Harmonic balance applied to a 2D nonlinear finite-element magnetic model with motion and circuit coupling

In this work, the harmonic balance approach is applied to a 2D nonlinear finite-element magnetic model with motion, coupled to a nonlinear circuit. The case study comprises a six-pole three-phase surface-mounted permanent magnet generator connected to a six-pulse full-wave diode bridge rectifier. Simulations are performed at fixed generator speed in two operating cases: with an open-circuit DC bus and supplying a load resistance. Both time stepping and harmonic balance approaches are deeply discussed focusing on the model under study, along with relevant implementation details. Harmonic balance results are compared with benchmark time stepping simulations in terms of voltage and current waveforms, progressively expanding the harmonic spectrum. The computational cost of the two approaches is reported as well. Simulation accuracy is satisfying with regard to time stepping benchmark results: relative errors on total harmonic distortion and global root-mean-square values are lower than 3% and 1%, respectively. However, the time stepping approach outperforms the harmonic balance one, due to the relatively short initial transient of the chosen case study. Further improvements on practical implementation are needed to exploit the potentialities of harmonic balance technique.