# Detection and Optimization of Photovoltaic Arrays' Tilt Angles Using Remote Sensing Data
## 2 Methodology  
The overall workflow of the proposed method is illustrated in Figure 2. In the first stage, VHR imagery is utilized to detect individual 2D modules using a U-shaped semantic segmentation model, which returns a coarse result that is then further refined using the Fine Optimization Module (FOM). The 2D width and height of each module can be easily extracted from the resulting detection. This segmentation approach takes advantage of advanced convolutional layers and skip connections inherent in the U-shaped architecture to effectively handle variations in PV module appearance due to different illumination conditions, module types, and partial occlusions. The subsequent refinement through FOM further corrects inaccuracies, addressing issues such as merging modules in close proximity or splitting larger modules erroneously.  
In the second stage, airborne LiDAR data are processed into a 2.5D topological grid. This aids in estimating the tilt and aspect angles of the detected modules, which can then be used together with width and height information extracted from VHR imagery, allowing for accurate 3D reconstruction and positioning within the grid. In addition, the grid provides a detailed representation of the surrounding environment. It is crucial to note that typical airborne LiDAR point cloud data lack sufficient density to detect the entire modules' 2D or 3D structures, as typical airborne LiDAR scans contain 5 to 10 points per 1 m\({}^{2}\)[3]. Thus, VHR imagery remains indispensable. It should be noted that merely three 3D points detected on a module, from LiDAR scanning, are adequate to determine its geometric plane, as well as tilt and aspect angles from the plane's normal vector. The detected and reconstructed 3D modules are then grouped into their respective 3D arrays based on their proximity and characteristics by using a clustering algorithm. Since the clustering process incorporates both geometric attributes (i.e., slope and aspect angles) and spatial  
Figure 2: Workflow of the proposed method for optimization of detected arrays’ tilt angle based on fusion of VHR imagery and airborne LiDAR data.  
position, it ensures that the modules belonging to the same physical PV array are accurately grouped together.  
In the last stage, the optimization process then iteratively conducts a simulation of hourly solar irradiance throughout the entire year (i.e., solar potential) for each module (within a given array) after the hypothetical tilt angle change in each optimization iteration. The irradiance simulation considers the additional input of the location's Typical Meteorological Year (TMY) for the direct and diffuse irradiance data and optionally modules' specifications if electricity production is to be estimated. Moreover, the irradiance simulation considers direct and anisotropic Perez diffuse irradiances, as well as shadowing in-between PV arrays and from surrounding surfaces (e.g., buildings, hills) represented in the 2.5D grid. The optimization result is an optimal tilt angle estimation for each PV array, in order to maximize annual solar irradiance for corresponding modules for the given array.  
The next three subsections provide a more detailed description of the proposed method, covering the detection of 2D modules, their 3D reconstruction, and finally the optimization of their tilt angles.