Stochastic Optimal Control Problem of Wind Turbine with Too Low Wind Speed in Short Time

When the wind speed is smaller than a cut-in speed, a double-fed asynchronous offshore wind turbine may be cut-off, which is actually not necessary because the wind speed may become larger than the cut-in speed in a short while. This type of cut-offs, which occur frequently in practice, may shorten the life of the wind turbines and also bring serious fluctuations to power systems. In this paper, we propose a control method to avoid this type of stops with energy storage installed locally. With the dynamics of the wind turbine, we formulate a torque-based stochastic linear quadratic optimal control problem which is solved from a forward differential equation and an adjoint equation. An analytical form of control input is derived, with which the unnecessary stops can be avoided with energy-saving.