Subdomain Reduction by Dirichlet-to-Neumann Mappings in Time-Domain Electrical Machine Modeling

Time-domain finite element methods (FEM) are widely used for numerical solution of boundary value problems (BVP) arising from rotating electrical machines. Typically, the equations corresponding to discretizations of the rotor and the stator are solved simultaneously every time step, together with equations that couple them during rotation. We present a method for reformulating rotor and stator subproblems in time-domain BVPs into implicit Neumann boundary conditions determined by spectral Dirichlet-to-Neumann mappings. Thus, solution of the FE equations for the reformulated subproblem is no longer necessary every time step and significant reduction in solution time is often achieved. To demonstrate the effectiveness of the method, we discuss its application in two test cases. In the first test case, reformulated stator subproblem in a BVP for a squirrel-cage induction machine is coupled to an FE model of the rotor. In the second test case, both subproblems in a BVP for a synchronous reluctance motor are reformulated. Results are compared with those obtained with full two-dimensional transient FE analysis.