Multiconductor Transmission Lines Research Articles

Исследование методов построения адаптивных сеток при квазистатическом анализе многопроводных линий передачи методом моментов.

The features of the quasi-static analysis of multiconductor transmission lines by the method of moments, based on the calculation of the matrices of the primary per-unit-length parameters of the line, are described. A brief overview of methods for adaptive mesh refinement is given. Comparison of their efficiency is carried out on the example of calculating capacitive matrices of various multiconductor transmission lines. The optimal values of the parameters methods which reduce computation costs are determined. It is shown that their use gives a significant increase in performance in the multivariate analysis of multiconductor transmission lines relatively to fine uniform meshes.

A Node-to-Node Admittance Functions Implementation of an Improved Frequency Dependent Multiconductor Transmission Line Model

The electromagnetic interference (EMI) performances of the interconnects and cables can be predicted via a standard multi-conductor transmission line (MTL) model, while the latter is not valid for the evaluation of power rail collapse and ground bounce responses. To circumvent the limitations, a more general and feasible improved MTL representation is presented in this paper. It physically incorporates the partial resistance and partial inductance parameters of all signal and reference conductors. To consider the frequency dependent behavior of the per-unit-length (PUL) electrical parameters in time domain simulations, a terminal description for this improved MTL model with any desired length is demonstrated. Subsequently, an equivalent node-to-node admittance functions (NAFs) implementation for this terminal representation is carried out. The correctness and effectiveness of the NAFs circuit model in time domain is then numerically validated by analyzing two dedicated examples.

基于CUDA的多导体传输线方程迭代QR分解的并行算法

基于CUDA的多导体传输线方程迭代QR分解的并行算法

Comparing the New Improved RLC and CMTL Models for Measuring Partial Discharge in Transformer Winding

Nowadays, one of the most well-known methods for accurate simulation of the fast-transient phenomenon as well as the study and location of partial discharge (PD) in transformer windings is the method based on winding modeling. In this regard, the circular multi-conductor transmission line (CMTL) model, which is an improved model of the MTL model, has been proposed as the finest solution since it is acceptable in an extensive frequency range and it can investigate the effect of winding rotation by considering the radius and angle variables. However, one of the fundamental problems of using the CMTL model is that a set of large equations, known as complete admittance matrices, must be solved for all winding turns, which typically contain thousands of turns. To overcome this problem, we presented an improved RLC model, which has the same accuracy as the CMTL model in terms of frequency validity range and less computational complexity. In this model, the variables of length and curvature of the turns are also considered in the formulations. Although this method is theoretically accurate, its reliability method must also be determined in practice and how the PD signal propagation must be carefully considered due to the problems in high-frequency modeling of the winding. Numerical analyses and laboratory measurements resulting from the use of PD pulses on a 20 kV winding of a distribution transformer, as well as a 63 kV, 30 MV winding, revealed that a valid frequency range is extendable up to 5 MHz for the proposed improved model without a significant increase in computational complexity.

Modelling of Transmission Lines Inside Modern Integrated Semiconductor and Test Boards

The main purpose of this paper is to present the methodology for calculating the electromagnetic behaviour of real integrated circuit (IC) parts using a no-mesh local Finite Differential Method (FDM). Furthermore, the comparison of computational results and measurements is presented. All considerations are based on typical long transmission lines (TLs) in modern ICs. The obtained results have been analysed in detail and compared with measured values. The measurement data are de-embedded using the test board model. This problem is illustrated in this paper based on a practical example of the Multi-Conductor Transmission Lines test structure whose electrical responses to various excitations are presented and analysed in detail.

An efficient time-domain method for the electromagnetic transient response of multiconductor transmission lines excited by an electromagnetic field

An efficient time-domain method based on the waveform relaxation with transverse partitioning (WR-TP) techniques and the delay extraction passive compact circuit (DEPACT) macromodel is presented for evaluating the electromagnetic (EM) transient response of multiconductor transmission lines (MTLs) excited by an external EM field. Firstly, the equivalent distributed sources due to the tangential components of the electric field are introduced into the MTLs equations. Then, the TLs are divided into a cascaded of DEPACT subnetworks, where the telegrapher’s equations of lossless TLs are decoupled by applying the WR-TP techniques. And the relaxation sources over the lossy TLs are updated by using the waveform scaling algorithm, which can completely avoid performing the numerical convolution. Finally, the equivalent circuit is established and the transient responses induced on the lines can be obtained by using the circuit simulation software PSCAD.

A Method for Diagnosing Soft Short and Open Faults in Distributed Parameter Multiconductor Transmission Lines

This paper aims to develop a method for diagnosing soft short and open faults occurring in a distributed parameter multiconductor transmission line (DPMTL) terminated at both ends by linear circuits of very high frequency, including lumped elements, which can be passive and active. The diagnostic method proposed in this paper is based on a measurement test performed in the AC state. To write the diagnostic equations, the DPMTL is described by the chain equations in the frequency domain. For each considered fault, the line is divided into a cascade-connection of two lines, and a set of the diagnostic equations is written, taking into account basic circuit laws and the DPMTL description. This set includes nonlinear complex equations in two unknown real variables consisting of the distance from the beginning of the line to the point where it occurs and the fault value. To solve these equations, a numerical method has been developed. The procedure is applied to the possible soft shorts that can occur between all pairs of the line conductors, and the actual fault is selected. The method has also been adapted to the detection and location of open faults in DPMTL. Numerical examples, including three-conductor and five-conductor transmission lines, show that the diagnostic method is effective and very fast, and the CPU time does not exceed one second.

Lightning analysis of adjacent grounding systems using multi-conductor transmission line method

The analysis of adjacent grounding systems under lightning currents which is responsible for many safety problems to human beings and damages to devices is very important. In this study, the behaviours of such grounding grids under lightning conditions which are not well documented in the literature are analysed using the multi-conductor transmission line method in a two-layer soil model. To achieve this goal, the expressions related to the study of a single grounding grid extracted from the recent study of the authors are developed to be appropriate to the analysis of adjacent grounding systems under lightning currents. Also, through the representation of the connectivity matrix, the analysis of the adjacent grounding grids with any size and degree of complexity is facilitated. Furthermore, the behaviours of the adjacent grounding grids under different lightning and soil characteristics are examined and some conclusions are derived.

Multiconductor Transmission Line Modeling of Crosstalk Between Cables in the Presence of Composite Ground Planes

Modern transportation systems, such as aircraft, are increasingly replacing metal body parts for composite materials, such as carbon-fiber reinforced plastics. Despite the multiple advantages in terms of weight, size, and fuel consumption, this trend is posing a challenge for protection of cables against electromagnetic interference. Early risk assessment and optimization of cable design in modern aircraft require reliable methods that can quickly and accurately estimate crosstalk behavior in the presence of lossy ground planes. This article presents two novel methods to incorporate such lossy ground planes into the crosstalk modeling of cable bundles. The first method considers the ground plane as a discrete collection of cylindrical conductors. In the second method a ground impedance matrix is derived for lossy ground planes with a finite thickness. Results of both methods are compared to full-wave simulations and measurements, yielding excellent results in terms of accuracy and computation times. The discretized ground plane method is also applied to the case of wire pairs that are enclosed by two ground planes, both aluminum and carbon–fiber reinforced plastic, as a first step towards investigation of wiring that is embedded in thermoplastic material. Once more simulations and measurements are in good agreement.

Analysis of Multiconductor Transmission Lines Using the CN-FDTD Method

The Crank–Nicolson (CN) version of the finite-difference time-domain (FDTD) method is applied to the analysis of multiconductor transmission lines (MCTLs). Stability and dispersion issues are investigated for different cases, including single and multiconductor lossless and lossy lines. It is shown that for MCTLs, stability of the CN-FDTD method is conditioned by the structure of coupling matrices. Sufficient conditions for unconditional stability are derived. Four practical problems are analyzed using the CN-FDTD method and the results are compared to measurements and Leap-Frog method. For the first three cases, it is observed that using the CN method, the Courant number can be increased by the factor of 50 with good agreement with measurement results.

Stable thin‐wire model of buried pipe‐type power distribution cables for 3D FDTD transient simulation

Underground cables such as pipe-type cables are widely used in urban power industry. In this study, an advanced thin-wire model of the pipe-type cables is 3D FDTD simulations. In this model, the multi-conductor cables are represented with two-level transmission line equations. A stabilising technique with a 1D spatial low-pass filter is proposed to maintain computational stability. Frequency-dependent losses are fully considered by using a vector-fitting technique. The proposed thin-wire model is validated with the multi-conductor transmission line theory analytically and the traditional FDTD method numerically. Good agreements are observed. It is found that the simulation maintains stability for 360,000-time steps. Compared to the traditional FDTD method, the memory space and computation time of the proposed model can be reduced by 73% and 98%, respectively. Induced lightning currents in a cable connection station are analysed. It is found that, without considering soil ionisation and soil stratification, the peak current in the metallic armour is 1.54 times as much as the one with considering these non-linear effects. It can be reduced by 9.04% and 18.6% if the cable is buried at depths of 1 m and 1.5 m, compared with the case of a 0.5 m buried depth.

Imbalance difference model for prediction of unintentional radiated emission from 10-wire power cable using for power line communication

Electromagnetic fields unintentionally radiated from power-line communications used in factories interfere with wireless communications. It is important to distinguish the mechanism of this undesired and unintentional radiation from that of wired communication as it affects wireless communications. In particular, unintentional radiated emissions should be reduced in order to construct a stable wired/wireless communication network. This paper focuses on power-line communication as it is used in a factory. The power distribution network in the factory consists of multiple cables bundled together. The effects of cables other than the power cable that applies the communication signal to the radiated electromagnetic field are investigated. Some of the signal power reaching the reciever is converted into common-mode current by an imbalance mismatch. The common-mode current is one of the main causes of unwanted electromagnetic radiation. To predict this conversion, an imbalance difference model is created to account for multi-conductor transmission lines such as those in the power distribution network of the factory. The proposed model can calculate the amount of common-mode excitation associated with changes in the load condition of the power lines. To verify the proposed method, the authors measured the change in common-mode current due to the difference in pairs of power lines to which the signal is applied. The calculation using the proposed model could estimate the amount of reduction in common-mode current to within an error of 1 dB.

Predicting formulae for effective length of counterpoise wires buried in ionized, dispersive and inhomogeneous soils

PurposeThe purpose of this paper is to investigate the ionization and dispersion effects in combination with the inhomogeneity of soil simultaneously on the effective lengths of counterpoise wires.Design/methodology/approachImproved multi-conductor transmission line model is used for computing effective length of counterpoise wires considering all aspects of soils.FindingsThe simulation results show that the ionization and dispersion effects simultaneously results in placing the effective length between situations where only one effect is considered. Also, predicting formulae for effective length of counterpoise wires considering all effects are proposed.Originality/valueA sensitivity analysis on the effective lengths of counterpoise wires considering all aspects of soils is carried out.

The electromagnetic interferance caused by high voltage power lines along the electrical railway equipment

The identification of risks linked to electromagnetic compatibility (EMC) in the electric railway is a major concern in identifying EMC problems and analyzing the unintentional various external disturbing sources as well as the probability of occurrence of interference, the level of interference along the railway system. The purpose of this analysis is to determine the electromagnetic interaction coupling generated by the high voltage (HV) lines located along the railway line by analyzing the voltage induced in the signaling transmission cables such as the European rail traffic management system/European train control system (ERTMS/ETCS) through the multi-conductor transmission line (MTL) theory which may have an impact on the transmitting information. Dubanton method and approximate calculation will be applied and simulated through COMSOL Multiphysics tool in order to analyze if the protection distance and coupling conditions are respected by the railway standards.

Performance analysis of mixed CNT bundle interconnects at 10 nm technology

In recent past, the cross-coupling crosstalk becomes a dominating factor due to the closer proximity of wire that reduces the performance of coupled interconnects at lower technology. To overwhelm interconnect problems, this work demonstrates a comprehensive study of unshielded and active shielded spatially arranged mixed carbon nanotube (CNT) bundle (SMCB) and randomly distributed mixed CNT bundle (RMCB) interconnects at 10 nm technology. Using a driver-interconnect-load setup, a unique multi-conductor transmission line and an equivalent single conductor model is proposed considering the impact of different CNT diameters with their associated line and coupling parasitics. A resistive and CNT field-effect transistor (CNTFET) driver model is considered at 10 nm technology to demonstrate the impact of single line delay, cross-coupling delay, and power dissipation for the densely packed bundle at global lengths. It is observed that a CNTFET-based realistic RMCB exhibits on an average 29.19 and 39.56% reduced single line delay and power dissipation, respectively compared to different SMCB configurations at 700 µm interconnect lengths. Moreover, a shielded RMCB encouragingly provides an improved immunity of cross-coupling impact for the on-chip interconnects at 10 nm technology. Therefore, from fabrication and modelling aspects, a randomly distributed MCB can be proved as emerging interconnect for next-generation on-chip applications.

Multiconductor Transmission Line Model for an Antenna With High-Impedance Ground Plane

We present a circuit model for an antenna above a 2-D high-impedance surface (HIS) ground plane with an arbitrary number of rows. Multiconductor transmission lines model coupling in the joint antenna and HIS structure. Discontinuities are modeled as circuit elements using closed-form expressions. One 2-D electromagnetic simulation is used to extract the per-unit-length capacitance parameters of the multiconductor transmission line structure. Input impedance predicted by the transmission line model agrees with full-wave simulations from low frequencies to above the second series resonance of the structure. The rms error in predicted $S_{11}$ of two example structures with respect to HFSS simulation is reduced by a factor of more than 2.5 compared to our previous work.

Modal waves in multiconductor transmission lines by using fundamental matrix response

The differential equations that model voltage and current for a multiconductor transmission line are written in matrix form. Supposing a time exponential solution through of the modal analysis the modal waves are obtained and solution of a ordinary matrix differential equation, thus determining the amplitude for voltage and current. The modal waves are given in terms of the fundamental matrix solution associated to the ordinary matrix differential equation. The decomposition of the modal waves in forward and backward propagators are used for determine the reflection and transmission matrices for junction in transmission lines. Circulant symmetric transmission lines are discussed, case in that the values for the self-impedance are the same as well as the mutual-impedance values and the same considerations to the admittance matrix. In particular, for these transmission lines are characterized the propagation constants and is observed that the number of multiconductors has effects only on a specific propagation constant. Numerical example of one multiconductor transmission line is presented allowing to observe important aspects of the methodology developed.

Alternative method using recursive convolution for electromagnetic transient analysis in balanced overhead transmission lines

This study proposes an alternative method to calculate the transient responses of multi-conductor overhead transmission lines based on ABCD representation, recursive convolutions and numerical method for rational approximation in the frequency-dependent curves. In the classical universal line model, the characteristic admittance matrix Y c ( ω ) and propagation matrix H ( ω ) are represented by rational functions. In H ( ω ) , previous and correct identification of the modal travelling times is required. However, these modal travelling times are estimated numerically, which do not offer good accuracy in some cases. This fact has a considerable effect on the rational representation of H ( ω ) itself and consequently on the transient responses. In the alternative method, a previous estimation of the modal travel times is unnecessary because when using the ABCD representation for each propagation mode, a direct relation exists between the currents and tensions of the receiving and sending ends. These relationships are fitted by smooth rational functions, and then, using recursive convolution methods, the authors obtain the explicit equations of the currents and voltages to calculate the transient responses. The results demonstrate that the alternative method is accurate when compared with the frequency-domain solution of the transmission line transformed to the time domain using the numeric Laplace transform and with the Bergeron method.

Extraction of winding parameters for 33/11 kV, 30 MVA transformer based on finite element method for frequency response modelling.

This paper proposes an alternative approach to extract transformer’s winding parameters of resistance (R), inductance (L), capacitance (C) and conductance (G) based on Finite Element Method (FEM). The capacitance and conductance were computed based on Fast Multiple Method (FMM) and Method of Moment (MoM) through quasi-electrostatics approach. The AC resistances and inductances were computed based on MoM through quasi-magnetostatics approach. Maxwell's equations were used to compute the DC resistances and inductances. Based on the FEM computed parameters, the frequency response of the winding was obtained through the Bode plot function. The simulated frequency response by FEM model was compared with the simulated frequency response based on the Multi-conductor Transmission Line (MTL) model and the measured frequency response of a 33/11 kV, 30 MVA transformer. The statistical indices such as Root Mean Square Error (RMSE) and Absolute Sum of Logarithmic Error (ASLE) were used to analyze the performance of the proposed FEM model. It is found that the simulated frequency response by FEM model is quite close to measured frequency response at low and mid frequency regions as compared to simulated frequency response by MTL model based on RMSE and ASLE analysis.

Determining the exact location of partial discharge in coil insulation of high-voltage machine using high-frequency model of the machine

The current study is aimed at investigating the exact location of partial discharge (PD) in coil insulation of a 6 KV/250 KW induction machine. Since measured PD signals have frequency components of kilohertz (KHz) to megahertz (MHz), it is necessary to employ fast and very fast transient models of electrical machines for locating PDs. In this study, a PD current pulse with MHz frequency component is injected to the multi-conductor transmission line model of each turn of the coil with frequency validity of >1 MHz. Considering coils as an interface between voltage source and finite element region, all circuit and field equations are rewritten to obtain the system final matrix, so that PD pulse is extracted. Experiment and simulation results show high accuracy of developed model to determine the exact location of PD.