  This paper presents a model for detecting high-impedance faults (HIFs) using
parameter error modeling and a two-step per-phase weighted least squares state
estimation (SE) process. The proposed scheme leverages the use of phasor
measurement units and synthetic measurements to identify per-phase power flow
and injection measurements which indicate a parameter error through $\chi^2$
Hypothesis Testing applied to the composed measurement error (CME). Although
current and voltage waveforms are commonly analyzed for high-impedance fault
detection, wide-area power flow and injection measurements, which are already
inherent to the SE process, also show promise for real-world high-impedance
fault detection applications. The error distributions after detection share the
measurement function error spread observed in proven parameter error
diagnostics and can be applied to HIF identification. Further, this error
spread related to the HIF will be clearly discerned from measurement error.
Case studies are performed on the 33-Bus Distribution System in Simulink.
