Frequency-dependent Model Research Articles

Numerical analysis of the frequency-dependent Jiles-Atherton hysteresis model using the example of Terfenol-D material

<p>The Jiles-Atherton model has been widely used in describing the hysteretic property of a magnetic material or device. However, the calculation errors are not so easily discovered. With a complex expression, the frequency-dependent Jiles-Atherton model should be solved numerically with appropriate settings. This paper proposes an effective solving method for this model and describes some necessary analysis built on the numerical results. In the numerical method proposed in this manuscript, the anhysteretic magnetization was calculated by the secant method, and the trapezoidal rule was utilized to form the implicit function, which can be calculated by the fixed-point iteration. Compared to the other common methods, the proposed one has a friendly expression and fast computation speed. The Terfenol-D material was taken as an example for the numerical analysis. The feasible region was determined and the commonly used approximation that neglects the term of the magnetic field when calculating the magnetic induction intensity was tested. At last, the required number of sampling points per period was reached to guarantee high precision from analyzing its influence on the computation precision. The proposed numerical method is helpful for high-precision solutions of the frequency-dependent Jiles-Atherton model. The results from the numerical analysis can also help users avoid some incorrect calculations when employing this hysteresis model.</p>

State-of-power estimation for lithium-ion batteries based on a frequency-dependent integer-order model

Power capability of lithium-ion batteries is strongly correlated with electric vehicle’s accelerating and braking performance. However, the estimate of state-of-power relies highly on battery models, whose accuracy usually increases with the complexity. We here propose a simple and accurate frequency-dependent integer-order model for battery state-of-power estimation. First, a random search-pseudo gradient descent algorithm is proposed to identify the parameters of our model from electrochemical impedance spectroscopy in the frequency domain. Then, the proposed model is mathematically derived in the time domain. Next, two strategies are developed to estimate battery state-of-power under different constraints — using particle swarm optimization and direct inversion algorithms. Finally, our method is experimentally verified: the proposed frequency-dependent model shares similar complexity compared with the conventional integer-order model, while its accuracy is competitive to that of the fractional-order model. With such a simple and accurate model, our state-of-power estimation error is 90% smaller than that based on the conventional integer order model, and the computational time is 99.8% lower than that corresponds to the fractional-order model. Since the proposed method is developed upon the conventional integer-order model, it has a strong potential for real-life application and can be easily integrated into the existing battery management systems.

A novel apparent power loss based distributed generator siting and sizing method considering dependent loads

In the present paper, it is first established that even though the standard Active Power Loss Sensitivity Factor (APLSF) based technique for Renewable Energy based Distributed Generation (REDG) system excels with respect to many available technical assessment indicators, its performance falls short in case of line loss reduction and power transfer capacity improvement indicators. On further investigation through Dynamic Fault Tree Analysis technique, it is found that the unsatisfactory performance of APLSF stem from neglecting reactive power loss and line reactance. Therefore, a novel apparent power loss augmented technique coined as Dynamic Loss Evaluation Indicator (DLEI) method is proposed here. The suitability of the proposed method is validated on IEEE 33 and 85 bus distribution systems for both voltage and voltage and frequency dependent load models and it is shown that the aforementioned indicators are improved along with the other indicators like voltage profile and voltage stability to name a few. For further validation, contingency and power quality analysis are also carried out and improved performance is observed in DLEI method when compared against the APLSF based method.

An implantable ISM band antenna for biomedical application

Abstract This article presents a compact implantable antenna for biomedical use in the ISM band (2.4–2.48 GHz). The antenna is designed with Roger RT/duroid 6010.2LM high permittivity substrate of thickness 0.25 mm, and feed with a 50 Ω co-axial feed. A hybrid-loop resonator slot structure and C & I-shaped slots in the radiating patch has enabled the antenna to work in the ISM band. Via less ground makes this design simple, easier to fabricate, and a suitable candidate for implantable application. The proposed antenna occupies a small volume of 0.0984 λ 0 × 0.082 λ 0 × 0.00468 λ 0 and retained 152 MHz bandwidth (2.4077–2.5599 GHz with FBW 7.64 %) with a maximum gain of −22 dBi where λ 0 is guided wavelength. The projected antenna has good performance in the multi-layer tissue model, male human head voxel model, frequency-dependent skin model, and in muscle phantom by maintaining a minimum −20 dB return-loss in the ISM band. The proposed antenna’s Device Integration using a frequency-dependent skin phantom was performed and the results are well-suited for biomedical applications in the ISM band. The bare antenna was used to study the Specific Absorption Rate (SAR) in the human scalp. Where for 1 g and 10 g tissues the investigated results are 626.05 W/kg and 84.4 W/kg for an input power of 1 W, however the input power is limited to maximum 2.55 mW (for 1 g tissue) and 23.56 mW (for 10 g tissue) to comply with IEEE SAR guidelines. The qualities of the manufactured antenna are verified in a skin-imitating gel and animal tissue that exhibits good agreement with the simulation outcomes.

Dynamic state estimation based protection using multi-section multi-layer frequency dependent line model for underground cables in MMC-HVDC grids

Dynamic state estimation based protection using multi-section multi-layer frequency dependent line model for underground cables in MMC-HVDC grids

Convolution Based Time Domain Fault Location Method for Lines in MMC-HVDC Grids With Distributed and Frequency Dependent Line Model

Convolution Based Time Domain Fault Location Method for Lines in MMC-HVDC Grids With Distributed and Frequency Dependent Line Model

Analytical Double-2D Frequency-Dependent Leakage Inductance Model for Litz-Wired High-Frequency Transformer

Accurate and fast calculation of frequency-dependent leakage inductance is critical for the optimization of the high-frequency transformer with Litz wire winding. The analytical method is widely used due to its high computation speed. However, its computation accuracy is limited due to the following factors. i) One-dimensional (1D) or two-dimensional magnetic field model (2D) has unsatisfying accuracy for the transformer with a rotationally asymmetric structure. ii) The skin and proximity effect factors based on the multilayer foil winding are inaccurate for the Litz wire winding in the calculation of frequency-dependent magnetic energy. This paper proposes a double-2D frequency-dependent leakage inductance model for the transformer with Litz wire winding. It uses the image method to calculate the 2D leakage magnetic field inside and outside the core window, respectively, which considers the rotationally asymmetric structure in leakage inductance calculation. The round conductor model is proposed for the frequency-dependent magnetic energy calculation. The single strand in a Litz wire is taken as the basic modeling object of the round conductor model, which is more detailed than the multilayer foil winding model for the Litz wire winding. The comparison between the experiment, FEM, state-of-the-art models and the proposed model is conducted for eight transformers with E-core, U-core, round or rectangular Litz wire winding. The proposed model shows satisfying computation accuracy in the whole frequency band. And the computational speed of the proposed model is 100 times that of the FEM.

Free-field characterization of locally reacting sound absorbers using Bayesian inference with sequential frequency transfer

The in situ absorption characteristics of sound-absorbing samples are generally estimated inversely from sound field measurements above the sample’s surface. However, the entire measurement process is subject to numerous sources of uncertainty, which cannot be accounted for using deterministic inference methods. This paper introduces a Bayesian framework, including sequential frequency transfer to infer point estimates and uncertainty ranges of the frequency-dependent surface admittance, the corresponding sound absorption coefficient and the associated measurement and model uncertainty. The inference is conducted in two phases: in the initial phase, the absorption characteristics and the measurement and model uncertainty at a predefined initial frequency are inferred based on a weakly informative prior. Extensive prior predictive checks are conducted to find the best trade-off between a weak level of informativeness of the prior and physically meaningful predictions of the sound field above the absorber. In the sequential phase, the posterior mean at an analyzed frequency serves as the prior mean at the subsequent frequency. The framework is applied to simulated as well as real free-field measurements of the specific impedance above two different rock wool samples. The measurements are conducted with a combined pressure-particle velocity probe and the samples are assumed to exhibit local reaction behavior. For the investigated samples, a minimum number of four individual measurements of the specific impedance already allows for an accurate estimation of the frequency-dependent absorption characteristics and the associated measurement and model uncertainty, particularly for frequencies above 600 Hz. Due to the proposed sequential frequency transfer, the computational effort of the sampling-based Bayesian inference at a discrete frequency is significantly reduced. This paves the way for efficient inference of frequency-dependent model parameters while overcoming the curse of dimensionality associated with the inference of stochastic processes. The proposed framework lays the foundation for accurate and efficient inference of frequency-dependent parameters in models beyond the field of acoustics.

Comparison of Rational Krylov and Vector Fitting in Transient Simulation of Transmission Lines and Cables

This paper presents stringent comparisons between Vector Fitting (VFIT), Relaxed Vector Fitting (R-VFIT) and Rational Krylov Fitting (RKFIT) techniques in the fitting of transmission line and cable functions to rational forms while accounting for the frequency dependence of electrical parameters. The fitting procedures encapsulate new solution strategies to improve fitting performance. Various case studies are presented to assess the performance of RKFIT in terms of model order reduction, passivity violation and computing times. In addition, the use of RKFIT in obtaining the frequency dependent cable model (FDCM) is demonstrated for the first time together with a resolved case study that showed unstable behavior with the universal line model (ULM) methodology.

Rational Function Approximation of Transformer Branch Impedance Matrix for Frequency-Dependent White-Box Modeling

Transformer white-box models are used by the manufacturers to calculate internal winding voltages during the lightning impulse test. The model can also be applied in general network studies, but the model accuracy should then be improved, considering the many different voltage waveforms and frequencies that can exist in the system. Accuracy improvements are achievable by including the frequency-dependency of the branch impedance matrix via rational function approximation, but the large size of the matrix makes such modeling very difficult. Two suitable methods for passive rational modeling are presented, based on vector fitting and residue perturbation in either phase domain or modal domain. Application to a power transformer shows that the two methods are capable of fitting a 213×213 branch impedance matrix with a 6 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order passive pole-residue model in a few seconds. The resulting model is included in a complete white-box state-space model of the transformer that is compatible with a previously implemented model interface for EMTP. An efficient procedure is presented for validating the simulation result by the Numerical Laplace Transform. Comparison with a measurement shows that the inclusion of the frequency dependency gives a better reproduction of the measured waveshape than a previously proposed damping-factor model.

Development of a Novel Magneto-Rheological Elastomer-Based Semi-Active Seat Suspension System

Human operators in the transportation sector are exposed to whole-body vibration (WBV) while driving. Occupational exposure to WBV, predominant at low frequencies (&lt;20 Hz), has been linked to spinal injuries and reduced functioning. This study aims at the design development of a novel semi-active seat suspension system featuring magneto-rheological elastomers (MREs) to mitigate the WBV. The proposed suspension system allows a greater range of strokes, while ensuring the MRE remains within an acceptable level of deformation. Several MRE samples were fabricated and characterized under shear mode. Afterward, a field- and frequency-dependent phenomenological model was developed to predict the viscoelastic properties of MREs as functions of both the excitation frequency and applied magnetic field. The MRE material model was subsequently used to design and optimize an adaptive seat suspension system incorporating a C-shaped MRE-based isolator in parallel and series with passive springs. The proposed adaptive seat suspension system demonstrated a frequency shift of 29% by increasing the applied current from 0 to 2 A. Finally, a 6-DOF lumped parameter model of a seated human subject combined with the proposed semi-active suspension system featuring the MRE isolator has been formulated to investigate the vibration transmissibility from the floor to the subject’s head.

Optimization of Equipment Operation in Power Systems Based on the Use in the Design of Frequency-Dependent Models

This article is devoted to the biggest problem of our time: the development of modern and highly efficient equipment for energy systems. We propose improved mathematical models for starting asynchronous motors in isolated power systems. The results of experiments carried out on a model of an isolated network are presented. Both frequency-dependent and frequency-independent models were used. A comparison of various models is given. The advantages of the frequency-dependent model, which provides a more accurate representation of the processes, are shown. The obtained results were discussed, and the possibility of their use for future research was assessed.

Stochastic competitive release and adaptive chemotherapy.

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemoresistance in the tumor by managing the ecological mechanism of competitive release of a resistant subpopulation. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of N cells, with a chemotherapy control parameter, C(t), which we use to dynamically impose selection pressure on the sensitive subpopulation to slow tumor growth and manage competitive release of the resistant population. The adaptive chemoschedule is designed based on the deterministic (N→∞) adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model (N=10K-50K) to ascertain the cumulative effect of the stochastic fluctuations on the efficacy of the adaptive schedules over multiple rounds. We quantify the stochastic fixation probability regions of the R and S populations in the HSR trilinear phase plane as a function of the control parameter C∈[0,1], showing that the size of the R region increases with increasing C. We then implement an adaptive time-dependent schedule C(t) for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles over multiple rounds of adaptive therapy. The variances increase subquadratically through several rounds before the evolutionary cycle begins to break down. Despite this, we show the stochastic adaptive schedules are more effective at delaying resistance than standard maximum tolerated dose and low-dose metronomic schedules. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes (i.e., different values of N) if the goal is to maintain a sustained balance among competing subpopulations of cells to avoid chemoresistance via competitive release in a stochastic environment.

Research on concentrated frequency-dependent parameter model for short overhead transmission lines based on first-order rational function fitting

The impedance of power lines is influenced by geological conditions and skin effect, resulting in frequency-dependent characteristics. In this study, a centralized parameter frequency-dependent line model based on first-order rational function fitting is investigated for short overhead transmission lines. The proposed model incorporates a parallel branch consisting of resistance and inductance obtained through rational function fitting, which mimics the frequency-dependent behavior of the line. The coupling between multiple conductors is represented using controlled sources. Comparative analysis of fitting accuracy and computational efficiency across various orders of rational functions reveals that the first-order rational function fitting offers superior computational efficiency while maintaining high accuracy in the medium and low-frequency range. Simulation results demonstrate that the proposed model, when disregarding wave propagation effects, exhibits comparable accuracy to the distributed parameter line model while achieving higher computational efficiency. Moreover, in transient analysis predominantly influenced by power frequency, the proposed model outperforms the frequency-independent pi(π) line model in terms of accuracy.

Estimating distance to transient and restriking earth faults in high-impedance grounded, ring-operated distribution networks using current ratios

Earth faults occur frequently in distribution networks, and in resonant grounded networks they are challenging to locate precisely due to their naturally low fault current. Transient and restriking faults are more challenging still due to the short time available for the fault location logic, as well as the absence of steady-state conditions. This paper investigates the performance of three fault location methods utilizing the ratios of various current components in a network operated in a closed-ring configuration. A frequency dependent model of a distribution network is used to simulate transient and restriking faults, and both isolated grounding and resonance grounding are considered. The results show that fault location based on negative-sequence currents is able to locate transient faults, and its accuracy of a few hundred metres is comparable to what has been observed during permanent faults. A zero-sequence method is observed to be less accurate, particularly in resonant grounded networks. A transient method is also proposed, and while it is fast, it is ultimately limited by the presence of loads and branches in the network. It is concluded that the negative sequence method is best suited for transient and restriking faults.

Evaluation of lightning-originated stress on distribution class surge arresters

The paper focuses on evaluating the stress on distribution class surge arresters (SAs) caused by lightning strikes. It proposes a procedure for estimating the statistical distribution of energy absorbed by SAs due to both indirect and direct lightning strikes, which is a crucial step for assessing the probability of SAs failure. Two different SA representations are considered, namely, a static nonlinear resistance and a dynamic, frequency dependent model. After analyzing the overvoltage and current waveforms caused by lightning strikes and considering the effect of flashover occurrence, the paper assesses the effect of several factors on the current and energy absorption, namely the presence of a periodically grounded shield wire, of the grounding resistance value, and of the distance between subsequent SAs. The analysis shows that the static model can be considered accurate enough for evaluating the stress originated by direct and indirect lightning on distribution class SAs.

Passivity enforcement of wideband model through a new and full perturbation formulation

Passive component models are necessary to ensure numerical stability in the simulation of electromagnetic transients in power systems. However, it is challenging to represent transmission lines and cables with frequency-dependent wideband models that are accurate, efficient, and passive. This paper proposes a new method for the passivity enforcement of wideband line and cable models. The wideband models rely on pole-residue identification of characteristic admittance and propagation function in rational forms. In case the resulting models are not passive, the proposed method simultaneously applies perturbation to the residue matrices of characteristic admittance and propagation function. The set of equations related to passivity enforcement through the residues of propagation function in phase domain is complex and presented for the first time in this paper. The proposed approach minimizes the overall perturbation for maintaining passivity as opposed to the existing simplified approaches that rely on the perturbation of the residues of either characteristic admittance or diagonal elements of propagation function. The performance of the method is validated with application cases, and it is shown that it outperforms the existing methods that seek simplification in problem formulation.

A novel frequency-dependent lattice Boltzmann model with a single force term for electromagnetic wave propagation in dispersive media

Electromagnetic wave simulation is of pivotal importance in the design and implementation of photonic nano-structures. In this study, we developed a lattice Boltzmann model with a single extended force term (LBM-SEF) to simulate the propagation of electromagnetic waves in dispersive media. By reconstructing the solution of the macroscopic Maxwell equations using the lattice Boltzmann equation, the final form only involves an equilibrium term and a non-equilibrium force term. The two terms are evaluated using the macroscopic electromagnetic variables and the dispersive effect, respectively. The LBM-SEF scheme is capable of directly tracking the evolution of macroscopic electromagnetic variables, leading to lower virtual memory requirement and facilitating the implementation of physical boundary conditions. The mathematical consistency of the LBM-SEF with the Maxwell equations was validated by using the Champman-Enskog expansion; while three practical models were used to benchmark the numerical accuracy, stability, and flexibility of the proposed method.

Petrophysical parameters inversion for heavy oil reservoir based on a laboratory-calibrated frequency-variant rock-physics model

Heavy oil has high density and viscosity, and exhibits viscoelasticity. Gassmann's theory is not suitable for materials saturated with viscoelastic fluids. Directly applying such model leads to unreliable results for seismic inversion of heavy oil reservoir. To describe the viscoelastic behavior of heavy oil, we modeled the elastic properties of heavy oil with varying viscosity and frequency using the Cole-Cole-Maxwell (CCM) model. Then, we used a CCoherent Potential Approximation (CPA) instead of the Gassmann equations to account for the fluid effect, by extending the single-phase fluid condition to two-phase fluid (heavy oil and water) condition, so that partial saturation of heavy oil can be considered. This rock physics model establishes the relationship between the elastic modulus of reservoir rock and viscosity, frequency and saturation. The viscosity of the heavy oil and the elastic moduli and porosity of typical reservoir rock samples were measured in laboratory, which were used for calibration of the rock physics model. The well-calibrated frequency-variant CPA model was applied to the prediction of the P- and S-wave velocities in the seismic frequency range (1–100 Hz) and the inversion of petrophysical parameters for a heavy oil reservoir. The pre-stack inversion results of elastic parameters are improved compared with those results using the CPA model in the sonic logging frequency (∼10 kHz), or conventional rock physics model such as the Xu-Payne model. In addition, the inversion of the porosity of the reservoir was conducted with the simulated annealing method, and the result fits reasonably well with the logging curve and depicts the location of the heavy oil reservoir on the time slice. The application of the laboratory-calibrated CPA model provides better results with the velocity dispersion correction, suggesting the important role of accurate frequency dependent rock physics models in the seismic prediction of heavy oil reservoirs.

An Enhanced Method to Achieve Exact DC Values for Frequency-dependent Transmission lines

This paper proposes an improved method to enhance the dc response of a frequency-dependent transmission line model used in EMT studies. A modification to the rational function approximation of propagation and characteristic admittance matrices of a transmission line is introduced to enforce exact dc values at 0 Hz. Furthermore, weighting factors are applied to improve accuracy at low frequencies. Finally, the order of the propagation function is reduced to decrease the computational effort.The validity of the proposed approach is demonstrated using examples involving underground cables and overhead lines. First, the effect of dc correction is demonstrated by comparing transmission line frequency domain characteristics. In addition, time domain simulations via open and short circuit conditions show a more accurate simulation of HVDC transmission lines with the proposed method.