  Data attacks on meter measurements in the power grid can lead to errors in
state estimation. This paper presents a new data attack model where an
adversary produces changes in state estimation despite failing bad-data
detection checks. The adversary achieves its objective by making the estimator
incorrectly identify correct measurements as bad data. The proposed attack
regime's significance lies in reducing the minimum sizes of successful attacks
to more than half of that of undetectable data attacks. Additionally, the
attack model is able to construct attacks on systems that are resilient to
undetectable attacks. The conditions governing a successful data attack of the
proposed model are presented along with guarantees on its performance. The
complexity of constructing an optimal attack is discussed and two polynomial
time approximate algorithms for attack vector construction are developed. The
performance of the proposed algorithms and efficacy of the hidden attack model
are demonstrated through simulations on IEEE test systems.
