# Optimal Management of High-Voltage Line Congestions Using Power Source Redispatching
## 4 Calculation Results and Discussion
### Computational Case
Since this is a conventional source, taking part in maintaining the power balance, the renewable energy source with the largest share, i.e., G-103 (\(u_{\text{94-95,103}}\) = 0.177 in Table 4), was taken for optimization. As mentioned earlier, conventional sources do not take part in the optimization process, but they provide the power \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Line** & **P\({}_{\text{94-95}}\)** & \multicolumn{8}{c}{**Line Sources Affecting the Line**} \\ \hline From–To & MW & G-91 & G-99 & G-100 & G-103 & G-105 & G-110 & G-111 & G-112 & G-125 \\ \hline \multicolumn{10}{c}{Power generated by the source, MW} \\ \cline{2-10}  & 48.867 & 91.456 & 59.878 & 67.025 & 9.576 & 11.760 & 21.964 & 10.621 & 95.815 \\ \cline{2-10}  & \multicolumn{8}{c}{Source coefficients \(u_{il,k}\) according to Equation (1)} \\ \cline{2-10}
94-95 & 43.64 & 0.047 & 0.033 & 0.223 & 0.177 & 0.010 & 0.074 & 0.074 & 0.101 \\ \cline{2-10}  & \multicolumn{8}{c}{Power flowing through the line, originating from a given source, MW} \\ \cline{2-10}  & 2.305 & 3.045 & 13.354 & 11.873 & 0.096 & 0.871 & 1.627 & 0.787 & 9.686 \\ \cline{2-10}  & \multicolumn{8}{c}{Power contribution of the source to the line load 94-95 [\%]} \\ \cline{2-10}  & 5.28 & 6.98 & 30.60 & 27.20 & 0.22 & 2 & 3.73 & 1.80 & 22.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Share of selected RES in the line load between nodes 94 and 95. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Line** & **P\({}_{\text{100-103}}\)** & \multicolumn{3}{c}{**Line Sources Affecting the Line**} \\ \hline From–To & MW & G-103 & G-110 & G-111 & G-112 \\ \hline \multicolumn{10}{c}{Power generated by the source, MW} \\ \cline{2-6}  & & 67.025 & 11.760 & 21.964 & 10.621 \\ \cline{2-6}  & & \multicolumn{8}{c}{Source coefficients \(u_{il,k}\) according to Equation (1)} \\ \cline{2-6}
100-103 & 53.33 & 0.689 & 0.273 & 0.273 & 0.273 \\ \cline{2-6}  & & \multicolumn{8}{c}{Power flowing through the line from a given source, MW} \\ \cline{2-6}  & & 46.209 & 3.215 & 6.006 & 2.904 \\ \cline{2-6}  & & \multicolumn{8}{c}{Power contribution of the source to the line load 100-103 [\%]} \\ \cline{2-6}  & & 79.21 & 5.51 & 10.30 & 4.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Share of selected RES in the line load between nodes 100 and 103.  
balance in the system. These sources, together with their \(p_{R}\) coefficients, are presented in Table 6. The values of \(w_{k}\) coefficients, calculated for different cases using Equation (12), are presented in Table 6. In case 1 (C1), the source connected to node 10 was responsible for maintaining the power balance. The remaining cases are presented in Tables 6 and 7. In the optimization calculations, a vector of decision variables \(\mathbf{x}\) (power values in previously selected RESs) was sought to eliminate the threats in the form of overloaded lines. Table 8 presents the results for five different cases (C1, C2, C3, C4, and C5), which were described earlier. It should be noted that, in case 1, bus 10 was assumed as the balancing node. Based on the obtained results, it can be stated that the minimum power reduction takes place in case 1 (C1) when assuming balancing bus 10. The balancing node is assumed to be the node located at the end of the network. However, this is a theoretical case that does not occur in practice. If the power loss caused by the optimal power reduction in RESs is covered by conventional sources, then the most favorable is case 3 (C3). It is the closest to reality. In reality, conventional sources are responsible for the power balance in the power system. Case 2 (C2) is also favorable, but in this operating state, it seems to be less favorable than C3. In practice, therefore, both cases can be considered, depending on