There have been major advancements in recent years to enhance situational awareness in power distribution systems by using advanced sensor technologies. Smart meters and distribution-level phasor measurement units (D-PMUs) are among the most common sensors that have been deployed recently in power distribution networks. Included in the captured time-series of the measurements from these sensors, there are ``events'', that are generally unscheduled, infrequent, and often unknown in their type and nature. Therefore, in practice, we often do not have any prior knowledge about the events until they occur. In this regard, such sensor measurements can be seen as time series that are in form of unlabeled data. Accordingly, in this thesis, we address the analysis of events in the selected types of smart grid time series by using unsupervised machine learning. We start by the analysis of time series in smart meter data to extract events and abnormalities. Our analysis also includes extracting proper choices of features and methods. Next, we move to the analysis of the time series data from D-PMUs that have a much higher resolution and carry more information than the measurements from smart meters as they also measure phase angles. Accordingly, three versions of unsupervised event detection methods are developed, which work based on generative adversarial networks and deep recurrent neural networks. These methods, specifically focused on high frequency and small time series windows of one D-PMU data. Results based on real-world sensor data show that by learning normal behaviour of the system via the proposed methods, we can extract the events more accurately compared to the prevalent methods. Subsequently, a two-step unsupervised clustering method is also proposed, which works based on a linear mixed integer programming formulation to cluster events in time series from D-PMUs. Finally, to address the task of unsupervised event clustering for a situation within a low observable distribution system with only a handful of available D-PMUs, a novel unsupervised graph representation learning model is developed. The developed unsupervised clustering model, extracts the time domain features from the time series in fundamental and harmonics phasor measurements, and then it takes advantage of the system topology by using graph learning models to separate, characterize, and classify the events.