Brushing Up on the Urbanek Black Box Arc Model

We reconsider the black box model by Urbanek of electric-arc in air-blast circuit breakers or in circuit breakers characterized by an electro-negative gas (e.g., SF₆) as quenching medium. It has the unique characteristic to account for the dielectric breakdown that possibly reignites the arc. We show some of its main features that have been almost hidden from the first publication of the model in the literature. The conductance in the Urbanek model plays two roles: 1) it effectively represents the conductance of the burning arc when positive and 2) it is a thermodynamic indicator when negative. This thermodynamic indicator is used to eventually trigger a restrike of the arc. We show that this switching behavior can be formally analyzed by considering the model as an hybrid dynamical system. In this paper, we reconsider it and show its main dynamic properties through some case studies.