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Recent studies have considered thwarting false data injection (FDI) attacks against state estimation in power grids by proactively perturbing branch susceptances. This approach is known as moving target defense (MTD). However, despite of the deployment of MTD, it is still possible for the attacker to launch stealthy FDI attacks generated with former branch susceptances. In this paper, we prove that, an MTD has the capability to thwart all FDI attacks constructed 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 ≥ 2n, where n + 1 is the number of buses); (ii) the susceptances 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 a single branch (no matter it is perturbed or not) can always be modified by the attacker. Nevertheless, in order to …