## 6 Numeric Simulation Result
### Load Tracing Test  
Table 3 shows the active and reactive load contribution of the proposed method. In the proposed method, the real power of load bus 4 provided by Wind_3 is over 21%, while 0%  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Branch from–to**} & \multirow{2}{*}{\begin{tabular}{c} **Sending-End** \\ **LoadFlow Solution** \\ **Active/Reactive** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Coal\_1** \\ **Contribution** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Gas\_2 Contribution** \\ **Condition** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Wind\_3 Contribution** \\ **1 + 2 + 3** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Summation** \\ **1 + 2 + 3** \\ \end{tabular} } \\ \hline
1–2 & 0.2868 / \(-\)0.1542 & 0.3604/ 0.0056 & \(-\)0.0539 / \(-\)0.0997 & \(-\)0.0197 / \(-\)0.0601 & 0.2868 / \(-\)0.1542 \\
1–4 & 0.4358/ 0.2012 & 0.3996/ 0.0912 & 0.0154/ 0.0421 & 0.0209/ 0.0679 & 0.4358 / 0.2012 \\
1–5 & 0.3560/ 0.1126 & 0.3186/ 0.0628 & 0.0385/ 0.0576 & \(-\)0.00121 / \(-\)0.0078 & 0.3560 / 0.1126 \\
2–3 & 0.0293 / 0.1227 & 0.0925/ 0.086 & 0.0647/ 0.1112 & \(-\)0.1279 / 0.2425 & 0.0293 / 0.1227 \\
2–4 & 0.3309/ 0.4606 & 0.0339 / \(-\)0.0167 & 0.1733/ 0.2545 & 0.1237/ 0.2227 & 0.3309 / 0.4606 \\
2–5 & 0.1551/ 0.1535 & 0.0658 / \(-\)0.0040 & 0.0788/ 0.1230 & 0.0105/ 0.0346 & 0.1551/ 0.1535 \\
2–6 & 0.2625/ 0.1240 & 0.1790/ 0.0095 & 0.1188/ 0.1728 & \(-\)0.00353 / \(-\)0.0584 & 0.2625 / 0.1240 \\
3–5 & 0.1912/ 0.2318 & \(-\)0.0182/ \(-\)0.0099 & 0.0251/ 0.0328 & 0.1843/ 0.2088 & 0.1912/ 0.2318 \\
3–6 & 0.4377/ 0.6073 & 0.1267/ 0.0390 & 0.0356/ 0.1009 & 0.2754/ 0.4673 & 0.4377 / 0.6073 \\
4–5 & 0.0408 / \(-\)0.0494 & 0.0293 / \(-\)0.0152 & 0.0264/ 0.0053 & \(-\)0.0149/ \(-\)0.0395 & 0.0408 / \(-\)0.0494 \\
5–6 & 0.0161 / \(-\)0.0966 & 0.0437 / \(-\)0.0007 & 0.0021 / \(-\)0.0156 & \(-\)0.0296/ \(-\)0.0803 & 0.0161 / \(-\)0.0966 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Accuracy check of the proposed method for active/reactive flow (MVA base = 100 MVA).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Branch from–to**} & \multirow{2}{*}{
\begin{tabular}{c} **Sending-End** \\ **Load Flow** \\ \end{tabular} } & \multicolumn{2}{c}{**Coal\_1 Contribution**} & \multicolumn{2}{c}{**Gas\_2 Contribution**} & \multicolumn{2}{c}{**Wind\_3 Contribution**} \\ \cline{2-10}  & & **Proposed** & **[Bialek]** & **[Kirschen]** & **Proposed** & **[Bialek]** & **[Kirschen]** & **Proposed** & **[Bialek]** & **[Kirschen]** \\ \hline \hline
**1–2** & 0.2868 & 0.3604 & 0.287 & 0.287 & \(-\)0.0539 & 0 & 0 & \(-\)0.0197 & 0 & 0 \\
**1–4** & 0.4358 & 0.3996 & 0.436 & 0.436 & 0.0154 & 0 & 0 & 0.0209 & 0 & 0 \\
**1–5** & 0.3560 & 0.3186 & 0.356 & 0.356 & 0.0385 & 0 & 0 & \(-\)0.0012 & 0  
wind power was found with the other two methods. That is, the green power from Wind_3 will not reach bus 4 using the other two methods. Similarly, zero reactive contribution can reach bus 6 from Coal_1. The proposed method also indicates that power will flow in every network conductor once it is connected, which is in line with [PERSON]'s law. This is a very different observation from other published methods.