# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Case 12: IEEE 118-Bus System
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multicolumn{10}{c}{Actual power output of generators (MW)} \\ \(P_{G1}\)–\(P_{G9}\) & 24.200 & 0.000 & 0.010 & 0.000 & 403.000 & 85.730 & 20.000 & 11.000 & 20.100 \\ \(P_{G10}\)–\(P_{G18}\) & 0.030 & 196.000 & 281.006 & 10.910 & 7.150 & 16.000 & 0.060 & 5.000 & 48.410 \\ \(P_{G19}\)–\(P_{G27}\) & 41.900 & 19.000 & 194.020 & 49.305 & 30.900 & 32.400 & 149.991 & 148.291 & 0.000 \\ \(P_{G28}\)–\(P_{G36}\) & 354.488 & 350.901 & 458.200 & 0.000 & 0.010 & 0.000 & 15.873 & 19.617 & 0.000 \\ \(P_{G3}\)–\(P_{G45}\) & 431.986 & 0.000 & 3.599 & 507.001 & 0.000 & 0.000 & 0.000 & 0.000 & 233.400 \\ \(P_{G46}\)–\(P_{G45}\) & 38.090 & 0.010 & 4.101 & 29.008 & 6.005 & 35.100 & 36.400 & 0.010 & 0.000 \\ \hline \multicolumn{10}{c}{Voltage magnitude of generators (p.u.)} \\ \(V_{G1}\)–\(V_{G9}\) & 1.017 & 1.045 & 1.037 & 1.080 & 1.100 & 1.033 & 1.032 & 1.036 & 1.030 \\ \(V_{G10}\)–\(V_{G18}\) & 1.067 & 1.093 & 1.099 & 1.056 & 1.044 & 1.051 & 1.034 & 1.028 & 1.017 \\ \(P_{G19}\)–\(V_{G27}\) & 1.025 & 1.044 & 1.058 & 1.033 & 1.032 & 1.033 & 1.052 & 1.060 & 1.060 \\ \(P_{G28}\)–\(V_{G36}\) & 1.068 & 1.073 & 1.081 & 1.053 & 1.057 & 1.051 & 1.043 & 1.028 & 1.060 \\ \(V_{G3}\)–\(V_{G45}\) & 1.071 & 1.077 & 1.074 & 1.095 & 1.072 & 1.071 & 1.075 & 1.059 & 1.062 \\ \(V_{G46}\)–\(V_{G54}\) & 1.049 & 1.036 & 1.032 & 1.026 & 1.031 & 1.038 & 1.023 & 1.047 & 1.063 \\ \hline \multicolumn{10}{c}{Transformers’ tap (p.u.)} \\ \(T_{1}\)–\(T_{9}\) & 1.040 & 1.050 & 0.971 & 0.977 & 1.000 & 1.010 & 0.976 & 0.970 & 0.980 \\ \hline \multicolumn{10}{c}{VAR compensating units (MVAR)} \\ \(Q_{C1}\)–\(Q_{G9}\) & 29.900 & 0.000 & 0.000 & 2.000 & 19.669 & 6.000 & 9.000 & 27.991 & 29.900 \\ \(Q_{C10}\)–\(Q_{C14}\) & 29.9995 & 9.0001 & 29.9996 & 1.000 & 11.0050 & \
\begin{tabular}{c} Cost \\ (USD/h) \\ \end{tabular} & 129,543.56 &
\begin{tabular}{c} \(\mathrm{P}_{\mathrm{Loss}}\) \\ (MW) \\ \end{tabular} & 76.2098 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Optimal results for Case 12. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{10}{c}{**Optimizer**} & **Min** & **Mean** & **Max** & **Std.** & **Time (s)** \\ \hline AGTLBO & **129.543.6** & **129.551.9** & **129.562.4** & **8.5** & **737.2** \\ CS-GWO (Crisscross Search Based Grey Wolf Optimizer) [65] & 129,544.0 & 129,558.9 & 129,568.8 & 10.7 & 4252.5 \\ MSA (Moth Swarm Algorithm) [16] & 129,640.7 & - & - & - & - \\ FPA (Flower Pollination Algorithm) [16] & 129,688.7 & - & - & - & - \\ MFO (Moth-frame Optimization) [16] & 129,708.1 & - & - & - & - \\ PSOGSA (Particle Swarm Optimization and Gravitational Search Algorithm) [14] & 129,733.6 & - & - & - & - \\ IABC (Improved Artificial Bee Colony Optimization) [66] & 129,862.0 & 129,895.0 & - & 40.8 & 4157.8 \\ MCSA (Modified Crow Search Optimizer) [67] & 129,873.6 & - & - & - & - \\ MRao-2 [68] & 131,457.8 & - & - & - & 1160.3 \\ Rao-2 [68] & 131,490.7 & - & - & - & 804.6 \\ Rao-3 [68] & 131,793.1 & - & - & - & 806.7 \\ Rao-1 [68] & 131,817.9 & - & - & - & 808.0 \\ SSO (Social Spider Optimization) [68] & 132,080.4 & - & - & - & - \\ FHSA (Fuzzy Harmony Search Algorithm) [001] & 132,138.3 & 132,138.3 & 132,138.3 & 0.0 & - \\ ICRO (Improved Colliding Bodies Optimization) [11] & 135,211.6 & - & - & - & - \\ GWO (Key Wolf Optimizer) [25] & 139,948.1 & 142,989.3 & 145,484.6 & 797.8 & 1766.2 \\ EWOA (Effective Whale Optimization Algorithm) [69] & 140,175.8 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Optimal decision variables settings for Case 12. Based on the results obtained in this study, it is evident from comparing the effects that the CS-GWO and AGTLBO algorithms are very close in their solutions. In addition, the new, improved CS-GWO algorithm is modern and robust, while the investigated system's dimensions are considerable. As a result of this minor difference, the proposed algorithm can be further improved in the future. In contrast, the proposed algorithm has an Std It that is much lower, thereby making it more reliable.