Nonlinear optimal control of variable speed wind turbines using optimal homotopy asymptotic method

This paper presents a new nonlinear optimal controller for wind energy conversion systems. This study utilizes a new strategy to solve the Hamilton–Jacobi–Bellman (HJB) equation and design a nonlinear optimal controller for wind turbines. The optimal homotopy asymptotic method (OHAM) is applied to derive the solution of the HJB equation corresponding to variable-speed wind turbines. The OHAM controller ensures proper tracking and achieves maximum wind power extraction while preventing excessive loads on the drive train. The proposed control strategy can provide fast convergence and rapid transient responses with high precision and small control input. The OHAM strategy requires a few iterations and can adjust the convergence domain and the convergence rate. The proposed OHAM controller is compared and evaluated with some existing control strategies. The obtained results indicate that OHAM achieves a suitable compromise between maximizing aerodynamic power capture and minimizing low-speed shaft oscillation.