# Fault Location in Double Circuit Medium Power Distribution Networks Using an Impedance-Based Method
## 5 Conclusions  
Double circuit lines are gaining popularity in distribution networks, mainly due to the increasing loads and the lack of public corridors. Automatic fault location in distribution networks is challenging, and it is even more difficult in double circuits than in single circuit lines. In this paper, a new fault location algorithm for double-circuit distribution networks is presented. In the proposed algorithm, a new quadratic equation is obtained using the power system equations and KVL and KCL. In this method, the voltage and current from the beginning of the feeder are used and the new equation is proved for calculating the equivalent impedance of each section. It is calculated using two over change the Fortescue transform to abs and upside. In the presented technique, the \(\pi\) line model, the lines' capacitors effect, and the mutual effect of the lines on each other are considered. To the best of our knowledge, the improved algorithm is the first of its kind which supports double-circuit distribution networks. In this method, for each section of the distribution feeder, the proposed iterative algorithm is run and the location of the fault is determined. The maximum errors recorded from the faults were in T-offs, especially at the end of the T-offs. In our study, different fault distances, different resistances, and different inception angles were considered. The simulation results show that the maximum recorded error was 0.65%, which confirms a satisfactory performance. For the future, our focus will be on the effect of DG on fault location in double circuit power distribution networks. We will also try to obtain a new and more accurate equation for locating faults in double circuit power distribution networks. Conceptualization, R.D. and S.M.S. ; Methodology, R.D. and S.M.S. ; Software, R.D. and S.M.S. ; Formal Analysis, R.D., S.M.S., H.R.S. and M.T. ; Investigation, S.M.S. ; Resources, R.D., H.R.S. and M.T. ; Writing-Original Draft Preparation, R.D. and S.M.S. ; Writing-Review & Editing, M.T. and H.R.S. ; Visualization, R.D. and S.M.S. ; Supervision, R.D., H.R.S. and M.T. ; Project Administration, R.D. ; Funding Acquisition, R.D., H.R.S, and M.T. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Average Error Percentage (\%)** & **Maximum Error Percentage (\%)** & **Fault Inception Angle Degrees** \\ \hline
0/19 & 0/51 & 0 \\
0/18 & 0/50 & 30 \\
0/19 & 0/49 & 45 \\
0/17 & 0/50 & 90 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Effect of fault inception angle on the proposed method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Fault Type**} \\ \cline{2-5}
**Fault Location** & **Single-Phase** & **Double-Phase** & **Double-Phase** & **Three Phases** \\
**(km)** & **to Ground** & **to Each Other** & **to Ground** & **to Ground** \\ \cline{2-5}  & \multicolumn{4}{c}{**Average Error Percentage**} \\ \hline
6 & 0.0821 & 0.1380 & 0.1105 & 0.0683 \\
12 & 0.1202 & 0.2103 & 0.2055 & 0.1352 \\
22 & 0.9577 & 0.7376 & 0.7352 & 0.5015 \\
30 & 1.0751 & 0.9100 & 0.9098 & 0.6872 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of running the proposed algorithm considering measurement error. **Funding:** This research received no external funding. **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature**  
\(V_{Salc}\) voltage at the beginning of section  
\(I_{Salc}\) current at the beginning of section  
\(zz_{abc}\) matrix of line impedance  
\(Y_{alc}\) admittance matrix or line capacitance  
\(V_{Ralc}\) voltage at the end of line  
\(I_{Ralc}\) current at the end of line  
\(V_{S1,2,0}\) positive, negative Seq. voltage at the beginning of section  
\(I_{S1,2,0}\) positive, negative Seq. injection current at the beginning of section  
\(V_{F1,2,0}\) positive, negative Seq. Fault point voltage at the fault point  
\(I_{F1,2,0}\) positive, negative Seq.