Solving Maxwell Equations in Hybrid Electrical Vehicle to Optimal Design by Multi-Objective Optimization Algorithms

Hybrid Electrical Vehicles (HEVs) have three magnetic field sources: armature winding currents; permanent magnets; and field winding current. To initiate the investigation, the magnetic field distributions due to those sources are obtained. First, Maxwell’s equations need to be solved. Then, the machine is analyzed and the operational indices such as unbalanced magnetic force (UMF) in x- and y direction and instantaneous torque are calculated by using the magnetic flux density distribution. Next, various magnetization patterns, which are presented based on Fourier series, are considered to investigate their influences on the performance of the machine. It is assumed the volume of the machine is determined thanks to thermal considerations. As a result, it is constant so it is maximized average torque instead of torque per volume ratio. After that, the average and ripple of the instantaneous torque are expressed in terms of pole arc to pole pitch ratio by using curve fitting. Finally, the optimal value of average torque and torque ripple are also computed by multi-objective optimization algorithms.