# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Discussion on Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{4}{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 \(V_{19}\) (p.u.) & 0.95 & 1.05 & 1.0332 & 1.0326 & 1.0311 & 1.0310 & 1.0309 & 1.0331 & 0.9940 & 0.9947 \\ \(V_{20}\) (p.u.) & 0.95 & 1.05 & 1.0383 & 1.0376 & 1.0359 & 1.0358 & 1.0357 & 1.0381 & 0.9994 & 1.0000 \\ \(V_{21}\) (p.u.) & 0.95 & 1.05 & 1.0381 & 1.0387 & 1.0367 & 1.0364 & 1.0352 & 1.0392 & 0.9997 & 1.0000 \\ \(V_{22}\) (p.u.) & 0.95 & 1.05 & 1.0387 & 1.0392 & 1.0373 & 1.0370 & 1.0358 & 1.0397 & 1.0004 & 1.0007 \\ \(V_{23}\) (p.u.) & 0.95 & 1.05 & 1.0365 & 1.0362 & 1.0355 & 1.0355 & 1.0352 & 1.0370 & 1.0000 & 0.9999 \\ \(V_{24}\) (p.u.) & 0.95 & 1.05 & 1.0320 & 1.0318 & 1.0306 & 1.0305 & 1.0294 & 1.0326 & 0.9945 & 0.9945 \\ \(V_{25}\) (p.u.) & 0.95 & 1.05 & 1.0366 & 1.0351 & 1.0344 & 1.0343 & 1.0330 & 1.0367 & 1.0000 & 1.0000 \\ \(V_{26}\) (p.u.) & 0.95 & 1.05 & 1.0193 & 1.0178 & 1.0170 & 1.0169 & 1.0156 & 1.0193 & 0.9820 & 0.9820 \\ \(V_{27}\) (p.u.) & 0.95 & 1.05 & 1.0479 & 1.0457 & 1.0453 & 1.0453 & 1.0436 & 1.0477 & 1.0122 & 1.0122 \\ \(V_{28}\) (p.u.) & 0.95 & 1.05 & 1.0353 & 1.0377 & 1.0399 & 1.0405 & 1.0348 & 1.0397 & 0.9999 & 1.0369 \\ \(V_{29}\) (p.u.) & 0.95 & 1.05 & 1.0365 & 1.0339 & 1.0333 & 1.0333 & 1.0314 & 1.0358 & 1.0000 & 1.0000 \\ \(V_{30}\) (p.u.) & 0.95 & 1.05 & 1.0220 & 1.0195 & 1.0190 & 1.0190 & 1.0171 & 1.0215 & 0.9851 & 0.9851 \\ \hline \hline \multicolumn{11}{c}{**The transmission power via \(i\)-th line to \(j\)-th (MW)**} \\ \hline \(i\)**-th** & \(j\)**-th** & **min** & **max** & **Case 1** & **Case 2** & **Case 3** & **Case 4** & **Case 5** & **Case 6** & **Case 7** & **Case 8** \\ \hline \(1\) & \(2\) & \(-130\) & \(130\) & \(115.303\) & \(89.8875\) & \(36.7666\) & \(26.3472\) & \(129.998\) & \(64.6271\) & \(114.884\) & \(78.3493\) \\ \(1\) & \(3\) & \(-130\) & \(130\) & \(62.3312\) & \(50.2764\) & \(27.3180\) & \(25.1841\) & \(68.8903\) & \(38.0489\) & \(61.8038\) & \(44.0164\) \\ \(2\) & \(4\) & \(-65\) & \(65\) & \(32.6647\) & \(27.4189\) & \(18.8148\) & \(19.8278\) & \(35.3420\) & \(21.8517\) & \(32.4656\) & \(24.1042\) \\ \(3\) & \(4\) & \(-130\) & \(130\) & \(58.1391\) & \(46.7745\) & \(24.6186\) & \(22.5298\) & \(64.6006\) & \(35.0427\) & \(57.4753\) & \(40.7758\) \\ \(2\) & \(5\) & \(-130\) & \(130\) & \(63.1242\) & \(57.9938\) & \(38.9298\) & \(39.2685\) & \(66.4483\) & \(47.1054\) & \(64.3868\) & \(52.0719\) \\ \(2\) & \(6\) & \(-65\) & \(65\) & \(44.2342\) & \(36.4673\) & \(24.7146\) & \(25.4699\) & \(48.7312\) & \(28.8743\) & \(43.7856\) & \(31.9784\) \\ \(4\) & \(6\) & \(-90\) & \(90\) & \(51.4320\) & \(40.3901\) & \(26.4317\) & \(25.3668\) & \(59.1888\) & \(31.3824\) & \(54.3112\) & \(35.0825\) \\ \(5\) & \(7\) & \(-70\) & \(70\) & \(14.5951\) & \(15.9078\) & \(8.9353\) & \(6.8790\) & \(13.3175\) & \(12.4278\) & \(20.7297\) & \(14.2529\) \\ \(6\) & \(7\) & \(-130\) & \(130\) & \(34.6959\) & \(36.8083\) & \(29.2347\) & \(28.9089\) & \(34.4332\) & \(33.2495\) & \(34.5826\) & \(35.1701\) \\ \(6\) & \(8\) & \(-32\) & \(32\) & \(11.1907\) & \(1.0398\) & \(1.2698\) & \(1.2257\) & \(20.9236\) & \(1.0144\) & \(14.8467\) & \(0.9188\) \\ \(6\) & \(9\) & \(-65\) & \(65\) & \(37.3850\) & \(41.5175\) & \(21.8485\) & \(14.3270\) & \(41.8665\) & \(21.5371\) & \(39.6149\) & \(26.9585\) \\ \(6\) & \(10\) & \(-32\) & \(32\) & \(21.5345\) & \(26.5973\) & \(15.3814\) & \(9.5859\) & \(21.0635\) & \(13.9521\) & \(26.1334\) & \(19.9261\) \\ \(9\) & \(11\) & \(-65\) & \(65\) & \(30.3903\) & \(35.9626\) & \(36.6858\) & \(35.9739\) & \(33.8135\) & \(39.