# Power Flow Calculation Methods for Power Systems with Novel Structure UPFC
## 5 Conclusions  
This paper deduces a decoupled UPFC model based on the general structure UPFC. Three power flow calculation methods applicable to both the novel structure UPFC and the conventional structure UPFC are proposed, and the characteristics of these methods are analyzed and validated. The main conclusions are summarized as below:  
1. Using the UPFC model proposed in this paper, the UPFC with different structures can be easily integrated in a power flow calculation.
2. The power flow calculation method (\"original method\"), which strictly corrects the power mismatch equations and the Jacobian matrix, can maintain good convergence characteristics under different control targets; however, because this method requires modifications of the Jacobian matrix, it is more complicated in terms of program implementation.
3. The simplified method, which only modifies the power mismatch equations based on the UPFC equivalent power injections and does not modify the Jacobian matrix, can realize the power flow calculation in existing calculation programs. However, when the UPFC has a great effect on power flow regulation, the iteration number of this method will increase significantly.
4. The improved method, which considers the impact of the Jacobian matrix modifications in the UPFC equivalent power injections, can also realize power flow calculation in existing power flow calculation programs, and this method is superior to the simplified method in terms of convergence characteristics.
5. For the conventional structure UPFC, if the series converter controls the active power and reactive power of the line, and the shunt converter controls the AC bus voltage, only one item is needed to be modified in the Jacobian matrix. The addition of the UPFC has little effect on the Jacobian matrix, thus the convergence characteristics of the three methods are very close.  
The comparison of these methods is summarized in Table 5. The method with more stars (\(\bigstar\)) is better. It should be noted that because all these methods are based on the Newton-Raphson algorithm, they have the same disadvantages, such as the need to update and factorize the Jacobian matrix in iteration. Various novel methodologies are developed to overcome these disadvantages [28; 29]. In future works, the method to integrate the UPFC into these methodologies should be studied.  
**Author Contributions:** Investigation, writing: [PERSON]; Supervision, [PERSON] All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Headquarters Research Projects of State Grid Corporation of China, grant number SGTYHT/15-JS-191.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Programming**} & \multicolumn{2}{c}{**Performance**} \\ \cline{2-5}  & **Jacobian Matrix** & **UPFC Equivalence** & **Convergence Characteristic** & **Computing Time** \\ \hline Original method & \(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\)\(\bigstar\)\(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\)\(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\) \\ Simplified method & \(\bigstar\)\(\bigstar\)\(\bigstar\)\(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\) \\ Improved method & \(\bigstar\)\(\bigstar\)\(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\) & \(\bigstar\)\(\bigstar\)\(\bigstar\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of the proposed methods. “\(\bigstar\)” is used to score methods, the method with more stars (\(\bigstar\)) is better.