Vector Fitting Research Articles

Lightning induced disturbances in the power network considering losses, frequency effect and non-linearities

The malfunctions and even the material damage caused by lightning stroke are generally significant in electrical networks.. To help design equipment that can withstand lightning disturbances (e.g. electrical insulation, surge arresters, etc.), while compromising with the economic problem, researchers and engineers use numerical simulation. In this paper, we propose a new modeling to study the direct or indirect impact of lightning stroke on an electrical network of power transmission overhead lines or overhead or underground power cables. This modeling is carried out directly in the time domain and takes into account the losses, the frequency dependence and the presence of components with non-linear behavior (example: surge arresters). The new formalism that we propose uses the transmission line equations, the numerical method of Finite Differences Time Domain (FDTD) and the approximation technique called vector fitting. To stimulate the direct or indirect effects of lightning, our modeling is carried out with only the 1D spatial discretization (1D meshing) of the conductive parts, and provides access simoulenatlously to transient voltages and currents at any point of the network. Also consideration to surge arresters is rendered easy in our modeling.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models.

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model. The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation. The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress. Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

A Gray-Box Stability Analysis Method of Grid-Connected Inverter Considering Synchronization Dynamics

The Grid-Connected Inverter (GCI) can be considered a gray box when circuit and controller parameters are missing due to intellectual property rights or parameter variations caused by aging, which poses an impediment to assessing the stability of the system. This paper presents a gray-box stability analysis method based on impedance identification of GCI considering the synchronization dynamics. The impedance frequency responses of GCI are measured by the frequency scanning method on the dq-frame. Meanwhile, the influence of synchronization dynamics and background harmonics is theoretically investigated. A vector fitting (VF) algorithm, co-designed with impedance identification, is then applied to generate polynomial transfer functions. Based on the obtained transfer functions, the stability of the GCI can be judged by the distance relationship between the prohibited area boundary and the center of the gershgorin-circle through the distance formula. Finally, the experiments of both RT-LAB and experimental prototypes are conducted to verify the feasibility of the proposed method.

Rational Approximation of Nonlinear Systems Via NL-VF

This paper presents an alternative vector fitting (VF)-based approach to generate a rational model of nonlinear system behaviors. The proposed approach, named here as nonlinear VF (NL-VF), has its fundament in the previously proposed time-domain VF (TD-VF). TD-VF generates rational models using TD input/output responses and numerical convolution. Unlike TD-VF, NL-VF utilizes input/output vectors in the frequency domain (FD) to produce a rational approximation of the corresponding transfer function/matrix. The input/output FD vectors are obtained in this paper by a numerical Laplace transform (NLT) algorithm. Alternatively, input/output TD vectors available from any solution algorithm can be transformed to FD via NLT and used in the NL-VF approach. Computational efficiency and accuracy of the NL-VF are compared with the TD-VF technique for the single-phase case. It is demonstrated that NL-VF gives more accurate results than TD-VF, in particular when the data is calculated from a time-window, which does not capture the system slow dynamics. Also, unlike TD-VF, NL-VF can handle in a natural way FD weighting, thus exhibiting error control. The proposed approach is applied in this paper to 1) a boost converter circuit, and 2) a network involving simultaneously a three-phase grid-tied photovoltaic (PV) system and a nonlinear reactor load.

An arbitrary-order fully discrete Stokes complex on general polyhedral meshes

In this paper we present an arbitrary-order fully discrete Stokes complex on general polyhedral meshes. We enrich the fully discrete de Rham complex with the addition of a full gradient operator defined on vector fields and fitting into the complex. We show a complete set of results on the novelties of this complex: exactness properties, uniform Poincaré inequalities and primal and adjoint consistency. The Stokes complex is especially well suited for problem involving Jacobian, divergence and curl, like the Stokes problem or magnetohydrodynamic systems. The framework developed here eases the design and analysis of schemes for such problems. Schemes built that way are nonconforming and benefit from the exactness of the complex. We illustrate with the design and study of a scheme solving the Stokes equations and validate the convergence rates with various numerical tests.

Phase De-Embedding of Narrowband Coupled- Resonator Networks by Vector Fitting

This paper introduces a simple and effective way to de-embed the constant phase loading and transmission line from the simulated or measured S-parameter data of a narrowband coupled-resonator network by vector fitting. The phase-corrected S-parameters can be converted to Y-parameters to prepare for rational function approximation and extraction of the coupling matrix for the purpose of computer-aided tuning. This method is applicable to many narrowband coupled-resonator networks including microwave bandpass filters and diplexers. Examples including a simulated triple-mode bandpass filter and a measured wire- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}$ </tex-math></inline-formula> junction diplexer are given to demonstrate the effectiveness of the new technique.

Selected numerical methods to model the fractional-order system behavior of nonlaminated magnetic actuators

Abstract Nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like e. g. hysteresis. Known analytical models lead to trans-cendental system descriptions with fractional-order characteristics, not suited for the actuator control. Although analytical approximations resolve the issue, the inclusion of minor perturbations leads to impractical model orders, which require simplifications and compromise the model accuracy. This article studies numerical methods to directly approximate the transcendental systems or measurement data, allowing for a high accuracy with sufficiently low orders. We improve existing approaches like Levy’s method and vector fitting and apply them to a fractional-order system. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximations.

ASMR 자극을 이용한 정서 형용사 유사성 비교

Autonomous Sensory Meridian Response (ASMR) has been well known to elicit a sense of psychological stability and calmness. Kim and Kim (2022) found that ASMR can be represented in the core affective space of valence. Using this data set, I investigated if ten emotion adjectives (angry, fearful, irritated, happy, calm, gay, sad, anxious, gloomy, and peaceful) which were used as ratings scales also can be represented in the affective space of valence and arousal. Correlation analyses, multidimensional scaling, and vector fitting were performed. The results showed that emotion adjectives were significantly represented on both dimensions. In sum, I confirmed that emotion words as well as emotion-eliciting stimuli are mapped onto the affective space, consistent with the core affect theory (Russell, 1980).

Optimized high-frequency white-box transformer model for implementation in ATP-EMTP.

• High-frequency white-box transformer models can be implemented in EMTP. • ATP can be used to calculate fast transients in power systems. • Transformer models can be formulated as equivalent circuit or in state-space form. • The electromagnetic model can be obtained using FEMM. • Vector fitting and particle swarm optimization are combined to obtain de model parameters. Although several high frequency white-box transformer models have been proposed in the literature, the methodology for their implementation in some programs based on EMTP has not been addressed in detail. This is true in particular for ATP, for which the representation of large transformer models is particularly problematic. This work aims to enable the use of ATP to model detailed transformer equivalent circuits, which would otherwise be seriously questioned. To establish these circuit models, the following must be taken into account: model reduction, magnetic circuit decoupling, avoid numerical instability, limit and optimize the use of resistors, generate ATP versions capable of processing large models. To this end, three generally valid methodologies are presented to reduce the model without compromising the accuracy of the calculation results and, finally, additional specific methodologies are implemented to reduce and adapt the models in the ATP environment. The application of these methodologies results in six possible variants of reduced models, which were successfully validated through a case study used by CIGRE JWG A2/C4.52 to verify the accuracy of transformer models.

A New Approach to Represent the Corona Effect and Frequency-Dependent Transmission Line Models in EMT-Type Programs

This paper presents an accurate and efficient model to represent the corona effect and frequency dependence of line parameters in electromagnetic transient simulations. The new method, named the voltage and frequency dependent line model (VFDLM), can be seen as a more general case of the well-known frequency-dependent (FD) or wideband (WB) line models, wherein the characteristic admittance and propagation function are considered voltage- and frequency-dependent parameters. The time domain traveling wave equations are solved using recursive convolutions and rational approximation through vector fitting (VF). Since the model can be represented by Norton equivalents, it is totally compatible with EMT-type programs. The model is validated through comparisons with three field measurement data available in the literature, and good agreement could be observed between them, showing that the VFDLM is a stable, efficient, and accurate approach to represent the corona effect in EMT-type programs.

Debye Representation of Frequency Dependent Ground for LEMP Analysis With RC-FDTD

Finite-difference time-domain (FDTD) method combined with the recursive convolution technique is applied to compute lightning electromagnetic pulses (LEMP) for dispersive ground adopting Longmire and Smith (LS) model in two-dimensional cylindrical coordinates. The novelty of our study is that, to the best of our knowledge, the LEMP simulation has been realized in the time-domain for the first time by directly using the parameters of the LS dispersive soil model by treating the ground as a multipole Debye medium without using approximate techniques such as vector fitting. As a numerical example, the LEMP is simulated above and under the dispersive ground with buried rock formation, which is also modeled as the dispersive Debye medium. The performed simulations are compared at distances of 500 m, 5 km, and 50 km away from the lightning channel for both first stroke and subsequent stroke. The results show that the case of dispersive ground and the rock leads to a difference of up to 61.77% with respect to using constant electrical parameters.

Model-Based VF Technique for Parasitic Reflections Reduction of Frequency-Domain Chipless RFID Systems

In a frequency-domain chipless RFID system, the backscattered signal from a tag is directly obtained in the frequency domain over limited bandwidth. However, to reduce the parasitic reflections, it is crucial to obtain the backscattered signal in the time domain. This letter proposes a precise quasi-analytic method, known as the model-based vector fitting (VF) technique, to provide the closed-form equation of the backscattered response in the time domain. The proposed method successfully recovers a tag’s identification (ID) among parasitic reflections using a single tag measurement without requiring prior knowledge about the tag.

Circuit Modelling of Broadband Antenna Using Vector Fitting and Foster Form Approaches for IoT Applications

Computation of the broadband antenna impedance behavior requires the wideband lumped equivalent circuit. This work aims to provide a comprehensive study of broadband antenna equivalent circuit models over broad frequency ranges for Internet of Things (IoT) applications using multiple approaches. The first approach is a Foster approximation, which is based on the antenna-simulated scattering parameters and impedance data. The second concerns a vector-fitting fitting approximation, which is based on the antenna-simulated impedance/admittance data. The studied antenna is modeled based on the radiating element’s geometry and the multifractal slots, in addition to the DGS (Defected Ground Plane) effects. Applying these techniques, wideband lumped equivalent circuits of the antenna have been computed which are in good agreement with measurement data. These models could be useful for the enhancement of the performance of a broadband antenna and its systematic design as well as offering the advantage of saving computation time for full-wave simulations and facilitating the solution of problems that have both an electromagnetic part as well as a circuit part. For further analysis, the Gaussian pulse has been generated to drive a time-domain analysis of the current and power response waveforms antenna behavior under load.

Transmission Lines Impedance Fitting Using Analytical Impedance Equation and Frequency Response Analysis

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.

Vector Fitting–Cauchy Method for the Extraction of Complex Natural Resonances in Ground Penetrating Radar Operations

In this paper, we obtain the Complex Natural Resonances of an object from the backscattered response in the frequency domain with a novel rational function approximation method based on both Vector Fitting and Cauchy methods. We determine the system order and an initial set of poles, which are used as a basis for a rational function approximation. The results from the simulations and experiments show an improvement in the reconstructed signals and the accuracy of the CNRs calculated, with an increased tolerance to the critical Signal-to-Noise Ratio. This is being used in the problem of GPR landmine humanitarian detection in Colombia.

Neural Network With Fourier Series-Based Transfer Functions for Filter Modeling

The Fourier series is introduced as a transfer function (TF) in the artificial neural network (ANN) for parametric modeling of microwave filters in this letter. The reported pole-residue-based TF leads to an order-changing problem of input samples from vector fitting, which is usually solved with an order-tracking technique or data classification. The proposed Fourier series-based TF does not have to carry out the time-consuming operation because the only coefficient order can be determined for all input samples in an iterative process. Compared with the pole-residue-based TF, moreover, the ANN training involves a small number of TF coefficients in the proposed method. The predicted electromagnetic (EM) response is obtained from the coefficients of the ANN output. An example of the ultrawideband (UWB) filter is employed to verify the effectiveness of the Fourier series-based TF.

Wideband Simulations of Periodic Structures by the Hybrid Spectral FDTD/TD-VFz Method

The spectral finite-difference time-domain method is combined with the discrete-time time-domain vector fitting (TD-VFz) algorithm to analyze three-dimensional (3-D) periodic structures excited by oblique incident plane waves over a wide frequency band. The time signal reconstruction with TD-VFz produces an untruncated response over an infinite time window allowing an accurate spectral result, especially near the cutoff frequency separating the spectrum propagating wave region of the evanescent wave region.

Parameterized Modeling Incorporating MOR-Based Rational Transfer Functions With Neural Networks for Microwave Components

Neuro-transfer function (neuro-TF) methods are deemed as powerful tools in modeling the electromagnetic (EM) behavior of microwave passive components. Existing neuro-TF methods either endure the issue of &#x201C;order-changing&#x201D; or the issue of mismatch of poles/zeros, both calling for specific algorithms to process the data of the transfer function coefficients as a part of model development. This letter proposes a novel neuro-TF method to eliminate the two issues simultaneously by using combined neural networks and model-order reduction (MOR)-based rational transfer functions. In the proposed method, the coefficients of the transfer function are computed by the MOR technique instead of vector fitting. The use of MOR allows the order of the transfer function to remain constant in different regions in the design parameter space, thereby avoiding the issue of &#x201C;order-changing.&#x201D; Additionally, the coefficients of the rational transfer function resultant from MOR are naturally sorted according to the order of frequency, which eliminates the issue of mismatch of poles/zeros and subsequently improves modeling accuracy. Compared with existing neuro-TF methods, the proposed method achieves better modeling accuracy for the same geometrical variations. Two microwave examples are utilized to demonstrate the advantages of the proposed method.

Dielectric Response Model for Transformer Insulation Using Frequency Domain Spectroscopy and Vector Fitting

This paper proposes a rational approximation-based approach to find positive real parameters for the extended Debye model (EDM), aimed at condition assessment of insulation systems of power transformers. The EDM can model the slow and fast polarization phenomenon, including relaxation mechanisms with different relaxation times within a composite dielectric material. In the proposed approach, the complex permittivity of the transformer’s composite insulation is approximated via rational functions, as given by the vector fitting (VF) software tool, and the EDM parameters are identified from the obtained poles/residues. To guarantee positive real parameters, i.e., a physically realizable circuit, VF is internally modified to calculate the final residues of the rational approximation via a constrained linear least-squares problem without resorting to further post-processing algorithms, as in existing methods, hence without affecting fitting accuracy. The effectiveness of the parametrized EDM is demonstrated in two ways: (a) by reconstructing frequency domain spectroscopy (FDS) curves provided via measurements in new oil-immersed power transformers and (b) by the comparison of the calculated polarization current given by EDM versus real measurements in time domain. The achieved fitting accuracy in most of the cases is above 99 percent for the reconstructed FDS curves, while the polarization current waveform is reproduced with good agreement.

A New Approach on Modeling of Pulsed-Power Loads

Pulsed power sources provide high-power waves with high frequency (HF) content for a wide range of applications. Conventionally, a simple resistance is employed for the most prevalent pulsed power loads. However, the load model can highly affect the efficiency of source design. This paper contributes to fill this gap by considering the HF behavior of the loads. Accordingly, a new approach has been proposed to present a general HF lumped-circuit model for pulsed power loads. The frequency response of the loads is identified using the Finite Integration Technique (FIT). Subsequently, an equivalent circuit model is established based on the vector fitting (VF) algorithm. The applicability of the approach has been verified by comparison with two experiments, i.e. Vircator and coaxial reactor as the loads. It is indicated that the HF-based model can significantly improve the simulation results to be in good agreement with experiments. The results present that while a pure-resistive load model could lead to about 30% error in the estimation of the characteristics of output voltage, it is about less than 5% in the case of the proposed HF load model.