4.1. Simulations Results
The photovoltaic array mentioned earlier is employed to evaluate its performance in the presence of the snow, considering various scenarios. Under standard test conditions (STC), the array outputs the following parameters:
PMPP,STC = 1875 W,
VMPP,STC = 347 V,
IMPP,STC = 5.4 A,
ISC,STC = 6.06 A,
VOC,STC = 460 V. This study considers the following conditions for all scenarios: module tilt angle= 30°,
G(
0) = 1000 W/m
2,
T = 25 °C. A tilt angle of 30
° was selected based on a review of the literature, especially [
12]. The work presented in this paper is valid for any tilt angle that is selected.
This section examines different scenarios to analyze the characteristic curves of the PV array, power losses, and other performance metrics under snowy conditions. These scenarios account for the impacts of snow coverage and snow sliding, which are modeled using the proposed method. Additionally, since factors like wind velocity and snow melt can influence snow clearing and the residual snow on the photovoltaic modules, other snow patterns are also considered. The performance of the system is evaluated by incorporating various module interconnection schemes.
Investigating the impact of different partial shading patterns is a common approach for assessing the performance of PV systems, as noted in several studies [
19,
20,
22,
25]. In this paper, a similar approach is applied to snow-covered modules to analyze the performance of a PV system under snowy conditions.
Scenario 1: This scenario investigates the impact of snow on the performance of the PV array when it is completely covered by consistent snow at various depths (h = 0 cm or STC for no snow, h = 1 cm, h = 2 cm, h = 3 cm, h = 4 cm, and h = 5 cm). This scenario is chosen because snow can accumulate on the modules to varying depths depending on the snowfall. Snow sliding is excluded from consideration in this test.
Figure 3 displays the characteristic curves (P-V and I-V) of the photovoltaic array. It is important to note that the P-V curves and the performance of the PV array for the SP, TCT, BL, and HC interconnection schemes are similar due to the uniform snow coverage. For the series interconnection, power losses and the maximum power point (G
MPP) are similar to those of the other interconnections. However, the open circuit voltage (V
OC) is five times higher than that of the other interconnections, and the short circuit current (I
SC) is five times smaller.
As the snow accumulation on PV modules increases, the amount of irradiation decreases, causing the P-V and I-V curves to shift downward, indicating a decrease in the power output of the array.
In Scenario 1, the power losses and the impacts of varying snow depths on the performance of the PV array are summarized in
Table 1. The indices ΔP (%), G
MPP, open circuit voltage (V
OC), and short circuit current (I
SC) for different snow depths are provided.
Based on the results, the power loss increases significantly with the snow depth. Specifically, the power loss is 38.9% when the PV array is coated with 1 cm of snow and 93% when the depth is 5 cm. As the snow depth increases, both the VOC and ISC are reduced. Given that the snow coverage is evenly distributed across the whole PV array in this scenario, the bypass diodes remain deactive, meaning that the power losses are purely due to the shading caused by the snow coverage.
If the method described in [
15] were used instead, the generated power of the PV array would be zero at any snow depth (h = 1 cm, h = 2 cm, h = 3 cm, h = 4 cm, and h = 5 cm), as the model assumes that snow completely prevents power generation.
In Scenario 2, the study investigates the impacts of snow shedding on a 1 cm snow depth coverage over the PV array, under the assumption that there is no wind. The snow evenly slides down the modules, which is common in real-world conditions.
Key operating conditions for the array are:
According to Equation (6), snow sliding occurs under these conditions, and based on Equation (7), the snow slides down by 0.1 of the array’s length per hour. Therefore, over a two-hour period, the snow sliding distance would be about 0.2 of the array length, equivalent to the length of single module in the study array (which is 5 × 5).
In this scenario, the snow coverage and snow sliding are depicted in
Figure 4, for cases where the snow sliding is zero (A = 0) and when it slides by 0.2 (A = 0.2).
The study also considers other snow sliding levels (i.e., A = 0.4, A = 0.6, A = 0.8, and A = 1) for further analysis.
This scenario aims to simulate the real-world behavior of snow sliding on PV modules, providing insight into how varying snow sliding levels affect the array’s performance.
In Scenario 2, the P-V and I-V characteristic curves of various levels of snow sliding are presented in
Figure 5, with various snow sliding stages:
A = 0: No snow sliding occurs, and the array is completely covered with uniform snow.
A = 0.2: After two hours of snow sliding.
A = 0.4: After four hours of snow sliding.
A = 0.6: After six hours of snow sliding.
A = 0.8: After eight hours of snow sliding.
A = 1: After ten hours, the array is completely clean, with no snow left.
As the snow moves down the modules, the clean areas receive more irradiance, while the remaining snow-covered areas receive less. This causes two maximum power points (MPP) to appear in the P-V curves for some snow sliding levels (A = 0.2, 0.4, 0.6, 0.8). The presence of two MPPs occurs because as snow slides down, the irradiance distribution across the array becomes non-uniform, creating both a local maximum power point (local MPP) and a global maximum power point (global MPP).
When snow slides, the clean modules (exposed to more irradiance) begin to generate power, and as a result, the bypass diodes become activated. This prevents reverse biasing of shaded cells and reduces the likelihood of damage due to hot spotting.
This scenario highlights how snow sliding improves the PV array’s performance by gradually reducing the snow coverage, allowing more modules to generate power and optimizing overall system efficiency.
As the snow slides down the PV array, the bypass diodes are activated at higher voltages, and this results in different maximum power points (MPP) occurring at varying voltage levels. This is especially evident in Scenario 2, where snow sliding affects the performance of the array.
For the SP, TCT, BL, and HC module interconnections, the P-V curves and performance are similar since the snow coverage and snow sliding level are uniform, and each module has a bypass diode in parallel. However, for the series interconnection scheme, the open circuit voltage (VOC) is 5 times higher than that of the other interconnection schemes, and the short circuit current (ISC) is 1/5 of the ISC in the other schemes. Despite these differences, the power losses and the global maximum power point (GMPP) remain similar to those of the other interconnection types.
The key performance indices, including ΔP (%), G
MPP, V
OC, and I
SC, are summarized in
Table 2 for various snow sliding levels:
Maximum power loss is observed at about 38.9% when the array is fully snow-covered (A = 0).
The lowest power loss occurs at 20%, which is associated with snow sliding level A = 0.8, where four rows of the array are clear and only one row remains fully covered with snow.
For A = 0 and A = 1, the P-V curves exhibit only single power point because the irradiance is uniform across modules, and no bypass diodes are triggered.
In summary, the snow sliding process leads to gradual improvement in the PV array’s performance by reducing power losses, increasing GMPP, and ensuring the array generates more power as snow slides off the modules. This improvement is reflected in the reduction of power losses from 38.9% at A = 0 (full snow coverage) to 20% at A = 0.8 (partial snow sliding).
Table 3 compares the Global Maximum Power Point (GMPP) of the PV array for different snow sliding levels when using the proposed model (the method presented in your study) and the model presented in [
15]. Using the proposed method results in the PV array generating more power at each snow sliding level compared to the model in [
15], where the power of the snow-covered modules is neglected. This highlights the advantage of the proposed model, as it more accurately reflects the real-world PV array in snow-covered conditions by considering partial power generation from snow-covered modules.
Scenario 3: In this scenario, different snow depths are applied to the individual rows of the PV array, reflecting the real-world conditions where snow accumulation varies across the modules due to the slope of the roof and other environmental factors such as wind. The detail of this scenario is as follows:
The results demonstrate how the snow coverage variation across different rows influences the array’s overall power generation, including the activation of bypass diodes and shifts in maximum power points.
In Scenario 3, the snow coverage varies across the rows of the 5 × 5 PV array, with the snow depth increasing as we move from the upper to the lower rows: h = 1 cm for the first row (#11 to #15), h = 2 cm for the second row (#21 to #25), h = 3 cm for the third row (#31 to #35), h = 4 cm for the fourth row (#41 to #45), and h = 5 cm for the fifth row (#51 to #55), as shown in
Figure 6a. Snow sliding, as modeled in Scenario 2, is also considered in this scenario, with simulations performed every two hours to assess the array’s performance under different snow sliding levels (A = 0, A = 0.2, A = 0.4, A = 0.6, A = 0.8, A = 1). The P-V and I-V characteristic curves for these levels are shown in
Figure 7, illustrating how snow sliding affects the performance of the array with varying snow depths across the rows.
In this scenario, the snow sliding trend for levels A = 0.4, A = 0.6, A = 0.8, and A = 1 follows a similar pattern to that observed for A = 0.2 in
Figure 6b. For A = 0, where the array is fully covered in snow, the PV array generates the minimum power (284.7 W), and the P-V curve exhibits five maximum power points. These five points correspond to the activation of five bypass diodes, one for each row, due to the varying snow depths in each row. This pattern persists for A = 0.2, where five distinct levels of irradiation are received by the rows, as shown in
Figure 6b. As snow slides down and the snow depth decreases, the number of maximum power points in the P-V curve decreases, with four points observed for A = 0.4 and continuing with fewer points as snow sliding increases.
The results from Scenario 3 show that the maximum power losses decrease significantly as snow slides down, from 84.8% for a fully snow-covered array (A = 0) to 20% for A = 0.8. As snow slides off, the open-circuit voltage (V
OC) increases due to the higher irradiation received by the modules. This scenario demonstrates how power losses and the number of maximum power points in the P-V curve change during snow sliding on a non-uniformly snow-covered array. Similar trends are observed across different array interconnection schemes.
Table 4 provides the detailed values for the global maximum power point (G
MPP), power losses, V
OC, and I
SC at different snow sliding levels.
Table 5 compares the GMPP for various snow sliding levels, showing that the proposed model allows the PV array to generate more power than the method presented in [
15].
In Scenario 4, the snow depth on the modules of each row is different, but the same snow coverage pattern is applied to all five rows, as shown in
Figure 8a. This scenario simulates the effect of non-uniform snow coverage in a roof-mounted PV array due to the horizontal component of wind, which can cause variations in snow depth within a row. For this scenario, uniform snow sliding is assumed, with conditions set as T = 25 °C, G = 1000 W/m
2, and a tilt angle of 30°. Simulations are performed every two hours, corresponding to the snow sliding level of one complete row.
The PV array characteristic curves for SP, TCT, BL, and HC interconnections at different snow sliding levels (A = 0, A = 0.2, A = 0.4, A = 0.6, A = 0.8) are shown in
Figure 9 and
Figure 10.
At various snow sliding levels, two irradiation levels are observed at each column due to the location of bypass diodes and the module connection. Consequently, by adjusting the voltage of the array, only one bypass diode is activated, leading to two maximum power points on the P-V curve. As shown in
Table 6, the power losses are 73% when the array is fully covered by snow (A = 0), but they decrease as the snow slides off, reaching 20.2% for A = 0.8. Initially, as snow begins to slide down, the global maximum power point corresponds to the second point on the P-V curve.
As snow sliding continues, the first maximum power point becomes the global one, causing a significant change in the voltage at which the maximum power point occurs. The results for all four interconnections (SP, TCT, BL, and HC) are very similar, with only minor differences observed. However, these differences are not significant, as they do not occur at the global maximum power points. This indicates that the interconnection scheme has a minimal impact on the global performance of the PV array under snow sliding conditions.
For the series interconnection scheme, the P-V and I-V curves, as shown in
Figure 11, exhibit different characteristics compared to the other interconnection schemes, including a varying number of maximum power points. This behavior is attributed to the activation of bypass diodes and the specific module configuration within the array. The presence of multiple local maximum power points increases the difficulty in identifying the global maximum power point.
As shown in
Table 7, when compared to other interconnections, the series interconnection results in higher power losses. These losses decrease from 84.8% when the array is fully snow-covered (A = 0) to 20.3% when A = 0.8, indicating improved performance as snow slides off the modules.
Table 8 compares the G
MPP of the PV array for different snow sliding levels, when the proposed model and the method presented in [
3] are used. It is observed that by using the proposed method, the PV array can generate more power in different snow sliding levels.
In Scenario 5, snow removal from PV modules is not solely reliant on sliding, as various factors influence the process, such as ambient temperature, wind speed, snow thickness, the type of snow, and the surface material of the modules. Based on these factors, different snow accumulation patterns are considered in Scenarios 5, 6, and 7 to investigate the array’s performance. These patterns take into account how snow may accumulate differently on modules, potentially leading to variations in power generation. The impact of these varying snow coverage conditions on the PV array’s performance is explored in detail for different configurations in these scenarios.
In Scenario 5, two distinct snow accumulation patterns are analyzed on the PV array, as shown in
Figure 12. Pattern 1 involves the first column being clear, while the remaining columns are non-uniformly covered by snow. Pattern 2 has the first two columns clear, with the other columns covered non-uniformly by snow. These patterns occur when snow icing happens on the modules, particularly in shaded areas of the roof, leading to uneven snow coverage.
The resulting P-V and I-V characteristic curves for these two patterns, across different interconnection schemes (SP, TCT, BL, and HL), are presented in
Figure 13 and
Figure 14, respectively. For the series configuration, the characteristic curves are shown in
Figure 15. In both patterns, regardless of the configuration, the P-V curves exhibit five maximum power points, though these points vary across different interconnection configurations.
In Pattern 1, the global maximum power points (G
MPP) for the different interconnection configurations are as follows: 551.9 W for TCT, 530.3 W for SP, 519.7 W for BL, 523 W for HC, and 435.7 W for the series (S) configuration. It is evident that the TCT configuration achieves the highest G
MPP, while the series configuration results in the lowest G
MPP. In Pattern 2, a similar trend is observed, but due to the presence of two clean columns, the P-V and I-V curves are smoother compared to Pattern 1. The performance indices for this scenario are given in
Table 9 and
Table 10.
In Pattern 2, the minimum and maximum power losses are 60.7% and 50.9%, corresponding to the series (S) and TCT configurations, respectively. For all module interconnection schemes, V
OC and ISC are the same, except for the series interconnection, where V
OC is higher and ISC is lower. The results suggest that the TCT configuration performs the best, achieving the lowest power losses.
Table 11 and
Table 12 compare the global maximum power points (G
MPP) of the PV array for different module interconnections in Scenario 5, using both the proposed model and the method from [
15]. It is found that the G
MPP is higher when the proposed model is used, as it allows the snow-covered modules to generate power depending on the snow depth on them.
In Scenario 6, part of the PV array is non-uniformly covered by snow, as depicted in
Figure 16. This pattern occurs when snow removal is inconsistent across the modules, with some parts of the array retaining snow longer due to factors like wind, icing, or shading. The performance of the roof-mounted PV array under this scenario was analyzed for all configurations, and the P-V and I-V curves are presented in
Figure 17 and
Figure 18. In this scenario, the P-V curves exhibit 3 or 4 maximum power points, caused by the activation of bypass diodes due to varying levels of irradiance on the modules. The global maximum power points (GMPP) for the different interconnection schemes are 1064 W for TCT, 987 W for SP, 960 W for BL, 923 W for HC, and 894 W for the series (S) interconnection scheme.
In this scenario, the V
OC, I
SC, and power losses for different interconnection configurations are provided in
Table 13. The TCT configuration exhibits the lowest power losses, approximately 43.3%, while the SP and BL configurations follow with slightly higher losses. The series (S) configuration, however, experiences the highest power losses, around 52.3%. This trend highlights the superior performance of the TCT configuration in minimizing power losses when compared to the other interconnection schemes.
Table 14 compares the G
MPP of the PV array for different module interconnections in Scenario 6, when the proposed model and the method presented in [
3] are used.
In Scenario 7, a random snow coverage pattern, similar to the one used for partial shading in [
44], is considered. This pattern results from non-uniform snow accumulation, snow melting, or snow removal on the modules, and may also be influenced by wind gusts. The snow coverage on the modules is illustrated in
Figure 19. The system’s P-V and I-V curves for various interconnection configurations are shown in
Figure 20 and
Figure 21. In this scenario, the power losses for the different configurations are 59.1%, 65.7%, 63.3%, 66%, and 64.8% for the TCT, SP, BL, HC, and S configurations, respectively. It is observed that the TCT configuration achieves the best performance with the highest efficiency, generating about 767 W of power.
The maximum generated power, VOC, and ISC for all configurations in Scenario 7 are provided in
Table 15. The HC configuration experiences the highest power losses in this scenario.
Table 16 compares the GMPP of the PV array for different module interconnections in Scenario 7, using both the proposed model and the method presented in [
15]. The results from all the studied scenarios demonstrate that the efficiency of a PV array can be significantly reduced under snowy conditions. However, the degree of this reduction depends on the snow accumulation and removal patterns. Additionally, the module interconnection scheme plays a critical role in determining system efficiency. Across all scenarios, the TCT configuration consistently exhibited the highest efficiency and the lowest system losses under snowy conditions.