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In this paper, a novel system level sequential design optimization method is presented for switched reluctance motor (SRM) drive systems. First, the multiobjective optimization problem for the SRM drive systems is defined. Then, all parameters of the drive systems, including the motor level and control level are divided into two subspaces according to their influences on the objectives. Finally, the optimization of each subspace is performed sequentially until a convergence criterion is met. The sensitivity analysis, the approximate models, and the genetic algorithm are employed for the implementation. Besides, the space reduction method is introduced to reduce the computational cost. The step size of each control factor will be halved in the next iterative process. To verify the effectiveness of the proposed method, An SRM drive system with a 12/10 configuration and angle position method, is investigated.&lt;br/&gt;&lt;br/&gt;I. Introduction&lt;br/&gt;Due to the absence of any windings and magnets in the rotor, the switched reluctance motors (SRMs) provides the best alternatives for the other machines under harsh environments of extremely high temperatures and pressures [1]. The trade-offs to the overall consideration and the implementation of multiobjective optimization are necessary to meet the requirements for different applications. Previous works are mostly on component level rather than the system level [2]. Theoretically, assembling individually optimized components into a system cannot guarantee the optimal system performance as each part is coupled to each other. Thus, the perfect cooperation of motor and control levels should be optimized simultaneously. The main problem in the system level optimization is the computation burden due to the abundant optimization variables. In this paper, the space reduction strategy will be integrated into the system level optimization flowchart.&lt;br/&gt;&lt;br/&gt;II. System-Level Sequential Subspace Design Optimization&lt;br/&gt;An SRM drive system with a 12/10 configuration and angle position method, will be investigated, as shown in Fig. 1.&lt;br/&gt;The optimization flowchart is presented in Fig. 2, and it can be divided into the following steps.&lt;br/&gt;&lt;i&gt;Step 1&lt;/i&gt;: Define the system level optimization model, including objective function, constraints, and design parameters.&lt;br/&gt;The optimization problem can be defined as&lt;br/&gt;min: &lt;i&gt;f&lt;/i&gt;(x&lt;i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;)&lt;br/&gt;&lt;i&gt;s.t.&lt;/i&gt; &lt;i&gt;g&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;(x&lt;i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;)≤0, &lt;i&gt;i&lt;/i&gt;=1,2,…,&lt;i&gt;n&lt;/i&gt; (1)&lt;br/&gt;x&lt;i&gt;&lt;sub&gt;sl&lt;/sub&gt;&lt;/i&gt;≤x&lt;i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;≤x&lt;i&gt;&lt;sub&gt;su&lt;/sub&gt;&lt;/i&gt;&lt;br/&gt;where x&lt;i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;f&lt;/i&gt;, &lt;i&gt;g&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; are the design parameter vector, objective and constraints of motor, respectively, x&lt;i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt; consists of motor parameter vector and control parameter vector, x&lt;i&gt;&lt;sub&gt;sl&lt;/sub&gt;&lt;/i&gt; and x&lt;i&gt;&lt;sub&gt;su&lt;/sub&gt;&lt;/i&gt; are the lower boundary and upper boundary, respectively.&lt;br/&gt;&lt;i&gt;Step 2&lt;/i&gt;: Divide all the parameters in motor and control aspects into two subspaces. X&lt;sub&gt;1&lt;/sub&gt; and X&lt;sub&gt;2&lt;/sub&gt; represent the significant and non-significant subspaces, respectively.&lt;br/&gt;&lt;i&gt;Step 3&lt;/i&gt;: Optimize X&lt;sub&gt;1&lt;/sub&gt;. Generate samples and simulate their response by using the orthogonal array (OA) [1]. An OA with a higher level with 5 levels can be assigned to X&lt;sub&gt;1&lt;/sub&gt;. The Kriging model [2] is developed based on the data. Then, conduct the optimization by using non-dominated sorting genetic algorithm (NSGA) II. The optimal solution is selected for the next subspace.&lt;br/&gt;&lt;i&gt;Step 4&lt;/i&gt;: Optimize X&lt;sub&gt;2&lt;/sub&gt;. In this step, an OA with 3 levels is assigned to X&lt;sub&gt;2&lt;/sub&gt;. The optimal solution is selected by the same implementation in step 3.&lt;br/&gt;&lt;i&gt;Step 5&lt;/i&gt;: Termination judgement. Compute the motor performance with the obtained optimal design and compare it with the last objective. If the relative error is less than a given value, terminate the optimization process and output the optimal design. Otherwise, go to the next step.&lt;br/&gt;&lt;i&gt;Step 6&lt;/i&gt;: Reduce the design space of the design parameters in X&lt;sub&gt;1&lt;/sub&gt; and X&lt;sub&gt;2&lt;/sub&gt;, respectively. Assume the initial design space of an optimization variable is [&lt;i&gt;a&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt;], and the optimal value of this variable is &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;.&lt;br/&gt;For X&lt;sub&gt;1&lt;/sub&gt; in which there are 5 levels for each design parameter with a step size 2&lt;i&gt;d&lt;/i&gt;, the next design space and new levels are&lt;br/&gt;[&lt;i&gt;a&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt;+&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt;+2&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt;+3&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt;+4&lt;i&gt;d &lt;/i&gt;], &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;–2&lt;i&gt;d&lt;/i&gt;&amp;lt;&lt;i&gt;a &lt;/i&gt;;&lt;br/&gt;[&lt;i&gt;b&lt;/i&gt;-4&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt;-3&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt;-2&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt;-&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;b &lt;/i&gt;], &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;+&lt;i&gt;d&lt;/i&gt;&amp;gt;&lt;i&gt;b &lt;/i&gt;; (2)&lt;br/&gt;[&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;-2&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;-&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;, &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;+&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;+2&lt;i&gt;d &lt;/i&gt;], &lt;i&gt;others&lt;/i&gt;&lt;br/&gt;For X&lt;sub&gt;2&lt;/sub&gt; in which there are 3 levels for each design parameter with a step size 2&lt;i&gt;d&lt;/i&gt;, the next design space and new levels are&lt;br/&gt;[&lt;i&gt;a&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt;+&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt;+2&lt;i&gt;d &lt;/i&gt;], &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;-&lt;i&gt;d&lt;/i&gt;&amp;lt;&lt;i&gt;a &lt;/i&gt;;&lt;br/&gt;[&lt;i&gt;b&lt;/i&gt;-2&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt;-&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;b &lt;/i&gt;], &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;+&lt;i&gt;d&lt;/i&gt;&amp;gt;&lt;i&gt;b &lt;/i&gt;; (3)&lt;br/&gt;[&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;-&lt;i&gt;d&lt;/i&gt;, &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;, &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;+&lt;i&gt;d &lt;/i&gt;], &lt;i&gt;others&lt;/i&gt;&lt;br/&gt;It can be found that the step size is halved during the space reduction.

**References:**

[1] G. Lei, C. Liu, Y. Li, D. Chen, Y. Guo, and J. Zhu, “Robust Design Optimization of a High-Temperature Superconducting Linear Synchronous Motor Based on Taguchi Method,” &lt;i&gt;IEEE Trans. Appl. Supercond., &lt;/i&gt;vol. 29, no. 2, pp. 1-6, 2019.&lt;br/&gt;[2] K. Diao, X. Sun, G. Lei, Y. Guo, and J. Zhu, “Multiobjective System Level Optimization Method for Switched Reluctance Motor Drive Systems Using Finite Element Model,” &lt;i&gt;IEEE Trans. Ind. Electron., &lt;/i&gt;2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/049f17176bb7e82372435001c0f56fc3.png)
Fig. 1.  Experimental platform.

![](https://assets.underline.io/uploads/markdown_image/1/image/a8eae6d01509bb9f93443b74ef2e21d0.jpg)
Fig. 2.  Flowchart of the optimization strategy.

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 System Level Sequential Subspace Design Optimization of Switched Reluctance Motor Drive Systems Based on Space Reduction Strategy

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In this paper, a novel system level sequential design optimization method is presented for switched reluctance motor (SRM) drive systems. First, the multiobjective optimization problem for the SRM drive systems is defined. Then, all parameters of the drive systems, including the motor level and control level are divided into two subspaces according to their influences on the objectives. Finally, the optimization of each subspace is performed sequentially until a convergence criterion is met. The sensitivity analysis, the approximate models, and the genetic algorithm are employed for the implementation. Besides, the space reduction method is introduced to reduce the computational cost. The step size of each control factor will be halved in the next iterative process. To verify the effectiveness of the proposed method, An SRM drive system with a 12/10 configuration and angle position method, is investigated. I. Introduction Due to the absence of any windings and magnets in the rotor, the switched reluctance motors (SRMs) provides the best alternatives for the other machines under harsh environments of extremely high temperatures and pressures [1]. The trade-offs to the overall consideration and the implementation of multiobjective optimization are necessary to meet the requirements for different applications. Previous works are mostly on component level rather than the system level [2]. Theoretically, assembling individually optimized components into a system cannot guarantee the optimal system performance as each part is coupled to each other. Thus, the perfect cooperation of motor and control levels should be optimized simultaneously. The main problem in the system level optimization is the computation burden due to the abundant optimization variables. In this paper, the space reduction strategy will be integrated into the system level optimization flowchart. II. System-Level Sequential Subspace Design Optimization An SRM drive system with a 12/10 configuration and angle position method, will be investigated, as shown in Fig. 1. The optimization flowchart is presented in Fig. 2, and it can be divided into the following steps. Step 1: Define the system level optimization model, including objective function, constraints, and design parameters. The optimization problem can be defined as min: f(xs) s.t. gi(xs)≤0, i=1,2,…,n (1) xsl≤xs≤xsu where xs, f, gi are the design parameter vector, objective and constraints of motor, respectively, xs consists of motor parameter vector and control parameter vector, xsl and xsu are the lower boundary and upper boundary, respectively. Step 2: Divide all the parameters in motor and control aspects into two subspaces. X1 and X2 represent the significant and non-significant subspaces, respectively. Step 3: Optimize X1. Generate samples and simulate their response by using the orthogonal array (OA) [1]. An OA with a higher level with 5 levels can be assigned to X1. The Kriging model [2] is developed based on the data. Then, conduct the optimization by using non-dominated sorting genetic algorithm (NSGA) II. The optimal solution is selected for the next subspace. Step 4: Optimize X2. In this step, an OA with 3 levels is assigned to X2. The optimal solution is selected by the same implementation in step 3. Step 5: Termination judgement. Compute the motor performance with the obtained optimal design and compare it with the last objective. If the relative error is less than a given value, terminate the optimization process and output the optimal design. Otherwise, go to the next step. Step 6: Reduce the design space of the design parameters in X1 and X2, respectively. Assume the initial design space of an optimization variable is [a, b], and the optimal value of this variable is x0. For X1 in which there are 5 levels for each design parameter with a step size 2d, the next design space and new levels are [a, a+d, a+2d, a+3d, a+4d ], x0–2d&lt;a ; [b-4d, b-3d, b-2d, b-d, b ], x0+d&gt;b ; (2) [x0-2d, x0-d, x0, x0+d, x0+2d ], others For X2 in which there are 3 levels for each design parameter with a step size 2d, the next design space and new levels are [a, a+d, a+2d ], x0-d&lt;a ; [b-2d, b-d, b ], x0+d&gt;b ; (3) [x0-d, x0, x0+d ], others It can be found that the step size is halved during the space reduction.

**References:**

[1] G. Lei, C. Liu, Y. Li, D. Chen, Y. Guo, and J. Zhu, “Robust Design Optimization of a High-Temperature Superconducting Linear Synchronous Motor Based on Taguchi Method,” IEEE Trans. Appl. Supercond., vol. 29, no. 2, pp. 1-6, 2019. [2] K. Diao, X. Sun, G. Lei, Y. Guo, and J. Zhu, “Multiobjective System Level Optimization Method for Switched Reluctance Motor Drive Systems Using Finite Element Model,” IEEE Trans. Ind. Electron., 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/049f17176bb7e82372435001c0f56fc3.png)
Fig. 1. Experimental platform.

![](https://assets.underline.io/uploads/markdown_image/1/image/a8eae6d01509bb9f93443b74ef2e21d0.jpg)
Fig. 2. Flowchart of the optimization strategy.

poster

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:**
![](https://assets.underline.io/uploads/markdown_image/1/image/5294b7a5d713fb5088771a6e3f541dca.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/9c5f62a25b747646f0aef4435e76cb57.jpg)

 Experimental determination of equivalent iron loss resistance for prediction of iron losses in a Switched Reluctance machine

—In this paper, an improved direct instantaneous torque control (DITC) with sliding mode control and gray wolf optimization algorithm (GWOA) is proposed suppress torque ripple and enhance the anti-interference ability. First, the sliding mode speed controller based on a novel reaching law is designed to reduce torque ripple and startup time. Second, an anti-disturbance sliding mode observer is presented and combined with the SMSC to build up an anti-disturbance composite speed control strategy. Then, the GWOA is employed to automatically tune the parameters including the turn-on angle, turn-off angle, and coefficient in speed controller and observer for better comprehensive performance. Finally, the simulation and experimental results indicate that the proposed control method behaves well in aspects of the dynamic response and robustness, anti-interference ability, and torque ripple suppression. Introduction Due to many inherent features such as robust structure, no windings and PMs on the rotor, wide speed regulating range and high reliability, switched reluctance motors (SRMs) are becoming one potential candidate for hybrid electric vehicle (HEV) applications [1],[2]. However, SRM suffers from high torque ripple owing to the salient structure and nonlinear magnetization characteristics, which limits further development [3]. Direct instantaneous torque control The structure diagram of the DITC system combining speed controller and disturbance observer is shown in Fig. 1. The instantaneous torque obtained by the look-up table method is taken as the control quantity and then sent to torque controller after comparing with reference torque. Design of speed controller Based on conventional reaching law, an improved adaptive law is established as: ds/dt=-[k1s/[δ+(1-δ)e-α|s|]+k2|s|β]sgn(s), k1 &gt;0, k2 &gt;0, 0 &lt; δ &lt; 1, α &gt; 0, 1 &lt; β &lt; 2. The adaptive law is introduced into the speed controller to further suppress the chattering and increase convergence speed correspondingly. Design of disturbance observer based on modified STA In order to improve the anti-interference ability, the disturbance observer based on modified STA was employed in DITC system. The modified STA is defined as: du/dt=-λ1|u|1/2+lsgn(u)+u1, du1/dt=-λ2|u|2l sgn(u). Gray wolf optimization algorithm for auto-tuning The GWOA mimics the strict hierarchy and predatory behaviour of gray wolves in nature, which has been widely used in some specific applications. In the social hierarchy, gray wolves are divided into the wolf α, β, δ, and θ from high to low, which represent the best solution, the second-best solution, the third-best solution, and candidate solution, respectively. The mathematical model of the encircling behaviour of gray wolf can be expressed as follows: D=｜CXp-X｜ X(t+1)=｜Xp-A×D｜ where t is the current iteration number, D is the distance between the gray wolf and prey, X and Xp represent the position vector of the gray wolf and prey. The coefficient vectors C and A can be calculated as A=2a×r1-a C=2r2 where r1 and r2 are random vectors in [0, 1], and a is linearly decreased from 2 to 0 over the course of iterations. The mathematical model of the hunting behavior of gray wolf are shown as follows: Dp=｜CXp-X｜ Xn=｜Xp-A×Dp X(t+1)=(X1+X2+X3)/3 where the subscript p denotes α, β and δ, respectively, n denotes 1, 2 and 3, respectively, and Xn is the movement instructions given by α, β and γ, respectively. Compared with other algorithms, the GWOA stands out due to the feature of strong local search capability and high convergence rate. However, GWOA is hard to achieve a satisfactory result in solving complex optimization problems, which is likely to fall into a local solution. Simulation and experimental validation Simulations and experiments using DITC system with conventional PI and proposed sliding mode control method are compared to verify the accuracy and effectiveness. The test devices and platform for the dynamic characteristics is shown in Fig. 2.

**References:**

[1] X. Sun, K. Diao, G. Lei, Y. Guo, and J. Zhu, "Real-Time HIL Emulation for a Segmented-Rotor Switched Reluctance Motor Using a New Magnetic Equivalent Circuit," IEEE Transactions on Power Electronics, vol. 35, no. 4, pp. 3841-3849, 2020. [2] W. Ding, G. Liu, and P. Li, "A Hybrid Control Strategy of Hybrid-Excitation Switched Reluctance Motor for Torque Ripple Reduction and Constant Power Extension," IEEE Transactions on Industrial Electronics, 2019. [3] N. Yan, X. Cao, and Z. Deng, "Direct Torque Control for Switched Reluctance Motor to Obtain High Torque–Ampere Ratio," IEEE Transactions on Industrial Electronics, vol. 66, no. 7, pp. 5144-5152, 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/79aee5419adcc98c0bc3c2c5d3d44f95.jpg)
Fig. 1. Block diagram of DITC system.

![](https://assets.underline.io/uploads/markdown_image/1/image/a3f52b982b68d7134611f6ffa97e78dc.jpg)
Fig. 2. Devices and platform for testing dynamic characteristics.

 Research on Sliding Mode DITC Based on Gray Wolf Optimization Algorithm for SRM

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.

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

This paper proposes a unified control method to improve the ability of switched reluctance motors (SRM) to cope with variable operating conditions. The traditional single control method has obvious defects. The control method proposed in this paper is based on a 12/10 pole SRM. In the three-phase SRM (TSRM) mode, direct instantaneous torque control (DITC) is utilized to reduce torque ripple at low speed. In the six-phase SRM (SSRM) mode, A current-adjusted angular position control is used to increase the speed range and reduce torque ripple in high speed. The principle of dynamic coordinated control is utilized to implement switching between different modes to improve the performance of SRM. 1. Introduction A novel unified control method is proposed, which uses DITC and current control in the overlapped phase area to reduce torque ripple and obtain a wider speed range [1]. Compared with the traditional control method, the method has obvious advantages, but the speed adjustment range needs to be further expanded. Multi-objective optimization function and finite element method (FEA) are used to determine the motor parameters [2]. Experimental results prove that an SRM with 12/10 pole can be used not only as a three-phase motor but also as a six-phase motor. However, the paper does not propose a control method for switching between different modes. A unified control method is proposed for SRM in different modes. 2. The proposed method The multimode switched reluctance motor (MMSRM) is mainly composed of stator, rotor and coils. The electromagnetic performance of the TSRM and SSRM are analyzed via FEA. The flux distribution of the TSRM when one phase is excited is shown in Fig. 1 (a). MMSRM is utilized as a six-phase motor. When phase A is excited, the magnetic flux distribution at the aligned position is shown in Fig. 1(b). Compared with SSRM, TSRM has a higher instantaneous torque [2]. But the torque ripple also increases. In the low-speed range, MMSRM is used as TSRM. The direct instantaneous torque control can effectively reduce torque ripple. At the same time, the load capacity range of SRM is expanded. As the speed increases, the back electromotive force (EMF) voltage of the machine increases, which limits the ability of the controller to adjust the current. SRM enters the single pulse mode, and it is impossible to accurately track the reference current. Current-adjusted angular position control is used to reduce torque ripple in high speed. A paper confirms that the turn-off angle increases with increasing speed [1]. The calculation of the turn-off angle can be expressed as equation (1). Θd=180°+aIactual+bω+cI2actual+dωIactual +eI3actual +fωI3actual (1) where a, b, c, d, e, and f are the machine-specific coefficients, Iactual is the actual phase, and ω is the operating speed. For switching under different modes, the principle of dynamic coordinated control is utilized. Establishing the corresponding optimization objective function can greatly improve the overall efficiency of the motor. The unified control principle is shown in Fig. 2. The input parameters of the dynamic coordinated control principle are obtained through the input of working condition parameters and SRM state feedback. The unified control principle is shown in Figure 2. The input of the dynamic coordinated control principle is obtained through the input of working condition parameters and SRM state feedback. Equation (2) is used to establish the principle of SRM mode switching. Q1={x∈x1│(v&lt;vs) and (ω=0)} Q1'={x∈x1│(v&gt;vs) and (ω&gt;0)} Q2={x∈x2 } Q3={x∈x1, x∈x2 } (2) where Q, x1 and x2 respectively represent the mode judgment code, the trigger condition of TSRM and the trigger condition of SSRM. v, vs and ω respectively represent the vehicle speed, threshold of vehicle speed and motor speed.

**References:**

[1] Y. Hu, W. Ding, T. Wang, S. Li, S. Yang, and Z. Yin, "Investigation on a Multimode Switched Reluctance Motor: Design, Optimization, Electromagnetic Analysis, and Experiment," IEEE Trans. Ind. Electron., vol. 64, no. 12, pp. 9886-9895, 2017. [2] T. Husain, A. Elrayyah, Y. Sozer, and I. Husain, "Unified Control for Switched Reluctance Motors for Wide Speed Operation," IEEE Trans. Ind. Electron., vol. 66, no. 5, pp. 3401-3411, 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1428014bbed5c4ef46e91dfe58bf6b13.jpg)
Fig. 1. Topology of the SRM. (a) Excitation state of TSRM. (b) Excitation state of SSRM.

![](https://assets.underline.io/uploads/markdown_image/1/image/32ccbb86e7142e3f2cfd1c85cc387baf.jpg)
Fig.2. Schematic diagram of the unified control.

System Level Sequential Subspace Design Optimization of Switched Reluctance Motor Drive Systems Based on Space Reduction Strategy

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