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Estimation of Participation Factors Using the Synchrosqueezed Wavelet Transform
This paper proposes a data-driven approach for estimating participation factors for a power system using only simulation results on selected disturbances. The approach is purely response-based and does not need a linearized system model for eigen-analysis, which makes it applicable to systems whose detailed, complete mathematical models are not available. Considering the unavoidable nonlinearity as exhibited in the transient period of a system response, the Synchrosqueezed Wavelet Transform is applied to simulated responses for modal analysis to obtain participation factors. Based on simulations of Kundur's two-area system using both the electromagnetic transient model and phasor model, the participation factors estimated by the proposed approach are compared with two other signal processing tools, the Prony analysis and continuous wavelet transform, and are also benchmarked with conventional model-based participation factors.
Physics-Based Feature Extraction from Bulk Time-Series PMU Datasets for Event Detection
In this work, two physics-based feature extraction techniques are developed for bulk time-series phasor measurement unit (PMU) datasets collected from the field to train the machine learning model for anomaly detection. Two approaches have been developed to extract useful features for different types of events. An admittance-based feature extraction technique is developed to detect events that involve line outages and system topology variations. The developed algorithm extracts the system equivalent admittance variation. Additionally, Fielder’s Theory is utilized to further reduce the potential computation burden by sectionalizing large-scale grids and datasets into smaller areas. Second, an oscillation-based feature extraction technique is developed to detect low-frequency oscillations in power grids. The dominant oscillation modes in the grids are extracted using energy-sorted Prony analysis. The extracted dominant oscillation modes by the developed work exhibit a high fitting resolution. Finally, the developed techniques have been validated using large-scale and real-world datasets.
Web-based wide-area monitoring platform for ringdown and clustering analytics in power systems
This paper introduces an open-source research platform for monitoring the Mexican interconnected power grid, allowing real-time processing and information extraction of the grid’s dynamic condition. Moreover, the platform is a Python-based development that embeds different ringdown and clustering analytics tools. In the case of ringdown analysis, the modal information can be extracted using some of the most known algorithms, i.e., Prony analysis, eigensystem realization algorithm (ERA), and matrix pencil (MP). For clustering analysis, the coherent behaviour of generator and non-generator buses is provided by applying recent state-of-the-art techniques such as affinity propagation, K-means, hierarchical agglomerative clustering, and typicality data analysis. The results of up to 93 PMUs show that this open-source platform suits researchers’ and engineers’ power system dynamic analysis requirements.
Simultaneous Forward-Backward Prony Estimation
Power system dynamic stability can be evaluated through the analysis of transient oscillations that occur following significant system events. One of the earliest methods for this type of study is Prony analysis, which estimates the system's electromechanical modes. While previous studies have highlighted advantages of performing Prony analysis on data in the forward and backward directions, the proposed method does so simultaneously. As a result, signal poles corresponding to electromechanical modes can be distinguished from spurious poles more reliably. The method also produces a single mode estimate, where independent application in the forward and backward directions would produce two estimates for each mode. The method is validated using simulated and measured power system data.
Influence of Numerical Modeling Approaches on Damped Behavior of Flexible Beams: Preprint
Composites structures are widely used in aerospace and wind energy applications for their excellent stiffness and strength-to-weight properties. In these structures, structural damping is critical to predict vibration amplitudes, performance, and reliability. Structural damping is of particular interest for slender wings, rotorcraft blades, and wind turbine blades that can exhibit complex vibration phenomena and are frequently modeled with geometrically exact beam theory (GEBT). Standard approaches of stiffness proportional or modal damping merely assign user defined values and cannot predict damping behavior. This work compares stiffness proportional damping to two more advanced damping approaches: modal strain energy and Prony series. The modal strain energy approach uses a sectional analysis tool to calculate the beam stiffness and postprocess internal stresses from GEBT simulations. The internal stresses are then used to calculate modal damping factors. The Prony series is implemented within GEBT to directly model viscoelastic behavior of the composites. These approaches are compared by modeling the evolution of the damping factors of a realistic flexible wind turbine blade with varying rotational speed. Discrepancies between the approaches suggest areas for future modeling development, but differences in nonlinear damping values are less than current uncertainties about the magnitude of structural damping.
Automated label flows for excited states of correlation functions in lattice gauge theory
Extracting excited states from lattice gauge theory correlation functions can be achieved through $χ^2$ minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. Further, as an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.
Beyond Generalized Eigenvalues
Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials which we call block Prony method (BPM).
Beyond Generalized Eigenvalues in Lattice Quantum Field Theory
Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's (or related) method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials. As these algebraic methods are well known for producing extensive spectral information about statistically-noisy data, the method should be paired with some information criteria, like the recently proposed Bayesean model averaging.
pyvisco [SWR-22-30]
pyvisco is a Python library that supports the identification of Prony series parameters for linear viscoelastic materials described by a Generalized Maxwell model. The necessary material model parameters are identified by fitting a Prony series to the experimental measurement data. pyvisco allows for the identification of Prony series parameters from experimental data measured in either the frequency-domain (via Dynamic Mechanical Thermal Analysis) or time-domain (via relaxation measurements). The experimental data can be provided as raw measurement sets at different temperatures or as pre-processed master curves. An optional minimization routine is included to reduce the number of Prony elements. This routine is helpful in Finite Element simulations where reducing the computational complexity of the linear viscoelastic material models can shorten the simulation time. See also, https://pypi.org/project/pyvisco/
Properties of the Inter-area Modes of the U.S. Eastern Interconnection System
With an increase in the oscillation events observed in the U.S. Eastern Interconnection (EI), it has become increasingly important to have a good understanding of the EI system oscillatory behavior. However, as compared to the Western Interconnection system (WI), not much work has been done in this regard for the EI system. Therefore, in this paper, a thorough analysis is carried out to identify inter-area modes and their properties for the EI system using model-based approach. Multi-channel Prony method is used in this paper for estimating system modes and mode-shapes.
A Prony-based curve-fitting method for characterization of RF pulses from optoelectronic devices
Not Available
Filtered Rayleigh-Ritz is all you need
Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.