Optimization Algorithms for Sustainable Operation of Multi-Unit Hydropower Plants

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Abstract
The work presented in this article concerns numerical studies on optimization methods used for the sustainable utilization of the energy potential of water, converting it into electricity in a hydropower plant equipped with more than one unit. These methods allow for maximization of production in given hydrological conditions, leading to the balanced, lossless, and environmentally friendly use of the renewable energy source that is water. Methods are selected from three groups, i.e., analytical, enumeration, and randomized. The results of calculations of optimal points of selected test functions carried out using the Broyden–Fletcher–Goldfarb–Shanno Limited-Memory Version (L-BFGS-B), Explicit Complete Enumeration (ECE), and Genetic Algorithm (GA) methods provided basic information on the features of these methods. Based on these tests, the GA method was selected to solve the problem of the optimal load distribution in a hydropower plant equipped with three identical hydro units. The defined optimization problem consisted of finding a configuration of hydro units in operation that would guarantee the maximum efficiency of the power plant under the imposed hydrological conditions. During the numerical studies, a number of calculations were performed to identify the impact of procedures and parameters characteristic of the optimization methods on the obtained results. Particular attention was paid to the GA method and penalty functions, enabling the elimination of results from the area of prohibited solutions.

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