  The technology of differential privacy, adding a noise drawn from the Laplace
distribution, successfully overcomes a difficulty of keeping both the privacy
of individual data and the utility of the statistical result simultaneously.
Therefore, it is prevalent to use a rechargeable battery as the noise for
achieving differential privacy in the application of smart grid. Unfortunately,
to the best of our knowledge, we observe that the existing privacy protection
mechanisms cannot satisfy differential privacy, when considering physical
restrictions of the battery in practice. In this paper, we first classify two
types of challenges caused by two physical restrictions, the maximum
charging/discharging rate and the capacity of battery. We then propose a
stateless privacy protection scheme by exploring a boundary-changeable
distribution for noise, and prove this scheme satisfies differential privacy,
with regard to the first type of challenge. We further explain the difficulty
to achieve differential privacy under the second type of challenge, and
formalize the definition of a relaxed differential privacy. Finally, we present
a stateful privacy protection scheme that satisfies the relaxed differential
privacy. Experimental analysis shows that the maximum privacy leakage of our
privacy protection schemes at each time point stably outperforms that of the
existing work.
