A three-phase multi-legged transformer model in ATP using the directly-formed inverse inductance matrix

A new transformer model based on core topology is developed. The model simulates the transformer as a set of coupled inductances. Winding flux linkages are chosen as state variables and currents are computed from the flux linkages using the directly-formed inverse inductance matrix, the Γ-matrix. Due to the strong magnetic coupling among the windings, the inductance matrix of a transformer is ill-conditioned. Directly forming the Γ-matrix will not only speed up the computation but also make it more stable. Transformer core saturation is represented by its anhysteretic magnetization curve. Eddy current and hysteretic losses of the core, and stray losses of the transformer are accounted for by a resistive load on the secondary. Winding capacitances are lumped to the terminals, the model is thus accurate up to 5 kHz. A supporting routine is written to generate λ-i curve data for each segment of the core and the other input data for EMTP. The model has been incorporated into the Alternative Transients Program (ATP), the BPA EMTP, for evaluation, and has passed the benchmark test of the GPU line energization test of 1973