# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### IEEE 57-Bus Test System
#### 4.3.3 Case 11: Minimizing the Fuel Cost, Emission, Voltage Deviation and Losses  
We found all four objective functions in the ultimate case of power flow optimization, as in [16; 62]:  
\[OF_{9}=\sum_{i=1}^{NG}(\alpha_{i}+b_{i}P_{Gi}+c_{i}P_{Gi}^{2})+OF_{3}+\lambda v* \sum_{i=1}^{NPQ}|V_{i}-1.0|+\lambda p*P_{Loss} \tag{34}\]  
The weight elements are designated as \(\lambda v\) = 1000, \(\lambda p\) = 100 and \(\lambda e\) = 1000 to stabilize the problem dissimilar goals. The findings in Table 14 show that AGTLBO is a suitable and accurate algorithm for solving the OPF problem in power systems in comparison with MOMICA (Multi-Objective Modified Imperialist Competitive Algorithm) [62], MOICA (Multi-Objective Imperialist Competitive Algorithm) [62], MNSGA-II (Modified Non-dominated Sorting GA-II) [62], BB-MOPSO (Bare-Bones Modified Particle Swarm Optimization) [62], and NKEA (Neighborhood Knowledge-based Evolutionary Algorithm) [62]. Table 15 also contains the final solution for this scenario. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**Algorithms**} & \multicolumn{1}{c}{**AUC-TTA (Modified**} & \\
**Control Variables Settings** & **EADDE (Evolving Ant Direction Differential** & **Imperialist Competitive** & **Imperialist Competitive** & **AGTLBO** \\  & **Evolution) [63]** & **Algorithm) [45]** & **Learning Algorithm) [45]** & \\ \hline \(V_{G1}\) (p.u.) & 1.0058 & 0.9923 & 0.9908 & 1.0224 \\ \(V_{G2}\)(p.u.) & 1.0026 & 0.9997 & 1.0020 & 1.0202 \\ \(V_{G3}\) (p.u.) & 1.0108 & 1.0232 & 1.0191 & 1.0140 \\ \(V_{G5}\) (p.u.) & 1.0370 & 0.9998 & 1.0000 & 1.0282 \\ \(V_{G8}\) (p.u.) & 1.0619 & 1.0038 & 1.0024 & 1.0477 \\ \(V_{G9}\) (p.u.) & 1.0248 & 1.0139 & 1.0165 & 1.0152 \\ \(V_{G12}\) (p.u.) & 1.0208 & 1.0399 & 1.0421 & 1.0093 \\ \(T_{4-18}\) (p.u.) & 0.9840 & 1.1000 & 0.9570 & 1.0141 \\ \(T_{4-18}\) (p.u.) & 1.0167 & 0.9270 & 1.0083 & 0.9424 \\ \(T_{2-12}\) (p.u.) & 1.0047 & 0.9754 & 0.9725 & 0.9949 \\ \(T_{2-25}\) (p.u.) & 1.0205 & 1.0355 & 1.0700 & 0.9914 \\ \(T_{24-25}\) (p.u.) & 1.0219 & 1.0857 & 1.0618 & 1.0112 \\ \(T_{24-26}\) (p.u.) & 1.0081 & 0.9958 & 0.9957 & 1.0256 \\ \(T_{27-29}\) (p.u.) & 1.0077 & 0.9955 & 0.9992 & 1.0016 \\ \(T_{34-32}\) (p.u.) & 0.9276 & 0.9121 & 0.9194 & 0.9397 \\ \(T_{11-41}\) (p.u.) & 0.9007 & 0.9000 & 0.9000 & 0.9000 \\ \(T_{15-45}\) (p.u.) & 0.9332 & 0.9073 & 0.9118 & 0.9553 \\ \(T_{14-46}\) (p.u.) & 0.9540 & 0.9924 & 0.9958 & 0.9566 \\ \(T_{10-31}\) (p.u.) & 1.0014 & 1.0223 & 1.0259 & 0.9714 \\ \(T_{13-49}\) (p.u.) & 0.9499 & 0.9000 & 0.9000 & 0.9275 \\ \(T_{11-49}\) (p.u.) & 0.9893 & 0.9912 & 0.9595 & 0.9506 \\ \(T_{40-56}\) (p.u.) & 0.9002 & 0.9648 & 1.0272 & 0.9934 \\ \(T_{90-57}\) (p.u.) & 1.0252 & 0.9000 & 0.9000 & 0.9427 \\ \(T_{95-6}\) (p.u.) & 1.0062 & 1.0162 & 1.0185 & 0.9975 \\ \(Q_{C18}\) (MVAR) & 19.6200 & 4.7000 & 0.0000 & 5.0604 \\ \(Q_{C25}\) (MVAR) & 19.1500 & 19.7700 & 20.7800 & 16.7240 \\ \(Q_{C53}\) (MVAR) & 11.0900 & 29.1100 & 30.0000 & 15.2132 \\ \hline Cost (s/h) & 42,051.44 & **41,974.4346** & 41,959.1774 & **41,707.9679** \\ Emission (t/h) & - & - & - & 1.9194 \\ V.D. (p.u.) & 0.7882 & 0.5416 & 0.539 & 15.7901 \\ Power losses (MW) & 19.32 & 20.303 & 19.909 & 0.7099 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Optimal results by different algorithms for Case 11.