# Simulation-Based Shading Loss Analysis of a Shingled String for High-Density Photovoltaic Modules
## 3 Results and Discussion  
### Shading Characteristics of Shingled Strings  
The shingled string shown in Figure 11 consists of five divided solar cells. These five cells, which were used to create a shingled string, were shaded using shading ratios of 5%, 10%, and 20% in the vertical direction, as shown in the Figure 11. In this paper, we analyzed the power ratio before and after shading to determine the shading characteristics of shingled PV modules. Table 2 presents the simulation results based on the vertical shading ratio of the shingled string. As the shading ratio increased, the \(\rm I_{sc}\) value of the shingled string decreased. In particular, when the shading ratio was 20%, one divided cell was completely covered, resulting in an efficiency approaching 0%. Table 3 presents the values that were actually measured. The measured power ratio of the shingled string was 84.16%, and the simulation value was 84.17% for a shading ratio of 5%. When the shading ratio was raised to 10%, the measured and simulated power ratios were 55.71% and 56.18%, respectively. When the shading ratio was 20%, the measured and simulated values were both close to 0%. Thus, the simulation and measurement confirmed the accuracy of the model, which had an error rate of less than 1%. Figure 11: Vertical shading patterns of a shingled string with a shading ratio of (**a**) 5%, (**b**) 10%, and (**c**) 20%. Figure 10: Circuit diagram and structure diagram of conventional PV module. Figure 12 shows images of shingled strings with shading ratios of 5%, 10%, and 20% in the horizontal direction of the shingled string. The simulated and measured values of the shading characteristics of the shingled string as a function of the horizontal shading ratio are presented in Tables 4 and 5, respectively. In the case of horizontal shading, the I\({}_{\text{sc}}\) and efficiency decreased as the shading ratio increased, but the reduction in these values was less compared to the reductions observed for vertical shading. This is because, in the case of vertical shading, the shaded area of one divided cell is very large, the I\({}_{\text{sc}}\) of the divided cell is very low, and the current of the other divided cells also decreases owing to the current mismatch [19,20]. In contrast, in the case of horizontal shading, when viewed as a single divided cell, less shading occurred compared to that in the vertical direction, resulting in a smaller loss of output and I\({}_{\text{sc}}\) compared to the cell with vertical shading. A comparison of the simulated and measured results for horizontal shading indicates that the shading ratios of 5%, 10%, and 20% yield similar efficiencies and the decrease in I\({}_{\text{sc}}\) is much less compared to vertical shading. Thus, even with horizontal shading, the simulation and measurement confirmed the accuracy of the model, which had an error rate of less than 1%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **No Shading** & **5\% Shading** & **10\% Shading** & **20\% Shading** \\ \hline Size (cm\({}^{2}\)) & 235.05 & 235.05 & 235.05 & 235.05 \\ I\({}_{\text{sc}}\) (A) & 1.88 & 1.44 & 0.933 & 0.0042 \\ V\({}_{\text{oc}}\) (V) & 3.34 & 3.3404 & 3.32 & 3.06 \\ FF (\%) & 78.35 & 86.26 & 89.48 & 40.08 \\ Eff (\%) & 21.00 & 17.66 & 11.82 & 0.02 \\ P\({}_{\text{m}}\) (W) & 4.93 & 4.15 & 2.77 & 0.005 \\ Power ratio (\%) & 100 & 84.17 & 56.18 & 0.104 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dependence of the simulated shading characteristics on the vertical shading ratio of a 5-cell shingled string. Figure 12: Horizontal shading pattern of a shingled string with a shading ratio of (**a**) 5%, (**b**) 10%, and (**c**) 20%. A graph of the power rate of a shingled string versus horizontal and vertical shading is shown in Figure 13. The efficiency of the shingled string decreased sharply with vertical shading compared with horizontal shading. This result shows that the shingled module is also more susceptible to shading in the vertical direction than in the horizontal direction.