In this paper, the development and application of the radial basis function-finite difference (RBF-FD) method and the RBF-finite difference time domain (RBF-FDTD) method for solving electrical transient problems in power systems that are defined by the time-dependent ordinary differential equations (ODEs) and the time-dependent partial differential equations (PDEs), respectively, are presented. RBFs such as Gaussian (GA), Multiquadric (MQ), Inverse Quadric (IQ), and Inverse Multiquadric (IMQ) are used in these numerical methods to formulate the central finite difference approximations of the first- and second-order derivatives of a function. The algorithm of selecting “optimal” shape parameters for our basis functions is also applied, specifically to increase the accuracy of the suggested methods with regard to high accuracy needs. Finally, the accuracy, effectiveness, and applicability of our new approaches are evaluated through simulations of the switching transient voltages on a typical electrical circuit and a 220 kV single-phase transmission line, lightning-induced voltages on a 110 kV single-phase overhead distribution line, and transient voltages along two horizontal grounding electrodes excited by lightning impulse sources. The obtained numerical results demonstrate that our proposed RBF-based numerical approaches compare favorably to the traditional numerical methods.

This paper introduces an advanced application of the Radial Basis Function–Finite-Difference Time-Domain (RBF-FDTD) method, as proposed in [1], for computing lightning-induced transient voltages in grounding systems. The approach models grounding structures as non-uniform transmission lines, governed by telegrapher’s equations with space- and time-varying parameters—inductance L(x, t), conductance G(x, t), and capacitance C(x, t)—while accounting for electromagnetic coupling across complex grounding configurations. Leveraging the method’s inherent flexibility and precision, extensive numerical simulations were conducted on two horizontal grounding electrodes and three benchmark grounding grids, validating its capability to accurately capture both localized and distributed transient effects. The results underscore the robustness, computational efficiency, and practical utility of RBF-FDTD in analyzing transient electromagnetic phenomena in power system grounding infrastructures. This study not only confirms the method’s superiority in modeling intricate grounding responses but also offers critical insights for enhancing the design and optimization of grounding systems under lightning and fast-transient conditions.

This paper presents an advanced application of the Radial Basis Function–Finite-Difference Time-Domain (RBF-FDTD) method, as introduced in [1], to solve the field-to-line coupling equations for simulating lightning-induced voltages on overhead distribution lines. Simulation results for a typical 1-km, 110-kV line obtained using both the RBF-FDTD and conventional FDTD methods are compared against benchmark solutions from the Lightning-Induced Overvoltage (LIOV) software to validate accuracy and determine the optimal shape parameters for the RBFs. The RBF-FDTD method exhibits high accuracy and reduced numerical dispersion, particularly when the shape parameters are optimally selected. Furthermore, the effects of critical physical factors—including lightning electromagnetic field models, imperfect ground conductivity, and corona discharge dynamics—on the induced voltages are analyzed through error evaluation. The results confirm the proposed method’s capability for reliable and efficient simulation of lightning transients, providing valuable insights for the design and protection of power distribution systems against fast transient overvoltages.

Lightning-induced voltages on overhead distribution lines present a formidable obstacle to ensuring the reliability of power systems, evaluated through conventional numerical techniques, such as the Finite Difference Time Domain (FDTD) method and the Finite Element Time Domain (FETD) method. This study proposes a novel implementation of the Radial Basis Function-Finite Difference Time Domain (RBF-FDTD) method, extending the foundation of our previous work to address the field-to-line coupling equations governing such systems. The effectiveness and accuracy of this approach are rigorously validated through RBF-FDTD numerical simulations, applied to both horizontal and vertical configurations of a 1 km, 110 kV multi-conductor distribution line, as well as a real-world three-phase overhead line in Vietnam. In this study, the impact of various parameters, including line geometry, the presence of ground wires, and the influence of perfectly and imperfectly conducting ground, on the lightning-induced voltages are investigated. The simulation and computational results are in good agreement with findings from prior studies, underscoring the potential of the RBF-FDTD method as a robust tool of practical implications.

In this paper, we introduce the development of the Finite Difference Matrix Operators (FDMO) algorithm for solving the three-dimensional (3D) electromagnetic problem governed by the Laplace–Poisson equation. Specifically, we propose a novel approach by integrating the FDMO approach with non-uniform mesh of the 3D solution domain, optimizing computational efficiency and adaptability for complex grounding system geometries, to compute and analysis the earth potential distribution in grounding systems. The study considers two typical grid configurations—square and L-shaped of IEEE Std 80^™—as well as a real-world grounding system of high voltage substation in Vietnam. The results of potential distribution, touch, and step voltages obtained from the proposed method demonstrate high agreement with those computed using the Finite Element Method (FEM) and IEEE Std 80^™, confirming the accuracy, robustness, and practical utility of the proposed method for the grounding design of high voltage substations in power systems.

Lightning location systems provide valuable and vital data for study of lightning on the earth. Developed nations already built not only one but aslo many lightning location networks in their territories in order to collect highly reliable national dataset of lightning. Moreover, these national lightning detection systems are linked together to increase both the collecting range and the accuracy. However, in Vietnam, lightning location systems are not payed enough attention on. Therefore, the authors attempt to provide an overiew of lightning location systems and their importance to the field of lightning protection in this research. The paper provides an overview of the operating principles of popular lightning location systems in the world. Besides, typical lightning activity data extracted from Blitzortung lightning location system in Vietnam are presented. In addition, a number of studies around the world using lightning data from these location systems to improve the lightning protection performance of transmission lines are briefly introduced. These results and information show the vital role of lightning location systems not only in lightning protection but also in analyzing the causes of failures on power systems.