Multi-objective optimization of a variable flux reluctance machine for high-torque operations

This paper proposes a new multi-objective optimization approach to investigate the feasibility of 12/10 variable flux reluctance machines for heavy-duty applications requiring a high-torque generation. Eight parameters describing the geometry of the variable flux reluctance machine are optimized by the tournament selection-based genetic algorithm aiming at the minimum torque ripple, maximum torque density, and efficiency. A 2-D magnetostatic finite element method model is coupled with the nonlinear single-valued magnetization curve of the soft-magnetic material to calculate the objective function. Boundaries of the optimization variables are determined by scaling an existing design. Two constraints are introduced for the winding temperature and developed torque to reduce the number of optimization variables. The torque constraint, 500 Nm, is achieved by selecting a suitable stack length while the constraint of 100 °C maximum winding temperature is satisfied by the applied current density, which a 3-D analytical steady-state thermal model calculates. The magnetic vector hysteresis property of the soft-magnetic material is investigated at the end of the optimization to improve the estimation of torque and efficiency. The optimal variable flux reluctance machine exhibits 20.4 Nm/L torque density, 5.2% torque ripple, and 92.8% efficiency at the base speed of 1200 rpm.