Grey-box modeling for hot-spot temperature prediction of oil-immersed transformers in power distribution networks

E. M.V. Blomgren*, F. D'Ettorre, O. Samuelsson, M. Banaei, R. Ebrahimy, M. E. Rasmussen, N. H. Nielsen, A. R. Larsen, H. Madsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Power transformers are one of the most costly assets in power grids. Due to increasing electricity demand and levels of distributed generation, they are more and more often loaded above their rated limits. Transformer ratings are traditionally set as static limits, set in a controlled environment with conservative margins. Through dynamic transformer rating, the rating is instead adapted to the actual working conditions of the transformers. This can help distribution system operators (DSOs) to unlock unused capacity and postpone costly grid investments. To this end, real-time information of the transformer operating conditions, and in particular of its hot-spot and oil temperature, is required. This work proposes a grey-box model that can be used for online estimation and forecasting of the transformer temperature. It relies on a limited set of non-intrusive measurements and was developed using experimental data from a DSO in Jutland, Denmark. The thermal model has proven to be able to predict the temperature of the transformers with a high accuracy and low computational time, which is particularly relevant for online applications. With a six-hour prediction horizon the mean average error was 0.4–0.6 °C. By choosing a stochastic data-driven modeling approach we can also provide prediction intervals and account for the uncertainty.

Original languageEnglish
Article number101048
JournalSustainable Energy, Grids and Networks
Number of pages14
Publication statusPublished - 2023

Bibliographical note

Funding Information:
This work was supported by the Flexible Energy Denmark (FED) project funded by Innovation Fund Denmark under Grant No. 8090-00069B and Ebalanceplus project funded by the European Union’s Horizon 2020 under the grant agreement number of 864283 . The authors also would like to thank Claus Schack Urup for technical support and providing the data for this study.


  • Data-driven modeling
  • Distribution grid flexibility
  • Dynamic transformer rating
  • Grey-box modeling
  • Thermal model


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