Bihua Zhou

Analysis of Lightning-Induced Voltages on Overhead Lines Using a 2-D FDTD Method and Agrawal Coupling Model

In this paper, the lightning-generated electromagnetic fields over lossy ground produced by lightning strikes either to flat ground or to a tall tower are calculated using the 2-D finite-difference time-domain (FDTD) method. The resultant horizontal and vertical electric fields are used as forcing functions in the discretized Agrawal electromagnetic coupling equations for the calculation of induced voltages on overhead horizontal conductors without employing the Cooray-Rubinstein formula. Comparison of the results with those obtained using the 3-D FDTD method and with experimental data found in the literature is used to test the validity of the examined method. The approach employed here generally provides sufficient accuracy while allowing significant reduction in computation time and storage requirements as compared to the 3-D FDTD method. From the analysis carried out in this paper, induced voltages appear to be strongly dependent on ground conductivity, somewhat influenced by return-stroke speed, and essentially independent of return-stroke model [transmission-line (TL), modified transmission line with linear current decay with height (MTLL), or modified transmission line with exponential current decaywith height (MTLE)].

Efficient Implementation for 3-D Laguerre-Based Finite-Difference Time-Domain Method

When the Laguerre-based finite-difference time-domain (FDTD) method is used for electromagnetic problems, a huge sparse matrix equation results, which is very expensive to solve. We previously introduced an efficient algorithm for implementing an unconditionally stable 2-D Laguerre-based FDTD method. We numerically verified that the efficient algorithm can save CPU time and memory storage greatly while maintaining comparable computational accuracy. This paper presents new efficient algorithm for implementing unconditionally stable 3-D Laguerre-based FDTD method. To do so, a factorization-splitting scheme using two sub-steps is adopted to solve the produced huge sparse matrix equation. For a full update cycle, the presented scheme solves six tri-diagonal matrices for the electric field components and computes three explicit equations for the magnetic field components. A perfectly matched layer absorbing boundary condition is also extended to this approach. In order to demonstrate the accuracy and efficiency of the proposed method, numerical examples are given.

Using a Two-Step Finite-Difference Time-Domain Method to Analyze Lightning-Induced Voltages on Transmission Lines

A novel high-efficient two-step finite-difference time-domain (FDTD) method is proposed to analyze the lightning-induced voltages on transmission lines (TLs) in this paper. The proposed method includes two steps. The first step is to calculate, using the 2-D FDTD method, electromagnetic fields that are radiated from a vertical lightning channel and illuminate the nearby TLs. The second step is to calculate, using the 3-D FDTD method, the electromagnetic response of the TL that is illuminated by the incident electromagnetic fields added at the total field-scattered field connecting the boundary of the 3-D space. To validate the proposed two-step FDTD method, the results calculated using the two-step FDTD method are compared with those calculated with Agrawal coupling model, and with those calculated using the 3-D FDTD method. The two-step FDTD method shows high computational efficiency in analyzing lightning-induced voltages on TLs.

A Novel 3-D Weakly Conditionally Stable FDTD Algorithm

For analyzing the electromagnetic problems with the flne structures in one or two directions, a novel weakly conditionally stable flnite-difierence time-domain (WCS-FDTD) algorithm is proposed. By dividing the 3-D Maxwells equations into two parts, and applying the Crank-Nicolson (CN) scheme to each part, a four sub-step implicit procedures can be obtained. Then by adjusting the operational order of four sub-steps, a novel 3-D WCS-FDTD algorithm is derived. The proposed method only needs to solve four implicit equations, and the Courant{Friedrich{Levy (CFL) stability condition of the proposed algorithm is more relaxed and only determined by one space discretisation. In addition, numerical dispersion analysis demonstrates the numerical phase velocity error of the weakly conditionally stable scheme is less than that of the 3-D ADI-FDTD scheme.

A new 2-D FDTD method applied to scattering by infinite objects with oblique incidence

A new two-dimensional (2-D) finite-difference time domain (FDTD) method applied to scattering by infinite objects with oblique incidence is proposed. 2-D Maxwells equations, differential equations, and perfectly matched layer (PML) absorbing boundary conditions (ABC) are derived. The incident wave, computed by the 1-D FDTD method, is set on the connecting boundary. The accuracy and the efficiency of the proposed method have been verified by comparing the results of the split-field periodic FDTD method, the sine-cosine method, and the transmission line theory method with the proposed method.

A Novel 3-D HIE-FDTD Method With One-Step Leapfrog Scheme

This paper presents a novel 3-D leapfrog hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method. By first adopting the Peaceman-Rachford scheme and then the one-step leapfrog scheme, the proposed HIE-FDTD algorithm is implemented in the same manner as the traditional finite-difference time-domain method in which the implicit scheme was applied only in the direction where a fine grid was applied and the explicit scheme was applied in two other directions where a larger grid was used. Further, by introducing auxiliary field variables denoted by e and h, the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Numerical analysis demonstrated that the Courant-Friedrichs-Lewy stability condition of the proposed HIE-FDTD method is determined only by one grid cell size, which is more relaxed than those of the existing HIE-FDTD methods, and the numerical dispersion error is less than that of the alternating-direction implicit method.

Unconditionally Stable FDTD Method for Solving Oblique Incident Plane Wave on Periodic Structures

For solving the problem of the oblique incident plane wave over planar periodic objects, an implicit finite-difference time-domain (FDTD) method is proposed by introducing the Crank-Nicolson (CN) scheme to the field transformation technique. Unlike the previous approaches of field transformation method, this technique does not need to introduce additional field components to handle extra terms and is unconditionally stable as proved by a stability analysis. The accuracy and efficiency of the proposed method is verified by comparing with the split-field method.

An improved cuckoo search optimization algorithm for the problem of chaotic systems parameter estimation

This paper proposes an improved cuckoo search (ICS) algorithm to establish the parameters of chaotic systems. In order to improve the optimization capability of the basic cuckoo search (CS) algorithm, the orthogonal design and simulated annealing operation are incorporated in the CS algorithm to enhance the exploitation search ability. Then the proposed algorithm is used to establish parameters of the Lorenz chaotic system and Chen chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the algorithm can estimate parameters with high accuracy and reliability. Finally, the results are compared with the CS algorithm, genetic algorithm, and particle swarm optimization algorithm, and the compared results demonstrate the method is energy-efficient and superior.

Numerical Study of Lightning-Induced Currents on Buried Cables and Shield Wire Protection Method

In this paper, the two-step finite-difference time-domain method of solving full-wave Maxwells equations is adopted to analyze the lightning electromagnetic pulse (LEMP) coupling to buried cables. The influences of lightning strike point, cable length, and ground conductivity on the LEMP coupling to buried cable are evaluated. The method of using shield wires to decrease the lightning-induced currents on the buried cables is proposed, and the protection efficiencies of different installing ways of the shield wires are evaluated. The numerical results show that when the lightning strike point is in the axial direction of the cable, the coupling is rather strong; the induced current acutely increases as the lightning strike point approaches the cable; when the length of the cable does not exceed about 150 m, the induced currents at the cable ends increase as the length increases, whereas once the length of the cable exceeds 150 m, the induced currents begin to decrease; the shield wires can effectively decrease the lightning-induced currents on the buried cables, closer the shield wire, greater the protection efficiency, and more shield wires provide greater protection efficiency.

Unconditionally Stable FDTD Method Based on LOD Scheme for Analysis of 2-D Periodic Structures

For modeling periodic structures at oblique incidence, an unconditionally stable finite-difference time-domain technique is presented by applying the locally one-dimensional (LOD) scheme to the field transformation technique. By splitting the space operator matrix in an appropriate way, the transformed Maxwells equations can be subdivided into two sub-steps for an efficient implementation. The accuracy and efficiency of the proposed method are verified by comparing with the results of the reference [4] and the split-field method respectively.