PMU-Assisted Bad Data Detection in Power Systems

In this paper, we study bad data detection in a power system by strategically placing phasor measurement units (PMUs) at various buses across the power grid. We propose to optimize PMU placements by maximizing the probability of detecting bad data maliciously injected in the power grid. An optimum bad data detector is first developed by following the NeymanPearson criterion. The corresponding detection probability is shown to be an increasing function of the Kullback-Leibler (KL) divergence between the data distributions with and without bad data, respectively. Thus maximizing the detection probability is equivalent to maximizing the KL divergence. Since the bad data used in an attack is unknown, the PMU placement algorithm is developed by following a max-min criterion, that is, maximizing the minimum KL divergence under the assumption of the least detectable attack vector. Simulation results show that using the KL divergence as a design metric results in significant performance gains over existing methods that are developed based on critical measurements.