# An Improved Mixed AC/DC Power Flow Algorithm in Hybrid AC/DC Grids with MT-HVDC Systems
## Appendix A
)** & \(\theta\) (\({}^{\circ}\))** & \(P\) & \(Q\) & \(P\) & \(Q\) \\ \hline
1 & 1.047 & \(-\)12.504 & – & –  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Branch**} & \multicolumn{6}{c}{**From Bus Injection**} & \multicolumn{2}{c}{**To Bus Injection**} & \multicolumn{2}{c}{**Power Losses**} \\ \cline{2-9}  & **From** & **To** & \(P\) & \(Q\) & \(P\) & \(Q\) & \(P\) & \(Q\) \\ \hline
1 & 1 & 2 & \(-154.00\) & \(-31.28\) & \(  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Branch**} & \multicolumn{3}{c}{**From Bus**} & \multicolumn{1}{c}{**To Bus**} & \multicolumn{1}{c}{**Power Losses**} \\ \cline{2-5}  & **From** & **To** & \(P\) & \(P\) & \(P\) \\ \hline
1 & 1 & 2 & 5.27 & \(-\)5.26 & 0.01 \\
2 & 1 & 4 & 49.69 & \(-\)49.03 & 0.65 \\
3 & 2 & 3 & 46.03 & \(-\)45.47 & 0.56 \\
4 & 3 & 4 & \(-\)1.65 & 1.65 & 0.00 \\
5 & 5 & 6 & 17.79 & \(-\)17.67 & 0 \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Bus**} & \multicolumn{2}{c}{**Voltage**} & \multicolumn{2}{c}{**Generation**} & \multicolumn{2}{c}{**Load**} \\ \cline{2-7}  & \(|V|\) **(p.u.)** & \(\theta\) (\({}^{\circ}\))** & \(P\) & \(Q\) & \(P\) & \(Q\) \\ \hline  
(-\)3.746 & 540.00 & \(-\)26.63 & – & – \\
38 & 1.027 & 1.612 & 830.00 & 16.42 & – & – \\
39 & 1.030 & \(-\)16.197 & 1000.00 & 126.31 & 1104.00 & 250.00 \\  & **Total:** & & 6303.41 & 1484.80 & 6254.23 & 1387.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 44: Results of Mixed AC/DC PF calculations in Case 7-4. AC bus data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Bus**} & \multicolumn{2}{c}{**Voltage**} & \multicolumn{2}{c}{**Generation**} & \multicolumn{2}{c}{**Load**} \\ \cline{2-7}  & \(|V|\) **(p.u.)** & \(\theta\) (\({}^{\circ}\))** & \(P\) & \(Q\) & \(P\) & \(Q\) \\ \hline
1 & 1.046 & \(-\)5.461 & – & – & 97.60 & 44.20 \\
2 & 1.060 & 1.265 & – & – & – & – \\  
(-\)8.849 & 1000.00 & 115.54 & 1104.00 & 250.00 \\  & **Total:** & & 6321.04 & 1265.84 & 6254.23 & 1387.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 46: Results of Mixed AC/DC PF calculations in Case 7-5. AC bus data. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Branch**} & \multicolumn{3}{c}{**From Bus**} & \multicolumn{1}{c}{**To Bus**} & \multicolumn{1}{c}{**Power Losses**} \\ \cline{2-5}  & **From** & **To** & \(P\) & \(P\) & \(P\) \\ \hline
1 & 1 & 2 & \(-\)2.20 & 2.20 & 0.00 \\
2 & 1 & 4 & 40.95 & \(-\)40.51 & 0.44 \\
3 & 2 & 3 & 42.43 & \(-\)41.96 & 0.47 \\
4 & 3 & 4 & 0.73 & \(-\)0.73 & 0.00 \\
5 & 5 & 6 & 41.86 & \(-\)41.22 & 0.64 \\
6 & 5 & 7 & 41.85 & \(-\)41.21 & 0.64 \\
7 & 5 & 8 & 41.87 & \(-\)41.23 & 0.64 \\
8 & 6 & 7 & \(-\)0.01 & 0.01 & 0.00 \\
9 & 6 & 8 & 0.01 & \(-\)0.01 & 0.00 \\  & & & & **Total:** & 2.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 48: Results of the mixed AC/DC PF calculations in Case 7-5. DC bus data. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Bus DC**} & \multicolumn{2}{c}{**Bus Injection**} & \multicolumn{1}{c}{**Total Loss**} \\ \cline{2-4}  & \(P\) & \(Q\) & \(P\) \\ \hline
1 & \(-\)40.00 & \(-\)20.00 & 1.25 \\
2 & \(-\)46.04 & 74.15 & 1.42 \\
3 & 40.00 & 40.00 & 1.23 \\
4 & 40.00 & 40.00 & 1.24 \\
5 & \(-\)127.33 & \(-\)12.11 & 1.75 \\
6 & 40.00 & 30.00 & 1.22 \\
7 & 40.00 & 20.00 & 1.2 \\
8 & 40.00 & 40.00 & 1.24 \\  & & & **Total:** & 10.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 49: Results of the mixed AC/DC PF calculations in Case 7-5. DC branch data. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Branch**} & \multicolumn{6}{c}{**From Bus Injection**} & \multicolumn{2}{c}{**To Bus Injection**} & \multicolumn{2}{c}{**Power Losses**} \\ \cline{2-9}  & **From** & **To** & \(P\) & \(Q\) & \(P\) & \(Q\) & \(P\) & \(Q\) \\ \hline
1 & 1 & 2 & \(-\)254.22