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

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  • 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
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    References listed on IDEAS

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    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.
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    5. 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.
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    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.

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