Synchronization and chaos control in coupled Non-identical systems: application in Wind Turbine-Grid coupled power systems

Abstract

The increasing number of renewable energy systems coupled to the grid can lead to electrical energy losses when the currents or voltages of the two systems are not synchronized. Many mathematical models have investigated the phenomenon of synchronization in coupled systems. Here, we mathematically model the dynamics of a wind turbine-grid coupled system as a periodically driven Duffing resonator coupled to a Van der Pol oscillator with both position and velocity coupling. We consider the fluctuating nature of the wind as the only external driving force. We integrate the coupled system of equations under different coupling strengths and driven frequencies using the Runge-Kutta method of order 4(RK4). The result suggests that synchronization can be achieved at higher coupling strengths even with small values of the driven frequencies than at lower coupling strengths. At higher values of the driven frequency, the system exhibits chaotic behavior for both strong and weak couplings but with synchronization maintained only for the strong coupling case. Our results suggest chaos and synchronization can be controlled in this system by turning appropriate parameters.