# Detection and Optimization of Photovoltaic Arrays' Tilt Angles Using Remote Sensing Data
## 3 Results
Figure 8a shows the orthorectified satellite imagery along with the information from the corresponding PV systems, whereas Figure 8b,c visualize the reconstructed 3D modules from LiDAR and VHR data using FT-UnetFormer, colored by the array grouping. Details on the tilt and aspect angles extracted from the PV systems, as well as the dimensions of the modules, are provided in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PV System** & \(\beta\) & \(\gamma\) & \(\mid\)_PVA_\(\mid\) & \(\mid\)_PVM\({}_{w}\times\)PVM\({}_{h}\)_ & **kWp** \\ \hline A & 20\({}^{\circ}\) & 200\({}^{\circ}\) (SW) & 54 & 1649 \(\times\) 991 & 228 \\ B & 6\({}^{\circ}\), 5\({}^{\circ}\) & 100\({}^{\circ}\) (E), 270\({}^{\circ}\) (W) & 2 & 1649 \(\times\) 991 & 45 \\ B & 6\({}^{\circ}\), 5\({}^{\circ}\) & 120\({}^{\circ}\) (E), 270\({}^{\circ}\) (W) & 2 & 1649 \(\times\) 991 & 45 \\ B & 13\({}^{\circ}\) & 200\({}^{\circ}\) (S), 270\({}^{\circ}\) (W), 100\({}^{\circ}\) (E) & 6 & 1649 \(\times\) 991 & 49 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of \(\beta\) and \(\gamma\) angles of individual modules, as well as their sizes (i.e., \(\mid\)_PVM\({}_{w}\times\)PVM\({}_{h}\)_), number of arrays per system (i.e., \(\mid\)_PVA_\(\mid\) ), and installed capacity. Figure 7: Visualization of validation site in Maribor, Slovenia, where (**a**) is the constructed 2.5D classified grid from LiDAR data, (**b**) is the estimated normal vectors over the grid, (**c**) is the simulated average hourly shadowing per annum, and (**d–f**) present simulated average hourly direct, diffuse, and total irradiances per annum. To validate the accuracy of the detected modules coupled with the solar irradiance simulation, additional specifications of the modules installed in all four photovoltaic systems were obtained. Each system utilizes Bisol BMU-215-2/233-type modules (233 Wy) with a nominal efficiency of 14.25% per square meter. The inverter model used is the Sunny Tripower STP 17000 TL-10 [2]. The installed capacities of the PV systems A, B, C, and D are 228 kWp, 45 kWp, 45 kWp, and 49 kWp, respectively [2]. A comparison was made between the actual independent measurements (from 2018 to 2022 timespan) of electricity production from these PV systems and the estimated production derived from the irradiance simulation on the 3D reconstructed modules. To simulate electricity production, the estimated solar irradiance was multiplied by the nominal efficiency of each PV system (as detailed in Table 2). The simulated electrical energy production for each array was aggregated to the corresponding PV system. The estimation error was calculated using the Mean Absolute Percentage Error (MAPE) metric, and the comparative results are presented in Table 3.  
Figure 8: Validation site in Maribor, Slovenia, where (**a**) is a satellite imagery of the site with annotations of the considered PV systems, (**b**) is reconstructed 3D arrays over 2.5D grid from airborne LiDAR and VHR data, and (**c**) is a zoom-in into the given PV systems. Finally, the arrays have been optimized to have an optimal tilt angle based on the proposed method of using the SA algorithm. Figure 9 shows a comparison of real tilt angles and optimally detected tilts for each array. Moreover, to verify that SA found the optima, the annual solar irradiance per array has been estimated using an exhaustive search by trying all physically viable tilt angles, as seen in Figure 10. The optimization results at the PV system level are shown in Table 3, where improvements from 1.5 % to 4.9 % were observed. This is not surprising, as the arrays installed at systems A and D had already tilt angles close to optimum based on the geographic latitude, while the spacing ensured minimum shadowing. On the other hand, the tilt angle could not be significantly changed for systems B and C, which were installed on slightly sloped rooftops, and the increase in tilt would increase the amount of shadowing between modules due to no spacing between modules.