The present invention relates to a wind turbine system with multiple rotors, particularly to a method for damping torsional oscillations in components of such wind turbine systems.

BACKGROUND OF THE INVENTION

In order to achieve further improvements in the development of wind turbines, a new wind turbine system has been developed. The new wind turbine system includes a plurality of wind turbine modules or nacelles and, therefore, a plurality of rotors. The wind turbine modules are mounted on a support structure which may include a plurality of support arms for the wind turbine modules. In order to obtain a design of the support structure which is economically attractive, components of the support structure such as the support arms may be dimensioned so that the resulting components have relative low stiffness. Low stiffness lead to lower resonance frequencies which may come close to the operating frequencies of the wind turbine. Accordingly, such low-stiffness components may be excited to oscillate which may lead to increased wear of the multi-rotor wind turbine.

Particularly, it has been experienced that support arms may be excited into torsional oscillations.

Accordingly, there is a need for improving multi-rotor wind turbines in order to handle these problems.

SUMMARY OF THE INVENTION

It is an object of the invention to improve multi-rotor wind turbines, particularly to improve multi-rotor wind turbines with respect to avoiding or limiting structural oscillations, particularly torsional oscillations.

In a first aspect of the invention there is provided method for damping torsional oscillations in a multi-rotor wind turbine, the multi-rotor wind turbine comprises a multi-rotor support structure, a plurality of wind turbine modules mounted to respective support arms of the multi-rotor support structure, each of the wind turbine modules comprises a rotor with pitch-adjustable rotor blades, the method comprises

- obtaining a torsion signal indicative of a torsional movement of at least one of the support arms,

- determining pitch modification signals for the rotor blades of at least one of the wind turbine modules based on the torsion signal,

- applying the pitch modification signals to the pitch-adjustable rotor blades of the at least one of the wind turbine module so as to dampen the torsional oscillations.

Advantageously, the pitch-adjustable rotor blades can be used to generate torque variations which counteracts the torsional oscillations in the multi-rotor wind turbine, particularly in the support arms. Thus, based on the torsion signal of the torsional movement of a support arm, e.g. of a particular wind turbine module, a pitch modification signal can be determined and applied to the pitch system of the wind turbine module to dampen the torsional oscillations. For example, torsion signal may be a torsional velocity signal of the torsional movement. Due to the possibility for active damping of torsional oscillations in a support arm it becomes possible to design the support arms with reduced stiffness since possible torsional oscillations can be damped actively instead of using rigid support arms to avoid resonances at low frequencies. According to an embodiment the pitch modification signals are determined based on an angular position of the rotor of the at least one wind turbine module. By determining the pitch modification signals based on the angular rotor position, e.g. by use of a D/Q transformation, the variation of the pitch modification signal can be synchronized with the rotor position to obtain optimal damping. Thus, determining the pitch modification signals may comprise transforming the torsion signal, or a signal derived therefrom, into a rotating coordinate system based on the angular position of the rotor of the at least one of the wind turbine module.

Additionally, the pitch modification signals may be determined based on an offset of the rotor of the at least one wind turbine module. This offset may be time offset or angular offset of the rotor position. This offset will allow for compensation of for pitch system response and delays introduced by the filtering.

According to an embodiment the pitch modification signals are determined by filtering the torsion signal, or a signal derived therefrom. Thus, the filtering may be based directly on the torsion signal or a signal derived from the torsion signal such as a torsion signal which has been filtered or otherwise processed.

For example, the filtering of the torsion signal, or a signal derived therefrom, may comprise performing a first filtering such as band pass filtering before performing the transformation of the torsion signal into the rotating coordinate system.

Advantageously, the band pass filtering may be used to remove or damping amplitudes of frequency components of the torsion signal which are not relevant.

Thus, the pitch compensation signal may be determined more efficiently and/or the pitch compensation signal may be determined to limit unnecessary pitch activity of the pitch system.

According to an embodiment, the filtering of the torsion signal or a signal derived therefrom, comprises performing a second filtering, e.g. band stop filtering, after performing the transformation of the torsion signal into the rotating coordinate system. Advantageously, by applying a filtering after the transformation into a rotating coordinate system, oscillations in the torsion signal due to blade oscillations such as blade edge oscillations may be damped. As an alternative to use of band stop filters, the second filtering may implement band pass or low pass filters which are arranged to remove frequency components which are not relevant or undesired for the purpose of damping torsional oscillations. According to an embodiment, the filtering of the torsion signal, or a signal derived therefrom, comprises performing the first and the second filtering before and after performing the transformation of the torsion signal into the rotating coordinate system, respectively. In this way oscillations in the torsion signal due to rotor speed oscillations and blade oscillations may be filtered to obtain an efficient damping signal.

The multi-rotor support structure may comprises a tower and at least two support arms extending away from the tower on opposite sides of the tower. The tower may be supported, e.g. by ground or floating supports. Alternatively, the multi- rotor support structure may be manufactured without a common tower where the support arms are connected to other structures, e.g. directly to a ground or floating support. According to an embodiment, the method comprises obtaining a first torsion signal indicative of a torsional movement of a first support arm and a second torsion signal indicative of a torsional movement of a different second support arm. Since torsional oscillations of different supports arms may be different, i.e. they may be different in frequency and/or phase and amplitude, it may be required to determine pitch modification signals independent from each other based on different torsion signals.

According to an embodiment, the determining of the pitch modification signals comprises modifying a phase of the pitch modification signals relative to the torsion signal. Advantageously, the phase modification may improve damping of the torsional oscillations since the phase modification compensates dynamics of the mechanical system such as the dynamics of the rotor blades. The phase modification may be obtained by use of a PD, PID, lead or lag controller or a MIMO or MISO controller, or combinations thereof, for determining the pitch modification signals on basis of the torsion signal, or multiple torsion signals in case of a MIMO or MISO controller. Alternatively or additionally, the phase modification may be obtained by applying a phase shift to the angular position signal of the rotor, i.e. the azimuth angle of the rotor. A second aspect of the invention relates to a control system for damping torsional oscillations in a multi-rotor wind turbine, the multi-rotor wind turbine comprises a multi-rotor support structure, a plurality of wind turbine modules mounted to respective support arms of the multi-rotor support structure, each of the wind turbine modules comprises a rotor with pitch-adjustable rotor blades, where the control system is arranged to perform the method according to the first aspect. The control system may include various control modules such as input and output modules for receiving and outputting control signals and processing modules for implementing the method of the first aspect. A third aspect of the invention relates to a computer program product comprising software code adapted to control a multi-rotor wind turbine when executed on a data processing system, the computer program product being adapted to perform the method according to the first aspect. The computer program product may be provided on a computer readable storage medium or being downloadable from a communication network. The computer program product comprise instructions to cause the data processing system, e.g. in the form of a controller, to carry out the instruction when loaded onto the data processing system.

In general, a controller or control module may be a unit or collection of functional units which comprises one or more processors, input/output interface(s) and a memory capable of storing instructions that can be executed by a processor. A fourth aspect of the invention relates to a multi-rotor wind turbine comprising a multi-rotor support structure, a plurality of wind turbine modules mounted to respective support arms of the multi-rotor support structure, each of the wind turbine modules comprises a rotor with pitch-adjustable rotor blades, the multi- rotor wind turbine further comprises a control system according to the second aspect.

Although embodiments of the method for damping torsional oscillations are particularly advantageous for multi-rotor wind turbines, it is noted that the method may also be advantageous for single-rotor wind turbines for damping torsional oscillations of the single tower which supports the single-rotor generator. Thus, in order to damp torsional oscillations in the tower of the single-rotor wind turbine, the pitch modification signal may be determined so that the blades generate counteracting torques acting around the longitudinal axis of the tower. According to an embodiment, the application of the method for damping torsional oscillations in a multi-rotor wind turbine may be enabled dependent on a damping condition, e.g. a measured or otherwise determined signal or value. For example, the application of the method, e.g. determination and application of the pitch modification signals may be enabled based on the torsion signal, e.g. based on a comparison of the torsion signal such as a mean value of the torsion signal with a threshold value. Advantageously, the damping algorithm can be disabled if the torsional oscillations are relatively small, e.g. below a threshold, so that a high pitch activity is avoided when damping of oscillations is less important.

According to an embodiment, the application of the method for damping torsional oscillations in a multi-rotor wind turbine may comprise reducing the rotor speed. The rotor speed reduction may be applied alternatively to applying the pitch modification signals or may be applied together with the pitch modification signals. For example, in case of a sensor fault the torsion signal may be unavailable or faulty. In such cases, a safety mode for damping torsional oscillations based on rotor speed reduction may be invoked. In other situations, the damping achieved by applying the pitch modification signals may be insufficient to provide sufficient damping and, therefore, a rotor speed reduction may be invoked in addition to or as an alternative to the pitch damping.

In general, the various aspects and embodiments of the invention may be combined and coupled in any way possible within the scope of the invention. These and other aspects, features and/or advantages of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will be described, by way of example only, with reference to the drawings, in which

Fig. 1A shows a multi-rotor wind turbine,

Fig. IB shows an alternative multi-rotor wind turbine,

Fig. 1C shows a definition of torsional oscillation,

Fig. 2 shows a feedback speed controller of a wind turbine module, Fig. 3A shows a damping system for determination of the pitch modification signals,

Fig. 3B shows a control system for damping torsional oscillations in a multi-rotor wind turbine,

Fig. 4 shows examples of torsional oscillations and damping of the oscillations using methods according to different embodiments, and

Fig. 5 shows alternative embodiments of the damping system for determination of the pitch modification signals. DESCRIPTION OF EMBODIMENTS

Fig. 1A shows a multi-rotor wind turbine 100 which comprises a plurality of wind turbine modules 101 mounted to support arms 102 of a multi-rotor support structure 103. The multi-rotor support structure 103 may be configured in various ways. For example as illustrated, the multi-rotor support structure 103 may comprise a tower 104 and support arms 102 extending outwardly from the tower 104 so that the wind turbine modules 101 are placed away from the tower 104 and on opposite sides of the tower 104.

Fig. IB illustrates an alternative multi-rotor wind turbine 100 which does not comprise a common tower 104. Instead the support arms 102 extend from the foundation 130, e.g. a ground or floating foundation, so that two or more wind turbine modules 101 are sufficiently separated from each other at a given height or different heights. Each of the wind turbine modules 101 comprises a rotor 111, a power generation system (not shown) driven by the rotor and a rotor blade pitch adjustment system (not shown) for pitching rotor blades 112. The power generation system and the pitch adjustment system may be included in nacelles 113 and hubs of the nacelles 113, respectively, of the respective wind turbine modules 101. The angular rotor position of the rotor 111 is denoted by Φ.

Each of the plurality of wind turbines modules 101 may be mounted on an end- part of the support arms 102, as illustrated, though other positions on the beam structures are possible, particularly when more than one wind turbine module is mounted on an a single support arm 102. Specifically, Fig. 1A shows a multi-rotor support structure 103 with one upper beam structure 105 which comprises two support arms 102 extending on opposite sides of the tower 104 and a similar lower beam structure 105. In this example, each of the beam structures 105 carry two wind turbine modules 101, but other embodiments are of course conceivable. For example, each beam structure 105 may carry four wind turbine modules 101 with two on each side of the tower 101. In another example, the multi-rotor support structure has three beam structures 105 including lower, middle and upper beam structures 105, respectively having six, four and two wind turbine modules 101. A simple multi-rotor wind turbine may comprise two wind turbine modules carried by respective two support arms 102 extending on opposite sides of the tower 104.

The plurality of wind turbine modules 101 carried by the multi-rotor support structure 103 may be in the same vertical plane, or they may be shifted relative to each other. In the wind turbine modules 101, the kinetic energy of the wind is converted into electrical energy by a power generation system (not shown), as it will be readily understood by a person skilled in wind turbines.

Individual wind turbine modules 101 are referred to as the first to fourth wind turbine modules lOla-lOld.

The power generation system is controllable to adjust its power production by adjusting the pitch of the rotor blades 112 or by controlling a power converter to adjust the power production. The pitch-adjustable rotor blades may be adjustable in accordance with a collective pitch reference which is common for all blades 112 of a given rotor 111 as well as individual pitch references for individual rotor blades 112 of a given rotor 111. Accordingly, the pitch adjustment system may be configured to control the rotor blades 112 of a given rotor 111 by individual pitch adjustments or by a collective pitch adjustment.

The support arms 102 may be excited to deform around the longitudinal axis 120. For example, due to wind shear, pitch misalignment, yaw errors, turbulence or tower/support arm shadow effects on blade aerodynamics, the wind loads on the rotor blades 112 may generate a torque acting around the longitudinal axis 120 of the support arms 102 which excite torsional oscillations a.

Particularly, when the support arms have a low torsional stiffness, e.g. due to a design with thin or thin-walled support beams, significant torsional oscillations a may be excited. Particularly, for multi-rotor wind turbines 100, the problem with low stiffness of support arms may arise due to designs where the support arms 102 are supported by other structures, e.g. guy wire structures. Such designs which use thin support arms 102 may be attractive to reduce production costs.

Torsional oscillations a cause wear or possibly damage of the multi-rotor support structure 103 and the wind turbine modules 101. Therefore, a more expensive design would be required in order to take into account the anticipated wear. If the torsional oscillations are too high they may cause turbine control system to shut down the wind turbine.

Fig. 1C illustrates the torsional oscillation a, e.g. as a rotational oscillation of the of the wind turbine module 101 around the longitudinal axis 120. Fig. 2 illustrates a feedback speed controller 200 of a wind turbine module 101 for controlling rotation speed of the rotor 111 by determination of a collective pitch reference 6col. The feedback speed controller may be configured to control rotation speed in different load modes such as partial and full load modes. The partial load state is characterised in that the wind speed is not high enough to enable generation of the nominal or rated electrical power from the generator. In this state the pitch and the rotor speed are controlled to optimize aerodynamic efficiency of the wind turbine module 101. The full load state is characterised in that the wind speed is high enough to enable generation of the nominal or rated electrical power. In the full load state the rotor speed is controlled via the pitch so as to achieve a controlled, e.g. substantially constant, extraction of wind energy by the blades to achieve a power production close to the nominal power. The feedback speed controller may be implemented with individual partial and full load controllers, e.g. by use of PID or similar control schemes. However, the feedback speed controller may be implemented in other ways, e.g. by use of model based control or other control methods arranged for determining the collective pitch reference and/or individual pitch references 6rl-6r3.

The determination of the collective pitch reference 6col may be determined dependent on a difference between a generator speed reference coref, e.g. an optimum generator speed coopt or a rated generator speed corated, and a measured generator speed am. In addition to the speed signals coref and am, the pitch reference may be determined based on other input signals included in measurement set, ms.

In practice, since the pitch only varies little in the partial load state as a function of wind speed, the collective pitch reference 6col may be set to an optimum pitch 6opt which maximises the aero-dynamic efficiency of the rotor in the partial load state. In the partial load state, the rotation speed may be controlled via the generator power reference Pref which affects the generator torque so that the difference between generator speed reference coref and the measured generator speed am is minimized. Alternatively, the generator or shaft torque may be set, e.g. via the power reference Pref, to match the aerodynamic torque which can be determined based on the measured rotational speed squared and multiplied by an optimal mode gain. Fig. 2 shows that individual pitch signals 6rl-6r3 for the rotor 111 of one of the multi-rotor wind turbine modules 101a are determined on basis of the collective pitch reference 6col and individual pitch modification signals ΔΘ1-ΔΘ3. The individual pitch signals 6rl-6r3 may obtained by adding the collective pitch reference 6col to the pitch modification signals ΔΘ1-ΔΘ3, i.e. so that 6rl = θοοΙ + ΔΘ1, 6r2 = 6col + ΔΘ2 and so forth. The combination of the pitch modification signals ΔΘ1-ΔΘ3 and the collective pitch reference 6col may be performed by a summation unit 201.

According to an embodiment, the torsional oscillation a is reduced based on a method which includes obtaining a torsion signal 311 (see Fig. 3) indicative of a torsional movement a of at least one of the support arms 102. Based on the torsion signal, pitch modification signals ΔΘ1-ΔΘ3 are determined for individual rotor blades 112 of at least one of the wind turbine modules 101. The pitch modification signals ΔΘ1-ΔΘ3 are determined so that resulting moments from pitching of the blades counteracts the torsional oscillations. The determined individual pitch signals ΘΓ1-ΘΓ3 are applied to the pitch-adjustable rotor 112 blades of at least one of the wind turbine modules 101 so that a damping of the torsional movement a and torsional oscillations is achieved. The counteracting effect can be achieved by cyclic variations of the pitch modification signals ΔΘ1-ΔΘ3 as a function of angular rotor position Φ of the rotor. The pitch modification signals ΔΘ1-ΔΘ3 can be varied so that a variation in the lift and drag forces on the blades 112 is created dependent on the angular rotor position Φ so that the blades experience an out of plane force generating a varying torque M on a support arm 102 around the longitudinal axis 120.

According to an embodiment, in order to obtain the desired damping of the torsional oscillations a, the generated torque M(t) should be proportional with the torsional velocity (i(t) and in anti-phase, i.e. M(t) = - K (i(t), where K is a suitable factor which can be determined according to the desired damping effect.

Accordingly, the pitch modification signals ΔΘ1-ΔΘ3 may be determined based on the angular position Φ of the rotor of at least one of the wind turbine modules in order to obtain the correct synchronization with the rotation of the rotor 111. Furthermore, the pitch modification signals ΔΘ1-ΔΘ3 may be determined based on torsional velocity (i(t) in order to obtain efficient damping.

Alternatively, the pitch modification signals ΔΘ1-ΔΘ3 may be determined based on torsional displacements or positions a or based on both torsional displacements a and torsional velocity (t). Use of the torsional displacement, either alone or in combination with torsional velocity, could artificially increase the torsional stiffness due an increased closed-loop frequency. The torsional displacement signal a(t) could be combined with the torsional velocity (i(t) in a MIMO controller as explained in connection with Fig. 5. In general, since torsional oscillations of different support arms 102 of different wind turbine modules 101 are different, e.g. in terms of different amplitudes, frequencies and phases, the pitch modification signals ΔΘ1-ΔΘ3 may be

determined individually for one or more of the wind turbine modules 101.

However, in case there is a structural coupling between support arms 102 which supports different wind turbine modules 101, or in case two or more wind turbine modules are mounted on the same support arm, the pitch modification signals ΔΘ1-ΔΘ3 may be determined for two or more of the wind turbine modules 101. The damping of torsional oscillations may be applied both during power production and idling. Accordingly, the pitch modification signals ΔΘ1-ΔΘ3 may be combined with the collective pitch reference 6col as determined during idling, partial, full load and other modes where the rotor 111 is rotating. Fig. 3A illustrates a damping system 300 for determination of the pitch

modification signals ΔΘ1-ΔΘ3. Although the diagram includes different

components 301-304, it is understood that different embodiments may be based on different combinations of one or more of these components. In general, the pitch modification signals ΔΘ1-ΔΘ3 may be determined based on the torsional velocity d(t) as described above for obtaining a counter-acting torque M(t). Thus, according to one embodiment the pitch modification signals ΔΘ1-ΔΘ3 are determined based on the torsional velocity multiplied with a factor K. The torsional velocity d(t) may be obtained based on acceleration signals such as torsional acceleration signals (¾(t) obtained from acceleration sensors which could be attached to each of the wind turbine module 101 or attached to the support arms 102. The torsional velocity could also be obtained by other suitable means arranged to output a signal indicative of torsional movement a including but not limited to: a GPS signal, an inclinometer, an inertial measuring unit (IMU), a Kalman filter or positional sensors. Torsion signals 311 indicative of torsional movement a include torsional displacements a, torsional velocities d(t), torsional accelerations (¾(t) and other signals which can be processed to provide a torsional displacement, velocity or acceleration signal. The torsional velocity d(t) can be obtained e.g. by

differentiation of a torsional displacement signal a(t) or integration of a torsional acceleration signal (¾(t). The differentiation and integration processes may be implemented as filters. For example, integration may be implemented with a 1st order low pass filter such as a leaky integrator tuned with suitable frequency. As an alternative to the filters a type of state estimation can be used, for example, kalman filter or other types of observers. Thus, in general, the pitch modification signals ΔΘ1-ΔΘ3 can be obtained on basis of a torsion signal 311 indicative of torsional movement a including signals which can be processed into a signal indicative of torsional movement a. Such signals which relate to or are indicative of a torsional movement a includes signals obtained from nacelle or tower load measurements. Nacelle measurements includes, as mentioned above, displacement, velocity or acceleration of the wind turbine nacelles 113. These measurements could be obtained from acceleration sensors attached to the nacelles 113 of the wind turbine modules 101. Tower load measurements include load measurements of the tower 104 at locations where the support arms 102 extends outwardly, e.g. at locations 106 near locations where the support arms are engaging the tower 104. The load measurements could be obtained from load sensors, e.g. strain gages, or they could be obtained based on acceleration signals from accelerations sensors or estimated based on other measurements.

In order to obtain the correct synchronization with the rotor position Φ, the velocity (i(t) multiplied with a factor K is transformed from a coordinate system with reference in nacelle or support structure to a rotating coordinate system, i.e. a coordinate system which rotates with the rotation of the rotor 111. Methods for transforming the the velocity (i(t) into a rotating coordinate system includes direct quadrature (D/Q) transformations and Coleman or MBC transformations. As illustrated in Fig. 3A, the transformation into the rotating coordinate system results in the three pitch modification signals ΔΘ1-ΔΘ3.

In Fig. 3A the factor K multiplication is denoted by element 301 and the transformation into a rotating coordinate system is denoted by element 303 which performs the transformation based on the angular position Φ which may be obtained from a rotary position sensor, processing of the generator output or by other means. As illustrated in Fig. 3A, the determination of the pitch modification signals ΔΘ1- ΔΘ3 may include filtering the torsion signal 311, or a signal derived therefrom. The purpose of the filtering may be to remove frequency components which are not relevant for the purpose of damping torsional oscillations and/or in order to select frequency components which are essential for the damping.

For example, the filtering of the torsion signal, or a signal derived therefrom, may include a first filtering 302 before the transformation of the torsion signal into the rotating coordinate system. The first filtering may be performed by use of a band pass filter 302 for the purpose of selecting frequencies around a first center frequency fl of the band pass filter.

Alternatively or additionally, the filtering may include performing a second filtering 304 after performing the transformation of the torsion signal into the rotating coordinate system. Accordingly, the second filtering may be performed on the signals derived from the torsion signal 311 including the derivation of the transformation into the rotating coordinate system. Thus, the second filtering may be performed on each of the signals from the D/Q transformation 303 associated with individual blades 112 of a rotor 111. The second filtering may be performed by use of a band stop filter 304, a plurality such as three band stop filters 304 or, in general, one filter 304 for each of the pitch modification signals. The purpose of the band stop filter is to remove components of the torsion signal around a center frequency f2. Thus, the band stop filter may have a center frequency at f2. Alternatively, the band stop filters 304 may be configured as band pass filters 304 where the pass frequency is selected low enough to remove oscillations at the frequency f2. As another alternative, the filters 304 performing the second filtering may be configured as low pass filters 304 having a cut-off frequency low enough to remove oscillations at the frequency f2.

Two or more band pass filters 302 and/or band stop filters 304 may be arranged in series in order to pass and/or stop two or more frequencies of the torsion signal 311.

In order to perform both the first and second filtering of the torsion signal 311, or a signal derived therefrom, the first and the second filters 302, 304 may be arranged before and after the D/Q transformation element 303, respectively. Fig. 3B shows a control system 390 for damping torsional oscillations in a multi- rotor wind turbine 100. The control system 390 may be arranged so that it comprises the summation 201 and the damping system 300 in order to perform an embodiment of the invention. Fig. 4 illustrates examples of torsional oscillations a and damping of the

oscillations using methods according to different embodiments. The upper coordinate system illustrates torsional oscillation velocities d(t) as a function of oscillation frequency f. Curve 401 shows an example of torsional velocity oscillations (i(t) in case no damping is introduced. Curve 401 shows a peak at frequency fa which is the 3P oscillation frequency of the wind turbine module 101. In a 3-blade wind rotor 111, the anisotropies in the wind field, such as shear, turbulence and shadow effects, are periodically sampled by the rotor three times per revolution (3P). This causes a major source of excitation at the 3P frequency. Accordingly, for a 3-blade rotor 111 the 3P frequency is three-times the rotation frequency. The 3P excitation is then transferred to the support arm 102 as torsional oscillations. The frequency of excitation is proportional to the number of blades in the rotor, e.g. for 2-bladed rotor, the excitation is at two-times the rotation frequency (2P). Curve 402 shows the torsional velocity oscillations in an example where the pitch modification signals ΔΘ1-ΔΘ3 are determined on basis of K d(t) and transformed into the rotating coordinate system according to the damping system 300.

Accordingly, the pitch modification signals ΔΘ1-ΔΘ3 are determined damping system 300 but without the band pass and band stop filters 302, 304.

Curve 402 shows that the 3P oscillations have been damped, but that new oscillations are generated at frequencies fb and fc. The blades 112 of the exemplary rotor 111 used for the simulation have blade edge resonance frequencies at fb which are close to the 3P oscillations at fa. Here the blade frequencies are referred to in the non-rotating reference frame, also known as the backward whirling frequency. The 3P oscillations couple with the blade edge resonance frequencies at fb so that new torsional oscillations are excited at fb. Furthermore, significant torsional oscillations are excited at fc, where fc = fb2 + f_lP. The blade edge oscillations are cause by an oscillation mode where the blades vibrates edge-wise, i.e. substantially in the plane of the rotor 111.

The lower coordinate system illustrates the pitch modification signal ΔΘ1 as a function of oscillation frequency f. Due to the D/Q transformation, the frequencies fb transform into frequencies fbl and fb2, where fb2 = fb + f_lP and fbl = f b - f_lP, where f_lP is the rotation frequency of the rotor. The frequency fc transforms in a similar way.

Curve 412 shows significant peaks for the pitch modification signal ΔΘ1 at fbl and fb2 which leads to high pitch activity. High pitch activity may lead to increase wear of the pitch components and blades 112. Furthermore, even though the 3P oscillations have been damped, new oscillations have been excited.

It is noted that for other wind turbine modules 101, e.g. where the resonance frequencies of the blades are not as close to the 3P frequency as is the case for the present simulation example, the damping system 300 without the band pass and/or band stop filters 302, 304 could work fine and produce satisfactory damping since other resonance modes are not excited. For example, for wind turbine modules 101 where the 3P frequency does not excite other resonance modes, it may be sufficient with a band pass filter 302 with a center frequency which matches the 3P frequency or no filters may be required at all.

Curve 403 shows the torsional velocity oscillations in an example where the pitch modification signals ΔΘ1-ΔΘ3 are determined according to the damping system 300 with the band pass filter 302 but without the band stop filters 304.

In the exemplary simulation, the band pass filter 302 has a center frequency corresponding to the 3P frequency. The bandwidth of the filter may have different values and may be determined and optimized through design simulations.

Similarly to curve 402, curve 403 shows that the 3P oscillations have been damped, but that new oscillations are generated at frequencies fb. Thus, in comparison with curve 402, new oscillations are not generated at fc. Curve 413 also shows high pitch activity at fbl and fb2.

Curve 404 shows the torsional velocity oscillations in an example where the pitch modification signals ΔΘ1-ΔΘ3 are determined according to the damping system 300 as illustrated with the band pass filter and the band stop filters 304.

In the exemplary simulation, the band stop filters 304 have center frequencies at fb2, i.e. the blade edge frequency after the D/Q transformation. The bandwidth is determined by simulation similarly to the band pass filter. As mentioned above, the band stop filters 304 could be implemented alternatively as band pass or low pass filters 304 where the pass frequency is selected low enough to remove oscillations at the frequency f2. For example, the pass frequency of the band pass filter 304 could be set to fbl = fb - f_lP. Similarly, the cut-off frequency of the low pass filter 304 could be set to a frequency at or below fbl = f b - f_lP.

Curve 404 shows that the torsional velocity oscillations have been damped significantly and curve 414 also show that the pitch activity required for obtaining the damping is significantly reduced compared to other filters. Accordingly, the damping system 300 may be designed in different ways.

However, for blades 112 which are designed with low stiffness, e.g. in order to reduce manufacturing costs and weight of the blades, resonance modes of the blades may come close to the 3P frequency. In such situations the particular design of the damping system 300 as illustrated in Fig. 3A may be advantageous.

For example, when the blade edge frequency fb or other oscillation modes of blades 112 are close to the 3P frequency fa, a damping system 300 including both band pass and band stop filters 302, 304 may be particularly advantageous.

Fig. 5 illustrate alternative configurations of the damping system 300 for determination of the pitch modification signals ΔΘ1-ΔΘ3. Components 301-304, 501 and different arrangements of the torsion signal 311 may be arranged in different combinations to obtain such alternative configurations.

The torsion signal 311 may include one or more signals as indicated by the input arrows. For example, the torsion signal 311 may include the displacement signal a(t) and the torsional velocity (i(t). Other signals which may be included comprise signals obtained from nacelle and/or tower load measurements, such as

displacement, velocity or acceleration signals of the nacelle and load signals relating to the load exerted by the torsional forces of the support beams 102 on the tower 104. In an embodiment which includes a plurality of torsion signals 311, at least one of the signals is a signal corresponding to the torsional velocity d(t). As an alternative to the factor K multiplication element 301 - i.e. a proportional (P) controller - the control element 301 may be configured as a PD, PID, lead or lag controller or a combination thereof.

Additionally, the control element 301 may be configured as a MIMO controller configured to receive multiple torsion signals 311 and to generate a single output on basis of these signals. Such MIMO controller may be referred to as a MISO controller, i.e. a multi-input, single-output controller. The MIMO or MISO controller may include any of the P, PD, PID, lead or lag controller including combinations of these. For example, the torsion signal d(t),311 may be input to a PD controller and the torsional velocity signal (i(t), 311 may be input to a P controller and the output of the P and PD controller may be combined to provide a single input signal to the band pass filter 302. The use of a PD, PID, lead or lag controller instead of a simple P controller has shown to provide improved damping of the torsional oscillations a. The reason for the improved damping may be due to the phase shift of the input signal 311. In principle, if the input signal 311 is a torsional velocity d(t), no phase change should be added to the input signal and therefore the P-controller 301 which does not affect the phase of the input signal could be a suitable control element of the damping system 300. However, due to dynamic properties of the mechanical system, e.g. dynamic properties of blades 112, a phase shift of the torsional velocity (i(t) has shown to improve damping properties. Any of the PD, PID, lead or lag controller changes the phase between the input signal 311 and the output of the controller 301. The parameters of the controller may be determined by simulation and/or by experiments.

As an alternative to use of phase-modifying PD, PID, lead or lag controllers, the phase of the torsional velocity (i(t) may be modified by combining the velocity signal with other signals. For example, a combination, such as a linear

combination, of the displacement signal a(t) and the torsional velocity (t) provides a signal which has similar characteristics as would have been obtained by phase shifting d(t) provided that the input is a sinusoid. Such a linear

combination may be obtained by the MIMO or MISO controller. The MIMO or MISO controller may also be combined with one or more phase-modifying PD, PID, lead or lag controllers.

As another alternative to the above-mentioned methods for modifying the phase of the input signal 311, a phase shifter 501 may be included in the damping system 300 to add a phase shift to the angular position Φ. The phase shifter 501 modifies the phase of the pitch modification signals ΔΘ1-ΔΘ3 and, therefore, provides the same effect with respect to phase changes as the above-mentioned phase-modifying PD, PID, lead or lag controllers and the MIMO or MISO controller. Again, the phase shifter 501 may be used in the damping system together with any of the alternatives of the control element 301.

Thus, in general the determination of the pitch modification signals ΔΘ1-ΔΘ3 may comprise a modification of the phase of the pitch modification signals ΔΘ1-ΔΘ3 relative to the torsion signal 311 or one or more of a plurality of the torsion signals 311 where the phase modification is performed by use of any of the above-mentioned phase affecting methods. As illustrated in Fig. 5, the filters 304 may be configured as low pass filters as an alternative to band stop filters. The low pass filters 304 are designed so that the frequency component f2 is properly damped. The low pass filters can be

implemented with any of the above-mentioned configurations of the damping system 300 in Fig. 5 and Fig. 3A.

Although the present invention has been described in connection with the specified embodiments, it should not be construed as being in any way limited to the presented examples. The scope of the present invention is to be interpreted in the light of the accompanying claim set. In the context of the claims, the terms "comprising" or "comprises" do not exclude other possible elements or steps. Also, the mentioning of references such as "a" or "an" etc. should not be construed as excluding a plurality. The use of reference signs in the claims with respect to elements indicated in the figures shall also not be construed as limiting the scope of the invention. Furthermore, individual features mentioned in different claims, may possibly be advantageously combined, and the mentioning of these features in different claims does not exclude that a combination of features is not possible and advantageous.