## 3 Methodology
### Thermal Model to Determine Module Temperature
calculated according to the geometry of junction box and ambient conditions such as wind speed, air temperature and ground temperature. Convective heat transfer is described as:  
\[Q_{conv}=A\cdot\left(T_{jb}-T_{air}\right)\cdot k\cdot\frac{\sqrt[3]{Nu_{ natural}^{3}+Nu_{ford}^{3}}}{L} \tag{11}\]  
where \(A\) is the total surface area of junction box, \(k\) is the thermal conductivity of the air, \(L\) is characteristic length of junction box, \(Nu_{natural}\) is the Nusselt number with free convection, and \(Nu_{ford}\) is the Nusselt number with forced convection. In the natural convection, the Churchill-Bernstein equation is valid for a wide range of the Prandtl number and Reynolds number [30]. The Nusselt number with free convection can be written as:  
\[Nu_{natural}=\left\{ \begin{array}{c}0.68+\frac{0.67(G_{r}\cdot P_{r})^{1/4} }{\left[1+(\frac{0.492}{P_{r}})^{9/16}\right]^{4/8}},G_{r}\cdot P_{r}<10^{9}\\ \left(0.825+\frac{0.387(G_{r}\cdot P_{r})^{1/6}}{\left[1+(0.492/P_{r})^{9/16} \right]^{8/2}}\right)^{2},G_{r}\cdot P_{r}>10^{9}\end{array} \right.,\ G_{r}= \frac{g\cdot\cos(\theta)\cdot\alpha_{v}\cdot\left(T_{jb}-T_{air}\right)\cdot L ^{3}}{v^{2}} \tag{12}\]  
As described in [31], the transition from laminar to turbulent flow was determined by the critical values. Measurements were taken when the wind speed was not too high, so the Reynolds number was usually less than its critical values. The Nusselt number for the forced convection can be described as [31]:  
\[Nu_{ford}=\left\{ \begin{array}{c}0.664R_{e}^{1/2}P_{r}^{1/3},R_{e}=\frac{uL} {v}<5\times 10^{5}\\ (0.037R_{e}^{4/5}-871)P_{r}^{1/3},R_{e}=\frac{uL}{v}>5\times 10^{5}\end{array} \right. \tag{13}\]  
where \(G_{r}\) is the Grasshof number, \(P_{r}\) is the Prandtl number, \(R_{e}\) is the Reynolds number, \(u\) is wind speed, \(v\) is dynamic viscosity, \(g\) is gravity acceleration, \(\theta\) is the angle of PV module and \(\alpha_{v}\) is the swelling coefficient. The \(G_{r}\), \(P_{r}\), \(R_{e}\), \(v\), \(\alpha_{v}\) give the information about the air. The radiative heat exchange is simplified by considering parallel planar bodies with the same area (\(A\)). According to the Stefan-Boltzmann law, the radiation heat equation is rewritten by the air temperature and the horizontal irradiance:  
\[Q_{rad}=\varepsilon_{1}\cdot A\cdot\sigma\cdot\left(2\cdot T_{jb}^{4}-\left(0.0552\cdot T_{air}^{2/3}\right)^{4}-\left(T_{air}+0.03\cdot G_{h}\right)^{4}\right) \tag{14}\]  
where \(\varepsilon_{1}\) is emissivity coefficient of junction box, \(\sigma\) is Stefan-Boltzmann number, \(5.67\times 10^{-8}\) W\(\cdot\)m\({}^{-2}\cdot\)k\({}^{-4}\), \(G_{h}\) is horizontal irradiance. Finally, the PV module temperature can be estimated using the thermal model based on the steady state approach prediction as:  
\[T_{\text{mod}ule}(t)=T_{jb}(t)-\frac{\left(T_{jb}(t+h)-T_{jb}(t)\right)\cdot \rho\cdot V\cdot c+h\cdot\left(Q_{conv}+Q_{rad}\right)}{h\cdot\lambda\cdot A_{ 1}} \tag{15}\]  
where \(h\) is the time interval. Then, the testing outdoor platform is further developed, that includes RT1, and weather station as shown in Figure 8. RT1 measures horizontal irradiance (\(G_{h}\)) and PV module backsheet temperature (\(T_{measured}\)). The weather station obtains the air temperature (\(T_{air}\)) and wind speed (\(u\)). Validation experiments show good linearity in \(R^{2}\) of 0.922 between the calculated module temperature and the actual measured module backplane temperature in Figure 9. The proposed thermal model is well implemented to convert the temperature in the junction box to the temperature of the PV module backsheet. This will help capture the temperature of each module in PV system and allow for future monitoring at module level. Besides, the calculated temperature will be further input into the data matrix. It was specially noted that the thermal model is independent of module type and junction box.