## 4 Test and Results
### Static TNP
#### 4.1.1 Garver System  
The Garver system has 6 buses and 15 right-of-ways for the addition of new circuits (lines and transformers). The generation capacity is 1110 MW and the expected demand is 760 MW. In this case, it is supposed a maximum of 4 circuits in each right-of-way. For all simulations, a population of 20 individuals (\(k_{p}\)) was considered, with \(k_{s}\) equal to 3%, \(k_{dr}\) equal to 5% and \(k_{m}\) equal to 5% (selection, diversification and mutation rates, respectively). A summary of results for this system is presented in Table 2.  
Test 1: The best solution found by HEGA for the static TNEP problem without SCC and active power losses has a total investment cost of US$110.00 \(\times\) 10\({}^{6}\) and no load shedding. This solution is equal to the one reported in [15]. This solution is found by the HEGA after executing 46 LPs with a computational time of 0.047 min. The configuration is: \(n_{3-5}=1\), and \(n_{4-6}=3\).  
Test 2: The solution found by HEGA for the static TNEP problem with SCC and without active power losses is equal to test 1 (no lines compensation).  
Test 3: The best solution found by HEGA for the static TNEP problem considering active power losses and without SCC has a total investment cost of US$130.00 \(\times\) 10\({}^{6}\) and no load shedding. This solution is found by the HEGA after executing 13 LPs with a computational time of 0.046 min. The found configuration is: \(n_{2-3}=1\), \(n_{3-5}=1\), \(n_{4-6}=3\)  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Compensation Rate** & **Compensation Cost** \\  & **(\% of Circuit Reactance)** & **(\% of Circuit Inves. Cost)** \\ \hline
1 & 30\% & 10\% \\
2 & 40\% & 15\% \\
3 & 50\% & 20\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Series Capacity Compensation Types.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test** & **Total Cost** & **Power Losses** & **LPs** & **Time** & **Configuration** & **Compensated** \\  & **(10\({}^{6}\) USS)** & **(MW)** & **Executed** & **(min)** & **(min)** & **(min)** \\ \hline
1 & 110.00 & – & 40 & 0.045 & \(\begin{array}{c}n_{3-5}=1,\\ n_{4-6}=3\end{array}\) & – \\ \hline
2 & 110.00 & – & – & – & \(\begin{array}{c}n_{3-5}=1,\\ n_{4-6}=3\end{array}\) &
\begin{tabular}[]{c}No \\ compensated \\ lines \\ \end{tabular} \\ \hline
3 & 130.00 & 29.51 & 129 & 0.121 & \(\begin{array}{c}n_{2-3}=1,\\ n_{3-5}=1,\\ n_{4-6}=3\end{array}\) & – \\ \hline
4 & 116.00 & 36.62 & 139 & 0.181 & \(\begin{array}{c}n_{2-6}=1,\\ n_{3-5}=1,\\ n_{4-6}=2\end{array}\) &
\begin{tabular}[]{c}n_{4-6}=2\\ (type 1) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of results for the Garver system (static TNEP).  
Test 4: The best solution found by HEGA for the static TNEP problem with SCC and active power losses has a total investment cost of US$116.00 \(\times\) 10\({}^{6}\) and no load shedding. This solution is found by the HEGA after executing 139 LPs with a computational time of 0.18 min. The total active power loss is equal to 36.62 MW. The added circuits have an investment cost equal to US$110.00 \(\times\) 10\({}^{6}\), and are added in the following right-of-ways: \(n_{2-6}=1\), \(n_{3-5}=1\), and \(n_{4-6}=2\). The investment cost of the SCC devices is equal to US$6.00 \(\times\) 10\({}^{6}\), and the compensated line is: \(n_{4-6}=2\) (type 1).