Dynamic-Feasibility-Aware Coordination of Converter-Based Virtual Inertia in Active Distribution Networks

Converter-interfaced resources in active distribution networks (ADNs) can provide virtual-inertia support, but inertia coordination based on initial frequency-response metrics, such as the rate of change of frequency (RoCoF) and frequency nadir, may not fully capture dynamic interactions among converters, affecting inertia-setting feasibility. This paper proposes a dynamic-feasibility-aware coordination method for converter-interfaced resources with heterogeneous converter dynamics, considering grid-forming (GFM) and grid-following (GFL) configurations. Reduced-order dynamic simulation samples are generated to train Gaussian process regression surrogates that learn mappings from inertia settings to initial frequency-support metrics and feasibility indicators, enabling evaluation during optimization. Full-window frequency and voltage security and tail-oscillation behavior are incorporated through feasibility constraints, restricting the search to feasible regions. The nonconvex problem is solved using grid-assisted multi-start sequential least-squares programming. Case studies on a modified United Kingdom Generic Distribution System (UKGDS) EHV1 network show that admissible inertia settings and robustness margins depend strongly on GFM/GFL composition under sensitivity and disturbance tests. In the all-GFM case, the proposed method preserves nearly the same initial frequency support as frequency-performance-oriented optimization while excluding settings that cause sustained oscillations and frequency-limit violations, maintaining the point of common coupling (PCC) frequency within 49.846–50.000 Hz.