Comparison between a PI and LQ-regulation for a 2 MW wind turbine

This paper deals with the design of controllers for pitch regulated, variable speed wind turbines where the controller is used primarily for controlling the (rotor and generator) speed and the electric power through a collective pitch angle and the generator torque. However, other key parameters such as loads on the drive train, wings and tower are in focus. The test turbine is a 2 MW turbine used as a bench mark example in the project ”Aerodynamisk Integreret Vindmøllestyring” partly founded by the Danish Energy Authority under contract number 1363/02-0017. One of the control strategies investigated here in this report, is based on a LQ (Linear time invariant system controlled to optimize a Quadratic cost function) strategy. This strategy is compared to a traditional PI strategy. As a control object a wind turbine is a nonlinear, stochastic object with several modes of operation. The nonlinearities calls for methods dealing with these. Gain scheduling is one method to solve these types of problems and the PI controller is equipped with such a property. The LQ strategy is (due to project time limitations) implemented as a fixed parameter controller designed to cope with the situation defined by a average wind speed equal to 15 m/sec. The analysis and design of the LQ controller is performed in Matlab and the design is ported to a Pascal based platform and implemented in HAWC. In general a LQ controller can be designed as a compromise between minimizing several effects including the performance parameters as well as the control effort parameters. In this report, however (and due to project time limitiation), only the produced electric power has been in focus. In the comparison between the two strategies the produced electric power for the LQ controller has indeed been kept within a more narrow interval than for the PI controller. One of the costs is however a high pitch angular speed. In one of the LQ designs this costs (in terms of the pitch angular speed) is unrealistic high. In a redesign the maximum pitch angular speed is reduced, but still higher that in the case of the traditionally PI controller. For reducing the pitch speed, further development in connection the LQ design, should be directed i a direction where the pitch speed directly is included in the design cost function. Also for reducing the loads, these should be included in the design model and given a weight in the control objective function. The work has been carried out under contract with the Danish Energy Agency ”Aeroelastic intregratet control” ENS1363/02-0017. Print: Pitney Bowes Management Services Denmark A/S, 2005.