# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Cases Definition
#### 4.2.8 Case 8: Minimizing the Fuel Cost, Emission, Voltage Deviation and Losses  
We found all four objective functions in the last case of OPF problem in the 30-bus scheme, similar to MSA [16] and MOMICA [62], which can be considered a systematic, objective function for OPF problems. The weight factors are nominated as in [61] with \(\lambda v\) = 21, \(\lambda p\) = 22 and \(\lambda e\) = 19 for the steadiness of problem different objectives. It can be observed that the proposed algorithm is a suitable and accurate algorithm for the problem of optimum control flow in power systems, based on the results compared with the other algorithms such as MFO (Moth-Flame Optimization) [16], MSA (Moth Swarm Algorithm) [16],  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Emission (t/h)** & **Fuel Cost (USD/h)** & **V.D. (p.u.)** & **Power Losses (MW)** \\ \hline AGTLBO & 0.2290 & **858.9928** & 0.9428 & 4.5300 \\ TLBO & 0.2307 & 859.0191 & 0.9152 & 4.5687 \\ MSA (Moth Swarm Algorithm) [16] & 0.2289 & 859.1915 & 0.92852 & 4.5404 \\ SF-DE (Differential Evolution Integrated Superiority of Feasible Solutions) [61] & 0.2289 & 859.1458 & 0.92731 & **4.5245** \\ \hline \hline \end{tabular}
\end{table}
Table 7: Optimal results by different algorithms for Case 6.  
The bus voltage profile for the best solution obtained in a 30-bus system is shown in Figure 3. It can be seen from the figure that the voltages in the bus are often within the specified range.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Emission (t/h)** & **Fuel Cost (USD/h)** & **V.D. (p.u.)** & **Power Losses (MW)** \\ \hline AGTLBO & 0.3639 & **803.7385** & **0.0947** & 9.8718 \\ TLBO & 0.3565 & 804.2391 & 0.1056 & 9.9565 \\ MPSO (Modified Particle Swarm Optimization) [16] & 0.3636 & 803.9787 & 0.1202 & 9.9242 \\ MPO (Moth-Flame Optimization) [16] & 0.3635 & 803.7911 & 0.10563 & 9.8685 \\ MOICA (Multi-Objective Impartial Competitive Algorithm) [62] & - & 805.0345 & 0.1004 & - \\ NKEA (Neighboroned Knowledge-based Evolutionary Algorithm) [62] & - & 804.9612 & 0.099 & - \\ BB-MOPSO (Barre-Bones Modified Particle Swarm Optimization) [62] & - & 804.9639 & 0.1021 & - \\ MNSG-A-II (Modified Non-dominated Sorting GA-II) [62] & - & 805.0076 & 0.0989 & - \\ MOONICA (Multi-Objective Modified Impartial Competitive Competitive Algorithm) [62] & 0.3552 & 804.9611 & 0.0952 & 9.8212 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Optimal results by different algorithms for Case 7.  
Figure 3: The voltage profile of the Cases 1 to 8.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Emission (t/h)** & **Fuel Cost** (USD/h)** & **V.D. (p.u.)** & **Power Losses (MW)** \\ \hline AGTLBO & 0.2529 & **830.1559** & 0.2975 & **5.5823** \\ TLBO & 0.2538 & 831.3186 & 0.2982 & 5.5847 \\ MPO (Moth-Flame Optimization) [16] & 0.25231 & 830.9135 & 0.33164 & 5.9971 \\ MSA (Moth Swarm Algorithm) [16] & 0.25258 & 830.639 & **0.29385** & 5.6219 \\ MOICA (Multi-Objective Impartial Competitive Algorithm) [62] & 0.267 & 831.2251 & 0.4046 & 6.0223 \\ NKEA (Neighboroned Knowledge-based Evolutionary Algorithm) [62] & 0.2491 & 834.6433 & 0.4448 & 5.8935 \\ BB-MOPSO (Barre-Bones Modified Particle Swarm Optimization) [62] & **0.2479** & 833.0345 & 0.3945 & 5.6504 \\ MNSG-A-II (Modified Non-dominated Sorting GA-II) [62] & 0.2527 & 834.5616 & 0.4308 & 5.6606 \\ MOMICA (Multi-Objective Modified Impartial Competitive Algorithm) [62] & 0.2523 & 830.1884 & 0.2978 & 5.5851 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Optimal results by different algorithms for Case 8.