Ringdown Data Research Articles

Measurements of N2 + ions in an inductively coupled plasma using saturated cavity ringdown spectroscopy

Abstract This paper presents a unique study of the bulk plasma characteristics in a low pressure inductively coupled nitrogen plasma. Saturated cavity ringdown spectroscopy (sat-CRDS) has been used to determine the absolute number densities and translational temperatures of N2 +(X, ν = 0). The effect of saturation is readily accounted for by using an effective saturation parameter, Seff , and determined by a simple method employing measurements at two different gain settings of the detection system. The appropriateness of this method is confirmed by comparison with fitting individual ringdown data using a time-dependent saturation parameter, S(t), within the local approximation model for sat-CRDS; the two methods are in excellent agreement in returning absolute number densities and translational temperatures. N2 +(X, ν = 0) number densities are determined across a matrix of pressure (10 − 100 mTorr) and rf power (200 − 400 W) conditions with maximum number densities of ca. 1.3 × 1010 cm−3 while translational temperatures range from 600 − 1500 K.

Improving the accuracy and the estimation time of inter-area modes in power system based on Tufts-Kumaresan algorithm

ABSTRACT In this paper, a new method based on the Tufts–Kumaresan (TK) algorithm is used to process nonstationary signals and extract system modes. This new algorithm for mode estimation is proposed to improve estimation accuracy under dynamic conditions. The key contribution in TK is the use of multiple orthogonal sliding windows rather than a single pair of sliding windows. Simulation results under various scenarios, such as different types of faults and load changes are used to evaluate the performance of the proposed method. The proposed method will accurately extract system modes. This method will also reduce the required memory and the calculation time of estimation in nonstationary signals. In complement to successful applications in studying the dynamic behavior of the power system, identifying and analyzing low-frequency electromechanical oscillations, and removing signal noise, this method can accurately estimate the modes of a power system. To validate the accuracy of the proposed method, the Wavelet and the Prony methods have been used for comparison. The proposed method is implemented using simulated ringdown data of standard two-area power system and real measurement data of the WSCC system breakup on 10 August 1996.

Influence of cavity ring-down data interception on time constant measurement accuracy

光腔衰荡方法是目前测量光学元件超高反射率（反射率&gt;99.9%）的唯一方法。介绍了一种对光腔衰荡法中激光信号强度与时间关系的优化提取方法。设计了基于光腔衰荡法的光学元件超高反射比的测试系统，通过对采集的光腔衰荡曲线数据进行分段指数拟合，将光腔衰荡曲线数据分为5段，对每段指数拟合结果对应的<i>R</i>² (R-square)和RMSE（root mean squared error）值进行对比分析，计算每段指数拟合的衰荡时间。实验结果表明：截取光腔衰荡曲线数据40%～60%部分拟合得到的结果最接近真实值，求得对应的腔镜的反射率为99.988 977%。最后通过与腔镜的自身反射率进行比较，表明该种数据拟合方法能有效地测量腔镜的反射率，并能减小实验数据本身带来的误差。

Searching for a ringdown overtone in GW150914

We reanalyze the GW150914 postmerger data searching for quasinormal modes beyond the fundamental, quadrupolar mode. There is currently an ongoing disagreement in the literature about whether, and to what extent, the data contains evidence for a quasinormal mode overtone. We use a frequency-domain approach to ringdown data analysis that was recently proposed by the authors. Our analysis has several advantages compared to other analyses performed mainly in the time domain; in particular, the source sky position and the ringdown start time are marginalized over (as opposed to simply being fixed) as part of a Bayesian ringdown analysis. We find tentative evidence for an overtone in GW150914, but at a lower significance than reported elsewhere. Our preferred analysis, marginalizing over the uncertainty in the time of peak strain amplitude, gives a posterior on the overtone amplitude peaked away from zero at $\ensuremath{\sim}1.8\ensuremath{\sigma}$.

Probing chromatic onsets of gravitational wave overtones

The ringdown data of both GW150914 and GW190521_074359 (GW190521r) show evidence supporting the presence of an overtone. All of the previous studies adopt a fundamental assumption, which was motivated more by convenience than by first principles, that the first overtone and the fundamental mode share a same onset. In this work, for the first time, we relax such an assumption, and we aim to probe the possible chromatic onsets of these two components within the GW150914 and GW190521r ringdown data. For both events, we bound the onset lags to be $\mathrm{\ensuremath{\Delta}}{t}_{0}\ensuremath{\ge}5{M}_{f}$ at probabilities of $\ensuremath{\ge}94.7%$, where ${M}_{f}$ is the mass of the remnant black hole formed in the merger. This result moderately favors the nonsimultaneous excitation between the fundamental mode and the first overtone in the ringdown.

Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation

Ringdown gravitational waves of compact object binaries observed by ground-based gravitational-wave detectors encapsulate rich information to understand remnant objects after the merger and to test general relativity in the strong field. In this work, we investigate the ringdown gravitational waves in detail to better understand their property, assuming that the remnant objects are black holes. For this purpose, we perform numerical simulations of post-merger phase of binary black holes by using the black hole perturbation scheme with the initial data given under the close-limit approximation, and we generate data of ringdown gravitational waves with smaller numerical errors than that associated with currently available numerical relativity simulations. Based on the analysis of the data, we propose an orthonormalization of the quasinormal mode functions describing the fundamental tone and overtones to model ringdown gravitational waves. Finally, through some demonstrations of the proposed model, we briefly discuss the prospects for ringdown gravitational-wave data analysis including the overtones of quasinormal modes.

Clustered R3LS: A novel approach for online estimation of power system dominant dynamics

Estimating electromechanical oscillations of power systems plays a crucial role to infer about their stability. In this paper it is proposed a new method in which dominant dynamics of power systems are inferred by analyzing pole estimates produced by several regularized robust recursive least squares (R3LS) implementations operating individually — each one with a different set of autoregressive moving average exogenous (ARMAX) model orders. The proposed method is named “Clustered R3LS”, since it properly adapts the so-called K-means clustering algorithm to automatically model regions of pole agglomeration produced by these individual R3LS implementations. An additional strategy for ignoring (discarding) poles identified as spurious is also part of the proposed Clustered R3LS algorithm. From a practical point of view, Clustered R3LS is here shown to more effectively track dominant dynamics of power systems when compared to Classical R3LS, which is based on analyzing only pole estimates produced by a single R3LS implementation operating with a fixed set of ARMAX model orders that is usually hard to tune. Three case studies are here used to validate the proposed Clustered R3LS method for both ambient and ringdown data. The first and second case studies are based on two well known benchmark models proposed for the analysis of oscillatory dynamics in power systems, whereas the third case study considers actual power system data extracted during a large-scale event from the Brazilian Interconnected Power (BIP) system.

Estimation of power system inertia: A Comparative assessment of measurement-Based techniques

The increasing penetration of converter-interfaced renewable energy sources (RESs) is expected to reduce the overall system inertia. Additionally, due to the intermittent nature of RESs, the overall inertia of modern power systems will vary significantly during the day, resulting in frequency stability issues. In this uncertain environment, it is important for power system operators to monitor in real-time the overall system inertia. Scope of this paper is to systematically evaluate the performance of the most known measurement-based inertia estimation techniques. These include ARMAX-based methods and methods based on the sliding window concept. Algorithmic details and distinct characteristics of each method are presented and discussed. The effect of several parameters on the accuracy of the examined methods is investigated by means of Monte Carlo simulations. For the analysis both ringdown and ambient data are considered. The performance of the examined methods is evaluated under different network conditions and configurations, using simulation results obtained from a system frequency response model and the IEEE 9-Bus system. The applicability of both approaches is also assessed using laboratory measurements.

Development of an in situ analysis system for methane dissolved in seawater based on cavity ringdown spectroscopy.

This paper reports the development of a compact in situ real-time concentration analysis system for methane dissolved in seawater by using a continuous-wave cavity ringdown spectroscopy (CRDS) technique. The miniaturized design of the system, including optical resonance cavity and control and data acquisition-analysis electronics, has a cylindrical dimension of 550 mm in length and 100 mm in diameter. Ringdown signal generation, data acquisition and storage, current driver, and temperature controller of the diode laser are all integrated in the miniaturized system circuits, with an electrical power consumption of less than 12 W. Fitting algorithms of the ringdown signal and spectral line are implemented in a digital signal processor, which is the main control chip of the system circuit. The detection sensitivity for methane concentration can reach 0.4 ppbv with an approximate averaging time of 240 s (or 4 min). Comparing the system's measurement of ambient air against a high-quality commercial CRDS instrument has demonstrated a good agreement in results. In addition, as a "proof of concept" for measuring dissolved methane, the developed instrument was tested in an actual underwater environment. The results showed the potential of this miniaturized portable instrument for in situ gas sensing applications.

Model order estimation methods for low frequency oscillations in power systems

Estimation of low frequency oscillation modes is important for taking remedial actions to ensure the small signal stability of the power system. This paper proposes three approaches to estimate the model order of low frequency oscillations using ringdown data from Phasor Measurement Units. The first approach uses a sequential cumulative sum test on the eigenvalues of the autocorrelation matrix of the signal data to estimate the model order. The second approach estimates the model order based on the eigenvalue contribution in the trace of the autocorrelation matrix. The third algorithm uses sum of squares of the eigenvalues to estimate the model order. All the methods are compared to ascertain their efficacy in estimating the model. The algorithms are tested on oscillation data obtained for WSCC 9 bus system simulated on RTDS and the field data from a generating station in India.

A multi-signal instrumental variable vector fitting method for estimating inter-area electromechanical modes of power systems

When it comes to estimating dynamics (modes) of interconnected power systems through transient (ringdown) data, one can expect more realistic estimates for the compound system if multiple signals distributed over different locations can be used simultaneously during modal estimation. In this context, the contributions of this paper are twofold. First, it is proposed a multi-signal ringdown time-domain Vector Fitting method (‘multi-signal RTD-VF’) which is capable of modeling multiple ringdown signals simultaneously. This method appropriately generalizes the ‘single-signal RTD-VF’ method, which processes ringdown signals independently, i.e., one at a time. Second, it is proposed an instrumental variable (IV) extension of multi-signal RTD-VF. By guaranteeing local optimums after algorithm convergence, such a ‘multi-signal IV-RTD-VF’ formulation may be used for further refining estimates provided by regular multi-signal RTD-VF. Two numerical examples are used to validate the proposed methods. The first example considers actual ringdown data sets extracted from North American Eastern Interconnection (NAEI) and Brazilian Interconnected Power (BIP) systems, whereas the second one considers mode identification of a synthetic signal corrupted by colored noise.

Estimating electromechanical oscillation modes from synchrophasor measurements in China Southern Power Grid

This paper proposes a generalized inverse and mode assurance criterion based stochastic subspace identification (GMSSI) method to improve the electromechanical mode estimation efficiency in China Southern Power Grid (CSG). Stochastic subspace identification (SSI) is first employed to estimate the state subspace model of power system from synchrophasor measurements. Then, a model order determination criterion is proposed to estimate the model order and the state matrix of power system is obtained. To accurately separate the electromechanical modes from trivial modes, the generalized inverse of SSI is used to estimate another state matrix. Further, the mode filtering and mode assurance criterion (MAC) are developed to distinguish the electromechanical modes. Simulation data and field-measurement data from CSG are used to evaluate the performance of the proposed GMSSI method. The comparison between existing measurement-based mode estimation methods and the proposed GMSSI demonstrates that the proposed GMSSI exhibits highly accurate, efficient and robust performance in estimating electromechanical modes from both ringdown and ambient data in bulk power grid.

A novel time-domain linear ringdown method based on vector fitting for estimating electromechanical modes

This paper proposes a novel method, called Ringdown Time-Domain Vector Fitting (RTD-VF), for estimating electromechanical modes in interconnected power systems. Such a method authentically extends, to the context of ringdown analysis, the well known Time-Domain Vector Fitting (TD-VF) method, which has already been successfully applied within other power systems areas. The proposed method is based on a state-space discretization framework which enables ringdown events to be effectively estimated when described as artificial unit impulse responses. Moreover, RTD-VF completely avoids the necessity to perform discrete Fourier transforms (DFTs) of ringdown data sequences. Three case studies are used to validate the proposed method. One of the examples considers a synthetic test signal, whereas the other two case studies consider actual ringdown data sets extracted from the North American Eastern Interconnection (NAEI) system and from the Brazilian Interconnected Power (BIP) system.

Estimating electromechanical oscillation modes from synchrophasor measurements in bulk power grids using FSSI

Multi-order stochastic subspace identification (MOSSI) has been extensively used to estimate the electromechanical oscillation modes from probing, ambient and ringdown data. It has been validated with good performances, while the computational burden is still a major obstacle. This study develops a fast iterative MOSSI (FSSI) approach for computational enhancement of MOSSI in mode estimation. In the proposed approach, an initial cluster of eigenvalues is formulated through FSSI with repetitive calculations (RCs), and electromechanical oscillation mode separation (EOMS) is utilised to discriminate the electromechanical modes. The RCs within the FSSI is calculated through changing the model order successively over the defined range given by a mean of singular values based order determination strategy. Additionally, the proposed approach is highly reliable against prevalent measurement noises owing to RCs and the EOMS. The performance of the proposed method is evaluated in Kundur's two-area test system by comparing with MOSSI, Prony and autoregressive moving average exogenous. Its applicability for both the ringdown and ambient data is also demonstrated with the phasor measurement units field-measurement data from the China Southern Power Grid. The results confirmed the accuracy, robustness and efficiency of the proposed approach for oscillation mode estimation.

ARMAX-Based Transfer Function Model Identification Using Wide-Area Measurement for Adaptive and Coordinated Damping Control

One of the main drawbacks of the existing oscillation damping controllers that are designed based on offline dynamic models is adaptivity to the power system operating condition. With the increasing availability of wide-area measurements and the rapid development of system identification techniques, it is possible to identify a measurement-based transfer function model online that can be used to tune the oscillation damping controller. Such a model could capture all dominant oscillation modes for adaptive and coordinated oscillation damping control. This paper describes a comprehensive approach to identify a low-order transfer function model of a power system using a multi-input multi-output (MIMO) autoregressive moving average exogenous (ARMAX) model. This methodology consists of five steps: 1) input selection; 2) output selection; 3) identification trigger; 4) model estimation; and 5) model validation. The proposed method is validated by using ambient data and ring-down data in the 16-machine 68-bus Northeast Power Coordinating Council system. The results demonstrate that the measurement-based model using MIMO ARMAX can capture all the dominant oscillation modes. Compared with the MIMO subspace state space model, the MIMO ARMAX model has equivalent accuracy but lower order and improved computational efficiency. The proposed model can be applied for adaptive and coordinated oscillation damping control.

Preliminary investigation into feasibility of dissolved methane measurement using cavity ringdown spectroscopy technique

For the exploration of gas hydrate resources by measuring the dissolved methane concentration in seawater, a continuous-wave cavity ringdown spectroscopy (CW-CRDS) experimental setup was constructed for trace methane detection. A current-modulation method, rather than a cavity-modulation method using an optical switch and a piezoelectric transducer, was employed to realize the cavity excitation and shutoff. Such a current-modulation method enabled the improvement of the experimental setup construction and stability, and the system size and stability are critical for a sensor to be deployed underwater. Ringdown data acquisition and processing were performed, followed by an evaluation of the experimental setup stability and sensitivity. The obtained results demonstrate that great errors are introduced when a large fitting window is selected if the analog-to-digital converter has an insufficient resolution. The ringdown spectrum of methane corresponding to the 2v3 band R(4) branch was captured, and the methane concentration in lab air was determined to be 2.06 ppm. Further experiments for evaluating the quantitative ability of this CW-CRDS experimental setup are underway from which a high-sensitivity methane sensor that can be combined with a degassing system is expected.

A Non-Stationary Analysis of Low-Frequency Electromechanical Oscillations Based on a Refined Margenau-Hill Distribution

This paper focuses on the use of quadratic time-frequency distributions (QTFDs) to characterize the temporal variation of low-frequency electromechanical oscillations (LFEOs) using ringdown data. A refined Margenau-Hill distribution (MHD) and a procedure to extract the instantaneous frequencies and damping factors as well as initial phase angles of system low-frequency modes when the analyzed signal is multi-component are proposed. The refinement process enjoys a fast-converging iterative algorithm and without loss of generality it can be applied to other QTFDs for using in other applications. A non-stationary synthetic signal as well as simulated ringdown data of a 5-area, 16-machine power system and real measured data of Western Systems Coordinating Council (WSCC) system are used to demonstrate the efficiency of the proposed method in the presence of measurement noise.

Identification of interarea modes from ringdown data by curve-fitting in the frequency domain

Low damping ratios of interarea modes in the power system result in peaks at their natural frequencies in the discrete Fourier transform (DFT) representation of ringdown data. This has been a motivation to develop a nonparametric DFT-based modal identification method. However, this method has difficulty estimating damping ratios. This paper proposes a parametric DFT-based method to solve such a problem in the non-parametric one. To effectively remove the decaying dc component in ringdown data, the proposed method uses a difference sequence between two sets of ringdown frequency data with oscillation against each other. This method estimates coefficients of the numerator and denominator in the Laplace transform of the frequency difference sequence by curve-fitting of DFT values around peak frequencies. Then, modal natural frequencies and damping ratios are calculated from estimated coefficients of the denominator. This method is compared to a non-parametric DFT-based method and a Prony-based method through simulations on the signal-to-noise ratio and is applied to identify real power systems from ringdown frequency data in the Frequency Monitoring Network system.

Real-time tracking of electromechanical oscillations in ENTSO-e Continental European Synchronous Area

Small signal stability is a crucial aspect of accurately keeping control in modern interconnected power systems, in order to ensure the required security and reliability standards. Such an aspect could represent a serious limiting factor in the search for ever higher power system exploitation levels. Hence, in order to exploit the existing networks as much as possible, ensuring at the same time adequate security levels, the system operators must monitor the electromechanical oscillations continuously, estimating their fundamental parameters (e.g. frequency, damping factor/ratio, amplitude and phase), and determining the actual dynamic stability margins. Nowadays, electromechanical oscillations tracking can be performed in real time thanks to the quick development of wide area measurement/monitoring systems, and the employment of so-called measurement-based methods (a.k.a. mode meters). In this regard, the paper presents a performance comparison among several measurement-based methods currently operating on the Italian Wide Area Monitoring (WAM) platform. The main objective of this investigation is to analyze the behavior of each of them with respect to actual critical/not critical electromechanical oscillations recorded on the European Network Transmission System Operators for Electricity (ENTSO-e) Continental Synchronous European System (CESA). The considered case studies cover a large variety of situations that can be encountered in the ordinary ENTSO-e CESA operation: local and inter-area oscillations; single mode and multi-mode power signals; ambient and ringdown data; and so on. By keeping in mind that usually no best estimator exists, owing to the lack of an optimality definition, the present analysis aims at examining whether some algorithms are generally more suitable than others, with respect to the variety of aforementioned situations. In detail, the measurement-based methods considered in this work are the Tufts–Kumaresan method, Hankel Singular Value Decomposition-VarPRO, Hilbert–Huang Transform, its refined Empirical Mode Decomposition with Fourier-Based Masking Technique (R-EMD), and a recently published Hilbert Transform-based estimation algorithm. Obviously, this set of estimation techniques cannot be considered exhaustive for the research problem under analysis. Nonetheless, it represents a collection of the major, recent and most fashionable methodologies implemented in actual WAM architectures.

Sensitivity Limits of Continuous Wave Cavity Ring-Down Spectroscopy

An optimized nonlinear least-squares fit algorithm for data processing in cavity ring-down spectroscopy (CRDS) is discussed, which improves the calculation efficiency substantially over using a general purpose fitting package. Theoretical absorption sensitivity limits for both the detector noise and the shot noise limited situations are derived and compared with experimental results. The effect of limiting the bandwidth of detection system on ring-down signal is discussed and compared with real ring-down data. The optimal trigger level and fitting interval are obtained for continuous wave cavity ring-down spectroscopy (cw-CRDS) in both the detector noise and shot noise limits, with the resulting sensitivity in units of cm(-1) per (Hz(1/2)) derived. Interestingly, it is found that the optimized shot noise limited sensitivity in cw-CRDS method is, in principle, comparable with the ultimate sensitivity of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS).