Admittance matrix models of three-phase transformers with various neutral grounding configurations

Nodal admittance matrix models are obtained for wye-connected three-phase transformers with various grounding impedance configurations. The derivations have been performed using computational symbolic algebra, avoiding the necessity for simplifying assumptions. An original model for the general case of a wye-wye transformer, with grounding impedances on both primary and secondary neutrals, is given. It is shown that this model does not correspond to the simple combination of the previously known formulae for cases where neutral impedance occurs on either the primary side only or the secondary side only. It is also demonstrated that the new model simplifies to the well-known limiting cases for solid grounding and no grounding. A model is also given for multiple transformers sharing a single neutral grounding impedance.