Hybrid Synchronization with Continuous Varying Exponent in Decentralized Power Grid

TL;DR

This paper studies a hybrid synchronization transition in a decentralized power grid model with mixed oscillator types, revealing hysteresis, critical exponents, and phase transitions that impact grid stability.

Contribution

It introduces a model with mixed first- and second-order oscillators showing novel hysteresis and phase transition behaviors relevant to power grid stability.

Findings

Discontinuous synchronization transition with hysteresis observed.

Critical damping inertia varies with oscillator mixture fraction.

Single-cluster to multi-cluster phase transition identified.

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.