Non-Linear and Linear Model Based Controller Design for Variable-Speed Wind Turbines

Variable-speed, horizontal axis wind turbines use bladepitch control to meet specified objectives for three regions of operation. This paper focuses on controller design for the constant power production regime. A simple, rigid, non-linear turbine model was used to systematically perform trade-off studies between two performance metrics. Minimization of both the deviation of the rotor speed from the desired speed and the motion of the actuator is obtained through systematic selection of proportional-integral-derivative controller gain values. The gain design is performed using a non-linear turbine model and two linear models. The linear models differ only in selection of linearization point. The gain combinations resulting from design based upon each of the three models are similar. Performance under each of the three gain combinations is acceptable according to the metrics selected. The importance of operating point selection for linear models is illustrated. Because the simulation runs efficiently, the non-linear model provides the best gain design, but careful selection of the linearization point can produce acceptable gain designs from linear models. INTRODUCTION Utility-scale wind turbine manufacturers have recently begun to explore the advantages of variable-speed operation. Because variable-speed wind turbines have the potential for increased energy capture, controller design has become an area of increasing interest. Blade-pitch regulation provides means for initiating rotation, varying rotational speed to extract power at low wind speeds, and maintaining power production at a maximum level. Controllers must be designed to operate in each of these regions, but this study pertains only to the power regulation regime. The power regulation regime is entered when the turbine reaches the design rotor speed for maximum power production. Under these conditions, rotational speed is constrained to a specified maximum value through blade-pitch regulation. Fluctuations in wind speed are accommodated to prevent large excursions from the desired rotational speed. Thus the power production is also constrained to a relatively constant level. In addition to maintaining a constant rotational speed, actuator movement must be restrained to prevent fatigue and thermal overload. The combination of maintaining a constant rotational speed and minimizing actuator motion are the control objectives specified for the power regulation regime. Controller design has centered mainly on simple, linear, proportional-integral-derivative (PID) controllers that are easily implemented in the field environment. Gain selection for these controllers has traditionally been a trial and error process relying on the experience and intuition of the engineers. The systematic method used in this study, reduces the reliance on intuition and results in a controller design that is optimized for the specified performance metrics. This PID controller establishes the baseline performance to which more sophisticated controllers can be compared. Sophisticated controllers such as state estimation based controllers provide the potential for control of multiple inputs and outputs. These controllers could be used to mitigate fatigue of blades in addition to regulating rotor speed. However, these sophisticated controllers often require a linear model for their design. A comparison of the PID controller design based upon a non-linear model and the design based upon two linear models is presented in order to illustrate the design’s dependence on the model used. Also, a comparison of operating point selection for the linear model is included. DYNAMIC MODEL The simple, rigid, non-linear turbine model developed for the purpose of controller design by Kendall et al. (1997), was used for this design study. The geometry and aerodynamic characteristics of the simulated turbine resemble those of a Grumman Windstream-33, 10-m diameter, 20-kW turbine. The National Renewable Energy Laboratory’s National Wind