Modified simultaneous perturbation stochastic approximation method for power capture maximization of wind turbines

Abstract

As traditional resources are becoming scarce, renewable energy is a recent topic receiving greater concern. Among the renewable energies, wind power is a very popular type of energy extracted from wind which is readily available in the environment. The use of wind power all over the world is receiving increased attention. Horizontal axis wind turbines are the most popular equipment for extracting power form the wind. One of the problems of using wind turbines is how to maximize the wind power capture. In this paper, a method for maximizing the rotor power coefficient of a wind turbine is proposed. Simultaneous Perturbation Stochastic Approximation (SPSA) is an efficient way for extremum seeking. It is different from the classical gradient based extremum seeking algorithms. For maximizing the rotor power coefficient, it only needs two objective function measurements to take a step toward the next extremum approximation. The one measurement SPSA is a modification of SPSA method developed in this work. Instead of using measurements of two positions occurring at random directions away from the current position, it uses the measurement of one position in a random direction and the measurement of the current position to estimate the gradient. Usually, the rotor power coefficient is not easily measurable. For speed regulation, a nonlinear robust speed controller is used in this work. The controller produces an estimate of the aerodynamic torque of wind turbine. The quality of this estimate improves with time. From that, a good estimate of power coefficient can be obtained. Simulations in MATLAB are executed with a model of a wind turbine based on its dynamic equations. From simulations, it can be seen that the one measurement SPSA method works very well for the wind turbine. It changes the tip speed ratio and blade pitch simultaneously, and the power coefficient reaches its maximum value quickly in a reliable manner. The power capture optimization is then implemented in FAST, a turbine simulation model created by NREL which is used to test the 5MW NREL reference turbine. From the results, it is evident that the wind turbine reaches the maximum power coefficient rapidly.