Stochastic Optimal Control Problem of Maximum Energy Capture for Wind Turbines Based on Dynamic Programming Principe

Large-scale offshore wind turbines are equipped with different control systems, which empower them to reach the maximum power output at various wind speeds. The randomness of the wind determines the requirement for wind turbines to function at varying wind speeds, and these speeds affect the functional state of the turbines. Since the wind speed falls within the interval between the cut-in wind speed and the rated wind speed, the output power of the generator remains lower than the rated power. This article studies the problem of maximum energy capture of wind turbines under this situation. With a fixed pitch angle, to optimize the rotational speed of the wind turbine rotor as much as possible, we regulate the electromagnetic torque of the generator. The wind is characterized as a random process. Fully considering the randomness of the wind, a stochastic differential equation (SDE) is established based on the random interference it brings. By the solving of the SDE through the principle of dynamic programming, an analytical expression of the electromagnetic torque is derived. In the actual operation of wind farms, the electromagnetic torque can reach the target value by changing the generator current.