Transformer modeling using line-to-line voltages in ungrounded power distribution networks

The three-phase power flow problem is typically formulated, based on phase components, as the solution of the phase-to-ground voltages at each bus. For four-wire multigrounded wye systems these phase voltages are well-defined quantities. In systems which contain ungrounded three-wire delta sections, the ground reference is lost in the delta sections and the corresponding phase-to-ground voltages become undefined. This leads to divide-by-zero errors in the power flow solution using standard formulations. This paper advocates the use of phase-to-ground voltages in wye sections and line-to-line voltages in delta sections. Thus, the problem of ill-defined voltages is completely removed from the formulation. This approach requires various modifications to the standard network models and this summary focuses on the different transformer models that may be encountered in systems with wye and delta sections. We note that the models can be easily incorporated into an implicit Z_bus Gauss power flow algorithm, and was used successfully to solve real-life systems with a mixture of grounded wye and ungrounded delta sections.