A High-Precision, All-Rectangle-Based Method Linearly Concave Hydropower Output in Long-Term Reservoir Operation

Hao Zheng, Yan Huang, Yongqiang Wang, Feixiang Hou, Yong Xu, Cheng Chen, Suzhen Feng and Jinwen Wang ()
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Hao Zheng: Water Resources Management, Changjiang River Scientific Research Institute, Wuhan 430010, China
Yan Huang: Water Resources Management, Changjiang River Scientific Research Institute, Wuhan 430010, China
Yongqiang Wang: Water Resources Management, Changjiang River Scientific Research Institute, Wuhan 430010, China
Feixiang Hou: Faculty of Electric Power Engineering, Kunming University of Science and Technology, Kunming 650500, China
Yong Xu: Faculty of Electric Power Engineering, Kunming University of Science and Technology, Kunming 650500, China
Cheng Chen: Hubei Key Laboratory of Digital River Basin Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Suzhen Feng: Hubei Key Laboratory of Digital River Basin Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Jinwen Wang: Hubei Key Laboratory of Digital River Basin Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Energies, 2025, vol. 18, issue 19, 1-23

Abstract: The nonlinearity and non-convexity of the hydropower output function (HOF) make it very challenging to search for the optimal solution to the hydropower scheduling problem, which, however, can be more easily solved with consistency by mathematical programming if the HOF can be properly linearized with high accuracy. In this paper, a detailed review of different linear concaving approximation methods to model the HOF is presented, and a high-precision, all-rectangle linear concaving approximation method is proposed. It avoids the drawback of existing rectangular grid linear approximation methods which introduce a large number of integer variables and reduce solution efficiency by avoiding the accurate expression of fitting error at the corner points. It is mathematically proved that the method based on this rectangular subdivision can converge to any concave function with arbitrary precision as the grid resolution increases. The approximated results of the output functions of the four cascaded hydropower plants in the Lancang River show that both the proposed method and the existing method can reduce the average fitting error from 2.16% of installed capacity to 1.49% compared to the high-efficiency method. Although the proposed method is slower in solving speed than the high-efficiency method, it is significantly better than the unstable existing method.

Keywords: reservoir operation; hydropower output function; piecewise linearization; linear programming; rectangular grid (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: 2025
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