The reliability and robustness of the power system have gained increasing attention as the trend of including more information infrastructures into the current power grid. The stealthy attack is a kind of cyber attack that is undetectable to any residue-based detection scheme. Our previous work [1] has shown that the existence of such attacks can be eliminated by rotationally switching off one of some preselected links which contain a spanning tree of the network graph. In this paper, we extend our previous work, to consider the case when the attack is only stealthy in some of the topologies. The possible consistent deviations of the estimated states are formulated. We show that as the attack is stealthy in more topologies, the flexibility of such deviations is linearly decreased. Several cases are studied to show this trade-off.