## 4 Results and Discussion
It was also observed for this network that the results of use case 1 are better than use case 2 due to the limitation on capacitor values in use case 2. Voltage profile and line flow for 85 node RDN are shown in Figures 8 and 9, respectively. Prior to compensation, it can be observed that the voltage at some buses violate the limits. These scenarios are improved after optimization and the constraints are satisfied. The maximum value of voltage is 0.9961 pu at node 2 and minimum voltage is 0.8505 pu at node 76. In use case 1, the maximum voltage is 0.9981 pu at node 2 and minimum voltage is 0.9100 pu at node 76. Similarly, for use case 2, the maximum voltage is improved from 0.9961 to 0.9979 pu at node 2 and minimum voltage is improved from 0.8505 to 0.9068 pu at node 7. In Figure 8, line flow of uncompensated and compensated cases are shown. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Items**} & \multirow{2}{*}{**Uncompensated**} & \multicolumn{6}{c}{**Compensated**} \\ \cline{3-8}  & & \multirow{2}{*}{**PGSA**} & \multirow{2}{*}{**DSA**} & \multirow{2}{*}{**GA**} & \multicolumn{3}{c}{**ACO Algorithm**} & \multicolumn{2}{c}{**Proposed Algorithm**} \\  & & & & **Use Case1** & & **Use Case2** & & **Use Case1** & & **Use Case2** \\ \hline \hline \multirow{10}{*}{kvar injected at node} & \multirow{6}{*}{-} & \multirow{6}{*}{150 (6)} & 48.4 (26) & \multirow{6}{*}{120.3 (38)} & \multirow{6}{*}{186 (4)} \\  & & & 214 (28) & & & & \\  & & 150 (6) & 103.1 (37) & & & & \\  & & 150 (6) & 120.3 (38) & & & & \\  & & 150 (8) & 178 (39) & 186 (4) & & & \\  & & 150 (14) & 100 (51) & 150 (7) & 150 (7) & 150 (27) & 300(25) \\  & & 150 (17) & 212.5 (54) & 10 (13) & 300 (8) & 203.5 (30) & 150 (48) \\  & & 150 (18) & 101.5 (55) & 280 (13) & 300 (19) & 439.4 (64) & 600 (51) \\  & & 200 (7) & 150 (26) & 4.6 (59) & 300 (27) & 300 (27) & 459 (64) \\  & & 1200 (8) & 150 (26) & 157 (60) & 320 (26) & 300 (32) & 295 (51) & 300 (18) \\  & & 908 (58) & 150 (30) & 112.5 (61) & 250 (31) & 300 (48) & 150 (67) & 150 (68) \\  & & 450 (37) & 104 (62) & 205 (35) & 300 (61) & 150 (19) & 300 (12) \\  & & 150 (57) & 9.3 (66) & 200 (53) & 300 (68) & 150 (19) & 150 (61) \\  & & 150 (61) & 100 (69) & 220 (61) & 300 (80) & 161 (46) & 150 (61) \\  & & 150 (66) & 67 (72) & 330 (68) & 300 (80) & 286 (80) & 150 (44) \\  & & 300 (69) & 112.5 (74) & & & & \\  & & 150 (80) & 71.9 (76) & & & & \\  & & & 356.2 (80) & & & & \\  & & & 31.2 (82) & & & & \\  & & & & & & & \\ Total kvar injected & - & 2308 & 2550 & 2207 & 2726 & 2550 & 2134.9 & 2250 \\ Active loss (kW) & 319 & 174.9 & 144.0 & 146 & 143.3 & 143.9 & 140.9 & 145.2 \\ Reactive loss (kvar) & 182 & - & - & - & - & - & 80.7 & 82.6 \\ Active loss reduction (\%) & - & 44 & 54.4 & 53.7 & 54.6 & 54.4 & 55.8 & 54.5 \\ Reactive loss reduction (\%) & - & - & - & - & - & - & 55.7 & 54.6 \\ \(V_{min}\) at node & 0.85 (76) & 0.90 (54) & 0.92 (54) & 0.92 (55) & 0.92 (54) & 0.92 (27) & 0.91 (76) & 0.91 (76) \\ \(V_{max}\) at node & 0.99 (2) & 0.99 (2) & 0.99 (2) & 0.99 (2) & 0.99 (2) & 0.99 (2) & 0.99 (2) & 0.99 (2) \\ Annual cost USD ($)/year & 53,619 & 29,385 & 24,194 & 24,538 & 24,082 & 24,171 & 23,670 & 24,394 \\ Capacitor cost USD ($)/year & - & 1154 & 1275 & 1103 & 1363 & 1275 & 1067.4 & 1125 \\ Net saving USD ($)/year & - & 24,234 & 29,425 & 29,081 & 29,537 & 29,448 & 29,949 & 29,225 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results comparison of \(N_{2}\) for \(CS_{1}\). Figure 8: Voltage profile for \(N_{2}\) in \(CS_{1}\).