Simulation of three-phase transformer inrush currents by using backward and numerical differentiation formulae

• We examine numerical methods suitable for the simulation of extremely stiff systems.
• The BDF/NDF methods completely damp out unwanted numerical oscillations.
• The proposed methods have excellent properties of accuracy and stability.
• We suggest implementation of the hybrid method within the EMTP-type programs.

This paper presents a simplified model of a three-phase transformer developed in the state-space form using the linear graph theory. The algorithm for generating the coefficient matrixes of the state-space equation is described. Stiff detection procedures of differential equation systems that describe the three-phase transformer inrush current transients are explained. It is shown that the time-domain transient response of three-phase transformers mathematically describes extremely stiff systems. The numerical integration methods based on strong stable (A and L) backward differentiation formulae are used to solve extremely stiff differential equation systems arising from the state-space formulation of the transformer inrush current transient equations. A comparison of the measured and simulated three-phase transformer inrush currents showed very good agreement. The proposed procedure of modeling and the simulation method are useful tools that can be applied to other electrical transients where extremely stiff systems appear.