Distributed frequency synchronization and phase-difference tracking for Kuramoto oscillators and its application to islanded microgrids

Yanbing Mao, Ziang Zhang

Abstract: This paper addresses the problem of asymptotical frequency synchronization and phase-difference tracking for Kuramoto oscillators with N distinct natural frequencies. Through the stability analysis of Kuramoto oscillators with distributed phase-difference tracking controllers, we discover that by controlling phase-difference tracking errors and their integrations, the individual frequencies can asymptotically synchronize to the average natural frequencies of the group and phase differences can asymptotically track the given references. We also extend the proposed phase-difference tracking control to islanded microgrids assuming there are local controllers maintaining the voltage stability, to achieve frequency synchronization and control angle differences of voltages. Simulations, including the numerical examples of a network of N = 4 Kuramoto oscillators and an islanded microgrid consisting of two frequency-droop controllers and two loads, are provided to verify the effectiveness of proposed control strategies.