Abstract
Power transformers are essential components of electric power transmission systems operating under diverse environmental conditions. Their thermal performance strongly influences insulation aging, operational reliability, and power system stability. Conventional empirical thermal models, including the IEC 60076-7 standard, often exhibit limited predictive capability under extreme climate conditions. This study proposes a Physics-Informed Neural Network (PINN) integrated with an advanced Multi-Physics Transformer Thermal Model (MTTM) to improve transformer thermal prediction while preserving physical consistency. The proposed framework identifies research gaps in transformer thermal modeling, optimizes the PINN training strategy to reduce computational cost and improve predictive performance, evaluates integration with the OSIsoft PI System architecture, and validates the model using geographically diverse datasets. A case study conducted on a 500 MVA, 400/220 kV transformer demonstrated a root mean square error of 1.12°C and a mean absolute error of 0.89°C, representing a 48% improvement over the IEC 60076-7 standard. Although PINN training requires significant GPU resources, the trained model performs real-time inference within 12 milliseconds. Validation using multiple transformer datasets confirmed the robustness, scalability, and practical applicability of the proposed framework for dynamic transformer rating and asset management, with an estimated annual economic benefit of approximately USD 1.45 million.
Keywords
Physics-informed neural network Transformer thermal modeling Extreme climate Hot-spot temperature Dynamic rating Insulation aging Multi-physics coupling Uncertainty quantificationReferences
- T. V. Oommen, "Moisture equilibrium in cellulose insulation," IEEE Electrical Insulation Magazine, vol. 19, no. 2, pp. 17-23, 2003.
- Climate Change 2021: The Physical Science Basis, IPCC, Cambridge University Press, 2021.
- IEEE Std C57.91-2011, IEEE Guide for Loading Mineral-Oil-Immersed Transformers and Step-Voltage Regulators, IEEE, 2012.
- IEC 60076-7:2018, Power Transformers—Part 7: Loading Guide for Oil-Immersed Power Transformers, 2nd ed., International Electrotechnical Commission, 2018.
- D. Susa, M. Lehtonen, and H. Nordman, "Dynamic thermal modelling of power transformers," IEEE Trans. Power Delivery, vol. 20, no. 1, pp. 197-204, Jan. 2005.
- M. K. Pradhan and T. S. Ramu, "Estimation of the hottest spot temperature (HST) in power transformers considering thermal inhomogeneity of the windings," IEEE Trans. Power Delivery, vol. 19, no. 4, pp. 1704-1712, Oct. 2004.
- Y. Zhang et al., "Multiscale electromagnetic–thermal–fluid field coupling model for oil-immersed transformers," Frontiers in Mechanical Engineering, vol. 11, 2025.
- A. H. K. Al-Obaidi et al., "Numerical investigation of conjugate heat transfer in oil-immersed power transformer," CFD Letters, vol. 16, no. 5, pp. 1-16, 2024.
- T. Manoj et al., "Monitoring of transformer hotspot temperature using support vector regression combined with wireless mesh networks," Energies, vol. 17, no. 24, 2024.
- L. Xu et al., "A transformer oil temperature prediction method based on data-driven and multi-model fusion," Processes, vol. 13, no. 2, 2025.
- G. Swift, T. S. Molinski, and W. Lehn, "A fundamental approach to transformer thermal modeling—Part I: Theory and equivalent circuit," IEEE Trans. Power Delivery, vol. 16, no. 2, pp. 171-175, Apr. 2001.
- S. Whitaker, "Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles," AIChE Journal, vol. 18, no. 2, pp. 361-371, 1972.
- A. N. A. Gorgan et al., "Power transformer hot spot temperatures estimation considering solar irradiation and moisture in cellulose," International Journal of Applied Engineering Research, vol. 14, no. 7, pp. 1642-1651, 2019.
- F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 6th ed., Wiley, 2007.
- T. V. Oommen, "Moisture equilibrium charts for transformer insulation drying practice," IEEE Trans. Power Apparatus and Systems, vol. PAS-103, no. 10, pp. 3062-3067, 1984.
- T. V. Oommen, E. M. Petrie, and S. R. Lindgren, "Thermal evaluation of insulating materials and systems for transformers," IEEE Electrical Insulation Magazine, vol. 26, no. 2, pp. 13-20, 2010.
- Z. Li et al., "Fourier neural operator for parametric partial differential equations," International Conference on Learning Representations (ICLR), 2021.
- L. Lu et al., "Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators," Nature Machine Intelligence, vol. 3, pp. 218-229, 2021.
- Y. Yang and P. Perdikaris, "Adversarial uncertainty quantification in physics-informed neural networks," Journal of Computational Physics, vol. 394, pp. 136-152, 2019.
- D. P. Kingma and M. Welling, "Auto-encoding variational Bayes," International Conference on Learning Representations (ICLR), 2014.
- India Meteorological Department, "Climate of Rajasthan," IMD Pune, 2023.
- Central Electricity Authority, "Performance review of power sector in India," Ministry of Power, Government of India, 2024.
- CIGRE Working Group A2.37, Transformer Thermal Modeling, CIGRE Technical Brochure 659, 2016.
- IEEE Std C57.161-2018, IEEE Guide for Interpretation of Moisture Related Parameters in Transformer Insulating Oil, IEEE, 2018.
- T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning, 2nd ed., Springer, 2009.
- I. Loshchilov and F. Hutter, "Decoupled weight decay regularization," International Conference on Learning Representations (ICLR), 2019.
- Y. Bengio et al., "Curriculum learning," International Conference on Machine Learning (ICML), 2009.
- J. R. Jang, "ANFIS: Adaptive-network-based fuzzy inference system," IEEE Trans. Systems, Man, and Cybernetics, vol. 23, no. 3, pp. 665-685, 1993.
- M. Raissi, P. Perdikaris, and G. E. Karniadakis, "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations," Journal of Computational Physics, vol. 378, pp. 686-707, 2019.
- M. Lehtonen and T. Nousiainen, "Dynamic thermal rating of power transformers: State of the art review," International Conference on Electricity Distribution (CIRED), 2021.
- D. Susa and M. Lehtonen, "Dynamic thermal modeling of power transformers: Further development—Part I," IEEE Trans. Power Delivery, vol. 21, no. 4, pp. 1971-1980, Oct. 2006.
- U.S. Department of Energy, Climate Change and the Electricity Grid, DOE/PI-0009, 2019.
- B. McMahan et al., "Communication-efficient learning of deep networks from decentralized data," International Conference on Artificial Intelligence and Statistics (AISTATS), 2017.
- European Network of Transmission System Operators for Electricity, Ten-Year Network Development Plan 2024, ENTSO-E, 2024.
- S. I. Hamad, "Utilizing Convolutional Neural Networks for the Identification of Lung Cancer," International Journal of Computational and Electronic Aspects in Engineering, vol. 6, no. 1, pp. 35-41, 2025.
- A. A. H. Kjwan, "Adaptive Covert Communication Framework for 6G Networks Integrating Quantum Cryptography and AI-Augmented Physical Layer Security," International Journal of Computational and Electronic Aspects in Engineering, vol. 5, no. 4, pp. 203-213, 2024.