This paper considers the problem of real-time detection and classification of power quality disturbances in power delivery systems. We propose a sequential and multivariate disturbance detection method (aiming for quick and accurate detection). Our proposed detector follows a non-parametric and supervised approach, i.e., it learns nominal and anomalous patterns from training data involving clean and disturbance signals. The multivariate nature of the method enables joint processing of data from multiple meters, facilitating quicker detection as a result of the cooperative analysis. We further extend our supervised sequential detection method to a multi-hypothesis setting, which aims to classify the disturbance events as quickly and accurately as possible in a real-time manner. The multi-hypothesis method requires a training dataset per hypothesis, i.e., per each disturbance type as well as the ’no disturbance’ case. The proposed classification method is demonstrated to quickly and accurately detect and classify power disturbances.