## 5 Critical Analysis of the Results  
This section presents some analysis and discussion of the results achieved by the proposed approach. In the static planning of the Garver system using the proposed \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multirow{2}{*}{
\begin{tabular}{c} **Total Cost** \\ **(10\({}^{6}\) US)** \\ \end{tabular} } & \multirow{2}{*}{**LPs**} & **Time** & **Stage Cost** & **Power Losses** & **Configuration** & **Compensated Lines** \\ \cline{6-9}  & & & & 1 & 116.00 & – & \(n_{12-14}=1,n_{20-21}=1,n_{24-30}=2,\) & – \\  & & & & & \(n_{4-6}=1,n_{19-25}=1,n_{24-35}=2,n_{35-6}=2\) & – \\ \cline{6-9}
1 & & & & 2 & 40.015 & – & \(n_{2-5}=1,n_{30-21}=1,n_{32-12}=1,n_{3-6}=2,\) & – \\ \cline{6-9}  & & & & 3 & 27.198 & – & \(n_{33-02}=2,n_{38-31}=2,n_{4-30}=1,\) & – \\ \hline \multirow{6}{*}{2} & \multirow{6}{*}{183.213} & \multirow{6}{*}{8988} & \multirow{6}{*}{2.68} & \multirow{6}{*}{1} & 116.00 & – & \(n_{12-14}=1,n_{20-21}=1,n_{24-30}=2,\) & – \\  & & & & & \(n_{44-6}=1,n_{19-25}=1,n_{42-52}=2,n_{35-6}=2\) & No compensated lines \\ \cline{6-9}  & & & & 2 & 40.015 & – & \(n_{2-5}=1,n_{30-24}=1,n_{30-21}=1,n_{35-6}=2,\) & No compensated lines \\ \cline{6-9}  & & & & 3 & 27.198 & – & \(n_{33-02}=2,n_{18-31}=2,n_{42-33}=1,\) & No compensated lines \\ \hline \multirow{6}{*}{3} & \multirow{6}{*}{195.08} & \multirow{6}{*}{34,326} & \multirow{6}{*}{13.74} & \multirow{6}{*}{2} & 116.100 & 495.40 & \(n_{12-14}=1,n_{20-21}=1,n_{42-43}=2,\) & – \\  & & & & & \(n_{44-6}=1,n_{19-25}=1,n_{42-52}=2,n_{35-6}=2\) & – \\ \cline{6-9}  & & & & & & \(n_{2-5}=1,n_{30-21}=1,n_{31-41}=1,\) & – \\ \cline{6-9}  & & & & & \(n_{44-6}=1,n_{35-6}=1\) & – & – \\ \cline{6-9}  & & & & 3 & 35.415 & 488.15 & \(n_{33-02}=1,n_{32-31}=1,n_{44-30}=1,\) & – \\ \cline{6-9}  & & & & & 116.10 & 406.39 & \(n_{12-14}=1,n_{20-21}=1,n_{42-43}=2,\) & No compensated lines \\ \cline{6-9}  & & & & & & \(n_{44-6}=1,n_{35-6}=1,n_{35-6}=2,n_{35-6}=2,n_{35-6}=2\) & No compensated lines \\ \cline{6-9}  & & & & & & \(n_{44-6}=1,n_{35-6}=1,n_{35-6}=1,n_{35-6}=1,\) & No compensated lines \\ \cline{6-9}  & & & & & 31.433 & 1064.23 & \(n_{13-18}=1,n_{35-6}=1,n_{35-6}=1,\) & \(n_{20-21}=1\) (type 2) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of results for the South Brazilian 46-bus system (multistage TNEP). methodology, a difference of 14.00 \(\times\) 10\({}^{6}\) US$ is found, i.e., 10.78% cheaper than the planning without SCC. For the multistage planning of the same system, 6690 \(\times\) 10\({}^{6}\) US$ is found, that is, 7.4% more economical than planning without SCC. For the IEEE-24 static bus system, it was 27,600 \(\times\) 10\({}^{6}\) US$, that is, 15.16% more economical than planning without SCC, and for multistage planning, it was 11,090 \(\times\) 10\({}^{6}\) US$, that is, 4.65% more economical than planning without SCC. The expansion cost for the southern Brazilian system in the static planning was 0.450 \(\times\) 10\({}^{6}\) US$, that is, 0.593% more economical than planning without SCC, and for the multistage planning it was 3.40 \(\times\) 10\({}^{6}\) US$, that is, 1.74% cheaper than planning without SCC. According to Figure 7, the Garver system in topology (a) presents an investment cost of 110.00 \(\times\) 10\({}^{6}\) US$ with 4 new circuits, which matches the optimal planning reported in the specialized literature for this system. Topology (b) shows the optimal planning of the same system considering the effect of power losses. In this case, the investment costs increase to US$130.00 \(\times\) 10\({}^{6}\) US$, and 5 transmission lines are added. This extra cost is attributable to the effect of power losses and evidences the importance of considering them to reach more accurate expansion plans. The result of the planning considering power losses and SCC devices is depicted in Topology (c). In this case, an investment cost of 116.00 \(\times\) 10\({}^{6}\) US$ is required.