Echo Response of Faults in Transmission Lines: Models and Limitations to Fault Detection

Abstract

This paper introduces models of the time-domain echoes generated by faults in transmission lines excited by test signals, e.g., as in applications of time-domain reflectometry. Faults here considered include local modifications of the propagation characteristics of a transmission line. It is shown that the response of faults are strongly dispersive in nature, which implies that the peak of their echo is far from providing an accurate measure of the severity of the fault, as it heavily depends on the frequency content of the test signal, as well as on the length of the fault. It is argued that fault detection in transmission lines is an ill-posed problem that requires a priori knowledge on the fault itself. These results are important for applications of time-domain reflectometry methods, particularly for early-warning monitoring of potentially critical faults from their onset, since it is shown that echoes from faults tested at relatively low frequencies can lead to underestimate their actual severity.

Low Frequency Model-Based Identification of Soft Impedance Faults in Cables

“…where d o is the geometrical distance between the fault and the testing port, ν is the frequency, k = 2πν/v the propagation constant of the cable and v the speed of propagation. The fault reflectivity was found in [13] to be Figure 1. Double impedance-step representation of a local fault in a transmission line of characteristic impedance Zo.…”

“…with w the length of the fault. Its accuracy was demonstrated in [13] together with its practical implications for fault testing and risk assessment. Eq.…”

“…Eq. (4) was shown in [13] to scale roughly with the frequency ν as long as ν f o , where f o is the critical frequency of the fault…”

“…Recalling that TDR echoes in presence of hard faults are expected to be proportional to the test signal, one could be tempted to think that the peaks in the echo represent the partial reflections from the two ends of the region spanned by the impedance fault. The inaccuracy of this interpretation was discussed in [13] and it is especially troublesome since these peaks only depend on the bandwidth of the test signal.…”

“…Fundamental limitations to the use of TDR methods for soft-fault testing were highlighted in [13]. In particular, the amplitude of TDR echoes was shown not to represent an accurate estimator of how severe a fault is, as echoes also strongly depend on other parameters, e.g., the bandwidth of the test signal, p(t), and the fault length w. In [14] it was shown that echoes generated by soft faults with a very different degree of severity can be practically identical, if tested at frequencies well below f c /4, with f c the fault characteristic frequency…”