Damping of Wind Turbine Tower Oscillations through Rotor Speed ...

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e obtained analyzing fig. 12. This figure shows comparison of Bode plots of controllers designed with different values of desired tower damping D'. Figure 12: Bode plots of input-output pole placement controllers designed to achieve different values of tower damping D'. From fig. 12 it becomes clear that increased tower damping results in high pass controller behavior. This has a consequence of increased pitch activity which in turn results in additional oscillations and finally cancels out the advantages of proposed design methodology. So a tradeoff between desired increase in tower damping and pitch activity has to be made. 6. Full state feedback controller The input-output pole placement controller described in section 5 has shown some promising results but its ability to damp the tower oscillations is limited. Key cause for this is the fact that it doesn't use information about actual tower oscillations but only rotor speed feedback. Damping of tower oscillations by addition of tower top speed feedback to PID controller is proposed in [1]. Tower top speed measurement can be obtained from tower top acceleration measured by accelerometers that are nowadays almost a standard part of wind turbine control system. In our approach we use slightly different methodology. Instead of extended PID controller we use full state feedback controller designed using pole placement method. Desired closed loop behavior is chosen in the same way as for described pole placement controller. For this purpose process model (13) has to be rewritten in the state space form: x� = A⋅ x+ B⋅u, y = C⋅ x+ D⋅u. (19) State variables used for system description and control are rotor speed ω , rotor acceleration ω� , tower top speed x� t and tower top acceleration x�� t , while system inputs are wind speed v w , pitch angle β and generator torque M g : ⎡ω⎤ ⎢ ⎡ v ⎤ w � ω ⎥ ⎢ ⎥ x = ⎢ ⎥, u = β x ⎢ ⎥. (20) ⎢�⎥ t ⎢ ⎥ ⎢M⎥ g x ⎣ ⎦ ⎣��t ⎦ Rotor speed and tower acceleration are measured variables while other two states are derived from them. Using Ackermann's formula [6] vector of feedback gains for selected states can be calculated. System with such a controller was tested in Bladed using the same wind stepwise change as in sections 4 and 5. Simulation results are shown in the figures 13- 15. From these figures it can be seen that full state feedback controller maintains good rotor speed regulation while at the same time achieving better damping of the tower oscillations and practically removing the oscillatory movement of the tower. The pitch activity in this case increases considerably so a tradeoff between tower oscillations' damping and pitch activity is necessary. To examine the behavior of three described controllers in more realistic conditions the system behavior in 3D turbulent wind field was simulated in Bladed. Further information about simulations of 3D turbulent wind fields can be found in e.g. [7]. Let's just mention here that turbulent wind field was generated in Bladed Rotor speed [rpm] 25 24.5 24 23.5 23 22.5 22 0 10 20 30 40 50 60 70 t [s] Figure 13: Response of rotor speed of the system controlled with full state feedback controller.
Pitch angle [deg] 16 15 14 13 12 11 10 9 8 7 0 10 20 30 40 50 60 70 t [s] Figure 14: Response of pitch angle of the system controlled with full state feedback controller. Tower top displacement [m] 0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 0 10 20 30 40 50 60 70 t [s] Figure 15: Response of tower top displacement of the system controlled with full state feedback controller. using Kaimal spectrum recommended by the international standards for wind turbine design [8]. To gain valid information about system behavior in 3D turbulent conditions it is necessary for the simulations to last for at least 10 minutes what generates lots of data. Therefore, simulation results are not presented here due to limited space. Simulations in 3D turbulent wind field have shown that inputoutput pole placement controller in turbulent conditions achieves only modest improvement of tower oscillations when compared to the PID controller. The reason for this is the mentioned fact that input-output controller doesn't use information about actual tower oscillations. On the other hand full state feedback controller maintains shown ability to reduce tower oscillations even under turbulent winds. The cost of that is increased pitch activity what must be taken into account to avoid pitch system excessive wear. Simple design method proposed in this paper makes it possible to easily change the desired increase in tower damping and to achieve a tradeoff between reduction of tower oscillations and increase of pitch activity. 7. Conclusion The control system for variable speed pitch controlled wind turbine is presented. The wind turbine system is highly nonlinear and its parameters change significantly with change of wind speed. Furthermore wind turbine mechanical structure is very flexible and can easily be driven into oscillatory behavior. All this makes the controller design a very demanding task. In this paper three methods for wind turbine pitch controller design are compared. It is shown that classic PID controller can assure good rotor speed regulation but tower oscillations are very pronounced. To reduce these undesired oscillations two alternative control structures are investigated: input-output pole placement controller and full state feedback controller. The design objective for these controllers, besides good rotor speed regulation, was the increase of tower damping. Both controllers have shown that owing to increased pitch control activity it becomes possible to damp the tower oscillations. To test the controllers' performances in more realistic conditions simulation under 3D turbulent wind field were conducted in Bladed. It was observed that under such conditions only slight reduction of tower oscillations is achieved by input-output pole placement controller. On the other hand full state feedback controller has shown that is capable of reducing the tower oscillations even under turbulent conditions. The achieved damping of tower oscillations leads to fatigue reduction what enables production of lighter and less expensive wind turbines. This can result in reduction of the price for electrical energy generated by wind turbines. Acknowledgements This work was financially supported by Končar – Electrical Engineering Institute and the Ministry of Science Education and Sports of the Republic of Croatia. References [1] T. Burton, D. Sharpe, N. Jenkins, E. Bossanyi, "Wind energy handbook," John Wiley and sons, 2001. [2] P. Novak, T. Ekelund, I. Jovik and B. Schmidtbauer, "Modeling and control of variable-speed wind-turbine drive-system dynamics," Control system magazine, Vol. 15, No. 4, pp. 28-38, 1995.
Page 1 and 2: March 29 - April 1 International Co
Page 3 and 4: Pr = Pw⋅ CP. (3) The theoretical
Page 5 and 6: transition to Laplace domain simple
Page 7: From (16) and (17) it follows that

Damping of Wind Turbine Tower Oscillations through Rotor Speed ...

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