Virtual Temperature Sensors in Power Transformers Using Neural Ordinary Differential Equations

2026-08-13

AI Summary

Existing thermal modeling approaches for power transformers struggle to simultaneously achieve real-time performance, generalization capability, and physical consistency. This work proposes a virtual temperature sensor based on Neural Ordinary Differential Equations (Neural ODEs), which, for the first time, embeds a simplified heat conduction equation into the Neural ODE framework to enable physics-informed continuous-time dynamic modeling. The resulting method offers interpretability, a standardized architecture, and cross-device generalization, making it suitable for heterogeneous transformers. Validation on fifteen transformers in Norway—spanning diverse designs and cooling strategies—demonstrates that the model robustly, accurately, and physically consistently predicts thermal dynamics.

Abstract

Accurate modeling and forecasting of power transformer thermal behavior are critical for reliability, asset lifetime, and optimized power system operation. Numerical approaches such as finite element methods (FEM) and computational fluid dynamics (CFD) offer high fidelity but are computationally expensive, require complex mesh generation, and are often impractical for real-time or large-scale applications, particularly when transformer geometries are unknown. Lumped-parameter thermal models are more practical but depend on transformer-specific thermal constants and may fail to capture dynamic responses under varying operating and environmental conditions. Purely data-driven machine learning methods, including artificial neural networks, convolutional neural networks, and long short-term memory (LSTM) networks, have shown success in forecasting transformer temperatures but typically require large volumes of high-quality training data and may produce physically inconsistent or uninterpretable results. This paper develops a physics-aware Neural Ordinary Differential Equation (Neural ODE) framework for forecasting transformer thermal behavior from real-world time-series data. Neural ODEs model system dynamics in continuous time, providing smooth trajectory prediction and a natural representation of continuously evolving thermal dynamics. A key contribution is the integration of simplified heat-transfer equations directly into the Neural ODE formulation. The model is evaluated across datasets from fifteen transformers in different regions of Norway with varying designs and cooling mechanisms. The results demonstrate that the developed Neural ODE framework provides a standardized, physics-aware, and robust forecasting approach for heterogeneous transformer units.

Problem

• power transformer
• thermal modeling
• temperature forecasting
• physics-aware modeling
• real-time application

Innovation

• Neural ODE
• physics-aware modeling
• transformer thermal forecasting
• virtual temperature sensor
• continuous-time dynamics