# Fault Detection Algorithms in Medium-Voltage Direct-Current (MVDC) Grids
## 4 Discussion  
Each of the six algorithms used in this analysis--OC, UV, ROCOC, ROCOV, differential, and LIVRD--has unique advantages in terms of fault detection. However, when evaluating their application in real-time fault identification, particularly in crucial renewable energy networks, it is essential to consider their computational demands and feasibility for practical deployment. Overcurrent (OC) protection works by detecting when the current passing through a circuit exceeds a predefined threshold. While effective for protecting against short circuits and overloads, its computational demands are relatively simple, which allows it to be fast and efficient. However, its detection time increases significantly in the case of high-resistance faults. We found the limits of the algorithm (8 \(\Omega\) for pole-to-pole faults and 3 \(\Omega\) for pole-to-ground faults), which may be problematic in time-sensitive protection systems where a swift response is required. Undervoltage (UV) protection reacts when the voltage falls below a set threshold, which can lead to system failure or damage. Although effective at identifying drops in voltage, it becomes less sensitive when the fault resistance is high. Its computational complexity is moderate, but it may not be suitable for cases where faults need to be addressed quickly, as its performance is compromised in scenarios involving higher fault resistance. ROCOC (rate of change of current) protection improves fault detection by considering both the magnitude of the current and its rate of change. This approach enhances the sensitivity to rapid changes in fault conditions, which leads to quicker identification and more immediate action. This makes the ROCOC ideal for real-time applications where it is crucial to isolate faults rapidly. However, its computational complexity is higher than that of OC and UV, requiring more processing power to analyze the changes in current over time. ROCOV (rate of change of voltage) protection detects changes in voltage and reacts to sudden variations in voltage levels. Like the ROCOC, it is designed to detect fast-changing faults, but it is more specialized for voltage fluctuations. The computational complexity of the ROCOV is similar to that of the ROCOC, as both algorithms need to process instantaneous voltage measurements and calculate the rate of voltage change, which can place a higher load on the system, especially in large renewable energy grids. Differential current protection compares the incoming and outgoing current in a system or component, with discrepancies indicating faults. While this method is highly reliable for identifying internal faults, it involves more complex calculations due to the continuous monitoring of multiple current values. Additionally, its performance may be \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 L24**} & \multicolumn{8}{c}{Detection Time at R24 (ms)} & \multicolumn{8}{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\%** & **0\%** \\ \hline \multirow{3}{*}{LIVRD} & R = 0.01 \(\Omega\) & 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 \(\Omega\) & 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 \(\Omega\) & 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 17: Fault at link L24, detection times at R24 and R42, for the LIVRD algorithm.