A Sparse Representation Approach to Online Estimation of Power System Distribution Factors

In this paper, we propose a method to compute linear sensitivity distribution factors (DFs) in near real time without relying on a power flow model of the system. Specifically, we compute the injection shift factors (ISFs) of a particular line of interest with respect to active power injections at all buses (all other DFs can be determined from ISFs). The proposed ISF estimation method relies on the solution of an underdetermined system of linear equations that arise from high-frequency synchronized measurements obtained from phasor measurement units. We exploit a sparse representation (i.e., one in which many elements are zero) of the vector of desired ISFs via rearrangement by electrical distance and an appropriately chosen linear transformation, and cast the estimation problem into a sparse vector recovery problem. As we illustrate through case studies, the proposed approach provides accurate DF estimates with fewer sets of synchronized measurements than earlier approaches that rely on the solution of an overdetermined system of equations via the least-squares errors estimation method.