## 6 Results and Discussions
### 118-Bus System
#### 6.3.2 Results with Reducing the Search Space by SBDMT  
PODESCA is reapplied on the OPSC problem with a reduced search space by the SBDMT, where it is limited to only 25 buses. The search spaces of SBDMT, CLSF, and PLI are compared in Table 13, where \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Method** & **CSA [8]** & **ABC [27]** & **HSA [27]** & **HHA [26]** & **IMA-PLI [27]** & **PODESCA** \\ \hline  & 32 & 1500 & 32 & 850 & 49 & 488 & 32 & 1500 & 39 & 1500 & 5 & 50 \\  & 39 & 1500 & 35 & 1050 & 50 & 165 & 40 & 1500 & 43 & 1000 & 34 & 1150 \\  & 40 & 550 & 40 & 1300 & 51 & 349 & 70 & 900 & 70 & 1000 & 39 & 1500 \\  & 70 & 950 & 50 & 800 & 52 & 753 & 74 & 1100 & 74 & 1000 & 48 & 600 \\  & 74 & 750 & 70 & 550 & 53 & 425 & 89 & 1500 & 86 & 900 & 74 & 1500 \\  & 86 & 1050 & 73 & 1300 & 54 & 377 & 104 & 300 & 91 & 1500 & 86 & 850 \\  & 108 & 1500 & 79 & 1200 & 56 & 375 & 106 & 900 & 107 & 850 & 91 & 1200 \\  & 118 & 1200 & 105 & 700 & 70 & 626 & 112 & 400 & 109 & 850 & 109 & 1150 \\ SCs & - & - & 106 & 250 & 71 & 513 & 118 & 1300 & 118 & 1200 & 118 & 1150 \\ locations & - & - & 109 & 800 & 72 & 386 & - & - & - & - & - & - \\ and sizes & - & - & 110 & 1200 & 73 & 432 & - & - & - & - & - & - \\ (kVAr) & - & - & - & - & 74 & 272 & - & - & - & - & - & - \\  & - & - & - & - & 75 & 509 & - & - & - & - & - & - \\  & - & - & - & - & 76 & 192 & - & - & - & - & - & - \\  & - & - & - & - & 77 & 170 & - & - & - & - & - & - \\  & - & - & - & - & 79 & 714 & - & - & - & - & - & - \\  & - & - & - & - & 110 & 281 & - & - & - & - & - & - \\  & - & - & - & - & 111 & 641 & - & - & - & - & - & - \\  & - & - & - & - & 112 & 793 & - & - & - & - & - & - \\  & - & - & - & - & 113 & 974 & - & - & - & - & - & - \\  & - & - & - & - & 115 & 493 & - & - & - & - & - & - \\ \hline Total No. of locations & 8 locations & 11 locations & 21 locations & 9 locations & 9 locations & 9 locations & 9 locations \\ \hline Total kVAr & 9000 & 10,000 & 9928 & 9400 & 9800 & 9150 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Comparison of results between PODESCA and other methods for the 118-bus system. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Method** & **APL (\%)** & **LR (\%)** & **V\({}_{min}\)** & **p(u.u.)** & **VD (p.u.)** & **Ann. cost (\$/Year)** & **Net sax. (\%)** & **Net sax. (\%)** & **Net sax. (\%)** & **SD** \\ \hline Without SCs & 1297.95 & - & 0.8688 & 0.3576 & 682,202.52 & - & - & - \\ \hline CSA [8] & 858.89 & 33.64 & 0.9060 & - & 501,392.60 & 178,917.80 & 26.30 & - \\ ABC [27] & 854.39 & 33.99 & 0.9089 & - & 505,887.40 & 174,423.00 & 25.64 & - \\ HSA [27] & 926.10 & 28.26 & - & - & 549,418.20 & 130,892.20 & 19.24 & - \\ IHA [26] & 853.46 & 34.06 & 0.9004 & - & 501,160.31 & 179,150.5 & 26.33 & 1051.6 \\ IHA-PLI [27] & 843.15 & 34.85 & 0.9020 & - & 497,737.50 & 182,572.80 & 26.80 & 550.70 \\ PODESCA & 842.16 & 35.12 & 0.9072 & 0.1771 & 493,969.50 & 188,233.02 & 27.59 & 184.433 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Optimal locations and sizes of SCs by PODESCA comparing to other methods for the 118-bus system. this comparison demonstrates the difference between the three techniques. It also shows that only bus 5 among the selected locations by PODESCA in the first case is not included in the search space. By using the SBDMT's search space, PODESCA's results are obtained, where the selected locations in this case are: 34, 39, 48, 72, 74, 85, 91, 108, and 118. It is clear that some selected locations and sizes of SCs are different from the first case (without reducing the search space). Therefore, a comparison between the obtained results without and with reducing the search space is required as presented in Tables 14 and 15. As is seen in those two tables, the total installed capacity is 9250 kVAr with the reduced search space, which is slightly higher than that in the first case.