# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Case 12: IEEE 118-Bus System  
A large-scale IEEE 118-bus system [16] is being investigated for additional verification of the proposed AGTLBO algorithm's effectiveness and scalability. The number of control variables increases from 24 to 130 compared to the IEEE 30-bus system. Increasing the number of generators complicates the OPF problem. Active and reactive power requirements for the system are 4242 MW and 1439 MVAR, respectively. To be comparable to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Control Variables** & **AGTLBO** & **Control Variables** & **AGTLBO** \\ \hline \(P_{G1}\) (MW) & 149.2946 & \(T_{24-25}\) (p.u.) & 0.9861 \\ \(P_{G3}\) (MW) & 51.8000 & \(T_{24-26}\) (p.u.) & 1.0194 \\ \(P_{G2}\) (MW) & 100.0000 & \(T_{24-25}\) (p.u.) & 1.0999 \\ \(P_{G6}\) (MW) & 100.0000 & \(T_{7-29}\) (p.u.) & 1.0262 \\ \(P_{G9}\) (MW) & 100.0000 & \(T_{11-41}\) (p.u.) & 1.0999 \\ \(P_{G8}\) (MW) & 378.9279 & \(T_{34-32}\) (p.u.) & 0.9220 \\ \(P_{G12}\) (MW) & 384.0338 & \(T_{15-45}\) (p.u.) & 0.9771 \\ \(V_{G2}\)(p.u.) & 1.0559 & \(T_{10-51}\) (p.u.) & 1.0018 \\ \(V_{G1}\) (p.u.) & 1.0599 & \(T_{14-6}\) (p.u.) & 0.9731 \\ \(V_{G3}\) (p.u.) & 1.0420 & \(T_{13-99}\) (p.u.) & 0.9265 \\ \(V_{G6}\) (p.u.) & 1.0487 & \(T_{11-43}\) (p.u.) & 0.9330 \\ \(V_{G9}\) (p.u.) & 1.0321 & \(T_{39-57}\) (p.u.) & 0.9085 \\ \(V_{G8}\) (p.u.) & 1.0600 & \(T_{40-56}\) (p.u.) & 0.9700 \\ \(V_{G12}\) (p.u.) & 1.0237 & \(T_{9-55}\) (p.u.) & 1.0140 \\ \(T_{4-18}\) (p.u.) & 1.0298 & \(\mathcal{Q}_{\mathrm{C18}}\) (MVAR) & 3.2131 \\ \(T_{4-18}\) (p.u.) & 0.9801 & \(\mathcal{Q}_{\mathrm{C25}}\) (MVAR) & 19.4187 \\ \(T_{21-20}\) (p.u.) & 0.9831 & \(\mathcal{Q}_{\mathrm{C35}}\) (MVAR) & 18.2685 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Optimal decision variables settings for Case 11. Figure 5: The voltage profile of the Cases 9 to 11.  
other state-of-the-art heuristic algorithms described in the literature, the objective function in examples 1 and 9 is to minimize the fuel cost. Table 16 summarizes the best solutions achieved using the suggested AGTLBO algorithm. In Table 17, this result is compared to the results of other algorithms under investigation and some other techniques reported in the literature, including CS-GWO [65]; MSA [16], FPA [16], MFO [16], PSOGSA [44], IABC [66], MCSA [67], MRao-2 and Rao algorithms [68], SSO [32], FHSA [57], ICBO [11], GWO [25], and EWOA [69]. According to this table, the AGTLBO outperforms various optimization techniques used to solve the large-scale OPF. The CS-GWO achieves praiseworthy results while working with such a large-scale system. According to the obtained simulation data, the minimum cost obtained from AGTLBO is 129,543.60 USD/h, which is less than the results of other algorithms. By employing the AGTLBO, the objective function of CS-GWO, MSA, FPA, MFO, PSOGSA, IABC, MCSA, MRao-2, Rao-3, Rao-1, SSO, FHSA, ICBO, GWO, and EWOA are decreased by 0.40 USD/h, 97.10 USD/h, 145.10 USD/h, 164.50 USD/h, 190.0 USD/h, 318.40 USD/h, 330.0 USD/h, 1914.20 USD/h, 1947.1 USD/h, 2249.50 USD/h, 2274.30 USD/h, 2536.8 USD/h, 2594.70 USD/h, 5578.0 USD/h, 10,405.0 USD/h, and 10,632.0 USD/h, respectively, which demonstrates the effectiveness of AGTLBO.