IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v18y2025i10p2461-d1653296.html
   My bibliography  Save this article

Statistical Foundations of Generative AI for Optimal Control Problems in Power Systems: Comprehensive Review and Future Directions

Author

Listed:
  • Elinor Ginzburg-Ganz

    (The Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel)

  • Eden Dina Horodi

    (The Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel)

  • Omar Shadafny

    (The Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel)

  • Uri Savir

    (The Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel)

  • Ram Machlev

    (The Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel)

  • Yoash Levron

    (The Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel)

Abstract

With the rapid advancement of deep learning, generative artificial intelligence (Gen-AI) has emerged as a powerful tool, unlocking new prospects in the power systems sector. Despite the evident success of these methods and the rapid growth of this field in the power systems community, there is still a pressing need for a deeper understanding of how different evaluation metrics relate to the underlying statistical structure of the models. Another related important question is what tools can be used to quantify the different uncertainties, which are inherent in these problems, and stem not only from the physical system but also from the nature of the generative model itself. This paper attempts to address these challenges and provides a comprehensive review of existing evaluation metrics for generative models applied in various power system tasks. We analyze how these metrics align with the statistical properties of the models and explore their strengths and limitations. We also examine different sources of uncertainty, distinguishing between uncertainties inherent to the learning model, those arising from measurement errors, and other sources. Our general aim is to promote a better understanding of generative models as they are being applied in power systems to support this fascinating growing trend.

Suggested Citation

  • Elinor Ginzburg-Ganz & Eden Dina Horodi & Omar Shadafny & Uri Savir & Ram Machlev & Yoash Levron, 2025. "Statistical Foundations of Generative AI for Optimal Control Problems in Power Systems: Comprehensive Review and Future Directions," Energies, MDPI, vol. 18(10), pages 1-54, May.
  • Handle: RePEc:gam:jeners:v:18:y:2025:i:10:p:2461-:d:1653296
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/18/10/2461/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1996-1073/18/10/2461/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yin, Linfei & Zhang, Bin, 2021. "Time series generative adversarial network controller for long-term smart generation control of microgrids," Applied Energy, Elsevier, vol. 281(C).
    2. Qi, Yuchen & Hu, Wei & Dong, Yu & Fan, Yue & Dong, Ling & Xiao, Ming, 2020. "Optimal configuration of concentrating solar power in multienergy power systems with an improved variational autoencoder," Applied Energy, Elsevier, vol. 274(C).
    3. Dong, Wei & Chen, Xianqing & Yang, Qiang, 2022. "Data-driven scenario generation of renewable energy production based on controllable generative adversarial networks with interpretability," Applied Energy, Elsevier, vol. 308(C).
    4. Huang, Xiaoqiao & Li, Qiong & Tai, Yonghang & Chen, Zaiqing & Liu, Jun & Shi, Junsheng & Liu, Wuming, 2022. "Time series forecasting for hourly photovoltaic power using conditional generative adversarial network and Bi-LSTM," Energy, Elsevier, vol. 246(C).
    5. Dalla Valle, Alessandra & Furlan, Claudia, 2011. "Forecasting accuracy of wind power technology diffusion models across countries," International Journal of Forecasting, Elsevier, vol. 27(2), pages 592-601, April.
    6. Dalla Valle, Alessandra & Furlan, Claudia, 2011. "Forecasting accuracy of wind power technology diffusion models across countries," International Journal of Forecasting, Elsevier, vol. 27(2), pages 592-601.
    7. Wei, Hu & Hongxuan, Zhang & Yu, Dong & Yiting, Wang & Ling, Dong & Ming, Xiao, 2019. "Short-term optimal operation of hydro-wind-solar hybrid system with improved generative adversarial networks," Applied Energy, Elsevier, vol. 250(C), pages 389-403.
    8. Luo, Zheng & Lin, Xiaojie & Qiu, Tianyue & Li, Manjie & Zhong, Wei & Zhu, Lingkai & Liu, Shuangcui, 2024. "Investigation of hybrid adversarial-diffusion sample generation method of substations in district heating system," Energy, Elsevier, vol. 288(C).
    9. Mansour, Shaza H. & Azzam, Sarah M. & Hasanien, Hany M. & Tostado-Veliz, Marcos & Alkuhayli, Abdulaziz & Jurado, Francisco, 2024. "Wasserstein generative adversarial networks-based photovoltaic uncertainty in a smart home energy management system including battery storage devices," Energy, Elsevier, vol. 306(C).
    10. Zhai, Xiangyu & Li, Zening & Li, Zhengmao & Xue, Yixun & Chang, Xinyue & Su, Jia & Jin, Xiaolong & Wang, Peng & Sun, Hongbin, 2025. "Risk-averse energy management for integrated electricity and heat systems considering building heating vertical imbalance: An asynchronous decentralized approach," Applied Energy, Elsevier, vol. 383(C).
    11. Ye, Lin & Peng, Yishu & Li, Yilin & Li, Zhuo, 2024. "A novel informer-time-series generative adversarial networks for day-ahead scenario generation of wind power," Applied Energy, Elsevier, vol. 364(C).
    12. Dumas, Jonathan & Wehenkel, Antoine & Lanaspeze, Damien & Cornélusse, Bertrand & Sutera, Antonio, 2022. "A deep generative model for probabilistic energy forecasting in power systems: normalizing flows," Applied Energy, Elsevier, vol. 305(C).
    13. Xuejiao Gong & Bo Tang & Ruijin Zhu & Wenlong Liao & Like Song, 2020. "Data Augmentation for Electricity Theft Detection Using Conditional Variational Auto-Encoder," Energies, MDPI, vol. 13(17), pages 1-14, August.
    14. Zhang, Xiangyu & Glaws, Andrew & Cortiella, Alexandre & Emami, Patrick & King, Ryan N., 2025. "Deep generative models in energy system applications: Review, challenges, and future directions," Applied Energy, Elsevier, vol. 380(C).
    15. Niu, Dongxiao & Yu, Min & Sun, Lijie & Gao, Tian & Wang, Keke, 2022. "Short-term multi-energy load forecasting for integrated energy systems based on CNN-BiGRU optimized by attention mechanism," Applied Energy, Elsevier, vol. 313(C).
    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. Zhang, Xiangyu & Glaws, Andrew & Cortiella, Alexandre & Emami, Patrick & King, Ryan N., 2025. "Deep generative models in energy system applications: Review, challenges, and future directions," Applied Energy, Elsevier, vol. 380(C).
    2. Feng, Zhong-kai & Wang, Xin & Niu, Wen-jing, 2025. "Complementary operation optimization of cascade hydropower reservoirs and photovoltaic energy using cooperation search algorithm and conditional generative adversarial networks," Energy, Elsevier, vol. 328(C).
    3. Ye, Lin & Peng, Yishu & Li, Yilin & Li, Zhuo, 2024. "A novel informer-time-series generative adversarial networks for day-ahead scenario generation of wind power," Applied Energy, Elsevier, vol. 364(C).
    4. Liuqing Gu & Jian Xu & Deping Ke & Youhan Deng & Xiaojun Hua & Yi Yu, 2024. "Short-Term Output Scenario Generation of Renewable Energy Using Transformer–Wasserstein Generative Adversarial Nets-Gradient Penalty," Sustainability, MDPI, vol. 16(24), pages 1-20, December.
    5. Mahdi Khodayar & Jacob Regan, 2023. "Deep Neural Networks in Power Systems: A Review," Energies, MDPI, vol. 16(12), pages 1-38, June.
    6. Turowski, M. & Heidrich, B. & Weingärtner, L. & Springer, L. & Phipps, K. & Schäfer, B. & Mikut, R. & Hagenmeyer, V., 2024. "Generating synthetic energy time series: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 206(C).
    7. Mousavi, Rashin & Mousavi, Arash & Mousavi, Yashar & Tavasoli, Mahsa & Arab, Aliasghar & Kucukdemiral, Ibrahim Beklan & Alfi, Alireza & Fekih, Afef, 2025. "Revolutionizing solar energy resources: The central role of generative AI in elevating system sustainability and efficiency," Applied Energy, Elsevier, vol. 382(C).
    8. Zhao, Wei & Shao, Zhen & Yang, Shanlin & Lu, Xinhui, 2025. "A novel conditional diffusion model for joint source-load scenario generation considering both diversity and controllability," Applied Energy, Elsevier, vol. 377(PC).
    9. Mohammad Mahdi Forootan & Iman Larki & Rahim Zahedi & Abolfazl Ahmadi, 2022. "Machine Learning and Deep Learning in Energy Systems: A Review," Sustainability, MDPI, vol. 14(8), pages 1-49, April.
    10. Lingxue Lin & Zuowei You & Fengjiao Li & Jun Liu & Chengwei Yang, 2025. "A Two-Stage Hidden Markov Model for Medium- to Long-Term Multiple Wind Farm Power Scenario Generation," Energies, MDPI, vol. 18(8), pages 1-15, April.
    11. Bessi, Alessandro & Guidolin, Mariangela & Manfredi, Piero, 2021. "The role of gas on future perspectives of renewable energy diffusion: Bridging technology or lock-in?," Renewable and Sustainable Energy Reviews, Elsevier, vol. 152(C).
    12. Chen, Junjie & Liu, Pei & Lin, Borong & Zhou, Hao & Papachristos, George, 2025. "The diffusion of prefabrication technology and its potential for CO2 emissions reduction in China: A combined system dynamics and agent-based study," Technological Forecasting and Social Change, Elsevier, vol. 210(C).
    13. Toka, Agorasti & Iakovou, Eleftherios & Vlachos, Dimitrios & Tsolakis, Naoum & Grigoriadou, Anastasia-Loukia, 2014. "Managing the diffusion of biomass in the residential energy sector: An illustrative real-world case study," Applied Energy, Elsevier, vol. 129(C), pages 56-69.
    14. Tibebu, Tiruwork B. & Hittinger, Eric & Miao, Qing & Williams, Eric, 2022. "Roles of diffusion patterns, technological progress, and environmental benefits in determining optimal renewable subsidies in the US," Technological Forecasting and Social Change, Elsevier, vol. 182(C).
    15. Kurdgelashvili, Lado & Shih, Cheng-Hao & Yang, Fan & Garg, Mehul, 2019. "An empirical analysis of county-level residential PV adoption in California," Technological Forecasting and Social Change, Elsevier, vol. 139(C), pages 321-333.
    16. Duan, Hong-Bo & Zhu, Lei & Fan, Ying, 2014. "A cross-country study on the relationship between diffusion of wind and photovoltaic solar technology," Technological Forecasting and Social Change, Elsevier, vol. 83(C), pages 156-169.
    17. Lee, Chul-Yong & Huh, Sung-Yoon, 2017. "Forecasting the diffusion of renewable electricity considering the impact of policy and oil prices: The case of South Korea," Applied Energy, Elsevier, vol. 197(C), pages 29-39.
    18. Furlan, Claudia & Mortarino, Cinzia, 2018. "Forecasting the impact of renewable energies in competition with non-renewable sources," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P2), pages 1879-1886.
    19. Mei Yang & Hong Fan & Kang Zhao, 2019. "PM 2.5 Prediction with a Novel Multi-Step-Ahead Forecasting Model Based on Dynamic Wind Field Distance," IJERPH, MDPI, vol. 16(22), pages 1-21, November.
    20. Qing Zhou & Zhengyi Wu & Wenchong Chen & Wenqing Chen & Yao Liang, 2024. "Two‐sided networks coordination for manufacturing technology standards' diffusion from home to host countries: A one‐leader and multiple‐followers Stackelberg game with multiple objectives," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 45(4), pages 2108-2129, June.

    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:jeners:v:18:y:2025:i:10:p:2461-:d:1653296. 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.