmonics are relatively small. The 17th and 19th order harmonics are evidently suppressed, which have the same number of pole pairs as the stator slot harmonics. Hence, the torque ripple caused by the slot harmonics can be mitigated. The fifth and seventh order harmonics slightly increase, but the influences of them are not severe as that of the stator slot harmonics when a short-pitched double-layer winding is adopted. For validation, Fig. 2(b) shows the results of the output torque waveform as a function of time at the nominal load. Compared with the initial rotor, it is salient that the torque ripple is effectively suppressed after optimization.

**References:**

[1] A. Vagati, M. Pastorelli, G. Francheschini, IEEE Transactions on Industry Applications, vol. 34, no. 4, pp. 758-765, July-Aug. 1998, doi: 10.1109/28.703969. [2] N. Bianchi, S. Bolognani, D. Bon and M. Dai Pre, IEEE Transactions on Industry Applications, vol. 45, no. 3, pp. 921-928, May-june 2009, doi: 10.1109/TIA.2009.2018960. [3] M. Cheng, P. Han and W. Hua, IEEE Transactions on Industrial Electronics, vol. 64, no. 8, pp. 6063-6074, Aug. 2017, doi: 10.1109/TIE.2017.2682792. [4] C. Di, I. Petrov and J. J. Pyrhönen, IEEE Transactions on Magnetics, vol. 54, no. 12, pp. 1-12, Dec. 2018, Art no. 8111012, doi: 10.1109/TMAG.2018.2873279.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/945e93b891cd547a409babe20dea51a8.jpg)
Fig. 1 Concept of the VPMHM and the flux density distribution in the air gap. (a) Model of the VPMHM (b) Implementation of the VPMHM with the actual rotor.

![](https://assets.underline.io/uploads/markdown_image/1/image/4c46c91241441ae7dee9138088d02dd8.jpg)
Fig. 2 The results before and after the optimzation. (a) Harmonics produced by the SynRM rotor under the excitation of a VPMHM. (b) The output torque waveform as a function of time at the nominal load.

 Torque Ripple Optimization for Synchronous Reluctance Motors based on a Virtual Permanent Magnet Harmonic Machine

1.Introduction In recent years, the demand for highly efficient motors is increasing to reduce energy consumption due to the increase in energy cost. Synchronous reluctance motor (SynRM) without magnet on the rotor is regarded as an ideal substitute for permanent magnet synchronous motor to obtain high efficiency, but SynRM has the disadvantages of low power factor and high torque ripple [1]. By insetting PMs within the flux barriers of SynRM, permanent magnet assisted synchronous reluctance motor (PMaSynRM) shows better performance in many aspects including torque, efficiency, and power factor [2]. The main challenge for an optimal design of PMaSynRM is to optimize the multiple design variables while ensuring the reliability of the rotor structure [3]. A novel multi-objective optimization method for PMaSynRM is proposed in this paper to realize high efficiency and low torque ripple. Based on the sensitivity analysis results of design variables, a sequential subspace optimization method (SSOM) [4] is implemented. Meanwhile, artificial neural network (ANN) [5] and multi-objective article swarm optimization (MOPSO) are used to train surrogate models and perform multi-objective optimization about electromagnetic and structural fields to reduce the required number of the time-consuming finite element analysis (FEA). 2. Winding Configurations and Comparison High torque ripple is a major disadvantage that limits the application of reluctance motors. Fractional-slot windings can obtain the relatively lower torque ripple by reducing the high-order torque harmonics generated by slot harmonics, but PMaSynRM rotors associated with fractional-slot windings cannot maintain the expected reluctance torque contribution since the difference between d-axis and q-axis flux distribution and rotor pole spacing. The windings with an odd number of slots per pole pair are the exception, which can reduce torque ripple while maintaining the saliency ratios of PMaSynRM. Therefore, six typical slot-pole number combinations are compared under the same 4-poles rotor, thermal constraints and main dimensions in this paper to investigate the performance of PMaSynRM. Compared to the integer-slot winding, the fractional-slot winding has more harmonic content, which will result in greater iron loss. At the same time, the high harmonic content also produces a great harmonic leakage that reduces the power factor of the motor. The analysis result is verified by FEA as shown in Tab.1. Fractional-slot concentrated-winding of 6-slot 4-pole can get minimum copper loss but the lowest torque and power factor due to its low winding factor and high harmonics. The efficiency and power factor are improved as the number of slots increases except for the 21-slot 4-pole motor whose harmonic content is the highest among the motors with similar slots. Integer-slot distributed-winding of 36-slot 4-pole motor has a maximum efficiency and power factor, but its torque ripple is quite high. Considering all performances of the motor, the 30-slot 4-pole motor was chosen to be the optimal solution. 3. Multi-objective Optimization It is difficult to get optimal solutions if more than 10 structural variables are optimized simultaneously. To solve multi-parameter optimization problem and reduce the computational cost, a multilevel design optimization method based on sequential subspace is proposed. Firstly, 15 design variables are selected for the optimization. Analysis of variance techniques based on the design of experiment (DOE) method is used to carry out a sensitivity analysis of parameters and the optimization variables are divided into two subspaces: the significant parameter subspace X1 and the minor parameter subspace X2. The specific multilevel optimization flowchart is given in Fig.1. The convergence error is set as 1%. Then, a surrogate model that can replace both the electromagnetic field and structural field FEA of the motor is trained by the ANN to improve optimization efficiency. To further reduce the required number of FEA simulations, the orthogonal experimental design method is adopted to generate a training set for the surrogate model. Ultimately, a multi-objective optimization is performed using the MOPSO algorithm to search for an optimal design that yields high efficiency and low torque ripple. 4.Conclusion The surrogate model successfully converges after three subspace optimizations, and its results are in good agreement with the FEA. Compared to the initial design, the optimal design yields a much higher efficiency (increased by 1.5%) and lower torque ripple (decreased by 65%) with the same volume, and the maximum stress of the rotor is about 180MPa at rated load condition. The proposed multilevel optimization method can significantly alleviate the computing burden and is suitable for the high-dimensional optimization of the PMaSynRM.

**References:**

1. N. Bianchi, M. Degano and E. Fomasiero, "Sensitivity Analysis of Torque Ripple Reduction of Synchronous Reluctance and Interior PM Motors", IEEE Transactions on Industry Applications, vol. 51, pp. 187-195(2015). 2. S. Ooi, S. Morimoto and Y. Inoue, "Performance Evaluation of a High-Power-Density PMASynRM With Ferrite Magnets", IEEE Transactions on Industry Applications, vol. 49, pp. 1308-1315(2013). 3. S. S. R. Bonthu, S. Choi and J. Baek, "Design Optimization With Multiphysics Analysis on External Rotor Permanent Magnet-Assisted Synchronous Reluctance Motors", IEEE Transactions on Energy Conversion, vol. 33, pp. 290-298( 2018). 4. G. Lei, C. Liu and Y. Guo, "Techniques for Multilevel Design Optimization of Permanent Magnet Motors", IEEE Transactions on Energy Conversion, vol. 30, pp. 1574-1584(2015). 5. J. Song, F. Dong and L. Wang, "An Efficient Multiobjective Design Optimization Method for a PMSLM Based on an Extreme Learning Machine", IEEE Transactions on Industrial Electronics, vol. 66, pp. 1001-1011(2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7b9404c935dc088ecba0b6ccd8aeac6c.jpg)
Table.1 Performance of machines with different slots

![](https://assets.underline.io/uploads/markdown_image/1/image/c4651860507cd70d4a65deb4c8e351ac.jpg)
Fig. 1 Multilevel optimization framework for PMaSynRM design

 Multi-physic Fields Surrogate-assisted Optimization of a Permanent Magnet Assisted Synchronous Reluctance Motor

Switched Reluctance Machine has progressed as a suitable contender in the family of electrical machines for its high starting torque and better performance in different operating conditions. The need of accurate modeling of this machine is therefore dependent on the accurate determination of losses of which iron loss is exigent. This paper aims to determine iron loss from the equivalent circuit of the machine based on the input data tables that are directly obtained from the experiments performed on an existing 4-phase switched reluctance machine. The experimental determination of the iron losses has been compared with those who were predicted under the same operating conditions. Equivalent Circuit of Switched Reluctance Motor The iron losses calculation from the equivalent circuit of the switched reluctance machine (SRM) is presented in [1] that included two ends i.e., unaligned and miss-aligned positions of the machine. Whereas an intermediate position was not taken into consideration. Fig. 1 shows an equivalent circuit in which R represents phase winding resistance, L is self-inductance, and resistive branch ‘r’ that is dependent on rotor position, change in flux linkage, and frequency of phase switching. This element is connected in parallel to ‘L’ to represent the iron loss in the core of the machine [1]. The arrangement i.e., the parallel combination of ‘r’ and ‘L’ shown in the circuit Fig. 1 [1] describes the flux penetration and eddy current in the magnetic core of the motor. A review on different methods for loss calculations of SRM is given in [2]. Results For purpose of the illustration, the waveforms of currents and in the equivalent circuit are shown in Fig.2 (a). Fig.2 (b) shows the equivalent iron-loss-resistance vs. flux- linkage in the intermediate position of currents and in the equivalent circuit of Fig.1.

**References:**

1. Corda, J. and Jamil, S.M., 2009. Experimental determination of equivalent-circuit parameters of a tubular switched reluctance machine with solid-steel magnetic core. IEEE Transactions on Industrial Electronics, 57(1), pp.304-310. 2. Li, S., Zhang, S., Habetler, T.G., and Harley, R.G., 2019. Modeling, Design Optimization, and Applications of Switched Reluctance Machines—A Review. IEEE Transactions on Industry Applications, 55(3), pp.2660-2681.

**Images:**
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