Modeling and Simulations of Ferroresonance by Using BDF/NDF Numerical Methods

The predictive power of transient ferroresonance simulations depends mainly on the accuracy and fidelity of the power transformer model used for simulating complete systems involving all relevant network components. This paper considers three ways of transformer iron-core modeling relevant for ferroresonance simulations that are presented in detail. The presented transformer models are suitable for the state-space form of differential equation systems that describe the ferroresonance effect. Before solving the obtained differential equation systems, their numerical eigenvalues were analyzed in detail. This eigenvalue analysis has revealed a very stiff nature of the obtained equation systems. The obtained equation systems are solved by using a A- and L-stable numerical differentiation formulas (NDF) numerical technique, with the aim of suppressing undesired numerical oscillations. The obtained numerical results are verified by comparison against the available experimental results. The presented analysis shows that the suggested transformer model based on a hysteretic core inductor provides the most accurate results in terms of voltage and current waveforms and their peak values during the steady-state and transient ferroresonance. The analyzed transformer core models can be implemented in the existing Electromagnetic Transients Program-type simulation tools by using a combination of the trapezoidal and proposed NDF2 method.