Model-Free Voltage Estimation in Distribution Systems via Physics-Informed Learning for High PV Penetration

Abstract

Accurate model-free voltage estimation is essential for distribution networks with high photovoltaic (PV) penetration. This paper presents a physics-informed neural network (PINN) that embeds a physically interpretable loss based on voltage sensitivity—the linear relationship between changes in active power and voltage—so that the model internalizes network behavior rather than surface correlations. Unlike prior physics-informed approaches that rely on Jacobian matrices derived from known network equations, the proposed method derives all physical constraints solely from historical smart-meter measurements, enabling truly model-free deployment suitable for distribution system operators (DSOs) and aggregators who lack detailed feeder models. Using a detailed Japanese distribution model, the proposed method achieves superior accuracy to a conventional neural network, particularly in extrapolation: it reliably estimates voltages under high PV penetration even when trained only on no-PV data. Inference is one to two orders of magnitude faster than conventional power-flow calculations (approximately 20× on CPU and 230× on GPU) with negligible runtime overhead, making the approach practical for real-time operational monitoring and long-term planning.