## 4 Test and Results
### Static TNP
#### 4.1.3 South Brazilian 46-Bus System  
The South Brazilian 46-bus system has 46 buses and 71 right-of-ways for the addition of new circuits. The generation is 10,545 MW, and the demand is 6880 MW. This system has no limits in the number of circuits that can be added to the right-of-ways. In this case, a population of 50 individuals (\(k_{p}\)) was considered, with \(k_{s}\) equal to 4%, \(k_{dr}\) 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 4.  
Test 1: The best solution found by the proposed approach for the static TNEP problem without SCC and active power losses has a total investment cost of US$72.87 \(\times\) 10\({}^{6}\) and no load shedding. The solution is equal to the one reported in [15]. This solution is found by the HEGA after executing 274 LPs with a computational time of 0.131 min. The found configuration is: \(n_{2-5}=1\), \(n_{13-20}=1\), \(n_{20-23}=1\), \(n_{20-21}=2\), \(n_{42-43}=1\), \(n_{46-6}=1\), and \(n_{5-6}=1\).  
Test 2: The solution found by the algorithm for the static TNEP problem with SCC and without active power losses has a total investment cost of US$64.98 \(\times\) 10\({}^{6}\) and no load shedding. This solution is found by the HEGA after solving 3154 LPs with a computational time of 2.28 min. The added circuits have a total investment cost of US$63.16 \(\times\) 10\({}^{6}\), and are added in the following right-of-ways: \(n_{20-23}=1\), \(n_{20-21}=2\), \(n_{42-43}=1\), \(n_{46-6}=1\), \(n_{5-6}=2\). The SCC devices have investment cost equal to US$1.82 \(\times\) 10\({}^{6}\), and the compensated lines are: \(n_{5-8}=1\) (type 1), and \(n_{13-20}=1\) (type 2). Test 3: The best solution found by the HEGA for the static TNEP problem considering active power losses and without SCC has a total investment cost of US$75.90 \(\times\) 10\({}^{6}\) and \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & **Total Cost** & **Power Losses** & **LPs** & **Time** & \multirow{2}{*}{**Configuration**} & **Compensated** \\  & **(10\({}^{6}\) USS)** & **(MW)** & **Executed** & **(min)** & & **Lines** \\ \hline \multirow{6}{*}{1} & \multirow{6}{*}{72.87} & \multirow{6}{*}{–} & \multirow{6}{*}{274} & \multirow{6}{*}{0.131} & \(n_{2-5}=1\), & \multirow{6}{*}{–} \\  & & & & & & \(n_{13-20}=1\), & \\  & & & & & \(n_{20-23}=1\), & \\  & & & & & \(n_{20-21}=2\), & \\  & & & & & \(n_{42-43}=1\), & \\  & & & & & \(n_{46-6}=1\), & \\  & & & & & \(n_{5-6}=1\) & \\ \hline \multirow{6}{*}{2} & \multirow{6}{*}{63.16} & \multirow{6}{*}{–} & \multirow{6}{*}{3154} & \multirow{6}{*}{2.28} & \(n_{20-23}=1\), & \multirow{6}{*}{–} \\  & & & & & \(n_{20-21}=2\), & \\  & & & & & \(n_{24-43}=1\), & \\  & & & & & \(n_{46-6}=1\), & \\  & & & & & & \(n_{5-6}=2\) & \\ \hline \multirow{6}{*}{3} & \multirow{6}{*}{75.90} & \multirow{6}{*}{603.18} & \multirow{6}{*}{608} & \multirow{6}{*}{0.36} & \(n_{18-20}=1\), & \multirow{6}{*}{–} \\  & & & & & \(n_{20-23}=1\), & \\  & & & & & \(n_{20-21}=2\), & \\  & & & & & \(n_{42-43}=1\), & \\  & & & & & \(n_{46-6}=1\), & \\  & & & & & \(n_{5-6}=2\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of results for the South Brazilian 46-bus system (static TNEP). no load shedding. This solution is found by the HEGA after solving 608 LPs with a computational time of 0.36 min. The found configuration is: \(n_{18-20}=1\), \(n_{20-23}=1\), \(n_{20-21}=2\), \(n_{42-43}=1\), \(n_{46-6}=1\), and \(n_{5-6}=2\).