Optimal hydropower operation of multi-reservoir systems: hybrid cellular automata-simulated annealing approach

Hydropower operation of multi-reservoir systems is very difficult to solve mostly due to their nonlinear, nonconvex and large-scale nature. While conventional methods are long known to be incapable of solving these types of problems, evolutionary algorithms are shown to successfully handle the complexity of these problems at the expense of very large computational cost, particularly when population-based methods are used. A novel hybrid cellular automata-simulated annealing (CA-SA) method is proposed in this study which avoids the shortcomings of the existing conventional and evolutionary methods for the optimal hydropower operation of multi-reservoir systems. The start and the end instances of time at each operation period is considered as the CA cells with the reservoir storages at these instances are taken as the cell state which leads to a cell neighborhood defined by the two adjacent periods. The local updating rule of the proposed CA is derived by projecting the objective function and the constraints of the original problem on the cell neighborhoods represented by an optimization sub-problem with the number of decision variables equal to the number of reservoirs in the system. These sub-problems are subsequently solved by a modified simulated annealing approach to finding the updated values of the cell states. Once all the cells are covered, the cell states are updated and the process is iterated until the convergence is achieved. The proposed method is first used for hydropower operation of two well-known benchmark problems, namely the well-known four- and ten-reservoir problems. The results are compared with the existing results obtained from cellular automata. Genetic algorithm and particle swarm optimization indicating that the proposed method is much more efficient than existing algorithms. The proposed method is then applied for long-term hydropower operation of a real-world three-reservoir system in the USA, and the results are presented and compared with the existing results.