Identification Of Dominant Modes Research Articles

Dominant mode identification for grey-box grid-tied converters

The dominant modes of the system can be described by the critical eigenvalues, which reflect the stability and stability margin. This paper proposes a dominant mode identification (DMI) method to assess the stability of the grey-box grid-tied converter. First, the analytical relationship between the eigenvalues and the transfer function is clarified based on the small-signal model. Furthermore, the critical eigenvalues are estimated by the system’s transfer function. On this basis, the discrete transfer function of the grey-box grid-tied converter is constructed utilizing the frequency sweeping technique. Finally, the critical eigenvalues are determined using the measured data based on the customized particle swarm optimization algorithm. The method can apply to different grid connection scenarios of converter-based components and is easy to implement. The DMI method can not only assess the stability margin of grey-box grid-tied converters in operation, but also predict the stability of black-box converters after being connected to the grid in the planning stage.

Dominant mode identification and influence mechanism investigation of frequency oscillations as affected by automatic generation control

Several frequency oscillation events have recently been observed in practical power grids, which are strongly related with dynamic process of AGC (automatic generation control). This kind of oscillations are caused by the phase relation mismatching between mechanical powers and rotational speeds and the detailed dynamic performance and oscillation mechanism are not clear and deserve in-depth investigations. Motivated by this, this paper establishes the state-space model of multi-area AGC systems containing different kinds of generator units and time-scale dynamics. Without distinguishing AGC and PFR (primary frequency regulation) modes, Homotopy method is applied to identify the dominant mode and thus analyze the key influencing factors of frequency oscillations affected by AGC dynamics. The method can clearly establish the congruent relationship between eigenvalues and state variables and is more rapid and intuitive to identify the dominant mode for AGC oscillations. The correctness and feasibility of the proposed method are validated by time-domain simulations and results analysis. Finally, simulations are performed in single-area as well as four-area system based on real data to demonstrate the proposed model and method. And relevant parameter influence mechanism and oscillation performances are investigated for AGC system oscillations.

The E-DVA method for multi-modal pushover analysis and dominant modes

Pushover analysis is an incremental quasi-static procedure for evaluating the seismic behavior of buildings accounting for their non-linear behaviour. The simplest and classical version of this method is based on the following assumptions: (i) the structure has a vertical plane of symmetry; (ii) there is a single horizontal earthquake component, parallel to the plane of symmetry; (iii) the structural dynamic behavior in this plane is governed by a dominant mode of vibration. These assumptions prevent asymmetric buildings to be accurately analyzed accounting for torsion effects. Moreover, even for symmetric structures and single component earthquakes, the effect of higher modes is not taken into account. In order to overcome these limitations, several multi-modal generalizations of the basic pushover analysis method have been proposed in the past years. In this paper, a new multi-modal approach is presented. Inspired by the Direct Vectorial Addition (DVA) method, the load pattern for the pushover analysis is defined as a linear combination of modal load patterns. The novel approach improves the original DVA by introducing an operative procedure for the calculation of modal combination factors (called “α-factors”). This Enhanced DVA (E-DVA) method is based on the notion of elliptical response envelopes and allows several earthquake components to be taken into account simultaneously. In addition, an approach is proposed for the identification of dominant modes and for their use into the definition of the pushover load pattern. Furthermore, this paper describes a method to obtain the equivalent Single-Degree-of-Freedom (SDoF) oscillator properties in the general multi-modal case under multi-component earthquake, with the corresponding factors for the capacity curve normalization. The defnition of response spectrum for multi-component earthquakes is also given. For illustrative purposes, the E-DVA method is applied to a non-symmetric structure (SPEAR building), and the main results are presented and discussed.

Dominant Mode Identification and Influence Mechanism Investigation of Frequency Oscillations as Affected by Automatic Generation Control

Dominant Mode Identification and Influence Mechanism Investigation of Frequency Oscillations as Affected by Automatic Generation Control

Modeling Microbial Adaptations to Nutrient Limitation During Litter Decomposition

Microbial decomposers face large stoichiometric imbalances when feeding on nutrient-poor plant residues. To meet the challenges of nutrient limitation, microorganisms might: (i) allocate less carbon (C) to growth vs. respiration or excretion (i.e., flexible C-use efficiency, CUE), (ii) produce extracellular enzymes to target compounds that supply the most limiting element, (iii) modify their cellular composition according to the external nutrient availability, and (iv) preferentially retain nutrients at senescence. These four resource use modes can have different consequences on the litter C and nitrogen (N) dynamics–modes that selectively remove C from the system can reduce C storage in soil, whereas modes that delay C mineralization and increase internal N recycling could promote storage of C and N. Since we do not know which modes are dominant in litter decomposers, we cannot predict the fate of C and N released from plant residues, in particular under conditions of microbial nutrient limitation. To address this question, we developed a process-based model of litter decomposition in which these four resource use modes were implemented. We then parameterized the model using ∼80 litter decomposition datasets spanning a broad range of litter qualities. The calibrated model variants were able to capture most of the variability in litter C, N, and lignin fractions during decomposition regardless of which modes were included. This suggests that different modes can lead to similar litter decomposition trajectories (thanks to the multiple alternative resource acquisition pathways), and that identification of dominant modes is not possible using “standard” litter decomposition data (an equifinality problem). Our results thus point to the need of exploring microbial adaptations to nutrient limitation with empirical estimates of microbial traits and to develop models flexible enough to consider a range of hypothesized microbial responses.

Identification of Low-Frequency Oscillation Modes Using PMU Based Data-Driven Dynamic Mode Decomposition Algorithm

Power system inter-area oscillations curtail the power transferring capabilities of the transmission lines in a large interconnected power system. Accurate identification of dominant modes and associated contributing generators is important to avoid power system failures by taking appropriate remedial measures. This paper proposes a multi-channel Improved Dynamic Mode Decomposition (IDMD) algorithm-based modal analysis technique using Synchrophasors measurement. First, a reduced-order dynamic power system model is estimated and using this model dominant oscillation modes, corresponding modes shapes, damping ratio, coherent group of generators, participation factors are determined. To improve the accuracy data stacking technique is used to capture detailed information of the system. An optimal hard threshold technique is utilized to select the most optimal model order to avoid uncertainties due to the presence of high level of measurement noise. The study results show that the proposed algorithm gives an accurate and robust solution even in systems having high level of noise in the measurement data. The performance of the proposed technique is tested on simulated data from two-area four-machine system and wNAPS 41-bus 16-generator system with PMU measurements corrupted with different levels of measurement noise. To further strengthen the viewpoint, the proposed method is validated on real-time PMU measurement from ISO New England data to validate the accuracy of the proposed work.

The E-DVA method: A new approach for multi-modal pushover analysis under multi-component earthquakes

Pushover analysis is an incremental quasi-static procedure for evaluating the seismic behavior of buildings accounting for their non-linear behavior. The simplest and classical version of this method is based on the following assumptions: (i) the structure has a vertical plane of symmetry; (ii) there is a single horizontal earthquake component, parallel to the plane of symmetry; (iii) the structural dynamic behavior in this plane is governed by a dominant mode of vibration. These assumptions prevent asymmetric buildings to be accurately analyzed accounting for torsion effects. Moreover, even for symmetric structures and single component earthquakes, the effect of higher modes is not taken into account. In order to overcome these limitations, several multi-modal generalizations of the basic pushover analysis method have been proposed in the past years. In this paper, a new multi-modal approach is presented. Inspired by the Direct Vectorial Addition (DVA) method, the load pattern for the pushover analysis is defined as a linear combination of modal load patterns. The novel approach improves the original DVA by introducing an operative procedure for the calculation of modal combination factors (called “α-factors”). This Enhanced DVA (E-DVA) method is based on the notion of elliptical response envelopes and allows several earthquake components to be taken into account simultaneously. In addition, an approach is proposed for the identification of dominant modes and for their use into the definition of the pushover load pattern. Furthermore, this paper describes a method to obtain the equivalent Single-Degree-of-Freedom (SDoF) oscillator properties in the general multi-modal case under multi-component earthquake, with the corresponding factors for the capacity curve normalization. The definition of response spectrum for multi-component earthquakes is also given. For illustrative purposes, the E-DVA method is applied to a non-symmetric structure (SPEAR building), and the main results are presented and discussed.

Implications of the selection of a particular modal decomposition technique for the analysis of shallow flows

ABSTRACTThis work deals with the capabilities of two synoptic modal decomposition techniques for the identification of the spatial patterns and temporal dynamics of coherent structures in shallow flows. Using two different experimental datasets it is shown that due to the linear behaviour of large-scale, quasi-two-dimensional flow structures, there are almost no differences in the identification of dominant modes between the results obtained from a traditional proper orthogonal decomposition and the more recently developed dynamic mode decomposition. However, it is also shown that nonlinear dynamics can arise in the transition of these structures to a quasi-two-dimensional behaviour, which can result in the proper orthogonal decomposition identifying structures composed of multi-frequencies, a sign of a convoluted dynamics. Thus dynamic mode decomposition is recommended instead for the analysis of such phenomena. In addition, this paper introduces a simple ranking methodology for the use of the dynamic mode decomposition technique in shallow flows, which is based on the results of the proper orthogonal decomposition.

Identification of dominant modes of single-layer reticulated shells under seismic excitations

Single-layer reticulated shells are a type of spatial lattice structures with closely spaced natural frequencies and significant higher mode effects. An accurate calculation of the seismic responses of these structures necessitates the modal combination of dozens or even hundreds of modes when using mode superposition method. To precisely identify the modes that are significantly contributory to the seismic responses, the time-averaged modal strain energy ratio, denoted as TAMSER for brevity, is derived and then selected as the only evaluation metric, taking into account both the modal characteristics of a given structure and the spectral characteristics of an input ground motion. In terms of this metric, a methodology for identifying dominant modes is developed for structure systems under unidirectional or multi-directional seismic excitation. Based on this methodology, the dominant modes of two typical single-layer reticulated shells are identified and investigated, and then the responses resulting from the modal combination of these identified dominant modes are compared to that of the first 30 and 250 modes, as well as the time history analysis results. It is finally concluded that this proposed methodology is capable of accurately identifying the dominant modes of single-layer reticulated shells subjected to seismic excitations, and the incorporation of the identified dominant modes only into the modal combination is appropriate and sufficient to consider the higher modes effects and to get a satisfactory engineering accuracy in the mode superposition analysis.

Identification of Dominant Low Frequency Oscillation Modes Based on Blind Source Separation

On-line monitoring and analysis of low frequency oscillation (LFO) are important for stability and security of a power system. This paper proposes a blind source separation (BSS) based method for LFO modal analysis of one-channel measured signal, which consists of a second-order blind identification (SOBI) algorithm and the Hilbert transform (HT) technique. This is the first time when a BSS technique is applied as a modal decomposition tool in this field. The proposed SOBI-HT based dominant mode identification method combines an iteration procedure with an identification procedure to determine the model order, and then identify dominant modes. The performance of the proposed method is evaluated on numerical simulation signals and a record of real data, verifying its effectiveness and accuracy.

Synchrophasor measurement‐based correlation approach for dominant mode identification in bulk power systems

This study proposes a novel synchrophasor measurement-based correlation approach to identify the dominant oscillation modes in bulk power systems. In the proposed approach, the reference channel (RC) of cross-correlation (CC) is optimally selected based on residue analysis. With the selected RC, the CC of field-measurement data is formed to extract the free-decay system responses. Then, eigensystem realisation algorithm (ERA) is applied to the extracted responses to estimate the system state-space model. A practical model order selection strategy for ERA is proposed to determine the system model order. Further, cross-coherence spectrum is employed to distinguish the dominant modes from the eigenvalues of the estimated state-space model. The proposed method can achieve accurate and robust solutions in the presence of different levels of errors and noises in measurement data. The effectiveness of the proposed method has been verified in a 16-generator, 68-bus test system as well as the China Southern Power Grid system.

Identification of dominant modes in random dynamical and aeroelastic systems

Identification of dominant modes is an important step in studying linearly vibrating systems, including flow-induced vibrations. In the presence of uncertainty, when some of the system parameters and the external excitation are modeled as random quantities, this step becomes more difficult. This work is aimed at giving a systematic treatment to this end. The ability to capture the time-averaged kinetic energy is chosen as the primary criterion for selection of modes. Accordingly, a methodology is proposed based on the overlap of probability density functions (pdf) of the natural and excitation frequencies, proximity of the natural frequencies of the mean or baseline system, modal participation factor, and stochastic variation of mode shapes in terms of the modes of the baseline system — termed here as statistical modal overlapping. The probabilistic descriptors of the natural frequencies and mode shapes are found by solving a random eigenvalue problem. Three distinct vibration scenarios are considered: (i) undamped and damped free vibrations of a bladed disk assembly, (ii) forced vibration of a building, and (iii) flutter of a bridge model. Through numerical studies, it is observed that the proposed methodology gives an accurate selection of modes.

Optimal reduction of inelastic seismic demands in high‐rise reinforced concrete core wall buildings using energy‐dissipating devices

SUMMARYRecently, the issue of large inelastic seismic force demands at severe ground shakings such as maximum considered earthquake level has been highlighted in the conventionally designed high‐rise reinforced concrete core wall buildings. Uncoupled modal response history analysis was used in this study to identify the modes responsible for the large inelastic seismic force demands. The identification of dominant modes and mean elastic design spectra of seven representative ground motions for different damping ratios has led to the identification of three control measures: plastic hinges (PHs), buckling‐restrained braces (BRBs) and fluid viscous dampers (FVDs). The identified control measures were designed to suppress the dominant modes responsible for the large inelastic seismic force demands. A case‐study building was examined in detail. Comparison of the modal as well as the total responses of the case‐study building with and without the control measures shows that all the control measures were effective and able to reduce the inelastic seismic demands. A reduction of 33%, 22% and 27% in the inelastic shear demand at the base and a reduction of 60%, 22% and 26% in the inelastic moment demand at mid‐height were achieved using the PHs, BRBs and FVDs, respectively. Furthermore, a reduction of about 30–40% in the inelastic seismic deformation demands was achieved for the case of the BRBs and FVDs. The study enables us to gain insight to the complex inelastic behavior of high‐rise wall buildings with and without the control measures. Copyright © 2011 John Wiley & Sons, Ltd.

ケーブルを介して曳航される滑空機系の固有値解析（第1報）

An analysis model for numerical estimation of eigenvalues of “a cable-towed glider” system is presented in this paper. This paper takes up longitudinal dynamics of the system. A cable dynamics is formulated as a distributed parameter system with flexibility extensibility and curvature of cable. For a specific example of a horizontal towing validity of the estimated eigenvalues is verified by the results of an identification of dominant modes found in the transient response of the system and stability of the system is analyzed based on root-loci regarding the relative height of a glider to a tug-plane. Modes dominantly affected by curvature of cable are also specified.

Identification of dominant modes in the interface between two conducting fluids

There are several applications in magnetic fluid dynamics where it is important to know the behavior of separation surfaces between fluids. Our magnetic field tomography system enables to reconstruct interface shapes between two conducting fluids on the basis of magnetic field measurements. A simple direct searching strategy for an identification of dominant modes of the interface in a cylindrical two-fluid system is presented

B3 有効質量を用いた拘束のない構造物のモード選定

The purpose of this paper is to show that the effective mass is a useful indication also in identifying dominant mode of unconstrained structures. Effective mass concept works well for structures with constraint, but it does not work for unconstrained structures with rigid-body modes. This is the reason all the effective masses for elastic modes are zero. A way to use the effective mass for dominant mode identification of unconstrained structures is to put zeros into elements in rigid-body modes. Although the effective mass takes different values by which element is replaced with zero and by zeroing rate, modes with large effective mass are dominant mode. However, we cannot necessarily judge that modes with small effective mass are not dominant for a zeroing rate. It is found that it is effective to select a zeroing node that modes are asymmetry with respect to the node in identifying dominant modes. A numerical example is given to show that the proposed method is effective for dominant mode identification of unconstrained structures.

Conducted electromagnetic emissions in induction motor drive systems. I. Time domain analysis and identification of dominant modes

Stray components distributed in a pulsewidth modulation (PWM) drive system form parts of resonant circuits which can be excited to produce radio frequency (RF) noise driven by the pulsed switching action of the power devices. The dynamic response of such circuits is complex. It is essential to identify the dominant oscillation modes in the system so that electromagnetic interference (EMI) reduction techniques can be effectively implemented. This paper (Part I) investigates the mechanisms of conducted EMI emissions associated with a typical PWM inverter induction motor drive system. A numerical model, which includes the high-frequency effects within the machine, is established to evaluate the emissions in the time domain. The dominant high-frequency current paths are identified, and this allows the oscillation frequencies to be predicted from knowledge of the component values. The analysis is confirmed using laboratory measurements. Simplified frequency domain methods for direct calculation of the emission spectra based on the dominant high-frequency current paths are discussed in Part II.

Dominant Failure Modes for Structures with Stochastic Load Processes

Modal Failure probability (MFP) has no unique definition in time-invariant analysis, and true MFPs cannot be obtained without information on load history. Knowledge of true MFPs of a structure is important for design, since different failure modes have different consequences. Therefore, dominant mode identification methods for structures with time-varying random loading are needed. To this end, a three-phase method based on the first passage probability is presented to identify systematically the dominant failure modes when loads and/or resistances are stochastic processes. In phase I, the modes with higher pseudo modal outcrossing rates are identified. In phase II, modes are chosen which refine the partial system state limit surface such that the total outcrossing rate of the modes selected in phase I is minimized. Modes selected in phases I and II with outcrossing rates below a tolerance level are discarded in phase III. A rigid-plastic frame structure is provided to illustrate the effectiveness of the method. Mathematical programming formulation based on the kinematic theorem for plasticity is used to carry out the maximization and minimization processes.

Reaction-diffusion system with Brusselator kinetics: Control of a quasiperiodic route to chaos.

A methodology for controlling complex dynamics and chaos in distributed parameter systems is discussed. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling route to chaos exists in a defined range of parameter values, is used as an example. Poincar\'e maps and singular value decomposition are used for characterization of quasiperiodic and chaotic attractors and for the identification of dominant modes. Tested modal feedback control schemes based on identified dominant spatial modes confirm the possibility of stabilization of simple quasiperiodic trajectories in the complex quasiperiodic or chaotic spatiotemporal patterns.