A generalized closed-form equation for the shaded collector fraction in solar arrays on rolling or undulating terrain is provided for single-axis tracking and fixed-tilt systems. The equation accounts for different rotation angles between the shaded and shading trackers, cross-axis slope between the two trackers, and offset between the collector plane and axis of rotation. The validity of the equation is demonstrated through comparison with numerical ray-tracing simulations and remaining minor sources of error are quantified. Additionally, a simple procedure to determine backtracking rotations for each row in an array installed on the rolling terrain (varying in the direction perpendicular to the tracker axes) is provided. The backtracking equation accounts for a desired shaded fraction (including complete shade avoidance) as well as an axis-collector offset. Test cases are provided to facilitate implementation of these equations.

中文翻译：

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起伏地形上单轴跟踪器的阴影分数和回溯

为单轴跟踪和固定倾斜系统提供了滚动或起伏地形上太阳能电池阵列中阴影收集器部分的广义闭式方程。该方程考虑了阴影跟踪器和阴影跟踪器之间的不同旋转角度、两个跟踪器之间的横轴斜率以及收集器平面和旋转轴之间的偏移。通过与数值光线追踪模拟的比较证明了该方程的有效性，并对剩余的次要误差源进行了量化。此外，还提供了一个简单的程序来确定安装在起伏地形上的阵列中每一行的回溯旋转（在垂直于跟踪器轴的方向上变化）。回溯方程考虑了所需的阴影部分（包括完全的阴影避免）以及轴收集器偏移。提供测试用例以促进这些方程的实现。