The increasing penetration of Distributed Energy Resources (DERs) in active distribution networks introduces significant voltage volatility. Traditional model-based control strategies often struggle to maintain voltage stability due to accurate parameter unavailability and time-varying topology. To address these challenges, this paper proposes a robust Measurement-Feedback Online Gradient Descent (MF-OGD) algorithm for real-time voltage regulation. Unlike conventional methods that rely on explicit network models, the proposed MF-OGD approach leverages real-time voltage measurements to correct gradient estimation errors, thereby implicitly compensating for both parametric mismatches and structural linearization inaccuracies. We provide rigorous theoretical guarantees for closed-loop stability and asymptotic tracking error under bounded disturbances. Furthermore, the framework is extended to a joint active–reactive power control scheme to ensure feasibility under severe operating conditions. Comprehensive simulations on the IEEE 33-bus and IEEE 69-bus standard test feeders validate the scalability and effectiveness of the proposed method. Numerical results demonstrate that the MF-OGD controller successfully maintains nodal voltages within the safety range, limiting the maximum voltage deviation to 0.022 p.u. even under 50% model parameter uncertainty. Additionally, the algorithm achieves a low tracking Root Mean Square Error (RMSE) of approximately 0.014 p.u. in the 69-bus system. Notably, the accumulated regret per node increases only marginally (from 0.032 to 0.038) as the network scale doubles, confirming the algorithm’s superior scalability and robustness compared to conventional open-loop baselines.
Wu et al. (Sun,) studied this question.