Multiconductor Transmission Line Systems Research Articles

Application of Extended Matrix Pencil Method in Multiport Frequency-Dependent Network Equivalent and the Transient Analysis of Multiconductor Transmission Line System

In this paper, an extended matrix pencil method (EMPM) is proposed to achieve the equivalent analysis of a multiport system. First, the Hankel matrix constructed by the sampling data from multiple ports is integrated into an extended matrix. Then, operations, including singular value decomposition, order reduction, and solution of matrix pencil, are carried out for the extended matrix to calculate the common poles. Further, the residue matrix of the multiport system is solved by the least square method. Furthermore, for the multiconductor transmission line (MTL) system containing the frequency-dependent network (FDN) loads, a combination of the EMPM and piecewise linear recursive convolution (PLRC) is proposed to complete its transient analysis. The corresponding voltage expressions at the connection point of the MTL and FDN are analytically derived. Finally, the effectiveness of the EMPM in analyzing the FDN equivalent and that of the proposed combination of the EMPM and PLRC in analyzing the transient response of the MTL system containing the FDN are verified by numerical examples.

Study on the Electromagnetic Interference of Shielded Cable in Rail Weighbridge

In view of the electromagnetic interference (EMI) of the signal shielded cable in the rail weighbridge, the interference source is analyzed on the basis of the field measurement and investigation, and methods of suppressing the crosstalk voltage of the shielded cable are proposed. First, the capacitive coupling model between the power line and the shielded cable is established, and the coupling model between the shielded layer and the core is developed. Later, the distribution parameters of the multi-conductor transmission line system are extracted by the commercial software ANSYS based on the finite element method. Then the coupling voltages of the shielded layer and the core can be calculated; compared with the measured results, the accuracy and effectiveness of the proposed method are verified. Finally, the EMI suppression methods are proposed and its effectiveness is verified. The EMI of the shielded cable is very common in engineering, and this method has a good reference value for solving the similar problems.

Analysis of Transient Response of Jointless Track Circuit Based on Multiconductor Transmission Lines Theory

In order to ensure the train operation safety, it is necessary to analysis the transient response of track circuit in complex electromagnetic environment. According to the distribution characteristics of transmission lines in traction electric network and the structure of ZPW‐2000 jointless track circuit, the multiconductor transmission lines model of the traction electric network combined with the track circuit is established. The model cannot be calculated directly due to the presence of parallel or terminated nonlinear lumped elements in the track circuit. For this problem, the new analytical method is proposed, which is based on finite difference time domain (FDTD) method to solve the transmission line part, Thevenin's theorem with state variable method to solve the equations of the terminated nonlinear track circuit. The solution equation of multiconductor transmission line system is obtained by combining the two parts. The relevant parameters of the model can be calculated by finite element method. In ATP‐EMTP, the simulation results verify the correctness of the expression. In addition, through the transient response experiment of track circuit, it is confirmed that the transmission characteristics of transient signal on rail are consistent with the calculation results in this paper. Finally, the influence of signal frequency, ballast resistance on track surface voltage, and the influence of interline coupling voltage by the conductivity (σ) and the permittivity (ε) are studied. It provides theoretical reference for the anti‐interference analysis of track circuits. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Uncertainty Quantification of the Crosstalk in Multiconductor Transmission Lines via Degree Adaptive Stochastic Response Surface Method

The degree adaptive stochastic response surface method is applied to analyze statistically the crosstalk in multiconductor transmission lines (MTLs). The coefficient of polynomial chaos expansion (PCE) is obtained based on the least angle regression. The truncation degree of PCE is iterated using the degree adaptive truncation algorithm, and the optimal proxy model of the crosstalk of the original MTLs that satisfies the actual error requirements is calculated. The statistical properties of crosstalk in MTLs (such as mean, standard deviation, skewness, kurtosis, and probability density distribution) are obtained. The failure probability of the electromagnetic compatibility in the MTLs system is considered. The global sensitivity indices of crosstalk-related factors are analyzed. Finally, the proposed method is proved to be effective compared with the conventional Monte Carlo method. The uncertainty quantification of crosstalk in MTLs can be calculated efficiently and accurately.

Theoretical Study of Lumped Parameter Circuits and Multiconductor Transmission Lines for Time-Domain Analysis of Electromagnetic Noise

In order to find the origins of electromagnetic noise in the time domain, we formulate a system of lumped parameter circuits and multiconductor transmission lines (MTL). We present a discretized approach to treat any lumped parameter circuits and MTL systems, and the boundary conditions between these systems, where the lumped parameter circuits are described by coupled differential equations, and the MTL systems by coupled partial-differential equations. The introduction of the time-domain impedance and the element matrices enables us to perform a time-domain analysis that includes dependent sources and the coupling devices in the framework of the circuit theory. For three-line systems, we are able to calculate the coupling of the normal, common, and antenna modes, and to find out methods to reduce the noise.

Iterative Solution of MTL Based on the Spatial Decomposition and the Second-Order FDTD

To reduce the computational time for solving multiconductor transmission lines (MTL), an iterative solution with a spatial decomposition and the second-order finite-difference time domain (FDTD) is presented. The coupling effects among the MTL are equivalent by a set of distributed voltage and current sources, which decouples the MTL. The voltages and the currents along the lines are evaluated by the second-order FDTD at each iteration step, and the equivalent distributed sources are updated accordingly. The solution of MTL is obtained when convergence is reached. The proposed approach is validated by the numerical examples. The major advantage of the proposed approach, by nature, is an inherent parallel algorithm, which will reduce the computational time, especially for the MTL system with nonlinear devices.

An improved method for expressing the transient ground resistance of overhead transmission lines by exponential polynomial

In this study, a method is proposed for expressing the transient ground resistance of the overhead transmission lines (TLs) by the exponential polynomial. The relation of the poles due to the rational approximation of the ground resistance between the ground conductivity, permittivity and the line geometry is fully discussed. A concept of ‘normalise poles’ is introduced, which makes it very easy to evaluate the poles according to any ground conductivity, permittivity and line geometrical geometry. A new and easily programmed method is achieved which can overcome the uncertain error caused by the conventional vector fitting method when approximating the ground resistance. Based on this method, a recursive convolution can be achieved for analysing the multi-conductor TLs system, so good efficiency can be obtained. Several examples are provided to demonstrate the validation of the proposed method for evaluating the transient ground resistance with different ground parameters and line geometry, and an application on calculating the lightning induced voltages of the overhead TLs system is also provided.

A rigorous matrix procedure for calculating the line constants and wave parameters of uniform MTLs using SMT/PMU

Summary Real-time monitoring of the operation state of wide-area transmission line links has become possible with the help of phasor meter units. Synchronized information acquired by phasor meter units needs to be adequately processed to permit the accurate estimation of the line constants of the transmission link. In this paper, a novel general rigorous compact procedure for correctly processing the measured voltage and current phasors of uniform multiconductor transmission line systems is proposed. The procedure based on the ABCD matrix and on modal analysis techniques applies to transposed or untransposed multiconductor transmission lines, with arbitrary geometry, number of conductors, and length. The proposed algorithm, adequate for multiport structures, avoids the approximations usually required by ordinary methods mostly focused on lumped parameters and on 2-port approaches. The proposed matrix procedure is illustrated and validated using simulation results.

Passivity enforced circuit model of frequency‐domain responses with source elements

AbstractThis paper presents an equivalent circuit model with source elements for systems containing external field. The coupling effect of the external field is considered with current sources (Is) added to the expression of admittance matrix (Y) of the system. The frequency‐domain responses of Y and Is could be fit to the rational polynomials with vector fitting method and then converted to equivalent circuits with the proposed method. As the dual quantities of Y and Is, the circuit extraction method from Z and Vs is also introduced. Passivity enforcement of the RLC elements in the circuits is realized with the optimization method. A novel circuit structure for the multi‐port system is proposed with this method based on the equivalence of the field‐port coupling and port‐port coupling. The proposed model is demonstrated to be effective to extract the equivalent circuits of the multiconductor transmission line system under an incident wave.

An Efficient Model of the Electromagnetic Field Radiated from Different PLC Configurations

The present work proposes a simplified model to assess the radiation from multi-conductor transmission line systems, without determining the current distribution along the conductors. One is just required to take into account the value of the current and the first two derivatives at the near and far end, respectively. The proposed method simplifies the measurement procedures thus enabling the estimation of some quantities related to hardly accessible or completely inaccessible measurement points, and also accelerating the simulation itself. Furthermore, the current distribution along the wire is carried out by using the Matrix Pencil Method. Consequently, the evaluation of the two first derivatives at the near and far ends is then more accurate.

Modal Analysis of Weakly Coupled Electromagnetic Systems Using Tridiagonal Toeplitz Matrices

In the analysis of weakly coupled electromagnetic systems, consisting of several identical equidistant components, the coupling matrix is often approximated by tridiagonal Toeplitz matrices, whose eigenvalues and eigenvectors can be determined in closed-form. The theory of tridiagonal Toeplitz matrices is not new, it can be found in several linear algebra articles and math books, but its presentation is usually very dense and far from appealing to the electrical engineer. This paper has two goals. The first is of tutorial nature —we present a concise review of the modal analysis of tridiagonal matrices. The second goal is to call the reader’s attention to the inherent fragilities of the tridiagonal matrix approximation —we discuss and work out application examples, dealing with multiconductor transmission line systems, where the approximation is shown to clearly fail.

Application of Stochastic Differential-Algebraic Equations in Hybrid MTL Systems Analysis

The paper deals with the application of stochastic differential-algebraic equations (SDAE) in the field of the time-domain simulation of hybrid (lumped/distributed) systems with randomly varying parameters. A core of the method lies on the theory of stochastic differential equations (SDE) considering the system responses as stochastic processes. However, due to a hybrid nature of the system, namely its lumped parameter part, non-differential (algebraic) parts arise generally in the solution. Herein, multiconductor transmission lines (MTL) play a role of the distributed-parameter parts of the hybrid system. The MTL model is designed as a cascade connection of generalized RLCG T-networks, while the state-variable method is applied for its description. The MTL boundary conditions are incorporated through a modified nodal analysis (MNA) to cover arbitrarily complex circuits. System responses are formed by the sets of stochastic trajectories completed by corresponding sample means and respective confidence intervals. To get the results a weak stochastic backward Euler scheme is used, consistent with the Itô stochastic calculus. All the computer simulations have been performed in the Matlab language environment. DOI: http://dx.doi.org/10.5755/j01.eee.20.5.7098

New circuit theory of multiconductor transmission lines resulting from a new practice of noise reduction

In modern life, we are surrounded by and filled with electromagnetic noise caused by the dominant use of energy in the form of electricity. This situation is brought about by the fact that the noise is not understood theoretically. A new practice of noise reduction was introduced for the construction of Heavy Ion Medical Accelerator in Chiba (HIMAC). The key concept is a symmetric three-line circuit that arranges power supplies, noise filters and magnets around a third central ground line. A continuous theoretical effort forced us to find a new circuit theory involving a multiconductor transmission-line system starting from Maxwell’s equations without any approximation. We discuss the essence of all of these experimental and theoretical developments with the hope to remove unnecessary electromagnetic noise not only from power supplies, but also from all electric devices. The newly derived circuit theory of multiconductor transmission lines is universal, and establishes the validity of the practice of noise reduction.

Efficient Reciprocity-Based Algorithm to Predict Worst Case Induced Disturbances on Multiconductor Transmission Lines due to Incoming Plane Waves

In this paper, an efficient reciprocity-based algorithm is proposed to predict the worst case voltages and currents induced by external plane waves at the ports of a multiconductor transmission-line system. The proposed algorithm consists of two main steps. In the first step, the far-field radiation of the multiconductor transmission-line system is fully characterized by a minimal number of full-wave simulations. In the second step, this information is used to efficiently evaluate the voltages and currents induced by a plane wave with arbitrary angles of incidence and polarization. After this, their worst case values can be easily found. The main advantage of the proposed algorithm is that no new full-wave simulations are required if different incoming plane waves or different sets of terminations at the ports of the multiconductor transmission-line system are to be considered.

Transient analysis of the EM field coupling to multi-conductor transmission lines using the NILT method

A simple and efficient numerical inversion Laplace transform (NILT) algorithm is implemented in MATLAB environment based on the quotient difference method to solve the problem of electromagnetic (EM) field coupling to lossy or lossless multi-conductor transmission lines (MTL) illuminated by an EM incident field. Two major points are treated in this work for the lossy MTL system excited by an incident EM field; the first one is the optimum equivalent circuit taking into consideration the different physical concepts based on the transmission line theory and the second point deals with the choice and implementation of the numerical method for less computing time and for efficient results. In this paper, the effect of the EM coupling is treated and it is based on the superposition effect of each distributed voltage current sources using the NILT numerical method. Results of the near end and far end voltages and currents for an MTL system are presented and displayed for two types of microwave (MW) structures in the time domain for the case of a plane wave excitation. It has been shown that a non-homogeneous MW structure or multilayered system with a specific choice of the dielectric constant has an advantage for less transient EM coupling due to the external EM field.

Modeling Indirect Lightning Strikes for Railway Systems With Lumped Components and Nonlinear Effects

Induced voltages due to lightning strikes along multiconductor transmission line (MTL) systems terminated with different loads at line ends have been widely studied by solving telegraphers' equations using the finite-difference time-domain method. However, MTL systems with lumped series and shunt-connected devices/components along the lines have not attracted much attention. There are methods available for introducing lumped components along MTL systems. In this paper, a method previously developed by the authors will be used to determine induced voltages across transformers connected to the catenary wire and track-circuit relay units along the MTL system representative of a Swedish single-track railway system for the case of indirect lightning strikes. Nonlinearities like soil ionization and insulator flashovers are also considered. It is found that both the nonlinearities and lumped components together dominate the induced-voltage amplitude and wave shapes across devices/components.

Indirect Lightning-Induced Voltages Along a Railway Catenary-Track Multiconductor Transmission-Line System With Lumped Components

Transients caused by field-to-wire coupling due to lightning strikes in the vicinity of multiconductor transmission lines (TL) have been widely studied. In those studies, the lines represent single overhead lines, power lines, and the like with lumped loads/devices at line terminations. In electrified railway power systems, series or shunt devices, such as transformers, converters, switchgear, and signal equipments, are distributed along the TL system. In this paper, the indirect lightning effects on a typical railway catenary-track multiconductor TL system with lumped components, namely, booster and auto transformers (BT and AT systems), and track circuits, are studied. It is found that the induced voltage wave shapes and amplitudes at any point along the line are dominated by BT or AT system type, and that the voltages appearing across AT windings are higher than for the corresponding BT windings. However, the induced voltages across the track circuits are less dependent on system type and most affected by the introduction of components.

A Method for Interfacing Lumped-Circuit Models and Transmission-Line System Models With Application to Railways

Transient analysis of lossy multiconductor transmission lines (MTLs) has been studied using the finite-difference time-domain (FDTD) method with lumped loads/devices connected at line terminations. In electrified railway networks, series and shunt devices (whose circuit models are derived either from experiments/borrowed off the shelf), e.g., transformers, converters, switchgear, signal equipments, etc., are found distributed along the MTL system. To simulate such railway systems involving both transmission lines (TLs) and lumped circuits, an interface technique between TL systems, which is solved using FDTD, and all the lumped circuits, which are solved using alternative transients program/electromagnetic transients program software (circuit solver), is proposed. This sufficiently accurate method is simple to apply as only instantaneous voltages and currents are transmitted between the stand-alone FDTD routine and circuit solver. Moreover, the user avoids coding complex circuit models within the FDTD, while at the same time, efficiently uses the potential of accurate frequency-dependent loss models (nonexistent in circuit software) coded in FDTD. The technique is applied on typical electrified railway systems to demonstrate how traction transformers, track circuits, and line interconnections affect the propagating voltages and currents. The method could be beneficial for transient protection and insulation coordination studies in electrified railway systems.

Convergence of Transverse Waveform Relaxation for the Electrical Analysis of Very Wide Transmission Line Buses

In this paper, we study the convergence and approximation error of the transverse waveform relaxation (TWR) method for the analysis of very wide on-chip multiconductor transmission line systems. Significant notational simplicity is achieved in the analysis using a splitting framework for the per-unit-length matrix parameters of the transmission lines. This splitting enables us to show that the state-transition matrix of the coupled lines satisfies a linear Volterra integral equation of the second kind, whose solution is generated by the TWR method as a summable series of iterated kernels with decreasing norms. The upper bounds on these norms are proved to be O(k r/r !), where r is the number of iterations and k is a measure of the electromagnetic couplings between the lines. Very fast convergence is guaranteed in the case of weak coupling (k Lt 1). These favorable convergence properties are illustrated using a test suite of industrial very large scale integration global buses in a modern 65-nm CMOS process, where it is shown that few ( ap 3) Gauss-Jacobi iterations are sufficient for convergence to the exact solution.

Topological realizability conditions and their interpretation for admittance matrices of an MTL system with mode delays

In a previous study by the authors regarding passive multiconductor transmission line (MTL) system quasi-TEM mode delay, we encounter longitudinal immittance matrix functions (LIMFs) whose behavior initially appears problematic, yet they are shown to be passive. This paper addresses the constraints on the realization of the admittance matrix and the physical interpretation of the realized circuits in the passive, common-ground microstrip system.