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- W4297849455 abstract "Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a common grid frequency on complex network topologies. In this paper we study a second-order rotator model in the large network limit. We merge the recent theory of random graph limits for complex small-world networks with approaches to first-order systems on graphons. We prove that there exists a well-posed continuum limit integral equation approximating the large finite-dimensional case power grid network dynamics. Then we analyse the linear stability of synchronized solutions and prove linear stability. However, on small-world networks we demonstrate that there are topological parameters moving the spectrum arbitrarily close to the imaginary axis leading to potential instability on finite time scales." @default.
- W4297849455 created "2022-10-01" @default.
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- W4297849455 date "2018-07-10" @default.
- W4297849455 modified "2023-09-27" @default.
- W4297849455 title "Power Network Dynamics on Graphons" @default.
- W4297849455 doi "https://doi.org/10.48550/arxiv.1807.03573" @default.
- W4297849455 hasPublicationYear "2018" @default.
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