The implementation of the sliding mode control (SMC) for load frequency control of power networks becomes difficult due to the chattering phenomenon of high-frequency switching. This chattering problem in SMC is extremely dangerous for actuators used in power systems. In this paper, a continuous control strategy by combining a second-order mode and integral siding surface is proposed as a possible solution to this problem. The proposed second-order integral sliding mode control (SOISMC) law not only rejects chattering phenomenon in control input, but also guarantees the robustness of the multi-area power network, which has an effect on parametric uncertainties such as the load variations and the matched or mismatched parameter uncertainties. Moreover, the reporting of the simulation indicates that the proposed controller upholds the quality requirement by controlling with operating conditions in the larger range, rejects disturbance, reduces the transient response of frequency, eliminates the overshoot problem, and can better address load uncertainties compared to several previous control methods. The simulation results also show that the proposed SOISMC can be used for practical multi-area power network to lessen high parameter uncertainties and load disturbances.

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.