Three-Phase Unbalanced Power Flow Using a $\pi$-Model of Controllable AC-DC Converters

Microgrids are unique in that they can combine unbalanced three-phase systems with other AC and DC network sections, which may include a range of renewable energy sources, energy storage elements, and controllable AC-DC converters. Existing unbalanced power flow techniques such as the Ladder Iterative Technique and the three-phase Newton-Raphson (NR) method can analyze microgrids in sections but lack a complete system representation. Hence, there is a need for a power flow algorithm that considers the complete system model and solves it. A novel π-model of a controllable AC-DC converter and a single set of power balance equations for modeling a grid comprising multiple three-phase AC and DC sections is proposed. The π-model of a controllable AC-DC converter enables its inclusion into the network bus admittance matrix (YBUS) along with three-phase AC and DC network sections. Verification of the π-model is also described in the paper. The results of power flow studies with three-phase balanced and unbalanced AC and DC network sections are presented. The outcome of the π-model verification study and power flow study show that the proposed π-model is consistent and accurate. While the proposed model was developed for microgrids, it is applicable for all power system analysis applications.