Disruptive innovations in electrical machine design optimization are observed in this paper, motivated by emerging trends. Improvements in mathematics and computer science enable more detailed optimization scenarios that cover evermore aspects of physics. In the past, electrical machine design was equivalent to investigating the electromagnetic performance. Nowadays, thermal, rotor dynamics, power electronics, and control aspects are included. The material and engineering science have introduced new dimensions on the optimization process and impact of manufacturing, and unavoidable tolerances should be considered. Consequently, multifaceted scenarios are analyzed and improvements in numerous fields take effect. This paper is a reference for both academics and practicing engineers regarding recent developments and future trends. It comprises the definition of optimization scenarios regarding geometry specification and goal setting. Moreover, a materials-based perspective and techniques for solving optimization problems are included. Finally, a collection of examples from the literature is presented and two particular scenarios are illustrated in detail.

Modern Electrical Machine Design Optimization: Techniques, Trends, and Best Practices

This paper proposes a comprehensive framework for multiobjective design optimization of switched reluctance motors (SRMs) based on a combination of the design of experiments and particle swarm optimization (PSO) approaches. First, the definitive screening design was employed to perform sensitivity analyses to identify significant design variables without bias of interaction effects between design variables. Next, optimal third-order response surface (RS) models were constructed based on the Audze-Eglais Latin hypercube design using the selected significant design variables. The constructed optimal RS models consist of only significant regression terms, which were selected by using PSO. Then, a PSO-based multiobjective optimization coupled with the constructed RS models, instead of the finite-element analysis, was performed to generate the Pareto front with a significantly reduced computational cost. A sample SRM design with multiple optimization objectives, i.e., maximizing torque per active mass, maximizing efficiency, and minimizing torque ripple, was conducted to verify the effectiveness of the proposed optimal design framework.

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Multiobjective Optimization of Switched ReluctanceMotors Based on Design of Experiments and ParticleSwarm Optimization

The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape optimization problem is formulated by introducing a tracking-type cost functional to match a desired rotation pattern. The magnetic field generated by permanent magnets is modeled by a nonlinear partial differential equation of magnetostatics. The shape sensitivity analysis is rigorously performed for the nonlinear problem by means of a new shape-Lagrangian formulation adapted to nonlinear problems.

Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics

Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape under investigation, as well as on intrinsic shape metrics. From a numerical point of view, domain integral forms of shape derivatives seem promising, which rather require an outer metric on the domain surrounding the shape boundary. This paper tries to harmonize both points of view by employing a Steklov-Poincar\'e type intrinsic metric, which is derived from an outer metric. Based on this metric, efficient shape optimization algorithms are proposed, which also reduce the analytical labor, so far involved in the derivation of shape derivatives.

Efficient PDE constrained shape optimization based on Steklov-Poincar\'e type metrics

Shape optimization of an electric motor subject to nonlinear magnetostatics

We aim at finding an optimal design for an interior permanent magnet electric motor by means of a sensitivity-based topology optimization method. The gradient-based ON/OFF method has been successfully applied to optimization problems of this form. We show that this method can be improved by considering the mathematical concept of topological derivatives (TDs). TDs for optimization problems constrained by linear partial differential equations (PDEs) are well understood, whereas little is known about TDs in combination with nonlinear PDE constraints. We derive the TD for an optimization problem constrained by the equation of nonlinear 2-D magnetostatics, illustrate its advantages over the sensitivities used in the ON/OFF method, and show numerical results for the optimization of an interior permanent magnet electric motor obtained by a level-set algorithm, which is based on the TD.

Topology Optimization of Electric Motor Using Topological Derivative for Nonlinear Magnetostatics

A multi-material topology optimization algorithm based on the topological derivative

In this paper, we present a framework for automated shape differentiation in the finite element software NGSolve. Our approach combines the mathematical Lagrangian approach for differentiating PDE-constrained shape functions with the automated differentiation capabilities of NGSolve. The user can decide which degree of automatisation is required, thus allowing for either a more custom-like or black-box–like behaviour of the software. We discuss the automatic generation of first- and second-order shape derivatives for unconstrained model problems as well as for more realistic problems that are constrained by different types of partial differential equations. We consider linear as well as nonlinear problems and also problems which are posed on surfaces. In numerical experiments, we verify the accuracy of the computed derivatives via a Taylor test. Finally, we present first- and second-order shape optimisation algorithms and illustrate them for several numerical optimisation examples ranging from nonlinear elasticity to Maxwell’s equations.

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Peter Gangl

Papers

Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics

Shape optimization of an electric motor subject to nonlinear magnetostatics

Topology Optimization of Electric Motor Using Topological Derivative for Nonlinear Magnetostatics

A multi-material topology optimization algorithm based on the topological derivative

Fully and semi-automated shape differentiation in NGSolve