# Simulation-Based Shading Loss Analysis of a Shingled String for High-Density Photovoltaic Modules
## 2 Materials and Methods
### Modeling the Shading of Shingled PV Modules  
First, to understand the shading characteristics of the shingled string, a 5-bonding shingled string was produced. In the case of the manufactured shingled string, an overlap of 0.17 cm was applied. The fabricated shingled string was measured using a solar simulator under STCs without lamination. The shading pattern applied to the shingled string was measured by extending the shading in the horizontal and vertical directions. Figures 5 and 6 schematically show the shading pattern applied to the shingled string.  
Figure 4: Model for the simulation of the shingled PV module.  
Figure 5: Vertical shading pattern applied to shingled string. The width of the shading pattern was varied as follows: (a) 0.7 cm, (b) 1.5 cm, (c) 3.135 cm.  
When modeling the shingled string, we applied the overlap loss that occurs as a result of the shadow caused by the use of the shingled technique. \(V_{string\_shading}\) is expressed using Equation (4) to apply the shading to the front surface of the PV module in addition to the overlap loss. In the case of V\({}_{\text{input}}\), as a device for controlling the photovoltaic current value of the divided solar cells, shading was also input by calculating the shaded area in each divided cell. In addition, to exclude the already reflected overlap shadow loss, the overlap area was subtracted from the total divided cell area. Figure 7 schematically explains the parameters in Equation (4) and shows the corresponding equivalent circuit diagram used for the PSpice simulation.  
\[V_{string\_shading}=(1-\frac{\text{{Shading area in divided solar cell}}}{(\text{Divided solar cell area}-\text{{Overlap area}})})\times V_{overlap} \tag{4}\]  
The shingled sun module simulates the shading characteristics by adjusting V\({}_{\text{input}}\) in the same way as the shingled string. However, in the case of a shingled PV module, the simulation was conducted in consideration of the loss caused by the front cover glass and EVA sheet, and the voltage value used as input to each divided cell was calculated using Equation (5).  
\[V_{module\_shading}=(1-\frac{\text{{Shading area in divided solar cell}}}{(\text{Divided solar cell area}-\text{{Overlap area}})})\times V_{module} \tag{5}\]  
Figure 6: Horizontal shading pattern applied to shingled string. The height of the shading pattern was varied as follows: (**a**) 0.7 cm, (**b**) 1.5 cm, (**c**) 3.135 cm.  
Figure 7: Schematic explanation of each shading parameter and a schematic drawing of the PSpice circuit.  
The shading pattern applied to the shingled PV module was measured by extending the shading in a horizontal direction in the same way as the shingled string and compared with the simulation. The solar module was measured using a module solar simulator (DKSMT-1520 SUL, Denken, Yufu, Japan). Figure 8 shows the shading pattern that was applied to the shingled PV module.  
Additionally, the same shading pattern was analyzed with the shingled PV module by measuring the shading characteristics of the conventional PV module. Figures 9 and 10 show the circuit of a shingled PV module and a conventional PV module. In the shingled PV module, 12 shingled strings were connected in series and each string consisted of 34 divided cells, which were connected in series. For this module, two bypass diodes were used. The conventional PV module consisted of 72 solar cells, which were connected in series, and a total of three bypass diodes were used.  
Figure 8: Shading pattern applied to shingled and conventional PV module.  
Figure 9: Circuit diagram and structure diagram of shingled PV module.