## 3 Methodology
### Thermal Model to Determine Module Temperature  
In fact, it is very difficult to measure the cells temperature directly when a manufactured PV module is in operation under outdoor conditions. Usually, many module-level/string-level studies in a PV field use the module backsheet temperature as the cell temperature. Because the temperature gradient between the module backsheet temperature and the cell temperature is very small when cell temperature is less than 60 \({}^{\circ}\)C in [27], the backsheet temperature of the PV module is considered to be the real module/cell temperature in this study. As described in Section 2, the used PV modules with the intelligent sensors in junction box are used for module-level monitoring in the smart PV system. The measured temperature is the temperature inside the junction box, and this temperature is higher than the real backside temperature of the PV module, as shown by the infrared image (IR) in Figure 6. It leads to the need for further conversion to the true backsheet temperature of the PV module. Therefore, a novel temperature thermal model has been developed to achieve temperature conversion based on the temperature (\(T_{jb}\)) in the junction box and our previous work [28]. According to the law of energy conversion and energy conservation, the junction box-PV module backsheet, junction box-temperature sensor, junction box-air have 3 forms of heat exchange: conductive heat, convective heat and radiative heat, as shown in Figure 7. The thermal model treats the junction box as a steady-state energy balance on the control volume:  
\[Q_{cond}-Q_{conv}-Q_{rad}-\rho\cdot v_{jb}\cdot c\frac{dT_{jb}}{dt}=0 \tag{9}\]  
where \(Q_{cond}\) is the total energy from PV module with heat conduction, \(Q_{conv}\) is the convection energy between the junction box and the flow, \(Q_{rad}\) is the radiation energy from the junction box to the ambient environment, \(\rho\) is the density of junction box, \(v_{jb}\) is the volume of junction box, \(c\) is the specific heat capacity of junction box. Figure 6: IR image of junction box. In the considered thermal model, the following assumptions have been made based on the study [29]:  
* One-dimension (1D) thermal model. * The isothermal surface is approximated as a flow node and therefore edge effects are neglected. * Negligible thermal capacitances. * Junction box temperature and backsheet temperature of module are considered uniform. * Ground temperature is equal to air temperature. * Convective heat transfer is evaluated using empirical equations and it assumes that the wind flows around the junction box. * According to the radiative heat transfer, the view factor is assumed to be unity, only the ground is visible on the rear surface of the junction box. * In fact, the bypass diodes in the junction box have a small forward-bias voltage, even if a current passes through it, it produces only a small amount of heat flow and those heat are neglected. The original heat of the junction box comes from the conductive heat exchange between the junction box and the PV module backsheet. The heat conduction equation is given by the following equation:  
\[Q_{cond}=-\lambda\cdot A_{1}\cdot\frac{dT\text{mod}ule}{dx} \tag{10}\]  
where \(\lambda\) is the thermal conductivity of the junction box, \(x\) is thickness of the contacted surface between the junction box and solar cells in PV module, \(A_{1}\) is the contacted area between the junction box and back sheet of PV module, \(T_{module}\) is backside temperature of PV module and equal to the following \(T_{calculated}\). The \(dT_{module}\)/\(dx\) is the temperature gradient along the thickness direction of the contacted surface between the junction box and solar cells in PV module. Further, it considers convection \(Q_{conv}\) and radiation \(Q_{nnd}\) exchanges of the back sides of junction box with the surrounding environments. The convection and radiation heat are  
Figure 7: Heat exchange of junction box.