Fast Numerical Model of Power Busbar Conductors Through the FFT and the Convolution Theorem

Skin and proximity effects can cause a non-uniform current distribution in the electrical conductors used in alternating current (ac) busbar systems, which increases resistance, decreases internal inductance, and causes asymmetries in the electromagnetic fields and forces. As no explicit solution for the ac resistance or the ac internal inductance of a rectangular conductor has been found, numerical methods are needed to obtain the distribution of the currents inside the busbars. In this paper, a novel numerical approach, based on the fast Fourier transform (FFT) and the convolution theorem, is proposed to model the rectangular conductors of the busbar system, based on the subdivision of the conductor in filamentary subconductors. This technique is know to lead to a dense, huge inductance matrix, that must be multiplied by the current vector, which limits its practical application. The proposed method replaces this matrix-vector multiplication with a simple element-wise vector product in the spatial frequency domain. The FFT speed makes the proposed method very fast and easy to apply. This approach is theoretically explained and applied to an industrial busbar system.