2024/07/10 by Jinha Park, Park, Jinha, B. Kahng +1
Computer Science · Engineering · #FOS: Physical sciences #Microgrid Control and Optimization #Network Time Synchronization Technologies #Nonlinear Dynamics and Pattern Formation #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2407.07312
openalex publication_date 2024/07/10 · openalex created_date 2024/07/13 · openalex updated_date 2026/07/28
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.