The integration of renewable energy sources has significantly impacted power system protection schemes, primarily by increasing short-circuit fault currents, which, in turn, raises the possibility of current transformer (CT) saturation, and by introducing bidirectional fault current flow, which interferes with the directional selectivity of relays in detecting downstream faults. This study presents a novel fault direction identification algorithm aimed at immunization against CT saturation effects, especially in medium voltage (MV) distribution grids integrated with renewable sources. To achieve this, two distinct computational frameworks have been developed and proposed. The first framework utilizes the modified least squares (MLSs) method, while the second employs a modified Kalman filter (MKF). Both algorithms calculate the fundamental current phase angle using a sub-cycle window of current samples, ensuring resilience to heavily distorted waveforms caused by CT saturation, even under conditions of deep saturation. The effectiveness of the proposed method is validated through numerous tests conducted on fault currents recorded via simulation scenarios and field measurements, considering various fault inception times, resistances, and locations, together with different neutral grounding arrangements. Comparative assessments of the two developed frameworks across different scenarios indicate that both methods exhibit promising performances, although the least square-based method demonstrates superior efficiency compared to the Kalman filter-based method.