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In this paper, we propose an efficient distortion-based privacy-preserving metering scheme that protects an individual customer's privacy and provides the complete power consumption distribution curve of a multitude of customers without privacy invasion. In the proposed scheme, a random noise is purposely introduced to distort customers' power consumption data at the smart meter so that data recovery becomes infeasible. Using the power consumption data and prior knowledge about added random noise, we develop an efficient algorithm for power consumption distribution reconstruction needed for power demand analysis and prediction. As a complete solution, our scheme also supports a privacy-preserving billing service. Using experimental results from real world single household power consumption data set and synthesized data of a large number of households, we demonstrate that the proposed scheme is robust against known attacks. Since it does not demand new facilities on existing smart grids, the proposed scheme offers a practical solution.