Distributed algorithms for convexified bad data and topology error detection and identification problems

• Distributed algorithms of bad data and topology error detection and identification are proposed.
• The mechanism relies on the Lagrangian dual decomposition and the chordal graph decomposition.
• The Rank-one approximation is achieved via a nuclear norm minimization.
• The proposed algorithm can handle both L1 norm and L2 norm in different formulations for detection and identification.
• A fully distributed implementation is achieved via an alternative coordinate descent optimization.

Large-scale smart grids call for online algorithms that are able to achieve the most accurate estimates. This paper shows how to achieve both the scalability and near globally optimal results for bad data and topology error detection and identification problems, by conducting fully distributed algorithms over convexified problem formulations. The proposed distributed decomposition is realized by (1) reducing a large network into much smaller network “cliques” which do not need extensive information exchange; (2) performing a Lagrangian dual decomposition in each clique and passing messages between cliques; and (3) conducting alternative coordinate descent optimization for robustness. To reduce the relaxation error in the convexification procedure, a nuclear norm penalty is added to approximate original problems. Finally, we propose a new metric to evaluate detection and identification results, which enables a system operator to characterize confidence for further system operations. We show that the proposed algorithms can be realized on IEEE test systems with improved accuracy in a short time.