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

We report the results of study of two models of power grids with hub cluster topology based on the second-order Kuramoto system. The first model considered is the small grid consisting of a consumer and two generators. The second model is the Nizhny Novgorod power grid. The areas in the parameter spaces of the grids that corresponds to different modes, including working synchronous one, of their operation are obtained. The dynamic stability of synchronous mode in the Nizhny Novgorod power grid model to transient disturbances of the power at its elements is tested. We show that the stability of peripheral elements of the grid to disturbances depends significantly on the lengths of their connections to the rest of the grid

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Power System Transient Stability Analysis via Second-Order Non-Uniform Kuramoto Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.960-961.1054 ◽

2014 ◽

Vol 960-961 ◽

pp. 1054-1057

Author(s):

Liu Yang ◽

Yu Feng Guo ◽

Ning Chen ◽

Min Hui Qian ◽

Xiao Ping Xue ◽

...

Keyword(s):

Stability Analysis ◽

Power System ◽

Transient Stability ◽

Stable Equilibrium ◽

Stability Margin ◽

Second Order ◽

Kuramoto Model ◽

Trapping Region ◽

Novel Approach ◽

Transient Stability Analysis

Based on frequency synchronization theory of the second-order non-uniform Kuramoto model, a novel approach for power system transient stability analysis is put forward by establishing the correspondence between the classic power system model and the second-order non-uniform Kuramoto model. This method relates network parameters with the region of attraction of the disturbed system’s stable equilibrium and thus the transient stability information of the disturbed system can be obtained by comparing the initial configuration with trapping region of the stable equilibrium of the disturbance-canceling system. The application of our approach to single machine infinite bus system shows that this method features a fast computation speed. It can determine the transient stability of the system when a certain perturbation acts on as well as offer the stability margin of the disturbed system, which is of great importance for practical use.

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Low-frequency oscillations in coupled phase oscillators with inertia

Scientific Reports ◽

10.1038/s41598-019-53953-1 ◽

2019 ◽

Vol 9 (1) ◽

Author(s):

Huihui Song ◽

Xuewei Zhang ◽

Jinjie Wu ◽

Yanbin Qu

Keyword(s):

Phase Fluctuation ◽

Low Frequency ◽

Power Grids ◽

Kuramoto Model ◽

Resonance Phenomenon ◽

Forced Oscillations ◽

Propagation Path ◽

Phase Oscillators ◽

Magnitude Distribution ◽

Periodically Driven

AbstractThis work considers a second-order Kuramoto oscillator network periodically driven at one node to model low-frequency forced oscillations in power grids. The phase fluctuation magnitude at each node and the disturbance propagation in the network are numerically analyzed. The coupling strengths in this work are sufficiently large to ensure the stability of equilibria in the unforced system. It is found that the phase fluctuation is primarily determined by the network structural properties and forcing parameters, not the parameters specific to individual nodes such as power and damping. A new “resonance” phenomenon is observed in which the phase fluctuation magnitudes peak at certain critical coupling strength in the forced system. In the cases of long chain and ring-shaped networks, the Kuramoto model yields an important but somehow counter-intuitive result that the fluctuation magnitude distribution does not necessarily follow a simple attenuating trend along the propagation path and the fluctuation at nodes far from the disturbance source could be stronger than that at the source. These findings are relevant to low-frequency forced oscillations in power grids and will help advance the understanding of their dynamics and mechanisms and improve the detection and mitigation techniques.

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