# An Improved Mixed AC/DC Power Flow Algorithm in Hybrid AC/DC Grids with MT-HVDC Systems
## Appendix A  
Note: \(P\) and \(Q\) are in \(MW\) and \(MVAR\), respectively. Figure 2: Single-line diagram of the modified IEEE 39-bus test system with two four-bus MT-HVDC systems. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Bus**} & \multicolumn{3}{c}{**Voltage**} & \multicolumn{3}{c}{**Generation**} & \multicolumn{3}{c}{**Load**} \\ \cline{2-9}  & **|V| (p.u.)** & \(\mathbf{\theta}\) (\({}^{\circ}\)) & \(\mathbf{P}\) & \(\mathbf{Q}\) & \(\mathbf{P}\) & \(\mathbf{Q}\) \\ \hline
1 & 1.060 & 0.000 & 133.64 & 84.32 & – & – \\
2 & 1.000 & \(-\)2.383 & 40.00 & \(-\)32.84 & 20.00 & 10.00 \\
3 & 1.000 & \(-\)3.895 & – & – & 45.00 & 15.00 \\
4 & 0.996 & \(-\)4.262 & – & – & 40.00 & 5.00 \\
5 & 0.991 & \(-\)4.149 & – & – & 60.00 & 10.00 \\
**Total:** & & & 173.64 & 51.48 & 165.00 & 40.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the mixed AC/DC PF calculations in Case 2. AC bus data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Bust DC**} & \multicolumn{3}{c}{**Bus Injection**} & \multicolumn{3}{c}{**Converter Voltage**} & \multicolumn{3}{c}{**Total Loss**} \\ \cline{2-7}  & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} \\ \hline
1 & \(-\)60.00 & \(-\)40.00 & 0.890 & \(-\)13.017 & 1.37 \\
2 & 20.76 & 7.14 & 1.007 & \(-\)0.655 & 1.14 \\
3 & 35.00 & 5.00 & 0.995 & 1.442 & 1.19 \\  & & & & & **Total:** & 3.70 \\ \hline \hline \multirow{2}{*}{**Bus DC**} & \multicolumn{3}{c}{**Converter Power**} & \multicolumn{1}{c}{**Filter**} & \multicolumn{3}{c}{**Transformer Loss**} & \multicolumn{3}{c}{**Reactor Loss**} & \multicolumn{1}{c}{**Converter Loss**} \\ \cline{2-7}  & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} \\ \hline
1 & \(-\)59.22 & \(-\)32.63 & \(-\)8.12 & 0.08 & 5.83 & 0.01 & 9.66 & 1.29 \\
2 & 20.76 & \(-\)0.65 & \(-\)9.02 & 0.01 & 0.54 & 0.00 & 0.70 & 1.14 \\
3 & 35.02 & \(-\)0.37 & \(-\)8.83 & 0.02 & 1.43 & 0.00 & 2.03 & 1.17 \\  & & & **Total:** & 0.11 & 7.80 & 0.01 & 12.39 & 3.60 \\ \hline \hline \multirow{2}{*}{**Bus DC**} & \multicolumn{3}{c}{**Grid Power**} & \multicolumn{1}{c}{**Trans. Filter Power**} & \multicolumn{3}{c}{**Filter**} & \multicolumn{3}{c}{**Conv. Filter**} & \multicolumn{3}{c}{**Conv. Power**} \\ \cline{2-7}  & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} \\ \hline
1 & \(-\)60.00 & \(-\)40.00 & \(-\)59.92 & \(-\)34.17 & \(-\)8.12 & \(-\)42.29 & \(-\)59.92 & \(-\)32.63 \\
2 & 20.76 & 7.14 & 20.76 & 7.68 & \(-\)9.02 & \(-\)1.35 & 20.76 & \(-\)0.65 \\
3 & 35.00 & 5.00 & 35.02 & 6.43 & \(-\)8.83 & \(-\)2.40 & 35.02 & \(-\)0.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the mixed AC/DC PF calculations in Case 2. Converter station data. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Bust**} & \multicolumn{3}{c}{**Generation**} & \multicolumn{3}{c}{**Load**} \\ \cline{2-5}  & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} & \multicolumn{1}{c}{**P**} & \multicolumn{1}{c}{**Q**} \\ \hline
1 & 133.93 & 84.93 & \(-\) & \(-\) \\
2 & 40.00 & \(-\)90.48 & 20.00 & 10.00 \\
3 & \(-\) & \(-\) & 45.00 & 15.00 \\
4 & \(-\) & \(-\) & 40.00 & 5.00 \\
5 & \(-\) & \(-\) & 60.00 & 10.00 \\
**Total:** & 1