Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis?
Not provided.
Engineering↗
SEARCH · Engineering Papers
Results for “eigenvalue analysis”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
High-Impedance Non-Linear Fault Detection via Eigenvalue Analysis with low PMU Sampling Rates
This work presents a hybrid data-driven and physics-based framework for high-impedance fault detection in power systems. An innovative method based on eigenvalue analysis is expanded and validated. Phasor Measurement Unit data is used to estimate eigenvalues corresponding to the powerlines being monitored. The projection and drift of these eigenvalues is then tracked and evaluated. Faults are detected as they drive eigenvalues outside of their normal zones. Eigenvectors are leveraged to support and validate the decisions made by the main algorithm. This technique holds several advantages over contemporary techniques in that it utilizes technology that is already deployed in the field, it offers a significant degree of generality, and so far it has displayed a very high-level of sensitivity without sacrificing accuracy. Validation takes place in the form of simulations in the IEEE 13 Node System considering a popular high-impedance non-linear fault model. Test results are encouraging indicating potential for real-life applications.
Paramo, Gian↗
A State-Space Model for Stability Boundary Analysis of Grid-Following Voltage Source Converters Considering Grid Conditions
With the growing significance of renewable energy resources and energy storage systems, the number of grid-connected inverters has been rising at an increasingly rapid pace. Generally, these inverters are directly integrated with the distribution network by synchronizing with the grid voltage at the point of common coupling. However, the low grid strength and varying R/X ratios, as the common characteristics of most distribution networks or weak grids, can lead to dynamic interactions that comprise stability and limit the power transfer capacity of grid-connected inverters. To ensure stable operation of the inverters, researchers must determine the stability boundary, described as the maximum power transfer capacity of grid-connected inverters under the premise of maintaining system small-signal stability. For this purpose, we propose to formulate a state-space model of the system in the synchronously rotating dq-frame of reference and perform eigenvalue analysis to determine the stability boundary. With a detailed model of the control structure and parameters of the grid-connected inverters, the stability boundary is identified as a surface with respect to different grid strengths and R/X ratios. Case study results of proposed eigenvalue analysis are compared with those of admittance model-based stability analysis as well as time-domain simulation using a switching model in Matlab/Simulink, validating the effectiveness and accuracy of the proposed eigenvalue analysis for stability boundary identification.
grid-connected inverters↗
A New Impedance-Based Modeling and Stability Analysis Approach for Power Oscillations Between Grid-Forming Inverters
This paper presents a new modeling and analysis approach to address the small-signal stability issues among interconnected grid-forming (GFM) inverters. A novel phasor domain “power impedance” model is developed to capture the terminal characteristics of GFM inverters. Based on the developed models, a sum-type impedance stability criterion is proposed to analyze the power oscillations between GFM Inverters. The developed models are validated with EMT simulations and the stability analysis results using the proposed stability criterion can match both EMT simulations and eigenvalue analysis. In addition, the application of the developed model can be extended to the stability analysis of large-scale power system with high penetration of GFM inverters.
Liu, Hanchao↗
An ODE-Enabled Distributed Transient Stability Analysis for Networked Microgrids
Networked microgrid (NMG) exhibits noteworthy resiliency and flexibility benefits for the mutual support from neighboring microgrids. With high penetration of distributed energy resources (DERs) and the associated controls, the transient stability analysis of NMGs is of critical significance. To address the issues of computation burdens and privacy in the centralized transient analysis, this paper devises an ordinary differential equation (ODE)-enabled distributed transient stability (DTS) methodology for NMGs. First, an ODE-based microgrid model is established to capture the dynamics in the droop control of DERs as well as network and load. Further, a distributed DTS is devised for the ODE representation of an NMG, allowing a privacy-preserving transient analysis of each microgrid while accurately reconstructing the frequency dynamics under droop controls in all DERs. In conclusion, extensive tests are performed to verify the validity of the ODE-based microgrid model through both dynamic response and eigenvalue analysis, and the efficacy of the DTS algorithm in simulating the large signal responses and the frequent fluctuations in NMG.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
A State-Space Model of an Inverter-Based Microgrid for Multivariable Feedback Control Analysis and Design
In this work, a synchronous model for grid-connected and islanded microgrids is presented. The grid-connected model is based on the premise that the reference frame is synchronized with the AC bus. The quadrature component of the AC bus voltage can be cancelled, which allows to express output power as a linear equation for nominal values in the AC bus amplitude voltage. The model for the islanded microgrid is developed by integrating all the inverter dynamics using a state-space model for the load currents. This model is presented in a comprehensive way such that it could be scalable to any number of inverter-based generators using inductor–capacitor–inductor (LCL) output filters. The use of these models allows designers to assess microgrid stability and robustness using modern control methods such as eigenvalue analysis and singular value diagrams. Both models were tested and validated in an experimental setup to demonstrate their accuracy in describing microgrid dynamics. In addition, three scenarios are presented: non-controlled model, Linear-Quadratic Integrator (LQI) power control, and Power-Voltage (PQ/Vdq) droop–boost controller. Experimental results demonstrate the effectiveness of the control strategies and the accuracy of the models to describe microgrid dynamics.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Structural stability and artificial buckling modes in topology optimization
Abstract This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.
Dalklint, Anna (ORCID:0000000346195205)↗
Synergistic data analytics for electromechanical oscillation in electric power systems
Accurate real-time estimation of the four electromechanical oscillation properties, i.e., dominant oscillation modes, mode shapes, participation factors, and coherent groups, is of great importance to assess and mitigate potential electromechanical oscillations in interconnected power systems. While eigenvalue analysis can realize such estimation, it requires precise linearized dynamic models and accurate parameters, which are highly difficult to obtain in practice. Data fusion-based modal estimation methods can extract the properties of electromechanical oscillations from measurement data without the power system model and parameters, but most of the time only one or two property assessments can be accomplished each time. To overcome this challenge, this paper presents a synergistic data analytics solution to characterize the dynamic behaviors of electromechanical oscillations from real-time measurement data. Here, the proposed method uses optimized variable projection, and it is capable of estimating all four electromechanical oscillation behavior properties from measured responses. Case studies are performed using the simulated measurement data of a 16-generator 68-bus test system and the field measurements collected by the PMUs deployed in the Yunnan Power Grid. The results demonstrate that the proposed synergistic data analytics solution can achieve satisfactory performance in capturing the properties of electromechanical oscillations from measurement data and exhibit strong robustness against measurement noise when compared with existing measurement-based methods.
42 ENGINEERING↗
Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems
The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.
Advection-dominated dynamical systems↗
A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate
SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.
58 GEOSCIENCES↗
AlgoSCR: an algorithm for solar contamination removal from radio interferometric data
Hydrogen intensity mapping is a new field in astronomy that promises to make three-dimensional maps of the matter distribution of the Universe using the redshifted 21cm line of neutral hydrogen gas (HI). Several ongoing and upcoming radio interferometers, such as Tianlai, CHIME, HERA, HIRAX, etc., are using this technique. These instruments are designed to map large swaths of the sky by drift scanning over periods of many months. One of the challenges of the observations is that the daytime data are contaminated by strong radio signals from the Sun. In the case of Tianlai, this results in almost half of the measured data being unusable. We try to address this issue by developing an algorithm for solar contamination removal (AlgoSCR) from the radio data. The algorithm is based on an eigenvalue analysis of the visibility matrix and hence is applicable only to interferometers. We apply AlgoSCR to simulated visibilities, as well as real daytime data from the Tianlai dish array. The algorithm can reduce strong solar contamination by about 95 per cent without seriously affecting other weaker sky signals and thus makes the data usable for certain applications.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Isochronous Architecture-Based Voltage-Active Power Droop for Multi-Inverter Systems
This article proposes an isochronous architecture for parallel inverters with only voltage-active power droop (VP-D) control for improving active power sharing as well as plug-and-play of multi-inverter-based distributed energy resources (DERs). The isochronous framework obviates the need for an explicit regulation of the frequency while allowing for sharing of reactive power. The article shows that the detrimental effects of circulating currents between inverters can be addressed in the framework developed. The isochronous architecture is implemented by employing a GPS to disseminate clock timing signals that enable the microgrid to maintain the nominal system frequency. Small signal eigenvalue analysis of a Multi-inverter Microgrid system near the steady-state operating point is presented to evaluate the system stability. Moreover, unlike traditional droop-based methods, the isochronous strategy lends itself to analytical guarantees which are developed in the article. Furthermore, the effect of delays in receiving GPS clock signals by an inverter is experimentally characterized and an inverter isolation mechanism is proposed that disconnects inverters facing large GPS communication delays. Hardware experiments on an 1.2 kVA-prototype and controller-hardware-in-the-loop validation on the CIGRE distribution network are conducted to demonstrate the effectiveness of the proposed architecture towards active and reactive power sharing between inverters with load scenarios.
24 POWER TRANSMISSION AND DISTRIBUTION↗
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).
Fleming, George T.↗
Eigenvalue-Based Micromagnetic Analysis of Switching in Spin-Torque-Driven Structures
We present an eigenvalue-based approach for studying the magnetization dynamics in magnetic nanostructures driven by spintronic excitations, such as spin-transfer torque and spin-orbit torque. The approach represents the system dynamics in terms of normal oscillation modes (eigenstates) with corresponding complex eigenfrequencies. The dynamics is driven by a small number of active eigenstates and often considering just a single eigenstate is sufficient. We develop a perturbation theory that provides semianalytical dynamic solutions by using eigenstates for the case in the absence of damping and spintronic excitations as a basis. The approach provides useful insights into dynamics in such systems and allows solving several difficulties in their modeling, such as extracting the switching current in magnetic random-access memories and understanding switching mechanisms. We show that the presented approach directly predicts the critical switching current, i.e., switching current for an infinite time. The approach also provides solutions for the switching dynamics allowing the switching current to be obtained for a finite switching time, provided that the system symmetry is broken, e.g., by tilting the polarizer, so that switching by a finite pulse is possible.
42 ENGINEERING↗