  Gaussian random attacks that jointly minimize the amount of information
obtained by the operator from the grid and the probability of attack detection
are presented. The construction of the attack is posed as an optimization
problem with a utility function that captures two effects: firstly, minimizing
the mutual information between the measurements and the state variables;
secondly, minimizing the probability of attack detection via the
Kullback-Leibler divergence between the distribution of the measurements with
an attack and the distribution of the measurements without an attack.
Additionally, a lower bound on the utility function achieved by the attacks
constructed with imperfect knowledge of the second order statistics of the
state variables is obtained. The performance of the attack construction using
the sample covariance matrix of the state variables is numerically evaluated.
The above results are tested in the IEEE 30-Bus test system.
