Hysteresis model in transient simulation algorithm based on BDF numerical method

This paper describes the way of implementing the hysteresis model in a transient simulation algorithm. The hysteresis model is not dependent on an integration step, thus it can be incorporated in a state-space form of a stiff differential equations system. The developed algorithm is based on a i-stable backward differentiation formulas-BDF numerical method. This method suppresses numerical oscillations in transient calculations. In addition, the algorithm, when used, eliminates the negative effect of "overshooting". Several simple test cases are demonstrated to show improvements and its suitability for simulation of low-frequency transformer transients such as inrush currents and ferroresonance. The realized hysteresis model can be incorporated in the EMTP-ATP by using the simplest combination of existing trapezoidal and proposed BDF method of order 1, known as theta method.