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 time and time respectively, where is the number of steps in the energy collection function, 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.

中文翻译：

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聚光太阳能发电厂中具有旋转运动约束的最佳能量收集


在基于抛物面槽式集热器 (PTC) 的聚光太阳能 (CSP) 发电厂中，以离散的时间间隔跟踪太阳，每个时间间隔代表集热器系统的一次移动。移动重型机械结构的行为可能会导致部件出现裂纹、弯曲和/或偏离其最佳光学位置。这反过来又降低了整个系统的整体能量捕获性能。在此背景下，我们介绍了 PTC 工厂非常感兴趣的两个组合优化问题。最小跟踪运动（MTM）问题旨在检测在给定范围内维持生产的同时所需的最小运动数量。最大能量收集（MEC）问题寻求在预定的运动次数内实现最佳的能量产生。假设能量收集函数由于 PTC 系统中元件的光学误差而包含任意数量的局部最大值/最小值，这两个问题都可以得到解决。 MTM和MEC问题分别在时间和时间上得到解决，其中 是能量收集函数的步数、太阳能结构的最大运动次数以及结构可以覆盖的最大振幅角。这些解决方案的优点在实际实验中得到了体现。虽然这些问题可以在多项式时间内解决，但我们建立了 MEC 问题的稍微修改版本的 NP 难度。所提出的算法是通用的，可以适用于安排其他 CSP 系统中的太阳能跟踪。