Abstract-Attack detection problems in the smart grid are posed as statistical learning problems for different attack scenarios in which the measurements are observed in batch or online settings. In this approach, machine learning algorithms are used to classify measurements as being either secure or attacked. An attack detection framework is provided to exploit any available prior knowledge about the system and surmount constraints arising from the sparse structure of the problem in the proposed approach. Well-known batch and online learning algorithms (supervised and semi-supervised) are employed with decision and feature level fusion to model the attack detection problem. The relationships between statistical and geometric properties of attack vectors employed in the attack scenarios and learning algorithms are analyzed to detect unobservable attacks using statistical learning methods. The proposed algorithms are examined on various IEEE test systems. Experimental analyses show that machine learning algorithms can detect attacks with performances higher than the attack detection algorithms which employ state vector estimation methods in the proposed attack detection framework.

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We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second.We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the log throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided.

We derive upper bounds on the transport capacity of wireless networks. The bounds obtained are solely dependent on the geographic locations and power constraints of the nodes. As a result of this derivation, we are able to conclude the optimality, in the sense of scaling of transport capacity with the number of nodes, of a multi-hop communication strategy for a class of network topologies.

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