Small-Signal Voltage Stability Analysis for Droop Controlled Inverter-based Microgrids: An Algebraic Graph Theory Perspective

A structure-preserving small-signal model is developed for the analysis of voltage stability in droop controlled microgrids. Several structural results are developed for the asymptotic stability of the voltage response, for both lossless and lossy network. These results indicate microgrid structures where stability is maintained regardless of droop and filtering parameters, and allow comparison of voltage and angle stability. Simulations are presented that support the theoretical results.