Structure-Preserving Model Reduction for Nonlinear Power Grid Network

2022/03/17 by Bita Safaee, Serkan Gugercin, Safaee, Bita +1
Engineering · Mathematics · Physics and Astronomy · #FOS: Electrical engineering #Model Reduction and Neural Networks #Numerical methods for differential equations #Power System Optimization and Stability #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2203.09021

openalex publication_date 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a structure-preserving system-theoretic model reduction framework for nonlinear power grid networks. First, via a lifting transformation, we convert the original nonlinear system with trigonometric nonlinearities to an equivalent quadratic nonlinear model. This equivalent representation allows us to employ the H₂-based model reduction approach, Quadratic Iterative Rational Krylov Algorithm (Q-IRKA), as an intermediate model reduction step. Exploiting the structure of the underlying power network model, we show that the model reduction bases resulting from Q-IRKA have a special subspace structure, which allows us to effectively construct the final model reduction basis. This final basis is applied on the original nonlinear structure to yield a reduced model that preserves the physically meaningful (second-order) structure of the original model. The effectiveness of our proposed framework is illustrated via two numerical examples.

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