An alternative method for locating faults in transmission line networks based on time reversal

We present an alternative method based on the time-reversal process to locate faults in transmission line networks. The proposed procedure considers different media for the forward and the backward propagation phases. Specifically, the transverse branch representing the fault is removed from the circuit in the backward propagation since its location represents the solution of the process and, therefore, is not known in advance. The advantage of the proposed method is twofold. First, the proposed backward model requires only one simulation for the time-reversed backward propagation phase, thus reducing significantly the computational burden. Second, we demonstrate that this modified backward propagation medium satisfies a property such that the fault location can be identified by computing, in the frequency domain, the argument of the voltage along the line. The theory is first formulated for the case of a lossless homogeneous single-phase transmission line; then, its applicability is extended to lossy inhomogeneous transmission line networks. A single-phase inhomogeneous transmission line and an inhomogeneous Y-shape network are specifically considered to support this claim. We show that the proposed procedure can provide high fault location accuracy (i.e., in the range of $\pm 1$ m), using only one observation point. Furthermore, we propose a criterion to link the bandwidth of the sampling system to the desired fault location accuracy.