Power quality disturbances (PQDs) have adverse effects on the performance of the electrical equipment and the overall system reliability, and therefore, the detection and diagnosis of PQDs are crucial. Typically, PQDs are classified as batch processing, where a PQD is detected for every 10 fundamental cycles (i.e., 200 ms). Nonetheless, the classification of PQD for every instant gives vital information and can be an online process. This paper presents a deep learning-based model for detecting and classifying 18 PQDs in a noisy environment using 1D Convolutional Neural Networks (CNN) and Temporal Convolutional Networks (TCN). The CNN and TCN facilitate the automatic extraction of meaningful features from the input PQD signals as they evade the typical three-stage classification approach using signal processing techniques. This leads to minimal computational burden and faster classification. Furthermore, the TCN has an additional feature of continuous detection of PQDs at each instant. The performance of the classifiers is measured in terms of classification accuracy and test time. A comparative analysis is performed with a CNN to provide a better insight into the merits of the proposed TCN model. The CNN model outperformed the TCN model by accurately classifying the signal under 20 dB noise. However, the TCN has the advantage of detecting the disturbances at every sample averaged over four samples (i.e., 1.25 ms), whereas the CNN outputs for every 200 ms.