## 2 Materials and Methods
### Measurement Calibration for Standardization  
Leaving aside the filtering, the next phase consisted of normalizing the irradiance measurements on the array plane and the short-circuit current. This was necessary because the panels, despite being equal, did not give exactly the same measurements. If both measurements were identical, the following step would not have been necessary. To correct  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Measure** & **Sensor** & **Initial Measurement Unit** & **Conversion Factor** & **Unit** & **\(\Delta\) Measure** & **Range** \\ \hline Short-circuit current (Isc) &
\begin{tabular}{c} Shunt 15 A/150 mV \\ KL0.5 KAYNOS \\ \end{tabular} & mV & 100 mV & A & \(\pm 1\times 10^{-2}\) (A) & (0, 15) (A) \\ \hline Panel temperature & Pt 100 RS PRO & \({}^{\circ}\)C & - & \({}^{\circ}\)C & \(\pm 1\times 10^{-4}\) (C) & \((-50,150)\) (C) \\ \hline \multirow{2}{*}{Tilted global irradiance} & 65 mV Compressed & mV & 15.385 mV & Wm\({}^{-2}\) & \(\pm 1\times 10^{-6}\) (Wm\({}^{-2}\)) & \((0,1000)\) (Wm\({}^{-2}\)) \\ \cline{2-6} Ambient temperature & HMP 60 Vasisals & mV & \(-40+50\) mV & \({}^{\circ}\)C & \(\pm 1\times 10^{-7}\) (C) & \((-40,60)\) (C) \\ \hline Relative humidity & HMP 60 Vasisals & mV & 50 mV & \% & \(\pm 1\times 10^{-7}\) (C) & \((0,100)\) (\%) \\ \hline Barometric pressure & PTB 110 Vasisals & mV & 500 + 0.24 mV & hPa & \(\pm 1\times 10^{-5}\) (hPa) & \((500,1100)\) (hPa) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Metrological analysis of sensors.  
this error, both the calibrated cell and the short-circuit current from the unmaintained panel were multiplied by two correction factors. These factors were calculated from reference measurements taken at midday on the first optimal day of plant operation under standard conditions. With these data, it was known, minute by minute, what loss originated from soiling accumulation on the unmaintained photovoltaic panel since the two panels were now calibrated; therefore, the final difference between the values from the two panels would be due only to soiling. In this work, the influence of soiling was very significant on the short-circuit current. To quantify the instantaneous losses as a percentage, the mathematical expression shown in Equation (1) was used [28].  
\[\text{Losses }(\%)=100\times\frac{\frac{\text{Isc}_{\text{estimated panel}}}{\text{Isc}_{\text{estimated panel}}\text{Ref}}-\frac{\text{Isc}_{\text{Sc}_{\text{maintenance--free panel}}}}{\text{Isc}_{\text{resistance--free panel}}\text{Ref}}}{\frac{\text{Isc}_{\text{estimated panel}}}{\text{Isc}_{\text{estimated panel}}\text{Ref}}} \tag{1}\]  
Once the standardization had been carried out, both panels should have always given the same measurements unless one of them was affected by an issue that does not occur in the other, as in whether they were maintained or not. If standardization was guaranteed, the only difference possible was that caused by soiling; therefore, this was the value used to model the equation. The soiling factor that could be extrapolated to a real plant would be that of the panel without maintenance, as panels can go years without receiving such maintenance.