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

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Wind speed [m/s] 18 17 16 15 14 13 12 0 10 20 30 40 50 60 70 t [s] Figure 4: Wind speed used for simulation 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 5: Response of rotor speed of the system controlled with PID 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 6: Response of pitch angle of the system controlled with PID controller. Tower top displacement [m] 0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 0 10 20 30 40 50 60 70 t [s] Figure 7: Response of tower top displacement of the system controlled with PID controller. While rotor speed and pitch angle behavior is satisfactory, attention should be paid to the tower top oscillations shown in fig. 7. It can be observed that tower top experiences lightly damped oscillatory behavior. These lasting oscillations, although small in magnitude, contribute to material fatigue and can lead to structure premature failure. So in the following sections two methods for controller design that aim at reduction of tower top oscillations are proposed. 5. Input-output pole placement controller In this section the pitch controller with inputoutput structure is designed using well known pole placement method [6]. As design objective in this method the desired behavior of the closed loop system has to be chosen. The pitch controller GPC is then designed to assure that closed loop system behaves in the chosen manner. Transfer functions (14) and (15) form the linearised wind turbine model that can be described with the principle scheme shown in fig. 8. Figure 8: Principle scheme of the linearised wind turbine model. From the principle scheme given in fig. 8 closed loop transfer function with respect to wind speed change can be derived: G CL_ w Δω() s Gw() s = = . (16) Δ v () s 1 + G () s G s G () s w CL PC SD ( ) The pitch controller GPC has to assure that closed loop transfer function (16) is equal to the chosen model transfer function Gm: ( ) ! G s = G () s . (17) CL _ w m β
From (16) and (17) it follows that pitch controller has a form of : 1 Gw() s −Gm() s GPC() s = ⋅ . (18) G s G () s G () s ( ) SD β m It should be noted that the above expression often needs to be modified to assure that the controller is causal. Details on this design method can be found in [6]. The crucial step in controller design using described method is the choice of model transfer function Gm. It is important to choose model transfer that is achievable for the system in scope and that assures its satisfactory behavior. One possibility that is very common in the literature is the use of standard forms such as Butterworth or binomial form. However, these forms can be rather difficult to relate to system physical properties. So another approach is used in this paper. As previously said our primary goal is the reduction of tower oscillations. Tower oscillations can be reduced if the tower modal damping increases what would require change in tower structural parameters such as mass and stiffness distributions. Our goal is to achieve similar increase of tower damping by means of pitch controller actions without change in tower structural parameters. In that sense as a controller design objective we set a desired increase of tower modal damping. In other words tower modal damping D in the last expression in (13) is replaced with desired modal damping D' thus forming system model with new set of parameters. This model is linearised and transfer functions (14) and (15) are calculated. Using calculated transfer functions PID controller is designed following the guidelines described in section 4. Having the controller designed it is possible to calculate closed loop transfer function (16). This closed loop transfer function, obtained using system with increased damping and PID controller is then regarded as desired model transfer functions Gm for the real system. In other words our goal is to design a controller that assures that real system behaves as its tower damping has increased. The system response with Pole placement controller was simulated in Bladed using previously described full featured model. Wind used for simulation was the same as in section 4. Simulation results are given in the figures 9-11. From these figures it can be seen that pole placement controller achieves almost the same regulation of rotor speed as PID Rotor speed [rpm] 25 24.5 24 23.5 23 22.5 22 0 10 20 30 40 50 60 70 t [s] Figure 9: Response of rotor speed of the system controlled with input-output pole placement 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 10: Response of pitch angle of the system controlled with input-output pole placement controller. Tower top displacement [m] 0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 0 10 20 30 40 50 60 70 t [s] Figure 11: Response of tower top displacement of the system controlled with input-output pole placement controller. controller does. This was to be expected since the PID controller is the "core" of the pole placement controller design. At the same time tower oscillations are more damped. Since the tower structure remains the same this damping is achieved by higher pitch control activity than in the case of PID controller. The question that naturally appears is the limit to which extend the tower oscillations can be damped in this way. Answer to this question can
Page 1 and 2: March 29 - April 1 International Co
Page 3 and 4: Pr = Pw⋅ CP. (3) The theoretical
Page 5: transition to Laplace domain simple
Page 9 and 10: Pitch angle [deg] 16 15 14 13 12 11

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

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