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Recent studies have considered thwarting false data injection (FDI) attacksagainst state estimation in power grids by proactively perturbing branchsusceptances. This approach is known as moving target defense (MTD). However,despite of the deployment of MTD, it is still possible for the attacker tolaunch stealthy FDI attacks generated with former branch susceptances. In thispaper, we prove that, an MTD has the capability to thwart all FDI attacksconstructed with former branch susceptances only if (i) the number of branches$l$ in the power system is not less than twice that of the system states $n$(i.e., $l \geq 2n$, where $n + 1$ is the number of buses); (ii) thesusceptances of more than $n$ branches, which cover all buses, are perturbed.Moreover, we prove that the state variable of a bus that is only connected by asingle branch (no matter it is perturbed or not) can always be modified by theattacker. Nevertheless, in order to reduce the attack opportunities ofpotential attackers, we first exploit the impact of the susceptanceperturbation magnitude on the dimension of the \emph{stealthy attack space}, inwhich the attack vector is constructed with former branch susceptances. Then,we propose that, by perturbing an appropriate set of branches, we can minimizethe dimension of the \emph{stealthy attack space} and maximize the number ofcovered buses. Besides, we consider the increasing operation cost caused by theactivation of MTD. Finally, we conduct extensive simulations to illustrate ourfindings with IEEE standard test power systems.

Analysis of Moving Target Defense Against False Data Injection Attacks on Power Grid