Spectral Transformation Algorithms for Computing Unstable Modes of Large Scale Power Systems
For power system stability analysis, this work provides a more efficient way to compute unstable modes, but the approach is incremental, extending existing Möbius transform techniques to a specific matrix pencil form.
This paper presents spectral transformation algorithms for computing eigenvalues with positive real part of large-scale power system models, using Möbius transforms to inhibit spurious eigenvalues and accelerate convergence. Tests on a 3156-order system demonstrate the method's effectiveness.
In this paper we describe spectral transformation algorithms for the computation of eigenvalues with positive real part of sparse nonsymmetric matrix pencils $(J,L)$, where $L$ is of the form $\pmatrix{M&0\cr 0&0}$. For this we define a different extension of Möbius transforms to pencils that inhibits the effect on iterations of the spurious eigenvalue at infinity. These algorithms use a technique of preconditioning the initial vectors by Möbius transforms which together with shift-invert iterations accelerate the convergence to the desired eigenvalues. Also, we see that Möbius transforms can be successfully used in inhibiting the convergence to a known eigenvalue. Moreover, the procedure has a computational cost similar to power or shift-invert iterations with Möbius transforms: neither is more expensive than the usual shift-invert iterations with pencils. Results from tests with a concrete transient stability model of an interconnected power system whose Jacobian matrix has order 3156 are also reported here.