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The finite-element analysis for the simulation of magnetic fields in electrical machines leads to an index-1 differential-algebraic equation (DAE) (as opposed to a conventional ordinary differential equation), because the electrical conductivity can be zero in certain regions. First, we construct a DAE-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 also holds if the rotation of the rotor is implemented by Nitsche’s method, which is an instance of the so-called mortar methods. [ABSTRACT FROM PUBLISHER]

Conservation of power in time-stepping finite-element (FE) simulation of electrical machines is studied. We propose a method for accurately obtaining the instantaneous time derivative of the FE solution, from which the instantaneous eddy-current losses and the rate-of-change of the magnetic field energy are calculated. The method is shown to be consistent with different time-integration schemes, unlike the typically used backward-difference (BWD) approximation, which is only accurate if the BWD method is also used for the time integration. We first formulate the FE equations for a locked-rotor induction machine as a differential-algebraic equation (DAE) system. An approach called the collocation method is then used to derive the BWD, trapezoidal (TR), and implicit midpoint integration rules in order to show how these methods approximate the solution in time. We then differentiate the constraint equations of the DAE to form a system from which the time derivative of the solution can be solved. The obtained derivative is shown to satisfy the power balance exactly in the collocation points. In case of the TR rule, the losses calculated with the proposed method are shown to be less sensitive to the time-step length than ones obtained with the BWD approximation for the time derivatives. The collocation approach also allows studying the power balance continuously during the time step. [ABSTRACT FROM PUBLISHER]