System Eigenvalue

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Ronald G Harley - One of the best experts on this subject based on the ideXlab platform.

  • dynamic System Eigenvalue extraction using a linear echo state network for small signal stability analysis a novel application
    International Joint Conference on Neural Network, 2010
    Co-Authors: Jiaqi Liang, G K Venayagamoorthy, Ronald G Harley
    Abstract:

    A large nonlinear dynamic System usually has complex dynamic modes corresponding to the System's Eigenvalues. These Eigenvalues govern the System's local behavior and thus are critical information for designing System operation and control strategies. Without the availability of the System's analytical model, which is often the case for large nonlinear Systems, the System's Eigenvalues need to be estimated. A linear echo state network (ESN) based method for extracting observable Eigenvalues of a dynamic System together with the participation factors of these Eigenvalues in the accessible System states is presented in this paper. A linear ESN is first trained to track the dynamic System's local responses under injected small perturbation signals. The dynamic System's Eigenvalues are then extracted from the ESN's weight matrices. Given the merit of fast training of ESNs, the ESN can be quickly retrained once the System operating point changes, and the System Eigenvalues can be reestimated. Application of the proposed Eigenvalue extraction method in the power System small-signal analysis is presented to demonstrate the effectiveness of the proposed method.

  • IJCNN - Dynamic System Eigenvalue extraction using a linear echo state network for small-signal stability analysis - a novel application
    The 2010 International Joint Conference on Neural Networks (IJCNN), 2010
    Co-Authors: Jiaqi Liang, G K Venayagamoorthy, Ronald G Harley
    Abstract:

    A large nonlinear dynamic System usually has complex dynamic modes corresponding to the System's Eigenvalues. These Eigenvalues govern the System's local behavior and thus are critical information for designing System operation and control strategies. Without the availability of the System's analytical model, which is often the case for large nonlinear Systems, the System's Eigenvalues need to be estimated. A linear echo state network (ESN) based method for extracting observable Eigenvalues of a dynamic System together with the participation factors of these Eigenvalues in the accessible System states is presented in this paper. A linear ESN is first trained to track the dynamic System's local responses under injected small perturbation signals. The dynamic System's Eigenvalues are then extracted from the ESN's weight matrices. Given the merit of fast training of ESNs, the ESN can be quickly retrained once the System operating point changes, and the System Eigenvalues can be reestimated. Application of the proposed Eigenvalue extraction method in the power System small-signal analysis is presented to demonstrate the effectiveness of the proposed method.

Jiaqi Liang - One of the best experts on this subject based on the ideXlab platform.

  • dynamic System Eigenvalue extraction using a linear echo state network for small signal stability analysis a novel application
    International Joint Conference on Neural Network, 2010
    Co-Authors: Jiaqi Liang, G K Venayagamoorthy, Ronald G Harley
    Abstract:

    A large nonlinear dynamic System usually has complex dynamic modes corresponding to the System's Eigenvalues. These Eigenvalues govern the System's local behavior and thus are critical information for designing System operation and control strategies. Without the availability of the System's analytical model, which is often the case for large nonlinear Systems, the System's Eigenvalues need to be estimated. A linear echo state network (ESN) based method for extracting observable Eigenvalues of a dynamic System together with the participation factors of these Eigenvalues in the accessible System states is presented in this paper. A linear ESN is first trained to track the dynamic System's local responses under injected small perturbation signals. The dynamic System's Eigenvalues are then extracted from the ESN's weight matrices. Given the merit of fast training of ESNs, the ESN can be quickly retrained once the System operating point changes, and the System Eigenvalues can be reestimated. Application of the proposed Eigenvalue extraction method in the power System small-signal analysis is presented to demonstrate the effectiveness of the proposed method.

  • IJCNN - Dynamic System Eigenvalue extraction using a linear echo state network for small-signal stability analysis - a novel application
    The 2010 International Joint Conference on Neural Networks (IJCNN), 2010
    Co-Authors: Jiaqi Liang, G K Venayagamoorthy, Ronald G Harley
    Abstract:

    A large nonlinear dynamic System usually has complex dynamic modes corresponding to the System's Eigenvalues. These Eigenvalues govern the System's local behavior and thus are critical information for designing System operation and control strategies. Without the availability of the System's analytical model, which is often the case for large nonlinear Systems, the System's Eigenvalues need to be estimated. A linear echo state network (ESN) based method for extracting observable Eigenvalues of a dynamic System together with the participation factors of these Eigenvalues in the accessible System states is presented in this paper. A linear ESN is first trained to track the dynamic System's local responses under injected small perturbation signals. The dynamic System's Eigenvalues are then extracted from the ESN's weight matrices. Given the merit of fast training of ESNs, the ESN can be quickly retrained once the System operating point changes, and the System Eigenvalues can be reestimated. Application of the proposed Eigenvalue extraction method in the power System small-signal analysis is presented to demonstrate the effectiveness of the proposed method.

B. Campbell - One of the best experts on this subject based on the ideXlab platform.

  • an efficient improvement of the aesops algorithm for power System Eigenvalue calculation
    IEEE Transactions on Power Systems, 1994
    Co-Authors: B. Campbell
    Abstract:

    This paper describes a simple but efficient modification to improve the well known PEALS/AESOPS algorithm for power System Eigenvalue calculation. The modified algorithm is a Newton-Raphson iteration scheme which converges significantly faster than AESOPS. The algorithm is linked to the operational transfer matrix equation method. An efficient operational matrix based formula is suggested to calculate the sensitivity of an electromechanical Eigenvalue with respect to the transfer function of a power System stabilizer. Results for a 21 generator power System are described. >

  • An improved algorithm for power System Eigenvalue calculation
    1993
    Co-Authors: B. Campbell
    Abstract:

    AESOPS is a well known algorithm for power System Eigenvalue calculation. This paper describes a modification to improve the efficiency of the method. The modified algorithm uses sparse techniques to solve the same equivalent network equations of AESOPS in each iteration but, unlike AESOPS, it is an exact Newton-Raphson iteration scheme, and converges significantly faster than AESOPS. Results for a 31 generator power System are described. >

G K Venayagamoorthy - One of the best experts on this subject based on the ideXlab platform.

  • dynamic System Eigenvalue extraction using a linear echo state network for small signal stability analysis a novel application
    International Joint Conference on Neural Network, 2010
    Co-Authors: Jiaqi Liang, G K Venayagamoorthy, Ronald G Harley
    Abstract:

    A large nonlinear dynamic System usually has complex dynamic modes corresponding to the System's Eigenvalues. These Eigenvalues govern the System's local behavior and thus are critical information for designing System operation and control strategies. Without the availability of the System's analytical model, which is often the case for large nonlinear Systems, the System's Eigenvalues need to be estimated. A linear echo state network (ESN) based method for extracting observable Eigenvalues of a dynamic System together with the participation factors of these Eigenvalues in the accessible System states is presented in this paper. A linear ESN is first trained to track the dynamic System's local responses under injected small perturbation signals. The dynamic System's Eigenvalues are then extracted from the ESN's weight matrices. Given the merit of fast training of ESNs, the ESN can be quickly retrained once the System operating point changes, and the System Eigenvalues can be reestimated. Application of the proposed Eigenvalue extraction method in the power System small-signal analysis is presented to demonstrate the effectiveness of the proposed method.

  • IJCNN - Dynamic System Eigenvalue extraction using a linear echo state network for small-signal stability analysis - a novel application
    The 2010 International Joint Conference on Neural Networks (IJCNN), 2010
    Co-Authors: Jiaqi Liang, G K Venayagamoorthy, Ronald G Harley
    Abstract:

    A large nonlinear dynamic System usually has complex dynamic modes corresponding to the System's Eigenvalues. These Eigenvalues govern the System's local behavior and thus are critical information for designing System operation and control strategies. Without the availability of the System's analytical model, which is often the case for large nonlinear Systems, the System's Eigenvalues need to be estimated. A linear echo state network (ESN) based method for extracting observable Eigenvalues of a dynamic System together with the participation factors of these Eigenvalues in the accessible System states is presented in this paper. A linear ESN is first trained to track the dynamic System's local responses under injected small perturbation signals. The dynamic System's Eigenvalues are then extracted from the ESN's weight matrices. Given the merit of fast training of ESNs, the ESN can be quickly retrained once the System operating point changes, and the System Eigenvalues can be reestimated. Application of the proposed Eigenvalue extraction method in the power System small-signal analysis is presented to demonstrate the effectiveness of the proposed method.

Robert G Parker - One of the best experts on this subject based on the ideXlab platform.

  • unusual gyroscopic System Eigenvalue behavior in high speed planetary gears
    Journal of Sound and Vibration, 2013
    Co-Authors: Christopher G Cooley, Robert G Parker
    Abstract:

    This study demonstrates unusual gyroscopic System Eigenvalue behavior observed in a lumped-parameter planetary gear model. While the model has been used for dynamic analyses in industrial applications, the focus is on the Eigenvalue phenomena that occur at especially high speeds rather than practical planetary gear behavior. The behaviors include calculation of exact trajectories across critical speeds, uncommon stability features near degenerate critical speeds, and unique stability transitions. These Eigenvalue behaviors are not evident in the vast literature on gyroscopic Systems.

  • On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua
    Journal of Applied Mechanics, 1998
    Co-Authors: Robert G Parker
    Abstract:

    In order to provide analytical Eigenvalue estimates for general continuous gyroscopic Systems, this paper presents a perturbation analysis to determine approximate Eigenvalue loci and stability conclusions in the vicinity of critical speeds and zero speed. The perturbation analysis relies on a formulation of the general continuous gyroscopic System Eigenvalue problem in terms of matrix differential operators and vector eigenfunctions. The Eigenvalue λ appears only as λ 2 in the formulation, and the smoothness of λ 2 at the critical speeds and zero speed is the essential feature. First-order Eigenvalue perturbations are determined at the critical speeds and zero speed. The derived Eigenvalue perturbations are simple expressions in terms of the original mass, gyroscopic, and stillness operators and the critical-speed/zero-speed eigenfunctions. Prediction of whether an Eigenvalue passes to or from a region of divergence instability at the critical speed is determined by the sign of the Eigenvalue perturbation. Additionally, Eigenvalue perturbation at the critical speeds and zero speed yields approximations for the Eigenvalue loci over a range of speeds. The results are limited to Systems having one independent eigenfunction associated with each critical speed and each stationary System Eigenvalue. Examples are presented for an axially moving tensioned beam, an axially moving string on an elastic foundation, and a rotating rigid body. The Eigenvalue perturbations agree identically with exact solutions for the moving string and rotating rigid body.

  • Vibration and Coupling Phenomena in Asymmetric Disk-Spindle Systems
    Journal of Applied Mechanics, 1996
    Co-Authors: Robert G Parker, C. J. Mote
    Abstract:

    This paper analytically treats the free vibration of coupled, asymmetric disk-spindle Systems in which both the disk and spindle are continuous and flexible. The disk and spindle are coupled by a rigid clamping collar. The asymmetries derive from geometric shape imperfections and nonuniform clamping stiffness at the disk boundaries. They appear as small perturbations in the disk boundary conditions. The coupled System Eigenvalue problem is cast in terms of extended eigenfunctions that are vectors of the disk, spindle, and clamp displacements. With this formulation, the Eigenvalue problem is self-adjoint and the eigenfunctions are orthogonal. The conciseness and clarity of this formulation are exploited in an eigensolution perturbation analysis. The amplitude of the disk boundary condition asymmetry is the perturbation parameter. Exact eigensolution perturbations are derived through second order. For general boundary asymmetry distributions, simple rules emerge showing how asymmetry couples the eigenfunctions of the axisymmetric System and how the degenerate pairs of axisymmetric System Eigenvalues split into distinct Eigenvalues. Additionally, properties of the formulation are ideal for use in modal analyses, Ritz-Galerkin discretizations, and extensions to gyroscopic or nonlinear analyses.