The RBF-FD and RBF-FDTD Methods for Solving Time-Domain Electrical Transient Problems in Power Systems

Abstract

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.