# High-impedance Fault Detection in DC Microgrid Lines Using Open-Set Recognition
## 4 Case Study
### Dataset  
The dataset includes various types of events, each represented by time series of current measurements, with a length of 1000 samples. These measurements are taken at the beginning of the line connecting passive load to the bus. Since the sampling frequency used is 10 kHz, the time duration of each time series is 100 ms, which is sufficient to capture the transients of interest. The elementary state of the microgrid is a steady state in which the current is flat with ripples originating from converter operations, and this state is included in the dataset. Load changes, such as the increase/decrease in generation or load, are also included. Finally, the responses of the microgrid to HIFs with different parameters are collected for testing of the method. The first two classes are used for training the classifier. The unknown class, in this case the HIF, is also included to test the OSR performance of the classifiers, but they are not seen by the classifier during the training procedure. Gaussian noise with zero mean and standard deviation of 0.01, is added to better approximate the real-world response. The entire dataset, without noise, can be found in the online repository [56]. The dataset contains 200 waveforms of normal operation and 21 HIF responses. A representative of each event is depicted in Figure 5. If the load is in its stationary state, the current remains flat throughout the entire window. Non-stationary events occur at t = 0. After the load change, the current reaches a new steady state. However, during HIF, even though a new steady state is achieved, the arcing phenomenon is clearly visible in time and frequency domains (Figure 6). The amplitudes that HIF achieves at high frequencies surpass those of stationary state and load change, thereby revealing a distinct difference.  
It is worth noting that standards for arc fault protection in PV systems exist, each defining the arc type, conductor size, fault location, and other requirements [57]. Even though subject of this research is a line that connects a passive load, the authors created dataset according to the IEC 63027 standard while also incorporating additional fault locations and current levels, as suggested in [58]. However, this aspect will be emphasized in future work, where the method will undergo experimental testing.  
During data preprocessing, each event occurrence is shifted in time to better represent the different times the event could appear and to augment the training data. Subsequently, each sequence is transformed from the time domain to the frequency domain using the fast Fourier transform (FFT), and the absolute value is taken. To simplify, the values at negative frequencies are added to their positive counterparts, and the dominant zero-frequency component is removed by zero multiplication. This reduces the input dimensionality to 500. Finally, the dataset is standardized. The two classes representing the stationary state and load change are encoded with numbers 0 and 1, respectively. The dataset is designed to serve as an example of the OSR problem but can also be used to test any HIF detection method.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Rated Value** \\ \hline Bus voltage & 500 V \\ VSC rated power & 15 kW \\ BESS capacity & 12 kWh \\ PV peak power & 6 kW @ 25 \({}^{\circ}\)C \\ Load & 5 kW \\ Line parameters & 20 m\(\Omega\), 62 \(\mu\)H \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters and rated values of bus, battery energy storage system, voltage-source converter, PV system, load and microgrid lines.