# Fault Detection Algorithms in Medium-Voltage Direct-Current (MVDC) Grids
## 3 Study Case and Results
### Link Faults
#### 3.2.5 Differential Algorithm  
As 1 ms communication time delay has been assumed each 200 km, due to the fault distance to the measurement relays, 0.06 ms and 0.25 ms time delays are applied for links L24 and L34, respectively. The selected threshold is 10 A.  
Figure 13a,b show a pole-to-pole fault in the 100% of link L34 and a pole-to-ground fault in the 50% of link L24, with a variation in the fault resistances in both cases. In Table 15, there is very little difference in the detection times for the different fault scenarios. This is because the length of the link is short, 12 km.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{Detection Time at R24 (ms)} & \multicolumn{8}{c}{Detection Time at R42 (ms)} \\ \cline{3-11}
**Fault at Link L24** & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} \\ \cline{3-11}  & **0\%** & **50\%** & **100\%** & **0\%** & **50\%** & **100\%** & **100\%** & **50\%** & **0\%** & **100\%** & **50\%** & **0\%** \\ \hline \multirow{3}{*}{ROCOV} & R = 0.01 \(\Omega\) & 0.010 & 0.040 & 0.070 & 0.010 & 0.040 & 0.070 & 0.070 & 0.035 & 0.010 & 0.070 & 0.040 & 0.010 \\ \cline{2-11}  & R = 2 \(\Omega\) & 0.010 & 0.040 & 0.070 & 0.010 & 0.040 & 0.070 & 0.070 & 0.035 & 0.010 & 0.070 & 0.040 & 0.010 \\ \cline{2-11}  & R = 20 \(\Omega\) & 0.010 & 0.040 & 0.070 & 0.010 & 0.040 & 0.070 & 0.070 & 0.035 & 0.010 & 0.070 & 0.040 & 0.010 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Fault at link L24, detection times at R24 and R42, for the ROCOV algorithm.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{Detection Time at R34 (ms)} & \multicolumn{8}{c}{Detection Time at R43 (ms)} \\ \cline{3-11}
**Fault at Link L34** & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} & \multicolumn{3}{c}{**P2P**} & \multicolumn{3}{c}{**P2G+**} \\ \cline{3-11}  & **0\%** & **50\%** & **100\%** & **0\%** & **50\%** & **100\%** & **100\%** & **50\%** & **0\%** & **100\%** & **50\%** & **0\%** \\ \hline \multirow{3}{*}{ROCOV} & R = 0.01 \(\Omega\) & 0.010 & 0.135 & 0.270 & 0.010 & 0.135 & 0.270 & 0.270 & 0.135 & 0.010 & 0.270 & 0.135 & 0.010 \\ \cline{2-11}  & R = 2 \(\Omega\) & 0.010 & 0.135 & 0.270 & 0.010 & 0.135 & 0.270 & 0.270 & 0.135 & 0.010 & 0.270 & 0.135 & 0.010 \\ \cline{2-11}  & R = 20 \(\Omega\) & 0.010 & 0.135 & 0.270 & 0.010 & 0.135 & 0.270 & 0.270 & 0.135 & 0.010 & 0.270 & 0.135 & 0.010 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Fault at link L34, detection times at R34 and R43, for the ROCOV algorithm.  
Figure 13: Differential currents: (**a**) pole-to-pole fault L34 link 100%, and (**b**) pole-to-ground fault L24 link 50%.  
However, in Table 16, as the length of the link increases, the detection times are higher. It has been proved, as found in the literature [32], that the highest detection times are for faults located in the midpoint of the link. This is because when the fault occurs in the middle of the link, the propagation time of the currents from the midpoint to each end, plus the communication delay, have to be taken into account. In the case of the fault at any end of the link, the propagation is faster because the fault is next to one of the relays, so the detection time will be faster.  
The most notable observation in this scenario is the communication time delay, which depends directly on the distance of the link and increases the detection time. For all the cases, the DC protection requirements are met.