Purpose

In this work, a method to design a slotless permanent magnet machine (SPMM) based on the joint use of an analytical model and deterministic global optimization algorithms is addressed. The purpose of this study is to propose to include torque ripples as an extra constraint in the optimization phase involving de facto the study of a semi-infinite optimization problem.

Design/methodology/approach

Based on the use of a well-known analytical model describing the electromagnetic behavior of an SPMM, this analytical model has been supplemented by the calculus of the dynamic torque and its ripples to carry out a more accurate optimized sizing method of such an electromechanical converter. As a consequence, the calculated torque depends on a continuous variable, namely, the rotor angular position, resulting in the definition of a semi-infinite optimization problem. The way to solve this kind of semi-infinite problem by discretizing the rotor angular position by using a deterministic global optimization solver, that is to say COUENNE, via the AMPL modeling language is addressed.

Findings

In this study, the proposed approach is validated on some numerical tests based on the minimization of the magnet volume. Efficient global optimal solutions with torque ripples about 5% (instead of 30%) can be so obtained.

Research limitations/implications

The analytical model does not use results from the solution of two-dimensional field equations. A strong assumption is put forward to approximate the distribution of the magnetic flux density in the air gap of the SPMM.

Originality/value

The problem to design an SPMM can be efficiently formulated as a semi-infinite global optimization problem. This kind of optimization problems are hard to solve because they involve an infinity of constraints (coming from a constraint on the torque ripple). The authors show in this paper that by using analytical models, a discretization method and a deterministic global optimization code COUENNE, this problem is efficiently tackled. Some numerical results show that the deterministic global solution of the design can be reached even if the step of discretization is small.

中文翻译：

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一种设计无槽永磁电机的确定性半无限全局优化方法

目的

在这项工作中，提出了一种基于联合使用分析模型和确定性全局优化算法的无槽永磁电机 (SPMM) 设计方法。本研究的目的是建议将转矩脉动作为优化阶段的额外约束，包括事实上的半无限优化问题的研究。

设计/方法/方法

在使用描述 SPMM 电磁行为的众所周知的分析模型的基础上，该分析模型补充了动态扭矩及其纹波的演算，以执行此类机电转换器的更准确的优化选型方法。因此，计算出的扭矩取决于一个连续变量，即转子角位置，从而定义了一个半无限优化问题。解决了通过使用确定性全局优化求解器（即 COUENNE）通过 AMPL 建模语言离散化转子角位置来解决此类半无限问题的方法。

发现

在这项研究中，所提出的方法在一些基于磁体体积最小化的数值测试中得到了验证。这样可以获得具有约 5%（而不是 30%）的转矩脉动的高效全局最优解。

研究限制/影响

分析模型不使用二维场方程解的结果。提出了一个强假设来近似 SPMM 气隙中磁通密度的分布。

原创性/价值

设计 SPMM 的问题可以有效地表述为半无限全局优化问题。这种优化问题很难解决，因为它们涉及无限的约束（来自对转矩脉动的约束）。作者在本文中表明，通过使用分析模型、离散化方法和确定性全局优化代码 COUENNE，可以有效地解决这个问题。一些数值结果表明，即使离散化步长很小，也可以达到设计的确定性全局解。