Numerical optimal control of a wind turbine system
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With the development of wind turbine technology and the need for maximizing wind energy harvesting, more wind turbines operate in the partial load region. Among many control algorithms developed for this region, controllers based on feedback of the global maximum power coefficient have been widely used. These control schemes offer good performance with simple implementations, but they may not be suited for wind turbines with limited rotor speed ranges. In such cases, the controller is challenged because the main feature ---the global maximum power coefficient--- is not achievable due to the turbine speed constraint. It is necessary to develop a controller to seek the achievable maximum power coefficient that leads to optimal wind energy capture. In this dissertation, the development of an optimal control framework to maximize wind energy capture for wind turbines with constrained turbine speed is first presented. Numerical optimal control techniques are applied to search for the achievable maximum power coefficient, with proposed modifications to make this task more computationally feasible. Mitigating the turbine generator torque variation, thus reducing the fatigue loading on turbine generator shaft, is also important for the partial load region operation. Including this aspect in the optimal control is then discussed. Furthermore, an approach of incorporating time-varying weightings into developing the optimal controller is introduced to seek further improvement on turbine generator torque variation reduction, thus fatigue reduction. In addition, the power generated by the wind turbine varies due to variation in the wind speed. Depending on the load demand and the wind speed, the wind turbine's operation switches between two modes: a multi-input-single-output (MISO) mode and a single-input-single-output (SISO) mode. Due to the wind turbine changes its dynamic behavior during the switching process, applying the traditional control methods to each corresponding mode may not be capable of maximizing the overall wind energy capture throughout the entire turbine's operation. Therefore, the development of an optimal control framework to maximize the overall wind energy capture for a switched wind turbine system is subsequently presented.