Estimation of dielectric recovery of fast opening commutating switches after short time arcs

Ultra-fast opening mechanical switches are proposed as key components for medium-voltage DC circuit breakers, enabling rapid fault current commutation to a parallel capacitor. After arc extinction in the commutating switch, the gas-filled gap is exposed to rapidly rising transient voltages, and the success of commutation depends on fast dielectric recovery. This paper presents a method to estimate the arc temperature at the time of arc extinction and its subsequent decay after full current interruption in a fast-elongating arc with short arcing times. A modified Lowke model, accounting for arc thermal inertia, is used to track the evolution of arc temperature and radius from arc initiation up to arc extinction. Post-extinction gas temperature decay is modeled using heat transfer in a simplified cylindrical geometry. Finally, the dielectric breakdown voltage of the gap is estimated via critical field theory, accounting for temperature-dependent breakdown fields.