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We consider the problem of detecting a fault on a transmission line from the residual vector of a synchrophasor state estimator (SynSE). For a transmission line under fault, we identify six operating modes depending upon location of the phasor measurement units (PMUs). We show that in five operating modes, the fault is seen in the residual vector while in one mode, the fault will not reflect in the residual vector. The analysis leads us to propose a remote backup protection scheme for supervised zone-3 operation of distance relays. In case of inadequate PMU penetration in the system, the implementation of SynSE can even be restricted to a small subsystem of critical lines.