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

Abstract

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.

An Analytical Determination of the Magnetic Field in a System of Finite-Length Ribbon Busbars

“…In the course of teaching the electromagnetic field theory, challenges often arise that require extensive calculations, not only in numerically solving problems [1][2][3][4][5][6][7][8][9] but also in their analytical resolution-involving integration, differentiation, rearrangement, and condensation of expressions, as well as seeking special solutions for terminal values of certain parameters or terminal domains [10][11][12][13][14][15]. The swift visualization of the obtained solutions is equally important, particularly spatial visualization, which enables us to understand the geometrical changes in a given configuration, the values of electrical parameters (current, voltage, external electric and magnetic fields, frequency, etc.…”

Formulas calculating the reactance of tubular busbars and their derivation in primary electrical connection schemes

“…An interesting vector synthesis method was proposed in reference 17 to solve the stray inductance of the laminated busbars connected to capacitors with switching power modules. In reference 18 a novel numerical approach based on the fast Fourier transform and the convolution theorem was proposed to model the rectangular conductors of the busbar system. In reference 19 a novel numerical technique, i.e., the Proper Generalized Decomposition, for the calculation of dc and ac internal inductances of rectangular conductors was introduced.…”