## 1 Introduction  
Faults on transmission lines disrupt the smooth operation of power systems; the robust finding of their location plays a vital role. Various fault location methods have been developed over the years; two categories, namely impedance-based methods [1; 2] and travelling-wave-based methods [3; 4], are well known. In the impedance-based methods, the fault position is determined by analysing the voltage and current measurements taken before and after the fault event, while in travelling-wave-based methods, the fault locations are computed by exploiting the transient signals produced by the fault. The accuracy of impedance-based methods can be influenced by the line configuration, fault resistance, load imbalance, and the presence of distributed generation sources [5; 6; 7]. On the other hand, the disadvantages of travelling-wave-based methods are as follows: (a) The data acquisition requires complicated signal processing techniques. (b) The problem of synchronising the time between multiple observation points is challenging. (c) In lossy transmission lines, the travelling waves will be distorted and attenuated during signal propagation. Therefore, the accurate calculation of the arrival time will be challenging. (d) In scenarios involving branched lines, fault-generated transient signals have to propagate over numerous junctions and will experience attenuation, resulting in a decrease in their intensity. (e) In a mixed overhead-undergroundcable transmission line power system, the travelling speed difference between multiple media will cause location bias [7; 8; 9; 10]. The time reversal theory, which was initially applied to the acoustic field, is used to address the issues of travelling-wave-based methods, in which ultrasonic pressure fieldsare recorded, time-reversed, re-emitted, and focused on the source target [11]. Recent applications of time reversal theory to electromagnetics have led to the development of a method called the EMTR-based disturbance localisation method. It has been utilised for the localisation of flash-overs and lightning discharges, where it has been demonstrated that the wave fronts generated by time-reversed electromagnetic fields are focused at lightning strike locations [12]. This concept is then employed for fault location in power grids, in which fault-generated transients observed at specific observation points are time-reversed and sent back to the same simulated system, focusing on the fault position [5; 7]. In this regard, researchers have extended its application to various power system network topologies while proposing new metrics and design criteria for fault position estimation. [PERSON] et al., for example, investigated the use of EMTR-based fault location algorithms in systems such as series-compensated, overhead-underground mixed cable, and multi-terminal HVDC transmission line networks [13; 14]. In [15], an alternative approach to that of [7] was proposed, where the fault position was determined on the basis of a particular range of the arguments of the voltage and transfer function. The authors of [16] showed that the computed fault signals at the actual fault position were the time-delayed copies of the fault-generated transient signals. The concept of mirrored minimum energy was proposed in [17], where it was demonstrated that, when time-reversed signals are back-propagated, their energy is minimum at the actual fault position. In [18], the EMTR-based norm criteria, namely the two-norm and P-norm for fault location computation, were introduced, and it was confirmed that the P-norm performed better. Moreover, The EMTR technique has been validated experimentally on a full-scale setup [19]. Currently, the EMTR technique can be defined as a correlation estimator between the transfer functions of the fault occurrence and fault estimation stages, yielding the correlation coefficient value (CCv) at the corresponding guessed fault location (GFL) [8].