Structure-preserving Model Reduction of Parametric Power Networks

TL;DR

This paper introduces a structure-preserving parametric model reduction method for linearized power network swing equations, ensuring accurate residue matching across parameters and demonstrated effectiveness through numerical examples.

Contribution

It presents a novel global basis approach that combines local $ ext{H}_2$-based reductions with residue analysis to preserve structure and accuracy in parametric power network models.

Findings

Achieves bounded $ ext{H}_2$ and $ ext{H}_$ errors across parameters.

Enriches the basis with residue analysis for improved accuracy.

Validated with two numerical examples.

Abstract

We develop a structure-preserving parametric model reduction approach for linearized swing equations where parametrization corresponds to variations in operating conditions. We employ a global basis approach to develop the parametric reduced model in which we concatenate the local bases obtained via $\mathcal{H}_2$-based interpolatory model reduction. The residue of the underlying dynamics corresponding to the simple pole at zero varies with the parameters. Therefore, to have bounded $\mathcal{H}_2$ and $\mathcal{H}_\infty$ errors, the reduced model residue for the pole at zero should match the original one over the entire parameter domain. Our framework achieves this goal by enriching the global basis based on a residue analysis. The effectiveness of the proposed method is illustrated through two numerical examples.