Skew µ with a power systems application

Abstract

Exploitation of the NP hard, mixed μ problem structure provides a polynomial time algorithm that approximates μ with usually reasonable answers. When the problem is extended to the skew μ formulation an extension of the existing μ methodology to the skew μ problem is required. The focus of this paper is to extend the μ bounds development to the skew μ problem and show skew μ bounds computation by way of various algorithms. The motivation for extending the μ problem to skew μ is driven by large scale power systems stability analysis. Power system analysis is computationally expensive and contains narrow hard-to-identify peaks in instability. To reduce computational load and improve accuracy, the power system analysis problem is translated into a skew μ problem. This is done by reformulating the state space power system model as a robust analysis problem with the frequency range of interest augmented to the state space model as an uncertainty. The superiority of the skew μ methods for many μ problems is demonstrated via analysis of 2 power system benchmark problems.