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Hua Ye - One of the best experts on this subject based on the ideXlab platform.

  • iterative Infinitesimal Generator discretization based method for eigen analysis of large delayed cyber physical power system
    Electric Power Systems Research, 2017
    Co-Authors: Hua Ye
    Abstract:

    Abstract To efficiently analyze the stability of large delayed cyber-physical power systems (DCPPS) incorporating wide-area damping controllers, an iterative Infinitesimal Generator discretization-based method (IIGD) for computing critical eigenvalues of the system is presented. IIGD contains three core techniques to guarantee efficiency and scalability. First, the sparsity of the Infinitesimal Generator's discretized matrix, which possesses identical spectrum to DCPPS, is explored by reformulating its blocks into Kronecker products. Especially, the dominant block is factorized as sum of Kronecker products of constant Lagrange vectors and system state matrices, which lays the basis of further utilizing the sparsities in the augmented state matrices of DCPPS. Second, the shift-invert preconditioning technique is applied to transform the required eigenvalues into those dominated in moduli. Third, the inverse iteration of the discretized matrix involved in sparse eigenvalue computation is iteratively achieved by utilizing the induced dimension reduction method (IDR(s)). Subsequently, the discretized matrix–vector product embedded in the method is efficiently implemented by exploiting the unique property of Kronecker product and the inherent sparsities in augmented system state matrices. The correctness, accuracy, efficiency and scalability of IIGD are extensively studied and thoroughly validated on the two-area four-machine test system and a real-life large transmission grid.

  • Enabling Highly Efficient Spectral Discretization-Based Eigen-Analysis Methods by Kronecker Product
    IEEE Transactions on Power Systems, 2017
    Co-Authors: Hua Ye
    Abstract:

    This letter presents a computationally efficient approach to implement the spectral discretization-based methods for eigenanalysis of large delayed cyber-physical power system by intensively exploiting the unique property of Kronecker product. Theoretical analyses and numerical tests demonstrate the novelty and effectiveness of the efficiently implemented explicit Infinitesimal Generator discretization method.

Bassam Bamieh - One of the best experts on this subject based on the ideXlab platform.

Marcus Weber - One of the best experts on this subject based on the ideXlab platform.

  • estimation of the Infinitesimal Generator by square root approximation
    Journal of Physics: Condensed Matter, 2018
    Co-Authors: Luca Donati, Martin Heida, Bettina G Keller, Marcus Weber
    Abstract:

    In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates, has become fundamental. Estimating the transition rates between molecular conformations is - from a mathematical point of view - an invariant subspace projection problem. We present a method to project the Infinitesimal Generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the Generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and Alanine dipeptide as high-dimensional system.

  • estimation of the Infinitesimal Generator by square root approximation
    arXiv: Computational Physics, 2017
    Co-Authors: Luca Donati, Martin Heida, Bettina G Keller, Marcus Weber
    Abstract:

    For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant subspace projection problem. A certain Infinitesimal Generator acting on function space is projected to a low-dimensional rate matrix. This projection can be performed in two steps. First, the Infinitesimal Generator is discretized, then the invariant subspace is approxi-mated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized Infinitesimal Generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correla-tion between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2d-diffusion process and Alanine dipeptide.

Peng Zhang - One of the best experts on this subject based on the ideXlab platform.

  • efficient eigen analysis for large delayed cyber physical power system using explicit Infinitesimal Generator discretization
    IEEE Transactions on Power Systems, 2016
    Co-Authors: Yutian Liu, Peng Zhang
    Abstract:

    Time delays significantly compromise the performance of wide-area measurement and control system and thus may jeopardize the stability of cyber-physical power systems (CPPS). A delayed CPPS (DCPPS) has a transcendental characteristic equation, leading to an infinite number of eigenvalues basically unsolvable by traditional eigen-analysis methods. In this paper, an explicit Infinitesimal Generator discretization (EIGD) approach is presented to tackle the traditionally intractable problem. First, the delayed differential equation of DCPPS is transformed to an ordinary differential equation by using an operator called Infinitesimal Generator. The operator is then optimally discretized, resulting in a highly structured, sparse and explicit approximant matrix. By exploiting the sparsity of the matrix and that of system matrices, the rightmost eigenvalues of the original DCPPS can be accurately computed. The contributions of the EIGD approach lie in the following: 1) it forms a theoretical foundation for accurately obtaining the critical eigenvalues of a CPPS with multiple delays; 2) it constructs a highly structured approximant matrix that enables efficient eigen-analysis of a large DCPPS by making full use of sparsity techniques; and 3) it integrates the shift-invert transformation, Arnoldi algorithm, Newton correction and eigen-sensitivity to form a computational framework for the analysis of large DCPPS. The accuracy, efficiency and scalability of EIGD have been extensively studied and thoroughly validated on the two-area four-machine test system and a practical large transmission grid.

Makan Fardad - One of the best experts on this subject based on the ideXlab platform.