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arXiv 1402.1780eess.SYcs.SY
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电力网络中的级联故障 - 分析与算法

Cascading Failures in Power Grids - Analysis and Algorithms

Columbia University(哥伦比亚大学);Laboratoire d’Informatique Fondamentale de Marseille(马赛基础信息学实验室)

Saleh Soltan, Dorian Mazauric, Gil Zussman

AI总结:

本文分析电力网络中级联线路故障的影响,提出基于伪逆矩阵的高效算法,探讨了电阻距离和伪逆矩阵在故障预测中的作用,证明了相关问题的计算复杂性。

摘要:

本文聚焦电力网络中传输系统中的级联线路故障。近期大规模停电事件展示了基于渗流和流行病模型的工具在建模级联故障方面的局限性。因此,我们通过计算工具和线性化功率流模型研究级联现象。我们首先获得关于电力网络导纳矩阵的Moore-Penrose伪逆矩阵的结果。基于这些结果,我们研究单一线路故障对其他线路流量的影响。我们还通过仿真展示了距离和电阻距离对故障后流量增加的影响,并讨论了与流行病模型的区别。我们随后研究级联特性,考虑诸如故障间距离和级联后满足的负荷(需求)比例(收益)等指标。我们利用导纳矩阵的伪逆矩阵开发一种高效的算法来识别级联故障演化,该算法可以作为级联缓解的构建块。最后,我们证明在各种指标下确定移除线路对级联影响最显著的集合是NP难问题,并引入一个简单的启发式方法用于最小收益问题。总体而言,结果表明使用电阻距离和导纳矩阵的伪逆矩阵提供了重要的见解,并可以支持高效算法的发展。

英文摘要:

This paper focuses on cascading line failures in the transmission system of the power grid. Recent large-scale power outages demonstrated the limitations of percolation- and epid- emic-based tools in modeling cascades. Hence, we study cascades by using computational tools and a linearized power flow model. We first obtain results regarding the Moore-Penrose pseudo-inverse of the power grid admittance matrix. Based on these results, we study the impact of a single line failure on the flows on other lines. We also illustrate via simulation the impact of the distance and resistance distance on the flow increase following a failure, and discuss the difference from the epidemic models. We then study the cascade properties, considering metrics such as the distance between failures and the fraction of demand (load) satisfied after the cascade (yield). We use the pseudo-inverse of admittance matrix to develop an efficient algorithm to identify the cascading failure evolution, which can be a building block for cascade mitigation. Finally, we show that finding the set of lines whose removal has the most significant impact (under various metrics) is NP-Hard and introduce a simple heuristic for the minimum yield problem. Overall, the results demonstrate that using the resistance distance and the pseudo-inverse of admittance matrix provides important insights and can support the development of efficient algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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