Asymptotic methods for calculating electric arc model parameters

A new method for calculating the parameters of electric arc models for power circuit breaker is developed. The methodology consists in the optimization of the theoretical arc voltage curve, as a function of a set of parameters, with respect to experimental data. Since the solution of the equation for the electric arc model cannot be obtained in general form, then, the theoretical arc voltage is an asymptotic solution obtained for one or several time-ranges. A case of the irregular behavior of the electric arc is analyzed. The developed methods are applied to obtain an improved arc model for a SF6 power circuit breaker previously published in the literature. The new model has a compact form and exhibits a good correlation between the measured and calculated voltage curves.