Three-phase transformer modelling for unbalanced conditions

A simple and systematic two-winding, three-phase transformer modelling for steady-state unbalanced conditions is proposed. The model is valid for three-legged, five-legged and triplex (transformer bank) core designs. It is derived from the primitive (or unconnected winding) equations of the transformer and uses two parameters only: the short-circuit and the zero-sequence magnetising impedances. Both phase and sequence nodal equations are systematically obtained for all possible phase shifts and all winding connections, including the isolated wyes and the impedance-grounded wyes on one or both transformer sides. The proposed model can be considered as a generalisation of the usual model in the literature (which is only valid for the transformer bank; moreover, only specific phase shifts have been developed and the impedance-grounded wyes are not usually considered). Furthermore, the zero-sequence scheme is analysed in depth, from which the following conclusions are highlighted: (1) the voltage of the neutral point in the isolated wye cases also depends on the connection of the other winding; (2) the zero-sequence admittances for all connections can be obtained from the zero-sequence admittances of the Y-z-Y-z connection by taking limits as (z) over tilde (np) or (z) over tilde (ns) tends to infinity or to zero. The study is divided into two parts. Part I is devoted to core modelling and to four detailed examples. Part II summarises the general procedure for all possible phase shifts, all winding connections and all core designs and also includes the numerical application examples.