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Vulnerability and stability of power grids modeled by second-order Kuramoto model: a mini review

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Abstract

In this work, we derive a model to study and simulate the dynamics of power grids that, after a few approximations, turns out to be the second-order Kuramoto model. We then use this model to perform some numerical simulations that relate to the vulnerability and stability of energy transmission networks. In relation to the stability, assuming the grid is fully functional, and therefore, is in the synchronous state, we analyze how the grid responds to large perturbations, and also, how this response can be influenced by the location of the node being perturbed. We also show how a simple change in the topology or in the transmission capacity of a line can affect the synchronization of the grid. Regarding the vulnerability, some indexes to identify dynamically vulnerable nodes and edges are presented.

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Notes

  1. power units are short for normalized power units

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Acknowledgements

The authors would like to thank Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq for the financial support, including grant 307714/2018-7. This research is also supported by grants 2015/50122 and 2018/03211-6 of São Paulo Research Foundation (FAPESP).

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Authors and Affiliations

  1. National Institute for Space Research, INPE, Associated Laboratory for Computing and Applied Mathematics, São José dos Campos, SP, 12243-010, Brazil

    Juliana C. Lacerda, Jussara Dias & Celso Freitas

  2. Institute of Science and Technology, Federal University of São Paulo, São José dos Campos, SP, 12247-014, Brazil

    Elbert Macau

Authors
  1. Juliana C. Lacerda
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  2. Jussara Dias
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  3. Celso Freitas
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  4. Elbert Macau
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Correspondence to Juliana C. Lacerda.

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Lacerda, J.C., Dias, J., Freitas, C. et al. Vulnerability and stability of power grids modeled by second-order Kuramoto model: a mini review. Eur. Phys. J. Spec. Top. 230, 3509–3517 (2021). https://doi.org/10.1140/epjs/s11734-021-00246-2

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