Detection of False Data Injection Attacks in Power Systems with Graph Fourier Transform

With the transition from the hardware dominated analog power system to a digitized cyber-physical "smart grid", protection from attacks from the cyber domain has become increasingly important. In particular, malicious injection of false data has the potential to cause severe consequences. Classical residual-based methods for bad data detection are unable to detect a well designed false data injection (FDI) attack, which is based on detailed knowledge of the system topology. The aim of this paper is to overcome this limitation by making use of the inherent graph structure of the grid. Based on approaches developed for signal processing on graphs and on analysis of the spectrum of the graph, the proposed method enables the detection of previously undetectable FDI attacks. The main requirement for the proposed detector is that the estimated grid state is smooth with respect to the underlying weighted graph determined by the admittance matrix, that is, it has a low variation. Then, detection based on analysis of the high frequency components of the graph Fourier transform may be possible, as a function of the underlying topology of the grid. The feasibility of this idea is demonstrated with a case study on the IEEE 14-bus test grid.