Topology based magnetic model for steady-state and transient studies for three-phase core type transformers

Existing matrix models for transformers reproduce specified short-circuit tests, portraying leakage flux in air, but do not explicitly model the core. Therefore, a precise relation between core flux and air flux is not clearly established. Core representation is defined simply on the basis of a specified excitation current (positive- and zero-sequence), permitting linear magnetizing branches to be incorporated in the matrix. Nonlinear inductances are connected separately at winding terminals to introduce core nonlinearities, however these are not identified physically with individual core limbs, making precise accommodation of hysteresis, saturation and eddy current effects difficult. Published models based on the duality existing between magnetic and electric circuits identify a means for correctly interfacing core flux with air flux, permitting core nonlinearities to be incorporated on a physical basis. However practical application of these models has been hampered by a difficulty in deriving the required model parameters. A formulation is presented here to build a topological model based on normally available test data. Results of short-circuit tests are presented demonstrating that existing matrix models can introduce errors