A light Darwin implementation of Maxwell’s equations to quantify resistive, inductive, and capacitive couplings in windings

High operating frequency is an enabler of high key performance indicators, such as increased power density, in electrical machines. The latter enhances the cross-coupling of resistive–inductive–capacitive phenomena in windings, which may lead to significant loss in performance and reliability. The full-wave Maxwell’s equations can be employed to characterize this coupling. To address the frequency instability that arises as a result, a simplification known as the Darwin formulation can be employed, where the wave propagation effects are neglected. Still, this modification is prone to ill-conditioned systems that necessitate intricate pre-conditioning and gauging steps. To overcome these limitations, a fast 2D formulation is derived, which preserves the current continuity conservation along the model depth. This implementation is validated experimentally on a laboratory-scale medium-frequency transformer. The computed impedances for the open- and short-circuit modes of the transformer are validated using measurements and compared with the multi-conductor transmission line model that is widely adopted for the analysis mentioned above. The developed formulation demonstrates a high accuracy and outstanding frequency stability in a wide frequency range, becoming an efficient and computationally light method to investigate the interconnected resistive, inductive, and capacitive effects in windings.