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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. [ABSTRACT FROM AUTHOR]

As technology advances, processor speeds are increasing at a rapid pace and digital systems require a significant amount of data bandwidth. As a result, careful consideration of signal integrity is required to ensure reliable and high-speed data processing. Crosstalk has become a vital area of research in signal integrity for electronic packages, mainly because of the high level of integration. Analytic formulas were analyzed in this study to identify the features that can predict crosstalk in multi-conductor transmission lines. Through the analysis, five variables were found and obtained a dataset consisting of 302,500, data points. The study evaluated the performance of various regression models for optimization via automatic machine learning by comparing the machine learning predictions with the analytic solution. Extra tree regression consistently outperformed other algorithms, with coefficients of determination exceeding 0.9 and root mean square logarithmic errors below 0.35. The study also notes that different algorithms produced varied predictions for the two metrics. [ABSTRACT FROM AUTHOR]

The coupling of electromagnetic pulse (EMP) with the star‐quad cable having reference conductor is analyzed by using the proposed model, which is based upon multi‐conductor transmission line theory. Expressions for common‐mode (CM) and differential‐mode (DM) currents are developed. Two cases are mainly discussed: the first case is the star‐quad cable with a central reference conductor, and the second case with the outside reference conductor. A rigorous comparison between these two cases shows that when the reference conductor is placed at the center, the magnitude of CM current is reduced dramatically, which is beneficial for electromagnetic compatibility (EMC). The CM current magnitude of the outside reference conductor is relatively very high due to the large CM current loop area, which is the least possible for the central reference conductor. There is no significant change in the DM current magnitude for both cases because the DM current has no direct dependence on the CM current loop area. A commercial software, FEKO, which utilizes the method of momentum (MoM), is used to compare the results of our proposed method, which are in good agreement. [ABSTRACT FROM AUTHOR]

High operating frequency is an enabler of high key performance indicators, such as increased power density, in electrical machines. The latter enhances the cross-coupling of resistive–inductive–capacitive phenomena in windings, which may lead to significant loss in performance and reliability. The full-wave Maxwell's equations can be employed to characterize this coupling. To address the frequency instability that arises as a result, a simplification known as the Darwin formulation can be employed, where the wave propagation effects are neglected. Still, this modification is prone to ill-conditioned systems that necessitate intricate pre-conditioning and gauging steps. To overcome these limitations, a fast 2D formulation is derived, which preserves the current continuity conservation along the model depth. This implementation is validated experimentally on a laboratory-scale medium-frequency transformer. The computed impedances for the open- and short-circuit modes of the transformer are validated using measurements and compared with the multi-conductor transmission line model that is widely adopted for the analysis mentioned above. The developed formulation demonstrates a high accuracy and outstanding frequency stability in a wide frequency range, becoming an efficient and computationally light method to investigate the interconnected resistive, inductive, and capacitive effects in windings. [ABSTRACT FROM AUTHOR]

In this paper, the multiconductor extension of the previously developed three-phase power flow algorithm (named PFPD_3P) is presented. This multiconductor formulation has a general validity for both distribution and transmission networks. An iterative matrix formulation for the solution is throughout expounded. The present method allows computing the electrical quantities of all the network conductors: the active conductors and the passive ones ( $i$ . $e$ ., OHL ground wires, IC metallic screens/armours, and GIL enclosures). These electrical quantities can be evaluated both at the network busbars and also along the lines. The knowledge of these quantities can be useful to perform: safety evaluations, power quality and electromagnetic compatibility studies. The electrical substations are carefully modelled, by considering the links between the passive conductors of different busbars and the earthing resistance of the meshed earth electrode. The algorithm is implemented in Matlab environment and tested by several fictitious networks. Eventually, in order to confirm the approach accuracy, the multiconductor results are compared with the equivalent single-phase ones and the three-phase power flow commercial software DIgSILENT PowerFactory.

This paper extends previous work on electromagnetic (EM) reciprocity theorem analysis from the single‐conductor to the more general multiconductor transmission line (MTL) case. The focus is on the EM coupling problem of an ideal MTL above a perfectly electrically conducting ground when excited by a plane wave. The proposed methodology addresses mutual coupling effects and mismatched loads in the MTL. The expression for the current along the MTL in the test (radiation) state is derived, considering these factors. A novel calculation method for the induced voltage at the load is then introduced, assuming consistent coupling between different lines in both test and receiving states. Numerical examples validate the proposed EM‐reciprocity method, offering an alternative approach for analyzing the field‐to‐line coupling problem in MTL model. [ABSTRACT FROM AUTHOR]

In high-frequency and high-speed digital systems, minimizing signal interference, delay, and loss is crucial. Therefore, the role of multiconductor transmission lines (MTLs) is highly significant, and computational electromagnetics (CEM) are essential for analyzing their characteristics. In this study, electromagnetic simulations were performed in two- and three-dimensional multiconductor transmission lines using the finite element method. Subsequently, a postprocessing technique was used to extract resistance, inductance, and capacitance matrices. The accuracy of the results was verified by comparing the results with those of Q3D, a commercial electromagnetic simulation software. [ABSTRACT FROM AUTHOR]

The features of calculating the matrices of per-unit-length parameters and characteristics of multiconductor transmission lines have been considered. The method of calculation of the matrices of primary per-unit-length parameters of multiconductor transmission lines has been presented. The criteria for the accuracy of the calculation of the capacitance matrix have been formulated. It has been noted that it is necessary to accurately account for the mutual influence between the transmission line conductors for a correct estimation of the distortions of the signals propagated in it. The influence of the per-unit-length parameters of multiconductor transmission lines on responses and eye diagrams at the end of their active conductors has been demonstrated. The influence of the distances from the extreme conductors to the boundaries of the cross-sections of transmission lines on the accuracy of calculating their capacitance matrices has been studied. Using the method of moments, it has been shown that known approaches to determining these distances do not always give accurate or efficient results. On the example of several transmission lines with different numbers of dielectric layers and conductors, as well as with the shield and without it, the minimum values of this distance at which it is possible to achieve an accurate and efficient calculation of their capacitance matrices have been determined. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of electromagnetic interference (EMI) in electric vehicle supply equipment (EVSE) charging cables, which can disrupt the communication signal for the real-time monitoring of the charging status, leading to the termination of charging. We propose a dedicated measurement jig for the Combined Charging System Combo Type 1 (CCS-CT1) cable structure and models its electrical characteristics of the jig using the impedance peeling technique for de-embedding. The obtained pure S-parameters of CCS-CT1 are then used to conduct a simulation of the signal integrity problem caused by Gaussian noise, which is the worst-case scenario that can occur in a typical charging system. This paper suggests that the root cause of this problem may be related to the high-power AC/DC conversion device included in the EVSE, which uses a switch-mode power conversion (SMPC) method that involves nonlinear operation and can result in increased harmonic noise and a more complex signal protocol for precise control. Finally, this study provides insights into the challenges of implementing high-speed charging systems and offers a solution for obtaining the accurate electromagnetic characteristics of charging cables. [ABSTRACT FROM AUTHOR]

Crosstalk is an undesirable factor that degrades the quality of data transmission in printed circuit boards (PCBs). The signal integrity (SI) in multiconductor transmission lines is controlled by using a large number of multiport tests and measurements, which require a lot of time and expensive laboratory equipment. Proposed signal processing methods based on blind identification allow a reduction in the measurement burden. Contrary to the traditional approach requiring knowledge of sampling time offset, input pseudorandom bit sequence (PRBS), and time delay between received data and transmitted PRBS, the proposed alternative method performs blind separation of measured data for the linear fit pulse response (LFPR) procedure. The waveform identification of the partial pulse responses is evaluated for additively mixed cyclostationary sources of the data, intersymbol interference, and crosstalk. A mixed matrix model of composed random vectors is considered. The proposed estimation procedure is based on preprocessing of measured data using principal component analysis (PCA) and following independent component analysis (ICA). It is shown that the proposed component analysis allows diagnostics of signal integrity using eye-diagram patterns and the channel operating margin (COM). [ABSTRACT FROM AUTHOR]

A possibility of improving protective characteristics of transmission lines by cascading of multiconductor modal filters (MFs) with different geometric configurations is studied. Three-conductor MFs based on an asymmetric coaxial structure and a microstrip line and four variants of cascade structures consisting of two and three sections of such MFs are considered. Simulation of the time response to an ultrashort pulse (USP) and parametric optimization are performed. Attenuation of USP by a factor of 27.4 is achieved. [ABSTRACT FROM AUTHOR]

A compact topology for implementing compact multiband bandpass filters is presented in this paper. To achieve the desired frequency response, two identical short-circuited multiconductor transmission lines (MTLs) and properly connected shunt open stubs are interconnected. Using this configuration, it is possible to design multiband bandpass filters effortlessly. As both the MTLs and the stubs are distributed elements, spur-line band-stop filters are added to mitigate the first replica of the structure's frequency response. To assess the behavior of the developed filter design procedure, a prototype consisting of a six fingers-MTL and two shunt open stubs has been designed, manufactured, and analyzed, showing excellent agreement between analytical and measured results, considering that no simulation or optimization process has been performed during the design process, just for result verification. Furthermore, it is possible to establish a design criterion that allows the fast and reliable synthesis of multiband responses by varying just a small number of geometrical parameters of the MTLs and the corresponding stubs. [ABSTRACT FROM AUTHOR]

An efficient time domain hybrid method, consisting of the finite-difference time-domain (FDTD) method, Norton's theorem, transmission line (TL) equations, and some interpolation techniques, is presented to realize the fast coupling simulation of branched lines (BLs) radiated by ambient wave. Firstly, the branched lines are decomposed into multiple independent multi-conductor transmission lines (MTLs) according to the branched nodes. Then the TL equations with interpolation techniques are employed to build the coupling model of each MTL. The transient responses on these MTLs are solved by the FDTD method, which are employed to extract the Norton circuits of these MTLs acting on the branched nodes according to the Norton's theorem. Finally, the correlation matrix of the voltages and currents at the ports of the branched nodes is derived and solved. Meanwhile, these voltages are fed back to the corresponding MTLs as boundaries to realize the interference signal transmission among the BLs. Numerical examples about the coupling of branched lines contributed by five wires in free space and complex environment are simulated and compared with that of traditional FDTD to verify the correctness and efficiency of this proposed method. [ABSTRACT FROM AUTHOR]

This paper provides a time domain method for solving the induced currents (and voltages) of frequency-dependent lossy multiconductor transmission lines (MTLs) model randomly excited by electromagnetic pulse (EMP) plane wave. The model is processed based on the generalized polynomial chaos expansion (gPCE) and improved finite difference time domain (FDTD). The improved FDTD method overcomes the shortcomings of the conventional method that oversimplifies the expression of conductor impedance. In addition, when quantifying the influence of uncertainty on induced values, general formula of the global sensitivity analysis is provided by defining the gPCE basis function sequence to solve the complicated search work. The verification shows that the improved FDTD method alone or combined with gPCE to solve the lossy MTLs model excited by EMP is superior to the conventional methods in solving time and accuracy. Finally, compared with the Monte Carlo method, the effectiveness of the sensitivity method is also verified. [ABSTRACT FROM AUTHOR]

To address the problem of winding turn-to-turn breakdown faults in 35 kV dry-type transformers in wind farms under overvoltage conditions, this paper establishes a simulation model based on the structural dimensions and material parameters of the transformer windings. The winding distribution parameters were calculated using the finite element method. The transient processes inside the high-voltage coil were calculated by constructing a multi-conductor transmission line model (MTL) that took into account the influence of the secondary winding. The voltage distribution of the winding was analysed for both lightning shock and extra-fast transient overvoltage conditions. The simulation results show that the maximum overvoltage between turns of the transformer winding under lightning shock is 5.282 kV; the maximum overvoltage between turns of the winding under very fast transient overvoltage is 11.6 kV, which occurs between the first 2–3 layers of the section, close to the insulation breakdown margin. On this basis, the transformer winding structure was optimised and the maximum inter-turn overvoltage after optimisation was 9.104 kV, reducing the likelihood of insulation breakdown by 24.1%. Finally, the accuracy of the winding structure optimisation simulation study was verified by testing the transformer's impulse voltage before and after optimisation, providing a reference for the stable operation of 35 kV dry-type transformers in wind farm practical applications. [ABSTRACT FROM AUTHOR]

We provide a new angle to investigate exceptional points of degeneracy (EPD) relating the current linear-algebra point of view to bifurcation theory. We apply these concepts to EPDs related to propagation in waveguides supporting two modes (in each direction), described as a coupled transmission line. We show that EPDs are singular points of the dispersion function associated with the fold bifurcation connecting multiple branches of dispersion spectra. This provides an important connection between various modal interaction phenomena known in guided-wave structures with recent interesting effects observed in quantum mechanics, photonics, and metamaterials systems described in terms of the algebraic EPD formalism. Since bifurcation theory involves only eigenvalues, we also establish the connection to the linear-algebra point of view by casting the system eigenvectors in terms of eigenvalues, analytically showing that the coalescence of two eigenvalues results automatically in the coalescence of the two respective eigenvectors. Therefore, for the studied two-coupled transmission-line problem, the eigenvalue degeneracy explicitly implies an EPD. Furthermore, we discuss in some detail the fact that EPDs define branch points in the complex frequency plane, we provide simple formulas for these points, and we show that parity-time (PT) symmetry leads to real-valued EPDs occurring on the real-frequency axis.

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. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative multiconductor transmission line model that combines the folded line equivalent with the modal transformation. The folded line equivalent decomposes the nodal admittance matrix of a transmission line into its open-circuit and short-circuit contributions. These contributions are fitted to rational functions, which are associated with Norton equivalent circuits based on their state space models. The proposed model uses an orthogonal matrix to transform voltages and currents from the phase domain to the folded line equivalent domain and vice versa. Because the transformation matrix is orthogonal, we represent it using ideal transformers in simulation software. First, we use a circuit representation of Clarke's matrix to decompose a transmission line into its modes. Then, each mode is decomposed into its open-circuit and short-circuit contributions using a circuit implementation of the proposed matrix. The proposed approach can accurately represent short lines in simulations with time steps equal to or greater than the propagation time of the transmission line. We compare the results obtained with the proposed approach to those obtained with power systems computer-aided design/electromagnetic transients including the DC universal line model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper proposed a kind of guard traces based on a subwavelength periodic structure to reduce the far-end crosstalk (FEXT) of parallel microstrip lines in the PCB. This technology can be used to improve the false triggering and signal transmitting capacity of a multiconductor transmission line circuit system. In order to explore the present novel guard trace effect on isolating electromagnetic interference (EMI), the frequency response of the mutual capacitance and mutual inductance of the overall circuit system was provided and an equivalent circuit model was built. In comparison to the conventional microstrip line for isolating the EMI between parallel microstrip lines, the novel guard trace can efficiently reduce the mutual capacitance and mutual inductance of the overall circuit system. Thus, it is favorable for suppressing the crosstalk between microstrip lines. The $S$ -parameters calculation result showed that this kind of subwavelength periodic microstrip guard trace can isolate the EMI between two microstrip lines more effectively. Particularly, the conventional grounded guard trace needs a lot of dense grounded holes, which severely influences the wiring design of various layers of a multilayer circuit board. However, the proposed guard trace requires only one grounded hole, which has little influence on the circuit wiring of each layer of a multilayer printed circuit board. In our experiment, the step function signal of 30 ps rise time was imported into one microstrip line to measure the FEXT of the other microstrip line. It was demonstrated by the measurement result that the subwavelength periodic microstrip guard trace can reduce the FEXT to be below 5% of the transmission signal amplitude and is more flexible in practice. In compliance with the actual demand for a high-speed circuit, three isolation structures were proposed, and their isolation effects on the electromagnetic coupling between microstrip lines were verified individually.

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. [ABSTRACT FROM AUTHOR]

When analyzing multiconductor transmission lines with the edge coupling by the method of moments, the matrices of per-unit-length parameters may be inaccurate, which leads to an unacceptable noncausal response at the end of the transmission line. The article proposes a simple technique of a nonuniform segmentation of multiconductor transmission lines with edge coupling boundaries to eliminate the inaccurate calculation of the capacitance matrix. This technique allows obtaining accurate capacitance matrices with the lowest computational costs on single-variant and multivariate analyses, as well as optimization or stability analysis. [ABSTRACT FROM AUTHOR]

We characterize all plane and modal waves of lossy multiconductor lines. They are obtained by solving matrix dierential equations in closed-form. First-order and second-order telegraph formulations are considered. Wavesare described in terms of a scalar basis coupled with a nite number of matrixiterates. Modal waves are decomposed in forward and backward propagators. This decomposition can be applied in obtaining transmission and reection matrices at junctions. Eects due to initial, boundary or external inputs are described in terms of an integral contribution due to initial data, a convolution due to external disturbances and a bilinear term involving boundary values. For a two conductor transmission line satisfying the Heaviside condition, the fundamental response is obtained for the rst-order system and for the telegraph formulation. Numerical examples are given for lossy and lossless transmission lines and for determination of initial values of steady solutions. [ABSTRACT FROM AUTHOR]

The increasing interest in employing wide-bandgap (WBG) drive systems has brought about very high power, high-frequency inverters enjoying switching frequencies up to hundreds of kilohertz. However, voltage surges with steep fronts, caused by turning semiconductor switches on/off in inverters, travel through the cable and are reflected at interfaces due to impedance mismatches, giving rise to overvoltages at motor terminals and in motor windings. The phenomena typically associated with these repetitive overvoltages are partial discharges and heating in the insulation system, both of which contribute to insulation system degradation and may lead to premature failures. In this article, taking the mentioned challenges into account, the repetitive transient overvoltage phenomenon in WBG drive systems is evaluated at motor terminals and in motor windings by implementing a precise multiconductor transmission line (MCTL) model in the time domain considering skin and proximity effects. In this regard, first, a finite element method (FEM) analysis is conducted in COMSOL Multiphysics to calculate parasitic elements of the motor; next, the vector fitting approach is employed to properly account for the frequency dependency of calculated elements, and, finally, the model is developed in EMTP-RV to assess the transient overvoltages at motor terminals and in motor windings. As shown, the harshest situation occurs in turns closer to motor terminals and/or turns closer to the neutral point depending on whether the neutral point is grounded or floating, how different phases are connected, and how motor phases are excited by pulse width modulation (PWM) voltages. [ABSTRACT FROM AUTHOR]

Rational function approximation is commonly used to fit the transmission line impedance over a wide frequency range. Nevertheless, it is computationally costly and challenging to implement in practical applications due to the high number of approximations required to fit the impedance curve for the high-frequency range. Therefore, a novel fitting method of multiconductor transmission line (MTL) based on the analytical impedance equation of a transmission line using the impedance frequency response measurement is presented in this paper. The proposed fitting method is a function of the transmission line length since it is based on the analytical impedance equation of a finite transmission line. Furthermore, the proposed model uses a constant set of equations and calculated parameters to fit the impedance frequency response for a wide range of frequencies. Moreover, the proposed model parameters are calculated using derived resonance equations and the impedance frequency response measurement. In addition, an algorithm is developed to further fit the proposed model to the impedance frequency response measurement of the transmission line. MTL impedance frequency response is measured using a real-time digital simulator (RTDS). To ensure the accuracy of the proposed model, a comparison between the proposed model and vector fitting (VF) is presented. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, impact of the causality of frequency-dependent models of soil on the effective area of grounding grids buried in single and two-layer soils is studied. In the analyses, the computationally efficient multi-conductor transmission line method is used. The simulation results show that the causality plays an important role on the effective area so that it can decrease or increase the effective area in comparison with the non-causal model. This reduction or increase depends on the low-frequency resistivity of dispersive soil and current waveform. The relative error due to non-causality is considerable only for the subsequent stroke current, whereas for the first stroke current, it is low enough to be ignored. In addition, the burial depth effect on the effective area in causal and non-causal-dispersive soils is investigated. With the aim of more accurate design, comprehensively predicting formulae for effective area versus low-frequency resistivity of soil, burial depth and current waveform under causal assumption are proposed. Finally, importance of effective area based on causal and non-causal models on the lightning-induced voltage on the soil surface is investigated. [ABSTRACT FROM AUTHOR]

Abstract In this study, the implementation of different corona discharge models in a transient program for overhead multiconductor lines based on the implicit Crank‐Nicolson Finite Difference Time Domain method is presented. Among different corona models available in the literature, two empirical models (Gary's and Suliciu's models) and a physics‐based model (Malik's model) are discussed, which are broadly used in EMT programs, and their predictions under fast‐front lightning surges and slow‐front switching impulses are assessed. The authors critically review the dynamic capacitance approach in terms of numerical accuracy, when dealing with slowly varying voltages, and applicability, regarding dispersive models assuming a non‐instantaneous charge‐voltage relation. The alternative voltage‐controlled generator approach is proposed, which is successfully included in the implicit Crank‐Nicolson scheme. One of the objectives of this study is to show how different corona models may predict overvoltages with huge discrepancies, depending on the transient waveform and the propagation distance, despite the similarity of the q‐v hysteresis curves. More evident discrepancies between models under fast‐front voltage waves are reported, rather than for switching impulses. The consistency of these results in terms of the models' features and q‐v curves is analysed, highlighting the necessity for new engineering tools for corona simulation of general predictive capability.

Thin-wire structures in the presence or absence of a ground plane are analyzed numerically in the time domain (TD) with the aid of the Cagniard–DeHoop method of moments (CdH-MoM). It is demonstrated that the TD solution of such problems can be cast into the form of discrete-time-convolution equations. Under the assumption of piecewise linear space–time axial current distribution, the elements of the TD impedance array are derived analytically in terms of elementary functions. Their approximations applying to multiconductor transmission lines are discussed. Illustrative numerical examples validating the TD solution are presented. [ABSTRACT FROM AUTHOR]

Based on the research of genetic algorithm (GA) to optimize the BP neural network algorithm, this paper proposes a method for predicting twisted wire crosstalk based on the algorithm. Firstly, the equivalent circuit model of a multi-conductor transmission line is established, combined with the method of similarity transformation, the second-order differential transmission line equations are decoupled into n groups of independent two-conductor transmission line equations, and the crosstalk is finally solved. Then the mathematical model of the twisted wire is established and its structural characteristics are analyzed, and the GA-BP neural network algorithm is used to realize the mapping of the electromagnetic parameter matrix of the twisted wire and the position of the twisted wire. Finally, the mapping relationship is substituted into the transmission line equation, and the near-end crosstalk (NEXT) and the farend crosstalk (FEXT) of an example three-core twisted wire are predicted based on the idea of cascade combined. By comparing with the transmission line matrix method (TLM), it can be seen that the method proposed in this paper is in good agreement with the crosstalk results obtained by the electromagnetic field numerical method, which verifies the effectiveness of the algorithm proposed in this paper. [ABSTRACT FROM AUTHOR]

Aiming at the problem of electromagnetic compatibility caused by the high-voltage electric drive system (HEDS) in electric vehicles, a model of the HEDS based on the vehicle is established to predict conducted electromagnetic interference (EMI) of the HEDS. First, the electromagnetic environment inside electric vehicles is analyzed theoretically. Then, the various parts of the HEDS are accurately modeled, which include the power buses, inverter, and motor. Based on the theory of multiconductor transmission line, a generic model of power buses suitable for two screening designs is presented. In order to accurately simulate the operating characteristics of the inverter, the drive circuit and the parasitic parameters of the dc-link capacitor block and the insulated gate bipolar transistor module are considered. The motor model takes into account the low-impedance antiresonance phenomenon in the measured motor impedance. Finally, the HEDS is simulated with PSPICE 16.6, and the simulation results agree well with the experimental measurements. The proposed model can accurately predict the system-level conducted EMI of the vehicle-mounted HEDS up to 100 MHz, with an error of 4 dB or less at almost all frequencies below 56 MHz and less than 7 dB at most frequencies in the 56–100 MHz. [ABSTRACT FROM AUTHOR]

With the increasing number of interconnected cables in electronic systems, the crosstalk between interconnected cables has played an important role in the intrasystem interference performance. However, the traditional routing method based on the shortest path cannot solve the problem of cable crosstalk. In this article, a novel cable harness routing method based on the expected maximum crosstalk is proposed. First, the closed-form expression for crosstalk based on the electrically small assumption is derived from the multiconductor transmission line (MTL) equation. According to this expression, the concept of maximum overlap length corresponding to the desired maximum crosstalk is developed. In addition, a conservative strategy is proposed to deal with higher frequency cable routing. The proposed routing method consists of the escape graph and the routing algorithm based on the maximum overlap length. A Dijkstra’s algorithm variant with the maximum overlap length as the constraint condition is proposed. The proposed method is applied to two single-ended and differential signals cable harness routing cases and compared with the traditional method to show that the routing results of the proposed method would keep the crosstalk between cable harness branches below the expected maximum crosstalk. [ABSTRACT FROM AUTHOR]

An umbilical cable is a compactly integrated cable consisting of electrical power cables, communication (electric signal) cables, and chemical transposition tubes. An umbilical cable is widely used in developing oil and gas resources of deep and ultra-deep water. With the increment of the length and the functional integration of umbilical cables, the crosstalk becomes a crucial issue in the cable design, and needs to be evaluated carefully before the fabrication and installation. Moreover, the twisted structure of communication cable cores has incurred extra difficulties to the crosstalk calculation. Nevertheless, it is not an easy task to model the complex twisted structure in existing models and methods of the crosstalk computation. In this regard, this paper proposes a numerical methodology for the crosstalk calculation considering the multi-conductor twisted structure of the cable cores. In the methodology, the four-wire twisted structure is modelled as a cascade of uniform multiconductor transmission line (MTL) sections, each wire section covering a length of 1/4 pitch, with abrupt interchanges of wire positions at the ends. The chain-parameter equation is introduced to describe the voltage and current transfer relationship in each MTL section. To obtain the numerical solutions of the twisted cable system, the port constraint equations and the permutation matrices are also required and developed. The per-unit-length parameters of the umbilical cable system are computed by numerical methods. The feasibility to engineering applications and accuracy of the proposed methodology is validated by experimental results, and the crosstalk characteristics of communication cables in a typical umbilical cable under different operating conditions are investigated. [ABSTRACT FROM AUTHOR]

This means that there is a finite HT ht in the vacuum for HT ht . At the conductor-air boundary where HT ht , HT ht must be continuous because it is tangential to the boundary. Looking at the surface wave, the transverse field also dominates for values of I r i where HT ht , with the transverse decay constant of the fields HT ht . [Extracted from the article]

This paper presents a new, improved approach to fault location in long and very long transmission lines, which uses measurements at both terminals of the line that do not need to be synchronized, using the satellite time-reference. The new method employs symmetrical component sequence voltage profiles that are computed using an innovative approach in which the detailed three-phase model of a multiconductor transmission line is represented as the series connection of several chain matrices. This allows the new method achieve the best performance, when compared to other 4 similar fault location approaches, requiring measurements at both terminals of a symmetrical line, considering all types of faults, under realistic variations in variables and parameters of the test system, including the effect of saturation of current transformers, and arc faults. The main advantage of this proposed technique is that it can be applied with no major changes in symmetrical and unsymmetrical transmission lines keeping its good performance. In addition, division of the line in chain matrices allows the new proposed approach to be applied in non-homogeneous lines. In this paper, for space reasons, the new approach is initially applied to symmetrical (ideally transposed) transmission lines only, with very successful and encouraging results. • This approach considers the detailed model of a multiconductor symmetrical line. • It achieves the best performance of all the considered algorithms of this type. • It was tested successfully considering 15 different realistic conditions. • Measurements do not have to be synchronized. • The simplicity of the algorithm, make it adequate to be implemented in a relay. [ABSTRACT FROM AUTHOR]

In this paper, the equivalent circuit model of interconnect channels in silicon interposer is developed for three-dimensional integrated circuit (3-D IC) based on the theory of multi-conductor transmission line (MTL). The deep neural network (DNN) is employed to learn the nonlinear mapping relationship between the geometric parameters and the distributed parameters, and it is demonstrated that the DNN has a high prediction accuracy. In the implementation, a coarse model is firstly developed by solving the scattering parameters of the model using the chain parameter matrix. The model is optimized using a knowledge-based neural network (KBNN), and a fine model is then established. The numerical examples demonstrate that the optimized model can achieve high accuracy. Finally, the inner contour of the worst-case eye diagrams of the channel is generated using the peak distortion algorithm (PDA), with the worst eye width and height obtained. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A multiconductor transmission-line (MTL) model is proposed with which to model the uniplanar compact electromagnetic bandgap structure (UC-EBG). The model is based on a 2-D arrangement of metamaterial-based electromagnetic bandgap structures (MTM-EBGs), with a central node region. The branches of this structure are modeled as conductor-backed coplanar waveguide segments with integrated series capacitors, while the node region is modeled as a grid of microstrip (MS) lines with suitably augmented propagation velocities. The dispersion properties of the canonical UC-EBG unit cell are simulated in Ansys HFSS and compared with those of an equivalent simulation model based on a 2-D arrangement of weakly loaded MTM-EBGs, as well as similar data produced by the MTL equivalent-circuit model, which are all found to be in agreement. It is then shown that additional capacitive loading allows for substantial miniaturization, a regime in which even better agreement is produced between the equivalent circuit model’s dispersion data and the data produced by an equivalent HFSS model. Using these data, the Bloch modes of this structure are analyzed in detail. Thus, the MTL perspective offers a recipe for producing highly miniaturized UC-EBG unit cells that may be successfully integrated into printed circuit board (PCB) systems for applications in parallel-plate noise and surface-wave (SW) mode suppression, among others. [ABSTRACT FROM AUTHOR]

The random wiring of automotive cable harness makes electromagnetic compatibility (EMC) analysis of the whole vehicle very complicated; thus, this paper proposes a simplification modeling technique to model the electromagnetic (EM) illumination on automotive cable harness. First, the stochastic process theory is applied to determine the cable route in a randomly bundling way. Then, the inductance and capacitance parameters of the cable harness at different location are established according to multiconductor transmission lines network (MTLN) theory. On this basis, the simplification modeling technique is developed to generate the electrical and geometrical parameters of the equivalent cable model. Finally, a model of shielded nine-conductor with randomly twisted and a model of unshielded nine conductor with stochastic wiring in the vehicle are performed to validate the proposed approach by full-wave simulation. The presented method simplifies the complexity of modeling the complete cable harness significantly with a good accuracy. [ABSTRACT FROM AUTHOR]

In the recent research world, the overall system performance primarily depends on interconnect delay instead of the gate delay at the nanoscale regime. The impact of spacing between the lines and shrinking technology are rigorously investigated on peak noise and delay under the crosstalk for rough-edged multi-layered graphene nanoribbon (MLGNR) at global lengths. Using a rough-edged MLGNR, a multi-conductor transmission line (MTL) model is accurately demonstrated by considering the effect of coupling capacitance and inter-layer tunnelling conductance. By incorporating lengths and spacing between the coupled MLGNR interconnect, the equivalent electrical model exhibits an insignificant error of 0.91% only. Moreover, the proposed equivalent model is used to demonstrate the delay under the influence of crosstalk and peak noise for coupled interconnect lines. Using industry standard HSPICE, the overall delay and peak noise under the crosstalk are reduced by 45.1% and 9%, respectively at advanced 14 nm technology in comparison to the 32 nm for a fixed layer of rough-edged MLGNR based global VLSI interconnects. [ABSTRACT FROM AUTHOR]

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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. [ABSTRACT FROM AUTHOR]

Pulsed current injection (PCI), as an important conducted susceptibility testing method, has been introduced in several standards. However, the selection of couplers for PCI tests has not been clearly specified, which leads to the fact that the injected electrical quantities by different couplers might be rather different and it is inadequate to inject the proper disturbance at the testing ports. So, it is of significance to evaluate their performance quantitatively and determine the usage scenarios for couplers. This article focuses on the quantitative performance evaluation of inductive and capacitive couplers including inductive ferrite-core clamps and capacitive coupling clamps. A distributed-parameter multiconductor transmission line (MTL) model has been proposed for couplers clamped on N wires. The validation test confirms the accuracy of the model in the bandwidth of PCI tests. The performances of an inductive coupler and a capacitive coupler are analyzed and compared based on MTL models. The selection criterion of the couplers is concluded as that a proper coupler should lead to higher time-waveform norms, which indicate possible nonlinear effects of the tested objects, such as the overcurrent, the turn-to-turn breakdown, and the component burnout. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the evaluation of currents and voltages along a multi-conductor transmission line having non-linear impedances due to the presence of ferromagnetic conductors; we assume that these impedances are function of the current carried by the relevant conductor so that the equivalent circuit modelling the line is non-linear and has to be solved by means of an iterative procedure. The present paper can be considered as a generalization of our previous works successfully applied to single-conductor lines with earth return. Some examples of application to typical 50-60 Hz interference studies between power/railway lines on telecommunication cables and pipelines are shown. [ABSTRACT FROM AUTHOR]

An efficient multiconductor transmission line (MTL) model of a shielded twisted wire pair (TWP) with apertures on its sheath is developed for predicting common mode (CM) and differential mode (DM) currents induced in the shielded TWP cable. Its transfer impedance and admittance with one-line apertures on its sheath are derived in a closed form. Therefore, the MTL equations are formulated and solved to obtain the CM and DM currents induced in the shielded TWP. Moreover, the proposed MTL model is generalized to be applicable for the braided–shielded TWP, in which the transfer impedance and admittance are formulated analytically. Results showed that the induced DM current inside the braided–shielded TWP is suppressed dramatically due to the uniform structure of the cable. The models are validated by comparing their results with those obtained by the commercial software FEKO; good agreements are obtained. [ABSTRACT FROM AUTHOR]

The high-frequency behavior of the stator winding is synthesized herein using a multiconductor transmission line model to study the potential location of excessive voltage stress, being the main cause of insulation failure within the winding. The comprehensive modeling approach proclaims that the voltage distribution within the winding is a result of the antiresonance phenomenon, which can be characterized by two oscillatory responses. One of the oscillatory response may lead to excessive voltage stress at the terminals of the machine, which have been reported extensively. However, it is the other oscillatory response, which engenders maximum voltage stress at the neutral end to the winding and prevails due to the superposition of traveling voltage waves. The latter is a sole characteristic of the stator winding and may be more detrimental to the winding insulation. Therefore, the stator winding remains under stress even with short or no cable. Furthermore, the article illustrates that increasing the cable up to a certain length can be potentially treacherous. The simulation results validate the identified phenomenon through the high-frequency model of the cable and the stator winding developed in MATLAB/Simulink environment. Further, the experimental results verify the aforementioned phenomenon on an automotive-grade 60 kW permanent magnet synchronous machine. [ABSTRACT FROM AUTHOR]