Hybrid Synchronization with Continuous Varying Exponent in Decentralized Power Grid
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929415889354752 |
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| author | Park, Jinha Kahng, B. |
| author_facet | Park, Jinha Kahng, B. |
| contents | 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 $β$ 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 $β(p)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid Synchronization with Continuous Varying Exponent in Decentralized Power Grid Park, Jinha Kahng, B. Statistical Mechanics 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 $β$ 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 $β(p)$ 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. |
| title | Hybrid Synchronization with Continuous Varying Exponent in Decentralized Power Grid |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2407.07312 |