Model-Free Voltage Calculation in Power Systems: Applying Gaussian Process Regression for Real-Time Voltage Estimation in DER-Rich Low-Voltage Networks

This paper explores a model-free approach to voltage calculation in low-voltage (LV) networks impacted by distributed energy resources (DERs) using Gaussian Process Regression (GPR). Traditional voltage calculations depend on detailed network models, which are often unavailable or outdated in LV networks. As DER penetration increases, such as photovoltaic (PV) systems and electric vehicles (EVs), accurate voltage predictions become essential for network stability. This study applies GPR as a probabilistic, nonparametric alternative that can capture complex relationships between power and voltage without relying on physical models. The GPR model is trained on synthetic smart meter data under varying DER scenarios—low (20%), medium (50%), and high (100%) penetration levels. Key findings indicate that GPR achieves high accuracy in low and medium penetration levels, with Root Mean Square Error (RMSE) values of 0.12 and 0.22, respectively, and adapts to increased uncertainty at higher penetration levels, providing robust prediction intervals. These results suggest that GPR offers a practical, scalable solution for real-time voltage estimation in DER-rich LV networks.