Energy Preserving Methods and Torque Computation From Energy Balance in Electrical Machine Simulations

Abstract

Finite element analysis for the simulation of magnetic fields in electrical machines leads to an index-1 differential algebraic equation (as opposed to a conventional ordinary differential equation), because the electrical conductivity can be zero in certain regions. First, we construct a differential-algebraic equation-compatible time integration scheme which is energy-balanced, meaning that in a linear system the input, stored and lost powers sum exactly to zero. Second, we use a method based on the energy balance to compute torque. We show that the energy balance method approaches the virtual work principle applied at remeshing layer as the time step is refined. A similar result holds also if the rotation of the rotor is implemented by Nitsche’s method, which is an instance of so-called mortar methods.