## 3 Methodology
### Defining Performance Indicators Based on I-V Characteristics  
The current-voltage (I-V) output characteristics of photovoltaic modules represent a detailed description of their solar energy conversion capability and efficiency. Understanding the electrical I-V characteristics of PV modules is essential in determining the output performance of PV modules. Furthermore, the open-circuit voltage (\(V_{\alpha}\)), short-circuit current (\(I_{sc}\)), current (\(I_{m}\)) and voltage (\(V_{m}\)) at MPP on the output characteristic (I-V curves) of the PV module are applied in expressing the performance indicators in current (\(PI_{\Delta I}\)) and voltage (\(PI_{\Delta V}\)) which is connected to particular irradiance \(G\) and module temperature \(T_{module}\), as following. \[PI_{\Delta I}(T_{\text{module}},G)=\frac{I_{sc}(T_{\text{module}},G)-I_{m}(T_ {\text{module}},G)}{I_{sc}(T_{\text{module}},G)} \tag{1}\]  
\[PI_{\Delta V}(T_{\text{module}},G)=\frac{V_{oc}(T_{\text{module}},G)-V_{m}(T_ {\text{module}},G)}{V_{oc}(T_{\text{module}},G)} \tag{2}\]\(I_{sc}\) (\(T_{module}\), \(G\)) and \(V_{oc}\) (\(T_{module}\), \(G\)) are calculated from irradiance (\(G\)) and module temperature (\(T_{module}\)) using the following equations [24; 25]:  
\[I_{sc}(T_{module},G)=I_{sc,ref}\cdot\left\{1+\alpha\cdot\left(T_{module}-T_{ ref}\right)\right\}\cdot\frac{G}{G_{ref}} \tag{3}\]  
\[V_{oc}(T_{module},G)=V_{oc,ref}\cdot\left\{1+a\cdot\ln\left(\frac{G}{G_{ref}} \right)+\beta\cdot\left(T_{module}-T_{ref}\right)\right\} \tag{4}\]  
where \(I_{sc}\) (\(T_{module}\), \(G\)) is the short-circuit current for particular irradiance \(G\) and module temperature \(T_{module}\),  
\(V_{oc}\) (\(T_{module}\), \(G\)) is the open-circuit voltage for particular irradiance \(G\) and module temperature \(T_{module}\);  
\(I_{sc,ref}\) and \(V_{oc,ref}\) are the short-circuit current and open-circuit voltage under STC;  
\(\alpha\) is the temperature coefficient of \(I_{sc}\) under STC;  
\(\beta\) is the temperature coefficient of \(V_{oc}\) under STC;  
\(a\) is the irradiance correction coefficient of \(V_{oc}\) under STC;  
\(T_{ref}\) is the module temperature at 25 \({}^{\circ}\)C;  
\(G_{ref}\) is the irradiance at 1000 W/m\({}^{2}\). The change of \(I_{sc,ref}\) and \(V_{oc,ref}\) over time is very slow in the initial period after the PV module installation in [26]; this paper ignores the natural aging of \(I_{sc,ref}\) and \(V_{oc,ref}\), the values of both parameters under standard conditions are used in following work. When the module temperature \(T_{module}\) is replaced directly by the \(T_{jb}\), the \(PI_{\_AI}\) (\(T_{module}\), \(G\)) and \(PI_{\_AV}\) (\(T_{module}\), \(G\)) turn to \(PI_{\_AI}\) (\(T_{jb}\), \(G\)) and \(PI_{\_AV}\) (\(T_{jb}\), \(G\)) which are expressed as:  
\[PI_{\_AI}\left(T_{jb},G\right)=\frac{I_{sc}\left(T_{jb},G\right)-I_{m}\left(T_ {jb},G\right)}{I_{sc}\left(T_{jb},G\right)} \tag{5}\]  
\[PI_{\_AI}\left(T_{jb},G\right)=\frac{V_{oc}\left(T_{jb},G\right)-V_{m}\left(T _{jb},G\right)}{V_{oc}\left(T_{jb},G\right)} \tag{6}\]  
where, the \(I_{sc}\) (\(T_{jb}\),\(G\)) and \(V_{oc}\) (\(T_{jb}\),\(G\)) are rewritten as:  
\[I_{sc}(T_{jb},G)=I_{sc,ref}\cdot\left\{1+\alpha\cdot\left(T_{jb}-T_{ref}\right) \right\}\cdot\frac{G}{G_{ref}} \tag{7}\]  
\[V_{oc}(T_{jb},G)=V_{oc,ref}\cdot\left\{1+a\cdot\ln\left(\frac{G}{G_{ref}} \right)+\beta\cdot\left(T_{jb}-T_{ref}\right)\right\} \tag{8}\]  
Then, the measured data for irradiance, temperature inside junction box, voltage at MPP, current at MPP on 24 April 2022 are applied in the Equations (5)-(8), which gives the following results in Figure 5. In Figure 5c, the referenced \(PI_{\_AI\_ref}\) (0.075) and \(PI_{\_AV\_ref}\) (0.189) are calculated from the values on the datasheet under STC. In the period between 10:30 a.m. and 5:00 p.m., the results indicate that \(PI_{\_AI}\) is shifted below the reference value, but \(PI_{\_AV}\) is approximately equal to the reference value.