# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Discussion on Results
Figure 9: Convergence of algorithms for Case 3. Figure 11: Convergence of algorithms for Case 5. Figure 12: Convergence of algorithms for Case 9. Figure 10: Convergence characteristics for Case 4. In addition, the detailed results for the different test cases on the IEEE-30 bus test system, including the reactive power generation in the value of the generator, the voltage magnitude at all the buses and the transmission power via lines, are shown in Table 19.  
In addition, the detailed results for the different test cases on the IEEE-30 bus test system, including the reactive power generation in the feature \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{2}{c}{**Limits**} & \multirow{2}{*}{**Case 1**} & \multirow{2}{*}{**Case 2**} & \multirow{2}{*}{**Case 3**} & \multirow{2}{*}{**Case 4**} & \multirow{2}{*}{**Case 5**} & \multirow{2}{*}{**Case 6**} & \multirow{2}{*}{**Case 7**} & \multirow{2}{*}{**Case 8**} \\ \cline{2-2} \cline{6-11}  & **Min** & & & & & & & & & & \\ \hline \multicolumn{11}{c}{Reactive power generation in the generators} \\ \hline \(Q_{C1}\) (MVar) & \(-20\) & 200 & 13.0435 & 6.2865 & \(-1.0687\) & \(-1.4183\) & 6.4658 & 2.3913 & 6.1482 & 5.8087 \\ \(Q_{C2}\) (MVar) & \(-20\) & 10 & 9.9850 & 9.9980 & 9.9953 & 9.9870 & 9.9983 & 10.0000 & 9.6782 & 9.9999 \\ \(Q_{C5}\) (MVar) & \(-15\) & 80 & 30.0398 & 28.5295 & 24.1889 & 24.1153 & 29.3115 & 25.8902 & 49.8828 & 26.4629 \\ \(Q_{C8}\) (MVar) & \(-15\) & 60 & 27.9835 & 28.7604 & 29.1378 & 29.2384 & 29.6445 & 29.4048 & 41.5309 & 29.2938 \\ \(Q_{C11}\) (MVar) & \(-10\) & 50 & 27.9447 & 30.9132 & 21.1152 & 19.8527 & 32.3006 & 26.2968 & 30.4476 & 20.7654 \\ \(Q_{C13}\) (MVar) & \(-15\) & 60 & 0.2229 & 4.9166 & 4.1780 & 4.1746 & 8.1319 & 6.0366 & 14.5693 & 8.7635 \\ \hline \multicolumn{11}{c}{Voltage magnitude at all the buses} \\ \hline \(V_{1}\) (p.u.) & 0.95 & 1.1 & 1.0835 & 1.0756 & 1.0628 & 1.0618 & 1.0810 & 1.0697 & 1.0427 & 1.0729 \\ \(V_{2}\) (p.u.) & 0.95 & 1.1 & 1.0604 & 1.0583 & 1.0562 & 1.0571 & 1.0577 & 1.0575 & 1.0230 & 1.0573 \\ \(V_{3}\) (p.u.) & 0.95 & 1.05 & 1.0500 & 1.0500 & 1.0500 & 1.0500 & 1.0500 & 1.0500 & 1.0081 & 1.0500 \\ \(V_{4}\) (p.u.) & 0.95 & 1.05 & 1.0422 & 1.0439 & 1.0468 & 1.0471 & 1.0431 & 1.0460 & 1.0001 & 1.0447 \\ \(V_{5}\) (p.u.) & 0.95 & 1.1 & 1.0334 & 1.0328 & 1.0375 & 1.0382 & 1.0302 & 1.0357 & 1.0151 & 1.0326 \\ \(V_{6}\) (p.u.) & 0.95 & 1.05 & 1.0394 & 1.0415 & 1.0439 & 1.0445 & 1.0391 & 1.0436 & 1.0034 & 1.0411 \\ \(V_{7}\) (p.u.) & 0.95 & 1.05 & 1.0290 & 1.0300 & 1.0332 & 1.0339 & 1.0275 & 1.0324 & 0.9999 & 1.0296 \\ \(V_{8}\) (p.u.) & 0.95 & 1.1 & 1.0383 & 1.0414 & 1.0439 & 1.0445 & 1.0368 & 1.0437 & 1.0065 & 1.0411 \\ \(V_{9}\) (p.u.) & 0.95 & 1.05 & 1.0393 & 1.0355 & 1.0416 & 1.0481 & 1.0357 & 1.0499 & 1.0000 & 1.0000 \\ \(V_{10}\) (p.u.) & 0.95 & 1.05 & 1.0467 & 1.0474 & 1.0453 & 1.0450 & 1.0437 & 1.0478 & 1.0084 & 1.0087 \\ \(V_{11}\) (p.u.) & 0.95 & 1.1 & 1.0923 & 1.0937 & 1.0806 & 1.0846 & 1.0968 & 1.0982 & 1.0595 & 1.0401 \\ \(V_{12}\) (p.u.) & 0.95 & 1.05 & 1.0500 & 1.0500 & 1.0500 & 1.0500 & 1.0500 & 1.0500 & 1.0087 & 1.0119 \\ \(V_{13}\) (p.u.) & 0.95 & 1.1 & 1.0502 & 1.0563 & 1.0542 & 1.0542 & 1.0606 & 1.0576 & 0.9879 & 1.0235 \\ \(V_{14}\) (p.u.) & 0.95 & 1.05 & 1.0401 & 1.0402 & 1.0402 & 1.0401 & 1.0396 & 1.0404 & 0.9996 & 1.0018 \\ \(V_{15}\) (p.u.) & 0.95 & 1.05 & 1.0399 & 1.0400 & 1.0393 & 1.0392 & 1.0389 & 1.0402 & 1.0005 & 1.0018 \\ \(V_{16}\) (p.u.) & 0.95 & 1.05 & 1.0426 & 1.0429 & 1.0415 & 1.0413 & 1.0412 & 1.0431 & 1.0005 & 1.0044 \\ \(V_{17}\) (p.u.) & 0.95 & 1.05 & 1.0433 & 1.0439 & 1.0420 & 1.0418 & 1.0407 & 1.0442 & 1.0008 & 1.0051 \\ \(V_{18}\) (p.u.) & 0.95 & 1.05 & 1.0337 & 1.0334 & 1.0321 & 1.0321 & 1.0319 & 1.0338 & 0.9944 & 0.9953 \\ \hline \hline \end{tabular}
\end{table} 
Table 19: The state variables for the best solutions for different test cases in the IEEE 30-bus system. Figure 13: Convergence of algorithms for Case 12.