# Optimal Management of High-Voltage Line Congestions Using Power Source Redispatching
## 4 Calculation Results and Discussion
### Computational Case
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Line** & **P\({}_{\textbf{16-17}}\)** & \multicolumn{6}{c}{**Line Sources Affecting the Line**} \\ \hline From–To & MW & G-17 & G-24 & G-25 & G-26 & G-27 & G-31 & G-72 & **G-113** \\ \hline \multicolumn{10}{c}{Power generated by sources, MW} \\ \cline{2-9}  & & 37.507 & 49.602 & 99.674 & 60.259 & 9.212 & 13.871 & 49.813 & 69.719 \\ \cline{2-9}  & & \multicolumn{6}{c}{Source coefficients \(u_{ll,k}\) according to Equation (1)} \\ \cline{2-9}
16-17 & 72.38 & 0.365 & 0.008 & 0.156 & 0.310 & 0.002 & 0.133 & 0.004 & 0.316 \\ \cline{2-9}  & & \multicolumn{6}{c}{Power flowing through the line, originating from a given source, MW} \\ \cline{2-9}  & & 13.695 & 0.381 & 15.551 & 18.679 & 0.022 & 1.847 & 0.187 & 22.036 \\ \cline{2-9}  & & \multicolumn{6}{c}{Power contribution of the source to the line load 16-17 [\%]} \\ \cline{2-9}  & & 18.92 & 0.53 & 21.48 & 25.80 & 0.03 & 2.55 & 0.26 & 30.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Share of selected RES in the line load between nodes 16 and 17. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Line** & **P\({}_{\textbf{17-113}}\)** & **Line Sources Affecting the Line** \\ \hline From–To & MW & G-113 \\ \hline \multicolumn{10}{c}{Power generated by the source, MW} \\ \cline{2-9}  & & 67.719 \\ \cline{2-9}  & & \multicolumn{6}{c}{Source coefficients \(u_{ll,k}\) according to Equation (1)} \\ \cline{2-9}
17-113 & 56.26 & 0.807 \\ \cline{2-9}  & & \multicolumn{6}{c}{Power flowing through the line from a given source, MW} \\ \cline{2-9}  & & 56.256 \\ \cline{2-9}  & & \multicolumn{6}{c}{Power contribution of the source to the line load 17-113 [\%]} \\ \cline{2-9}  & & \multicolumn{6}{c}{100} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Share of selected RES in the line load between nodes 17 and 113. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Line** & **P\({}_{\textbf{23-24}}\)** & **Line Sources Affecting the Line** \\ \hline From–To & MW & G-24 & G-72 \\ \hline \multicolumn{10}{c}{Power generated by the source, MW} \\ \cline{2-9}  & & 49.602 & 49.813 \\ \cline{2-9}  & & \multicolumn{6}{c}{Source coefficients \(u_{ll,k}\) according to Equation (1)} \\ \cline{2-9}
23-24 & 62.40 & 0.844 & 0.412 \\ \cline{2-9}  & & \multicolumn{6}{c}{Power flowing through the line from a given source, MW} \\ \cline{2-9}  & & 41.864 & 20.539 \\ \cline{2-9}  & & \multicolumn{6}{c}{Power contribution of the source to the line load 23-24 [\%]} \\ \cline{2-9}  & & 67.09 & 32.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Share of selected RES in the line load between nodes 23 and 24. As mentioned earlier, in the second step, the optimization task described in point 3 is solved using relations (6), (7), and (8). The decision variables are only those RESs that have the greatest impact on the overloaded lines. According to the results in Tables 1-5, these are sources G-113, G-24, and G-103. In the case under consideration, the detailed form of the objective function is as follows:  
\[F_{\text{obj1}}(\mathbf{x})=\sum_{j=1}^{3}P_{\text{G}j}=P_{\text{G-113}}+P_{\text{ G-24}}+P_{\text{G-103}} \tag{14}\]  
It is worth mentioning that, in the case of the 110 kV line of relation 16-17, the highest \(u_{ij,k}\) coefficient is possessed by source G-17 (u16-17,17 = 0.365), not G-113 (\(u_{\text{16-17,17}}\) = 0.365). However, due to the fact that source G-113 generates much greater power (\(P_{\text{g}}\) = 69.719 MW) than source G-27 (\(P_{\text{g}}\) = 37.507 MW) it has a greater impact on the load on the line between nodes 16 and 17. This is proven by the value of power flowing through this line (22.036 MW), which comes from the G-113 source. The power from the G-27 source, flowing through the 16-17 line, is 13.695 MW, which is significantly lower. Attention should also be paid to the lines between nodes 94 and 95. The biggest part in its load is taken by the G-100 source (\(u_{\text{94-95,100}}\) = 0.223 in Table 4).