Coordinated Adaptive Virtual Inertia and Virtual Impedance Control for Stability Enhancement in Ultra-Weak Mountainous Microgrids

<title>Abstract</title> <p>The global energy transition has accelerated the deployment of inverter-based resources (IBRs), leading to a significant reduction in systemic rotational inertia [1], [4]. While Virtual Synchronous Generator (VSG) control has emerged as a viable solution to emulate inertial response, its performance is severely degraded in “Ultra-Weak” grid environments characterized by high impedance and low short-circuit ratios (SCR) [1], [3]. This vulnerability was starkly demonstrated during the January 2026 Himachal Pradesh grid disruptions, where environmental stressors triggered widespread instability across 5,775 distribution transformers. This paper proposes a novel Coordinated Adaptive Virtual Inertia and Virtual Impedance (AVI) control strategy to address these stability bifurcations [5], [9]. Unlike traditional fixed-parameter VSG architectures, the proposed AVI law dynamically modulates virtual reactance and damping based on filtered frequency deviations and Rate of Change of Frequency (RoCoF) to mitigate measurement noise [4]. Small-signal stability analysis and eigenvalue trajectory mapping reveal that the proposed method extends the critical grid inductance stability limit from 5.10 mH to over 8.50 mH [6]. Time-domain simulations, benchmarked against contemporary 2026 adaptive strategies, confirm that the AVI-VSG reduces active power oscillations by 40% and maintains frequency nadir within safe operational limits (49.2 Hz) during severe load transients [8]. The proposed controller offers a robust, mathematically guaranteed framework for ensuring grid resilience in remote, mountainous distribution networks.</p>