## 5 Comparison of Operational and Short-Term Forecasting Models  
Table 7 shows the parameters comparison for assessing the PVPP generation forecast accuracy for various operational forecast models. As far as the models under consideration have different number of predictors, the adjusted \(R^{2}\) metrics is introduced as a model quality criterion. As in the previous case (short-term forecast), adjusted \(R^{2}\) also demonstrates how well the model fits the data, but the total score is adjusted according to the number of terms in the model:  
\[R_{adjusted}^{2}=1-\left(1-R^{2}\right)\times(k-1)/(k-n-1), \tag{13}\]  
where \(R^{2}\)--R-square measure; \(n\)--number of samples in the set; \(k\)--number of variables in the model. The error assessment analysis shows that the second-order autoregressive model AR(2) has the best indicators among the operational forecast models. The parameters characterizing the results of PVPP generation operational forecast accuracy assessment using the second-order autoregressive model AR(2) are presented in Table 8.  
Figure 11 demonstrates the comparison of the PVPP generation actual values, the PVPP generation STF using the initial data filtration by the k-means method and the operational forecast using the second-order autoregressive model AR(2). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Parameters**} \\  & \(E_{\Sigma}\)**, kW-h** & \(E_{ang}\)**, kW-h** & \(\sigma_{E}\)**, kW-h** & \(E_{\Sigma}^{\%}\)**, \%** & \(R_{adjusted}^{2}\) \\ \hline Model \(P\) & 346,892.60 & 1063.18 & 609.65 & 15.51 & 0.874 \\ Model \(MA\)(2) & 337,843.22 & 1035.45 & 593.75 & 15.11 & 0.887 \\ Model \(MA\)(3) & 347,495.89 & 1065.03 & 610.71 & 15.54 & 0.874 \\ Model \(MA\)(4) & 355,941.97 & 1090.92 & 625.56 & 15.92 & 0.862 \\ Model \(MA\)(5) & 364,991.34 & 1118.65 & 641.46 & 16.32 & 0.851 \\ Model \(AR\)(1) & 325,777.39 & 998.47 & 572.54 & 14.57 & 0.904 \\ Model \(AR\)(2) & 301,645.74 & 924.51 & 530.13 & 13.49 & 0.940 \\ Model \(AR\)(3) & 331,810.31 & 1016.96 & 583.15 & 14.84 & 0.895 \\ Model \(ARMA\)(1,2) & 328,793.85 & 1007.71 & 577.85 & 14.71 & 0.900 \\ Model \(ARMA\)(2,2) & 337,843.22 & 1035.45 & 593.75 & 15.11 & 0.887 \\ Model \(ARMA\)(3,2) & 358,958.43 & 1100.16 & 630.86 & 16.05 & 0.858 \\ Model \(ARMA\)(2,3) & 352,925.51 & 1081.67 & 620.26 & 15.78 & 0.866 \\ Model \(ARX\)(2,1) & 327,180.05 & 1002.77 & 575.01 & 14.63 & 0.902 \\ Model \(ARX\)(2,2) & 330,196.50 & 1012.01 & 580.31 & 14.77 & 0.898 \\ Model \(ARX\)(2,3) & 333,212.96 & 1021.26 & 585.61 & 14.90 & 0.893 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters comparison for PVPP operational forecast accuracy assessment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **26 February** & **21 May 2018–11 March** & **211 September** & **28 January** & **For All** \\  & **2018** & **June 2018** & **2018–20 September** & **2019–3 February 2019** & **Periods** \\ \hline \(W_{\Sigma}\), kW-h & 391,805.4 & 1,156,028.2 & 601,402.2 & 86,694.7 & 2,235,930.5 \\ \(E_{\Sigma}\), kW-h & 82,951.0 & 76,503.8 & 119,241.6 & 23,406.3 & 301,645.8 \\ \(E_{avg}\), kW-h & 505.8 & 384.4 & 917.2 & 289.0 & 530.1 \\ \(\sigma_{E}\), kW-h & 722.5 & 867.6 & 1011.8 & 440.0 & 924.5 \\ \(E_{\Sigma}^{\%}\), \% \% \(R^{2}\) & 21.17 & 6.62 & 19.83 & 27.00 & 13.5 \\  & \multicolumn{3}{c}{} & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The parameters calculating results for assessing the PVPP generation operational forecast accuracy. As one can see from Figure 10(a)-d, the operational forecast makes it possible to refine the short-term forecast, the curve of operational forecast absolute errors has a flat character compared to the short-term forecast, the absolute forecasting error values are closer to zero. Table 9 demonstrates the comparison of the short-term and operational PVPP generation forecasting accuracy. When dealing with stochastic phenomena, providing a 100% accurate forecast is problematic.