Low-detectability events such as open-phase conditions (OPCs) and low-current arcs (LCAs) in the onsite power system of nuclear power plants are difficult to detect using conventional protection schemes because the resulting voltage and current distortions are often minimal and transient. These events can persist undetected for long durations, leading to asymmetric loading, winding overheating, and increased risk of cascading equipment failures. This paper proposes a real-time two-stage convolutional neural network (CNN) framework that enables reliable detection of such events using only three-phase voltage and current measurements from a single load bus. In the first stage, a one-dimensional CNN (1D-CNN) monitors power quality disturbances (PQDs) within 5-cycle sliding windows, while a parallel reliability check mechanism periodically generates checkpoints to avoid missed detections. In the second stage, waveform segments corresponding to PQDs or checkpoints are transformed into time-frequency representations using signal-processing techniques such as the discrete wavelet transform (DWT) and empirical mode decomposition (EMD) from the Hilbert-Huang transform (HHT). These processed features are then classified using a two-dimensional CNN (2D-CNN). The proposed framework was validated through PSCAD/EMTDC simulations incorporating normal, OPC, and LCA conditions. The results demonstrate that the framework can accurately distinguish normal and abnormal events, with robust performance even under weak signal conditions. By combining data-driven PQD detection and selective event classification, the proposed method significantly reduces computational burden while maintaining real-time applicability, providing a practical and scalable diagnostic tool for onsite power systems of the nuclear power plant.