Vector Fitting Technique Research Articles

Lightning-induced voltage analysis on a three-phase compact distribution line considering different line models

This paper discusses the simulation of lightning-induced voltages on a three-phase compact distribution line considering either a first order finite-difference time-domain solution of telegrapher's equations or a version of Marti's transmission line model extended to include the influence of external electromagnetic fields, named EMD model. The validity of both models is first demonstrated by means of comparisons with lightning-induced voltages measured in rocket-triggered lightning experiments. It is then shown that the EMD model can be used in the simulation of lightning-induced voltages on compact distribution lines provided special attention is given to the model fitting in the modal domain, regardless if complex or real poles are used. Results obtained with the vector fitting technique are seen to be more reliable than those obtained using Bode's asymptotic method, which must be used with caution in the modeling of compact distribution lines. The obtained results are relevant because compact distribution lines contain both bare and covered conductors, which is likely to pose difficulties to the simulation of transients with transmission line models based on modal-domain theory.

Enhancements in vector fitting implementation by using stopping criterion, frequency partitioning and model order reduction

The Vector Fitting (VF) technique has become a mature rational approximation tool. This paper proposes two enhancements that increase the VF computational efficiency, resulting in reduced CPU time while maintaining a desired precision of the approximation. The first enhancement consists of a stopping criterion to automatically interrupt the VF iterative process when the fitting error does not vary significantly. The second one is based on frequency partition and order reduction of the rational model. The computational gain by the proposed enhancements is verified via fitting of a multi-input multi-output test system of considerable complexity that includes transmission lines modelled as distributed-parameter lines.

Multiphysics Parametric Modeling of Microwave Components Using Combined Neural Networks and Transfer Function

This paper proposes a new technique to develop an accurate multiphysics parametric model for microwave components to speed up the multiphysics modeling process. In the proposed technique, the artificial neural networks (ANNs) and pole/residue based transfer function are incorporated to represent the highly non-linear relationships between electromagnetic centric (EM-centric) multiphysics behaviors and multiphysics geometrical/non-geometrical design parameters. Vector fitting technique is utilized to obtain the poles/residues of the transfer function for each multiphysics sample. Since the relationship between multiphysics design parameters and the pole/residues of the transfer function is non-linear and unknown, two mapping functions are proposed to establish the mathematical links between the multiphysics design parameters and poles/residues. Parallel multiphysics data generation is proposed to generate the training and testing data for establishing the proposed multiphysics parametric model. A two stage training algorithm is proposed to guide the multiphysics training process. Once an accurate overall model is developed, it can be used to provide accurate and fast prediction of the multiphysics behavior of microwave components with geometrical and non-geometrical parameters as variables, and further can be used in the high level design. Compared with the existing multiphysics modeling methods, the proposed technique can achieve better model accuracy with high efficiency. The proposed technique provides an accurate and efficient methodology even when the coarse model or empirical model is unavailable. Two microwave examples are used to illustrate the validity of the proposed multiphysics parametric modeling technique.

Lightning-Generated Transients in Buildings With an Efficient PEEC Method

This paper presents a time-domain equivalent circuit approach for analyzing lightning-generated electromagnetic transients in modern buildings. The building is represented by a wire-plate structure and is modeled by the internal impedance and external inductance of current cells and the coefficients of potential cells. A vector-fitting technique is applied for modeling frequency-varying internal impedance for time-domain simulation. With this unique formulation, the number of unknown variables is reduced, and computational efficiency is improved significantly. Finally, lightning-generated impulse magnetic fields and voltages within a building are evaluated.

Frequency-Domain Fitting Techniques: A Review

This paper presents a theoretical review and comparisons between vector fitting, matrix-pencil-method, and Loewner matrix techniques for the fitting of frequency-domain functions. Firstly, the theoretical fundaments of each technique are briefly reviewed. Secondly, their computational performances and fitting accuracy are compared through different case studies. As for Loewner Matrix method, a novel implementation is proposed for a fair comparison with the other two techniques. Moreover, it is demonstrated that this novel implementation has some advantages over the traditional one. Finally, global remarks and recommendations are specified to take advantage of the capabilities exhibited by each technique.

A Loewner/MPM—VF Combined Rational Fitting Approach

This paper presents a novel methodology for the computation of rational models for electromagnetic transients simulations. The proposed methodology combines the capabilities of either the Loewner Matrix (LM) or the Matrix Pencil Method (MPM) for model-order identification with the high accuracy of the vector fitting (VF) technique. The proposed technique achieves improved performance compared with individual application of MPM, LM, and VF techniques. A unique advantage of the proposed algorithm is that the model order can be determined automatically.

Time-domain compact macromodeling of linear photonic circuits via complex vector fitting

In this paper, a novel baseband macromodeling framework for linear passive photonic circuits is proposed, which is able to build accurate and compact models while taking into account the nonidealities, such as higher order dispersion and wavelength-dependent losses of the circuits. Compared to a previous modeling method based on the vector fitting algorithm, the proposed modeling approach introduces a novel complex vector fitting technique. It can generate a half-size state-space model for the same applications, thereby achieving a major improvement in efficiency of the time-domain simulations. The proposed modeling framework requires only measured or simulated scattering parameters as input, which are widely used to represent linear and passive systems. Three photonic circuits are studied to demonstrate the accuracy and efficiency of the proposed technique.

Lightning protection design of solar photovoltaic systems: Methodology and guidelines

Solar photovoltaic (PV) system is one of the promising renewable energy options for substituting the conventional energy. PV systems are subject to lightning damage as they are often installed in unsheltered areas, and have vulnerable electronic devices. This paper proposes a partial element equivalent circuit (PEEC) method enhanced with the vector fitting technique for analyzing lightning transients in the PV systems. The frequency-dependent effects and ferromagnetic properties of structural steel are taken into account. Models of major components in the PV systems including structure steels, wiring in panels, and PV cells are provided. The non-linear surge protective device (SPD) is also considered in the modelling. An experiment on a PV panel is presented for the validation of the proposed method. The proposed procedure is finally applied to investigate lightning transients in a practical PV system. The lightning failure mode of bypass diodes is identified for the first time. The results can help to design effective lightning protection and select appropriate parameters of protective devices.

Thin-Wire Models for Inclined Conductors With Frequency-Dependent Losses

This paper presents the finite-difference time-domain (FDTD) thin-wire models of lossy wire structures with arbitrary inclination for transient analysis, which is difficult to address using the traditional FDTD methods. The frequency-dependent losses of the conductors are fully taken into account, and the vector fitting technique is applied to deal with frequency-dependent parameters for time-domain analysis. The bidirectional coupling within the lossy coaxial conductors is modeled. The currents in inner and outer conductors are not necessarily balanced. Three cases are presented for the investigation of wave propagation velocity, wave attenuation, and current distribution. These data are compared with analytical results and numerical results using other models. It is found that the proposed thin-wire models can depict the transient behaviors in the lossy inclined conductors with a velocity error of less than 1%, and an attenuation error of less than 1.5%.

Unconditionally Stable One-Step Leapfrog ADI-FDTD for Dispersive Media

A novel unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time domain is developed for modeling dispersive media. In contrast to previous approaches, the proposed method uses a vector fitting technique to incorporate various types of dispersive media through electric polarization terms governed by an auxiliary differential equation (ADE). Moreover, a semi-implicit finite-difference scheme is applied to the ADE to maintain the unconditional stability of the method. The stability is verified analytically by von Neumann analysis with the Jury criterion. Numerical experiments are carried out to illustrate the stability and accuracy. The proposed method is used to investigate surface plasmon polaritons (SPPs) on graphene sheets biased by an electrostatic field.

Lightning Grounding Grid Model Considering Both the Frequency-Dependent Behavior and Ionization Phenomenon

A grounding grid is essential to the lightning protection of power systems. This paper presents a modified partial element equivalent circuit method for predicting the transient behavior of the grounding grid. The frequency-dependent parameters of the grounding grid are obtained first by using the image method. Both modified nodal formulation and vector fitting techniques are applied to derive an extended equivalent network for time-domain simulation. In this method, the soil ionization effect is considered using a nonlinear resistance. The proposed method is verified with experimental results available in the literature. Finally, lightning transients in the grounding grid of a radio base station is presented. The ionization and propagation effects on grounding grid performance are discussed.

One-Step Leapfrog HIE-FDTD Modeling of Plasmonic Structures Using Partial-Fraction Dispersion Models

An improved one-step Leapfrog hybrid implicit-explicit finite-Difference Time-Domain (HIE-FDTD) method is developed for simulating complex plasmonic structures that comprise dispersive materials over an ultra-wide optical frequency range. The dispersive media is described by a partial fraction (PF) dispersion model by using the vector fitting technique and further implemented into the Leapfrog HIE-FDTD scheme via an auxiliary difference equation (ADE) formulation. The performance of the proposed method is evaluated in optical response of a multi-functional plasmonic structure which can act as a dynamically tunable band-stop filter and refractive index sensor. Simulation results demonstrate good numerical accuracy and high computational efficiency and may find some potential applications in sensing, detecting and optical communications.

Analysis of Graphene-Based Devices Using Wave Equation Based Discontinuous Galerkin Time-Domain Method

This letter extends wave equation-based discontinuous Galerkin time-domain (DGTD-WE) method to analyze the graphene-based devices. The numerical fluxes related to a general impedance transmission boundary condition in the DGTD-WE method have been proposed for the first time to model the graphene sheet as an infinite thin impedance surface. A vector-fitting technique is used to approximate surface conductivity of the graphene in terms of a series of partial fractions. Several graphene-based devices have been given to demonstrate the correctness and effectiveness of the proposed method.

Tunable hybrid metal–graphene frequency selective surfaces based on split‐ring resonators by leapfrog ADI‐FDTD method

A tunable hybrid metal–graphene frequency selective surface (FSS) based on split-ring resonators at mid-infrared frequencies is proposed and numerically investigated by an improved leapfrog alternating direction implicit (ADI)-finite-difference time-domain (FDTD) method. The graphene conductivity described by a new closed-form approximate expression is incorporated into the leapfrog ADI-FDTD through the vector-fitting technique and auxiliary differential equation approach. Numerical simulations show that the proposed method has good computational accuracy and higher efficiency compared to conventional FDTD method and analytical solutions. Besides, the transmission and reflection coefficients of the FSS can be effectively adjusted by changing the chemical potential of graphene, the layer number of graphene patch and operating temperature. This work provides a novel method for designing tunable devices for optical plasmonic applications.

Circuit Model Extraction of Parallel-Connected Dual-Passband Coupled-Resonator Filters

In this paper, an analytical coupling matrix extraction scheme is proposed for parallel-connected dual-passband coupled-resonator filters for the first time. Model-based vector fitting technique is adopted to fit the measured responses of the dual-passband filter (DPBF) with a set of rational functions, from which a transversal coupling matrix can be constructed. A novel coupling matrix transformation strategy is developed to transform the transversal coupling matrix to the one corresponding to the topology of a parallel-connected DPBF. A practical filter is used as a test example to demonstrate the extraction procedure. In diagnosing the coupling matrix of the test filter, two kinds of ambiguity problems are discussed in detail and are solved by a perturbation technique. This paper provides a general theoretic framework for computer-aided tuning of a parallel-connected dual-passband or multiple-passband filter.

Evaluation of the impact of different frequency dependent soil models on lightning overvoltages

This work assesses the influence of including the wideband behaviour of grounding systems in EMT-type programs on evaluation of transients resulting from direct lightning strikes to transmission lines. The grounding frequency behaviour is determined by using an accurate electromagnetic model and included in EMTP/ATP by means of an equivalent circuit derived from Vector Fitting technique. Furthermore, the impact of the frequency dependence of soil parameters on the lightning performance of transmission lines is addressed. It was found that representing the tower-footing grounding by a simple resistance can lead to significant errors in terms of grounding potential rise. However, for the overvoltages that appear across the insulator strings, the representation of the grounding system by a simple resistance leads to results whose accuracy is similar to those obtained using more complex representations which consider the wideband behaviour. Also, it was shown that the frequency dependence of soil parameters leads to a reduction of the grounding impulse impedance and causes a decrease of the backflashover rates, improving the lightning performance of transmission lines. In addition, the effect of considering the variation of soil parameters with frequency is more intense in the ground potential rise than in the overvoltages in the insulator strings.

Generation of the windowed multipole resonance data using Vector Fitting technique

The multipole representation provides an analytical way of Doppler broadening cross sections for neutron interactions and relies on a partial fraction decomposition that represents R-matrix resonance parameters by poles and residues. The windowed multipole method selectively broadens impactful poles and approximates the rest to increase the efficiency of the process. However, this process requires knowledge of the resonance parameters and certain limitations occur when additional channels are opened in the defined resolved resonance region such that only 2/3 of the ENDF/B-VII.1 nuclides can be processed. Some important nuclides needed in reactor applications such as Oxygen-16 and Hydrogen-1 are directly represented in point-wise form in the evaluation nuclear data library hindering the practicality of this approach. This paper presents a new fitting method for nuclear point-wise cross sections data that yields a pole and residue form analogous to the multipole representation. The Vector Fitting technique which originates from the field of signal processing was applied to the fitting of point-wise cross sections. Poles and residues from Vector Fitting were generated for Oxygen-16, Hydrogen-1, Boron-10 and Boron-11 and processed in the windowed multipole format. These new libraries were tested by direct comparison of the microscopic cross sections before and after Doppler Broadening, and by integral comparisons using a typical PWR pin cell from the BEAVRS benchmark. Results indicate that the new libraries are equivalent to the point-wise representation with the added benefit of allowing on-the-fly Doppler broadening without the need for temperature interpolation. Runtimes are approximately ∼28% slower using the multipole representation on this example problem compared to a single temperature ACE file.

Frequency-dependent models of overhead power lines for steady-state harmonic analysis: Model derivation, evaluation and practical applications

This paper presents a novel frequency-dependent model for electric power lines to be used in harmonic studies. First, the differential equations representing the distributed nature of the line electrical parameters are considered; frequency dependency due to the effect of ground return and the skin effect is then incorporated. These derived equations represent what in this paper is defined as the analytical model, used as benchmark for model comparison. The vector fitting technique is used here to approximate the analytical model and derive a frequency-dependent frequency domain model. A passive circuit realization of the proposed model in a PI structure is presented and can be directly implemented in steady-state analysis tools such as harmonic power flow solvers. This paper then presents the evaluation and verification of the proposed model for multiple test cases. The test cases of unbalanced three-phase lines for overhead and underground conductors are considered. Moreover, to evaluate system-level impacts of the proposed model, the IEEE 13 node test feeder is considered. Through the evaluation of the test results, it is shown that the proposed model is more accurate than currently-used steady state models such as the simple (nominal) PI or the constant PI (with constant parameters calculated at fundamental frequency) models in terms of steady state harmonic voltages and currents at the line terminals. Test results obtained using the proposed model are within comparable accuracy to the ones obtained using the electromagnetic and transient (EMT) model, without having to run computationally expensive time domain simulations.

Implicitly Coupled Electromechanical and Electromagnetic Transient Analysis Using a Frequency-Dependent Network Equivalent

This paper presents an improved solution of the implicitly coupled electromechanical and electromagnetic transient analysis problem using a frequency-dependent network equivalent (FDNE). In previous work, the fundamental frequency equivalent was used as the network equivalent of the external system. While simple, this fundamental frequency equivalent is only accurate for a single frequency, the fundamental frequency. This may lead to an inaccurate equivalent of the transient stability (TS) network. This paper extends previous work by using an FDNE derived from the vector-fitting technique. The FDNE is able to resolve the transient behavior over a wider frequency spectrum leading to a more accurate representation of the TS network. Results demonstrating the accuracy of the proposed scheme are presented on a 3-bus test system and the IEEE 118-bus system.

Comparative Study of Lossy Transmission Line Simulation Models for Eye-Diagram Estimation

The aim of this study is to investigate and compare two simulation models of lossy transmission lines (TLs) for signal integrity analysis by an eye-diagram evaluation. The first one is a SPICE model obtained by applying the vector fitting technique, and consists of a cascade of ZY-TL unit cells, where Z and Y take into account the frequency-dependent losses, and TL is an ideal transmission line. The second simulation model is based on the behavioral modeling technique and the time-domain convolution. The lossy interconnect is described by S -parameters as response of a step function. The numerical solution of the convolution integrals can be directly implemented in a mathematical tool or either used to derive a digital wave network that can be processed by digital signal processing techniques. A comparative study of the two simulation models with full-wave and experimental results is provided considering a realistic test case such as traces in a printed circuit board. The advantages and disadvantages of the two models are finally highlighted.