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Multiplex Centrality Measurements Applied to Islanded Microgrids

Vladimir Toro*, Eduardo Mojica-Nava, and Naly Rakoto-Ravalontsalama
International Journal of Control, Automation, and Systems, vol. 19, no. 1, pp.449-458, 2021

Abstract : This paper presents four centrality measurements applied to an alternating current (AC) microgrid (MG) modeled as a multiplex network. The MG secondary control is separated into a frequency and a power-sharing layers, each one with a different adjacency matrix. A physical layer is also considered with an admittance matrix representing the impedances among the inverters. Centrality measures are used to determine the importance of nodes in separate layers, thereafter adjacency and Laplacian matrices are redefined to calculate the role of nodes in the multiplex system. First, a global adjacency matrix is calculated by the matrix sum of each adjacency matrix. Second, the adjacency matrix is calculated by a supra-Laplacian matrix. The first eigenvalue of the perturbed matrix is used to determine the diffusivity in the network using as leaders the sets obtained by the centrality measures. The role of the nodes in the system is verified in a simulated MG model of 37 nodes. Degree centrality and energy Laplacian measures present similar sets of nodes; however, the fastest set of nodes is found using the Eigenvector measurements for uniform and supra Laplacian approach.

Keyword : Centrality measurement, degree, eigenvector, Laplacian, leader, microgrid, multiplex, Pagerank.

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