Virtual Temperature Sensors in Power Transformers Using Neural Ordinary Differential Equations

Abstract

Accurate modeling and forecasting of power transformer thermal behavior are critical for ensuring reliability, extending asset lifetime, and enabling optimized power system operation. Numerical approaches, such as finite element methods (FEM) and computational fluid dynamics (CFD), offer high fidelity but suffer from prohibitive computational costs, complex mesh generation, and limited feasibility in real-time or large scale applications, as well as often unknown geometries. Lumped-parameter thermal models provide a more practical alternative but depend on transformer-specific thermal constants and often fail to capture dynamic responses under varying operating and environmental conditions. Purely data-driven machine learning (ML) methods, including artificial neural networks (ANNs), convolutional neural networks (CNNs), and recurrent architectures such as long short-term memory (LSTM) networks, have shown success in forecasting transformer oil, winding, and hotspot temperatures; however, they typically require large volumes of high-quality training data and risk producing physically inconsistent or uninterpretable results. To overcome these limitations, hybrid frameworks such as physics-informed neural networks (PINNs) embed physical laws into the learning process, enabling physically consistent solutions while reducing data demands. This paper applies a physics-aware modeling of Neural Ordinary Differential Equations (Neural ODEs) adapted for forecasting transformer thermal behavior using real-world time-series data. Neural ODEs model system dynamics in continuous time, enabling smoother predictions, robustness to irregular sampling, and improved extrapolation capabilities compared to discrete-time models such as LSTMs. A key contribution of this work is the integration of simplified heat-transfer equations for power transformers directly into the Neural ODE, enabling a physics-aware formulation of the thermal dynamics. The model’s performance and generalization capabilities are evaluated across datasets from fifteen distinct transformers located in different regions of Norway, and characterized by varying designs and cooling mechanisms. The results demonstrate the success of the developed Neural ODEs framework to serve as a standardized, physics-aware, and robust forecasting tool for heterogeneous transformer units.