# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Cases Definition
#### 4.2.4 Case 4: Minimizing the Real Power Loss  
One of the most critical priorities of a power grid is to distribute electrical power so that the transmitting network's power losses are negligible. As a result, it has been recognized as a single function in this part, and optimization has been performed. The following is a summary of the objective function [16]:  
\[OF_{4}=P_{Loss}=\sum_{\begin{array}{c}k=1\\ k=(i,j)\end{array}}^{NTL}g_{k}(V_{i}^{2}+V_{j}^{2}-2V_{i}V_{j}\cos\delta_{ij})+P _{Cost} \tag{30}\]  
where \(P_{Loss}\) is the total active power losses of the transmission network. \(g_{k}\) is the conductance of branch \(k\). \(V_{i}\) and \(V_{j}\) are the voltages of \(i\)th and \(j\)th bus, respectively. \(NTL\) represents the number of transmission lines, \(\delta_{ij}\) indicates the phase difference of voltages between bus \(i\) and bus \(j\). Table 5 demonstrates the results of this case for the proposed algorithm in comparison with ABC (Artificial Bee Colony) [12], FPA (Flower Pollination Algorithm) [16], MFO (Moth-Flame Optimization) [16], MSA (Moth Swarm Algorithm) [16], DSA (Differential Search Algorithm) [22], GWO (Grey Wolf Optimizer) [25], Java [32], ARCBBO (Adaptive Real Coded Biogeography-Based Optimization) [51], EEA (Efficient Evolutionary Algorithm) [58], EGA (Enhanced Genetic Algorithm) [58], EGA-DQLF (En  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Emission** & **Fuel Cost** & **V.D. (p,u)** & **Power Losses** \\  & **(t/h)** & **(USD/h)** & & **(MW)** \\ \hline AGTLBO & **0.2048** & 944.3385 & 0,9017 & 3,2233 \\ TLBO & **0.2048** & 944.5446 & 0.7979 & 3,2944 \\ ARCBBO (Adaptive Real Coded Biogeography-Based Optimization) [51] & **0.2048** & 945.1597 & 0.8647 & 3,2624 \\ ABC (Artificial Bee Colony) [12] & **0.2048** & 944.4391 & 0.8463 & 3,2470 \\ GBICA (Gaussian Bare-Bones Imperialist Competitive Algorithm) [54] & 0.2049 & 944.6516 & - & - \\ FPA (Flower Pollination Algorithm) [16] & 0.2052 & 948.9490 & 0.4276 & 4.4920 \\ AGSO (Adaptive Group Search Optimization) [14] & 0.2059 & 953.6290 & - & - \\ DSA (Differential Search Algorithm) [22] & 0.2058 & 944.4086 & - & 3,2437 \\ MPO (Moth-Flame Optimization) [16] & 0.2049 & 945.4553 & 0.7097 & 3,4295 \\ MSA (Moth Swarm Algorithm) [16] & **0.2048** & 944.5003 & 0.8739 & 3,2358 \\ MSFLA (Modified Shuffle Frog Leaping Algorithm) [53] & 0.2056 & - & - & - \\ MPSO-SFLA (Modified Particle Swarm Optimization and Shuffle Frog Leaping Algorithm) [21] & 0.2052 & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimal results by different algorithms for Case 3.  
-hanced Genetic Algorithm to Decoupled Quadratic Load Flow) [59], and ALC-PSO (Particle Swarm Optimization with an Aging Leader and Challenges) [60]. According to the findings, the proposed improved algorithm was able to find a satisfactory solution in the required number of iterations. According to the obtained simulation data, the minimum cost obtained from AGTLBO is 3.0906 MW, which is less comparing to result of other algorithms. By employing the AGTLBO, the objective function of TLBO, ABC, FPA, MFO, MSA, DSA, GWO, Jaya, ARCBBO, EEA, EGA, EGA-DQLF, and ALC-PSO are decreased by 0.0198 MW, 0.0172 MW, 0.4755 MW, 0.0205 MW, 0.0099 MW, 0.0039 MW, 0.3194 MW, 0.0129 MW, 0.0103 MW, 0.1917 MW, 0.1534 MW, 0.1102 MW, and 0.0794 MW, respectively, which demonstrates the effectiveness of AGTLBO.