## 3 Methodology
### Validation of the TRNSYS Model  
[PERSON] et al. developed a numerical model for thermosyphon PV/T solar water heaters, and the numerical model was validated by experimental test results [21; 22]. Their simulation work was based on typical meteorological year (TMY) weather data of Hong Kong which is nearly at the same latitude and in the same climate as Guangzhou. For validation, the TRNSYS simulations based on TMY weather data of Hong Kong have been carried out using the developed TRNSYS model in this work. The tilt angle is taken to be the same as that in [PERSON] et al.'s simulation work (i.e., 35\({}^{\circ}\)). The time step for the TRNSYS simulations is 0.2 h.  
Figure 6 shows the monthly thermal efficiencies of [PERSON] et al.'s work and this work. Except in February, March, April, and August, the monthly thermal efficiencies are quite close in the other months. The largest difference between the two series of efficiencies is 1.42% (in March). For the purpose of calibration, the coefficient of variation of the root-mean-square error (CVRMSE) was determined using the following equation [23]:  
\[CVRMSE=\frac{\sqrt{\frac{\frac{n}{\mu=1}^{\frac{n}{\eta}}(\eta_{-}-\eta_{i})^{ 2}}{n-1}}}{\overline{\eta}}\times 100, \tag{10}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline Net Collector Area (m\({}^{2}\)) & 1.60 \\ Intercept efficiency of the collector (\%) & 56.6 \\ Efficiency slope the collector [kJ/(h-m\({}^{2}\)-K)] & 21.88 \\ Heat loss coefficient of PV/T panel [kJ/(h-m\({}^{2}\)-K)] & 34.52 \\ Tank height (m) & 0.96 \\ Pipe loss coefficient (kJ/(h-m\({}^{2}\)-K)) & 3.42 \\ Overall loss coefficient of storage tank (kJ/(h-K)) & 4.97 \\ Collector fin efficiency factor & 0.1454 \\ Collector plate absorptance & 0.95 \\ Cover transmittance & 0.94 \\ Temperature coefficient of solar cell efficiency (1/K) & 0.0045 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main parameters for the TRNSYS simulations.  
Figure 5: Monthly average cold water temperatures in Guangzhou.  
where \(n\) is the number of simulation predicted data in this work (\(n=12\)), \(\eta_{i}\) is the monthly thermal efficiency of the \(i\)th month in [PERSON] et al.'s work, \(\hat{\eta}_{i}\) is the monthly thermal efficiency of the \(i\)th month in this work, \(\overline{\eta}\) is the arithmetic mean of the monthly thermal efficiencies in [PERSON] et al.'s work. The CVRMSE was found to be 2.05%. The calibration result of CVRMSE value below 3% indicates that the prediction accuracy of the model developed in this work is very close to that of the model validated by experiment results in [PERSON] et al.'s work. The annual thermal efficiencies of [PERSON] et al.'s work and this work are respectively 38.1% and 38.18%, which are very close.  
The annual electrical efficiencies in [PERSON] et al.'s work and this work are respectively 9.6% and 11.97%. The difference in annual electrical efficiency mainly results from the difference in characteristic parameters of PV cells. The electrical efficiency at the same reference conditions and the temperature coefficient of the solar cell efficiency in [PERSON] et al.'s work were respectively 13% and 0.005/K, which results in an obvious efficiency decrease comparing to the efficiency in this work. It can be concluded that the annual electrical efficiencies in [PERSON] et al.'s work and this work would be close if such two characteristic parameters of PV cells were the same.