Design and comparison of passive tuned mass damper and active multivariable PD control methods to reduce the flapwise vibrations of wind turbine blade

The recent trend in wind power generation has been moving toward larger wind turbines, with an emphasis on high blade aerodynamic efficiency and minimal weight. This leads to more flexible wind turbine blades that are more susceptible to blade failure arisen from induced vibrations; which makes vibration control critical. In this paper, application of two control strategies to reduce wind turbine blade vibrations is investigated, offering an insight into how they compare and advantages and disadvantages of each. First, the turbine blade is modelled as an Euler-Bernoulli cantilever beam with three degrees of freedom. Most often, only the first mode of vibration is modelled in previous researches, causing significant error in cases of excitation close to higher resonant frequency and inadequacy of proposed solutions that place tuned mass dampers (TMDs) or actuators close to nodes of neglected modes of vibration, limiting their applicability. To address that, the system is truncated at three modes of vibration. NREL 5 MW wind turbine was used as reference wind turbine design in this study. To moderate vibration with a passive solution, a tuned mass damper is implemented in the model and its design parameters are found using a simple optimization algorithm. The designed TMD with a mass ratio of 5% reduced the peak value of displacement amplitude of blade tip to less than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1.2</mml:mn> </mml:mrow> </mml:math> meters under the defined excitation load. For an active solution, a modal control system configuration involving three actuators is described and a multivariable proportional-derivative (PD) control logic is implemented, with optimum gain values resulting from a systematic trial and error approach. The designed controller reduced the peak value of displacement amplitude of blade tip to less than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.15</mml:mn> </mml:mrow> </mml:math> meters under the defined excitation load. In either case, the interaction of TMD/actuator placement with mode shapes is discussed, and an adequate placement strategy is proposed. Presented results imply that, despite its many practical advantages, a passive vibration absorber may not be a viable solution in harsh conditions, whereas the designed active controller provides satisfactory performance with reasonable values of actuating force and displays extremely robust behaviour.