# Power Flow Calculation Methods for Power Systems with Novel Structure UPFC
## 4 Case Studies  
### WSCC 9-Bus Test System  
In order to compare the characteristics of the three power flow calculation methods (the original method, the simplified method, and the improved method), the Western System Coordinating Council (WSCC) 9-bus test system is modified [27]. As shown in Figure 4, a general structure UPFC is added in the system. The series converter is connected in line 4-5, and controls the power flow of the line. The shunt converter is connected with bus 6, and controls the voltage of bus 6 at 1 per unit (pu). The three power flow calculation methods are adopted, respectively, under an Intel(R) Core(TM) i7-5600U CPU personal laptop. All the calculations are initialized with a flat start, and terminated when the largest voltage magnitude change and the largest voltage phase angle change are both smaller than \(10^{-8}\) or the maximum iteration count (which is 50) is reached. When \(P_{c}+jQ_{c}=-30\) MW-j30 MVAr, the three calculation methods can all converge. The power flow calculation results of the three methods are the same, which are shown in Tables 1 and 2. It is shown that the results of the power flow calculations are reasonable, and the control targets of the UPFC are achieved. The accuracy of the simplified method and the improved method are verified. Furthermore, in order to compare the convergence characteristics of these methods, \(P_{c}\) is changed from \(-210\) MW to \(120\) MW. The iteration numbers required under different \(P_{c}\) are shown in Table 3 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Bus No.** & **Voltage/pu** & **Phase Angle/\({}^{c}\)** \\ \hline
1 & 1.000 & 0.000 \\
2 & 1.000 & 9.285 \\
3 & 1.000 & 4.147 \\
4 & 0.979 & \(-2.428\) \\
5 & 1.001 & \(-4.959\) \\
6 & 1.000 & 1.292 \\
7 & 0.983 & 0.114 \\
8 & 0.994 & 3.403 \\
9 & 0.952 & \(-4.534\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Bus voltage results. Figure 4: The Western System Coordinating Council (WSCC) 9-bus test system with the general structure UPFC. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**From Bus No.** & **To Bus No.** & **P/MW** & **Q/MVAr** \\ \hline
1 & 4 & 72.08 & 37.62 \\
2 & 8 & 163.00 & 17.80 \\
3 & 6 & 85.00 & 2.12 \\
4 & 5 & 28.53 & 14.94 \\
4 & 9 & 43.55 & 18.87 \\
5 & 6 & \(-60.00\) & 0.00 \\
6 & 7 & 21.71 & 4.15 \\
7 & 8 & \(-78.37\) & \(-11.00\) \\
8 & 9 & 84.09 & \(-0.03\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power flow results. and Figure 5. For the improved method, when the value of \(\lambda\) changes from 0 to 1 in steps of 0.05, the minimum number of iterations under different \(\lambda\) and the corresponding value of \(\lambda\) are given in Table 3. Besides, when \(\lambda\) is 0.1, the iteration number of the improved method is also presented in Table 3 and Figure 5.  
According to Table 3 and Figure 5, the following conclusions can be drawn:  
1. The number of iterations required by the original method is always the least. Under different control targets of the UPFC, the iteration numbers of the original method are always kept at about 5, and the change is very small. 2. When the power flow control target is close to the natural power flow (which is about \(-30\) MW), the number of iterations required by the simplified method is about 10, which is slightly more than the number required by the original method. However, when the regulation effect of the UPFC on power flow increases (for example, when \(P_{c}<-100\) MW), the number of iterations required by the simplified method increases significantly. 3. The improved method requires more iterations than the original method to achieve convergence; but compared with the simplified method, when the UPFC power flow regulation effect increases, the improved method has significantly fewer iterations than the simplified method. The number of iterations can be effectively reduced by simply using the improved method with \(\lambda=0.1\).