潮流网络的有向图建模与Kron约简
Modelling and Kron reduction of power flow networks in directed graphs
摘要：
电网是大型复杂系统，需要强大的计算能力进行监测和分析。Kron约简是图论中的一种通用约简方法，常用于电路的简化。在本文中，我们提出了一个新的公式的加权拉普拉斯矩阵的有向图。该矩阵被证明是严格等价的传统制定的拉普拉斯矩阵，并验证了良好的无损耗直流潮流网络的有向图建模。我们也提出了显着的性质，建议加权拉普拉斯算子和条件的Kron减少有向图和无耗直流潮流网络。通过IEEE-3、IEEE-5、IEEE-9、IEEE-14和IEEE RTS-96测试系统的仿真模型验证了降阶方法。
英文摘要：
Electrical grids are large-sized complex systems that require strong computing power for monitoring and analysis. Kron reduction is a general reduction method in graph theory and is often used for electrical circuit simplification. In this paper, we propose a novel formulation of the weighted Laplacian matrix for directed graphs. The proposed matrix is proved to be strictly equivalent to the conventionally formulated Laplacian matrix and is verified to well model a lossless DC power flow network in directed graphs. We as well present significant properties of the proposed weighted Laplacian and conditions of Kron reduction in directed graphs and in lossless DC power flow networks. The reduction method is verified via simulation models of IEEE-3, IEEE-5, IEEE-9, IEEE-14, and IEEE RTS-96 test systems.
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