IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i11p1785-d1665635.html
   My bibliography  Save this article

Mathematical and Machine Learning Innovations for Power Systems: Predicting Transformer Oil Temperature with Beluga Whale Optimization-Based Hybrid Neural Networks

Author

Listed:
  • Jingrui Liu

    (Chongqing University-University of Cincinnati Joint Co-op Institute, Chongqing University, Chongqing 400044, China)

  • Zhiwen Hou

    (Chongqing University-University of Cincinnati Joint Co-op Institute, Chongqing University, Chongqing 400044, China
    These authors contributed equally to this work.)

  • Bowei Liu

    (Chongqing University-University of Cincinnati Joint Co-op Institute, Chongqing University, Chongqing 400044, China
    These authors contributed equally to this work.)

  • Xinhui Zhou

    (Chongqing University-University of Cincinnati Joint Co-op Institute, Chongqing University, Chongqing 400044, China)

Abstract

Power transformers are vital in power systems, where oil temperature is a key operational indicator. This study proposes an advanced hybrid neural network model, BWO-TCN-BiGRU-Attention, to predict the top-oil temperature of transformers. The model was validated using temperature data from power transformers in two Chinese regions. It achieved MAEs of 0.5258 and 0.9995, MAPEs of 2.75% and 2.73%, and RMSEs of 0.6353 and 1.2158, significantly outperforming mainstream methods like ELM, PSO-SVR, Informer, CNN-BiLSTM-Attention, and CNN-GRU-Attention. In tests conducted in spring, summer, autumn, and winter, the model’s MAPE was 2.75%, 3.44%, 3.93%, and 2.46% for Transformer 1, and 2.73%, 2.78%, 3.07%, and 2.05% for Transformer 2, respectively. These results indicate that the model can maintain low prediction errors even with significant seasonal temperature variations. In terms of time granularity, the model performed well at both 1 h and 15 min intervals: for Transformer 1, MAPE was 2.75% at 1 h granularity and 2.98% at 15 min granularity; for Transformer 2, MAPE was 2.73% at 1 h granularity and further reduced to 2.16% at 15 min granularity. This shows that the model can adapt to different seasons and maintain good prediction performance with high-frequency data, providing reliable technical support for the safe and stable operation of power systems.

Suggested Citation

  • Jingrui Liu & Zhiwen Hou & Bowei Liu & Xinhui Zhou, 2025. "Mathematical and Machine Learning Innovations for Power Systems: Predicting Transformer Oil Temperature with Beluga Whale Optimization-Based Hybrid Neural Networks," Mathematics, MDPI, vol. 13(11), pages 1-34, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1785-:d:1665635
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/11/1785/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/11/1785/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mu, Guixiang & Wei, Qingguo & Xu, Yonghong & Li, Jian & Zhang, Hongguang & Yang, Fubin & Zhang, Jian & Li, Qi, 2025. "State of health estimation of lithium-ion batteries based on feature optimization and data-driven models," Energy, Elsevier, vol. 316(C).
    2. Meysam Beheshti Asl & Issouf Fofana & Fethi Meghnefi, 2024. "Review of Various Sensor Technologies in Monitoring the Condition of Power Transformers," Energies, MDPI, vol. 17(14), pages 1-40, July.
    3. Smyl, Slawek, 2020. "A hybrid method of exponential smoothing and recurrent neural networks for time series forecasting," International Journal of Forecasting, Elsevier, vol. 36(1), pages 75-85.
    4. Xia, Xuelei & Chen, Yang & Shen, Jiangwei & Liu, Yonggang & Zhang, Yuanjian & Chen, Zheng & Wei, Fuxing, 2025. "State of health estimation for lithium-ion batteries based on impedance feature selection and improved support vector regression," Energy, Elsevier, vol. 326(C).
    5. Lefeng Cheng & Tao Yu, 2018. "Dissolved Gas Analysis Principle-Based Intelligent Approaches to Fault Diagnosis and Decision Making for Large Oil-Immersed Power Transformers: A Survey," Energies, MDPI, vol. 11(4), pages 1-69, April.
    6. Yu Li & Xiaoxiao Lin & Jingsen Liu, 2021. "An Improved Gray Wolf Optimization Algorithm to Solve Engineering Problems," Sustainability, MDPI, vol. 13(6), pages 1-23, March.
    7. Wang, Xin & Liu, Xiang & Bai, Yun, 2024. "Prediction of the temperature of diesel engine oil in railroad locomotives using compressed information-based data fusion method with attention-enhanced CNN-LSTM," Applied Energy, Elsevier, vol. 367(C).
    8. Sun, Rongli & Chen, Junsheng & Li, Benchuan & Piao, Changhao, 2025. "State of health estimation for Lithium-ion batteries based on novel feature extraction and BiGRU-Attention model," Energy, Elsevier, vol. 319(C).
    9. Zhang, Xuedong & Zhao, Huanyu & Yao, Junhao & Wang, Zheng & Zheng, Yongshun & Peng, Tian & Zhang, Chu, 2025. "A multi-scale component feature learning framework based on CNN-BiGRU and online sequential regularized extreme learning machine for wind speed prediction," Renewable Energy, Elsevier, vol. 242(C).
    10. Fei Teng & Yafei Song & Xinpeng Guo, 2021. "Attention-TCN-BiGRU: An Air Target Combat Intention Recognition Model," Mathematics, MDPI, vol. 9(19), pages 1-21, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Yang & Gao, Guoqiang & Chen, Kui & He, Shuhang & Liu, Kai & Xin, Dongli & Luo, Yang & Long, Zhou & Wu, Guangning, 2025. "State-of-health prediction of lithium-ion batteries using feature fusion and a hybrid neural network model," Energy, Elsevier, vol. 319(C).
    2. Liu, Wei & Teh, Jiashen & Alharbi, Bader, 2025. "An asynchronous electro-thermal coupling modeling method of lithium-ion batteries under dynamic operating conditions," Energy, Elsevier, vol. 324(C).
    3. Xuemin Huang & Xiaoliang Zhuang & Fangyuan Tian & Zheng Niu & Yujie Chen & Qian Zhou & Chao Yuan, 2025. "A Hybrid ARIMA-LSTM-XGBoost Model with Linear Regression Stacking for Transformer Oil Temperature Prediction," Energies, MDPI, vol. 18(6), pages 1-22, March.
    4. Hewamalage, Hansika & Bergmeir, Christoph & Bandara, Kasun, 2021. "Recurrent Neural Networks for Time Series Forecasting: Current status and future directions," International Journal of Forecasting, Elsevier, vol. 37(1), pages 388-427.
    5. Yuhong Wang & Lei Chen & Hong Zhou & Xu Zhou & Zongsheng Zheng & Qi Zeng & Li Jiang & Liang Lu, 2021. "Flexible Transmission Network Expansion Planning Based on DQN Algorithm," Energies, MDPI, vol. 14(7), pages 1-21, April.
    6. Tian, Zhirui & Liu, Weican & Zhang, Jiahao & Sun, Wenpu & Wu, Chenye, 2025. "EDformer family: End-to-end multi-task load forecasting frameworks for day-ahead economic dispatch," Applied Energy, Elsevier, vol. 383(C).
    7. Spiliotis, Evangelos & Makridakis, Spyros & Kaltsounis, Anastasios & Assimakopoulos, Vassilios, 2021. "Product sales probabilistic forecasting: An empirical evaluation using the M5 competition data," International Journal of Production Economics, Elsevier, vol. 240(C).
    8. Oikonomou, Konstantinos & Damigos, Dimitris & Dimitriou, Dimitrios, 2025. "Globality in the metal markets: Leveraging cross-learning to forecast aluminum and copper prices," Resources Policy, Elsevier, vol. 103(C).
    9. Chenyuan Liu & Heng Li & Kexin Li & Yue Wu & Baogang Lv, 2025. "Deep Learning for State of Health Estimation of Lithium-Ion Batteries in Electric Vehicles: A Systematic Review," Energies, MDPI, vol. 18(6), pages 1-20, March.
    10. Feng, Zhanyu & Zhang, Jian & Jiang, Han & Yao, Xuejian & Qian, Yu & Zhang, Haiyan, 2024. "Energy consumption prediction strategy for electric vehicle based on LSTM-transformer framework," Energy, Elsevier, vol. 302(C).
    11. Oreshkin, Boris N. & Dudek, Grzegorz & Pełka, Paweł & Turkina, Ekaterina, 2021. "N-BEATS neural network for mid-term electricity load forecasting," Applied Energy, Elsevier, vol. 293(C).
    12. Bojer, Casper Solheim & Meldgaard, Jens Peder, 2021. "Kaggle forecasting competitions: An overlooked learning opportunity," International Journal of Forecasting, Elsevier, vol. 37(2), pages 587-603.
    13. Meysam Beheshti Asl & Issouf Fofana & Fethi Meghnefi & Youssouf Brahami & Joao Pedro Da Costa Souza, 2025. "A Comprehensive Review of Transformer Winding Diagnostics: Integrating Frequency Response Analysis with Machine Learning Approaches," Energies, MDPI, vol. 18(5), pages 1-38, March.
    14. Winita Sulandari & Yudho Yudhanto & Sri Subanti & Crisma Devika Setiawan & Riskhia Hapsari & Paulo Canas Rodrigues, 2023. "Comparing the Simple to Complex Automatic Methods with the Ensemble Approach in Forecasting Electrical Time Series Data," Energies, MDPI, vol. 16(22), pages 1-16, November.
    15. Yongmao Xiao & Renqing Zhao & Wei Yan & Xiaoyong Zhu, 2022. "Analysis and Evaluation of Energy Consumption and Carbon Emission Levels of Products Produced by Different Kinds of Equipment Based on Green Development Concept," Sustainability, MDPI, vol. 14(13), pages 1-18, June.
    16. Nghia Chu & Binh Dao & Nga Pham & Huy Nguyen & Hien Tran, 2022. "Predicting Mutual Funds' Performance using Deep Learning and Ensemble Techniques," Papers 2209.09649, arXiv.org, revised Jul 2023.
    17. You-Shyang Chen & Arun Kumar Sangaiah & Yu-Pei Lin, 2024. "Hyperautomation on fuzzy data dredging on four advanced industrial forecasting models to support sustainable business management," Annals of Operations Research, Springer, vol. 342(1), pages 215-264, November.
    18. Michał Jasiński & Tomasz Sikorski & Zbigniew Leonowicz & Klaudiusz Borkowski & Elżbieta Jasińska, 2020. "The Application of Hierarchical Clustering to Power Quality Measurements in an Electrical Power Network with Distributed Generation," Energies, MDPI, vol. 13(9), pages 1-19, May.
    19. Hector F. Calvo-Pardo & Tullio Mancini & Jose Olmo, 2020. "Neural Network Models for Empirical Finance," JRFM, MDPI, vol. 13(11), pages 1-22, October.
    20. Dag Tjøstheim & Martin Jullum & Anders Løland, 2023. "Some recent trends in embeddings of time series and dynamic networks," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 686-709, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1785-:d:1665635. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.