Cost-Benefit Analysis of Moving-Target Defense in Power Grids

We study moving-target defense (MTD) that actively perturbs transmission line reactances to thwart stealthy false data injection (FDI) attacks against state estimation in a power grid. Prior work on this topic lacks an analysis of the relationship between MTD's effectiveness (in detecting FDI attacks) and the associated cost of the perturbations (incurred by the grid operator). To address the issue, we present formal design criteria to select MTD reactance perturbations that are truly effective. Based on a key optimal power flow (OPF) formulation, we find that the effective MTD may incur a non-trivial operational cost. We show that MTD's detection capability and the associated cost depend on the separation between the column spaces of measurement matrices before and after the MTD perturbation. We use the metric of smallest principal angles between the subspaces to characterize the separation. We show that different degrees of the separation provide a spectrum of tradeoffs between the MTD's detection capability and its cost. Furthermore, we present closed-form expressions in the case of a two-bus system to illustrate the tradeoffs. While our analysis is primarily based on a direct current (dc) power flow model, we show that the perturbations designed using this model are also effective in detecting FDI attacks against ac power flows. Similarly, the cost-benefit tradeoff still holds under the ac power model. Extensive simulations, using the MATPOWER simulator and benchmark IEEE bus systems, verify and illustrate the proposed design approach that for the first time addresses both key aspects of cost and effectiveness of the MTD.