Numerical Calculations of Three-Phase Transformer Transients

A three-phase, two-winding transformer model is presented in this paper. Nonlinear magnetizing curves are piecewise linearized, while the input winding capacitances are lumped onto the transformer terminals. A stiff system of differential equations in a state space, describing the transformer transient behavior, is solved using the L-stable backward differentiation formulas (BDFs) numerical rule. It has been shown that using the BDF numerical rule has resulted in better stability properties than using the trapezoidal rule. A computer program has been developed for generation of variable-state waveforms. The developed program is suitable for simulations of low-frequency three-phase transformer transients such as inrush currents and ferroresonance. This computer program has proved to be numerically stable for the problems investigated in this paper. The results acquired in this way are compared to results obtained using MATLAB/Power System Blockset, as well as to results of laboratory measurements.