Grid-Forming Control and Transient Stability in 100% Inverter-Based Hybrid Microgrids

Abstract

The rapid decommissioning of synchronous generation and the proliferation of 100% inverter-based resources (IBRs) in medium-voltage distribution networks remove physical rotational inertia, rendering modern microgrids susceptible to severe electromechanical and electromagnetic instability. Quantifying the likelihood and severity of such large-signal disturbances is itself a statistical problem; see Bagré and Kaboré for a general treatment of asymmetric spatial extreme-value dependence in a different application context. Existing Grid-Forming (GFM) control schemes, such as droop control and Virtual Synchronous Machines (VSMs), provide synthetic inertia but rely on linear small-signal approximations that fail to guarantee large-signal transient stability during asymmetrical short circuits or sudden islanding. This paper presents an adaptive, decentralized Virtual-Oscillator Control (VOC) architecture based on a dead-zone oscillator circuit for hybrid solar-wind-battery microgrids. The controller dynamically regulates synthetic inertia and damping without requiring inter-inverter communication channels. We recast each inverter's oscillator as a Liénard-type nonlinear circuit and prove, via Liénard's theorem, existence and local orbital stability of a unique current-limiting limit cycle for every admissible parameter setting. We then use time-scale-separated averaging to reduce the interconnected network to slow amplitude-phase dynamics and show, building on existing almost-global synchronization results for coupled nonlinear oscillators, that the adaptively tuned network synchronizes in frequency and shares active/reactive power according to designer-specified set points from almost all initial conditions. High-fidelity electromagnetic transient (EMT) simulations of a 15-MVA hybrid microgrid show that the proposed adaptive VOC reduces frequency-nadir deviation by 64.1% and increases critical clearing time by 181.8% relative to conventional droop control, and achieves full phase recovery within 115 ms following a three-phase-to-ground fault.