## 4 Experiment Results  
In order to verify the influence of optical-electrical-thermal coupling on the cell along the optical axis, an outdoor experimental platform was built for test and verification. As shown in Figure 12, The experimental equipment is fixed on the sun tracker so that the lens and solar cell front are facing the sun at all times. The solar cell with the focusing spot irradiated on the surface is shown in the insect. The aperture area of the lens is 15,125 mm\({}^{2}\) and the focal length is 110 mm. The material of the Fresnel lens is PMMA and the size of  
Figure 11: Open-circuit voltage at different optical axis positions. (**a**) InGaP sub cell; (**b**) InGaAs sub cell; (**c**) Ge sub cell; (**d**) Triple-junction solar cell.  
the triple-junction cell is 5.5 mm \(\times\) 5.5 mm in which case the geometric concentration is about 500\(\times\).  
The experiment was carried out from 12:30 to 13:00 on the top floor of the Solar Energy Research Institute of Sun Yat-sen University in Guangzhou. During this period, the outdoor ambient temperature is around 36 \({}^{\circ}\)C. The temperature difference fluctuation is no more than 1 \({}^{\circ}\)C and the DNI is 830-850 \(\mathrm{w/m^{2}}\). Moreover, the average wind speed is 1 m/s. The experiment is carried out by adjusting the triaxial displacement table to change the relative distance between the Fresnel lens and the cell. The adjustment range is 10 mm away from the focal plane. The thermocouple for measuring the cell temperature is pasted on the back of the aluminum plate so that the focus incident on the cell surface was not interfered. Under the experimental conditions, the changes in the short-circuit current, open-circuit voltage, filling factor and output power of the triple-junction cell along the optical axis are shown in Figure 13a-d. It can be clearly seen that the short-circuit current decreases by 7.7%, the open circuit voltage decreases from 2.67 v to 2.62 v and the maximum output power decreases by 24%. Table 3 shows the key photovoltaic parameters and cell temperature with the different distances of the cell from the Fresnel. It can be seen that due to the non-uniformity, the output power is minimum near the focal plane and the temperature reaches maximum 63.2 \({}^{\circ}\)C, which is 6.4 \({}^{\circ}\)C higher than the maximum output power positions (Z = 108 mm). The irradiance and temperature would change slightly in a short time under the outdoor conditions, but the test results are basically consistent with the change trend calculated by the model.  
Figure 12: Outdoor performance test of the triple-junction solar cell. The insect shows the solar cell with the focusing spot irradiated on the surface.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Distance of the Cell** & **108** & **110** & **112** & **114** & **116** \\
**from the Fresnel (mm)** & & & & & \\ \hline \(T_{cell}\) (\({}^{\circ}\)C) & 56.8 & 62.2 & 63.2 & 58.2 & 51.9 \\ \hline \(I_{cc}\) (A) & 0.957 & 0.924 & 0.943 & 0.973 & 0.821 \\ \(V_{cc}\) (V) & 2.656 & 2.636 & 2.621 & 2.645 & 2.667 \\ \(FF\) & 0.783 & 0.726 & 0.617 & 0.687 & 0.777 \\ \(P_{max}\) (W) & 1.990 & 1.769 & 1.529 & 1.767 & 1.702 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The output performance and temperature of the cell at different positions of the optical axis.