The smart power grid of the future will be heavily dependent on accurate information from the users via smart meter readings. However, from the information on the users power profile much knowledge about the behavior can be acquired, resulting in a breach of privacy. To mask the power profile an energy storage system can be used that obfuscates the smart meter readings. In this paper, we investigate the storage capacity needed if the smart meter is required to report a constant power usage for the user, electricity as well as distributed heating, to the utility. Both single and multiple users per energy storage system are investigated using both derived as well as measured power profiles.