A Precise Time-Step Integration Method for Transient Analysis of Lossy Nonuniform Transmission Lines

The nonuniform transmission line is traditionally modeled and analyzed in the frequency domain. However, it is difficult to characterize and simulate nonuniform lossy transmission lines accurately in the time domain. A highly accurate and general approach for time domain analysis of lossy inhomogeneous transmission lines is described. The propagator method presented is an exact solution to the lossy telegrapher's equations based on the modal matrix technique. Simpson's rule is applied to produce a remarkably accurate numerically compatible result. An exponentially tapered transmission line example shows that this method is not only simple and efficient, but also an accurate technique for analyzing lossy nonuniform transmission lines with minimal numerical dispersion. Multiple sectioned transmission lines can be handled by a straightforward application of the presented equations.

Transient analysis of nonuniform lossy transmission lines with frequency dependent parameters

The vast majority of nonuniform transmission lines are no analytical solution except for a few special forms of transmission line. Dividing nonuniform transmission line into several equal parts, then each part can be regarded as uniform transmission line approximately. Using the theory of uniform transmission line to analyze nonuniform transmission line's transient response is the commonly used method. Composite Simpson's rule for transient analysis of nonuniform transmission lines is proposed in this paper. The exponential transmission matrix of nonuniform transmission line's equation is transformed into a general algebraic equation, which greatly simplifies the analysis on transient response for nonuniform transmission line. The simulation results illustrate the accuracy of the presented approach with examples.

A Meshless Time Domain Method is proposed to solve the telegrapher's equation for the Nonuniform Transmission Line. The approach is based on a combination of the Point Interpolation Method PIM and the Leapfrog algorithm. The accuracy of the proposed method is confronted with both the conventional FDTD and a wavelet expansion method. The strong stability of the computing scheme is set in evidence from the computational results for a linear tapered planar line.

A generalized method of moments (MoM)-SPICE iterative technique for field coupling analysis of multiconductor transmission lines (MTLs) in the vicinity of complex structures is presented. Telegrapher's coupling equations are modified with additional distributed voltage and current sources for more accurate analysis of the total current induced onto transmission line bundles in the presence of complex structures. These additional voltage and current sources are introduced to enforce the electric field boundary condition and continuity equation on MTLs beyond the quasi-static regime. The surrounding structure is modeled via the MoM and a SPICE-like simulator is used to simulate equivalent circuit model of the MTLs extracted via the partial element equivalent circuit method. The proposed technique is based on perturbation theory with the quasi-static current distributions on the transmission lines still assumed to be dominant. Validation examples for single and MTLs are given in the presence of complex structures.

The objective of this paper is to present a moment method numerical technique based on a combined approach of using a ”quasi-dynamic”, a “dynamic” and an asymptotic approach for the analysis of non-uniform microstrip transmission lines and discontinuities using the grounded dielectric slab Green’s Functions. To validate the approach, the regions of validity the quasi-dynamic and asymptotic approximations have been determined in terms of the microstrip physical parameters. Finally, numerical examples have been solved and checked with available data.

This article analyzes the E-field response in the test volume of bounded wave simulator (BWS) in time domain (TD) based on nonuniform multiconductor transmission lines (NMTLs) and electric dipole theory. First, the transmission lines (TLs) in BWS are modeled as a NMTL system and divided into a certain number of cascaded uniform multiconductor TLs (MTLs). Second, the current distribution in frequency domain (FD) along the TLs of BWS is determined based on the theory of MTL and the chain parameter matrix (CPM) when sinusoidal continuous wave signals of different frequencies are fed into BWS. Third, the E-field at field point of the test area of BWS is calculated by summing the E-field radiated by all the currents on the TLs in BWS via the electric dipole theory. Finally, the E-field response in TD is solved via discrete Fourier transform (DFT) and inverse DFT (IDFT). The validity of the proposed algorithm is investigated by analyzing an example of BWS, which is measured experimentally. It has been shown from the established results that the proposed method leads to an effective technique for analyzing the E-field response in the test volume of BWS. Related research in this article can provide some guidance in the analysis of BWS and transient electromagnetic field radiation sensitivity test (RS 105).

In order to analyze the switching transient electromagnetic fields generated by the aerial busbars in substation, the one-dimensional (1-D) time domain finite element (TDFE) method is presented to analyze the transient wave process in multi-conductor transmission lines (MTLs) with branches. Based on the Pade's approximation and on Prony's method, the iterative equations of the aerial MTLs are reported. Iterative formulae are also presented to determine the boundary conditions at the nodes of the branches in this paper. The proposed method avoids the Gibbs effect of the finite difference time domain (FDTD) method. An aerial busbars model in a 500 kV substation is analyzed when circuit breakers and disconnect switches are closed. The numerical results are in good agreement with those calculated by Bergeron's method and FDTD method.

Based on the reciprocity theorem, a simple method for the analysis of the radiated electromagnetic fields from a arbitrary nonuniform lossless transmission line with a linear termination is presented. The radiation problem is solved using the known solution of the coupling problem. The method of the solution for the coupling problem in nonuniform transmission lines is based on the steplines approximation of the nonuniform transmission line and quasi-TEM assumptions. An example of nonuniform transmission line is then solved to show the capabilities of the present method.

A new fast time-domain method is proposed to calculate the overvoltages in transformer winding under the very fast transient overvoltage (VFTO). Based on multiconductor transmission line (MTL) model, which combines the theory of compact finite difference (CFD) with the precise integration method (PIM), using vector fitting and recursive convolution to calculate the frequency-dependent parameters. By comparison with traditional MTL approach, the proposed method can improve the calculation efficiency. For validation, the calculated results are compared with the measurements on a transformer winding model and the result is satisfactory. (6 pages)

This work presents a SPICE macromodel for fast transient analysis of lossy multiconductor transmission line (MTL) interconnects in the presence of electromagnetic interference (EMI). A simplified formulation based on split representation at both ends of the MTL structure for computation of equivalent sources in the time-domain is described. A passive and compact macromodel based on delay extraction and closed-form representation is used to describe the distributed nature of the MTL stamp. The proposed algorithm, while guaranteeing the stability of the simulation by employing passive macromodels, provides significant speed-up for EMI analysis of transmission line networks, especially with large delay and low losses.

This paper presents a multiple time-step solver based on a time-domain explicit integration algorithm for improving the computational speed of high-voltage transmission line electromagnetic transient (EMT) simulation. For weakly rigid EMT models of high-voltage transmission lines, the previous precise Runge-Kutta integration method with a small time step is adopted; for strongly rigid nonlinear EMT models of high-voltage transmission lines, a an improved precise integration method using a large time step is used for the solver of EMT simulation. Practical simulations for overvoltages of high-voltage transmission line show that multiple time-step EMT solver can be applied to different cases of EMT simulation for transmission line.

This paper describes an efficient approach for sensitivity analysis of lossy transmission lines in the presence of non-linear terminations. Sensitivity information is derived from the macromodels based on delay extraction and matrix-rational approximation of Telegrapher's equations. The method enables sensitivity analysis of interconnect structures with respect to both electrical and physical parameters. An important advantage of the proposed approach is that the derivatives of the stamp of the transmission line with respect to per-unit-length parameters are obtained analytically.

In this paper, a discrete time-domain method to analyze multiple coupled nonuniform lossless transmission lines has been presented. The solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation, the system of coupled nonuniform transmission lines is decomposed into a large number of coupled steplines with different characteristics. Then, using modal decomposition method, the system of coupled partial differential equations for each step is decomposed to a set of uncoupled ordinary wave equation. Using time-domain approach and invoking the boundary condition at the discontinuities of the adjacent steps, each step is modeled as continuous time linear filter characterized by a time-domain transfer matrix. Finally, this continuous time linear filter (for band limited input signal), is modeled as a discrete time-domain linear filter with constant matrix coefficients using sampling theorem. The method proposed here can be implemented using general purpose software packages like MATLAB.

Very fast transient overvoltage (VFTO) is very dangerous for the transformer which is directly connected to gas insulated substations (GIS). In this paper, the multi-conductor transmission line (MTL) model is used to analyze the overvoltage distributions of transformer windings under VFTO. A fast algorithm based on precise integration method (PIM) and Krylov subspace technique is proposed. Furthermore the points with its frequency greater than 20 MHz can be ignored for more computational efficiency. A test core-type transformer winding is studied, and there is a good agreement between the simulation results and the measurement ones. The algorithm used in this paper is about 8 times faster than the traditional frequency-domain algorithm. Furthermore, overvoltage distributions in 800 kV power transformer under VFTO are calculated.