Due to the complex rotor design of reluctance synchronous machines, a finite element analysis is essential for the accurate calculation of machine relevant performance objectives. Reluctance synchronous machines tend to have a large torque ripple, if this objective is not considered during the machine design. This necessitates a large number of simulation steps, resulting in a high computational burden and a long simulation time per design evaluation. Therefore, an efficient optimization algorithm is required. This paper proposes a complete framework for single-objective machine design optimization using Gaussian process regression and Bayesian optimization. Focusing on reluctance synchronous machine design, different kernel functions (squared exponential, Matern, rational quadratic) and hyperparameter configurations ´ are assessed for regression accuracy of the optimization objectives mean torque, torque ripple, and power factor. The impact of noise in the input data on the regression results is also investigated. Bayesian optimization with the infill criterion Expected Improvement is finally used to perform machine design optimization for 18 design variables. Bayesian optimization outperforms the classical algorithms such as genetic or particle swarm algorithms. It results in a faster design optimization, even for such a high number of design variables.

During the design of electrical machines, multiple performance objectives need to considered. Although stochastic optimization algorithms are extensively employed for this purpose, a primary drawback is the time-consuming and substantial number of design evaluations. Bayesian optimization (BO) presents an alternative that can address multi-objective optimization in particular for objective functions which are expensive to evaluate. Probabilistic surrogate models based on Gaussian process regression (GPR) form its basis. The high accuracy of Gaussian processes and their uncertainty estimation render Bayesian optimization extremely efficient and effective. Nevertheless, Bayesian optimization is hardly used in the field of electric machine design. Consequently, this study explores, analyses and evaluates the application of global multi-objective Bayesian optimization for machine design. Employing four distinct Bayesian acquisition functions, the study conducts a three-objective design optimization of a reluctance synchronous machine characterized by 14 design variables. A comprehensive comparison with the most common NSGA-II reveals that significantly superior outcomes are achievable within a considerably shorter time.

Reluctance synchronous machines (RSMs) are characterized by high nonlinearities, cross-coupling effects and high torque ripple. This paper presents a nonlinear machine model of three-phase RSMs based on a nonlinear electromagnetic model including iron losses and a novel (extended) torque equation. The γ-component is used to consider asymmetries. The novel torque model provides a precise approximation of the machine’s torque ripple. Iron losses are covered as well. The nonlinear machine model with extended torque equation is implemented based on current, angle and speed dependent flux linkage and iron loss maps. Finally, the nonlinear and extended machine model is validated by comparing with state-of-the-art results obtained by finite-element analysis (FEA).