Abstract
Motivated by the modernized 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.
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Schedule a callMore From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
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