## 3 The Proposed Optimization Hybrid Algorithm
### OPF Solutions IEEE 30-Bus Network [56]
#### 4.1.6 Case 6: Minimization of Fuel Cost, Emissions, Voltage Deviation and Losses  
This study deals with two types of pollutant gases emitted from generating units, SO\({}_{\rm x}\) and NO\({}_{\rm x}\). By assigning appropriate coefficients for their price, attempts to minimize  
Figure 9: Convergence trends in Case 5.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Optimizer** & **Fuel Cost** & **Emission (t/h)** & **Power** & **V.D. (p.u.)** & \(J_{5}\) \\  & **(USD/h)** & & **Losses (MW)** & & \\ \hline MFO [56] & 803.7911 & 0.36355 & 9.8685 & 0.10563 & 814.3541 \\ DA-APSO [83] & 802.63 & - & - & 0.1164 & 814.2700 \\ SSO [81] & 803.73 & 0.365 & 9.841 & 0.1044 & 814.1700 \\ MOMICA [82] & 804.9611 & 0.3552 & 9.8212 & 0.0952 & 814.4811 \\ MPSO [56] & 803.9787 & 0.3636 & 9.9242 & 0.1202 & 815.9987 \\ MNSGA-II [82] & 805.0076 & - & - & 0.0989 & 814.8976 \\ TFWO & 804.2510 & 0.3639 & 10.1563 & 0.0998 & 814.2310 \\ TLBO & 804.7380 & 0.3671 & 9.9995 & 0.1065 & 815.3880 \\ TLTFWO & 803.6829 & 0.3636 & 9.8377 & 0.09450 & 813.1829 \\ \hline \hline \end{tabular}
\end{table}
Table 8: _Cont._the total amount of emission as given in Equation (25). This equations attempts to find minimum values of fuel cost, votage deviation, pollutant level, and power loss at the same time:  
\[J_{6} = \sum_{i=1}^{NG}\alpha_{i}+b_{i}P_{Gi}+c_{i}P_{Gi}^{2}+\phi_{p}\, \sum_{i=1}^{NTL}\sum_{\begin{subarray}{c}j=1\\ j\
eq i\end{subarray}}^{NTL}G_{ij}\,V_{i}^{2}\,+\,B_{ij}V_{j}^{2}\,-2V_{i}\,V_ {j}\cos\delta_{ij}+\phi_{e}\sum_{i=1}^{NL}\left|VL_{i}-1.0\right|\] \[+ \phi_{e}\min\sum_{i=1}^{NG}\Bigl{(}\alpha_{i}+\beta_{i}P_{Gi}+ \gamma_{i}P_{Gi}^{2}+\zeta_{i}\exp(\theta_{i}P_{Gi})\Bigr{)}+\,\lambda_{P} \Bigl{(}\,P_{\text{G1}}-P_{\text{G1}}^{\text{lim}}\,\Bigr{)}^{2}\] \[+ \lambda_{V}\sum_{i=1}^{NL}\Bigl{(}\,VL_{i}-VL_{i}^{\text{lim}} \Bigr{)}^{2}+\,\lambda_{Q}\sum_{i=1}^{NG}\Bigl{(}\,Q_{Gi}-Q_{Gi}^{\text{lim}} \Bigr{)}^{2}+\,\lambda_{S}\sum_{i=1}^{NTL}\Bigl{(}\,S_{i}-S_{i}^{\text{lim}} \Bigr{)}^{2}\]  
The present paper adopts \(\phi_{v}\) = 21, \(\phi_{p}\) = 22 and \(\phi_{e}\) = 19 [56] as the weight coefficients.  
Once again, the TLTFWO algorithm demonstrates its potential to deal with the formulated optimization problem. Table 9 lists the results of different algorithms when applied to the problem.  
As per this table, the minimum value of the objective function is 964.2506, which is smaller than its counterparts. The convergence curve of the total objective function in Case 6 by the TFWO, TLBO, and TLTFWO algorithms is displayed in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & \
\begin{tabular}{c} **Fuel Cost** \\ **(USD/h)** \\ \end{tabular} & **Emission (t/h)** &
\begin{tabular}{c} **Power** \\ **Losses (MW)** \\ \end{tabular} & **V.D. (p.u.)** & \(J_{6}\) \\ \hline SSO [81] & 829.978 & 0.25 & 5.426 & 0.516 & 964.9360 \\ MODA [84] & 828.49 & 0.265 & 5.912 & 0.585 & 975.8740 \\ MNSGA-II [82] & 834.5616 & 0.2527 & 5.6606 & 0.4308 & 972.9429 \\ PSO [81] & 828.2904 & 0.261 & 5.644 & 0.55 & 968.9674 \\ J-PPS3 [85] & 830.3088 & 0.2363 & 5.6377 & 0.2949 & 965.0228 \\ I-NSGA-III [86] & 881.9395 & 0.2209 & 4.7449 & 0.1754 & 994.2078 \\ MFO [56]] & 830.9135 & 0.25231 & 5.5971 & 0.33164 & 965.8080 \\ J-PPS2 [85] & 830.8672 & 0.2357 & 5.6175 & 0.2948 & 965.1201 \\ MOALO [13] & 826.2676 & 0.2730 & 7.2073 & 0.7160 & 1005.0512 \\ MSA [56] & 830.639 & 0.25258 & 5.6219 & 0.29385 & 965.2907 \\ BB-MOPSO [82] & 833.0345 & 0.2479 & 5.6504 & 0.3945 & 970.3379 \\ J-PPS1 [85] & 830.9938 & 0.2355 & 5.6120 & 0.2990 & 965.2159 \\ TFWO & 831.7219 & 0.2540 & 5.6523 & 0.2981 & 967.1586 \\ TLBO & 831.2634 & 0.2602 & 5.8517 & 0.3111 & 971.4777 \\ TLTFWO & 830.2863 & 0.2529 & 5.5868 & 0.2976 & 964.2506 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Optimal results of the present study in Case 6.