Analytical approximation of dynamic hysteresis loop and its application to a series ferroresonant circuit

New expressions for the dynamic hysteresis loop and for hysteresis losses are proposed. The loop is first represented by a general equation which leads to three simplified forms. One of these is particularly useful for the analysis of nonlinear circuits, because of its mathematical formulation. The characteristic polynomials which are involved in these expressions can be deduced from the experimental points on the hysteresis loop. This analysis is applied to the series ferroresonant circuit. Conditions for the ferroresonant jump and for the stability of the equilibrium points in the steady state are established in terms of the circuit parameters. The equation for the hysteresis losses is applied to molybdenum-Permalloy 4¿79.