Perturbation Finite Element Method for Efficient Copper Losses Calculation in Switched Reluctance Machines

Copper losses dissipated in the windings of electric machines are the sum of classical ohmic dc losses and additional ac eddy current losses. In fact, the level of eddy current losses is strongly correlated with the manner of disposition of coil conductors in machine slots. Then, to improve the efficiency in electric machines, the selection of an optimal winding configuration becomes substantial. Since eddy current losses derive from the strong electromagnetic coupling between current density and time-dependent magnetic field, which cannot be solved easily, numerical analyses, such as particularly the one using the finite element (FE) method, are often used. As for the FE modeling, it can employ moving band technique to perform the rotor motion and Newton-Raphson iterations to deal with the nonlinear behavior of magnetic circuits. It leads then to a substantial computational time that hinders any process of conception or optimization of winding geometries. To overcome this issue, a 2-D FE model reduction based on the perturbation method is proposed. It starts from one approximate FE solution of a simplified complete machine modeling to find fast but accurate solutions in slots subdomains when any variation of geometrical or physical data occurs. It allows adapting nonconforming meshes and provides clear advantages in repetitive analyses when we search the optimized winding configuration for a given number of turns.