Finite-time function projective synchronization control method for chaotic wind power systems

Abstract

Wind power is a rapidly growing renewable energy source that plays an increasingly important role in power systems. However, its dynamic behaviors are complex because of the instability of wind speed, strong coupling, highly nonlinear subsystems, and mass grid connections. Chaotic oscillation is one of the most typical complex dynamic behaviors of wind power systems. This behavior can seriously influence the stable operation of wind power systems and cause great harm. This study proposed a control method for finite-time function projective synchronization on the basis of the chaos synchronization principle and finite-time theory for wind power systems. Wind power systems with or without uncertain parameters were considered. First, we built a high-dimensional wind power system and analyzed its chaotic behaviors. Lyapunov exponents were derived to prove the existence of chaos and bifurcation. Second, we aimed to increase the robustness of the controller by adding parameter observers to the controller. The result helped solve the problem of unknown parameters. If a wind power system comprises unknown parameters, the unknown parameters can be defined as the system's states. An unknown parameter observer was designed to realize the identification of unknown parameters. Third, we proposed a control method for finite-time function projective synchronization. Finite-time stability theory and function projective synchronization theory were used to construct the controller. These theories can ensure the quick synchronization of a chaotic wind power system with a stable wind power system in finite time. Finally, the mathematical proof of the stability theorem was derived, and a corresponding numerical simulation was performed to validate the chaos control method for wind power systems.