IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v17y2025i5p2022-d1600512.html
   My bibliography  Save this article

Kullback–Leibler Divergence-Based Distributionally Robust Chance-Constrained Programming for PV Hosting Capacity Assessment in Distribution Networks

Author

Listed:
  • Chao Shen

    (School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China)

  • Haoming Liu

    (School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China)

  • Jian Wang

    (School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China)

  • Zhihao Yang

    (College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225000, China)

  • Chen Hai

    (College of Artificial Intelligence and Automation, Hohai University, Nanjing 211100, China)

Abstract

This paper addresses the challenge of assessing photovoltaic (PV) hosting capacity in distribution networks while accounting for the uncertainty of PV output, a critical step toward achieving sustainable energy transitions. Traditional optimization methods for dealing with uncertainty, including robust optimization (RO) and stochastic optimization (SO), often result in overly conservative or optimistic assessments, hindering the efficient integration of renewable energy. To overcome these limitations, this paper proposes a novel distributionally robust chance-constrained (DRCC) assessment method based on Kullback–Leibler (KL) divergence. First, the time-segment adaptive bandwidth kernel density estimation (KDE) combined with Copula theory is employed to model the conditional probability density of PV forecasting errors, capturing temporal and output-dependent correlations. The KL divergence is then used to construct a fuzzy set for PV output, quantifying its uncertainty within specified confidence levels. Finally, the assessment results are derived by integrating the fuzzy set into the optimization model. Case studies demonstrate its effectiveness of the method. Key findings indicate that higher confidence levels reduce PV hosting capacities due to broader uncertainty ranges, while increased historical sample sizes enhance the accuracy of distribution estimates, thereby increasing assessed capacities. By balancing conservatism and optimism, this method enables safer and more efficient PV integration, directly supporting sustainability goals such as reducing fossil fuel dependence and lowering carbon emissions. The findings provide actionable insights for grid operators to maximize renewable energy utilization while maintaining grid stability, advancing global efforts toward sustainable energy infrastructure.

Suggested Citation

  • Chao Shen & Haoming Liu & Jian Wang & Zhihao Yang & Chen Hai, 2025. "Kullback–Leibler Divergence-Based Distributionally Robust Chance-Constrained Programming for PV Hosting Capacity Assessment in Distribution Networks," Sustainability, MDPI, vol. 17(5), pages 1-23, February.
  • Handle: RePEc:gam:jsusta:v:17:y:2025:i:5:p:2022-:d:1600512
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/17/5/2022/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2071-1050/17/5/2022/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cho, Yongjun & Lee, Eunjung & Baek, Keon & Kim, Jinho, 2023. "Stochastic Optimization-Based hosting capacity estimation with volatile net load deviation in distribution grids," Applied Energy, Elsevier, vol. 341(C).
    2. Ismael, Sherif M. & Abdel Aleem, Shady H.E. & Abdelaziz, Almoataz Y. & Zobaa, Ahmed F., 2019. "State-of-the-art of hosting capacity in modern power systems with distributed generation," Renewable Energy, Elsevier, vol. 130(C), pages 1002-1020.
    3. Wu, Han & Yuan, Yue & Zhang, Xinsong & Miao, Ankang & Zhu, Junpeng, 2022. "Robust comprehensive PV hosting capacity assessment model for active distribution networks with spatiotemporal correlation," Applied Energy, Elsevier, vol. 323(C).
    4. Yao, Hongmin & Qin, Wenping & Jing, Xiang & Zhu, Zhilong & Wang, Ke & Han, Xiaoqing & Wang, Peng, 2022. "Possibilistic evaluation of photovoltaic hosting capacity on distribution networks under uncertain environment," Applied Energy, Elsevier, vol. 324(C).
    5. Li, Junkai & Ge, Shaoyun & Liu, Hong & Zhang, Shida & Wang, Chengshan & Wang, Pengxiang, 2023. "Distribution locational pricing mechanisms for flexible interconnected distribution system with variable renewable energy generation," Applied Energy, Elsevier, vol. 335(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. Emrani-Rahaghi, Pouria & Hashemi-Dezaki, Hamed & Ketabi, Abbas, 2023. "Efficient voltage control of low voltage distribution networks using integrated optimized energy management of networked residential multi-energy microgrids," Applied Energy, Elsevier, vol. 349(C).
    2. Vincent Umoh & Innocent Davidson & Abayomi Adebiyi & Unwana Ekpe, 2023. "Methods and Tools for PV and EV Hosting Capacity Determination in Low Voltage Distribution Networks—A Review," Energies, MDPI, vol. 16(8), pages 1-25, April.
    3. Karmaker, Ashish Kumar & Prakash, Krishneel & Siddique, Md Nazrul Islam & Hossain, Md Alamgir & Pota, Hemanshu, 2024. "Electric vehicle hosting capacity analysis: Challenges and solutions," Renewable and Sustainable Energy Reviews, Elsevier, vol. 189(PA).
    4. Enrico Dalla Maria & Mattia Secchi & David Macii, 2021. "A Flexible Top-Down Data-Driven Stochastic Model for Synthetic Load Profiles Generation," Energies, MDPI, vol. 15(1), pages 1-20, December.
    5. Zhu, Xingxu & Hou, Xiangchen & Li, Junhui & Yan, Gangui & Li, Cuiping & Wang, Dongbo, 2023. "Distributed online prediction optimization algorithm for distributed energy resources considering the multi-periods optimal operation," Applied Energy, Elsevier, vol. 348(C).
    6. Hao, Junhong & Feng, Xiaolong & Chen, Xiangru & Jin, Xilin & Wang, Xingce & Hao, Tong & Hong, Feng & Du, Xiaoze, 2024. "Optimal scheduling of active distribution network considering symmetric heat and power source-load spatial-temporal characteristics," Applied Energy, Elsevier, vol. 373(C).
    7. Md Tariqul Islam & M. Jahangir Hossain & Md. Ahasan Habib & Muhammad Ahsan Zamee, 2025. "Adaptive Hosting Capacity Forecasting in Distribution Networks with Distributed Energy Resources," Energies, MDPI, vol. 18(2), pages 1-25, January.
    8. Md Tariqul Islam & M. J. Hossain, 2023. "Artificial Intelligence for Hosting Capacity Analysis: A Systematic Literature Review," Energies, MDPI, vol. 16(4), pages 1-33, February.
    9. Muhyaddin Rawa & Abdullah Abusorrah & Yusuf Al-Turki & Martin Calasan & Mihailo Micev & Ziad M. Ali & Saad Mekhilef & Hussain Bassi & Hatem Sindi & Shady H. E. Abdel Aleem, 2022. "Estimation of Parameters of Different Equivalent Circuit Models of Solar Cells and Various Photovoltaic Modules Using Hybrid Variants of Honey Badger Algorithm and Artificial Gorilla Troops Optimizer," Mathematics, MDPI, vol. 10(7), pages 1-31, March.
    10. Ramitha Dissanayake & Akila Wijethunge & Janaka Wijayakulasooriya & Janaka Ekanayake, 2022. "Optimizing PV-Hosting Capacity with the Integrated Employment of Dynamic Line Rating and Voltage Regulation," Energies, MDPI, vol. 15(22), pages 1-19, November.
    11. Lewis Waswa & Munyaradzi Justice Chihota & Bernard Bekker, 2021. "A Probabilistic Conductor Size Selection Framework for Active Distribution Networks," Energies, MDPI, vol. 14(19), pages 1-19, October.
    12. G., Varathan & J., Belwin Edward, 2024. "A review of uncertainty management approaches for active distribution system planning," Renewable and Sustainable Energy Reviews, Elsevier, vol. 205(C).
    13. Yang, Shuxia & Wang, Xiongfei & Xu, Jiayu & Tang, Mingrun & Chen, Guang, 2023. "Distribution network adaptability assessment considering distributed PV “reverse power flow” behavior - a case study in Beijing," Energy, Elsevier, vol. 275(C).
    14. Yao, Hongmin & Qin, Wenping & Jing, Xiang & Zhu, Zhilong & Wang, Ke & Han, Xiaoqing & Wang, Peng, 2022. "Possibilistic evaluation of photovoltaic hosting capacity on distribution networks under uncertain environment," Applied Energy, Elsevier, vol. 324(C).
    15. C. Birk Jones & Matthew Lave & Matthew J. Reno & Rachid Darbali-Zamora & Adam Summers & Shamina Hossain-McKenzie, 2020. "Volt-Var Curve Reactive Power Control Requirements and Risks for Feeders with Distributed Roof-Top Photovoltaic Systems," Energies, MDPI, vol. 13(17), pages 1-17, August.
    16. Grzegorz Hołdyński & Zbigniew Skibko & Wojciech Walendziuk, 2024. "Power and Energy Losses in Medium-Voltage Power Grids as a Function of Current Asymmetry—An Example from Poland," Energies, MDPI, vol. 17(15), pages 1-18, July.
    17. Kuznetsov, G.V. & Kravchenko, E.V. & Pribaturin, N.A., 2024. "Influence of the air gaps between cells and the case of the storage battery on its representative temperatures," Energy, Elsevier, vol. 308(C).
    18. Ahmed I. Omar & Ziad M. Ali & Mostafa Al-Gabalawy & Shady H. E. Abdel Aleem & Mujahed Al-Dhaifallah, 2020. "Multi-Objective Environmental Economic Dispatch of an Electricity System Considering Integrated Natural Gas Units and Variable Renewable Energy Sources," Mathematics, MDPI, vol. 8(7), pages 1-37, July.
    19. Costa, Vinicius Braga Ferreira da & Bonatto, Benedito Donizeti, 2023. "Cutting-edge public policy proposal to maximize the long-term benefits of distributed energy resources," Renewable Energy, Elsevier, vol. 203(C), pages 357-372.
    20. Ibrahim Mohamed Diaaeldin & Mahmoud A. Attia & Amr K. Khamees & Othman A. M. Omar & Ahmed O. Badr, 2023. "A Novel Multiobjective Formulation for Optimal Wind Speed Modeling via a Mixture Probability Density Function," Mathematics, MDPI, vol. 11(6), pages 1-19, March.

    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:jsusta:v:17:y:2025:i:5:p:2022-:d:1600512. 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.