IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v15y2022i20p7565-d941561.html
   My bibliography  Save this article

A Novel Interval Programming Method and Its Application in Power System Optimization Considering Uncertainties in Load Demands and Renewable Power Generation

Author

Listed:
  • Dapeng Wang

    (College of Electrical and Information Engineering, Hunan University, Changsha 410082, China)

  • Cong Zhang

    (College of Electrical and Information Engineering, Hunan University, Changsha 410082, China)

  • Wanqing Jia

    (College of Electrical and Information Engineering, Hunan University, Changsha 410082, China)

  • Qian Liu

    (College of Electrical and Information Engineering, Hunan University, Changsha 410082, China)

  • Long Cheng

    (College of Electrical and Information Engineering, Hunan University, Changsha 410082, China)

  • Huaizhi Yang

    (College of Electrical and Information Engineering, Hunan University, Changsha 410082, China)

  • Yufeng Luo

    (College of Electrical and Information Engineering, Hunan University, Changsha 410082, China)

  • Na Kuang

    (Academic Affairs Office, Nanya Wangcheng School, Changsha 410019, China)

Abstract

This paper expresses the output power of renewable generators and load demand as interval data and develops the interval economic dispatch (IED), as well as interval reactive power optimization (IRPO) models. The two models are generalized into a specific type of linear interval programming (LIP) and nonlinear interval programming (NLIP), respectively. A security limits method (SLM) is proposed to solve LIP and NLIP problems. As for the LIP, the maximum radii of the interval variables are first calculated by the optimizing-scenarios method (OSM) for defining security limits, and the LIP is transformed into deterministic linear programming (LP), for which its constraints are the security limits, which can be solved by the simplex method. As for the NLIP, Monte Carlo simulations were used to obtain the maximum radii of the interval variables, and the average interval ratio of the interval variables is defined to compute the security limits for transforming the NLIP to deterministic nonlinear programming (NLP), which can be solved by using the interior point method. Finally, the IED and IRPO are used to verify the effectiveness and engineering of the proposed SLM.

Suggested Citation

  • Dapeng Wang & Cong Zhang & Wanqing Jia & Qian Liu & Long Cheng & Huaizhi Yang & Yufeng Luo & Na Kuang, 2022. "A Novel Interval Programming Method and Its Application in Power System Optimization Considering Uncertainties in Load Demands and Renewable Power Generation," Energies, MDPI, vol. 15(20), pages 1-19, October.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:20:p:7565-:d:941561
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/15/20/7565/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/15/20/7565/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nikolaos P. Theodorakatos & Miltiadis Lytras & Rohit Babu, 2020. "Towards Smart Energy Grids: A Box-Constrained Nonlinear Underdetermined Model for Power System Observability Using Recursive Quadratic Programming," Energies, MDPI, vol. 13(7), pages 1-17, April.
    2. Jiang, C. & Han, X. & Liu, G.R. & Liu, G.P., 2008. "A nonlinear interval number programming method for uncertain optimization problems," European Journal of Operational Research, Elsevier, vol. 188(1), pages 1-13, July.
    3. Abdollahipour, Armin & Sayyaadi, Hoseyn, 2022. "Optimal design of a hybrid power generation system based on integrating PEM fuel cell and PEM electrolyzer as a moderator for micro-renewable energy systems," Energy, Elsevier, vol. 260(C).
    4. Abdullah Shaheen & Ahmed Ginidi & Ragab El-Sehiemy & Abdallah Elsayed & Ehab Elattar & Hassen T. Dorrah, 2022. "Developed Gorilla Troops Technique for Optimal Power Flow Problem in Electrical Power Systems," Mathematics, MDPI, vol. 10(10), pages 1-29, May.
    5. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hessam Golmohamadi & Saeed Golestan & Rakesh Sinha & Birgitte Bak-Jensen, 2024. "Demand-Side Flexibility in Power Systems, Structure, Opportunities, and Objectives: A Review for Residential Sector," Energies, MDPI, vol. 17(18), pages 1-22, September.

    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. Da Li & Shijie Zhang & Yunhan Xiao, 2020. "Interval Optimization-Based Optimal Design of Distributed Energy Resource Systems under Uncertainties," Energies, MDPI, vol. 13(13), pages 1-18, July.
    2. Mahdi Zarghami & Nasim Safari & Ferenc Szidarovszky & Shafiqul Islam, 2015. "Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(12), pages 4285-4303, September.
    3. Shahenda Sarhan & Abdullah Shaheen & Ragab El-Sehiemy & Mona Gafar, 2023. "An Augmented Social Network Search Algorithm for Optimal Reactive Power Dispatch Problem," Mathematics, MDPI, vol. 11(5), pages 1-42, March.
    4. Samir A. Abass, 2012. "0-1 integer interval number programming approach for the multilevel generalized assignment problem," E3 Journal of Business Management and Economics., E3 Journals, vol. 3(9), pages 326-329.
    5. Jaime Pilatásig & Diego Carrión & Manuel Jaramillo, 2022. "Resilience Maximization in Electrical Power Systems through Switching of Power Transmission Lines," Energies, MDPI, vol. 15(21), pages 1-15, November.
    6. Tong Xin & Guolai Yang & Fengjie Xu & Quanzhao Sun & Alexandi Minak, 2021. "Modeling, Simulation and Uncertain Optimization of the Gun Engraving System," Mathematics, MDPI, vol. 9(4), pages 1-25, February.
    7. Rahaman, Mostafijur & Mondal, Sankar Prasad & Alam, Shariful & Metwally, Ahmed Sayed M. & Salahshour, Soheil & Salimi, Mehdi & Ahmadian, Ali, 2022. "Manifestation of interval uncertainties for fractional differential equations under conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    8. Hsien-Chung Wu, 2019. "Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables," Mathematics, MDPI, vol. 7(7), pages 1-105, June.
    9. Xiaobin Yang & Haitao Lin & Gang Xiao & Huanbin Xue & Xiaopeng Yang, 2019. "Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    10. Farzaneh Ferdowsi & Hamid Reza Maleki & Sanaz Rivaz, 2020. "Air refueling tanker allocation based on a multi-objective zero-one integer programming model," Operational Research, Springer, vol. 20(4), pages 1913-1938, December.
    11. Ćalasan, Martin & Abdel Aleem, Shady H.E. & Hasanien, Hany M. & Alaas, Zuhair M. & Ali, Ziad M., 2023. "An innovative approach for mathematical modeling and parameter estimation of PEM fuel cells based on iterative Lambert W function," Energy, Elsevier, vol. 264(C).
    12. He, Li & Huang, Guo H. & Lu, Hongwei, 2011. "Bivariate interval semi-infinite programming with an application to environmental decision-making analysis," European Journal of Operational Research, Elsevier, vol. 211(3), pages 452-465, June.
    13. Fabiola Roxana Villanueva & Valeriano Antunes Oliveira, 2022. "Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 896-923, September.
    14. Mrinal Jana & Geetanjali Panda, 2018. "$$\chi$$ χ -Optimal solution of single objective nonlinear optimization problem with uncertain parameters," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 165-186, March.
    15. P. Kumar & G. Panda, 2017. "Solving nonlinear interval optimization problem using stochastic programming technique," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 752-765, December.
    16. Jamal, Raheela & Zhang, Junzhe & Men, Baohui & Khan, Noor Habib & Ebeed, Mohamed & Jamal, Tanzeela & Mohamed, Emad A., 2024. "Chaotic-quasi-oppositional-phasor based multi populations gorilla troop optimizer for optimal power flow solution," Energy, Elsevier, vol. 301(C).
    17. Hussain A. Alhaiz & Ahmed S. Alsafran & Ali H. Almarhoon, 2023. "Single-Phase Microgrid Power Quality Enhancement Strategies: A Comprehensive Review," Energies, MDPI, vol. 16(14), pages 1-28, July.
    18. Yang, Rui & Mohamed, Amira & Kim, Kibum, 2023. "Optimal design and flow-field pattern selection of proton exchange membrane electrolyzers using artificial intelligence," Energy, Elsevier, vol. 264(C).
    19. S. Rivaz & M. Yaghoobi, 2013. "Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 625-649, September.
    20. Tong Xin & Guolai Yang & Liqun Wang & Quanzhao Sun, 2020. "Numerical Calculation and Uncertain Optimization of Energy Conversion in Interior Ballistics Stage," Energies, MDPI, vol. 13(21), pages 1-21, November.

    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:15:y:2022:i:20:p:7565-:d:941561. 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.