Analytical Optimization of BLDC Motor Magnetic Parameters for Electric Vehicles Using the Whale Optimization Algorithm: PSO Comparison and Cost Analysis

Abstract

In this study, the magnetic design parameters of brushless DC (BLDC) motors for electric vehicle applications remanent flux density (Br), magnet coverage ratio (α), and air-gap length (g) are optimized using an analytical framework with the Whale Optimization Algorithm (WOA) and Particle Swarm Optimization (PSO), within a search space defined by manufacturing and material feasibility limits reported in the literature. For each objective function (total harmonic distortion (THD), electromagnetic torque, and back electromotive force (back-EMF)), 100 independent runs are performed and evaluated using mean, variance, and standard deviation, supported by the Wilcoxon Signed-Rank test. The THD objective possesses a genuine interior optimum, where PSO converges more stably (variance 1.0420×10⁻⁵) while WOA shows stronger exploration (variance 3.2643×10⁻⁵); the Wilcoxon test (p = 1.86×10⁻⁹) confirms a statistically significant difference in favour of WOA. For torque and back-EMF, which are monotonic functions of the air-gap flux density, both algorithms converge to the same boundary-constrained optimum. From a practical perspective, the optimized parameters improve efficiency by about 2.5% and reduce NdFeB magnet usage by approximately 18% (~101 g), corresponding to an estimated saving of about $25 per motor.