On Stealthiness and Effectiveness of Moving Target Defense in Smart Grids

Recent studies have proposed moving target defense (MTD) to detect false data injection (FDI) attacks in power grids. To hide the activation of MTD from attackers, a hidden MTD (HMTD) has been proposed, which keeps the system power flow after MTD unchanged. It has been proved that HMTD cannot detect all FDI attacks because of its stealthiness requirements. However, the mathematical mechanism of MTD's stealthiness has yet to be revealed. The maximum detection capability of HMTD is also unclear. To address the abovementioned issues, we first analyze the maximum detection capability of HMTD based on graph theory and propose the topological condition to achieve it. Moreover, we study the essential characteristics of HMTD and find that all HMTD schemes are in a space spanned by branch parameters. We further propose a multistage HMTD (MHMTD) method to select multiple HMTD schemes in this space to maximize the detection capability. Experiments show that the MHMTD can maximize the detection capability of HMTD in all test systems with high stealthy probability.