  In this paper we develop a set of algorithms that can detect the identities
of malicious data-manipulators in distributed optimization loops for estimating
oscillation modes in large power system models. The estimation is posed in
terms of a consensus problem among multiple local estimators that jointly solve
for the characteristic polynomial of the network model. If any of these local
estimates are compromised by a malicious attacker, resulting in an incorrect
value of the consensus variable, then the entire estimation loop can be
destabilized. We present four iterative algorithms by which this instability
can be quickly detected, and the identities of the compromised estimators can
be revealed. The algorithms are solely based on the computed values of the
estimates, and do not need any information about the model of the power system.
Both large and covert attacks are considered. Results are illustrated using
simulations of a IEEE 68-bus power system model.
