Critical slowing-down as indicator of approach to the loss of stability
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Turitsyn_Critical slowing-down.pdf
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156.13 KB
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Author(s)
Podolsky, Dmitry
Turitsyn, Konstantin
Date Issued
November 2014
Journal
Proceedings of the 2014 IEEE International Conference on Smart Grid Communications (SmartGridComm)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Podolsky, Dmitry, and Konstantin Turitsyn. “Critical Slowing-down as Indicator of Approach to the Loss of Stability.” 2014 IEEE International Conference on Smart Grid Communications (SmartGridComm) (November 2014).
Version
Original manuscript
Abstract
We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations of the system state vector are driven by random variations of loads and intermittent renewable generation. In the vicinity of collapse the power system experiences so-called phenomenon of critical slowing-down characterized by slowing and simultaneous amplification of the system state vector fluctuations. In generic case of a co-dimension 1 bifurcation corresponding to the threshold of instability it is possible to extract a single mode of the system state vector responsible for this phenomenon. We characterize stochastic fluctuations of the system state vector using the formal perturbative expansion over the lowest (real) eigenvalue of the system power flow Jacobian and verify the resulting expressions for correlation functions of the state vector by direct numerical simulations. We conclude that the onset of critical slowing-down is a good marker of approach to the threshold of global instability. It can be straightforwardly detected from the analysis of single-node autostructure and autocorrelation functions of system state variables and thus does not require full observability of the grid.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/SmartGridComm.2014.7007616
