Comparison between Modal Analysis and Impedance-based Methods for Analysing Stability of Unbalanced Microgrids with Grid-forming Electronic Power Converters

Stability in unbalanced power systems has deserved little attention in the literature. Given the importance of this scenario in distribution systems with distributed generation, this paper revisits modal analysis techniques for stability studies in power systems, and explains how to tackle unbalanced power systems with voltage-dependent loads. The procedure is described in detail and applied to a low-voltage (LV) simple case study with two grid-forming electronic power converters and unbalanced loads. Results are then compared with those obtained with the popular impedance-based method. While the latter is easier to implement using simulation or field data, the former requires complete information of the system, but gives a better insight into the problem. Since both methods are based on a small-signal approximation of the system, they provide similar results, but they discern different information. A larger second case study based on an LV CIGRE distribution system is also analysed. Results are obtained using a detailed Simulink model of the microgrids with electronic power converters.