# 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 c c} \hline \hline  & **G-99** & **G-49** & **G-59** & **G-65** & **G-116** & **G-100** & **G-125** & **G-38** & **G-8** & **G-26** & **G-64** \\ \hline C2 & 600 & 200 & 300 & 800 & 800 & 200 & 300 & 400 & 1000 & 600 & 400 \\ \hline C3 & 508.3 & 139.6 & 255 & 719.4 & 719.4 & 102.8 & 204.1 & 359.7 & 899.3 & 539.6 & 359.7 \\ \hline C4 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 \\ \hline C5 & 91.7 & 60.4 & 45 & 80.6 & 80.6 & 97.2 & 95.9 & 40.3 & 100.7 & 60.4 & 40.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: List of sources responsible for maintaining the power balance with \(p_{R}\) coefficients for variants C1, C2, C3, and C4. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **G-99** & **G-49** & **G-59** & **G-65** & **G-116** & **G-100** & **G-125** & **G-38** & **G-8** & **G-26** & **G-64** \\ \hline C2 & 0.107 & 0.036 & 0.054 & 0.143 & 0.143 & 0.036 & 0.054 & 0.071 & 0.179 & 0.107 & 0.071 \\ \hline C3 & 0.106 & 0.029 & 0.053 & 0.15 & 0.15 & 0.021 & 0.042 & 0.075 & 0.187 & 0.112 & 0.075 \\ \hline C4 & 0.091 & 0.091 & 0.091 & 0.091 & 0.091 & 0.091 & 0.091 & 0.091 & 0.091 & 0.091 \\ \hline C5 & 0.116 & 0.076 & 0.057 & 0.102 & 0.102 & 0.123 & 0.121 & 0.051 & 0.127 & 0.076 & 0.051 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: List of sources responsible for maintaining the power balance along with the \(w_{k}\) coefficients determined using Equation (7) for variants C1, C2, C3, and C4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**RES**} & \multirow{2}{*}{\(\mathbf{P_{G}}\), MW**} & \multicolumn{4}{c}{**Calculation Cases/\(\mathbf{P_{\text{Gopt}}}\), MW**} \\ \cline{3-6}  & & **C1** & **C2** & **C3** & **C4** & **C5** \\ \hline G-24 & 50 & 50 & 38 & 39 & 37 & 38 \\ \hline G-113 & 70 & 42 & 36 & 36 & 35 & 36 \\ \hline G-103 & 90 & 48 & 47 & 48 & 36 & 25 \\ \hline Sum of power \(\Sigma P_{\text{G}}\), MW & 210 & 140 & 121 & 123 & 108 & 99 \\ \hline Power reduction \(\Sigma P_{\text{G}}\)-\(\Sigma P_{\text{Gopt}}\), MW & 70 & 89 & 87 & 102 & 111 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: List of RESs along with their generated power \(P_{\text{g}}\) and optimal power values \(P_{\text{Gopt}}\), which were determined in the optimization process. the considered failure state. Cases C4 and C5 are less favorable because the assumed power distribution factors are assumed arbitrarily, i.e., they have the same values (C4) or values resulting from the current generation (C5). In most of the calculation cases, the active constraints in the optimization problem were the permissible current capacities of 110 kV power lines between nodes 23 and 24, 94 and 95, and 17 and 113. The results obtained are illustrated in Figure 5.  
Figure 6 shows the course of the best values of the objective function in each iteration for the calculation case C3. The results obtained using the AIG algorithm were compared with the results obtained additionally using the Cuckoo Search (CS) algorithm and Particle Swarm Optimization. The results (objective function values) obtained using the three metaheuristic algorithms are similar as shown in Figure 6. The values of decision variables (power generated in the selected RES sources) are also comparable and are presented in Table 8. Based on Figure 6, it can be seen that the algorithm finds a solution after approximately 800 iterations. Figure 5: Visualization of optimal power values of selected RESs for the considered options. Figure 6: The course of the best values of the objective function for the C3 computation case. In the next step, calculations are performed once again for the best case (C3), assuming different weight values in the objective function (7), according to the following equation:  
\[F_{\text{obj2}}(\textbf{x})=\sum_{j=1}^{3}w_{j}\cdot P_{\text{Gj}}=w_{1}\cdot P _{\text{G-113}}+w_{2}\cdot P_{\text{G-24}}+w_{3}\cdot P_{\text{G-103}} \tag{15}\]  
The weights are determined based on the amount of congestion of individual power lines.