Identification of faults using sparse optimization

This paper describes a fault identification method based on the equivalence between the fault current drawn at an arbitrary point along a given line section and a pair of virtual superimposed current injections at the terminal nodes of the same line section. Therefore a fault can be located by estimating the pair of terminal current injections that would cause the recorded changes in bus voltages. One nice feature of this approach is that it is independent of fault type and fault resistance. Assuming the availability of an accurate three-phase network model and a sufficient set of synchronized voltage sensors, the fault identification problem can be formulated as a sparse linear estimation problem with m equations representing the measured buses and n (n > m) unknowns representing the changes in current injections, which are all null except for the ones corresponding to the terminal nodes of the faulted line section. The practical implementation of this approach relies on the efficient solution of an L₁ regularization problem and the proper placement of a sufficient number of measurements satisfying the conditions for a unique solution.