Frequency-dependent Model Research Articles

Analysis of Frequency-Dependent Network Equivalents in Dynamic Harmonic Domain

Rational function-based models have proved to be very efficient for accurate frequency-dependent modeling of power system components. These models are able to characterize the components terminal behaviours (analysing the admittance matrix) for nodal analysis. This provides a fast convergence and inherent stability to the solution routine of the model. This work presents a general framework for interfacing the dynamic phasor method to the rational models. That would be promising for the electromagnetic transient analysis (under harmonic distortion), in the frequency domain. Therefore, Y-element rational pole-residue models (employing the vector fitting method) are developed. Moreover, the pole-residue model is converted into the state-space representation. Next, the dynamic harmonic approach (in the frequency domain) is employed for harmonic analysis. It is shown that the order of state-space system can become a major concern for frequency-dependent networks analysis. Therefore, to generate a reduced-order model, the balanced realization theory is applied. Moreover, (for the sake of simplicity and efficiency) the trapezoidal integration rule is employed to discretise the state-space equations. For validation of the modelling, it is applied on three test case studies and results of these studies are compared with their time-domain analysis results.

A frequency-dependent ground-motion spatial correlation model of within-event residuals for Fourier amplitude spectra

Ground motion time series recorded at stations separated by up to about 50 km show a frequency-dependent spatial coherency structure, and the corresponding ground motion intensity measures are found to be correlated. As omitting this correlation can result in underestimation of seismic losses in risk analysis, it is critical to quantify the spatial correlation structure for ground motion Fourier spectra estimated at different sites during a single event within a region. Toward this goal, we have developed an empirical frequency-dependent spatial correlation model for the within-event residuals of effective Fourier amplitude spectra from the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation (NGA) West2 database. The correlation model shows slower decrease of the spatial correlation with distance at lower frequencies compared with higher frequencies, in agreement with the underlying ground motion data, and no significant dependence on the magnitude of the earthquakes is observed. We use this empirical model to incorporate frequency-dependent spatial correlation into a hybrid deterministic-stochastic broadband ground motion generation module, which successfully generates synthetic time series for seven western US earthquakes with frequency-dependent spatial correlation that closely mimics that of the empirical model. Furthermore, the method also significantly improves the correlation for spectral accelerations, cumulative absolute velocities, and Arias intensities, compared with that derived from the original broadband module.

Frequency-dependent nonlinear electromechanical coupling behaviors of ferroelectric composites

In this paper, a frequency-dependent micromechanics-based model is developed to study the nonlinear electromechanical coupling behaviors of ferroelectric composites which in general consist of ferroelectric inclusions and a polymer matrix. The coupling behavior not only depends on the volume concentration and the shape of the inclusions, but also on the frequency of external applied field. For the frequency-dependent properties, an exponential function is introduced to evaluate the remanent polarization and coercive field of the ferroelectric phase. Then a two-level micromechanics-based model is applied to obtain the hysteresis loops and butterfly-shaped responses of the ferroelectric composites at various frequencies. The first level model deals with the single ferroelectric phase by considering the evolution of domain switches while the second level is regarding to the two-phase ferroelectric composites. To verify the developed theory, we compared the calculated results with the existing experimental data for the hysteresis of electric displacement versus electric field and the butterfly-shaped strain versus electric field of the 1–3 type of composites with PZT fibers embedded in an epoxy matrix. The comparisons between theoretical calculations and experimental data show reasonable agreement. In the meantime, the influences of the shape and the volume concentration of the inclusions to the overall effective properties of the composites have been investigated and will shed the light for the design and structure architecture of the ferroelectric composites.

Generalized Frequency Dependent Small Signal Model for High Frequency Analysis of AlGaN/GaN MOS-HEMTs

Traditional lumped small signal equivalent circuit models of AlGaN/GaN metal oxide semiconductor high electron mobility transistors (MOS-HEMTs) are made up of constant valued circuit elements. Such models are unable to capture the high frequency behavior (above 20 GHz) of the device. In this work, a modified small signal equivalent circuit model of AlGaN/GaN MOS-HEMTs is presented. The key feature of the proposed model is that the values of the different circuit elements in the model are considered to be frequency dependent in nature and not constants. The frequency dependent value of each circuit element is mathematically represented using polynomial functions where the coefficients of the functions are determined via a least-square curve fitting approach. This frequency dependent attribute of the circuit element values ensures that the proposed model is very accurate at high frequencies without sacrificing the compactness of the model topology. The accuracy of the proposed model has been verified up to 50 GHz using experimentally measured Y-parameters of AlGaN/GaN MOS-HEMTs having a different gate dielectric and gate length.

Development of an Experimental Scaled-Down Frequency Dependent Transmission Line Model

The penetration of power electronic based equipment in the power grid has increased the co-occurrence of electromechanical and electromagnetic transients. Significant research efforts have been focused in the last decade to study these interactions. Frequency dependent transmission line models are indispensable to understand such interactions. This paper describes a systematic procedure for the development of an experimental scaled-down 220 V frequency dependent transmission line model of a 230 kV transmission line. A reduced order lumped parameter frequency dependent transmission line using modal transformation is derived for the 230 kV transmission line and scaled-down to 220 V. Clarke and inverse Clarke transformations are implemented using specially designed 1- $\phi $ transformers. The inductances of the scaled-down model are realized using amorphous cores. Line energization, balanced, and unbalanced fault studies are carried out using the experimental line. The experimental results are compared with the simulation results of a universal line and a constant parameter $\pi $ -model using EMTP-RV. The proposed experimental line properly captured important features of the frequency dependent line such as smoother wave shape during energization, traveling time, currents, and voltage magnitudes during the fault and after the fault removal.

A Node-to-Node Admittance Functions Implementation of an Improved Frequency Dependent Multiconductor Transmission Line Model

The electromagnetic interference (EMI) performances of the interconnects and cables can be predicted via a standard multi-conductor transmission line (MTL) model, while the latter is not valid for the evaluation of power rail collapse and ground bounce responses. To circumvent the limitations, a more general and feasible improved MTL representation is presented in this paper. It physically incorporates the partial resistance and partial inductance parameters of all signal and reference conductors. To consider the frequency dependent behavior of the per-unit-length (PUL) electrical parameters in time domain simulations, a terminal description for this improved MTL model with any desired length is demonstrated. Subsequently, an equivalent node-to-node admittance functions (NAFs) implementation for this terminal representation is carried out. The correctness and effectiveness of the NAFs circuit model in time domain is then numerically validated by analyzing two dedicated examples.

Time-Domain Fault Location Algorithm for Double-Circuit Transmission Lines Connected to Large Scale Wind Farms

This article introduces a new time-domain fault location algorithm for two-terminal parallel transmission lines connected to large scale wind farms. The proposed algorithm employs only a half-cycle data window of synchronized current samples at both line terminals to avoid inaccurate estimation of current phasors due to the generated sub- and inter-harmonics currents by the wind farms. The proposed algorithm does not need any transformation method to decouple the double-circuit transmission line. Moreover, it takes into consideration the effect of the line asymmetry and the potential couplings between the six phases. The fault location equation is deduced by equalizing the differential components of the calculated instantaneous voltages at the fault point, and then the fault distance is estimated directly without any iterative algorithm. The two-terminal parallel transmission line is emulated by PSCAD/EMTDC platform utilizing the frequency-dependent phase model, and the required calculations for fault location are conducted by MATLAB software. The proposed algorithm is tested for several fault resistances and fault locations, and all fault types, including cross-circuit faults. In addition, the effect of measurement, synchronization, and line parameters errors on the fault location accuracy is investigated. The obtained results confirm acceptable accuracy of the proposed fault location algorithm.

A New Approach to the Fault Location Problem: Using the Fault’s Transient Intermediate Frequency Response

The fault location problem has been tackled mainly through impedance-based techniques, the travelling wave principle and more recently machine learning algorithms. These techniques require both current and voltage measurement. In the case of impedance-based methods they can provide multiples solutions. In the case of the travelling wave approach it usually requires high sampling frequency measurements together with sophisticated identification algorithms. Machine learning techniques require training data and re-tuning for different grid topologies. This paper proposes a new fault location method based on the fault’s transient intermediate frequency response of the system immediately after a fault occurs. The transient response is characterized by the travelling wave phenomenon together with intermediate frequencies of oscillation, which are dependent on the faulted section and the fault location. In the proposed fault location solution, an offline methodology identifies these intermediate frequencies and their dependency on the fault location is fitted using a polynomial regression. The online fault location is performed using those polynomial regressions together with voltage measurements from the system and simple signal processing techniques. The full method is tested with an EMT simulation in PSCAD, using the exact frequency dependent model for underground cables.

Frequency and Power Dependence of Passive Intermodulation in Connectors With Contact-Material Nonlinear Modeling

Passive intermodulation (PIM) is generally regarded as an unavoidable interference in radio frequency (RF) circuit and system, which exhibits dynamic characteristics with the change of signal frequencies and powers. In this letter, a prediction model of frequency and power dependence of PIM is theoretically proposed and experimentally verified. Physical nonlinearities of truncated distortion and tunneling effect are introduced to provide explanations for the contact surface-induced PIM. Considering nickel is the nonlinear material source in connector coating, the impact of signal frequency on PIM is investigated by calculating the current density in the magnetic area coupled with skin effect theory. Through the combination of two PIM generation mechanisms, a novel equation-based equivalent circuit model is provided to simulate the third-order intermodulation (IM3) powers in connector resulting from different signal frequencies and powers. The frequency and power dependence characteristics are observed from both the theoretical predictions and measurements.

A magnetic field- and frequency-dependent dynamic shear modulus model for isotropic silicone rubber-based magnetorheological elastomers

Both experimental and modeling studies on the dynamic shear storage and loss moduli of isotropic magnetorheological elastomers (MREs) were carried out in this work. Isotropic MREs were prepared based on silicone rubber filled with different contents of micro-sized carbonyl iron particles (CIPs). The magnetization characteristics of the prepared MREs and their dynamic shear moduli at a linear viscoelastic (LVE) strain and under different magnetic flux densities were measured. Based on the magnetization model of MREs, the magnetic dipole theory, and the quantitative analysis on the frequency-dependence of magneto-induced dynamic shear moduli, a new magneto-induced shear modulus model that was dependent on the CIP content and frequency was proposed. The model parameters can be simply determined. Combining with the generalized Maxwell viscoelastic model, that was used to describe the zero-field shear moduli of MREs, a new macroscopic magneto-viscoelastic constitutive model was developed to describe the magnetic field- and frequency-dependent shear modulus of the isotropic MREs with different CIP contents. The developed magneto-viscoelastic constitutive model was verified by comparing the model calculations with experimental data. The results showed that in the LVE strain state, the proposed magneto-viscoelastic model could accurately predict the dynamic shear storage and loss moduli of the isotropic MREs with different CIP contents in broad ranges of frequency and magnetic flux density using the unified model parameters.

Role of defects and phonons in bandgap dynamics of monolayer WS2 at high carrier densities

We conduct ultrafast pump-probe spectroscopy in monolayer WS2 at high pump fluences to gain direct insight into interactions between a high density of carriers, defects, and phonons. We find that defects in the lattice play a major role in determining the relaxation dynamics by trapping the photoexcited carriers and acting as non-radiative recombination centers that emit phonons. In the high carrier density regime explored in our experiments, we observe substantial changes in the transient absorbance signal at unexpectedly long-time delays which we attribute to phonon-induced band gap modification. Our probe frequency dependent measurements and modeling indicate a renormalization of the bandgap by up to 23 meV. These results highlight the importance of defects and phonons for optical applications of monolayer transition metal dichalcogenides.

Multi-frequency fusion ultrasonic tomography for gas–liquid two-phase distribution imaging

Industrial ultrasonic tomography (UT) possesses a unique advantage in gas–liquid two-phase distribution measurement and has received broad attention over the past decades. Focusing on a liquid-dominated gas-inclusion distribution reconstruction, we propose the strategy of multi-frequency fusion UT (MFFUT), which comprehensively models the transmission attenuation and self-adaptive fusion of multi-frequency reconstruction images through processing the measurement data with a frequency-dependent forward model and a metric-weighted fusion algorithm. Significant improvements to edge/shape preservation and artifact suppression are observed in both simulative and experimental reconstruction results. Quantitatively, the proposed strategy has a lower relative error and a higher correlation coefficient than any single frequency reconstruction method within all major categories of the reconstruction algorithm and under all inclusion complexities. Accordingly, the MFFUT strategy is proved to provide more accurate gas bubble distribution measurement in industrial processes.

Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 2: Model Uncertainty and Optimal Parameterization

ABSTRACTIn a companion article, Safarshahi and Morozov (2020) argued that construction of distance- and frequency-dependent models for seismic-wave amplitudes should include four general elements: (1) a sufficiently detailed (parametric or nonparametric) model of frequency-independent spreading, capturing all essential features of observations; (2) model parameters with well-defined and nonoverlapping physical meanings; (3) joint inversion for multiple parameters, including the geometrical spreading, Q, κ, and source and receiver couplings; and (4) the use of additional dataset-specific criteria of model quality, while fitting the logarithms of seismic amplitudes. Some of these elements are present in existing models, but, taken together, they are poorly understood and require an integrated approach. Such an approach was illustrated by detailed analysis of an S-wave amplitude dataset from southern Iran. The resulting model is based on a frequency-independent Q, and matches the data closer than conventional models and across the entire epicentral-distance range. Here, we complete the analysis of this model by evaluating the uncertainties and trade-offs of its parameters. Two types of trade-offs are differentiated: one caused by a (possibly) limited model parameterization and the second due to statistical data errors. Data bootstrapping shows that with adequate parameterization, attenuation properties Q, κ, and geometrical spreading parameters are resolved well and show moderate trade-offs due to measurement errors. Using the principal component analysis of these trade-offs, an optimal (trade-off free) parameterization of seismic amplitudes is obtained. By contrast, when assuming theoretical values for certain model parameters and using multistep inversion procedures (as commonly done), parameter trade-offs increase dramatically and become difficult to assess. In particular, the frequency-dependent Q correlates with the distribution of the source and receiver-site factors, and also with biases in the resulting median data residuals. In the new model, these trade-offs are removed using an improved parameterization of geometrical spreading, constant Q, and model quality constraints.

A Study on External Electromagnetic Characteristics of Underground Cables With Consideration of Terminations

The characteristics of external electromagnetic fields (EEMFs) produced by underground cables in the lossy earth are further investigated and studied. This paper develops an excitation current in the cables with the bi-directional propagation for the calculations of the vectors of EEMFs. By adopting the newly proposed method in this paper, it allows the considerations of the terminating conditions and the lengths of the cable on the calculations of the vectors of EEMFs. Moreover, the vectors of EEMFs are calculated, compared and discussed using various load/source impedances. The effects of lengths of underground cables on the vectors of EEMFs are studied. Also, the frequency-dependent earth models are included into the investigations of the EEMFs. The results presented in this paper are compared and verified with the Numerical Electromagnetics Code.

Implementation of a frequency-dependent impedance boundary model into a room acoustic solver with time-domain finite element method

Implementation of a frequency-dependent impedance boundary model into a room acoustic solver with time-domain finite element method

Circuit-based grounding electrode considering frequency dependence for different input current

<p>This paper presents a simulation work of circuit-based grounding electrode considering frequency dependence of soil parameters for three input currents which are impulse, AC 50 Hz, and DC. The circuit parameters were determined by using Dwight and Sunde equations where a single horizontal grounding electrode was considered. Scott model was used for the frequency dependent model, to determine the frequency dependent soil resistivity and relative permittivity. It is found that the voltage response of the impulse current was highly affected (75.2%) by the frequency compared to the voltage response of AC 50 Hz and DC. The impulse current response also gave the lowest peak in the analysis by the influence of frequency which make it better compared to the two other inputs. Therefore, it can be concluded that the frequency dependent of soil parameters is crucial and need to be considered in the transient analysis for any kind of input current to obtain accurate results.</p>

Current differential relay characteristic for bipolar HVDC transmission line fault detection

This study proposes a new differential relay characteristic to detect internal faults on bipolar HVDC (high voltage direct current) transmission lines and discriminate accurately and in a timely manner both internal and external faults. In comparison with the conventional differential protection characteristic, the proposed relay characteristic avoids the need for an intentional time delay typically required to avoid nuisance fault detection. The sampling currents of the positive and negative poles are obtained from both line ends, and the noise is eliminated from the current signals using a stationary wavelet transform. Initially, a startup unit is utilised to activate the proposed protection scheme. The proposed current differential scheme adopts a biasing technique, which is based on the inherent transient behaviour of the bipolar HVDC system during both external and internal faults. The HVDC transmission line is implemented on the PSCAD/EMTDC platform utilising the frequency-dependent phase model, and it is tested considering numerous internal and external faults. Finally, the proposed current differential relay characteristic is tested considering different fault resistances up to 1000 Ω as well as different fault locations, including internal HVDC line faults and external faults at both rectifier and inverter sides. The obtained results confirm the robustness of the proposed protection scheme for bipolar HVDC transmission lines fault detection.

Development of a frequency-dependent constitutive model for hysteresis of shape memory alloys

In this study, a constitutive model based on Liang-Rogers’s relations is developed to characterize the effect of the excitation frequency in the hysteresis of shape memory alloys. Shape memory alloys are good candidates as smart actuators because of their high strain and power density, although the complex hysteresis behavior barricades their usage. Although constitutive models are one of the most potent methods to predict the shape memory alloys behavior, they cannot consider the effect of excitation frequency in active applications. In this paper, the Liang-Rogers model is modified to consider this effect using a linear relation between the excitation frequency and martensite transformation temperatures. A shape memory alloy-driven actuator as a morphing wing is employed to characterize the frequency effect on shape memory alloy hysteresis. Experimental results show that the hysteresis is widened when the excitation frequency increases. The modeling results show that the original model significantly fails to predict the correct behavior when the frequency increases, whereas the proposed model can adequately handle the frequency effect on the behavior of the shape memory alloy-driven actuator.

Frequency-dependent analytic models for scattering off finite half planes

Established theories of wave scattering off points and infinite reflectors have limitations for many problems encountered in wave propagation. Our goal is to extend acoustic scattering theory towards a model that not only describes conventional scattering but also the less idealized case of scattering off finite objects. We develop an analytic object-centric forward frequency domain model of the signal at the receiver. The expression is explicitly parameterized in terms of medium and finite object properties that explicitly incorporates frequency-dependence. Our construction uses perturbation theory and integrates over effective point sources along the object surfaces that acts as finite half planes. From this, we derive closed-form expressions using integral approximation methods; and we also determine frequency, material and geometry conditions under which the conventional theories and associated operators apply. We utilize limiting cases to guide and test our model. The model also provides nontraditional extensions of reflection theory, e.g., for sources with spherical radiation patterns. The unified treatment of the continuum of wave phenomena is not only important theoretically but may also be useful in frequency-based object-centric estimation, array optimization and designing signal processing and acquisition schemes.

Local-Measurement-Based High-Speed Protection for Half-Wavelength UHV Lines

The half-wavelength ultra-high-voltage transmission system is an alternative technique for bulk-power transmission over very long distances. However, the operations and fault-characteristics of such systems are extremely different from conventional ones. Therefore, there is an urgent need to propose a protection scheme that adapts to the characteristics of the half-wavelength line. Towards this end, a local-measurement-based approach is proposed. According to the frequency-dependent model of the half-wavelength line, this paper uses the wavelet transform to decompose the arrival of the aerial-modal surge into several frequency bands. To acquire better accuracy, a weighted average approach is employed to modify the surge arrival time in each frequency band. According to the surge arrival interval between the predefined low-frequency and high-frequency bands, all types of fault, except single-line-to-ground faults when the fault inception angle is at zero-crossings, can be identified in a very short time-window. Simulation results indicate that the proposed protection scheme has satisfactory performance against internal faults and is quite secure under external fault conditions. Using local measurement only, the reach of the proposed protection scheme is no less than 80% of the entire length of the line, and the resistive coverage is also sufficiently high for UHV transmission systems.