Anchor-LS-Aided Voltage-Sensitivity Estimation and Voltage-Constrained Droop Allocation for VPP-Based Frequency Regulation

This paper proposes a voltage-sensitivity estimation and droop-allocation framework for virtual power plant (VPP)-based frequency regulation in partially observable distribution feeders. In practical distribution systems, active-power adjustments by distributed energy resources (DERs) for frequency regulation may cause voltage excursions, while full real-time feeder information is often unavailable. To address this issue, an anchor-least-squares (Anchor-LS)-aided sensitivity-estimation method is developed using only point-of-common-coupling (PCC) voltage measurements and feeder-network information. Unlike state-estimation-based, data-driven, or optimization-heavy approaches that typically require wider measurement coverage, large training datasets, or repeated centralized computation, the proposed framework is designed for fast VPP-based frequency regulation under partial observability using only limited PCC measurements and feeder information. The proposed method reconstructs an approximate operating point and derives an operating-point-sensitive PCC voltage-magnitude-sensitivity matrix based on a coupled Z-bus formulation. Based on the estimated sensitivity, a voltage-constrained asymmetric droop-allocation framework is developed for under-frequency and over-frequency events, together with a practical iterative droop-adjustment method that mitigates PCC voltage violations without relying on a full optimization-based dispatch model. The proposed framework is validated through two case studies. In Monte Carlo simulations on the IEEE 33-bus feeder, the proposed sensitivity model reduced the mean RMSE by about 117 times compared with the common-path resistance method and by about 30 times compared with the conventional Z-bus method. In simulations on a practical 115-bus Korean distribution feeder, the proposed method achieved acceptable droop capacities comparable to those of a centralized LP baseline while reducing the mean computation time by about 3.2 times for both under-frequency and over-frequency events. These results confirm the practical usefulness of the proposed framework for fast VPP-based frequency regulation in real distribution networks under partial observability.