Multiplex Centrality Measurements Applied to Islanded Microgrids
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Multiplex Centrality Measurements Applied to Islanded Microgrids Vladimir Toro*, Eduardo Mojica-Nava, and Naly Rakoto-Ravalontsalama 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. Keywords: Centrality measurement, degree, eigenvector, Laplacian, leader, microgrid, multiplex, Pagerank.
1.
INTRODUCTION
Microgrids are autonomous electrical systems capable of working either connected or isolated from the power network, i.e., distribution system. The inverter is the basic unit in an AC MG to control the amplitude and frequency of the generated voltage. Voltage, frequency, active, and reactive powers are regulated to achieve the desired performance. When a highly inductive transmission line is assumed, active and reactive powers are controlled separately by making changes over frequency and voltage, respectively. Following the hierarchical control frame for MGs, a first loop corresponds to droop control that allows achieving the current sharing condition in a decentralized manner. However, droop control introduces some deviations from the reference values making necessary a second control loop to correct them while keeping the power-sharing condition. This correction can be made using either a centralized or a distributed controller. In [1], it is proposed a distributed control where the secondary controller corrects the frequency deviations keeping the power-sharing condition. Inverters are considered as agents that share frequency and active power-sharing information with their neighbors through different layers. Control and synchronization for systems with several layers have been studied and applied
to manage heterogeneity between agents [2, 3]. Systems with physical and communication networks are known as cyber-physical systems (CPS), a frequency and voltage restoration algorithm for MGs under attack is presented in [4]. Other app
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