Optimum node selection for protection under power grid state estimation

State estimation of a power grid under undetected power injection attacks is considered. With a known prior probabilistic description of the state variables, the maximum a posteriori probability (MAP) estimator is adopted. Undetected attacks lead to model mismatch, which may greatly degrade the estimation performance. The mean square error (MSE) of the MAP estimate under model mismatch is derived. Considering the case where we are able to protect a limited number of nodes under power injection attacks, we formulate and solve an optimization problem to select which nodes to protect to minimize the MSE degradation that the attacker can provide.