A Study of A-C Arc Behavior Near Current Zero by Means or Mathematical Models

The differential equations of two idealized models of the arc column proposed by previous writers have been combined into a composite model whose behavior approximates that of actual a-c power arcs in circuit breakers and fuses near a critical current zero for arc extinction. An extensive series of curves are presented showing, for this model, the variation with time just before and after current zero of arc resistance, arc current, arc power, and dielectric strength of the arc space under certain simplifying assumptions for three different forms of circuit recovery voltage. These quantities are expressed in terms of prior arc current and voltage and of a characteristic ``time constant´´ which depends upon the physical conditions imposed upon the arc. The model curves are compared with oscillographic measurements. The usefulness of such models in aiding the understanding of arc behavior in circuit interrupters and in correlating and making extrapolations from interrupting data is pointed out.