Abstract One of the requirements for the electric machine designer is to provide an optimal back-EMF waveform in a high-performance application such as electric vehicles (EV) or hybrid EVs (HEV) systems. This paper presents a design technique for the shaping of back-EMF waveforms in brushless permanent magnet (PM) AC and DC machines. At first, back-EMF waveforms are calculated by an analytical model based on the subdomain field model and the complex permeance function. The finite element and experimental results are used for the verification of the analytical model. Secondarily, the heuristic optimization algorithm is applied to the analytical model in order to search for optimal solutions where the objective function is composed of harmonics in target back-EMF. As a result, the optimal back-EMF waveform can be traced by matching the odd harmonics of the design candidate with those of the target waveform. Also, a detailed investigation of the winding factor is carried out to provide the key design techniques regarding the shape of back-EMF.

中文翻译：

---

一种在无刷交流和直流电机中使用启发式优化和绕组因子形成反电动势的设计技术

摘要 电机设计人员的要求之一是在高性能应用中提供最佳反电动势波形，例如电动汽车 (EV) 或混合动力电动汽车 (HEV) 系统。本文介绍了一种在无刷永磁 (PM) 交流和直流电机中形成反电动势波形的设计技术。首先，通过基于子域场模型和复磁导函数的解析模型计算反电动势波形。有限元和实验结果用于验证分析模型。其次，将启发式优化算法应用于解析模型，以搜索目标函数由目标反电动势中的谐波组成的最优解。因此，通过将设计候选的奇次谐波与目标波形的奇次谐波相匹配，可以追踪最佳反电动势波形。此外，还对绕组系数进行了详细研究，以提供有关反电动势形状的关键设计技术。