Fixed-Point Methods on Small-Signal Stability Analysis

TL;DR

This paper introduces the DDPSE fixed-point method, an improved algorithm for efficiently computing dominant eigenvalues and low damped modes in power system stability analysis, with proven quadratic convergence.

Contribution

The paper presents DDPSE, a modified fixed-point eigenvalue solver with quadratic convergence, tailored for power system stability and large-scale transfer function analysis.

Findings

DDPSE effectively computes dominant poles in transfer functions.

Both DDPSE and DPSE exhibit local quadratic convergence.

Methods are effective for low damped mode detection in large power systems.

Abstract

In this paper we introduce the Diagonal Dominant Pole Spectrum Eigensolver (DDPSE), which is a fixed-point method that computes several eigenvalues of a matrix at a time. DDPSE is a slight modification of the Dominant Pole Spectrum Eigensolver (DPSE), that has being used in power system stability studies. We show that both methods have local quadratic convergence. Moreover, we present practical results obtained by both methods, from which we can see that those methods really compute dominant poles of a transfer function of the type $c^T(A-sI)^{-1}b$, where $b$ and $c$ are vectors, besides being also effective in finding low damped modes of a large scale power system.