Optimal control for a wind system considering the time evolution of the wind speed and the variation of the kinetic energy

This paper proposes an original method of determining the maximum power function of a wind turbine at variable wind speeds. In this paper we determine the speed at which the system must work in order to obtain a maximum amount of electricity in a time interval of hours and days. For this purpose, we measure the wind speed and knowing the mechanical characteristic of the turbine, we calculate the optimum speed of the generator, such as during a long period of time (days) to obtain maximum energetic. There are presented a set of non-linear equations which models the wind turbine (WT) and the permanent magnet synchronous generator (PMSG), the determination of the mechanical rotation speed at different wind speeds in order to obtain the maximum power from the wind. The effectiveness of the proposed method evaluates the electrical load at the PMSG which can be a micro grid or a battery of electrical accumulators.