Gain-Scheduled <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-Optimal Control of Variable-Speed-Variable-Pitch Wind Turbines

Abstract

The fast-growing technology of large scale wind turbines demands control systems capable of enhancing both the efficiency of capturing wind power, and the useful life of the turbines themselves. l 1 -Optimal control is an approach to deal with persistent exogenous disturbances which have bounded magnitude (l ∞ -norm) such as realistic wind disturbances and turbulence profiles. In this brief, we develop an efficient method to compute the l 1 -norm of a system. As the control synthesis problem is nonconvex, we use the proposed method to design the optimal output feedback controllers for a linear model of a wind turbine at different operating points using genetic algorithm optimization. The locally optimized controllers are interpolated using a gain-scheduled technique with guaranteed stability. The controller is tested with comprehensive simulation studies on a 5 MW wind turbine using fatigue, aerodynamics, structures, and turbulence (FAST) software. The proposed controller is compared with a well-tuned proportional-integral (PI) controller. The results show improved power quality, and decrease in the fluctuations of generator torque and rotor speed.