| This thesis describes a fault location method which relies on scattered wide-area synchronized phasor measurements and usage of sparse estimation techniques. The main contribution is the way fault location is reformulated as a sparse estimation problem. Faulted system is modeled by equivalent terminal bus injections which would cause the same changes in bus voltages with the fault current drawn at any point along the faulted line. Once these injections are estimated, the fact that the ratio between equivalent injections at the two terminal buses depends only on the ratio of serial impedances on each side of the fault point can be used to locate the fault. It is shown that this formulation applies to both two terminal lines as well as teed lines regardless of fault type or resistance. Assuming availability of an accurate three-phase network model and a sufficient number of phasor measurements over the entire network, an underdetermined set of linear equations can be formed and then solved for the sparse equivalent bus injections. Then the problem fits naturally into a Least Absolute Shrinkage and Selection Operator (Lasso) formulation and can be solved via the Least Angle Regression (LARS) algorithm. Based on the condition for unique solution for Lasso problem, a scheme for optimal phasor measurement placement is also derived. Furthermore, alternations have been made to the basic implementation of LARS so that the method's reliability, robustness and efficiency is improved.;Using extensive simulations on both unbalanced three phase test case and wide-area network test case, the accuracy and efficiency of the proposed method with its alternations have been verified. |
