Data-Driven Physics-Informed LSTM for Voltage Regulation in Active Distribution Networks

The rapid integration of photovoltaic (PV) generation into active distribution networks (ADNs) creates a fundamental tension between maintaining tight voltage regulation and accommodating high distributed energy resource (DER) penetration levels. Conventional voltage control methods such as the droop control operate locally without coordination, while centralized optimal power flow requires full network observability and reliable real-time communication. Multi-agent deep reinforcement learning (MADRL) methods provide adaptive coordination but suffer from long training times and algorithmic complexity that prevent direct deployment on embedded inverter hardware. This paper proposes the Optimal Historical Selection and Forecasting (OHSF) scheme: a physics-informed long short-term memory (LSTM) network combined with an online sensitivity-based correction loop for medium-voltage ADNs. A composite loss function incorporating data-driven regression, an inter-PV voltage sensitivity penalty, and an inverter capability constraint produces reactive power setpoints that are inherently aware of physical limits, while the correction loop refines the predictions using real-time AC power flow feedback. The OHSF scheme supports a centralized full-network mode and a decentralized fallback mode in which the trained weights run locally on each inverter. Simulations under worst-case PV placement and network reconfiguration on the modified IEEE 33-bus and 69-bus test systems achieve an average voltage deviation across all PV buses of 0.701% and 0.601% at 172% DER penetration on the 33-bus system, and 0.804% and 0.806% at 242% DER penetration on the 69-bus system, while training 32 to 49 times faster than state-of-the-art MADRL methods.