Efficient calculation of critical eigenvalues in large power systems using the real variant of the Jacobi–Davidson QR method

Application of an improved BHESS-BR method to the small signal stability analysis of power systems

“…Direct calculation of the system state matrix according to Equation (2) is impractical for large-scale power systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. If the sparse structures of J A , J B , J C , and J D are considered, the system state matrix S can be computed efficiently.…”

“…Many practical partial eigenanalysis (also known as subspace) methods have been proposed to assess the small signal stability of large power systems since 1985 [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The inverse iteration method [2], the Newton's method [3], the orthogonal iteration method [4], the explicitly restarted Arnoldi method [5], and the lop-sided or two-sided simultaneous iteration method [6] were popular in the last century.…”

“…The block Arnoldi method, which uses Chebyshev polynomials to construct the restart vectors, is illustrated in [8]. In recent decade, two most widely used subspace methods are the implicitly restarted Arnoldi (IRA) method [9] and the Jacobi-Davidson (JD) method [10][11][12][13]. Furthermore, the subspace methods can be also used to compute the dominant poles of a high-order transfer function [14,15].…”

Adaptive critical eigenvalues tracing via projected continuation of invariant subspace

“…Critical eigenvalues related to instability are usually a small portion of the overall spectrum; therefore, the calculation of rightmost and least damping ratio critical eigenvalues has been closely studied. Many iterative algorithms seeking a specified set of eigenvalues on a single equilibrium have been applied to the small signal stability analysis of large‐scale power systems [4–7]. These exploit sparsity by avoiding the reduction of the sparse system Jacobian matrix to a dense state matrix; however, they offer no approach for ensuring a good initial guess, which is crucial to convergence and efficiency.…”

Machine learning in complex networks: modeling, analysis, and applications

“…Efficient methods have been developed for finding the leading eigenvalues of real-valued asymmetric matrices (Goldhirsch et al, 1987;Tsai et al, 2010). The magnitudes of the eigenvalues are related to the variations that the image possesses; hence, it is a natural carrier of information (Jolliffe, 2002).…”