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

Dapeng Wang, Cong Zhang (), Wanqing Jia, Qian Liu, Long Cheng, Huaizhi Yang, Yufeng Luo and Na Kuang
Additional contact information
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

Energies, 2022, vol. 15, issue 20, 1-19

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.

Keywords: interval uncertainty; linear; nonlinear; security limits method (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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