Structure-Preserving Model Reduction for Nonlinear Power Grid Network

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 $\mathcal{H}_2$-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.