Currently, thanks to the rapid development of wireless sensor networks and network traffic monitoring, the data stream is gradually becoming one of the most popular data generating processes. The data stream is different from traditional static data. Cluster analysis is an important technology for data mining, which is why many researchers pay attention to grouping streaming data. In the literature, there are many data stream clustering techniques, unfortunately, very few of them try to solve the problem of clustering data streams coming from multiple sources. In this article, we present an algorithm with a tree structure for grouping data streams (in the form of a time series) that have similar properties and behaviors. We have evaluated our algorithm over real multivariate data streams generated by smart meter sensors—the Irish Commission for Energy Regulation data set. There were several measures used to analyze the various characteristics of a tree-like clustering structure (computer science perspective) and also measures that are important from a business standpoint. The proposed method was able to cluster the flows of data and has identified the customers with similar behavior during the analyzed period.