Ill-conditioned Problem of Fault Location Equations for Three-Terminal Lines in Distribution Network by $\mu\mathbf{ MPMU}$

Three terminal line is a typical structure in distribution network, and its fault location has been the focus because of the large scale distributed generation integration. Recently, a parameter-free fault location method based on line voltage was proposed, which overcomes the problem that line parameters are unknown and only two line voltages can be measured in distribution network of China. Although it is more practical than previous methods, the RTDS test shows that the location equations of this method have ill-conditioned problems, that is, tiny measurement error causes too large deviation in the result. To study this problem, the ill-conditioned problem of the location equations is analyzed by condition number at first. Then the condition number of the location equations is calculated by simulation, and it is verified that the location results will produce a large error in the condition of small error of PSCAD simulation data and
$\mu \mathbf{MPMU}$
measurement data from RTDS device.