Quadratized model of nonlinear saturable-core inductor for time-domain simulation

This paper presents the nonlinear, time-domain model of a saturable-core inductor. The model is capable of accommodating high-order nonlinearities by representing the current-flux characteristic of the inductor by an analytical (closed form) polynomial function of high degree. An automated procedure is developed to transform the highly nonlinear model to a fully-equivalent quadratic model, without introducing any approximations. Subsequently, using the quadratic equivalent model, the algebraic companion form is developed based on the trapezoidal and the quadratic integration rules. The presented model can be utilized in transformer or surge arrester modeling to capture nonlinear phenomena that may occur, as for example, during energization of transformers. Such condition may appear during cold load pick-up after severe disturbances and transients in distribution feeders.