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        Multiplex Centrality Measurements Applied to Islanded Microgrids

        Vladimir Toro,Eduardo Mojica-Nava,Naly Rakoto-Ravalontsalama 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.1

        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-sharinglayers, each one with a different adjacency matrix. A physical layer is also considered with an admittance matrixrepresenting the impedances among the inverters. Centrality measures are used to determine the importance ofnodes in separate layers, thereafter adjacency and Laplacian matrices are redefined to calculate the role of nodesin 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 matrixis 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 energyLaplacian measures present similar sets of nodes; however, the fastest set of nodes is found using the Eigenvectormeasurements for uniform and supra Laplacian approach

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