Application of Physics-Informed Neural Networks in Thermal Modeling of Power Transformers

Core Project Introduction

This project is a PyTorch-based application of Physics-Informed Neural Networks (PINN), aiming to model the thermal dynamics of power transformers and predict hot spot temperatures, integrating physical constraints with data-driven methods. Project Basic Information:

• Original author/maintainer: mzaib1012
• Source platform: GitHub
• Original link: https://github.com/mzaib1012/Physics-Informed-Neural-Network-PINN-for-Thermal-Modeling-of-Power-Transformers
• Release date: May 26, 2026

Industrial Challenges in Thermal Management of Power Transformers

Power transformers are core equipment in power grids, and their reliable operation is critical to system stability. If iron core losses and winding copper losses generated during operation cannot be dissipated in time, internal temperatures will rise, accelerating insulation aging and even causing failures. Traditional thermal modeling relies on analytical formulas from IEEE/IEC standards. While computationally efficient, it requires a large number of empirical parameters and struggles to capture nonlinear behaviors under complex operating conditions. Prediction errors can reach 10-20°C when load fluctuates or ambient temperature changes. Hot spot temperature is a key indicator (difficult to measure directly as it is inside windings) that determines the insulation aging rate: for every 6-10°C increase in temperature, insulation life is halved. Accurate prediction is crucial for load strategies, cooling optimization, and lifespan extension.

Core Ideas and Technical Implementation of PINN

Core Idea: PINN embeds physical laws (e.g., heat conduction equations) into the neural network's loss function in the form of partial differential equations, enabling the model to fit data while satisfying physical constraints. It is suitable for scenarios where data is scarce but physical laws are clear (e.g., limited sensors inside transformers but clear heat conduction laws). Technical Implementation:

• Framework: PyTorch
• Network architecture: Fully connected network with 4-8 hidden layers, each with 50-100 neurons; activation functions are tanh or sin (facilitates high-order derivative calculation)
• Loss function: Data loss (difference between prediction and actual measurement) + Physical residual loss (residual of heat conduction equation calculated via automatic differentiation) + Boundary condition loss (satisfies heat dissipation boundaries)
• Training strategy: Adaptive weights (high weight for physical constraints in early stages, increased weight for data fitting in later stages)
• Additional function: Parameter identification (infer thermal physical parameters such as thermal conductivity from temperature data)

Unique Advantages of PINN in Transformer Thermal Modeling

1. Data Efficiency: Physical constraints provide regularization, allowing high accuracy with less training data, reducing sensor deployment and on-site testing costs.
2. Extrapolation Capability: Embedded physical laws enable reasonable extrapolation beyond the training data distribution, suitable for predicting extreme operating conditions (e.g., overload, cooling failure).
3. Physical Consistency: Predictions naturally satisfy principles like energy conservation, with no non-physical results such as negative temperatures or infinite growth, making it suitable for long-term simulations.
4. Interpretability: Physical residual loss quantifies prediction uncertainty; areas with large residuals indicate possible uncaught physical phenomena (e.g., eddy currents, oil flow short circuits).

Practical Applications and Engineering Value

• Online Monitoring: Deployed to monitoring platforms to estimate hot spot temperatures in real time (even in areas without direct sensors).
• Load Management: Supports dynamic capacity increase decisions, temporarily improving load capacity under safe conditions to enhance economic benefits during peak periods.
• Design Verification: Manufacturers can evaluate cooling schemes via simulation, optimize structures, shorten development cycles, and reduce test costs.
• Aging Assessment: High-precision temperature field distribution is used for cumulative calculation of insulation thermal aging, which is more accurate than traditional simplified methods, helping to formulate equipment maintenance strategies.

Technical Limitations and Future Directions

Current Limitations:

• High computational cost: Training requires solving high-order derivatives, leading to long training times for large-scale 3D simulations.
• Difficulty in handling complex geometries: The internal structure of transformers is complex; boundary handling requires integration with finite elements or domain decomposition.
• Insufficient turbulent convection modeling: Mainly applicable to laminar flow or simplified convection; embedding complex turbulence models (e.g., k-ε) needs further exploration. Future Directions:
• Transfer learning to adapt to different transformer models;
• Integration with digital twins for real-time condition monitoring;
• Combining Graph Neural Networks (GNN) to handle irregular grids;
• Developing efficient training algorithms to reduce computational costs.

Conclusion: Prospects of PINN in Intelligent Power Equipment Management

This project demonstrates the application value of PINN in thermal management of power equipment. By integrating physical laws and deep learning, it achieves data-efficient, physically consistent, and extrapolable temperature prediction. With the penetration of renewable energy and the popularization of power electronic devices, grid load characteristics are becoming more complex. Physics-data fusion methods like PINN are expected to become core technologies for next-generation intelligent power equipment condition monitoring and health management.