## 5 Results and Discussions
### System 3: The IEEE 118-Bus
#### 5.3.3 Case 3: Simultaneous Minimization of APL, VD, and VSI\({}^{-1}\)
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Technique** & \begin{tabular}{c} **Optimal** \\ **Locations** \\ \end{tabular} & \begin{tabular}{c} **Optimal** \\ **(MW/MVAr)** \\ \end{tabular} & \begin{tabular}{c} **APL** \\ **(kW)** \\ \end{tabular} & \begin{tabular}{c} **VD** \\ **(p.u.)** \\ \end{tabular} & \begin{tabular}{c} **VSI-1** \\ **(p.u.)** \\ \end{tabular} & \begin{tabular}{c} **VSI** \\ **(p.u.)** \\ \end{tabular} & \
\begin{tabular}{c} **L8\%** \\ **(p.u.)** \\ \end{tabular} &
\begin{tabular}{c} **SD** \\ \end{tabular} \\ \hline \hline \multicolumn{10}{c}{**Case 3.1: DGs with unity power factor (PF = 1)**} \\ \hline \multirow{10}{*}{QOTLBO [29]} & 43 & 1.5880(0).0 & \multirow{10}{*}{677.588} & \multirow{10}{*}{0.02330} & \multirow{10}{*}{1.1372} & \multirow{10}{*}{0.8794} & \multirow{10}{*}{47.80} & \multirow{10}{*}{-} \\  & 49 & 3.8459(0).0 & & & & & \\  & 54 & 0.9852(0).0 & & & & & & \\  & 74 & 3.1904(0).0 & 677.588 & 0.02330 & 1.1372 & 0.8794 & 47.80 & - \\  & 80 & 3.1632(0).0 & & & & & & \\  & 94 & 1.9527(0).0 & & & & & & \\  & 111 & 3.6013(0).0 & & & & & & \\ \hline \multirow{10}{*}{SPSA [32]} & 19 & 2.0313(0).0 & \multirow{10}{*}{564.104} & \multirow{10}{*}{0.03085} & \multirow{10}{*}{1.1420} & \multirow{10}{*}{0.8757} & \multirow{10}{*}{56.54} & \multirow{10}{*}{6.20E-03} \\  & 41 & 1.9135(0).0 & & & & & & \\  & 49 & 4.0113(0).0 & & & & & & \\  & 73 & 2.7996(0).0 & 564.104 & 0.03085 & 1.1420 & 0.8757 & 56.54 & 6.20E-03 \\  & 79 & 3.0734(0).0 & & & & & & \\  & 96 & 2.0861(0).0 & & & & & & \\  & 108 & 3.8194(0).0 & & & & & & \\ \hline \multirow{10}{*}{QODELFA} & 18 & 3.1920(0).0 & \multirow{10}{*}{561.000} & \multirow{10}{*}{0.0675} & \multirow{10}{*}{1.2032} & \multirow{10}{*}{0.8311} & \multirow{10}{*}{56.78} & \multirow{10}{*}{-} \\  & 39 & 2.7580(0).0 & & & & & & \\  & 48 & 1.2360(0).0 & & & & & & \\  & 66 & 1.4450(0).0 & 561.000 & 0.0675 & 1.2032 & 0.8311 & 56.78 & - \\  & 74 & 2.0650(0).0 & & & & & & \\  & 80 & 1.9480(0).0 & & & & & & \\  & 110 & 2.6780(0).0 & & & & & & \\ \hline \multirow{10}{*}{QODELFA} & **20** & **2.1256(0).0** & \multirow{10}{*}{554.682} & \multirow{10}{*}{0.0297} & \multirow{10}{*}{**1.1250**} & \multirow{10}{*}{0.8889} & \multirow{10}{*}{57.26} & \multirow{10}{*}{6.74E-03} \\  & 39 & **3.8797(0).0** & & & & & & \\  & 47 & **2.3173(0).0** & & & & & & \\ \cline{1-1}  & **73** & **2.8518(0).0** & **554.682** & **0.0297** & **1.1250** & **0.8889** & **57.26** & **6.74E-03** \\ \cline{1-1}  & **80** & **2.0957(0).0** & & & & & & \\ \cline{1-1}  & **91** & **2.4212(0).0** & & & & & & \\ \cline{1-1}  & **110** & **3.3766(0).0** & & & & & & \\ \hline \hline \multicolumn{10}{c}{**Case 3.2: DGs with lagging power factor (PF = 0.866)**} \\ \hline \multirow{10}{*}{SPSA [32]} & 19 & 1.8454/1.0656 & \multirow{10}{*}{1.0678} & \multirow{10}{*}{0.9109} & \multirow{10}{*}{86.37} & \multirow{10}{*}{1.30E-02} \\  & 39 & 2.2060(1).2 & & & & & \\ \cline{1-1}  & 50 & 3.6561(2).111 & & & & & \\ \cline{1-1}  & 74 & 2.2638(1).3071 & 176.969 & 0.00852 & 1.0978 & 0.9109 & 86.37 & 1.30E-02 \\ \cline{1-1}  & 80 & 2.4474(1).4132 & & & & & & \\ \cline{1-1}  & 90 & 2.0355(1).1753 & & & & & & \\ \cline{1-1}  & 108 & 3.4768(2).0076 & & & & & & \\ \hline \multirow{10}{*}{QODELFA} & **18** & **2.4594(1).4201** & \multirow{10}{*}{199} & \multirow{10}{*}{3.3315/1.9237} & \multirow{10}{*}{1.1204} & \multirow{10}{*}{**0.9071**} & \multirow{10}{*}{87.97} & \multirow{10}{*}{**2.21E-02**} \\ \cline{1-1}  & 39 & 2.3315(1).1233 & & & & & \\ \cline{1-1}  & 47 & 2.1185(1).2233 & & & & & \\ \cline{1-1}  & 73 & **2.4698(1).4377** & **156.142** & **0.00670** & **1.1024** & **0.9071** & **87.97** & **2.21E-02** \\ \cline{1-1}  & 80 & **1.8385(1).0616** & & & & & & \\ \cline{1-1}  & **91** & **2.3071(1).3322** & & & & & & \\ \cline{1-1}  & **110** & **3.1879(1).8407** & & & & & & \\ \hline \hline \end{tabular}