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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 milli-seconds) 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.

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a multi-fidelity neural network framework to solve this optimization problem. Our contribution is to develop a systematical computational procedure for the underlying problem in parallel with domain decomposition. Our analysis shows that the D3M approximation solution converges to the exact solution of underlying PDEs. Our proposed framework establishes a foundation to use variational deep learning in large-scale engineering problems and designs. We present a general mathematical framework of D3M, validate its accuracy and demonstrate its efficiency with numerical experiments.

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.