A power transmission system can be represented by a network with nodes and links representing buses and electrical transmission lines, respectively. Each line can be given a weight, representing some electrical property of the line, such as line admittance or average power flow at a given time. We use a hierarchical spectral clustering methodology to reveal the internal connectivity structure of such a network. Spectral clustering uses the eigenvalues and eigenvectors of a matrix associated to the network, it is computationally very efficient, and it works for any choice of weights. When using line admittances, it reveals the static internal connectivity structure of the underlying network, while using power flows highlights islands with minimal power flow disruption, and thus it naturally relates to controlled islanding. Our methodology goes beyond the standard -means algorithm by instead representing the complete network substructure as a dendrogram. We provide a thorough theoretical justification of the use of spectral clustering in power systems, and we include the results of our methodology for several test systems of small, medium and large size, including a model of the Great Britain transmission network.

We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincare duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant K-theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.Comment: 56 pages; v3: final version, to appear in CM

Abstract:Intentional controlled islanding is an effective corrective approach to minimise the impact of cascading outages leading to large-area blackouts. This paper proposes a novel methodology, based on constrained spectral clustering, that is computationally very efficient and determines an islanding solution with minimal power flow disruption, while ensuring that each island contains only coherent generators. The proposed methodology also enables operators to constrain any branch, which must not be disconnected, to be excluded from the islanding solution. The methodology is tested using the dynamic models of the IEEE 39-and IEEE 118-bus test systems. Time-domain simulation results for different contingencies are used to demonstrate the effectiveness of the proposed methodology to minimise the impact of cascading outages leading to large-area blackouts. In addition, a realistically sized system (a reduced model of the Great Britain network with 815 buses) is used to evaluate the efficiency and accuracy of the methodology in large-scale networks. These simulations demonstrate that our methodology is more efficient, in a factor of approximately 10, and more accurate than another existing approach for minimal power flow disruption.

Abstract. We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C * -algebras. We present a new description of bivariant K-theory in terms of noncommutative correspondences which is nicely adapted to the study of T-duality in open string theory. We systematically use the diagram calculus for bivariant K-theory as detailed in our previous paper [12]. We explicitly work out our theory for a number of examples of noncommutative manifolds.

Abstract. We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C *