# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### IEEE 57-Bus Test System
#### 4.3.2 Case 10: Minimizing the Fuel Cost While Improving Voltage Profile  
The key protection and operation indexes are bus voltages. In the OPF dilemma, taking only a cost-based target will result in a viable solution that delivers an unacceptable voltage profile. To account for voltage profile enhancement, the objective function may be thought of as defined in (33). Based on the findings in Table 12, the voltage profile of the 57-bus configuration in this case is clearly superior to that of Case 9. In addition, as compared to originally approved approaches such as MPSO (Modified Particle Swarm Optimization) [16], MFO (Moth-Flame Optimization) [16], MSA (Moth Swarm Algorithm) [16], EADDE (Evolving Ant Direction Differential Evolution) [63], MICA (Modified Imperialist Competitive Algorithm) [45], and MICA-TLA (Modified Imperialist Competitive Algorithm and Teaching Learning Algorithm) [45], the proposed algorithm was able to reach suitable and effective solutions. It can be seen from Table 12 that AGTLBO had a low value in emissions, fuel cost, and power losses, but the MSA algorithm was close. The worst in terms of power loss was the MICA algorithm, and in terms of fuel cost was the EADDE algorithm. The best algorithm in terms of voltage deviation is MICA-TLA (Modified Imperialist Competitive Algorithm and Teaching Learning Algorithm). Table 13 shows the optimal decision variables achieved by various algorithms for further study. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Algorithms**} & \multicolumn{2}{c}{**Fuel Cost**} & \multicolumn{2}{c}{**V.D. (p.u.)**} & \multicolumn{2}{c}{**Power Losses (MW)**} \\ \hline AGTLBO & 1.92 & 41,707.97 & 0.71 & **15.79** \\ TLBO & 2.00 & 41,715.20 & 0.71 & 16.17 \\ MPSO (Modified Particle Swarm Optimization) [16] & 2.01 & 41,721.61 & 0.68 & 16.25 \\ MFO (Moth-Flame Optimization) [16] & 2.01 & 41,718.87 & 0.68 & 16.22 \\ MSA (Moth Swarm Algorithm) [16] & 1.96 & 41,714.98 & 0.68 & 15.92 \\ EADDE (Evolving Ant Direction Differential Evolution) [63] & - & 42,051.44 & 0.79 & 19.32 \\ MICA (Modified Imperialist Competitive Algorithm) [45] & - & 41,974.43 & 0.54 & 20.30 \\ MICA-TLA (Modified Imperialist Competitive Algorithm and Teaching Learning Algorithm) [45] & - & 41,959.18 & **0.54** & 19.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Optimal results by different algorithms for Case 10. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{2}{c}{**Algorithms**} & \multicolumn{2}{c}{**Fuel Cost**} & \multicolumn{2}{c}{**V.D. (p.u.)**} & \multicolumn{2}{c}{**Power Losses (MW)**} \\ \hline AGTLBO & 1.901 & **41,678.310** & 1.618 & 15.064 \\ TLBO & 1.928 & 41,679.891 & 1.651 & 15.153 \\ ICBO (Improved Colliding Bodies Optimization) [11] & - & 41,697.330 & 1.317 & 15.547 \\ MPSO (Modified Particle Swarm Optimization) [16] & 1.944 & 41,678.676 & 1.340 & 15.127 \\ MFO (Multi-Flame Optimization) [16] & 2.004 & 41,686.412 & 1.294 & 15.611 \\ DSA (Differential Search Algorithm) [22] & - & 41,686.820 & 1.083 & - \\ LTLBO (Levy Teaching–Learning-Based Optimization) [28] & - & 41,679.545 & - & 15.159 \\ MICA (Modified Imperialist Competitive Algorithm) [45] & - & 41,683.048 & 1.449 & 15.266 \\ ARCBBO (Adaptive Real Coded Biogeography-Based Optimization) [51] & - & 41,686.000 & - & 15.377 \\ EADDE (Evolving Ant Direction Differential Evolution) [63] & - & 41,713.620 & 1.098 & 16.090 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Optimal results by different algorithms for Case 9.