## 3 Methodology
### Data Matrix and Input Data Filtering  
The data used in this paper are obtained by the following ways: current and voltage of each PV module, temperature in each junction box from the monitoring system; irradiance and module temperature of the reference module from RT1; and meteorological data from the weather station.  
First of all, some related parameters and notations based on data signature are defined as:  
\(ID_{system}\): PV system ID in real plant;  
\(ID_{string}\): PV string ID in PV system;  
\(ID_{module}\): PV Module ID in PV string.  
\(ID_{interate}\): inverter ID.  
\(t\): the local time.  
\(G_{th}\): horizontal irradiance, \(G_{th}\)(i) represents the irradiance of the \(i\)th horizontal radiation with time series.  
\(u\): wind speed.  
\(T_{air}\): air temperature, \(T_{air}\)(\(i\)) represents the temperature of the \(i\)th type of environmental configuration.  
\(T_{jb}\): the temperature in junction box, \(T_{jb}\)(\(i\)) represents the temperature of the \(i\)th type of environmental configuration in junction box.  
\(T_{measured}\): the measured module temperature, \(T_{measured}\)(\(i\)) represents the module temperature of the \(i\)th type of environmental configuration.  
Figure 4: Data acquisition and transmission of a smart PV system.  
\(T_{calculated}\): the calculated module temperature from temperature model, \(T_{calculated}(i)\) represents the calculated module temperature of the \(i\)th type of environmental configuration. \(G\): irradiance on the surface of module, \(G(i)\) represents the irradiance of the \(i\)th type of environmental configuration. \(I_{m}\): module current at MPP, \(I_{module}(k,j)\) represents the current of the \(j\)th module in \(k\)th strings. \(V_{m}\): module voltage at MPP, \(V_{module}(k,j)\) represents the voltage of the \(j\)th module in \(k\)th strings. \(P_{m}\): module power at MPP, \(P_{module}(k,j)\) represents the power of the \(j\)th module in \(k\)th strings. In the following data, the data structure body \(M\) in format of MATLAB is further formed from the above parameters, which includes the module location information, weather data and module performance data. \(M\).Location is used to sign the location of the module: \(M\).Location = [\(ID_{system}\), \(ID_{inverter}\), \(ID_{string}\), \(ID_{module}\)]. \(M\).Time describes the date and time of data: \(M\).Time = [_date_, _time_]. \(M\)._Weather_ represents the weather data with time series: \(M\).Weather = [\(T_{jp}\),\(T_{air}\),\(\mu\),\(G_{h}\), \(G\), \(T_{measured}\)]. \(M\).Module expresses module performance data: \(M\).Module = [\(I_{module}\), \(V_{module}\), \(P_{module}\), \(T_{calculated}\)]. Then, one cell (\(M\)) is created as \(M\) = {Location, Time, Weather, Module}. Thus, the data to be evaluated are a complex data matrix consisting of \(N_{s}\)\(\times N_{p}\) cells:  
\[\left[\begin{array}{cccc}M_{11}&M_{12}&\cdots&M_{1(Np-1)}&M_{1 Np}\\ M_{21}&M_{22}&\cdots&M_{2(Np-1)}&M_{2 Np}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ M_{(Ns-1)1}&M_{(Ns-1)2}&\cdots&M_{(Ns-1)(Np-1)}&M_{(Ns-1)Np}\\ M_{Ns1}&M_{Ns2}&\cdots&M_{(Ns-1)(Np-1)}&M_{NsNp}\end{array}\right]_{N_{s}\times N _{p}}\]  
where, \(N_{s}\) is module numbers in one substring, \(N_{p}\) is substring numbers in a PV system. As the data came from three measurement subsystems, it results in inconsistent sampling frequencies. So, all data will be filtered to the same dimensions and data intervals at the same time based on data fusion and data integration in MATLAB. Furthermore, any outliers will be removed during this process.