Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors

Abstract

[EN] AC lines of industrial busbar systems are usually built using conductors with rectangular cross sections, where each phase can have several parallel conductors to carry high currents. The current density in a rectangular conductor, under sinusoidal conditions, is not uniform. It depends on the frequency, on the conductor shape, and on the distance between conductors, due to the skin effect and to proximity effects. Contrary to circular conductors, there are not closed analytical formulas for obtaining the frequency-dependent impedance of conductors with rectangular cross-section. It is necessary to resort to numerical simulations to obtain the resistance and the inductance of the phases, one for each desired frequency and also for each distance between the phases' conductors. On the contrary, the use of the parametric proper generalized decomposition (PGD) allows to obtain the frequency-dependent impedance of an AC line for a wide range of frequencies and distances between the phases' conductors by solving a single simulation in a 4D domain (spatial coordinates x and y, the frequency and the separation between conductors). In this way, a general "virtual chart" solution is obtained, which contains the solution for any frequency and for any separation of the conductors, and stores it in a compact separated representations form, which can be easily embedded on a more general software for the design of electrical installations. The approach presented in this work for rectangular conductors can be easily extended to conductors with an arbitrary shape.