Hybrid synchronization with continuous varying exponent in modernized power grid.

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. • A mixture of inertial and non-inertial Kuramoto oscillators shows competing effects. • They cause over- and underdamped dynamics, resulting in a hybrid phase transition. • At the threshold, critical behavior shows a continuously varying critical exponent. • This offers insight into maintaining the stability of modernized power grids. [ABSTRACT FROM AUTHOR]