## 1 Introduction  
In modern electrical grids with distributed energy resources, such as wind turbine generator farms or inverter-based photovoltaic (IB-PV) array farms, protective relays play a critical role as digital devices capable of identifying circuit breaker statuses [1, 2], classifying fault types [3, 4], identifying fault locations [5, 6, 7], and conveying such information rapidly through light indicators or digital displays. Various types of relay protection logic are in place to execute essential functions [8], such as presenting applications to clear faults [9], localizing electrical faults within the grid or power lines [10], and identifying faulted electrical phases [11]. The initial step for engineers in assessing fault events involves examining the recorded events from relays. Consequently, they are required to assess the electrical fault state of the relay's behavior using recorded events to accurately identify the nature of the disturbances, a notably time-intensive task [12, 13, 14]. As electrical faults typically increase the current magnitude, a simple measure of the surge across each phase is employed to identify faulted phases [15]. In scenariosinvolving microgrids, whether connected to hydroelectric power sources (characterized by high inertia) or not, overcurrent relays can identify the faulted phases [16]. However, this method falls short in microgrids powered by inverter-based renewable energy sources because it is ineffective in distinguishing the nature of the faulted phases [16]. The most frequent electrical fault in an electrical grid is the phase-to-ground fault. This fault can be recognized by monitoring the voltages, which drop at the phases that are faulted [17]. Considering that during a fault state, the current increases while the voltage decreases, the ratio of voltage to current along power lines could serve as a reliable indicator of fault types. Alternatively, a data-driven strategy leveraging phasor measurement unit data has been proposed, which does not need a previous power system knowledge and can identify the most common types of electrical faults [18]. The impedance technique, which assesses both current and voltage magnitudes, offers another alternative for fault type identification [4]. The phase-to-ground fault apparent impedance is based on the distance elements for mho relays [19; 20], and it is represented on a resistance-reactance (R-X) diagram. This R-X plot indicates the impedance variation of the power line over time (apparent impedance) [21]. The protection is engaged when the apparent impedance measurements fall within the predetermined R-X circular plane [7]. The admittance algorithm was developed in [22]; it is a presetting method that requires the impedances of the power line sections to be known for computing the admittance measurements for each phase during the fault states, and the phase and ground boundaries are used to identify the electrical fault types. Machine learning (ML)-aided fault detection algorithms are being developed to meet the increasing data triangulation and demands in power grid systems. These developments are noteworthy given the insufficiency of traditional logic-based protection systems, as faults directly impact system reliability, safety, and cost. These algorithms have the potential to greatly enhance traditional protection and fault detection. For this reason, an artificial neural network-based optimizer has been developed considering the impact of emergencies on smart grids, such as carbon dioxide emissions, curtailments, etc. [23]. The reliability of power systems has been addressed in the literature by introducing a path-based mixed-integer second-order cone scheme [24] and by combining the roulette wheel selection with the Monte Carlo algorithms [25]. Five ML algorithms were investigated in [26] to identify different types of faults and resistances in a DC microgrid. Additionally, using IEEE 123 bus feeder simulated data, an ML-embedded relay was proposed in [27] to classify three fault conditions.