Observer Design for Collocated-Boundary Measurements of Transmission Line Governed by Telegraph Equations with Application to Fault Detection

Abstract

This paper addresses the problem of estimating the distributed state (i.e., current and voltage) along lossy transmission line (TL). The TL is represented by the hyperbolic-type partial differential equation (PDE), also known as Telegraph equations. To this end, we develop an observer that provides online estimates of the variables of interest, based only on collocated measurements at the ingoing boundary. The observer design relies on backstepping method involving input error injections entering the domain and boundary equations. The resulting collocated observer have explicit spatially varying gains. The distributed observer features exponential convergence and, in addition, proves to be useful for fault detection of the most frequent practical scenario, i.e., the single-phase to ground short-circuit. The observer performances are also highlighted by simulation results that illustrate the observer ability to detect and localize the fault precisely.