Simulation of low-frequency electromagnetic fields and electric circuits

Nowadays, electrical circuits and machines, e.g. motors, actuators, generators etc., are designed using computer simulations (virtual prototyping). Thus designers need reliable and efficient software that is based on robust numerical methods. The development of these methods is our focus. In particular for field/circuit coupled problems.

Often, simplified network models can simulate devices sufficiently accurately as electrical circuits (see Figure). However, the problem of increasing frequencies and decreasing size forces designers to account for wave propagation effects, eddy-currents, ferromagnetic saturation and hysteresis. Order-reduced equivalent models that are embedded in an electrical circuit can represent some effects. However, the representation of field-dependent nonlinearities and hysteresis effects is not straightforward. In those cases 3D models that account for spatially distributed effects have to be used.

The simulation becomes troublesome when a fine resolution in time domain is required. This occurs when simulating an electrical drive in which the machine requires 10 periods of 50 Hz to reach nominal speed while the switching of the Insulated Gate Bipolar Transistors in the frequency converter switches at 20 kHz, necessitating time steps in the order of microseconds. Since the field model consists typically of a few million degrees of freedom, all those unknowns have to be solved in every time step. Fortunately, the relevant time constants in electrical-energy converter are in the range of 50 Hz. Hence the field model does not have to be time-stepped at the same level of accuracy as the circuit model, in which fast switches are present. The use of adaptive multirate time-integration schemes can reduce the numerical complexity of the problem substantially (e.g. cosimulation).



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