Oepomo's algorithm for computing eigenvalue in system engineering

Abstract

Small signal stability is the ability of a system to maintain stability when subjected to small disturbances. Small signal analysis gives valuable data about the dynamic properties of the system and helps in its design, operation, and control. Time domain simulation and eigenvalue analysis are the two main ways to study system stability. Eigenvalue analysis are widely utilized to perform small signal stability analysis. The dynamic property of a system in response to small perturbations can be predicted by computing the eigenvalues and eigenvectors of the system matrix. The location of the eigenvalues can be used to study the system's performance. In addition eigenvectors can be used to predict the relative participation of the respective states in the corresponding disturbance modes. This paper described a new method and algorithm for the numerical solution of eigenvalues with the largest real part of essentially positive matrices. The method is based on a numerical implementation of Collatz's eigenvalue inclusion theorem for non-negative irreducible matrices. Finally, a numerical example is given to show the speed of convergence of the new algorithm.