# Fault Detection Algorithms in Medium-Voltage Direct-Current (MVDC) Grids
## 3 Study Case and Results
### Link Faults
#### 3.2.4 ROCOV Algorithm  
For this study, the threshold value selected for the ROCOV algorithm is set at 200 kV/ms, as in Section 3.1.4, considering absolute values. In the illustrated scenario shown in Figure 12, the rate of change of the voltages is negative due to the polarity change during fault occurrences.  
In Figure 12a, the fault is performed in the middle of link L24. The fault detection times are almost the same, 0.04 ms for R24 and 0.035 ms for R42, as reflected in Table 13. As the fault is in the middle of the link, the fault detection times are higher than if it was at one end of the link.  
In Figure 12b, the fault is simulated in the 0% of link L34, so relay R43 is 50 km away from the fault. This is clearly shown in Table 14, which illustrates how the distance to the fault has a direct effect on the increase in the fault detection time. The highest time is 0.27 ms, when the fault is at the opposite end of the link.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault at Link L24**} & \multicolumn{6}{c}{**Detection Time at R24 (ms)**} & \multicolumn{6}{c}{**Detection Time at R42 (ms)**} \\ \cline{2-13}  & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} \\ \cline{2-13}  & **0\%** & **50\%** & **100\%** & **0\%** & **50\%** & **100\%** & **100\%** & **50\%** & **0\%** & **100\%** & **50\%** & **0\%** \\ \hline \multirow{3}{*}{ROCOC} & R = 0.01 & 0.010 & 0.040 & 0.070 & 0.010 & 0.040 & 0.070 & 0.070 & 0.040 & 0.010 & 0.070 & 0.040 & 0.010 \\ \cline{2-13}  & R = 2 & 0.010 & 0.040 & 0.070 & 0.010 & 0.040 & 0.070 & 0.070 & 0.040 & 0.010 & 0.070 & 0.040 & 0.010 \\ \cline{2-13}  & R = 20 & 0.010 & 0.040 & 0.070 & 0.010 & 0.040 & 0.070 & 0.070 & 0.040 & 0.010 & 0.070 & 0.040 & 0.010 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Fault at link L24, detection times at R24 and R42, for the ROCOC algorithm.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault at Link L34**} & \multicolumn{6}{c}{**Detection Time at R34 (ms)**} & \multicolumn{6}{c}{**Detection Time at R43 (ms)**} \\ \cline{2-13}  & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} \\ \cline{2-13}  & **0\%** & **50\%** & **100\%** & **0\%** & **50\%** & **100\%** & **100\%** & **50\%** & **0\%** & **100\%** & **50\%** & **0\%** \\ \hline \multirow{3}{*}{ROCOC} & R = 0.01 & 0.010 & 0.145 & 0.310 & 0.010 & 0.145 & 0.310 & 0.310 & 0.145 & 0.010 & 0.310 & 0.145 & 0.010 \\ \cline{2-13}  & R = 2 & 0.010 & 0.145 & 0.310 & 0.010 & 0.145 & 0.310 & 0.310 & 0.145 & 0.010 & 0.310 & 0.145 & 0.010 \\ \cline{2-13}  & R = 20 & 0.010 & 0.145 & 0.310 & 0.010 & 0.145 & 0.310 & 0.310 & 0.145 & 0.010 & 0.310 & 0.145 & 0.010 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Fault at link L34, detection times at R34 and R43, for the ROCOC algorithm.  
Figure 12: ROCOV: **(a)** pole-to-pole fault L24 link 50%, and **(b)** pole-to-ground fault L34 link 0%.