Control of tower vibration
For both fixed and variable-speed machines the influence of the pitch controller on tower vibration and loading, described in Section 8.2.1, is one of the major constraints on the design of the control algorithm. The first tower fore-aft vibra-tional mode is essentially very lightly damped, exhibiting a strong resonant response which can be maintained at quite a high level even by a small amount of excitation which is naturally present in the wind. The strength of the response depends critically on the small amount of damping which is present, mostly aerodynamic damping from the rotor. The pitch control action modifies the effective damping of that mode. In designing the pitch controller, it is therefore important to avoid further reducing the already small level of damping, and if possible to increase it.
The design of control algorithms is covered in Section 8.4. This includes the choice of PID gains, as well as the addition of further terms to the controller which modify the overall dynamics in such a way as to help increase the tower damping. The use of modern control methods such as optimal state feedback is also discussed. This technique can help to achieve a suitable compromise between the competing objectives of speed or power control (achieved by regulating the in-plane loading) and tower vibration control (which depends on modifying the out-of-plane loading).
There is, however, only a certain amount of information in the measured speed or power signal. State estimators such as Kalman filters (Section 8.4.5) can be used to try to distinguish between the effects of wind speed changes and tower motion on the measured signal. However, it is also possible to enhance the information available to the controller by using an accelerometer mounted in the nacelle, which provides a very direct measure of tower fore-aft motion. By using this extra signal, it is in fact possible to reduce tower loads significantly without adversely affecting the quality of speed or power regulation.
The tower dynamics can be modelled approximately as a second-order system exhibiting damped simple harmonic motion, i.e.,
where x is tower displacement and F is the applied force, which in this case is predominantly the rotor thrust. AF is the additional thrust caused by pitch action. We can equate M with the tower modal mass and K with the modal stiffness, such that the tower frequency is \JK/M rad/s. The damping term D is small. The effective damping can clearly be increased if AF is proportional to —x. Clearly it is easier to measure acceleration than velocity, so the tower acceleration would have to be integrated to provide a measure of x. A suitable gain for AF can be estimated from the partial derivative from pitch to thrust, OF/dfi where p is the pitch angle, in order to achieve any particular additional damping DP:
It may sometimes be necessary to place a notch filter in series with this feedback term to prevent unwanted feedback from other components of tower acceleration, for example at blade-passing frequency. Figure 8.4 shows the results of a simulation with and without such an acceleration feedback term, in combination with a PID controller to control rotational speed. The simulations were driven with a realistic three-dimensional turbulent wind input. The speed control was hardly affected, and although there is a significant increase in pitch actuator activity, the pitch rates required are far from excessive. Clearly this technique is capable of increasing the tower damping substantially, almost eliminating the resonant response and dramatically reducing tower base loads. However, it requires an accelerometer which is reliable enough to be included in the contol loop and will not contribute significantly to turbine down-time. There has been no significant commercial application of this technique to date.
No tower damping With tower damping
Upper lines: tower top displacement (in) Lower lines: pitch rate (deg/s)
Figure 8.4 Use of a Tower Accelerometer to Help Control Tower Vibration
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