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In this article, we present a data obfuscation technique for smart meter data based on additive correlated noise. This noise is used to mask the data transmitted by different users to a third party, resulting in protection against eavesdroppers, but at the same time enabling the accurate recovery of statistics of the original data for use by the energy supplier. We analyze the proposed technique by studying its obfuscation performance and accuracy of statistics recovered from the masked data as a function of noise correlation with the users' data. Finally, we identify deep learning techniques such as generative adversarial networks for data obfuscation using correlated noise, and show preliminary results to demonstrate their performance in this scenario.