# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Cases Definition
#### 4.2.3 Case 3: Minimizing the Emission  
One of the most pressing concerns around fossil-fuel-based power production today is the emissions of different contaminants caused by the combustion of these fuels by generation units. As a result, the sum of pollution is known as a single component (as in the current research) or conjunction with other functions in the latest optimization articles. In this work, the emission function is given as [16]:  
\[OF_{3}=\sum_{i=1}^{NG}F_{Ei}(P_{Gi})=\sum_{i=1}^{NG}\Bigl{(}\alpha_{i}+\beta_{ i}P_{Gi}+\gamma_{i}P_{Gi}^{2}+\xi_{i}\exp(\lambda_{i}P_{Gi})\Bigr{)}+P_{Cost} \tag{29}\]  
where \(F_{Ei}\) signifies the amount of emission caused by the \(i\)th thermal generator. \(\gamma_{i}\), \(\beta_{i}\), \(\xi_{i}\) and \(\lambda_{i}\) are the emission coefficients of the \(i\)th generator, while \(\alpha_{i}\) (ton/h), \(\gamma_{i}\) (ton/h MW\({}^{2}\)), and \(\beta_{i}\) (ton/h MW) are related to SOX. Additionally, \(\lambda_{i}\) (1/MW) and \(\xi_{i}\) (ton/h) are related to NOX.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Algorithm** & **Emission (t/h)** & **Fuel Cost** & **V.D. (p.u.)** & **Power Losses (MW)** \\ \hline AGTLBO & 0.2835 & **646.4511** & 0.9046 & 6.7296 \\ TLBO & 0.2835 & 647.1344 & 0.8927 & 6.8409 \\ LTLBO (Levy Teaching-Learning-Based Optimization) [28] & 0.2835 & 647.4315 & 0.8896 & 6.9347 \\ MDE (Modified Differential Evolution) [49] & - & 647.8460 & - & 7.095 \\ MFO (Moth-Flame Optimization) [16] & 0.28336 & 649.2727 & 0.47024 & 7.2293 \\ IEP (Improved Evolutionary Programming) [50] & - & 649.3120 & - & - \\ MICA-TLA (Modified Imperialist Competitive Algorithm and Teaching Learning Algorithm) [45] & - & 647.1002 & - & 6.8945 \\ FPA (Flower Pollination Algorithm) [16] & 0.28083 & 651.3768 & 0.31259 & 7.2355 \\ SSO (Social Spider Optimization) [37] & - & 663.3518 & - & - \\ GABC (Gbest Guided Artificial Bee Colony Algorithm) [57] & - & 647.0300 & 0.8010 & 6.8160 \\ MSA (Moth Swarm Algorithm) [16] & 0.28352 & 646.8364 & 0.84479 & 6.8001 \\ MPSO-SFLA (Modified Particle Swarm Optimization and Shuffle Frog Leaping Algorithm) [21] & - & 647.5500 & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: Optimal results by different algorithms for Case 2.  
Table 4 compares the findings of AGTLBO, the original TLBO and several state-of-the-art methods such as ARCBBO (Adaptive Real Coded Biogeography-Based Optimization) [51], ABC (Artificial Bee Colony) [12], GBICA (Gaussian Bare-Bones Imperialist Competitive Algorithm) [54], FPA (Flower Pollination Algorithm) [16], AGSO (Adaptive Group Search Optimization) [14], DSA (Differential Search Algorithm) [22], MPO (Moth-Flame Optimization) [16], MSA (Moth Swarm Algorithm) [16], MPSO-SFLA (Modified Shuffle Frog Leaping Algorithm) [53], and MPSO-SFLA (Modified Particle Swarm Optimization and Shuffle Frog Leaping Algorithm) [21]. It can be shown that AGTLBO's solution has a lesser cost function value than those achieved from other approaches. According to the obtained simulation data, the minimum cost obtained from AGTLBO is 0.2048 t/h, which is less comparing to result of other algorithms. By employing the AGTLBO, the objective function of TLBO, ARCBBO, ABC, GBICA, FPA, AGSO, DSA, MFO, MSA, MSFLA, and MPSO-SFLA are decreased by 0.0 t/h, 0.0 t/h, 0.0 t/h, 0.0001 t/h, 0.0004 t/h, 0.0011 t/h, 0.0010 t/h, 0.0001 t/h, 0.0001 t/h, 0.0001 t/h, 0.0001 t/h, 0.0001 t/h, 0.0008 t/h, and 0.0004 t/h, respectively, which demonstrates the effectiveness of AGTLBO.  
There is no difference between the proposed algorithm and the TLBO, ARCBBO, ABC, or MSA algorithms, even though it has the same solution. The solution of 0.2048 is the global optimal solution to this problem, which can be described as the simplest objective function of load distribution. However, this problem involves other complicated functions and constraints to judge the performance of these optimization algorithm.