Distributed Finite-Time Control of Grid-Forming Inverters with Adaptive Virtual Impedance

Abstract

The widespread integration of solar photovoltaic and wind generation has transformed the operating paradigm of modern power systems, and the resulting displacement of synchronous generators leaves hybrid microgrids facing low inertia, poor voltage regulation, and inaccurate reactive power sharing. Grid-forming (GFM) inverters using conventional droop control exhibit an inherent trade-off between voltage restoration and reactive power sharing due to mismatched feeder impedances. To address this gap, this paper proposes a distributed finite-time secondary control framework coupled with an adaptive virtual impedance mechanism for islanded hybrid AC microgrids. Using non-smooth feedback control and multi-agent consensus theory, the proposed method guarantees finite-time restoration of frequency and voltage to their nominal values, overcoming the slow convergence of asymptotic controllers. A distributed adaptive virtual impedance loop further compensates for line impedance mismatches in real time, ensuring exact proportional reactive power sharing without central coordination. The framework is validated using Lyapunov stability criteria and evaluated on a modified IEEE 34-node test system with multiple renewable and storage units. Results show a 42% reduction in convergence time and a 95% improvement in reactive power sharing accuracy relative to state-of-the-art baselines, even under severe communication delays and dynamic load variations.