Multiple Bad Data Detectability and Identifiability: A Geometric Approach

A method for detecting and identifying multiple bad data in electric power networks is developed by providing a geometric interpretation of the familiar normalized residuals test for single bad data. This generalized multiple bad data test amounts to determining whether the residual vector lies in a subspace determined by the suspect measurements and whether any portions of that subspace are orthogonal to the residual vector. These tests can be performed efficiently using appropriate projection matrices. Thne notion of critical measurement (removal renders the network unobservable) is extended to critical k-tuples of measurements to determine which bad data hypotheses are actually testable. For example, gross errors in critical measurements are not detectable, and gross errors in a critical pair of measurements are detectable but not identifiable. More generally, k-2 gross errors in a critical k-tuple of measurements are identifiable while k or k-l gross errors are detectable but not identifiable. In essence, the set of testable hypotheses is determined by the geometry of the space spanned by all possible residual vectors. A procedure for selecting and pruning a suspect set of measurements is described. Examples for the IEEE 14 bus network are provided.