Time reversal has received increased attention during the past three decades as a method for source location/identification and has been successfully applied to various areas of engineering [e.g., Blomgren et al. (2002), Fink et al. (2003), Lerosey et al. (2007), Lemoult et al. (2011), Bacot et al. (2016), Rachidi et al. (2017)]. One of the areas in which the electromagnetic time reversal (EMTR) technique is applied is the problem of fault location in electrical power systems Manesh et al. (2012).

Electricity transmission and distribution networks are prone to various types of faults (e.g., single/three phase-to-ground faults) due to various potential causes, such as weather-related events (e.g., lightning, storms, freezing rain) or technical failures (e.g., insulation deterioration or breakdown). In this regard, reliable and efficient fault location techniques are of vital importance in electrical power systems to ensure the security and quality of electricity supply Saha et al. (2009), IEEE Std C37.114-2004 (2015), Furse et al. (2021). Within this context, various solutions have been proposed for the fault location problem since the 1950s Stringfield et al. (1957). They can be clustered in two main categories of fault location methods: 1) impedance- (or phasor-) based methods [e.g., Izykowski et al. (2011), Majidi and Etezadi-Amoli (2018)] and 2) traveling wave- (or high-frequency component-) based methods [e.g., Lopes et al. (2019), Naidu et al. (2019), de Magalhaes Junior and Lopes (2022)].

In 2012, the time-reversal technique was for the first time applied to address the fault location problem Manesh et al. (2012). Thanks to significant worldwide studies since then, the EMTR-based fault location method is nowadays considered as a reliable method that belongs to the category of traveling wave-based methods. By virtue of the inherent focusing property of the time-reversed back-injected waves (e.g., those associated with the fault-originated transients) onto the original source, the EMTR method has been shown to possess a number of advantages over classical traveling wave-based methods, such as its straightforward applicability to inhomogeneous media (i.e., mixed overhead and coaxial power cable lines), the potential use of a single observation (measurement) point, and no need for dedicated processing applied to fault-originated transients for wavefront arrival time detection.

The present paper covers both theoretical investigations and experimental activities. We first present for the novice reader the basics of the theoretical foundations of time reversal (Section 2). The application of EMTR to the fault location problem in power networks is discussed in Section 3. In particular, the specificities of the EMTR method compared to other traveling wave-based methods are discussed. Also, two subcategories of EMTR-based fault location methods (considering matched and mismatched media, respectively) are introduced. In Section 4 and Section 5, the two subcategories of EMTR methods are respectively reviewed, presenting their general features and discussing the metrics used to locate the focal point of the backward-propagated waves (which corresponds to the fault location). Experimental studies of the EMTR method using realistic-scale power networks are summarized in Section 6. Finally, Section 7 presents a discussion about the outstanding challenges of EMTR when applied to the fault location problem, mainly including: 1) the effect of imperfect knowledge of power network parameters (e.g., soil electrical parameters), 2) the effect of losses, 3) the need for appropriate signal processing to quantify the refocusing of the backward-propagating wave to the fault location, and 4) the need of further theoretical investigation for the EMTR method in mismatched media.

The concept of time reversal can be interpreted from different perspectives. It involves a fundamental operation consisting of reversing in time a given time-dependent physical quantity s(t), namely s t ⟼ T R s − t . (1) s(t) is a real and causal function with compact support in the sense that it is defined on a finite time interval 0 , T s such that s t = 0 , t < 0 , a n d t > T s . (2)

The time-domain operation of reversing s(t) corresponds to the complex conjugate operation in the frequency domain (denoted by the symbol *): S j ω ⟼ T R S j ω * , (3) with S (jω) being the Fourier transform of s(t).

Note that, to ensure causality, the time-reversal operation in the time domain is more practically carried out through s t ⟼ T R s T − t , (4) where T is the temporal length of the time window over which s(t) is observed, satisfying T⩾T _s .

The spread of time reversal in contemporary scientific and engineering communities largely stems from the comprehensive theoretical and experimental study on the time-reversal inherent focusing property in the early 1990s Cassereau and Fink (1992), Fink (1992), Fink (1993), Wu et al. (1992). Specifically, for waves (e.g., acoustic or electromagnetic) generated by a point source and possibly reflected, scattered, and distorted in given propagative media, the focusing property states that time-reversed measured waves, being back injected into the same medium where the forward propagation occurred, would retrace the originally followed paths and eventually converge in synchrony on the initial source location as if the time goes backward.

A time-reversal cavity is proposed as a two-step procedure to achieve the time reversal focusing property Fink (1992). As illustrated in Figure 1A, a closed surface in three dimensions is assumed to enclose a point-like source (red circle) and its surrounding medium, which can be inhomogeneous (the green region illustrates the presence of scatterers) ¹ . In the forward-propagation stage (also named the recording step or direct time ² ), the source-generated and distorted (by the surrounding inhomogeneous medium) waves are recorded by an infinite number of elementary transducers located on the imaginary surface of the cavity. In the backward-propagation stage (also named the reconstructing step or reversed time, see Figure 1B), those recorded waves are time reversed and back injected to propagate inward from the respective elementary transducers at the cavity surface. The resulting wave is a time-reversed copy of the original one and would finally converge back to the source location.

It can be noticed that a time-reversal cavity is a conceptual description that appears quite challenging to be implemented in reality since it theoretically requires an infinite number of measurements over the surface of the cavity. In practice, a time-reversal cavity is alternatively realized by means of a one/two-dimensional transducer array constituting the so-called time-reversal mirror Fink (1992), Fink (1993). As a consequence, a time-reversal mirror makes use of a limited number of transducers. It is shown that proper spatial distribution of the transducers on a limited angular aperture to sample sufficient wavefronts renders the focusing property achievable in practice Wu et al. (1992).

After the foundation studies in the field of acoustics, time reversal was later introduced into the field of electromagnetic waves under the general denomination of electromagnetic time reversal (EMTR) Lerosey et al. (2004), Carminati et al. (2007), de Rosny et al. (2010) and has been regarded as a promising technique in localizing electromagnetic transient sources Rachidi et al. (2017). Representative applications of EMTR include medical imaging [e.g., Kosmas and Rappaport (2005)], target detection [e.g., Mukherjee et al. (2017)], lightning discharge localization [e.g., Lugrin et al. (2014), Mostajabi et al. (2019)], soft fault location in wires [e.g., Kafal et al. (2016)], localization of electromagnetic interference sources [e.g., Karami et al. (2021a), Karami et al. (2021b), Li et al. (2021)], localization of partial discharges [e.g., Azadifar et al. (2020), Ragusa et al. (2022)], and locating faults in electrical power systems [e.g., Manesh et al. (2012)].

The EMTR-based fault location method is carried out in two steps corresponding to the forward- and backward-propagation stages, respectively. The procedure is described in detail below.

1) Forward-propagation stage: a fault occurrence generates traveling waves that propagate from the fault location towards power network terminals. The fault-originated transients are measured at a number of observation points situated at the terminals (i.e., sensors are generally distributed at the substations located at the power network terminals) or, in case, at other user-defined points.

It is evident that the EMTR-based fault location method is, in essence, dependent on post-fault traveling wave processes. Consequently, it keeps the advantages of traveling wave-based fault location methods, such as insensitivity to fault characteristics (i.e., fault type and impedance) and robustness against power-frequency boundary conditions (e.g., current transformers saturation and power-frequency injections from dispersed energy resources). Meanwhile, the EMTR method benefits from the inherent focusing property of time reversal, thus bringing additional advantages that are briefly summarized and explained in what follows.

Firstly, the EMTR method can be applied using a single observation point even with the presence of inhomogeneity and multiple branches in power networks. Draeger and Fink (1997) demonstrated the possibility of achieving the time-reversal focusing property using a single-channel (end) measurement in a closed reflective cavity. A power network is conventionally connected at its terminals to electrical equipment (e.g., power transformers) featuring high input impedance Greenwood (1991). Therefore, those terminals behave approximately as open circuits for the incident traveling waves initiated by a fault, resulting in the boundary conditions being quasi-fully reflective. Moreover, the more complex the propagative medium, such as a high degree of inhomogeneity or multiple scattering, the better the time-reversal focusing quality (e.g., a higher resolution) Derode et al. (1995), Derode et al. (2003). It is worth mentioning that power networks consisting of multiple conductors (e.g., three-phase systems) are generally configured in a topology involving multiple laterals and junctions. Moreover, power networks are increasingly constructed in a mixed pattern of overhead lines and underground cables and thus are inherently inhomogeneous media.

Another noticeable feature of the EMTR method lies in its wide applicability to different power networks. According to the existing publications, the EMTR method has been applied to both electrical power transmission and distribution systems, including diverse application scenarios, such as high-voltage direct current (HVDC) networks [e.g., Razzaghi et al. (2014), Zhang et al. (2017), Li et al. (2018), Tailor and Ukil (2019)], series-compensated transmission lines [e.g., Razzaghi et al. (2013b)], medium-voltage (MV) underground cable networks [e.g., da Costa et al. (2020), Kafal et al. (2021b)], and radial distribution networks [e.g., Razzaghi et al. (2013a), He et al. (2020a), Wang et al. (2020a)].

Lastly, as explained earlier, the EMTR method can be classified into the category of traveling wave-based fault location methods. It is worth further clarifying that the focus of the EMTR method is the processing of the full waveform of fault-originated transients rather than the wavefront arrival time as in classical time-of-arrival (ToA) methods. The precise estimation of the arrival instants of the reflected waves (either from the fault location or other line terminals) can be challenging in some realistic fault scenarios, such as the case featuring a small fault inception angle or high fault impedance. The EMTR method, on the other hand, has been proven to be effective in such cases [e.g., Wang et al. (2020b), An et al. (2021), Wang et al. (2022)].

During the past decade, the EMTR-based fault location methodology has been largely enriched with various fault location metrics, which can be classified into two main subcategories: 1) the matched EMTR-based fault location method, in which the medium in the direct time and reversed time are identical (see Section 4), and 2) the mismatched EMTR method, which involve a reversed-time medium with characteristics being (to a certain extent) different from the ones of the (original) medium in the direct time (see Section 5). The latter is motivated to eliminate the need for multiple simulations of fault currents at guessed fault locations and, thus, to reduce the computational time required in the backward-propagation stage. Furthermore, different types of full-scale experimental studies have been conducted, taking the initial step to incorporate the EMTR method into the daily operation of electrical power systems as a reliable and efficient fault location technique (see Section 6).

Different types of full-scale experiments, including field experiments and pilot tests, have been performed worldwide in the past years, with particular attention to assessing the fault location performance of the EMTR method in real power-system environments. So far, three experimental studies have been reported in the literature Wang et al. (2018a), Wang et al. (2020b), Kafal et al. (2021a). Note that a series of reduced-scale experiments in laboratory environments were also conducted during the same period, providing a preliminary validation of some of the foregoing EMTR fault location metrics [e.g., Razzaghi et al. (2013a), He et al. (2018)]. It should be noted that the focus of this section is to review experimental studies conducted on real power networks (see Table 1).

In 2016, EPFL and XJTU jointly conducted the first field experiment on a 677-m long overhead-line section of a 10-kV double-circuit power distribution network in Yuncheng city, Shanxi province, China Wang et al. (2018a). The experiment emulated a single-phase-to-ground fault by injecting a voltage pulse into one of the phase conductors when the targeted line was unenergized, whose set-up is schematically described in Figure 4A. The pulse waveform was designed to dominate a wide enough frequency band to cover the typical frequency spectrum of fault-generated transients. The experiment served to validate the EMTR-FCSE and -amplitude peak metrics. According to Wang et al. (2018a), He et al. (2018), both metrics are capable of accurately identifying the true fault location (i.e., Phase c of Tower No. 23).

The full-scale experimental study carried out in Wang et al. (2018a) was focused on assessing the applicability of the EMTR method in real power network environments. The fact remains that a fault event in the experiment was considered equivalent to injecting a voltage pulse to emulate post-fault transient processes. Also, to acquire the transient signal, a measurement chain composed of discrete instruments (e.g., broadband current probes and oscilloscopes, as illustrated in Figure 4A) was used.

In 2017, Wang et al. (2020b) conducted a series of pilot tests on a radial MV distribution feeder in Switzerland, as illustrated in Figure 5. Wang et al. (2020b) realized the deployment of the EMTR method into a National Instruments CompactRIO embedded controller coupled with sensing and triggering units. The fault location system integrated the functions of fault detection, data acquisition, electromagnetic transients (EMT) simulations (through demanding the EMTP-RV), and EMTR-based fault location processing. A range of faults of very different natures was intentionally triggered when the pilot distribution network was under normal operating conditions. Specifically, both solid and resistive fault cases (with fault impedance up to 30 Ω) were included in the test. In addition to permanent faults consequent upon a short circuit (realized by a switching maneuver using MV switchgear), single and intermittent arcing discharges were triggered (using spark gaps), emulating transient fault events.

The EMTR-FCSE and cross-correlation metrics were validated in the experiments, effectively locating both the fault location and the faulty phase in all the tested fault cases especially reaching a resolution of 10 m, namely distinguishing the true fault location from its adjacent guessed locations when they are 10 m apart Wang et al. (2020a), Wang et al. (2020b), as shown in Figure 6.

In 2021, Kafal et al. (2021b) reported a pilot test designed to validate the FasTR method in a realistic MV underground cable network in Switzerland. The pilot test utilized a 2.5-km long Y-shaped section of the cable network. Fault transient signals were generated by a manual switch operation of a circuit breaker. A fault location framework was also developed, coordinating distributed sensors (sharing a clock reference under the GPS protocol) and a fault location platform. The latter integrated a remote server communicating with the sensors to read measured transient signals and a computing unit executing the FasTR algorithm. The pilot test employed transient signals acquired by two sensors to construct the cost function, showing that the FasTR method provided an acceptable fault location accuracy with a minimum error of 27 m and a maximum of 54 m.

In summary, the theoretical studies on the EMTR-based fault location method over the past decade successfully demonstrated the effective use of the time-reversal focusing property for the fault location problem by proposing various metrics and algorithms. Also, the applicability of the EMTR method in real fault scenarios was validated in real-scale pilot tests.

Despite the achieved significant results demonstrating the performance of the EMTR method, we identify in what follows some of the most salient research questions, which are still not fully addressed in the literature so far, and future directions for research are indicated.

It is essential to reiterate that the EMTR method belongs to the category of traveling-wave methods. The simulation of the backward propagation is based on an accurate numerical representation of the targeted power network with reference to its actual configuration and parameters. However, a complete knowledge of a power network is not always attainable. For example, soil parameters (e.g., resistivity) can vary in time (in light of weather conditions) and in space (along the geographical span of the network and/or horizontal stratification), and are a function of the frequency. The problem of inferring the line parameters, either from actual measurements or through applying appropriate parameter estimation techniques, is therefore of capital importance and should be the subject of future investigation.

In the strict sense, the Telegrapher’s equations governing voltage/current wave propagation along transmission lines are time-reversal invariant under the assumption of either lossless or inverted-lossy media Razzaghi et al. (2014). Razzaghi et al. showed that a lossy backward-propagation model can be used in the EMTR-based fault location method. Recently, Cozza et al. (2021a) studied the influence of both propagation and termination losses on the fault location performance of full transient-based traveling wave methods. It was concluded that a biased fault location result could be yielded when propagation losses become comparable to dissipation in termination impedances. It is therefore important to consider the issue of losses more thoroughly, especially when the targeted power network is characterized by salient topological complexity or/and lengthy transmission lines, such as a distribution system composed of multiple main feeders or a point-to-point long-distance HVDC transmission system.

One of the important steps in every EMTR-based algorithm for source location is the choice of an appropriate metric to quantify the refocusing of the backward-propagating waves. As discussed earlier, several metrics have been proposed in the literature for this purpose. The metrics involve the evaluation of the fault signal parameters (energy, peak, etc.) or the similarity between two transfer functions or waveforms. Prior to applying the metric, the fault-originated transients should undergo appropriate signal processing to extract the resonance-frequency components and remove other parts, such as the main steady-state low-frequency signal. Furthermore, the combined effect of propagation losses and strong inhomogeneity might pose a problem for some metrics, such as the correlation estimator and cross-correlation metrics, to extract the transfer functions and recognize the resonance frequency from fault-originated traveling waves. This issue requires further attention and needs to be addressed in future studies.

The traditional approach using the time reversal process is to apply its time correlation properties that are valid if and only if the wave propagation can be represented by a linear system of differential equations with time-invariant parameters. In case this hypothesis is no longer verified, there are no theorems that identify the conditions that, if satisfied, guarantee the existence and uniqueness of the time-reversal operation. In view of that, future research is needed to identify these conditions. The consequence of these findings is of universal value: it will be possible not only to improve the existing time reversal methods targeting the precise source location in inhomogeneous and non-linear media but also to solve the problem of the optimum sensing placement that maximizes the energy focalization in the reversed time and thus increases the accuracy of the source location.

The concept of EMTR in mismatched media has been shown to be promising because it requires only one single simulation for the backward propagation, therefore, reducing significantly the computational burden of running multiple independent backward simulations as it is in the matched methods. However, the proposed properties and metrics are valid for specific and relatively simple topologies. For example, the scope of applying the mirrored minimum energy metric is limited in non-branched transmission lines. Further research is needed to apply EMTR in mismatched media to topologically-complex power networks.

Lastly, further experimental studies are necessary to pave the way for implementing the EMTR technique in different power networks. For example, pilot tests can be conducted in point-to-point or meshed HVDC systems.