  In this paper, we present a framework based on differential privacy (DP) for
querying electric power measurements to detect system anomalies or bad data.
Our DP approach conceals consumption and system matrix data, while
simultaneously enabling an untrusted third party to test hypotheses of
anomalies, such as the presence of bad data, by releasing a randomized
sufficient statistic for hypothesis-testing. We consider a measurement model
corrupted by Gaussian noise and a sparse noise vector representing the attack,
and we observe that the optimal test statistic is a chi-square random variable.
To detect possible attacks, we propose a novel DP chi-square noise mechanism
that ensures the test does not reveal private information about power
injections or the system matrix. The proposed framework provides a robust
solution for detecting bad data while preserving the privacy of sensitive power
system data.
