Extended distributed state estimation: A detection method against tolerable false data injection attacks in smart grids

False data injection (FDI) is considered to be one of the most dangerous cyber-attacks in smart grids, as it may lead to energy theft from end users, false dispatch in the distribution process, and device breakdown during power generation. In this paper, a novel kind of FDI attack, named tolerable false data injection (TFDI), is constructed. Such attacks exploit the traditional detector's tolerance of observation errors to bypass the traditional bad data detection. Then, a method based on extended distributed state estimation (EDSE) is proposed to detect TFDI in smart grids. The smart grid is decomposed into several subsystems, exploiting graph partition algorithms. Each subsystem is extended outward to include the adjacent buses and tie lines, and generate the extended subsystem. The Chi-squares test is applied to detect the false data in each extended subsystem. Through decomposition, the false data stands out distinctively from normal observation errors and the detection sensitivity is increased. Extensive TFDI attack cases are simulated in the Institute of Electrical and Electronics Engineers (IEEE) 14-, 39-, 118- and 300-bus systems. Simulation results show that the detection precision of the EDSE-based method is much higher than that of the traditional method, while the proposed method significantly reduces the associated computational costs.