Quadratic Polynomial Form of Electric Arc Furnace Equation

Abstract

A closed form solution to a differential equation used as the deterministic AC electric arc model exists only for some arc parameter values. The paper shows that periodic solutions for the other parameter values can be found by combining the harmonic balance method (HBM) and a continuation method. In order to avoid problems occurring when a large number of harmonics is required or the system contains strong nonlinearities, a transformation of the original equation has been proposed. Nonlinearities present in the equation have been transformed into purely polynomial quadratic terms. It facilitates application of the classical HBM and allows to follow periodic solutions of the arc equation when its parameters are varied. It also enables better understanding of the phenomena described by the equation and makes easier the extension of the arc model in order to cover the time-varying character of the arc waveforms. Theoretical considerations have been illustrated by a simulation experiment.