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Title: Modeling of thin wire structures for the FDTD method
Authors: Li, Binghao
Degree: Ph.D.
Issue Date: 2019
Abstract: The finite-difference time-domain (FDTD) method is an intuitive and powerful analysis technique to solve electromagnetic (EM) problems in the time domain. The FDTD method has the advantages of broadband field simulation, less memory space, easy implementation of parallel computing and others. Because of the weakness in simulating a large working volume with elaborate structures, several thin-wire model techniques were developed. However, these techniques cannot model lossy wires with cross sections with circular or non-circular shapes. The inclined thin-wire structures cannot be simulated with acceptable accuracy as well. They have limited values in the application of lightning surge analysis in practical wire structures, such as long power/signal line and cables, structural steel and others in power systems and building structures. In this thesis, three types of extended thin-wire models will be proposed to represent lossy wire structures for lightning surge analysis. These proposed models are then applied to investigate lightning transients in a building, a meteorological tower and a light rail system. The first extended thin-wire model is used to simulate lightning surge or wave propagation on lossy round wire structures. The wire structures are represented with time-domain cascade circuits and are integrated into a traditional thin-wire model in the FDTD simulation. The wire structures include solid round conductors, cylindrical tubes and coaxial cables, and the skin effect is fully considered. In the coaxial structure, the currents in both inner and outer conductors are not necessarily balanced. The proposed model has been validated analytically and numerically, and good agreements have been observed. It has been applied to analyze lightning current sharing in a lossy RF coaxial cable. Compared with the traditional FDTD method, this extended thin-wire model requests less memory space and computation time in the simulation. Lossy thin-wire structures with arbitrary inclination are quite common in the industry, which are difficult to address using traditional FDTD methods. An extended thin-wire model is then proposed. The frequency-dependent losses of the conductors are fully taken into account, and a vector fitting technique is applied to deal with frequency-dependent parameters in the time-domain analysis. The bidirectional coupling within the lossy coaxial conductors is modelled. The currents in inner and outer conductors are not necessarily balanced. Three cases are presented to investigate wave propagation velocity, wave attenuation, and current distribution. They are compared with analytical results and numerical results. It is found that the proposed thin-wire models can depict the transient behaviors in the lossy inclined conductors with the velocity error of less than 1%, and the attenuation error of less than 1.5%
To mimic lossy wire structures with non-circular cross sections for transient analysis, another thin-wire model is developed. Unique correction factors of field quantities and the surface electric field of wire structures are introduced in the model. The stability problem is investigated. A method, called high-frequency filtering method, is proposed to stabilize the computation stability. These parameters are both frequency-dependent and position-variant. They are evaluated in an initialization process and are applied in the updating process using an iterative convolution technique. The proposed method is validated with the transmission line theory analytically and the traditional FDTD method numerically. Six types of wire structures are tested, including rectangular, H-shape, cross-shaped, T-shape, L-shape and U-shape structures. Good agreements are observed. It is found that the computation time is reduced to 1% of that with the conventional FDTD method, and the computer memory to 30% in the tested case. General guidelines on wire zone meshing are provided as well. Finally, this method is applied to analyze lightning surges in a light rail system under a direct lightning stroke. Lightning surges induced in buildings are investigated with an FDTD method. When down conductors are used in a building to discharge lightning current, induced surges are observed in adjacent distribution circuits due to electric and magnetic coupling. They are different from those obtained using quasi-static models. The peak value of surge voltage in an open circuit is proportional to a logarithmic function of conductor spacing. The induced current in a short circuit can be directly determined using a closed-form formula. It is found that connected capacitors can reduce the induced surge voltages but may not be effective. SPDs are then recommended installing at two far ends of a distribution circuit. They are not required to dissipate substantial lightning surge energy observed in the down conductor. It is found that the surge currents in SPDs can be estimated using the closed-form formula as well. The proposed extended thin-wire models are applied for the simulations of a meteorological tower and a light rail system. For transient analysis, the meteorological tower, lightning current distribution, ground potential rise and step voltage are analyzed. It is found that the majority of the lightning current is discharged via the outermost steel cables and are dissipated to the earth by the horizontal grounding bars. Both the step voltage and ground potential are measured as well in three different grounding configurations. The safety of step voltage in the vicinity of the tower is also addressed. In the DC light rail, the diode boxes provided between rail tracks and fault current return wires are arranged to limit stray current. They are susceptible to damage during lightning strikes. The surge voltages on diode boxes are analyzed and simulated by the FDTD method under different conditions. The frequency dependent loss of wire conductors and lossy rail tracks are considered. It is found that rising front of return strokes, lightning channel locations and soil conductivity nearby affect the surge voltage significantly.
Subjects: Hong Kong Polytechnic University -- Dissertations
Finite differences
Pages: xxii, 219 pages : illustrations
Appears in Collections:Thesis

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