Newton–Raphson approach for the analysis of ferroresonant circuits

Abstract

During switching operations in a power system there is a possibility that an unloaded transformer may be energised by a voltage source through an intervening capacitor. The capacitor could be a stray capacitance between an energised transmission line and the transformer terminals, a capacitance between the open contacts of a circuit breaker or a capacitive divider of a capacitive voltage transformer. The series connection of an alternating voltage source, a linear capacitor and a saturable inductor is generally known as a ferroresonant circuit. Determination of the steady-state periodic responses of a ferroresonant circuit is described. The responses were obtained using a time-domain Newton-Raphson procedure and also using a hybrid technique. A continuation procedure is described for determining the multiple solutions of the ferroresonant circuit and the bifurcating solution branches.