A Smart-Meter (SM) measures and reports the energy consumption of a user at frequent time intervals, revealing critical private information about user's energy consumption behavior. The privacy of a SM system is studied in the presence of an Alternative Energy Source (AES). The privacy-power function is introduced to study the trade-off between the achievable information theoretic privacy and the average power that can be provided by the AES. A single-letter information theoretic expression is provided for the optimal privacy-power function, and its correspondence with the rate-distortion function is established. It is shown that the output alphabet can be restricted to be equal to the input alphabet without loss of optimality, which simplifies the numerical analysis significantly.