## 3 Methods
### Calculation of the Performance Loss Rate Using Linear Regression and STL  
In this work, PLR was evaluated using linear regression (LR), STL decomposition, and the YoY approach. With the first approach, PLR was computed by evaluating the PR\({}_{\mathrm{ann.}}\) time series using linear regression. With the second approach, the calculation of PLR involved three main steps. First, the decomposition of continuous monthly PR time-series into its components using STL (see Equation (1)). We used the annual-averaged temperature-corrected PR, PR\({}_{\mathrm{ann.}}\), as the base data from which the PLR was calculated. PR\({}_{\mathrm{ann.}}\) was calculated using Equation (14) [50].  
\[\mathrm{PR_{ann.}}=\frac{\sum_{\mathrm{i}}\mathrm{E_{ac,i}}}{\sum_{\mathrm{i}} \left[\mathrm{P_{0}}\Big{(}\frac{\mathrm{I_{i}}}{\mathrm{C_{ref}}}\Big{)} \Big{(}1-\frac{\gamma\mathrm{Pmp}}{100}\big{(}\mathrm{T_{m,ave}}-\mathrm{T_{m,i }}\big{)}\Big{)}\right]} \tag{14}\]  
where i is a given point in time, E\({}_{\mathrm{ac}}\) is the measured AC electrical generation (kWh).  
The STL algorithm extracts T\({}_{\mathrm{t}}\) using a locally weighted polynomial fitting. The STL decomposition results in the \"trend\", \"seasonal\", and \"residual\" components of the original temperature-corrected PR time series. STL has been implemented in other PV performance studies using the software R [1; 6; 19; 36]. Other studies such as [36; 51] have also applied STL without mentioning the tools used to implement it in the analysis of PV systems' time-series. In this work, the STL algorithm was implemented using a Python library named STLDecompose [52], according to the LOESS smoothing method [18]. The annual analysis period of 12 months is used, which represents the number of months in a year. To accommodate strong annual periodicity within the years of daily observations, if needed, a period of 365 days would be appropriate.  
Second, the calculation of the linear least-squares regression values of the \"trend\" component, T\({}_{\mathrm{t}}\), of the temperature-corrected PR follows, using Equation (15).  
\[\mathrm{T_{t}}{=}\mathrm{ax}+\mathrm{b} \tag{15}\]  
where x is an independent variable or the variable to make predictions, a is the slope of the regression line that represents the effect x has on T\({}_{\mathrm{t}}\), and b is the T\({}_{\mathrm{t}}\)-intercept. The final PLR value, in percentage, is the rate of change, either positive or negative, of the regression of the trend component. From the regression parameters, the relative PLR is computed using Equation (16) [53].  
\[\mathrm{PLR_{r}}=\frac{12a}{b} \tag{16}\]where 12 is the number of months in a year. Further, removing the denominator b, if needed, will result in an absolute value of PLR, also known as PL.  
As its name implies, the year-on-year (YoY) method uses performance time-series over year-on-year distributions. It aggregates the data points of the chosen metric between the same calendar days of subsequent years [54] by which the effects are minimized by comparing points at similar times of the year. The standard metric used in RdTools is renormalized power/energy values based on PVWatts.