Observer design based in the mathematical model of a wind turbine

As a result of increasing environmental concern, the impact of conventional electricity generation on the environment is being minimized and efforts are being made to generate electricity from renewable sources. One way of generating electricity from renewable sources is to use wind turbines that convert the energy contained in flowing air into electricity. The major contributions of this paper are as follows: 1) The mathematical model of a prototype of a wind turbine is presented. This mathematical model is obtained by using the Euler Lagrange method and the circuits theory. The data of a prototype are used for the simulations of the obtained model. The prototype is a windward wind turbine of three blades. 2) An observer to see the angular position of a blade and the angular velocity of a blade using the armature current in the wind turbine is proposed, and this observer is important because it is easy to have the measure of the third, but it is difficult to have the measure of the first and the second. 3) It is proven that the state error of the observer applied to the nonlinear model is exponentially stable. The stability of the proposed observer is based on the solution of the Lyapunov method.