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Recently published papers have proven the effectiveness of Electromagnetic time reversal (EMTR) in locating the position of faults such as phase-to-ground shunt connections in power grids. EMTR directly transposes the idea of focusing energy back to its source introduced in original time-reversal methods. The current interpretation of EMTR, based on metrics measuring energy or peak-amplitude of focusing, is shown to suffer from ambiguities that increase the risk of inaccurate fault location. After pointing out under what conditions time-reversal focusing occurs, an original frequency-domain reformulation of EMTR is introduced, showing that EMTR should more accurately be interpreted as a correlation estimator. New metrics based on this observation are introduced, taking into account the inhomogeneous transmission of electrical energy throughout complex networks, enabling a direct quantitative evaluation of the likelihood of locating a fault. Extensive numerical simulations confirm that the proposed formulation systematically improves the reliability of EMTR location estimates when faults occur in power grids of realistic complexity, highlighting the accrued risk that comes with the use of metrics that measure the scale of time-reversal focusing rather than its quality. Index Terms-Fault location, power grids, time reversal. I. INTRODUCTION T HE proper operation of power grids can be severely disrupted by events such as shunt faults where two or more conductors, subject to different potentials, become electrically connected through a low-impedance path, e.g., because of electrical arcs or phase-to-ground faults. The occurrence of such shunt faults is followed by transient signals that can be detected by a monitoring station, or probe, and subsequently used in order to estimate the fault position. A large number of methods has been introduced in the last decades for fault location in power grids, among which those based on travelling waves are of interested in the context of this paper [1]-[4]. A recent proposal for fault location is Electromagnetic Time Reversal (EMTR) [5], which is inspired by the idea of timereversal (TR) focusing [6], [7]. Its main appeal is its ability to locate faults from the transient signals they generate, as measured from a single probe. Its performance has been shown to depend on what kind of metrics are used, e.g., by monitoring S. He and Y. Xie are with

This paper discusses the mechanisms enabling spatial resolution in fault location methods based on full transient signals, as opposed to those only using their early-time portion. This idea is found in recent travelling-wave methods (TWM) and those based on electromagnetic time reversal (EMTR). Their spatial resolution is discussed in terms of the sensitivity of a system resonances to change in the fault position and their coherence bandwidth. It is proven that using the entire transient signal it is possible to bypass the Fourier transform uncertainty principle, which limits the spatial resolution of time-domain reflectometry and standard early-time TWM. Super-resolved fault location is shown to be possible only for resonating systems, enabling high spatial resolution without relying on wide-band data. A detailed theoretical analysis for laterals and numerical results for networks and a three-phase line show that significant differences can be observed for the spatial resolution associated to each resonance, most often resulting in a loss of spatial resolution. The interaction between separate resonant structures, such as laterals in networks and coupled conductors in three-phase lines are shown to be main cause of resolution loss.

This paper studies how propagation and termination losses affect full transient-based fault location techniques. Their accuracy is discussed in terms of both location uncertainty, caused by a limited spatial resolution, and systematic errors, caused by a bias in the fault-location metrics. This last case is proven to be by far likelier when propagation losses are higher than the dissipation in line termination loads. Two different location metrics are studied, namely correlation and normalized projection, as found in the literature, with correlation proven to be unbiased, since it benefits from two location mechanisms, namely frequency and time-decay matching of a line resonances, as opposed to projection, which only relies on the former mechanism. A numerical analysis of realistic lossy overhead lines confirms theoretical predictions about biased fault location and loss of spatial resolution and the role played by the frequency content of transient data. When applied to the modal analysis of a three-phase transmission line, these results help explaining why faults are located with widely variable accuracy depending on their distance and the bandwidth of the recorded transient, confirming that wide-band transient sampling does not necessarily results in the best location accuracy.

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This paper proves that the accuracy of singleended fault location techniques based on the correlation of fault transients in power lines can be significantly improved by inversefiltering transients first. The reason for this improved accuracy is found in the reduction of the duration of the fault surge signal, thus increasing the sensitivity of fault-location metrics to the fault position. Reported results show that by using the proposed filtering strategy, faster sampling rates systematically and significantly improve the location accuracy, as opposed to the case when no filter is applied, for which virtually no improvement is observed. Because of its higher spatial selectivity, the proposed fault-location technique required the development of a new synchronization method, which ensures a precise transient synchronization without the need for high-speed sampling. It is concluded that by jointly using the proposed transient filtering and synchronization solutions, correlation-based fault location can be significantly improved even when using sampling rates as low as 100 kHz. Extensive numerical simulations for a threephase transmission line confirm an improvement exceeding one order of magnitude in the fault location accuracy, for both lowand high-impedance faults.

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