An Efficient Method for Computing Exact Delay-Margins of Large-Scale Power Systems

This letter proposes an efficient method for computing the delay-margins of large-scale power systems with single constant delay. The method computes the margin by identifying the minimal delay under which some eigenvalues are about to cross the imaginary axis from the left to the right half complex plane. Based on the Rekasius substitution, a new characterization for the crossing points is developed, followed by a method for determining the delay margins. The method only involves eigen-value decomposition on a low-order matrix whose dimension is independent of the system scale. Further leveraging the sparsity of power systems makes it computationally very attractive for practical large-scale system applications.

I. Introduction

Amajor metric that quantifies robustness of a control system under the influence of time delays is the so-called delay margin. It is defined by the maximum delay a system can tolerate without losing stability. The existing methods to calculate delay margins can be classified into two groups, i.e., the time-domain and the frequency-domain methods.