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.

翻译：在基于抛物槽式集热器（PTC）的聚光太阳能（CSP）电站中，太阳跟踪以离散时间间隔进行，每个间隔代表集热器系统的一次运动。移动重型机械结构的动作可能导致部件产生裂纹、弯曲和/或从其最佳光学位置发生位移，进而降低整个系统捕获能量的整体性能。在此背景下，我们引入了两个组合优化问题，以限制集热器的跟踪步数，从而降低故障事件和污染物泄漏的风险。一方面，最小跟踪运动（MTM）问题旨在检测在将产量维持在给定范围内的前提下所需的最小运动次数。另一方面，最大能量收集（MEC）问题旨在通过预定次数的运动实现最优能量生产。这两个问题的求解均假设能量收集函数可能因PTC系统中元件的光学误差而包含任意数量的局部极大值/极小值。MTM问题和MEC问题分别在O(n)时间和O(n²mw*)时间内得到解决，其中n为能量收集函数中的步数，m为太阳能结构的最大运动次数，w*为该结构可覆盖的最大振幅角。实际实验展示了所提解决方案的优势。尽管这些问题可在多项式时间内求解，我们证明了MEC问题一个稍作修改版本的NP难性。所提出的算法具有通用性，可适用于其他CSP系统中的太阳跟踪调度。