Analysis of voltage stability characterization of radial distribution grids with high penetration of distributed energy resources

The high penetration of distributed energy resources (DER) in radial distribution grids shifts the voltage stability from low to high voltage. This paper presents an analytical framework for comparing voltage changes across different regimes. Six classical voltage stability indices (VSI, VSF, Lmn, FVSI, VQI, and L-index) are compared for the impact of photovoltaic, wind, and battery energy storage systems (BESS) on the IEEE 33-bus radial distribution test system. In the article, three scenarios of DER penetration - low (0–30%), moderate (30–70%), high (70–120%), and very high (>120% of peak load) are studied for the subsequent determination of energy saving and grid balancing regimes. The derived closed-form sensitivity factors ∂, VSI/∂PDER and ∂VSI/∂QDER, for radial branches with net reverse power flow, are obtained, and inverter control modes with Q(U) Volt-Var and P(U) Volt-Watt are suggested, compatible with EN 50549/IEEE 1547. The L-index for determining the optimal power flow (OPF) is analyzed. The proposed framework provides distribution system operators with an analytically sound, computationally efficient methodology for integrating DER.