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基于遗传算法的永磁无刷直流电机优化设计
A Systematic Approach to Optimized Design of PM BLDC with Genetic Algorithm
【作者】 杨剑；
【导师】 朱莉；
【作者基本信息】 上海交通大学 ， 电气工程， 2016， 硕士
【摘要】 本文采用遗传算法中的差分进化算法,配合多目标优化方法,在种群迭代时,通过引入精英保留策略和提出随机目标函数空间内按优化目标函数排序的多样化策略来保证Pareto最优解集的继承性和多样性,由此设计出基于多目标优化的差分进化算法;然后再从电磁场数值分析理论出发,对表面式永磁无刷直流电机内部气隙磁场进行解析计算,通过电机模型的适当简化,建立描述表面式永磁无刷直流电机内部磁场的数学解析模型,并结合边界条件求解出其解析表达式。本文提出的基于遗传算法的永磁电机优化设计可分为四个阶段:(1)通过将多目标优化理论和基本差分进化算法模型结合起来,建立针对多个优化目标优化设计的差分进化遗传算法数学模型。(2)引入矢量磁位作为辅助函数,通过傅里叶级数法在极坐标系中建立表面式永磁无刷直流电机的空载磁场解析模型——偏微分方程,然后再结合边界条件求解描述磁场唯一状态的解析表达式。(3)通过上一步求得的空载气隙磁场的解析表达式,推导空载情况下的相绕组感应电动势。(4)根据第一步建立的差分优化遗传算法数学模型和第二步到第五步建立的表面磁钢永磁无刷直流电机的解析数学模型,设计针对表面磁钢永磁无刷直流电机的基于约束的多目标优化设计遗传算法。应用群智能启发式优化算法结合解析法电机模型进行电机设计是电机优化设计领域的一个热点,由于本文提出的基于多目标差分进化算法的表面磁钢永磁电机优化设计方案得出的是一组最优解,故而能够提供多样化的选择方案,可根据工程实际选择;而且该方法对于电机设计具有一定的普适性,故而具有较为广泛的运用。
【Abstract】 From the basic differential evolution algorithm and multi-objective optimization theory,this thesis presents elitist archive and sorting tactic during filter of Pareto optimal solution and developed a multi-objective differential evolution algorithm.Then systematically analysis the instantaneous magnetic field distribution in the air gap region of the surface mounted permanent magnet brushless dc motor base on electromagnetic field theory,establishes the mathematic analytical model of the instantaneous magnetic field distribution in air gap in surface PM BLDC with some hypotheses commonly used in analytical models,and derivate the solutions with boundary condition.This thesis contains the following four aspects.(1)Establishment of basic differential evolution algorithm mathematic model and basic summary of multi-objective optimization theory, and them based on both above to developed multi-objective differential evolution algorithm.(2)Introduce the scalar magnetic potential as auxiliary function,established the mathematical analytical model of open-circuit field for surface PM BLDC in polar coordinate system with Fourier series,and then derivate the solutions with boundary condition.(3)Established the mathematical analytical model of armature-reaction field with Laplace equations of vector magnetic potential in air gap region in surface PM BLDC,and derivate the solutions.(4)Ignoring winding slot leakage inductance and end leakage inductance,derivate the back electromotive force of surface PM BLDC phase winding.(5)From the mathematical analytical model of multi-objective differential evolution algorithm,established the optimization design program of surface PM BLDC.Design the permanent magnet motors with swarm intelligence algorithm has been a forward research topic in the study of electrical machine.Since a Pareto optimal set is obtained in the design of surface PM BLDC based on multi-objective differential evolution algorithm in this thesis,so diversify design can be choose based on engineering practice.And the program presents in this thesis is universality for electrical machine design,so it can be widely promote in area of engineering optimization.