Optimal energy collection with rotational movement 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 displacement of components from their optimal optical positions. This, in turn, diminishes the overall energy capture performance of the entire system. In this context, we introduce two combinatorial optimization problems of great interest to PTC plants. The minimum tracking motion (MTM) problem is aimed at detecting the minimum number of movements needed while maintaining production within a given range. The maximal energy collection (MEC) problem seeks 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 maximums/minimums due to optical errors of the elements in the PTC system. The MTM and MEC problems are solved in O(n) time and O(n2m!*) time respectively, where n is the number of steps in the energy collection function, m the maximum number of movements of the solar structure, and !* 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.