Communication-Free Adaptive Virtual Impedance Control for Circulat-ing-Current Suppression in Parallel Droop-Controlled Microgrids

Communication-free droop control remains a practical backbone for parallel operation in low-voltage microgrids, valued for plug-and-play integration and robustness. However, impedance mismatches-either in the equivalent output impedances or in the feeder impedances-often lead to reactive-power sharing imbalances and circulating currents, which in turn constrain system per-formance and scalability. A unified mechanism linking droop control, reactive power sharing, and circulating-current formation is developed, showing that mismatched Q-U droop slopes are the primary driver of reactive circulating currents and the resulting steady-state behavior of the PCC voltage. Guided by this insight, we introduce an adaptive virtual impedance controller that uses only local reactive-power feedback and is implemented within the standard voltage-current dual-loop. Through implicit sensitivity analysis and a Lyapunov-based proof, we demonstrate monotonic reduction of the sharing error and closed-loop stability without requiring prior line-impedance knowledge or inter-unit communication. Time-domain simulations demonstrate reactive power shar-ing errors below 1% and circulating current suppression exceeding 93% under varying reactive load conditions. Overall, the pro-posed approach reconciles precise reactive power sharing with circulating-current suppression without altering physical feeders, providing an implementation-ready solution for reliable parallel operation of converters under varying conditions.