## 5 Results and Discussions
### System 2: The IEEE 69-Bus
#### 5.2.3 Case 3: Simultaneous Minimization of APL, VD, and VSI\({}^{-1}\)
Also, the VSI\({}^{-1}\) values obtained from all compared algorithms are approximately the same in this case, which gives the proposed algorithm the advantage of providing better compromised solutions than the methods in [28], while almost the same performance is noted from both QODELFA and SFSA in [32]. Moreover, when the power factor is set to 0.82 lag (Case 3.3), the APL, VD, and VSI\({}^{-1}\) are minimized to 4.297 kW, 0.00010, and 1.0234 p.u., respectively. This proves that when selecting the best value of DGs' power factor, better solutions can be achieved. Besides that, as demonstrated in Table 8 and Figure 13 for all cases (3.1, 3.2, and 3.3), the effectiveness of the proposed algorithm is verified by the small SDs and the fast convergence to the optimal solutions as well. As illustrated in Figure 14, the voltages at all buses of the IEEE 69-bus system for Case 3 are well enhanced, where the most improvement is achieved for Case 3.3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Technique**} & **Optimal** & **Optimal Sizes** & **APL** & **VD** & **VSI\({}^{-1}\)** & **VSI** \\  & **Locations** & **(MW/MVA)** & **(kW)** & **(p.u.)** & **(p.u.)** & **(p.u.)** & **(p.u.)** & **LR\%** & **SD** \\ \hline \hline \multicolumn{10}{c}{**Case 3.1: DGs with unity power factor (PF = 1)**} \\ \hline SIMBO-Q [28] & \begin{tabular}{c} 15 \\ 61 \\ 62 \\ \end{tabular} & \begin{tabular}{c} 0.7722/0.0 \\ 1.3526/0.0 \\ 0.8232/0.0 \\ \end{tabular} & 80.000 & 0.00070 & 1.0235 & 0.9770 & 64.44 & - \\ \hline QOSIMBO-Q [28] & \begin{tabular}{c} 15 \\ 61 \\ 63 \\ \end{tabular} & \begin{tabular}{c} 0.7754/0.0 \\ 1.4385/0.0 \\ 0.7235/0.0 \\ \end{tabular} & 79.700 & 0.00070 & 1.0237 & 0.9770 & 64.58 & - \\ \hline SFSA [32] & \
\begin{tabular}{c} 11 \\ 19 \\ 61 \\ \end{tabular} &
\begin{tabular}{c} 0.5703/0.0 \\ 0.4661/0.0 \\ 1.9674/0.0 \\ \end{tabular} & 72.445 & 0.00143 & 1.0485 & 0.9537 & 67.80 & 3.80E-05 \\ \hline
**QODELFA** & \begin{tabular}{c} **11** \\ **20** \\ **61** \\ \end{tabular} & \begin{tabular}{c} **0.6294/0.0** \\ **0.4386/0.0** \\ **1.9537/0.0** \\ \end{tabular} & **72.295** & **0.00150** & **1.0499** & **0.9525** & **67.87** & **2.12E-05** \\ \hline \hline \multicolumn{10}{c}{**Case 3.2: DGs with lagging power factor (PF = 0.95)**} \\ \hline SIMBO-Q [28] & \begin{tabular}{c} 15 \\ 56 \\ 62 \\ \end{tabular} & \begin{tabular}{c} 0.5380/0.1768 \\ 1.2817/0.4213 \\ 1.5000/0.4930 \\ \end{tabular} & 30.900 & 0.00020 & 1.0233 & 0.9772 & 86.27 & - \\ \hline QOSIMBO-Q [28] & \begin{tabular}{c} 14 \\ 60 \\ 61 \\ \end{tabular} & \begin{tabular}{c} 0.8276/0.2720 \\ 0.5339/0.1755 \\ 1.5000/0.4930 \\ \end{tabular} & 25.700 & 0.00020 & 1.0234 & 0.9771 & 88.58 & - \\ \hline SFSA [32] & \
\begin{tabular}{c} 11 \\ 18 \\ \end{tabular} &
\begin{tabular}{c} 0.5804/0.1908 \\ 0.4344/0.1428 \\ 1.8992/0.6242 \\ \end{tabular} & 20.774 & 0.00016 & 1.0234 & 0.9772 & 90.77 & 1.10E-04 \\ \hline
**QODELFA** & \
\begin{tabular}{c} **11** \\ **20** \\ **61** \\ \end{tabular} &
\begin{tabular}{c} **0.5797/0.1905** \\ **1.9013/0.6249** \\ \end{tabular} & **20.774** & **0.00015** & **1.0235** & **0.9770** & **90.77** & **1.24E-04** \\ \hline \hline \multicolumn{10}{c}{**Case 3.3: DGs with lagging power factor (PF = 0.82)**} \\ \hline
**QODELFA** & \
\begin{tabular}{c} **11** \\ **18** \\ **61** \\ \end{tabular} &
\begin{tabular}{c} **0.5058/0.3531** \\ **0.3859/0.2589** \\ **1.6939/1.1823 \\ \end{tabular} & **4.297** & **0.00010** & **1.0234** & **0.9771** & **98.09** & **2.27E-04** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results for the IEEE 69-bus RDS with simultaneous minimization of OF\({}_{1}\), OF\({}_{2}\) and OF\({}_{3}\).