## 3 Calculation Results and Analysis
### Analysis of the Optical-Electrical-Thermal Coupling Effect of Output Characteristics  
#### 3.3.1 Short-Circuit Current  
The change in the short-circuit current of the triple-junction cell along the optical axis is shown in Figure 7a. It can be seen that although the radiation power near the focal plane is the strongest, the short-circuit current of the cell is minimum near the focal plane and the maximum value on both sides (\(Z\) = 108.5 mm, 114.0 mm) is about 24% higher than it, which is related to the current mismatch between sub cells caused by non-uniform irradiance and dispersion effect. Figure 8 shows the variation in photogenerated current density of InGaP, InGaAs and Ge in the direction of cell surface and 0 mm is the center position of the cell. Figure 8a-f show the cases where the cell is placed at 108 mm, 109 mm, 110 mm, 111 mm, 112 mm and 114 mm, respectively. It can be seen that the photogenerated current is approximately Gaussian distributed and there is an obvious current mismatch between the sub cells especially in the central area. Comparing \(Z\) = 110 mm (on-focus position) with \(Z\) = 108 mm, when the cell is at the focal plane, the photogenerated current density of the InGaP sub cell is 3.427 A/mm\({}^{2}\) at 0 mm (center of the cell). InGaAs sub cell is 0.396 A/mm\({}^{2}\) and the photogenerated current density of the Ge sub cell is 0.219 A/mm\({}^{2}\). The photogenerated current density of the InGaP sub cell is significantly higher than that of the InGaAs and Ge sub cells and is about 16 times higher than that of Ge. When the cell is located at 108 mm, the current density of the InGaP sub cell is slightly higher than that of the InGaAs and Ge sub cells, which is about 4 times higher than the Ge sub cell. The current mismatch is greatly improved. It can also be seen that at the focal plane, the central photogenerated current density of InGaP is 265 times that of 1 mm from the cell center. Meanwhile, when \(Z\) = 108 mm, the central photogenerated current density of the upper sub cell at 0 mm is 1.5 times than that at 1 mm  
Figure 6: Surface temperature distribution of the receiver. (**a**) \(Z\) = 108 mm; (**b**) \(Z\) = 109 mm; (c) \(Z\) = 110 mm (focal plane); (**d**) \(Z\) = 111 mm; (**e**) \(Z\) = 112 mm; (**f**) \(Z\) = 114 mm. from the cell center. It can be seen that the lateral current caused by the non-uniformity of the focusing is also greatly improved. For a range of Z values between 108 to 110 mm, the photogenerated current of InGaP sub cell in the central area is greater than that of the InGaAs and Ge sub cell because short wavelengths basically have maximum radiation power while the radiation power of medium and long bands do not reach maximum value. When the cell is placed at the on-focus position, the PAR of short wavelengths is close to the maximum and the photogenerated current of InGaP sub cell in the central area also reaches maximum. For the InGaAs and Ge sub cells, the position of maximum PAR values are 111.4 mm and 112.3 mm so they have the maximum photogenerated current at relevant positions. Under non-uniform illumination, the overall short-circuit current of the multijunction solar cell is affected by vertical current mismatch between the sub cells. Generally, the overall output current will be limited by the minimum current of the sub cells [40; 41]. In order to explore the influence of vertical current mismatch, we calculated the short-circuit current of each sub cells [42]. Figure 9a shows the short-circuit current of the InGaP, InGaAs and Ge sub cells. The minimum values occur at 110 mm, 111 mm and 112 mm, respectively, which is affected by the non-uniformity of light spots of short, medium and long wavelengths. The optical axis position of the minimum short-circuit current is basically consistent with the position of the maximum PAR (Table 2). Moreover, current mismatch exists between sub cells in the range of \(Z\) values between 107 to 116 mm.