Fault location algorithms for transmission lines use the parameters of the transmission line to locate faults after the faults have occurred along the line. Although these parameters can be estimated by the phasor measurement units (PMUs) at the terminal(s) of the transmission line continuously, the uncertainty in the measurements will give rise to stochastic errors in the measured values. Thus, the uncertainty in measurements definitely influences the estimations of the parameters of the transmission line, which, in turn, influences the results of fault location algorithms. Inaccurate results of fault location algorithms may lead to costly maintenance fees and prolonged outage time. Therefore, in this article, we estimate the parameters of the transmission line considering the uncertainty in the measurements so that a more accurate fault location can be derived. The uncertainty in the measurements will be modeled as a stochastic distribution, and the maximum likelihood estimation (MLE) method will be adopted to reduce the uncertainty in the measurements. In addition, as an illustration, the telegrapher's equations will be used to calculate the parameters of the transmission line, and the two-terminal positive sequence network fault location algorithm will be used to locate the fault. In a simulation, a case study of a real-life transmission line the influence of the uncertainty in the measurements on the transmission line parameter estimations and the effectiveness of the MLE method for estimations are simulated and analyzed. The results show that the influence of the uncertainty in the measurements on the positive sequence network fault location algorithm should not be neglected and that the proposed method is very effective in significantly reducing the influence of the uncertainty in the measurements.

When the current differential protection is applied to very long transmission lines such as half-wavelength transmission lines, it suffers from the distributed capacitive current as well as from low sensitivity in case of a high-resistance fault. In case of an external fault, the variation of the line storage energy, the distributed resistance energy loss, and the energy injected from both ends of the transmission line satisfy the energy balance equation, and in this case the energy balance is independent of the line length. However, in case of an internal fault, the energy dissipated by the fault resistance breaks the energy balance. Based on the theory of energy balances, this paper proposes a novel pilot protection principle. Compared with the existing long-distance transmission line protection principles, the proposed pilot protection principle has the advantage of not being influenced by the distributed parameters of the long line, and in addition it is suitable for identification of high-resistance grounded faults. A simulation based on EMTDC/PSCAD illustrates the benefits of the proposed approach.