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arXiv · 2407.07312

Hybrid Synchronization with Continuous Varying Exponent in Decentralized Power Grid

Jinha Park·B. Kahng
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Abstract

Motivated by the decentralized power grid, we consider a synchronization transition (ST) of the Kuramoto model (KM) with a mixture of first- and second-order type oscillators with fractions $p$ and $1-p$, respectively. Discontinuous ST with forward-backward hysteresis is found in the mean-field limit. A critical exponent $\beta$ is noticed in the spinodal drop of the order parameter curve at the backward ST. We find critical damping inertia $m_*(p)$ of the oscillator mixture, where the system undergoes a characteristic change from overdamped to underdamped. When underdamped, the hysteretic area also becomes multistable. This contrasts an overdamped system, which is bistable at hysteresis. We also notice that $\beta(p)$ continuously varies with $p$ along the critical damping line $m_*(p)$. Further, we find a single-cluster to multi-cluster phase transition at $m_{**}(p)$. We also discuss the effect of those features on the stability of the power grid, which is increasingly threatened as more electric power is produced from inertia-free generators.

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Jinha Park, B. Kahng. 2024-07-10. Hybrid Synchronization with Continuous Varying Exponent in Decentralized Power Grid. https://arxiv.org/abs/2407.07312

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