Data-Driven False Data Injection Attacks Against Power Grids: A Random\n Matrix Approach

We address the problem of constructing false data injection (FDI) attacks\nthat can bypass the bad data detector (BDD) of a power grid. The attacker is\nassumed to have access to only power flow measurement data traces (collected\nover a limited period of time) and no other prior knowledge about the grid.\nExisting related algorithms are formulated under the assumption that the\nattacker has access to measurements collected over a long (asymptotically\ninfinite) time period, which may not be realistic. We show that these\napproaches do not perform well when the attacker has a limited number of data\nsamples only. We design an enhanced algorithm to construct FDI attack vectors\nin the face of limited measurements that can nevertheless bypass the BDD with\nhigh probability. The algorithm design is guided by results from random matrix\ntheory. Furthermore, we characterize an important trade-off between the\nattack's BDD-bypass probability and its sparsity, which affects the spatial\nextent of the attack that must be achieved. Extensive simulations using data\ntraces collected from the MATPOWER simulator and benchmark IEEE bus systems\nvalidate our findings.\n