## 6 Results and Discussions
### 85-Bus System
#### 6.2.1. Results without Reducing the Search Space  
PODESCA is applied on the OPSC problem in this case with a search space containing 84 buses. Considering five locations for SC placement, the results of full-load level are obtained and listed in Tables 7 and 8. As demonstrated in those tables, the results of PODESCA are compared to those from other methods in the literature [2; 23; 26; 28]. The optimal selected locations are 12, 30, 49, 60, and 69 with total installed capacity equal to 2000 kVAr, which is less than those from the other methods. In addition, both values of \(V_{min}\) and VD are improved to 0.9207 p.u. and 0.3121 p.u., respectively. The APL is decreased to 148.25 kW, which is lower than those obtained from plant growth simulation algorithm (PGSA) and MBA. However, this value is still higher than those from direct search algorithm (DSA), teaching learning-based optimization (TLBO), GSA, and improved harmony algorithm (IHA). Nevertheless, the annual cost obtained by the proposed algorithm (91,018.47 $/year) is less than the costs from the all other algorithms addressed in this comparison, which consequently led to the highest annual savings as well (74,920.8 $/year). Hence, by compromising the overall solutions, it can be noticed that PODESCA's results are regarded as better solutions than most of the other methods' solutions from the literature. Thus, the obtained results given in Tables 7 and 8 validate the proposed algorithm's effectiveness as well as its consistency especially when comparing the small SD value (0.01208) to that from IHA (358.240). Furthermore, Table 9 gives the optimal results for different load levels, where three fixed SCs with sizes of 250, 350, and 300 kVAr are injected at buses 12, 30, and 60, respectively. While the switched SCs are distributed as 200, 200, 350, 200, and 250 kVAr, respectively, at buses 12, 30, 49, 60, and 69. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Method** & **PGSA**[26] & **DSA**[26] & **TLBO**[2] & **GSA**[23] & **IHA**[26] & **MBA**[28] & **PODESCA** \\ \hline \multirow{8}{*}{SCs locations} & 7 & 200 & 6 & 150 & 4 & 300 & 8 & 150 & 8 & 250 & 8 & 800 & 12 & 450 \\  & 8 & 1200 & 8 & 150 & 7 & 150 & 12 & 150 & 29 & 350 & 27 & 300 & 30 & 450 \\  & 58 & 908 & 14 & 150 & 9 & 300 & 29 & 350 & 34 & 400 & 34 & 400 & 49 & 350 \\  & - & - & 17 & 150 & 21 & 150 & 36 & 450 & 54 & 150 & 58 & 400 & 60 & 500 \\  & - & - & 18 & 150 & 26 & 150 & 68 & 450 & 58 & 350 & 64 & 300 & 69 & 250 \\  & - & - & 20 & 150 & 31 & 300 & 83 & 1050 & 64 & 500 & - & - & - & - \\ \cline{1-1}  & - & - & 26 & 150 & 45 & 150 & - & - & 83 & 250 & - & - & - & - \\ \cline{1-1}  & - & - & 30 & 300 & 49 & 150 & - & - & - & - & - & - & - \\ \cline{1-1}  & - & - & 36 & 450 & 55 & 150 & - & - & - & - & - & - & - \\ \cline{1-1}  & - & - & 57 & 150 & 61 & 300 & - & - & - & - & - & - & - & - \\ \cline{1-1}  & - & - & 61 & 150 & 68 & 300 & - & - & - & - & - & - & - \\ \cline{1-1}  & - & - & 66 & 150 & 83 & 150 & - & - & - & - & - & - & - & - \\ \cline{1-1}  & - & - & 69 & 300 & 85 & 150 & - & - & - & - & - & - & - & - \\ \cline{1-1}  & - & - & 80 & 150 & - & - & - & - & - & - & - & - & - \\ \hline Total No. of & & & & & & & & & & & & & & \\ locations & 3 locations & 14 locations & 13 locations & 6 locations & 7 locations & 5 locations & 5 locations & 5 locations \\ \hline Total kVAr & 2308 & 2700 & 2700 & 2600 & 2250 & 2200 & 2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimal locations and sizes of SCs by PODESCA comparing to other methods for the 85-bus system.