On Theoretical Stability Proof and Stability Margin Analysis of Enhanced Droop-Free Control Schemes for Islanded Microgrids

This article studies enhanced droop-free control strategies with sparse neighboring communication for achieving effective active power sharing of distributed energy resources (DERs) while maintaining the frequency stability of islanded microgrids. The normalized active power consensus (NAPC) based droop-free control can share the load among controllable DERs in proportion to their available capacities. However, existing literature exclusively takes the asymptotic stability of the NAPC-based droop-free control for granted, lacking a comprehensive theoretical proof that is critical for ensuring its effective design and practical implementation. This article, for the first time, provides a thorough theoretical proof of the asymptotic stability of two NAPC-based droop-free control schemes: ordinary NAPC (O-NAPC) and amplifier-equipped NAPC (A-NAPC), by testifying that all effective eigenvalues have negative real parts. The effect of various system settings on the stability margins is further analyzed with respect to the average admittance of the electrical network, the sparseness of the communication network, and the average available capacity of controllable DERs. Based on the sensitivity of eigenvalues with respect to perturbations, a vulnerability analysis is conducted to identify the weaknesses in the microgrids. Case studies demonstrate that the available capacity of controllable DERs has the most decisive influence on the stability margin of NAPC-based droop-free control, while O-NAPC/A-NAPC control scheme is more suitable for microgrids with DERs of larger/ smaller available capacities.