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.

中文翻译：

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参数化电网的保结构降阶模型

我们为线性化摆动方程开发了一种保留结构的参数模型简化方法，其中参数化对应于工作条件的变化。我们采用全局基础方法来开发参数化约简模型，在该模型中，我们将通过基于$ \ mathcal {H} _2 $的插值模型约简所获得的局部碱基进行级联。对应于零的简单极点的基础动力学的残差随参数而变化。因此，要限制$ \ mathcal {H} _2 $和$ \ mathcal {H} _ \ infty $错误，在零范围内，极点的简化模型残差应与整个参数域上的原始残差匹配。我们的框架通过基于残渣分析丰富全球基础来实现此目标。通过两个数值例子说明了该方法的有效性。