Frequency-domain Modal Analysis Research Articles

Dynamic Response Analysis of Wind Turbine Structure to Turbulent Wind Load: Comparative Assessment in Time and Frequency Domains

This study investigates wind turbine structural dynamics using stochastic analysis and computational methods in both the time and frequency domains. Simulations and experiments are utilized to evaluate the dynamic response of a wind turbine structure to turbulent wind loads, with the aim of validating the results based on real wind farm conditions. Two approaches are employed to analyze the dynamic responses: the frequency domain modal analysis approach, which incorporates von Kármán spectra to represent the turbulent wind loads, and the time domain Monte Carlo simulation and Newmark methods, which generate wind loads and determine dynamic responses, respectively. The results indicate that, for a larger number of samples, both methods consistently yield simulated turbulent wind loads, dynamic responses and peak frequencies. These findings are further validated through experimental data. However, when dealing with a smaller number of samples, the time domain analysis produces distorted results, necessitating a larger number of samples to achieve accurate findings, while the frequency domain method maintains accuracy. Therefore, the accurate analysis of wind turbine structural dynamics can be achieved using simulations in both the time and frequency domains, considering the importance of the number of samples when choosing between time domain and frequency domain analyses. Taking these considerations into account allows for a more comprehensive and robust analysis, ultimately leading to more effective outcomes.

Oscillation Propagation Analysis of Hybrid AC/DC Grids With High Penetration Renewables

The high penetration of renewables has sparked new oscillatory concerns in hybrid AC/DC grids. Knowledge of the oscillation regarding its source and propagation mechanism, is crucial to system operation. In this respect, the frequency-domain modal analysis (FMA) provides a way (e.g., participation factor) to extract these oscillation properties, and has been widely applied in converter-based AC grids. Compared to AC grids, oscillation properties of hybrid AC/DC grids are much more complex. Such complexity mainly originates from the diversity of oscillation propagation behaviors in hybrid AC/DC grids, where a distinctive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local-area</i> oscillation will emerge. Therefore, a dedicated oscillation propagation analysis for hybrid AC/DC grids is desired, which is the main focus of this paper. First, the mechanism of the distinctive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local-area</i> oscillation is analyzed considering AC/DC coupled dynamics of converters. Then, a systematic method for the oscillation propagation analysis is presented, where indices for characterizing the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local-area</i> oscillation and its impact area are established. Finally, some propagation properties are discussed, by which a strategy for the online oscillation source locating is designed. Case studies are carried out in a typical hybrid AC/DC grid to validate the propagation analysis in this paper.

Frequency-Domain Modal Analysis for Power-Electronic-Based Power Systems

This letter presents two frequency-domain modal analysis methods, “peak-picking” and “circle fit” methods, used for current control interactions of grid-connected voltage-source converters (VSCs). Differing from the conventional resonance mode analysis, the modal impedances are analyzed with their Nyquist plots, instead of the magnitude-frequency response, which leads to an accurate prediction on the damping behavior of system. Experimental tests verify the theoretical modal analysis methods.

Frequency-Domain Modal Analysis of the Oscillatory Stability of Power Systems With High-Penetration Renewables

The increasing penetration of renewables into modern power systems is bringing new oscillatory stability concerns. It is of significance to find all oscillatory modes concerned and evaluate components’ participation into each mode, especially the dominant one. To address this issue, a frequency-domain modal analysis method is developed in this paper. It represents the target system with a networked impedance model and works out the oscillatory modes by locating the zeros of the determinant of the loop impedance matrix or nodal admittance matrix. Loop/nodal participation factors, branch observability, and component sensitivity are derived to give insight into the oscillation, including its origin, oscillation path, and contributive components. The proposed method has been conducted on a simple passive circuit and a practical wind power system that experienced actual subsynchronous resonance incidents. Theoretical results as well as electromagnetic transient simulations have verified its effectiveness. The proposed method has the potential to analyze very large power systems with high penetration of renewables.

Effect of Circumferential Location of Radial Injection on Rotordynamic Performance of Hybrid Air Foil Bearings

Air foil bearings (AFBs) are introduced as promising bearings for oil-free turbomachinery applications. AFBs provide reliable operation at high speed and high temperature with negligible power loss. Hybrid air foil bearing (HAFB) technology utilizes the radial injection of externally pressurized air into the traditional hydrodynamic AFB's film thickness through orifices attached to the top foil. Previous studies have reported enhancement in the rotordynamic stability of HAFBs compared to traditional hydrodynamic AFBs. HAFBs have several orifices distributed in the circumferential direction. In this study, the effect of the circumferential location of radial injection on the rotordynamic performance of the rotor-HAFB is studied. Analytical and experimental evaluations of the rotordynamic performance of a rotor supported by two single-pad HAFBs are presented. Parametric studies are conducted using three sets of single-pad HAFBs. The circumferential locations of orifices are different for each set. The presented simulation analyses consist of time-domain orbit simulation and frequency-domain modal analysis. Imbalance responses of rotor-HAFB were measured with various orifice locations and the results agree well with predictions. Comparison of the rotordynamic performance of HAFBs with different orifice configurations demonstrates substantial improvement in rotordynamic stability as well as enhancement in the stiffness and damping coefficients of HAFBs by choosing the best circumferential location for radial injection to control rotor eccentricity and attitude angle.

Alternative Modal Analysis of N-coupled Multi-conductor Power Lines

Cables and overhead lines are key components in electric power systems, with conductors belonging to those components being electromagnetically coupled. Time-domain analysis of steady-state and transient regimes in cables and power lines usually requires the use of frequency-domain modal analysis techniques where mode decoupling is achieved by solving an eigenvalue–eigenvector matrix problem. In this article, an alternative method is developed for the modal analysis of n-coupled multi-conductor transmission lines employing a simple intuitive approach. The method provides a speedy solution of the eigenvalue–eigenvector problem based on an initial guess for the modal transformation matrix; the accuracy of the method can be controlled and improved easily by iterating the proposed algorithm a few times. The method is exemplified with vertical and triangular single-circuit three-phase transmission lines choosing the Clarke matrix as the initial approximation for the modal transformation.

Surrogate model reduction for linear dynamic systems based on a frequency domain modal analysis

A novel model reduction methodology for linear dynamic systems with parameter variations is presented based on a frequency domain formulation and use of the proper orthogonal decomposition. For an efficient treatment of parameter variations, the system matrices are divided into a nominal and an incremental part. It is shown that the perturbed part is modally equivalent to a new system where the incremental matrices are isolated into the forcing term. To account for the continuous changes in the parameters, the single-composite-input is invoked with a finite number of predetermined incremental matrices. The frequency-domain Karhunen---Loeve procedure is used to calculate a rich set of basis modes accounting for the variations. For demonstration, the new procedure is applied to a finite element model of the Goland wing undergoing oscillations and shown to produce extremely accurate reduced-order surrogate model for a wide range of parameter variations.

In-operation modal analysis of containments using ambient vibration

The importance of preserving the structural integrity of a containment can never be overemphasized. Currently the structural integrity of the containment is evaluated periodically via various nondestructive inspection methods. However, these methods can only provide local integrity data, and cannot deliver continuous monitoring information on overall structural integrity. In this paper, the result of a feasibility study on utilizing ambient vibration measurements to monitor the structural integrity of a containment is presented. The ambient vibration testing was selected, because it can avoid the interruption of normal operation of power plants. For the purpose of the study, the ambient vibration of four different containments in Korea, i.e. Ulchin Unit 5, Wolsong Unit 2, Ulchin Unit 1, and Yeonggwang Unit 4, was measured and modal parameters were extracted via frequency domain modal analysis techniques. The experimental modes were then compared to the analytical modes estimated using finite element analysis to examine the correlation, and highly correlated modes were adopted in identifying structural parameters using a system identification method. The structural parameter selected in this study was the elastic modulus of the concrete, and the identified moduli were compared to design values and inspection results. The result shows the ambient vibration can be utilized in monitoring the structural integrity of a containment, though further extensive study needs to be conducted to identify and exclude the effect of ambient conditions such as temperature and humidity on resonant frequencies.

Enhancing surface plasmon polariton propagation lengths via coupling to asymmetric waveguide structures

We determine and analyze the properties of regenerated surface plasmon polaritons (R-SPPs) in an asymmetric waveguide structure [T.-W. Lee and S. K. Gray, Appl. Phys. Lett. 86, 141105 (2005)]. Both finite-difference time-domain (FDTD) calculations and frequency-domain modal analysis are employed. The FDTD results, which explicitly include excitation via attenuated total reflection, show an oscillatory dependence of the R-SPP propagation length ${L}_{x}$ as a function of core layer thickness $d$, with maxima corresponding to 30-fold propagation enhancements. For fixed incident light wavelength and angle, a variety of thicknesses can therefore be used to excite very long propagating SPPs. Modal analysis shows that the oscillations are due to tuning $d$ through the opening of new transverse magnetic waveguide modes. In addition to increased propagation lengths, surface confinement is not significantly deteriorated and large intensity enhancements in the propagation region can also be achieved.

A Polyreference Least Square Complex Frequency domain based statistical test for damage detection

Some current approaches in damage detection have led to the implementation of statistical algorithms, based on the so-called “local approach” assumption. The reference parameter is the modal signature of a state-space model of the studied system, and the tests aim at detecting small deviations in this signature without explicitly computing it. Moreover, the system inputs are assumed to be random white noises, modeling all the various and unknown influences on the system, either environmental or operational. Working with the outputs in time-domain, various tests were designed and experimented - e.g. the subspace-based chi-square test. On the other hand, efficient system identification algorithms working in the frequency domain have been designed, first dealing with experimental conditions - meaning there are known controlled inputs - but also offering promising perspectives with regards to the operational conditions - without any measurement of the inputs. In this paper, a frequency-domain statistical test for change detection is proposed, based on this recent frequency-domain modal analysis method and on the local approach to change detection.

Frequency domain modal analysis of earthquake input energy to highly damped passive control structures

AbstractA new complex modal analysis‐based method is developed in the frequency domain for efficient computation of the earthquake input energy to a highly damped linear elastic passive control structure. The input energy to the structure during an earthquake is an important measure of seismic demand. Because of generality and applicability to non‐linear structures, the earthquake input energy has usually been computed in the time domain. It is shown here that the formulation of the earthquake input energy in the frequency domain is essential for deriving a bound on the earthquake input energy for a class of ground motions and for understanding the robustness of passively controlled structures to disturbances with various frequency contents. From the viewpoint of computational efficiency, a modal analysis‐based method is developed. The importance of overdamped modes in the energy computation of specific non‐proportionally damped models is demonstrated by comparing the energy transfer functions and the displacement transfer functions. Through numerical examinations for four recorded ground motions, it is shown that the modal analysis‐based method in the frequency domain is very efficient in the computation of the earthquake input energy. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Torsional vibration of a back-to-back gearbox rig Part 1: Frequency domain modal analysis

The torsional vibration of a back-to-back gearbox system has been investigated experimentally and analytically. Gearboxes are typically part of a larger system, or drivetrain, which commonly includes electric motors, shafts, couplings, ball mills, turbines and generators. The dynamics of the system has been shown significantly to influence the gearbox response and requires inclusion in gearbox modelling. Assumptions are commonly made, however, to reduce the degrees of freedom of the model, and system dynamics is subsequently neglected. Receptance methods were applied to model a back-to-back gearbox system and were shown to be an effective modelling technique for geared system analysis. A detailed experimental modal analysis was performed using the swept-sine technique with an a.c. servomotor torsional exciter. Torsional excitation allowed for the dynamic response to be measured up to 1600 Hz. A multi-degree-of-freedom, frequency domain torsional model of the gearbox system was developed using receptances. The model included a combination of lumped-mass elements, and continuous shafts with distributed inertia and hysteretic damping. The modelled torsional natural frequencies were matched to the measured frequencies by the adjustment of system model parameters to achieve a high level of agreement. Matching of system natural frequencies resulted in the accurate prediction of the first nine associated torsional deflected shapes up to 1548 Hz. This paper presents the detailed results of a full torsional, modal analysis of a gearbox system, demonstrating receptance system modelling and an effective method for torsional excitation on rotating machines.

Variable Modal Parameter Identification for Non-Linear Mdof Systems. Part I: Formulation and Numerical Validation

This paper deals with the formulation of a frequency domain modal analysis technique that is applicable to weakly non-linear multi-degree of freedom (MDOF) systems with well-separated modes. The concept of linear modal superposition is combined with the normal non-linear mode technique, an approach that allows the formulation of a system identification procedure in terms of variable modal parameters. The numerical study was focused on a 4-DOF system with cubic stiffness non-linearity, and the modal parameters were obtained as functions of the modal amplitude. It was shown that the methodology was well suited to the study of practical cases for which the underlying linear model may be approximate. Similarly, the technique was found to be robust in the presence of measurement noise, though some adverse effects were observed for high noise levels. Once the variable modal parameters were extracted at some given force level, the non-linear responses were predicted at other force levels via synthesis of normal non-linear modes. The same responses were also obtained using a harmonic balance approach and very good agreement was obtained between the two sets of results. The procedure is well suited to the study of industrial cases because of its compatibility with existing finite element methods and linear modal analysis techniques.

Spatial-harmonic Neutron Spectrum Effect on Frequency-domain Modal Analysis of Regional Stability in BWR

An analysis method for BWR regional stability is developed in frequency-domain. Conventionally, the energy spectrum of fundamental eigenfunction has been applied to the calculation of first-harmonic void reactivity instead of the spectrum of first-harmonic eigenfunction. In the present method, the fine energy spectra of first-harmonics are applied to the evaluation of void reactivity. The spectra are obtained by assembly calculation considering the geometric bucklings of spatial harmonics.The present method is applied to the Ringhals 1 benchmark test problem. Comparing the present method with the method without the spectrum of first-harmonic eigenfunction, we can estimate the effect of the spectrum on the frequency-domain modal analysis of regional stabilities in BWRs. The decay ratio (DR) of regional stability is also calculated by these two methods. It is found that the latter method tends to underestimate the absolute value of void reactivity by about 10%. By considering the spectra of first-harmonic eigenfunction, the DR of regional stability was estimated larger by about 0.05.

Spatial-harmonic Neutron Spectrum Effect on Frequency-domain Modal Analysis of Regional Stability in BWR.

Spatial-harmonic Neutron Spectrum Effect on Frequency-domain Modal Analysis of Regional Stability in BWR.

Crosstalk analysis of interconnection lines and packages in high-speed integrated circuits

A novel approach for the analysis of crosstalk, propagation delay, and pulse distortion of interconnects in high-speed integrated circuits, packages, and circuit boards is presented. Based on frequency-domain modal analysis, a set of formulas is derived to describe the voltage and current transfer functions of coupled interconnects with arbitrary linear termination impedances and used to obtain analytical expressions for the time-domain waveforms for lossless multiconductors interconnection lines. The weak-coupling assumption is found to be only marginally valid. In a typical interconnection configuration, the secondary coupling of the disturbed line on the original signal line substantial and must be taken into account for accurate prediction of the waveforms. Simulation results are given to illustrate the influence of the layout parameters of the interconnects and the rise or fall times of the source signal. It is shown that ground conductors need to be placed on both sides of each of the signal lines to reduce crosstalk effectively. However, the presence of the ground conductors increases the layout complexity and results in more severe waveform distortion for the signal on the active line. >