## 4 Processing of Experimental Data  
To investigate the influence of solar radiation intensity on the performance of a direct-expansion solar heat pump water heater system, this study conducted several sets of experiments in the natural meteorological conditions of Fuzhou, China, from November to January. Seven sets of typical experimental data were selected for discussion and analysis of key operating parameters, including panel temperature, electricity generation, electrical efficiency, COP, back temperature, and exhaust temperature. Throughout the experiment, the temperature of the water tank was maintained at 40 \(\pm\) 2 \({}^{\circ}\)C.  
(1) Ambient temperature  
Given the minimal differences in ambient temperature between the various experimental groups, the study selected data from several experiments conducted under the condition of maintaining the ambient temperature at 16 \(\pm\) 1 \({}^{\circ}\)C.  
(2) Solar irradiance  
The solar irradiance meter recorded data once every minute; therefore, the calculated solar irradiance I\({}_{0}\) is the average value over the experimental period. (3) The mathematical model for the temperature of PVT and PV panels can be expressed as follows [7, 21, 25, 26]:  
\[T_{PVT}=30+0.0175\times(I-300)+1.14\times(T_{a}-25) \tag{1}\]  
\[T_{PV}=T_{a}+\frac{T_{NOCT}-20}{800}I \tag{2}\]  
In the formula, \(T_{PV}\) represents the temperature of the PV panel, in degrees Celsius (\({}^{\circ}\)C). \(T_{PVT}\) represents the temperature of the PVT panel, in degrees Celsius (\({}^{\circ}\)C). \(I\) represents the solar radiation intensity, in watts per square meter (W\(\cdot\)m\({}^{-2}\)). \(T_{NOCT}\) represents the nominal operating cell temperature (NOCT) of the photovoltaic cells, taken as 45 \({}^{\circ}\)C.  
\(T_{a}\) represents the ambient temperature, in degrees Celsius (\({}^{\circ}\)C). (4) Power generation of direct-expansion PVT heat pump system [22]. \[P=UI \tag{3}\]  
In the formula, \(U\) represents the output voltage of the PVT panel. \(I\) represents the output current of the PVT panel. (5) Photovoltaic efficiency of the direct-expansion PVT heat pump system [27]  
\[\eta_{\rm e}=\frac{UI}{GA} \tag{4}\]  
In the formula, \(U\) and \(I\) represent the output voltage and current of the PVT panel collector, respectively. \(G\) is the total solar irradiance on the inclined surface, measured in watts per square meter (W\(\cdot\)m\({}^{-2}\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instrument Name** & **Specification Model** & **Measurement Range** & **Accuracy** \\ \hline Heat Pump Flow Meter & LC82 & 0.1–5 m\({}^{3}\)/h & 0.2\% \\ Heat Pump Inlet/Outlet & SBWZP-230 & 0–100 \({}^{\circ}\)C & 1.0\% \\ Temperature Transducer & & & \\ intensity of solar radiation & RS-GZ-I20-2-65535 & 0–200,000 Lux & \(\pm\)0.7\% \\ Temperature Sensor & WZPX-145M & 0–100 \({}^{\circ}\)C & 0.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Schematic Diagram of the Experimental Setup. \(A\) is the area of the photovoltaic panel, measured in square meters (m\({}^{2}\)). (6) Theoretical photovoltaic efficiency of the PVT panel [28]. \[\eta_{\rm th}=\frac{Q_{\rm e}}{AG}\] (5) In the formula, \(Q_{e}\) represents the output electrical energy, measured in watts (W). \(G\) represents the total radiation intensity incident on the inclined surface, measured in watts per square meter (W\(\cdot\)m\({}^{-2}\)). \(A\) represents the area of the photovoltaic panel, measured in square meters W\(\cdot\)m\({}^{-2}\)). (7) The coefficient of performance for heating system. \[COP=\frac{Q_{h}}{W_{com}}\] (6) In the formula, \(Q_{h}\) represents the heat output of the system, measured in joules (J). \(W_{com}\) represents the power consumed by the compressor, measured in joules (J). **5. Results and Discussion** This study conducted experiments during the winter in Fuzhou, focusing on the detailed analysis of the impact of solar radiation intensity on the performance of the direct-expansion solar PVT heat pump system.