Many applications of machine learning and optimization operate on sensitive data streams, posing significant privacy risks for individuals whose data appear in the stream. Motivated by an application in energy systems, this paper presents OptStream, a novel algorithm for releasing differentially private data streams under the w-event model of privacy. The procedure ensures privacy while guaranteeing bounded error on the released data stream. OptStream is evaluated on a test case involving the release of a real data stream from the largest European transmission operator. Experimental results show that OptStream may not only improve the accuracy of state-of-the-art methods by at least one order of magnitude but also support accurate load forecasting on the privacy-preserving data.