The work, authored by A. Herrera-Orozco, C. Orozco-Henao, and J. Marin-Quintero, addresses a persistent gap in distribution protection. Most existing fault detection and location techniques were developed for permanent faults on overhead lines, where the fault signature persists long enough for impedance calculations or travelling-wave methods to converge. Underground networks complicate matters considerably: their high shunt capacitance, load imbalance, and limited visual accessibility make diagnosis harder, and the intermittent, sub-cycle nature of incipient faults means that many detection methods either miss them entirely or require extensive labelled datasets for training without offering any localisation capability.

The proposed method rests on a time-domain mathematical formulation of the faulted feeder. The authors model the underground shielded cable as a lumped-parameter equivalent circuit, with parameters derived from Carson’s equations and reduced to a three-by-three phase-domain representation through Kron’s reduction. When a single-phase-to-ground fault strikes, the strategy subtracts the pre-fault current from the during-fault current measured at the relay point, isolating the fault-induced component. This superimposed-component approach assumes that the load current and the currents in the non-faulted phases remain approximately unchanged during the short observation window, a simplification the authors explicitly flag as valid only for the brief interval associated with an incipient fault transient.

What emerges from this subtraction is a compact equation relating the measured faulted-phase voltage to three unknowns: the resistance and inductance of the line section up to the fault, and the arc voltage magnitude. Because the formulation is valid at every sampling instant, multiple instances of the equation can be stacked into an overdetermined linear system, which the authors solve with a Non-Negative Weighted Least Squares Estimator. The non-negativity constraint keeps the estimated parameters physically meaningful, and the weighting scheme assumes a ten percent composite measurement error, consistent with typical instrument transformer tolerances under transient conditions. Crucially, the method needs only a handful of samples to work: the authors set the absolute lower operational limit at 32 samples per 60 Hz cycle, well within the reach of legacy protection devices.

The detection logic borrows from distance protection, a principle traditionally confined to transmission systems. The estimated phase impedance is plotted against a polygonal relay characteristic, which the authors prefer over admittance-type characteristics for its flexibility in adjusting operating zones and its better sensitivity to high-resistance faults without risking maloperation from load encroachment. For permanent faults, the impedance trajectory moves into zone 1 and stays there until clearing. For incipient faults, it briefly enters the protection region before snapping back to the normal operating zone, so the strategy pairs the impedance comparison with a timer calibrated to typical incipient fault durations of one-quarter to one-half cycle, generating an alarm rather than a trip when the signature matches.

Validation took place on a real 13.8 kV underground distribution feeder in Southern Brazil, denoted East Private 1, modelled in ATP/EMTP with nine load buses, four three-phase laterals, XLPE 750 MCM main feeder cables, and 4/0 AWG aluminium tape-shielded laterals in flat buried configuration. The authors simulated 80 incipient fault scenarios using a dynamic arc model with varying arc voltage parameters, 80 matching permanent fault scenarios, and an additional 20 permanent fault cases using a simple linear resistance model. They also ran 45 non-fault events, including capacitor bank switching, load variations from 100 to 180 percent of nominal, and harmonic distortion, to test whether the strategy would stay quiet when it should.

The headline results are strong. Approximately 93 percent of the incipient fault scenarios were detected, and 95 percent were correctly identified even at the lowest tested sampling rate of 32 samples per cycle. For permanent faults, detection reached roughly 90 percent, rising to 100 percent when the simpler linear resistance fault model was used. Across all 215 evaluated events, overall classification accuracy was 85.6 percent, but among the 136 internal faults within the three protection zones, the relay triggered for 131, a fault-detection effectiveness of 96.3 percent. Among the 79 events outside the protected zones, only two, or 2.5 percent, were falsely identified as internal faults.

The method’s main weakness is a systematic under-reach: the estimated apparent impedance tends to run slightly higher than the actual fault impedance, particularly for faults near zone boundaries. The authors attribute this to four cumulative modelling simplifications, including the neglected pre-fault voltage drop, the quasi-constant arc voltage assumption within the narrow quarter-cycle processing window, the static parameter assumption of the least-squares estimator, and the invariance assumption for non-faulted phases. Distance estimation errors reflected this bias. For incipient faults, the mean error was minus 2.34 percent, corresponding to an average overestimation of 94.02 metres, with a mean absolute error of 3.80 percent. Permanent faults fared slightly worse, with a mean error of minus 5.53 percent, an average overestimation of 222.24 metres, and errors ranging between minus 1.34 and minus 12.74 percent.

A statistical sensitivity analysis based on analysis of variance added nuance to the picture. For incipient faults, the arc time constant dominated the estimated reactance, with a test statistic of 62.2976 and a p-value of 1.89 times ten to the minus nine, while arc voltage and sampling rate were also significant; fault distance was not. For estimated resistance, conventional ANOVA assumptions failed, so the authors applied a permutational alternative, finding that sampling rate had the largest effect, followed by the arc time constant. Under permanent fault conditions, all four factors were significant for reactance, but none reached significance for resistance. The authors caution that these statistics describe sensitivity within the tested factor levels and should not be read as causal conclusions.

The selectivity results may matter as much as the detection numbers. All 27 impedance points under load variation, all harmonic injection scenarios, and all capacitor switching events remained outside the protection zones, yielding 100 percent correct discrimination and no false tripping. Even the most critical capacitor switching transients, which produced the lowest estimated impedances, stayed well clear of the relay operating characteristic. The authors identify extension to networks with high penetration of inverter-based distributed energy resources as the principal direction for future work, since these resources can alter fault-current characteristics and voltage profiles in ways the current formulation does not yet capture. They also point toward hybrid approaches combining analytical models with data-driven residual techniques as a route to improving sensitivity to low-amplitude, non-stationary fault signatures under noisy measurements.

Subject of Research: A time-domain distance-relay protection strategy for detecting and locating incipient and permanent single-phase-to-ground faults in underground distribution networks with shielded cables.

Article Title: A new approach based in distance relay strategy to incipient fault detection and location in distribution networks with underground shielded cables: A time-domain system model with parameter estimation

Article References: Herrera-Orozco, A., Orozco-Henao, C., & Marin-Quintero, J. (2026). A new approach based in distance relay strategy to incipient fault detection and location in distribution networks with underground shielded cables: A time-domain system model with parameter estimation. Results in Engineering, 32, Article 113665. https://doi.org/10.1016/j.rineng.2026.113665

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113665

Keywords: underground distribution networks, incipient faults, distance relay, fault location, shielded cables, parameter estimation, time-domain model, arc voltage, ANOVA sensitivity analysis, sampling rate, NNWLSE, power system protection