As mentioned earlier, three buildings from the University of Alberta—the ADMIN, CAM, and EAS buildings—were used in this study to examine the multi-objective optimization leveraged by the pixel-based image processing method. Moreover, in this section, we present a set of optimal solutions based on the inter-row spacing of PV panels. The maximum PV generation and minimum overall payback period are also discussed.
3.1. Roof Recognition
Figure 6a shows the texture information of the ADMIN building, and its corresponding heightmap is shown in
Figure 6b.
Based on the methods mentioned in
Section 2.1, the authors of this work considered several building rooftop types: flat, slanted, and irregular. The roof recognition performance for the ADMIN and CAM buildings is evaluated in this sub-section as an example. A real-world satellite image of the ADMIN building is shown in
Figure 7a.
Figure 7b,c present the binary map of the ADMIN building before and after the identification step, respectively.
Figure 7b shows the original binary map of the ADMIN building where rooftops are connected together, which is very difficult to immediately use for further analysis.
Figure 7c shows the result after the identification process. It can be seen that the outer rooftop was separated from the inner rooftop, which is consistent with the real-world satellite image shown in
Figure 7a. In addition, it is clearly shown that most of the unwanted objects, including parapets and obstacles, were removed from binary maps. These objects were removed to avoid considering the area they occupy in the following calculations and to ensure a feasible and efficient PV installation.
Therefore, this algorithm was able to locate a small region in a rooftop that can fit at least one solar panel with the required walkways. Additionally, rooftops with significant height differences were separated to facilitate the analysis and independently optimize different rooftops.
The algorithm could also detect the difference between slopes to split challenging “joined” rooftops into their components, such as the wavy rooftops on the CAM building, as shown in the real-world satellite image of
Figure 8a. Similar to the ADMIN building,
Figure 8b,c show the binary maps of the CAM building before and after the identification step, respectively. By comparing
Figure 8b,c, it can be clearly seen that the wavy rooftop was correctly separated into its rooftop segments. Additionally, the unwanted objects, such as the parapets and obstacles, were removed from the heightmaps.
The classification results of the rooftop types; i.e., whether they were flat, slanted, or irregular; are depicted in
Figure 9 for the ADMIN and CAM buildings.
Figure 9a shows the rooftop of the ADMIN building, which only contains flat rooftops as shown in blue. However, the rooftop of the CAM building shown in
Figure 9b includes all three types of rooftops (flat, slanted, and irregular). The outer rooftop in blue was classified as a flat rooftop; and the wavy section in green, which is located in the center of the building, consisted of 14 slanted rooftops. Additionally, a small irregular shape in red at the bottom-left corner of the heightmap was classified as an irregular object. It can be concluded that the algorithm worked well for the ADMIN and CAM buildings, and rooftops were assorted with an accuracy of more than 95%.
Next, we discuss the confidence scores of polygon approximation results and corresponding roof IDs of the ADMIN and CAM buildings. Roof IDs represent the order of an approximated rectangular shape under the polygon approximation algorithm. For the ADMIN building, the first roof and second roof had confidence scores of 0.735 and 0.799, respectively.
Table 1 also presents the CAM building’s roofs IDs and their corresponding confidence scores. Note that roof 16 of the CAM building had a confidence score of 0 because it was classified as an irregular rooftop.
The roof IDs and their corresponding rooftops are shown in
Figure 10a,b for the ADMIN and CAM buildings, respectively. When comparing confidence scores with the labelled roof satellite images in
Figure 10, it can be seen that the smaller rooftops (rooftops with fewer corners) tended to obtain higher scores for their polygon approximation. Additionally, rooftops with wide, regular, and straightforward shapes were more likely to have higher scores; e.g., roof 15 was close to a perfect rectangle and had the highest accuracy score of almost 95% among all rooftops of the CAM building.
3.4. Optimization Results
After identifying the rooftops of the ADMIN, CAM, and EAS buildings, the proposed optimization method was applied to find the optimum solar PV layout for the buildings. As mentioned earlier, due to the nonlinear nature of the optimization problem, the search space method was used to find the optimal value.
Table 2 summarizes the optimum tilt angle (
), azimuth angle (
), and inter-row spacing (
). For each building, the system layout was chosen using the proposed enveloped min–max multi-objective optimization algorithm to maximize electricity generation while minimizing the cost of installation and electricity purchased from the grid in terms of payback period, as mentioned in Equation (12).
Table 2 presents the layout of the PV systems in the three buildings.
Based on the results from
Table 2, all panels on the three buildings are almost due south (between south and 20 degrees to the west); and their tilt angle is slightly lower than the latitude angle of the investigated location, which is 53
.
The best performance for a solar panel is when its azimuth angle is zero degrees in the northern hemisphere and 180 degrees in the southern hemisphere [
32]. However, in the present work, due to the sky cloudiness, shading of the surrounding objects, and adjacent panels, PV panel output could be influenced by some degrees of azimuth angle. Thus, the PV panels’ azimuth angle deviated from zero.
Table 3 presents the payback periods for each building based on the annual energy generation and the number of installed PV panels. The optimal payback years for ADMIN, CAM, and EAS were found to be 22.99, 27.20, and 26.91, respectively.
Figure 16a–c present the optimum layout of the PV system for the ADMIN, CAM, and EAS buildings’ roofs. The figures show the PV system layout in bird’s eye view and panel projection on the roofs.
The impact on panel arrangement in the ADMIN building due to three obstacles or irregular objects on the smaller roof and an obstacle on the larger roof is shown in
Figure 16a. Many obstacles that impact PV module layout on the EAS building are clear in
Figure 16c. In this figure, these obstacles are represented by enclosed white areas on the building rooftops.
In
Figure 16b, it can be seen that the panels were placed on the flat roof at an angle of 50 degrees, which makes them appear smaller than the actual size due to the top–down view; but because the slope of the slanted roofs is about 10 degrees, the size of the panels installed on them are seen closer to their actual size. It can also be observed that, as stated in the methodology section, PV modules were not installed on the roofs facing north. Minimal obstacles on a limited number of roofs of the CAM building can also be seen in
Figure 16b.
The other point gleaned from the above figures is the margin for fire safety seen around the PV panels on flat roofs. This is why panels were not installed in a small area of the flat roof of the CAM building. It can be seen that in slanted roofs, the margin had been neglected due to the presence of north-facing roofs that allow access to sloped roofs with panels. Furthermore, it can be observed from
Figure 16b that all the panels on slanted roofs are facing south. Of the 185 panels installed on the CAM building, seven are on flat roofs and 178 are on slanted roofs. So, slanted roofs are playing a crucial role in the electricity generation of the CAM building. The south direction of the panels on sloping roofs is due to following the roofs’ orientation.
As mentioned earlier, panels with an average brightness score of less than 0.6 are removed from the system.
Figure 17,
Figure 18 and
Figure 19 compare the PV systems with and without considering the shadow analysis for the three selected buildings.
In
Figure 17, the main shadow impact on the ADMIN building can be observed by the effect of the top-level roof (orange color) on the lower level (blue color), which depicts seven panels’ elimination from the top right part of the blue colored roof. However, it can also be clearly seen that the ADMIN building has the lowest shadow impact of the three buildings. On the other hand, due to the highest level of the CAM building, which is the level with slanted roofs, large shading areas are induced on the lower flat roof, as shown in
Figure 18. Therefore, many panels on the flat roof were removed. Thus, in both of these buildings, the shadow from different heights can be considered the primary shadow source that impacts the PV installation.
Another type of shadow generated by a tall building near the EAS building is also described and analyzed in this study. This type of shadow is only generated on the EAS building (the red box in
Figure 13 identifies the tall building). Therefore, as shown in
Figure 19b, PV panels on the bottom right of the EAS building were removed from the system. On the same figure, the removal of panels due to the building obstacles and the rooftops’ height difference is shown on the left side of the roof and the area between the top middle to the top right, respectively. Generally, the shadow impact generated by the roofs with different heights was the most dominant one and caused more panels elimination.
The resulting building energy generations are considered in
Table 4 in comparison to the number of panels and the amount of solar energy generation in two modes with and without shading impact.
As reported in
Table 4, the maximum and minimum reduction in energy generation due to obstacles’ shading impacts were 61.14% and 28.13% for the EAS building and the ADMIN building, respectively.
Figure 20,
Figure 21 and
Figure 22 are intended to aid understanding of objective function changes with controlled variables for the case study buildings. For the resulting simulated surfaces shown in these figures, the surface values between the actual points were approximated with minimal and negligible errors. In addition, the ultimate results of these figures represent the optimal payback years, the values of which are shown clearly in
Table 3. The optimal payback years for the installed PV systems on the ADMIN, CAM, and EAS buildings were 22.99, 27.20, and 26.91, respectively.
Obviously, the payback for the CAM building was relatively constant for all the values of tilt angle, azimuth angle, and inter-row spacings. The reason for this is that, as mentioned, out of 185 panels installed on the roofs, only seven panels were installed on the flat rooftop on which their tilt angle, azimuth angle, and inter-row spacing could be changed. However, the rest of the panels were installed on slanted roofs, whose tilt and azimuth angles were fixed and precisely equal to the slope and orientation of those roofs, respectively, with no distance between the arrays. Therefore, the number of installed panels on slanted roofs and their annual electricity generation were always the same over the optimization’s variables in the search space. Furthermore, installing a significant number of PV panels would be impractical due to the shadow created on the flat surface. Consequently, the CAM building was found to have a limited range of payback due to trivial changes in the initial cost and annual output.
In the ADMIN and CAM buildings, as we moved from the optimal tilt angle to the lower tilt angles, the investment cost was found to decrease due to a reduction in the number of PV panels. Conversely, when the tilt angle increased from the optimal value, more panels could be placed on the roof, which would increase the investment cost. Of course, this would increase the system’s power generation and, eventually, income. However, the total increase in investment costs outweighs the positive impact of the annual revenue increase, leading to a higher payback time. Furthermore, changing the PV panels’ orientation towards east or west reduces system output and consequently the annual revenue, while the initial investment does not change much. As a result, the payback time increases. Moreover, changing the azimuth angle in the optimization problem leads to a higher rate increment in the objective function values compared to the tilt angle.
It is also worth noting that the present work can be compared to the Google Project Sunroof. The mentioned calculator from Google provides usable hours of solar energy, available areas for panel installation, and estimates of net money saving using the address it receives from the user. However, it does not provide information regarding how to place panels on the roofs, and more importantly, it can only be used for the addresses in the United States and Puerto Rico [
48]. However, the current study’s privilege over the Google Project Sunroof is providing details of the layout of a PV system using optimization algorithms and considering economic aspects. Moreover, the proposed model also works for any city globally because it uses the sky clearness data.