## 6 Results and Discussions
### 118-Bus System
#### 6.3.2 Results with Reducing the Search Space by SBDMT
However, comparing to the first case, it is obvious that better results are attained regarding the distribution of the SCs' sizes along the selected locations, the APL (837.89 kW), VD (0.1761 p.u. ), the annual cost (492,225.66 $/year), and the annual savings (189,976.86 $/year), with a slightly lower \(V_{min}\) (0.9068 p.u.). Moreover, those results are achieved with much smaller SD than that obtained in the first case, where it reaches the value of 110.371. Those results manifest the effectiveness of the proposed methods even for a heavy-loaded large-scale RDS as the 118-bus system, where due to the increasement of the problem's complexity and its wide search space, several possibilities for selecting the optimal locations can be found with more than one feasible solution as is already achieved in both studied cases for this system. Consequently, without reducing the search space, PODESCA selects the optimal locations (including the limited-impact bus 5) with better results than those from the all other \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Technique** & \multicolumn{10}{c}{**The Reduced Search Space: Total: 25 Buses**} \\ \hline \multirow{2}{*}{CLSF} & 70 & 68 & 104 & 89 & 65 & 64 & 30 & 69 & 67 & 78 & 101 & 31 & 106 & 108 & 48 \\  & 103 & 33 & 66 & 34 & 110 & 23 & 102 & 44 & 105 & 36 & & & & \\ \hline \multirow{2}{*}{PLI} & 118 & 39 & 74 & 70 & 109 & 107 & 71 & 111 & 43 & 110 & 86 & 32 & 76 & 91 & 108 \\  & 40 & 85 & 72 & 31 & 102 & 56 & 97 & 46 & 61 & 48 & & & & \\ \hline \multirow{2}{*}{SBDMT} & 70 & 48 & 74 & 39 & 118 & 76 & 71 & 77 & 75 & 72 & 73 & 109 & 43 & 107 & 56 \\  & 111 & 85 & 86 & 110 & 78 & 69 & 34 & 40 & 108 & 91 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: The reduced search space by SBDMT comparing to CLSF and PLI for the 118-bus system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Description** & **Without SBDMT** & **With SBDMT** \\ \hline \multirow{5}{*}{SCs locations and sizes (kVAr)} & 5 & 50 & 34 & 1150 \\  & 34 & 1150 & 39 & 1500 \\  & 39 & 1500 & 48 & 600 \\  & 48 & 600 & 72 & 700 \\  & 74 & 1500 & 74 & 850 \\  & 86 & 850 & 85 & 900 \\  & 91 & 1200 & 91 & 1200 \\  & 109 & 1150 & 108 & 1100 \\  & 118 & 1150 & 118 & 1250 \\ \hline \multicolumn{2}{c}{Total No. of locations} & \multicolumn{2}{c}{9 locations} \\ \hline \hline Total kVAr & 9150 & & 9250 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparison between the optimal locations and sizes of SCs by PODESCA for the 118-bus system with and without reducing the search space by SBDMT. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Method** & **APL (kW)** & **LR (\%)** & **\(V_{min}\) (p.u.)** & **VD (p.u.)** & **Ann. cost (\$/Year)** & **Net save (\$/Year)** & **Net save (\%)** & **SD** \\ \hline \multirow{3}{*}{With SCs} & 1297.95 & - & 0.8688 & 0.3576 & 682,202.52 & - & - & - \\ \cline{2-10}  & Without SBDMT & 842.16 & 35.12 & 0.9072 & 0.1771 & 493,699.50 & 188,233.02 & 27.59 & 184.433 \\ \cline{1-1}  & With SBDMT & 837.89 & 35.45 & 0.9068 & 0.1761 & 492,225.66 & 189,976.86 & 27.85 & 110.371 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Comparison of PODESCA’s results for the 118-bus system without and with reducing the search space by SBDMT. methods. Furthermore, when utilizing the reduced search space by the SBDMT, the most potential buses for SC placement are kept (bus 5 is excluded). Hence, much better results than those in the first case are obtained with better consistency as well. In other words, the best results are obtained by applying the PODESCA while using the SBDMT's reduced search space.