New pole tip shapes mitigating torque ripple in short pitched and fully pitched switched reluctance motors

High torque ripple is one of the major disadvantages of switched reluctance motor (SRM). Although there are several publications in the literature addressing the full or partial solution to the problem for conventional SRM, no publication exists for the torque ripple reduction of recently emerging fully pitched SRM. This paper deals with finding best dimension set for a particular stator and rotor pole tip shape aiming to reduce torque ripple in both short pitched and fully pitched SRMs. Five new stator and rotor pole tip structures have been investigated and compared with conventional pole tip. Analyses have been performed with the finite element (FE) models of 6/43-phase short pitched and fully pitched SRM with unipolar excitation. With the proposed pole tips, torque ripple is reduced by 24.1% in short pitched SRM for 10 A phase current and by 22.6% in fully pitched SRM for 5.59 A phase current.     

Multi-objective optimization operation with corrective control actions for meshed AC/DC grids including multi-terminal VSC-HVDC

This paper presents a multi-objective optimal operation of meshed AC/DC power grids including multi-terminal voltage-source-converter-based high-voltage direct current (VSC-MTDC) systems. The proposed approach is modeled as a corrective security-constrained optimal power flow (CSC-OPF) problem, with the minimization of both the operation cost and power loss as the objectives. Moreover, it provides a cost-effective solution to assist in decision-making, and improves the system security during operation. The N − 1 contingency security criterion is enforced for both AC and DC transmission networks, and corrective control is used to eliminate or alleviate post-contingency security violations. The corrective control actions used in this paper include not only secure operation control actions, but also economical post-contingency corrective control of the multi-terminal VSC-HVDC. To increase the computation speed, a contingency screening technique is applied to CSC-OPF by efficiently selecting the most severe case of the N − 1 contingency, as obtained using a voltage security index (VSI). The proposed approach uses the non-dominated sorting genetic algorithm (NSGA-II) to find multi-objective OPF solutions by checking the post-contingency state feasibility while taking into account post-contingency corrective actions. Simulation results confirm the validity and effectiveness of this approach.     

Thermo-economic multi-objective optimization for a solar-dish Brayton system using NSGA-II and decision making

A 100 kW regenerative Brayton heat engine driven by the hybrid of fossil fuel and solar energy was considered for optimization based on multiple criteria. A thermodynamic model of such hybrid system was developed so that the power output, thermal efficiency and dimensionless thermo-economic performance with the imperfect performance of parabolic dish solar collector, the external irreversibility of Brayton heat engine and conductive thermal bridging loss could be obtained. Evolutionary algorithm based on NSGA-II (Elitist Non-dominated Sorting Genetic Algorithm) was employed to optimize triple-objective and dual-objective functions, where the temperatures of hot reservoir, cold reservoir and working fluid, the effectiveness of hot-side heat exchanger, cold-side heat exchanger and regenerator were considered as design variables. Using decision makings, including Shannon Entropy, LINMAP and TOPSIS methods, the final optimal solutions were selected from Pareto frontier obtained by NSGA-II. The results show that there exists an appropriate working fluid temperature to cause optimal solution under each given condition. The comparisons of triple-objective and dual-objective optimization with single-objective optimization indicate that multi-objective optimization can yield the more suitable results due to the lower deviation index from the ideal solution. In the analysis of triple-objective optimization, an expected result is obtained that the optimal values of the power out, efficiency and dimensionless thermo-economic performance of solar-dish Brayton system (68.65 kW, 0.2331 and 0.3077) are 22.6%, 34.9% and 18.4% respectively less than that of convectional Brayton heat engine. Finally, a range of functional relationship between the optimized objectives in Pareto frontier is fitted to provide more detailed insight into the optimal design of solar-dish Brayton system.     

基于分段式TSF的开关磁阻电机转矩脉动抑制技术

开关磁阻电机(Switched Reluctance Motor,SRM)的双凸极结构导致其运行时产生很强的转矩脉动,采用传统型转矩分配函数(Torque Sharing Function,TSF)时,电流峰值过高,铜耗过大,导致电机效率低,转矩脉动抑制效果不理想。针对这一问题,本文提出了新型分段式TSF,并以转矩脉动系数和电流变化率作为优化目标,利用遗传算法的全局寻优能力,对所提出的新型TSF中的变量参数进行优化,得到最优的TSF曲线及表达式,从而降低转矩脉动。仿真结果表明,本文所提出的新型TSF能够有效降低转矩脉动,同时降低电流峰值,减小铜耗,提高效率。     

Modified parameter optimization of distribution transformer design using covariance matrix adaptation evolution strategy

Optimal transformer design (TD) is a complex multi-modal, multi-objective, mixed-variable and non-linear problem. This paper discusses the application of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for distribution TD, minimizing four objectives; purchase cost, total life-time cost, total mass and total loss individually. Two independent variables; voltage per turn and type of magnetic material are proposed to append with the usual TD variables, aiming at cost effective, reduced weight, and energy efficient TD. Three case studies with three sets of TD vectors are implemented on 400 KVA, 20/0.4 KV transformer to demonstrate the superiority of Modified Design Variables (MDV), in terms of cost savings, material savings, and loss reduction. Simulation results of CMA-ES provide better TD on comparison with conventional transformer design procedure, branch and bound algorithm tailored to a mixed-integer non-linear programming, Self Adaptive Differential Evolution (SaDE), and real coded GA (RGA). Statistical analysis has proven the faster convergence and consistency of CMA-ES. Moreover, NSGA-II is applied for solving multi-objective TD optimization problem with the aim of providing tradeoff between conflicting TD objectives.     

一种抑制盘式永磁电机转矩脉动的方法

针对盘式永磁电机气隙磁密和反电动势中含有谐波、存在转矩脉动的问题,提出了一种磁极形状优化方法以降低盘式永磁电机气隙磁密波形和反电动势波形的畸变率、抑制转矩脉动。 建立了盘式永磁电机的等效磁网络模型,基于此模型解析计算出电机的空载反电动势,并通过有限元法进行了仿真验证。在确定最小气隙长度前提下,对不同磁极整形方法（即不整形、圆弧削极、偏心圆弧削极）气隙磁密、反电势、转矩脉动这些电磁性能进行了比较,得出了最佳优化方案。结果表明,优化设计后,气隙磁密波形和反电动势波形的畸变率明显减小,转矩脉动得到抑制。     

基于果蝇算法的开关磁阻电机多目标优化研究

针对采用传统算法对开关磁阻电机(SRM)本体进行多目标优化时存在算法复杂、调节参数多、计算量大且易陷入局部最优解等问题,提出一种基于果蝇算法(FOA)的SRM本体多目标优化设计方法。利用极限学习机算法建立SRM非参数模型,采用FOA算法对其进行优化,实现了SRM定转子极弧的全局最优设计,最后对该优化算法的效果进行了仿真验证,同时与传统粒子群优化算法(PSO)进行了对比分析,结果表明,FOA算法不仅获得了较PSO算法更好的转矩波动系数和效率指标,而且具有参数设置少、收敛速度快且不易陷入局部最优解等特点,具有较好的应用价值。     

基于遗传算法和转矩分配函数的开关磁阻电机转矩脉动抑制

开关磁阻电机(SRM)特殊的双凸极结构导致其运行时会产生很强的转矩脉动。传统的转矩分配函数(TSF)控制方法虽然可以在一定程度上起到抑制转矩脉动的作用,但是受到开关频率、功率电源电压值等物理条件的限制,仍会存在较大的转矩脉动。为此,提出了一种基于遗传算法的SRM TSF控制方案。利用遗传算法良好的寻优能力,在指数型TSF控制的基础上,将转矩脉动作为优化目标来寻取最优的开关角。将1台四相8/6极的SRM作为研究对象,搭建了以TMS320F28335为控制核心的试验平台。试验结果验证了基于遗传算法的TSF控制方法可以有效减小SRM的转矩脉动。     

Smart bacterial foraging algorithm based controller for speed control of switched reluctance motor drives

In this paper, a innovative methodology for Switched Reluctance Motor (SRM) drive control using Smart Bacterial Foraging Algorithm (SBFA) is presented. This method mimics the chemotactic behavior of the E. Coli bacteria for optimization. The proposed algorithm uses individual and social intelligences, so that it can search responses among local optimums of the problem adaptively. This method is used to tune the coefficients of a conventional Proportion–Integration (PI) speed controller for SRM drives with consideration of torque ripple reduction. This matter is done by applying the proposed algorithm to a multi-objective function including both speed error and torque ripple. This drive is implemented using a DSP-based (TMS320F2812) for an 8/6, 4-kW SRM. The simulation and experimental results confirm the improved performance of adjusted PI controller using SBFA in comparison with adjusted PI controller using standard BFA. Excellent dynamic performance, reduced torque ripple and current oscillation can be achieved when the coefficients of PI controller are optimized by using SBFA.     

磁极径向组合轴向磁场永磁电机转矩品质分析与优化设计

为了实现轴向磁场永磁(axial field permanent magnet,AFPM)电机大转矩惯量比、低转矩脉动等高品质转矩输出,提出磁极径向组合式的AFPM电机,采用传统表贴永磁与Halbach永磁阵列沿径向排列的转子结构。分析电机运行原理,推导电机功率尺寸方程;通过有限元方法对比分析该结构与传统表贴式结构的磁场分布、转矩、转矩脉动、反电动势及电感等电磁特性。在此基础上,基于响应面分析,构建多目标遗传优化设计方法,对电机转矩、齿槽转矩、反电动势和转矩脉动进行优化设计。最后,基于优选参数加工制造样机,并进行实验研究,验证了该电机结构的有效性和分析的正确性。     

Topology Optimization of Rotor Pole in Switched Reluctance Motor for Minimum Torque Ripple

Torque ripple is a major problem for switched reluctance motors, which may cause undesirable vibration and acoustic noise, especially at low speed. This paper presents an optimal topology structure of rotor for 8/6 pole switched reluctance motor by using the level set method. The nonlinear ferromagnetic material boundary of rotor pole is implicitly represented through an embedded level set function. This method is applied to obtaining the optimal distributions of material in the design domain for minimizing torque ripple and maximizing average torque. In the optimization objective function, the reluctivity of ferromagnetic material is selected as the design variable. The normal velocity is derived from sensitivity analysis, where the adjoint variable method is utilized. Two-dimensional finite element method is employed to calculate the electromagnetic parameters of this electric machine. Analysis results obtained from the transient simulation of electromagnetic field coupled with control circuit show that the torque ripple is reduced effectively by using the optimized rotor structure.     

基于新型定子极面结构的开关磁阻电机转矩脉动抑制研究

为抑制开关磁阻电机(SRM)转矩脉动,提出了一种新型定子极面结构,将传统均匀气隙结构改成两段式的非均匀气隙结构。以一台11 k W、1 000 r/min、12/8极SRM为例,通过建立二维场路耦合时步有限元模型,对此类结构进行了验证与优化。结果表明:此类结构能够在保证电机效率基本不变的情况下,有效抑制转矩脉动,为进一步提升SRM的设计与运行水平,提供了有益的参考。     

Multi-objective PID controller tuning for a FACTS-based damping stabilizer using Non-dominated Sorting Genetic Algorithm-II

Design of an optimal controller requires optimization of multiple performance measures that are often noncommensurable and competing with each other. Design of such a controller is indeed a multi-objective optimization problem. Non-Dominated Sorting in Genetic Algorithms-II (NSGA-II) is a popular non-domination based genetic algorithm for solving multi-objective optimization problems. This paper investigates the application of NSGA-II technique for the tuning of a Proportional Integral Derivate (PID) controller for a Flexible AC Transmission System (FACTS)-based stabilizer. The design objective is to improve the damping of power system when subjected to a disturbance with minimum control effort. The proposed technique is applied to generate Pareto set of global optimal solutions to the given multi-objective optimization problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Simulation results are presented and compared with a conventionally designed PID controller under various loading conditions and disturbances to show the effectiveness and robustness of the proposed approach. Finally, the proposed design approach is extended to a multi-machine power system to damp the modal oscillations with minimum control efforts.     

基于不同电机极对数对开关磁阻电机性能的影响研究

针对电机本体结构的改变可能会引起的电机性能的变化,采取实验研究法对两种额定参数相同的四相8/6极和四相16/12极相同功率不同结构的开关磁阻电机(SRM)进行实验研究。对两种不同极数结构SRM的绕组自感、互感、转矩大小及脉动影响和绕组电流等方面进行了电磁仿真分析。结果表明:8/6极开关磁阻电机与16/12极相比,前者具有各相绕组自感值大、互感值大、转矩大等优点,后者具有转矩脉动小的优点。此项研究对SRM电机本体设计和SRM的选型具有重要的指导意义。     

永磁同步电机低转矩脉动的稳健设计

在电机生产加工过程中引起的尺寸和形位公差、安装误差、材料属性偏差等噪声因子,造成了批量生产的电机间的转矩脉动特性分散,进而影响高精度永磁同步电机系统控制性能的一致性。为保证高精度场合用永磁同步电机的转矩脉动特性具有良好的稳健性,采用田口稳健设计方法,选取的噪声因子包括磁钢的周向安装位置、充磁角度、剩磁大小的误差、气隙加工误差、转子静态和动态偏心以及传感器安装误差等,通过优化磁钢、齿槽、气隙等电磁设计参数的名义尺寸,达到降低转矩脉动系数的均值和分散区间的目的。对比分析了稳健设计、正弦反电势设计和均匀气隙设计3种方案,结果表明,在相同噪声因子的影响下,与另两种设计方案相比,采用稳健设计方案,转矩脉动系数的均值和均方差显著降低。以转矩脉动系数作为优化目标,有效地满足了转矩脉动和平均转矩的多目标优化要求。     

基于多目标遗传算法的电机噪声优化

基于J-MAG软件建立了多目标优化有限元模型,将定转子冲片拓扑结构中影响电机性能的关键尺寸、位置进行参数化;采用软件内嵌的遗传优化算法,进行了电机单目标性能的优化,将转矩脉动、输出转矩、齿槽转矩作为本次电机优化的目标函数;分析了不同性能指标之间的关联性。通过各指标加权,综合考虑转矩脉动、输出转矩、齿槽转矩对电机振动噪声性能的影响,得出最优的设计方案;通过对比实验,验证了该优化方案的有效性。     

基于改进粒子群算法的开关磁阻电机本体优化

针对开关磁阻电机多变量、高非线性以及传统设计过程无法快速而准确获得最优方案的问题,提出一种基于Kriging模型和改进粒子群算法的参数优化策略。首先建立多目标优化模型,采用田口正交方法进行敏感性分析,依据灵敏度大小将优化变量分为两个子空间;其次为提高多目标粒子群算法的收敛速度和全局寻优精度,引入天牛须搜索算法中环境感应机制和遗传算法中交叉变异策略;最后建立Kriging模型,利用改进粒子群算法对两个子空间参数进行迭代寻优。实验结果表明,优化后的转矩脉动减少23%,平均转矩提高2.3%,在大幅度减少转矩脉动情况下保持了较大平均转矩。结论是改进的粒子群算法与Kriging模型相结合策略适用于开关磁阻电机优化过程,可显著提高优化效率,保证求解精度。     

An Improved Torque Sharing Function to Minimize Torque Ripple and Increase Average Torque for Switched Reluctance Motor Drives

Abstract—This article presents a novel torque ripple minimization approach based on the genetic algorithm (GA) for the switched reluctance motor (SRM) drives. The fitness function of the GA is designed on the basis of two main optimization criteria. The first optimization criteria; three objectives are defined to optimize commutation angles minimizing torque ripple and copper loss. The second optimization criteria; an objective is defined to eliminate the negative torque which decreases the average torque in SRM drives. The achievement of all objectives depends on the adjusting appropriate the commutation angles of the torque sharing functions (TSF) during the commutation period. All of conventional TSFs are dependent on three different commutation angles, namely turn-on, turn-off, and overlapping. Due to the nonlinear phase inductances of SRM, the delay of current rising and falling time are not unity in overlapping commutation region. To overcome the separation of the incoming and outgoing phase currents during the commutation region, rise angle, and fall angle are used instead of overlapping angle. GA is used to optimize the commutation angles of conventional (sinusoidal) TSF and improved (sinusoidal) TSF. At the same time, the elimination negative torque effects on torque ripple, average torque, and copper loss is investigated.     

基于有限元模型的SRM相电流模糊补偿控制

转矩脉动是开关磁阻电机(Switched Reluctance Motor,简称SRM)驱动系统中存在的一个突出问题。在SRM非线性电磁特性的有限元计算基础上,通过直接检测系统的输出转矩和模糊逻辑补偿控制器对SRM系统的相电流进行适当补偿,减小了转矩脉动成分。对一台四相、8/6极样机进行了仿真和实验。实验结果表明,通过对相电流的补偿控制能够使转矩脉动系数减小约50%,整个电机系统的平均输出转矩也得到了明显提高。     

少稀土非对称永磁电机的分层多目标优化分析

针对传统稀土永磁电机稀土材料用量高、永磁磁场不易调节问题,本文提出了一种少稀土非对称混合永磁电机,采用两种不同永磁材料励磁以降低稀土永磁材料的用量,混合永磁材料的非对称放置结构设计以改善电机的电感性能,提升电机弱磁升速性能。针对该电机相对复杂的结构,提出基于参数敏感度的分层多目标优化设计。对电机进行了参数化建模,建立包含转矩、转矩脉动、反凸极比和铁耗的多优化目标函数。通过参数敏感度分析对众多尺寸参数进行分层筛选,针对主敏感参数采取多目标遗传算法优化,而次敏感参数则采用响应面与多目标自适应优化结合的方法确定电机最优的尺寸参数,并对电机优化前后的电磁性能进行了分析比较,验证了优化方法的可行性,为该类复杂结构电机性能的改善提供了更加丰富的优化设计方法。