Detection of false data injection in power grid exploiting low rank and sparsity

Smart grids are vulnerable to cyber attacks because of the inevitable coupling between cyber and physical operations. Diagnosing such malicious false data attack has significant importance to ensure reliable operations of power grids. This task is challenging, however, when attackers inject bad data into power systems that are able to circumvent the traditional maximum residual detection method. By noticing the intrinsic low rank structure of temporal erroneous-free measurements of power grid as well as sparse nature of observable malicious attacks, we formulate the false data detection problem as low-rank matrix recovery and completion problem, which is solved by convex optimization that minimizes a combination of the nuclear norm and the l₁ norm. To efficiently solve this mixed-norm optimization, the method of augmented Lagrange multipliers is applied, which offers provable optimality and convergence rate. Numerical simulation results both on the synthetic and real data validate the effectiveness of the proposed mechanism.