论文标题
非线性电网网络的结构保存模型降低
Structure-Preserving Model Reduction for Nonlinear Power Grid Network
论文作者
论文摘要
我们为非线性电网网络开发了一个具有结构性的系统理论模型减少框架。首先，通过提升转换，我们将带有三角非线性的原始非线性系统转换为等效的二次非线性模型。这种等效表示允许我们将基于$ \ MATHCAL {H} _2 _2 $基于模型还原方法，二次迭代理性Krylov算法（Q-irka）作为中间模型减少步骤。利用了基础功率网络模型的结构，我们表明由Q-IRKA产生的模型降低碱基具有特殊的子空间结构，这使我们能够有效地构建最终模型减少基础。最终基础应用于原始的非线性结构，以产生简化的模型，该模型保留了原始模型的物理有意义的（二阶）结构。我们提出的框架的有效性通过两个数值示例说明了。
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.
