The optimal operation of multi-reservoir hydropower systems is challenging to solve because: 1) the input (e.g. inflow) imprecision and uncertainties need to be addressed; 2) the decision making process is multi-stage and dynamic; 3) the resulting optimization problem is often large-scale with a lot of decision variables and constraints; 4) the hydraulic coupling among the cascaded reservoirs complicates the problem; 5) owing to the various physical and operational constraints, it isn’t easy to find a feasible solution that satisfies all the constraints; 6) the hydropower performance model and the problem are usually nonlinear, could be nonconvex, discontinuous and non-differentiable, and even mixed-integer; and 7) sometimes multiple conflicting objectives are considered.

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The optimal operation of multi-reservoir hydropower systems is challenging to solve because: 1) the input (e.g. inflow) imprecision and uncertainties need to be addressed; 2) the decision making process is multi-stage and dynamic; 3) the resulting optimization problem is often large-scale with a lot of decision variables and constraints; 4) the hydraulic coupling among the cascaded reservoirs complicates the problem; 5) owing to the various physical and operational constraints, it isn’t easy to find a feasible solution that satisfies all the constraints; 6) the hydropower performance model and the problem are usually nonlinear, could be nonconvex, discontinuous and non-differentiable, and even mixed-integer; and 7) sometimes multiple conflicting objectives are considered.

Metaheuristics are promising optimization algorithms for tackling such operation problems. Based on a state-of-the-art powerful metaheuristic called comprehensive learning particle swarm optimization (CLPSO), enhanced CLPSO (ECLPSO) and multi-swarm CLPSO (MSCLPSO) are respectively proposed for single-objective optimization and multi-objective optimization. ECLPSO is well balanced in exploration and exploitation. MSCLPSO helps to find multiple nondominated solutions distributed reasonably over the true Pareto front, thereby providing the decision maker diverse information to determine the final tradeoff. When applying ECLPSO and MSCLPSO to the optimal operation of multi-reservoir hydropower systems, two strategies are proposed to handle the various physical and operational constraints: 1) the outflow and storage volume constraints are appropriately enforced to achieve a tradeoff between preserving diversity and facilitating convergence; and 2) with the penalty function technique adopted to penalize the constraint violations and convert the original constrained problem into an unconstrained one, the penalty factor is dynamically adjusted in order to encourage exploration of the search space in the beginning and gradually guide the search to concentrate in the feasible region. ECLPSO is applied to the short-term scheduling of a 4-reservoir hydrothermal power system with the objective of minimizing fuel cost and the long-term planning of China’s Xiluodu-Xiangjiaba-Threegorges 3-reservoir hydropower system with the objective of maximizing hydropower generation. MSCLPSO is applied to the long-term planning of China’s Threegorges-Gezhouba 2-reservoir hydropower system, with two conflicting objectives optimized simultaneously, i.e. maximizing hydropower generation and minimizing deviation from the outflow lower target in order to realize the system’s economic, environmental, and social benefits during the drought season. Experimental results on commonly used benchmark problems and the selected case studies demonstrate the satisfactory performance of ECLPSO, MSCLPSO, and the constraint enforcement and penalty factor adjustment strategies.

The input imprecision can be addressed by forecasting. A decomposition-based data-driven model called FT-SVR is proposed for the forecasting of monthly reservoir inflows and the Three Gorges Dam is taken as the case for study. FT-SVR forecasts the future based on antecedent records. The historical inflow time series contain oscillations of disparate scales, thus Fourier transform (FT) is used to appropriately decompose the series into multiple components with each decomposed component having a clear physical meaning. Support vector regression (SVR) is employed to develop an independent forecast model for each decomposed component. Furthermore, ECLPSO is applied to calibrate the parameters of each independent SVR model. Experimental results demonstrate that FT-SVR is able to give almost perfect forecasting of the monthly inflows for the Three Gorges Dam.