Accurate fault location reduces operating cost and outage time. This paper proposes a time-domain method to accurately locate faults in transmission lines, which only requires a very short data window (several milliseconds) during faults. First, the voltage distribution through the line during faults is accurately obtained by solving the matrix form partial differential equations using the proposed numerical scheme. The proposed numerical scheme is mathematically validated for the transmission line fault location problem, with the optimal selection of time and distance intervals to ensure stability and minimum solution error. Afterwards, the fault location is obtained via the extremum value of the voltage distribution. The method fully considers distributed parameters as well as asymmetry of the line. Extensive numerical experiments validated that (a) the proposed numerical scheme demonstrates advantages towards other numerical schemes; (b) the proposed method presents higher fault location accuracy compared to the existing method, independent of fault types, locations and impedances; and (c) the fault location accuracy is not sensitive towards fault inception angles, loading conditions, measurement errors and parameter errors. The proposed method works with relatively low sampling rates (80 samples per cycle) and is compatible with IEC 61850 standard in present digital substations.

Accurate fault location for underground cables in MMC-HVDC grids reduces the time finding faults as well as the system operational costs. For MMC-HVDC grids, the data window during faults is usually short. During such severe transients, the frequency dependent line parameters of the underground cables have strong influence on the fault location accuracy. In this paper, a novel fault location algorithm for underground cables in MMC-HVDC grids is proposed. First, a multi-layer model for the underground cable using partial differential equations is proposed, which considers the distributed and frequency dependent line parameters in time domain. Afterwards, the numerical finite difference solution of the multi-layer model is proposed to obtain the voltage distributions along the entire cable. Finally, the voltage method is applied to locate faults. Numerical experiments show that the multi-layer model accurately considers the frequency dependency of the cable parameters, and the solution of the model obtains accurate voltage distribution even during system transient. Extensive test cases prove that the proposed algorithm locates faults with less errors than the existing algorithm. The method is also compatible with a relatively low sampling rate (20 kHz) and a short data window (5 ms).

Failure probability evaluation for complex physical and engineering systems governed by partial differential equations (PDEs) are computationally intensive, especially when high-dimensional random parameters are involved. Since standard numerical schemes for solving these complex PDEs are expensive, traditional Monte Carlo methods which require repeatedly solving PDEs are infeasible. Alternative approaches which are typically the surrogate based methods suffer from the so-called “curse of dimensionality”, which limits their application to problems with high-dimensional parameters. For this purpose, we develop a novel hierarchical neural hybrid (HNH) method to efficiently compute failure probabilities of these challenging high-dimensional problems. Especially, multifidelity surrogates are constructed based on neural networks with different levels of layers, such that expensive highfidelity surrogates are adapted only when the parameters are in the suspicious domain. The efficiency of our new HNH method is theoretically analyzed and is demonstrated with numerical experiments. From numerical results, we show that to achieve an accuracy in estimating the rare failure probability (e.g., $10^{-5}$ ), the traditional Monte Carlo method needs to solve PDEs more than a million times, while our HNH only requires solving them a few thousand times.