Harmonic Sources’ Location and Emission Estimation in Underdetermined Measurement System

This article proposes a novel method for estimating multiharmonic sources in the underdetermined measurement system. In the proposed methodology, supposing that the number of harmonic measurements (HMs) is less than that of unknown state variables, the HM system can be mathematically described as underdetermined matrix equations, which has infinitely many solutions corresponding to all possibilities of the locations and the current emissions of the actual harmonic sources. Because the harmonic current emissions from nonharmonic source buses are approximately zero, by fitting the harmonic current emission of every possible nonharmonic source bus combinations and selecting the minimum fitting residual of all combination cases, thus, the true number, locations, and current emissions of harmonic sources are determined. Compared with the existing methods, the proposed method has less dependence on the placement of HMs and requires less prior information of harmonic sources. The effectiveness of the proposed method is verified by simulation and field case, with respect to a high correct location rate of more than 90%.