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.

翻译：本文提出了一种基于差分隐私的框架，用于查询电力测量数据以检测系统异常或不良数据。我们的差分隐私方法在隐藏用电量和系统矩阵数据的同时，通过发布用于假设检验的随机化充分统计量，使不受信任的第三方能够检验异常（如不良数据存在）的假设。我们考虑了一个被高斯噪声和代表攻击的稀疏噪声向量污染的测量模型，并观察到最优检验统计量是卡方随机变量。为检测潜在攻击，我们提出了一种新颖的差分隐私卡方噪声机制，确保检验不会泄露关于功率注入或系统矩阵的隐私信息。所提框架为保护敏感电力系统数据隐私的同时检测不良数据提供了稳健的解决方案。