An asynchronous MATE-multirate method for the modeling of electric power systems
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ORIGINAL PAPER
An asynchronous MATE-multirate method for the modeling of electric power systems V. A. Galván-Sánchez1 · José R. Martí2 · E. S. Bañuelos-Cabral1 · J. Sotelo-Castañón1 · J. L. García-Sánchez1 · J. A. Gutiérrez-Robles3 Received: 9 March 2020 / Accepted: 15 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The multiarea Thévenin equivalent (MATE) solution framework is used in this work to combine several subsystems, which are solved using different multiple and non-multiple time-step sizes. In the proposed asynchronous MATE-multirate (A-MATEmultirate) solution, each subsystem is solved with the integration step size that is most adequate for its own internal time constants. This paper relaxes the requirement of previous multirate techniques, in which the solution time-steps of different systems must be multiples or submultiples of each other. To this end, this paper introduces the concept of asynchronous updating, in which each subsystem is updated according to its own internal clock. This updating process is performed in a closed-form solution, with external subsystems represented by their interpolated Thévenin equivalents. Interpolation with future values without using extrapolation is possible in the electromagnetic transients program solution because the history source for future time-steps is calculated at previous time-steps. The exchange of information between subsystems is conditioned using filters to avoid numerical problems during the decimation of the fast subsystems and the interpolation of the slow subsystems. The effectiveness of the proposed methodology is verified with examples using multiple and non-multiple time-step sizes. Keywords Non-multiple time-step sizes · Asynchronous updating A-MATE-multirate · MATE · Decimation and interpolation filters
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E. S. Bañuelos-Cabral [email protected] V. A. Galván-Sánchez [email protected] José R. Martí [email protected] J. Sotelo-Castañón [email protected] J. L. García-Sánchez [email protected] J. A. Gutiérrez-Robles [email protected]
1
Department of Electrical Mechanical Engineering, University of Guadalajara, Av. Juárez No. 976, Guadalajara, Jalisco, Mexico
2
Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, Canada
3
Department of Mathematics, University of Guadalajara, Guadalajara, Mexico
Large complex systems usually contain subsystems in which some of the variables change more rapidly than others. Multirate methods have been proposed to make the solution of these systems more efficient by solving each subsystem with different time-step sizes according to the subsystems’ time constants. The need for multirate solutions exists across disciplines. For example, in chemistry it is possible to use the separation of time scales to simulate the dynamics of macromolecules, a simulation whose computational complexity is enormous [1, 2]. This paper will focus on the application o
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