The recent increase in renewable energy penetration at the distribution level introduces a multi-directional power flow that outdated traditional fault location techniques. To this extent, the development of new methods is needed to ensure fast and accurate fault localization and, hence, strengthen power system reliability. This paper proposes a data-driven ground fault location method for the power distribution system. An 11-bus 20 kV power system is modeled in Matlab/Simulink to simulate ground faults. The faults are generated at different locations and under various system operational states. Time-domain faulted three-phase voltages at the system substation are then analyzed with discrete wavelet transform. Statistical quantities of the processed data are eventually used to train an Artificial Neural Network (ANN) to find a mapping between computed voltage features and faults. Specifically, three ANNs allow the prediction of faulted phase, faulted branch, and fault distance from the system substation separately. According to the results, the method shows good potential, with a total relative error of 0,4% for fault distance prediction. The method is applied to datasets with unknown system states to test robustness.

Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by leveraging the kernel trick. Classic kernel methods learn a single layer of nonlinear features, whose representational power may be limited. Motivated by recent success of deep neural networks (DNNs) that learn multi-layer hierarchical representations, we propose a Stacked Kernel Network (SKN) that learns a hierarchy of RKHS-based nonlinear features. SKN interleaves several layers of nonlinear transformations (from a linear space to a RKHS) and linear transformations (from a RKHS to a linear space). Similar to DNNs, a SKN is composed of multiple layers of hidden units, but each parameterized by a RKHS function rather than a finite-dimensional vector. We propose three ways to represent the RKHS functions in SKN: (1)nonparametric representation, (2)parametric representation and (3)random Fourier feature representation. Furthermore, we expand SKN into CNN architecture called Stacked Kernel Convolutional Network (SKCN). SKCN learning a hierarchy of RKHS-based nonlinear features by convolutional operation with each filter also parameterized by a RKHS function rather than a finite-dimensional matrix in CNN, which is suitable for image inputs. Experiments on various datasets demonstrate the effectiveness of SKN and SKCN, which outperform the competitive methods.