Variable Speed Wind Turbine Control Using the Homotopy Perturbation Method

In this study, we present a method to obtain optimal control of the variable-speed fixed-pitch wind turbine using the homotopy perturbation method (HPM). In general, the optimal control problem for nonlinear systems should solve the Hamilton-Jacobi-Bellman (HJB) equation. The partial differential HJB equations that arise in optimal control problem, give closed-loop control law and it is difficult to obtain an exact solution of them for nonlinear systems. The main objective of this work is to employ the homotopy perturbation method to solve the HJB equation for a two-mass model of a wind turbine to capture the maximum power from the wind in below-rated wind speed. By applying this strategy, we obtained an approximate solution of the HJB equation for a two-mass model of the wind turbine with high accuracy. In the simulation section, we compare the results of the proposed HPM strategy with the nonlinear static state feedback control (NSSFE) approach. The presented results confirm that the HPM controller produces more electrical power while minimizing low-speed shaft oscillations by improving dynamic characteristics.