Mathematical development of the sampling frequency effects for improving the two-terminal traveling wave-based fault location

•The sampling frequency effects on the two-terminal traveling wave-based fault location method.•The sampling frequency effects are represented by lozenges in a time-space plane.•The time-space lozenges support a probabilistic analysis in order to find the fault with 100•The proposed mathematical development was assessed with both experimental data and simulations. This paper presents a deep analysis of sampling frequency effects on the classical two-terminal traveling wave-based transmission line fault location method performance, demonstrating that these effects can be represented by well-defined regions (in the format of lozenges) in a time-space plane. Thereby, it is demonstrated that the classical method estimates the fault location in predefined points due to sampling frequency-associated time resolution. Furthermore, faults at the same location can be randomly estimated in different predefined locations depending on the fault inception time, resulting in location uncertainties. Nevertheless, the proposed time-space lozenges support a probabilistic analysis in order to consider the sampling frequency effects by adding a probabilistic search field component to the classical fault location formulation which indicates the region in which the fault took place with 100% of certainty regarding the sampling frequency effects. Therefore, this paper also proposes an improvement on the classical method by considering the effects of the sampling frequency. The proposed approach was evaluated by means of digital simulations and validated experimentally in laboratory by the application of faults along a 1 km long cable.