# Fault Detection Algorithms in Medium-Voltage Direct-Current (MVDC) Grids
## 3 Study Case and Results  
In order to test and perform a comparison of the considered protection algorithms, all of them are implemented in the MVDC grid shown in Figure 2. It is a four-terminal MVDC system, which has been modified from the original HVDC system [25]. It consists of four half-bridge modular multilevel converters (MMCs), which are connected to 33 kV AC grids. The rated powers of the MMCs are 80 MVA for MMC1 and MMC2, 75 MVA for MMC3 and 85 MVA for MMC4. They are connected through five \(\pm\) 27 kV DC links with the following lengths: L12 = 2 km, L14 = 15 km, L13 = 60 km, L24 = 12 km and L34 = 50 km. At the end of each DC link (in the positive and negative poles), 100 mH limiting inductors are placed, connected in series with hybrid circuit breakers. When a fault occurs, the used fully selective fault protection strategy, as in [2], is able to isolate the faulty zone, allowing the normal operation of the rest of the grid. Figure 1: Voltage measurement at both sides of the inductor. In the AC side of MMC2, there is a PEM electrolyzer of 1 MW and 450 Vdc connected through a transformer and a rectifier. The transformer provides galvanic isolation to the electrolyzer. The electrolyzer has been modeled as indicated in [26]. Different fault scenarios have been analyzed, varying the type of fault, pole to pole (P2P) or positive pole to ground (P2G+), the fault location and the fault resistance (0.01 \(\Omega\), 2 \(\Omega\) and 20 \(\Omega\)), in order to determine which algorithm has the best performance, based on typical fault scenarios in MVDC networks, such as those caused by insulation degradation or weather-related events. These values were selected to cover a range of fault conditions that are common in practice. For link faults, the fault location has been varied too. A sampling frequency of 200 kHz has been chosen to enable high-speed fault detection, as it is the integer times the fundamental frequency 50 Hz of the AC system [27]. Different scenarios are going to be analyzed in order to determinate if they meet the DC protection requirements [28], which are the following:  
* Speediness: very fast detection up to a few ms; full operation of the breaker must be in less than 10 ms to prevent damage. * Selectivity: using a high sampling frequency to be able to discriminate external faults. * Sensitivity: to work properly against high-resistance faults. * Robustness: the effectiveness of the algorithm across different fault locations and system conditions. The simulations have been carried out using the PSCAD/EMTDC software, which is well suited for modeling and simulating the dynamic behavior of power systems, including the protection mechanisms in MVDC grids. The reference [29] presents a study conducted using this software and demonstrates how the operational dynamics of a real MVDC network can be accurately replicated. In [30], an event-based protection scheme for MVDC networks is introduced, addressing the shortcomings of single-ended and current differential methods. PSCAD facilitates the analysis of protection strategies, such as overcurrent and under-voltage, for example, and evaluates their performance under specific fault conditions. For this study, several assumptions were made during the simulations:  
* Steady-state conditions: It is assumed that the grid is operating under steady-state conditions prior to the fault occurrence. Any transients prior to fault inception are neglected, focusing only on the fault detection times after the fault is introduced. * Communication delays: In the case of communication-based algorithms (e.g., differential protection), it is assumed that the communication delay is 1 ms per 200 km, as per the typical configurations for long-distance MVDC systems. This assumption was important to take into account the potential impact of the communication delay impact on the fault detection times. Figure 2: MTDC grid with the considered link fault locations.