A 3-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 fl ux linkages are chosen as state variables and currents are computed fr om the flux linkages using the directly-formed inverse inductance matr ix, the Gamma-matrix. Due to the strong magnetic coupling among the wi ndings, the inductance matrix of a transformer is ill-conditioned. Dir ectly forming the Gamma-matrix will not only speed up the computation but also make it more stable. Transformer core saturation is represent ed by its anhysteretic magnetization curve. Eddy current and hysteresi s losses of the core, and stray losses of the transformer are accounte d for by a resistive load on the secondary. Winding capacitances are l umped to the terminals, the model is thus accurate up to 5 kHz A suppo rting routine is written to generate lambda-i curve data for each segm ent of the core and the other input data for EMTP. The model has been incorporated into the Alternative Transients Program (ATE), the BPA EM TP, for evaluation, and has passed the benchmark test of the GPU line energization test of 1973.