Multi-objective optimal design of an outer-rotor permanent-magnet synchronous generator for direct-drive wind energy system

This paper presents a multi-objective optimal design methodology for an outer-rotor Permanent Magnet Synchronous Generator (PMSG) intended for wind energy applications. The optimization process simultaneously minimizes the generator’s weight and total power losses, while ensuring compliance with constraints related to magnetic saturation, rated electromagnetic torque, and the maximum open-circuit Electromotive Force (EMF) generated by the permanent magnets. An analytical model of the PMSG, derived from Maxwell’s equations using the separation of variables method, is developed to express both the objective functions and the design constraints in terms of the generator’s geometric dimensions and parameters. The resulting nonlinear multi-objective optimization problem is solved using an enhanced Non-dominated Sorting Genetic Algorithm II (NSGA-II), incorporating a novel hybrid crossover strategy proposed in this study. This enhancement enables the generation of a high-quality Pareto front with well-distributed optimal solutions. The effectiveness of the proposed approach is demonstrated through the optimal design of a 10 kW outer-rotor PMSG, which is subsequently validated using Finite Element Method (FEM). The results confirm the efficiency, robustness, and applicability of the proposed optimization framework for high-performance wind energy generators.