Multiconductor Transmission Line Theory Research Articles

Analysis and Simulation Test of Electromagnetic Disturbance Mode Conversion in Secondary Circuit of Substation

Under ideal conditions, the electromagnetic interference experienced by the secondary circuit is manifested as a common mode. However, due to circuit imbalance, common mode disturbance is converted into differential mode disturbance, thereby presenting a danger to the normal functioning of secondary equipment. The investigation measured the distribution ratio of common mode voltages and differential mode voltages at the ports of secondary equipment during switching operations. A computational circuit model of the secondary circuit was established by using multi-conductor transmission line theory. The mechanisms and influencing factors of transformation from common mode to differential mode were analyzed, and a simulation test was carried out in a substation to explore the conversion law under impedance imbalance. The results showed that the differential mode voltage of the secondary equipment port was greater than the common mode voltage when the circuit breaker was in operation. Common-differential mode conversion in the secondary loop was predominantly caused by an imbalance in circuit structure and extraneous parameters. Differential mode disturbance generated by switch field side imbalance had a greater impact than that generated by protection chamber side imbalance. As the degree of imbalance increased, the differential mode voltage also increased.

Rapid Analysis of Bent Cable Crosstalk Based on Numerical Calculation

In this paper, a fast prediction method of cable crosstalk is introduced, which can simulate the crosstalk problem more accurately in the actual cable situation. The traditional flexible cable model considers few factors to truly reflect the spatial pose of the cable. In this paper, constraints of the assembly space are considered to truly reflect the structural characteristics of the cable, providing a theoretical basis for cable bundle layout in the virtual environment. Based on the element method and the theory of multi-conductor transmission lines, the crosstalk coupling model of curved cable is established. In this model, the traditional multi-conductor transmission line theory is improved, and the bending cable bundle model is divided into several equivalent subsegments by using the element method. In the subsegment, the multi-conductor transmission line theory is used for modeling, and the chain parameter method is used for crosstalk coupling analysis. The accuracy of the model introduced in this paper is verified by MATLAB and CST Studio simulation.

Uncertainty Quantification Method of Crosstalk Involving Braided-Shielded Cable

In this paper, in view of the uncertainty of geometric parameters of braided-shielded cable and structural parameters of the shield in practical problems, polynomial chaos expansions (PCE) is used to explore the uncertainty quantification of a crosstalk calculation model of braided-shielded cable. First, the model based on multi-conductor transmission line theory is expanded by PCE. Second, the truncation degrees of polynomials and sample size of PCE are determined by the leave-one-out method, and the statistical characteristic parameters of crosstalk are obtained by combining coefficients of polynomials. Compared with the calculation results of the Monte Carlo method, the mean value, standard deviation and probability density function obtained by the two methods are basically consistent, but the PCE method has obvious advantages in calculation efficiency. Finally, the influence of input variable parameters in the crosstalk calculation model of braided-shielded cable are calculated by combining the PCE and the Sobol’s global sensitivity analysis method, which provides theoretical guidance for the electromagnetic compatibility design of electrical and electronic equipment using braided-shielded cable.

A novel fault monitoring method based on impedance estimation of power line communication equipment

Due to the close relationship between power grid fault and impedance, there is a significant defect in the use of power line communication (PLC) equipment to monitor and locate power grid faults, which is the lack of real-time impedance information. Therefore, this study proposes a new fault monitoring method based on impedance estimation of power line communication equipment. The channel frequency response (CFR) obtained from the PLC receiver is used to estimate the high-frequency input impedance to monitor and locate the ground fault of the power grid in real time. Firstly, based on the multi-conductor transmission line theory, bottom-up channel modeling method and impedance estimation technology, the basic principles of fault monitoring and location methods are clarified. Then, modeling and analysis of cables in different situations are carried out, and the characteristics of the factors affecting the impedance in CFR are extracted by variational modal decomposition (VMD), and the estimation results of impedance are obtained by inversion analysis. Based on this, the impedance change and machine learning algorithm are used to track and identify the abnormal state of the power line to achieve high-sensitivity positioning of the cable fault. The simulation results show that the method has a good identification effect on high and low impedance cable fault, and has a better effect on low resistance fault monitoring. The fault location error is less than 2.13%, and has a good positioning accuracy.

Electromagnetic Transients in Multiconductor Transmission Lines

The theory of multiconductor transmission lines is based on the principle of superposition. According to this principle, any electric or magnetic field can be represented as the sum of individual electric or magnetic fields. This theory is used to analyze and design electrical systems involving multiple conductors. In this work, the procedures for analyzing electromagnetic transients in 3-conductor transmission lines are presented, which is the last step for generalization in the case of lines to “n” conductors. The paper presents elementary cases and a more general one to illustrate such an approach.

Time-Domain Coupling Model for Nonparallel Frequency-Dependent Overhead Multiconductor Transmission Lines Above Lossy Ground

Expansion of power grids has resulted in the construction of multiple transmission lines within constrained spaces inevitably making them nonuniform in nature. Existing transmission line models available in electromagnetic transient (EMT) simulators are based on classical multiconductor transmission line (MTL) theory with the assumption that the transmission lines are infinitely long and have uniform cross-sectional dimensions. This paper develops a time-domain model, namely dispersive scattered field transmission line (DSFTL) model, for multiconductor dispersive nonuniform overhead transmission lines above lossy, frequency-dependent ground. The proposed model which consists of closed-form equations in the time-domain has been implemented using a modified finite-difference time-domain (MFDTD) algorithm and integrated into an EMT simulator (PSCAD/EMTDC). Results have been compared with and verified by those obtained using a full-wave approach and measured data available in the literature. Simulations of nonuniform structures that include nonlinear components (such as breakers) have also been carried out under fault conditions.

A mathematical method for local defects and faults identification of 10 kV three‐core cable based on input impedance spectrum

Due to the strong coupling among the conductors of 10 kV three-core armored cables and the difficulty in identifying its defects and fault types, a method is proposed based on the input impedance spectrum. Firstly, the phase mode transformation matrix of a three-core cable is obtained by combining the multi-conductor transmission line theory with the loop analysis method to realize decoupling between conductors. Secondly, the input impedance matrices of a cable under different situations are derived. Based on this, a method is proposed to identify the local defects and fault types. The capacitive defects and inductive defects are identified according to the left or right offset of the amplitude spectrum; the short circuit and break faults of the cable can be identified according to the number of resonant points in the amplitude spectrum and the initial phase angle of the phase spectrum. Finally, to verify the correctness of the proposed method, a 10 kV three-core cable is taken as an example to carry out PSCAD circuit simulation and practical test. The results show that the proposed method can effectively identify the local defects and fault types of the three-core cable.

Analysis of Transient Response of ZPW-2000A Jointless Track Circuit Considering Frequency Variation.

In order to accurately analyze the influence of electromagnetic transient signals on the jointless track circuit when the electromagnetic transient signal propagates in the rail, it is necessary to consider the frequency-variable load terminated in the ZPW-2000A jointless track circuit and the frequency-variable loss inside the rail. A method is proposed for calculating the transient response of transmission lines system with frequency-variable end load of jointless track circuit. Firstly, the transmission lines model of jointless track circuit is established, based on multiconductor transmission lines theory, the model equation is deduced and discretized by finite difference time domain (FDTD). The vector fitting method is used to express the admittance of the tuning region in the track circuit, and the rational approximation function of the tuning region is derived from the poles, residues, and constants. The voltage and current at nodes in the tuning region are calculated by piecewise linear recursive convolution algorithm. Combined with the discrete transmission line equation, the current and voltage expression of the transient electromagnetic signal at the receiving end of the track circuit in time domain is obtained. Compared with state variable method, the error is less than 6%, which verifies the correctness of the proposed method. Finally, this paper studies the influence laws of different factors on the overvoltage at the receiving end of jointless track circuit and the weak links of jointless track circuit under the influence of transient electromagnetic signal. It provides theoretical reference for fault research and anti-interference analysis of ZPW-2000A jointless track circuit.

Application of the Transfer Matrix Approach to Direct Lightning Studies of Overhead Power Lines With Underbuilt Shield Wires—Part I: Theory

This work is devoted to the analysis of voltages produced on overhead distribution lines hit by direct lightning. We will consider arbitrary terminations at both line ends and, also, arbitrary positioning of the pole being struck. We will deal with lines protected by shield wires, placed either above or below the phase conductors. The analytical tools chosen to deal with such complex system are the transfer matrix method and the theory of multiconductor transmission lines with periodic grounding. The innovation of an artificial symmetrical unit cell has been introduced to eliminate the need of two characteristic wave impedance matrices and to ease computation flow.

Research on Radiated Disturbance to Secondary Cable Caused by Disconnector Switching Operation

With the development of smart grids, the application of localized relay protection devices has greatly reduced the distance between the secondary equipment and the primary equipment. The secondary equipment will be in a more complex electromagnetic environment during the operation of the GIS disconnector. The present study takes the multi-path electromagnetic disturbance on the secondary cable caused by the disconnector switching operation of the domestic 1000 kV ultra-high voltage GIS test circuit as the research background, solves the field-line coupling problem based on the finite integral technique, and combines the multi-conductor transmission line theory to solve the radiation disturbance and obtains its influencing factors. The results demonstrate that the radiated disturbance accounted for 16% of the overall electromagnetic disturbance when both ends of the shielding layer are grounded. The use of grounding at both ends of the shielding layer, reducing the height of the secondary cable wiring, avoiding the parallel arrangement of the secondary cables and the GIS pipe mother, and installing a low-pass filter, have different levels of suppression effects on electromagnetic disturbances. The research results will guide the reasonable arrangement of secondary cables in GIS substations to some extent and have reference significance for the protection of secondary equipment.

Protection of distribution overhead power lines against direct lightning strokes by means of underbuilt ground wires

In the present work we assess the lightning performance against direct strokes of overhead distribution lines, making use of the theory of multiconductor transmission lines with periodical grounding, recently developed by the authors. We assume that the lightning protection is provided by shield wires that are placed both above and below (underbuilt construction) the phase conductors. We adopt the transmission line model to include the propagation effects on the poles. We investigate the effects of geometrical parameters, and, by the analyses of different arrangements, we evaluate the impact on the lightning performance. The core of the work is the demonstration that addition of underbuilt ground wires can be a viable solution for improving the lightning protection of distribution lines.

Modelling of partial discharge pulse propagation in transformer windings using multi conductor transmission line modelling scheme

Power transformers are considered as an essential component in the electric power systems. They are placed in services in different circumstances like electrical, environmental and mechanical stresses, and through the progress of operation it can affect with various threats and hazards. Transformer failure should be diagnosed earlier in order to avoid its unsafe and unstable operation. The main reason for failure of insulation in power transformer is due to partial discharges. The partial discharge activity occurring in the transformer have to be identified earlier, afore it progresses into a complete discharge, otherwise it results in the maintenance of the device and causes loss of economic cost to the utilities. In this paper, multi conductor transmission line theory is used for the modelling of transformer windings and the partial discharge pulse propagation through the winding is simulated in the MATLAB Simulink. The effect of partial discharge on the windings are also discussed.

Signals Passing Through Asymmetric Faults in Transmission Lines

Unexpected results have been seen in multiple papers involving spread spectrum time domain reflectometry (SSTDR) measurements on twin lead cables with one line containing a fault. A small portion of the signal is able to transmit past the fault, reflect off the end of the cable, return back through the fault, and be recorded by the SSTDR. This paper explains the physics of why this can happen, and the effect of nearby ground planes. The transmission through the fault involves electric and magnetic fields coupling to nearby conductive objects. This coupling allows for a small amount of signal to move beyond the fault. We use multi-conductor transmission line theory to explain this effect. A finite difference time domain simulation of the multi-conductor system is compared to measured results to demonstrate why this effect occurs, and the effect of the nearby ground.

Application of the Transfer Matrix Approach to Direct Lightning Studies of Overhead Power Lines With Underbuilt Shield Wires—Part II: Simulation Results

This work investigates voltages on overhead distribution lines produced by direct strokes, protected by shield wires, placed both above and below phase conductors. An improved formulation based on transfer matrix method and theory of multiconductor transmission lines with periodic grounding allows to eliminate the need of two characteristic wave impedance matrices. Based on the theoretical formulation developed in the first part of this work, as well as on the models there presented for the pole and grounding systems, we report here a wealth of simulation results concerning the line overvoltages subsequent to a pole being hit by lightning. Results are discussed considering a variety of factors, namely, position of the victim pole, type of load at both ends of the line, presence or absence of underbuilt shield wires, waveform of the lightning current, soil parameters and parameters of the frequency-dependent impedance of the pole grounding system. The good performance of the developed method is assessed by comparing our results with some EMTP-RV simulations. The transfer matrix method is then used to show the effect of shield wires in conjunction with periodic grounding: we assess the effects of terminations, frequency dependent models of the pole footing and grounding systems and frequency dependent models of lossy ground.

Prediction and Suppression of Twisted-wire Pair Crosstalk Based on Beetle Swarm Optimization Algorithm

Based on the theory of multi-conductor transmission lines (MTL), this paper proposes a new method for predicting and suppressing crosstalk of twisted-wire pair (TWP). The per unit length (p.u.l) RLCG parameters change caused by the inconsistent cross-sectional shape of TWP, changes in parameters make it difficult to solve the telegraph equation. In this paper, the method of transmission lines cascade is used. TWP is divided into several segments, and p.u.l parameters of each segment are predicted. Compared with before method, we propose a higher precision algorithm—beetle swarm optimization (BSO) to optimize the weights of back-propagation (BP) neural network, which predict p.u.l parameters at each segment. On this basis, it is divided into two steps: 1) Use MTL frequency domain method combined with lines’ terminal conditions to solve crosstalk and compare with CST simulation results; 2) Use the singular value decomposition (SVD) method to add matrix modules at both ends of lines for suppressing crosstalk. The results show that proposed method in this paper is consistent with the simulation, and the accuracy is higher than before

Investigation of cable influence on the interturn transient voltage distribution in rotating machine windings using a three-phase model

Turn-to-turn and turn-to-ground transient voltages due to the surges which arrive at rotating machine terminals shall be known as exactly as possible to optimize the insulation design. Normally these overvoltages are obtained by Multiconductor Transmission Line Theory using only part of one phase of the stator winding by applying a surge at the line-end coil. Moreover, many works consider the feeding cable to analyze only the voltage at machine terminals by using a simple model for the motor. This paper analyses the influence of the cable length on the transient voltage distribution inside the machine by numerical simulations using a three-phase model for the machine windings. The results are obtained by a cable-motor model using Finite Elements Method (FEM). The model couples the transient magnetic fields solved in a 2D geometry with electric circuit elements. Results show that the cable length has influence on the transient voltage distribution, especially for the line-end coils from the phase where the surge has been applied to.

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.

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.

MTL-based modeling and analysis of the effects of TSV noise coupling on the power delivery network in 3D ICs

With the application of heterogeneous integration and advanced packaging technologies, the use of through-silicon vias (TSVs) to deliver the power supply has become popular in the design of stacked chips in three-dimensional integrated circuits. High-density vertical interconnections offer higher speed and bandwidth, but the electromagnetic coupling effect among TSVs becomes more serious. Therefore, investigation of the noise coupling among TSVs and analysis of its impact on the power supply become important considerations. An analytical model based on the theory of multiconductor transmission lines (MTLs) is presented herein to discuss such TSV noise coupling. The method can accurately and quickly estimate the noise coupling coefficient among a large number of TSVs and offers good practicability for similar structures and even the TSVs of complex structures. Further, the influence of TSV noise coupling and simultaneous switching noise from switching circuits on the supplied power voltage is discussed. Finally, the parameters of an actual Intel chip are taken as an example to analyze the supplied power voltage that reaches complementary metal–oxide–semiconductor (CMOS) circuits through the three-dimensional (3D) power distribution network after considering the power supply noise. The presented model is validated by comparing the calculation results with those obtained from a full-wave simulator. The runtime and memory consumption requirements are lower than those of the full-wave simulator.

Time-Domain Modeling of Field-to-Wire Coupling in Obliquely Oriented Multiwire Cables With Junctions Using JEMS-FDTD

Multiwire cable bundles located inside electrically large objects play a crucial role in ensuring their electromagnetic safety. The cable bundles are seldom parallel to the Cartesian coordinates and, hence, they are difficult to handle by using the finite-difference time-domain (FDTD) algorithm. Our motivation in this article is to develop an efficient time-domain field-to-wire coupling model for obliquely oriented multiwire cables with junctions, based on the multiconductor transmission line theory. The multiconductor transmission line equations are discretized by using the 1-D FDTD method. The distributed sources on the cables are obtained by adopting an interpolation technique. The junctions are handled by making use of three theorems. The per-unit-length parameters are extracted by solving an electric field integral equation using the 2-D method of moments. The proposed model has been incorporated into the 3-D full-wave in-house solver J Electromagnetic Solver-FDTD (JEMS-FDTD) to efficiently model the induced effects on the cable bundles located inside electrically large objects illuminated by an external electromagnetic field. To validate the accuracy of the algorithm, the induced currents on a five-wire cable bundle are derived and compared with those obtained from a commercial software. Additionally, the proposed methodology is applied to simulate the induced currents on a seven-wire cable bundle inside a vehicle illuminated by a plane wave.