A new three-triangle based method to linearly concave hydropower output in long-term reservoir operation. (1st July 2022) - Zheng, Hao; Feng, Suzhen; Chen, Cheng; Wang, Jinwen
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. This paper presents a new three-triangle based method to linearly concave the HOF without introducing any integer variables, and mathematically proves its equivalence in fitting accuracy to the all-triangle based method in which any active plane needs to be compared with all the other active planes to ensure it is active within its triangular grid, making the number of constraints be increased dramatically. The two methods are applied in approximating the HOFs of 4 hydropower reservoirs located in the Lancang River. The case studies show that the present linearization method can achieve a root-mean-square error (RMSE) at 2.05% on average of the installed power capacity, the same as the all-grid concaving method, but takes only less than 0.097s in solving the problem, 80 times faster than the all-grid concaving method. The present method should be very promising in solving the real-world hydropower scheduling problems, especially when the linearization needs to be done frequently during the solution procedure. Highlights: A new three-triangle based method to linearly concave the hydropower output function without any integer variables. Mathematically proves the model equivalence in fitting accuracy to the all-triangle based method. Achieving a root-mean-square error at 2.05% on average of the installed power capacity for the real-world hydropower. Achieving the same accuracy is 80 times faster than the all-grid concaving method.