## 5 Results and Discussions
### System 1: The IEEE 33-Bus
#### 5.1.1 Case 1: APL Minimization
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Technique** & **Optimal** & **Optimal Sizes** & **APL** & **VD** & **VSI\({}^{-1}\)** & **VSI** & **LR\%** & **SD** \\ \hline \hline \multicolumn{10}{c}{**Case 1.1: DGs with unity power factor (PF = 1)**} \\ \hline \multirow{3}{*}{SIMBO-Q [28]} & 14 & 0.7638/0.0 & \multirow{3}{*}{73.40} & \multirow{3}{*}{0.0151} & \multirow{3}{*}{1.1444} & \multirow{3}{*}{0.8738} & \multirow{3}{*}{65.21} & \multirow{3}{*}{-} \\  & 24 & 1.0415/0.0 & & & & & \\  & 29 & 1.1352/0.0 & & & & & \\ \hline \multirow{3}{*}{QOSIMBO-Q [28]} & 14 & 0.7708/0.0 & \multirow{3}{*}{72.80} & \multirow{3}{*}{0.0151} & \multirow{3}{*}{1.1358} & \multirow{3}{*}{0.8804} & \multirow{3}{*}{65.50} & \multirow{3}{*}{-} \\  & 24 & 1.0965/0.0 & & & & & \\  & 30 & 1.0655/0.0 & & & & & \\ \hline \multirow{3}{*}{MINLP [13]} & 13 & 0.8000/0.0 & \multirow{3}{*}{72.79} & \multirow{3}{*}{-} & \multirow{3}{*}{-} & \multirow{3}{*}{-} & \multirow{3}{*}{65.34} & \multirow{3}{*}{-} \\  & 24 & 1.0900/0.0 & & & & & & \\  & 30 & 1.0500/0.0 & & & & & & \\ \hline \multirow{3}{*}{SFSA [32]} & 13 & 0.8020/0.0 & \multirow{3}{*}{72.785} & \multirow{3}{*}{0.01509} & \multirow{3}{*}{1.1357} & \multirow{3}{*}{0.8805} & \multirow{3}{*}{65.50} & \multirow{3}{*}{5.91E-09} \\  & 24 & 1.0920/0.0 & & & & & & \\  & 30 & 1.0537/0.0 & & & & & & \\ \hline \multirow{3}{*}{**QODELFA**} & **13** & **0.8018/0.0** & \multirow{3}{*}{**72.785**} & \multirow{3}{*}{**0.01509**} & \multirow{3}{*}{**1.1358**} & \multirow{3}{*}{**0.8804**} & \multirow{3}{*}{**65.50**} & \multirow{3}{*}{**4.84E-08**} \\  & **24** & **1.0913/0.0** & & & & & & \\  & **30** & **1.0536/0.0** & & & & & & \\ \hline \multicolumn{10}{c}{**Case 1.2: DGs with lagging power factor (PF = 0.95)**} \\ \hline \multirow{3}{*}{SIMBO-Q [28]} & 13 & 0.8875/0.2917 & \multirow{3}{*}{29.00} & \multirow{3}{*}{0.00098} & \multirow{3}{*}{1.0367} & \multirow{3}{*}{0.9646} & \multirow{3}{*}{86.26} & \multirow{3}{*}{-} \\  & 24 & 1.0853/0.3567 & & & & & & \\  & 30 & 1.3092/0.4303 & & & & & & \\ \hline \multirow{3}{*}{QOSIMBO-Q [28]} & 13 & 0.8303/0.2729 & \multirow{3}{*}{28.500} & \multirow{3}{*}{0.00210} & \multirow{3}{*}{1.0493} & \multirow{3}{*}{0.9530} & \multirow{3}{*}{86.49} & \multirow{3}{*}{-} \\  & 24 & 1.1239/0.3694 & & & & & & \\  & 30 & 1.2398/0.4075 & & & & & & \\ \hline \multirow{3}{*}{SFSA [32]} & 13 & 0.8306/0.2730 & \multirow{3}{*}{28.533} & \multirow{3}{*}{0.00207} & \multirow{3}{*}{1.0493} & \multirow{3}{*}{0.9530} & \multirow{3}{*}{86.48} & \multirow{3}{*}{5.24E-08} \\  & 24 & 1.1256/0.3700 & & & & & & \\  & 30 & 1.2396/0.4074 & & & & & & \\ \hline \multirow{3}{*}{**QODELFA**} & **13** & **0.8302/0.2728** & \multirow{3}{*}{**28.533**} & \multirow{3}{*}{**0.00207**} & \multirow{3}{*}{**1.0493**} & \multirow{3}{*}{**0.9530**} & \multirow{3}{*}{**86.48**} & \multirow{3}{*}{**4.95E-07**} \\  & **24** & **1.1247/0.3697** & & & & & & \\ \cline{1-1}  & **30** & **1.2396/0.4074** & & & & & & \\ \hline \hline \multicolumn{10}{c}{**Case 1.3: DGs with lagging power factor (PF = 0.866)**} \\ \hline \multirow{3}{*}{KHA [31]} & 13 & 0.8530/0.4925 & \multirow{3}{*}{19.578} & \multirow{3}{*}{-} & \multirow{3}{*}{1.0769} & \multirow{3}{*}{0.9286} & \multirow{3}{*}{90.72} & \multirow{3}{*}{-} \\  & 24 & 0.9000/0.5196 & & & & & & \\ \cline{1-1}  & 30 & 0.8999/0.5196 & & & & & & \\ \hline \multirow{3}{*}{**QODELFA**} & **13** & **0.7582/0.4378** & \multirow{3}{*}{**15.347**} & \multirow{3}{*}{**0.00065**} & \multirow{3}{*}{**1.0317**} & \multirow{3}{*}{**0.9692**} & \multirow{3}{*}{**92.73**} & \multirow{3}{*}{**5.82E-07**} \\  & **24** & **1.0273/0.5930** & & & & & & \\ \cline{1-1}  & **30** & **1.2139/0.7009** & & & & & & \\ \hline \hline \end{tabular} The sign “-” means unreported.  
\end{table} 
Table 3: Results for the IEEE 33-bus RDS with active power loss (APL) minimization (objective function 1, (OF\({}_{1}\))).