Optimal energy collection with rotational movements constraints in concentrated solar power plants

In Concentrated Solar Power (CSP) plants based on Parabolic Trough Collectors (PTC), the Sun is tracked at discrete time intervals, with each interval representing a movement of the collector system. The act of moving heavy mechanical structures can lead to the development of cracks, bending, and/or displacements of components from their optimal optical positions. This, in turn, diminishes the overall performance of the entire system for energy capture. In this context, we introduce two combinatorial optimization problems to limit the number of tracking steps of the collector and hence the risk of failure incidents and contaminant leaks. On the one hand, the Minimum Tracking Motion (MTM)-Problem aims at detecting the minimum number of movements while maintaining the production within a given range. On the other hand, the Maximal Energy Collection (MEC)-Problem aims to achieve optimal energy production within a predetermined number of movements. Both problems are solved assuming scenarios where the energy collection function contains any number of local maximum/minimum due to optical errors of the elements in the PTCsystem. The MTM- and MEC-Problems are solved in O(n) time and O(n2mw*) time, respectively, being n the number of steps in the energy collection function, m the maximum number of movements of the solar structure, and w* the maximal amplitude angle that the structure can cover. The advantages of the solutions are shown in realistic experiments. While these problems can be solved in polynomial time, we establish the NP-hardness of a slightly modified version of the MEC-Problem. The proposed algorithms are generic and can be adapted to schedule solar tracking in other CSP systems.