A penalty-based adaptive secure estimation for power systems under false data injection attacks.

This paper proposes a penalty-based adaptive secure estimation method for multi-area power systems under false data injection (FDI) attacks, the adaptive secure estimation method specifically takes the characteristics of FDI attacks into account. Firstly, a new measurement modeling is delicately constructed for subarea of power systems, in which both the state and FDI attack information are well considered. Secondly, for convenient solving of constructed mixed variational inequality (MVI), series virtual nodes are effectively introduced to transfer the multi-area power systems with boundary nodes to a boundary system. Then, a penalty-based distributed estimation method is proposed to estimate the state of multi-area power systems under FDI attacks, where the penalty parameter can be adaptively adjusted based on the dynamic internal error and boundary error. Compared with some existing methods, the efficiency and accuracy of proposed method are improved, and the state and attack signals can be estimated simultaneously. Finally, a case study shows the effectiveness of proposed method.