On the Conditional Mutual Information in the Gaussian–Markov Structured Grids
On the Conditional Mutual Information in the Gaussian–Markov Structured Grids
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高斯-马尔可夫结构网格中的条件互信息
DOI：
10.1007/978-3-319-02150-8_9
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发表时间：
2014
影响因子：
--
通讯作者：
E. Jonckheere
中科院分区：
文献类型：
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作者：
Hanie Sedghi;E. Jonckheere
监控和数据采集（SCADA）状态估计器（SE）和相量测量单元（PMU）网络构成了通信基础设施，旨在为“智能电网”调度员提供广域总线相角和其他数据，可以从中评估电网的运行状态——如果测量结果在通往SCADA调度和/或PMU集中器的途中没有受到损害。不幸的是，这正是在所谓的“虚假数据注入”下发生的事情。在本章中，我们基于PMU数据的高斯马尔可夫随机场（GMRF）假设，开发了测量数据完整性的快速测试。这一假设是本章的基础，它得到了以下方面的支持：(i)许多波动代和可变负载证明了高斯分布假设的正确性，以及（ii）直流潮流方程，从该方程中推导出母线相角的近似1邻特性，本章将对此进行更具体的讨论。后一种拓扑性质是指两个随机变量之间的条件互信息不消失，当且仅当观察到它们所在的节点在对应图的边集中连接。在高斯分布假设下，条件互信息很容易从条件协方差中计算出来。然后证明了条件协方差检验（CCT）与网格图的游走和性和局部分离性可以从未妥协的测量数据中重建网格图。另一方面，对于损坏的数据，CCT只重建网格图边缘集的适当子集，从而触发报警。
The Supervisory Control and Data Acquisition (SCADA) State Estimator (SE) and the Phasor Measurement Units (PMUs) network constitute the communication infrastructures meant to provide the “smart grid” dispatcher with wide-area bus phase angles and other data from which the operational status of the grid can be assessed—if the measurements are not compromised somewhere along their way to the SCADA dispatch and/or the PMU concentrator. Unfortunately, this is precisely what happens under the so-called “false data injection.” In this chapter, we develop a fast test for measurement data integrity, based on the Gaussian Markov Random Field (GMRF) assumption on the PMU data. This assumption, fundamental to this chapter, is supported by (i) the many fluctuating generations and variable loads justifying the Gaussian distribution assumption and, as more specifically addressed in this chapter, (ii) the DC power flow equations from which an approximate 1-neighbor property of the bus phase angles is derived. The latter topological property refers to the conditional mutual information between two random variables being non-vanishing if and only if the nodes at which they are observed are linked in the edge set of the corresponding graph. Under the Gaussian distribution assumption, the conditional mutual information is easily computable from the conditional covariance. Then it is shown that Conditional Covariance Test (CCT) together with the walk-summability and the local separation property of grid graph allows the reconstruction of the grid graph from uncompromised measurement data. On the other hand, with corrupted data, CCT reconstructs only a proper subset of the edge set of the grid graph, hence triggering the alarm.
影响因子：
2.1
作者：
Friedman, Jerome;Hastie, Trevor;Tibshirani, Robert
通讯作者：
Tibshirani, Robert