Enhanced wind turbine wake mixing

Abstract

Method and wind turbine controller for controlling a wind turbine for improved wake mixing. The method comprises the steps of monitoring a periodic component of an air stream incoming on the at least first blade; controlling periodically and dynamically a pitch angle of the at least first blade over time according to a wake mixing control scheme on the basis of the monitored periodic component. For an array of at least a first wind turbine and a second downstream wind turbines, the method comprises controlling the first wind turbine such that the wake formed downstream of the first wind turbine follows a first periodic pattern, and controlling the second wind turbine such that the wake formed by the second turbine follows a second periodic pattern, wherein at least one of a frequency, a direction and / or a phase shift of the second periodic pattern is coordinated with the first pattern.

Description

[0001]ENHANCED WIND WAKE MIXING The present disclosure relates to a method for controlling a wind turbine, a wind turbine controller arranged for the method of controlling a wind turbine, and a wind turbine comprising the wind turbine controller arranged for the method of controlling the wind turbine and an array of wind turbines, wherein at least a second wind turbine comprises the wind turbine controller. To meet the climate goals, renewable energy sources such as solar and wind energy are required. The most effective approach for developing wind energy on a large scale is by placing individual wind turbines, either on land or offshore, in so-called wind farms. Such wind farms optimize costs, e.g. cabling, maintenance and installation. The exact distribution of wind turbines may depend on several parameters, such as soil conditions or sailing routes but the dominant wind directions play an important role in this design. Typically wind turbines are then placed with respect to each other such that their wakes interact the least with each other when the wind blows from dominant directions. Still, situations occur relatively often where the wake generated by an upstream turbine introduces interaction with the downstream turbines that significantly affect power generation. By wake is meant the region behind a turbine where the flow is changed. Turbines in a wake typically experience lower wind speeds and an increase in turbulence. This results in turn in lower power generation and increased fatigue loads on the downstream turbines. By wake recovery is meant the phenomenon where the wind speed in the wake returns to the free-stream velocity due to mixing with the ambient air. The wind condition and the turbine design itself determine when wake recovery takes place. The distance at which this happens is usually larger than multiple rotor diameters. It is estimated that average power losses due to turbine wakes are in the order of 10 to 20% of the total power output in large offshore wind farms. In addition to reduced power generation, the fatigue load is estimated to increase by 5 to 15%. In order to optimize the power output on the wind farm level, wind farm control research has thus been focussed in recent years on controlling the wake itself. In particular, a type of wind farm controllers facilitates early wake mixing with the surrounding (’free stream’) wind field by manipulating the flow in a dynamic manner. This method, known as Dynamic Induction Control (DIC) involves collectively pitching the blades at a certain frequency to change the magnitude of the thrust force. As a result, the induction factor varies, causing the flow immediately behind the turbine to consist of both fast- and slow-moving parts. These parts interact with each other due to their different velocities, thereby promoting wake mixing. The resulting pulsating shape of the flow is characteristic of this approach, which is commonly referred to as the ‘pulse’ method. A negative side effect of this dynamic actuation is the increase in fatigue loads, especially on the tower and pitch bearings. Dynamic Individual Pitch Control (DIPC) has proposed as an alternative to DIC. Like DIC, DIPC uses the pitch actuators to dynamically control the flow. However, instead of actuating the blades collectively, DIPC applies a phase shift to each blade. This delay causes the thrust vector to periodically change direction rather than the magnitude, resulting in a wake behind the turbine with a helical shape. This method is commonly referred to as the ‘helix’ approach. This approach is in particular explained in WO2021 / 096363 of the present applicant, which is hereby incorporated by reference regarding the control concept of DIPC. Compared to the ‘pulse’ approach, the ‘helix’ approach has certain advantages. First, thrust variations are significantly reduced because they are more evenly distributed across the rotor disc. However, the blades experience a slightly stronger loads increase compared to the ‘pulse’ approach. As wind turbine wakes propagate far downwind, other wind turbines in wind farms can be affected by them under certain wind directions. It is common to control turbines individually in wind farms. This is called greedy control, where each turbine aims to reach its optimal performance. As a result, downstream waked turbines will experience reduced power production and increased fatigue loads. By following a greedy control strategy, even when applying wake mixing control scheme to an upstream turbine, a wind farm will therefore still reach sub-optimal behaviour due to the waked downstream turbines. The distance at which wake recovery takes place is usually much larger than the distance between turbines in a wind farm, as placing turbines close together reduces costs. It may be a goal of the present disclosure, possibly next to other goals, to obtain a method for controlling a downstream wind turbine that reduces the wake effects of an incoming wake on the turbine as well as the wake effects of an outgoing wake, wherein at least one of the above- mentioned problems is at least partially alleviated. This goal, amongst other goals, may at least partially be met by a method for controlling a wind turbine comprising at least a first blade, the method comprising the steps of monitoring a periodic component of an air stream incoming on the at least first blade and controlling periodically and dynamically a pitch angle of the at least first blade of the wind turbine over time according to a wake mixing control scheme on the basis of the monitored periodic component. By monitoring a periodic component is meant regularly determining over time the value of the periodic component. In this way, the monitored periodic component of an incoming air stream, like a periodic wake of an upstream turbine, may be taken into account in the wake mixing control scheme of a downstream turbine. The wake mixing control scheme is typically used to reduce the wake effect downstream of the turbine, the enhanced pitch control by the addition of the periodic component further reduces the impact of an upstream wake on the power losses and / or fatigue loads of the turbine self. On the one hand, the energy production and / or the longevity are thus optimized at the level of the turbine by taking into account an incoming wind field while on the other hand the energy production of any downstream turbine is preserved at the level of the wind farm. A periodic component of an incoming stream may derive from an upstream turbine generating a periodic wake or any natural phenomenon creating a periodic air stream. In particular, a periodic component of an incoming air stream may be present in case of wake meandering. Wake meandering refers to a fluctuating movement of the whole wake region in the lateral and vertical directions. Wake meandering may involve a slowly changing frequency of the periodic component. In such a situation, the method may comprise an additional step of estimating said changing frequency. Although arranged for pitch angle control, the method could be arranged for other wake mixing control schemes in general, including for instance dynamic yawing. The principle of the method described here is therefore not limited to controlling a pitch angle insofar as the concept of controlling a wind turbine on the basis of the monitored periodic component as disclosed here may also be declined accordingly for other types of control. In an optional embodiment of the method, the step of controlling the pitch on the basis of the monitored periodic component comprises coordinating at least one of a frequency, a direction and / or a phase shift of the wake created downstream of the wind turbine with the monitored periodic component, preferably synchronizing in frequency and with a predetermined phase shift the wake created downstream of the wind turbine with the monitored periodic component. In this way, the wake created by the turbine may be controlled, preferably synchronized, with respect to the incoming air stream to amplify or attenuate the response of the turbine to the incoming air stream. Among the control parameters of the wake created downstream are the frequency of the wake if constant (or slowly varying, as mentioned above for wake meandering), the direction of the wake (in case of helical wake, two directions clockwise CW and Counter ClockWise CCW may be selected), and a phase shift of the wake. In an optional embodiment of the method, the at least one of a frequency, a direction and / or a phase shift of the wake created downstream is set according to a desired objective of power production and / or load mitigation. A desired objective may be to increase the power production or reduce load fatigue of the wind turbine. Depending on the desired objective, a frequency, a direction and / or a phase shift of the downstream wake may be set. In an optional embodiment of the method, the given phase shift is set to zero, such that the wake downstream of the wind turbine is in phase with the incoming air stream. Synchronizing an incoming wake in phase with a downstream wake implies reducing the pitch actuation at the turbine. Indeed a similar tilt and yaw response may be generated on a downstream turbine as in the upstream turbine with reduced pitch amplitude if the control of the downstream turbine is in phase with the incoming wake. In turn, a lower pitch amplitude will reduce pitch bearing fatigue. When a desired objective is load mitigation, an in-phase control may thus be selected as the preferred control strategy. It is noted that the phase difference (phase is a particularly important parameter for the power production. The predetermined phase shift may be set at a value maximising power production. The optimal phase shift for maximising power production may be established through simulation, through calculation based on sensed actual data, for instance through trial and error. Being in phase, phase-shifted with a given phase or entirely out of phase with the incoming wake may amplify or attenuate the response, directly affecting the fatigue of the wind turbine and / or the composition of the wake and consequently the production of any further downstream turbine. In an optional embodiment of the method, the wake mixing control scheme is a dynamic individual pitch control scheme, wherein the pitch of each blade of the wind turbine is controlled independently to periodically vary in time such as to create an helical wake downstream of the wind turbine. By changing the induction factor of a blade, one can locally vary the speed and direction of the wind exiting the turbine (rotor plane) and hereby actually change the location of the wake itself. Variations of the location of the wake increase the turbulent mixing, such that the distance required to transfer kinetic energy into the wake is decreased and any turbines that might be arranged downstream of the wind turbine are thereby much less affected by the wake. It is noted that more generally the dynamic individual pitch control scheme may be used to create a wake with a periodic component, not necessarily a fixed frequency helix, but potentially a meandering wake with a slowly varying frequency. Alternatively, the wake mixing control scheme is a dynamic collective pitch control scheme (pulse control) or a dynamic yaw control. In an optional embodiment of the method, wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises monitoring a phase φ of an incoming periodical wake. The phase φ as a function of time t may be defined as φ(t)=(ωt + φo), wherein ωand φo are the frequency and phase shift of a fundamental component of the incoming wake. In particular, the step of monitoring a periodic component of an air stream incoming on the at least first blade comprises monitoring at least one parameter of an incoming periodical wake modelled as up(t)= ^ℎ^^1αi sin(ωit + φi) , where αi, φi, ωi are the amplitude, phase shift and frequencies of component, and h is the number of periodic components. More in particular, the at least one parameter comprises a phase shift φi of a component of an incoming periodical wake, preferably a phase shift φoof a fundamental component of an incoming periodical wake. The phase φ of a periodic incoming air stream, typically a pulsed or helical wake, is an important characteristic at the level of the wind farm to coordinate the wake of the turbine concerned with the wake of an upstream turbine. Typically for an helical wake, monitoring the fundamental frequency component is sufficient. Yet more generally harmonics and other frequencies of interest can also be extracted using estimating methods. Alternatively, instead of being monitored locally, the phase φ of a periodic incoming air stream could be received by the turbine from an outside controller and / or an turbine. It is noted that the frequency ω is typically available, for instance from an upstream turbine. In an optional embodiment of the method, the step of monitoring the periodic component of an air stream incoming on the at least first blade comprises estimating and tracking said periodic component. Wind field and / or periodic input disturbances estimation may allow a precise control. By estimating is meant observing indirectly based on estimation techniques, typically but not necessarily using a model. Estimation techniques may be used when a model of a system is available, but the internal state of the system cannot be directly observed. In particular, estimating and tracking the periodic component comprises processing data measured at the turbine through a Kalman filter or a recursive least squares method. By estimating and tracking is meant regularly updating over time the estimation. In an optional embodiment of the method, the step of monitoring the periodic component of an air stream incoming on the at least first blade comprises measuring at least one state of the wind turbine, and preferably deriving an estimation of the periodic component on the basis of the measured state. In this way, the periodic component if it cannot be directly sensed, may be obtained indirectly from the measurement of one state of the wind turbine and the use of an estimator. In particular, the at least one state measured on the at least first blade comprises any one of the following: at least a root blade moment at the at least one blade, at least a tower signal including for example at least one tower moment (top, bottom) or a tower top acceleration, at least a wind velocity and / or wind direction at different points in a wind field in front or at the back of the wind turbine (typically usually a few seconds away)using a LIDAR (forward, backward). In this way, it is possible to obtain a preview of the wind field in front (and back) of the wind turbine. This allows more precise control since it can be used to anticipate the incoming wake better compared to load sensors. Backward lidar can be interesting because it can be used to provide feedback of the wake composition behind the turbine to the turbine controller. In an optional embodiment of the method, the wake mixing control scheme is configured for controlling the amplitude, location and / or direction of a wake formed downstream of the wind turbine. In this way, the wake may follow a pulse pattern, or an helical pattern as known in the art, or any other periodic pattern a skilled person may envisage to increase wake mixing. In an optional embodiment of the method, the wind turbine comprises at least two blades, and controlling the wind turbine comprises periodically and dynamically changing a pitch angle of each blade independently over time. In particular, when a first and second blade are present, the pitch angle of the first, respectively second, blade may each be changed over time dynamically according to a predefined periodic function, wherein the dynamic change of the pitch angle of the second blade differs by a phase offset with the dynamic change of the pitch angle of the first blade. In an optional embodiment of the method, is provided a method for controlling an array of at least a first wind turbine and a second wind turbine, wherein, for a given wind direction, the second wind turbine is arranged at least partially downstream in a wake of the first wind turbine, wherein each wind turbine comprises at least a first blade. The method comprises the steps of controlling the first wind turbine such that the wake formed downstream of the first wind turbine follows a first periodic pattern with a first frequency and a first phase shift, applying the method according to any of the above embodiments for controlling the second wind turbine such that the wake formed by the second turbine follows a second periodic pattern wherein at least one of a frequency, a direction and / or a phase shift of the second periodic pattern is coordinated with the first pattern. In particular, the second periodic pattern may be synchronised in frequency with the first pattern and phase shifted with a given phase shift with respect to the first pattern. In this way, the wake of the first turbine may be taken into account when controlling the second turbine, to reduce fatigue loads on the second turbine and / or increase its power output. In a second aspect of the disclosure, a wind turbine controller for controlling a wind turbine comprising at least a first blade is provided, said wind controller being configured for receiving data related to a periodic component of an air stream incoming on the at least first blade, monitoring the periodic component on the basis of the received data, generating control signals for controlling dynamically and periodically over time a pitch angle of the at least one blade of the wind turbine according to a wake mixing control scheme and on the basis of the monitored periodic component. Hereby, the advantages of the control method are applied in the controller. In a third aspect of the disclosure, there is provided a wind turbine further comprising at least a first blade, further comprising a wind turbine controller according to any of the above wind turbine controller claims. Hereby, a wind turbine is obtained that is able to improve the mixing of the wake that forms downstream as well as endures less fatigue loads and / or creates more power generation in view of the incoming air stream. In an optional embodiment of the disclosure, the wind turbine comprises at least two blades, preferably three blades, wherein controlling the wind turbine comprises periodically and dynamically changing a pitch angle of each blade independently over time. More generally the concept may be applied to horizontal axis wind turbines with a rotor, independently of the number of blades arranged on the rotor. In a fourth aspect of the disclosure, there is provided an array of at least two wind turbines, wherein, for a given wind direction, a second wind turbine is arranged at least partially downstream in a wake of a first wind turbine, wherein the first and second wind turbine each comprise at least a first blade, and wherein at the second turbine comprises a wind turbine controller according to any of the above wind turbine controller claims. Hereby, an array of turbines, e.g. a wind farm, is obtained wherein two turbines that are downstream of each other are configured for improving mixing in their wake, while the second turbine downstream is further configured to reduce fatigue loads and increase its power output in view of the wake of the first turbine. In turn, the electric energy production of the array of wind turbines can be further increased, optimized. The present disclosure is further illustrated by the following figures, which show exemplifying embodiments of the method for controlling the wind turbine according to the disclosure, and are not intended to limit the scope of the disclosure in any way, wherein: - Figure 1A schematically illustrates a horizontal xi wind turbine comprising a three bladed rotor; - Figure 1B schematically shows a pitched blade; - Figure 2A, 2B and 2C schematically show graphs representing average wake velocities at different distances behind a turbine controlled according to three different control schemes, with Figure 2A corresponding to a traditional greedy control, Fig 2B corresponding to a DIC control or ‘pulse’ control and Fig 2C corresponding to a DIPC control or ‘helix’ control; - Figure 3 schematically shows an array of two wind turbines, wherein the second wind turbine is arranged downstream in a wake of the first wind turbine; - Figures 4A, 4B and 4C schematically shows graph representing average wake velocities at different distances behind an array of two wind turbines like Figure 3, wherein the upstream turbine is controlled respectively according to Figure 2A, Fig.2B, or Fig 2C, while the downstream turbine is controlled according to Fig.2A; - Figure 5 shows a flow chart comprising different steps of a method of controlling a wind turbine according to the helix approach of Figure 2C; - Figure 6 schematically shows the wakes of wind turbines, wherein the second wind turbine is controlled according to an embodiment of the method of controlling a wind turbine in an array of two wind turbines; - Figure 7 schematically shows a helical wake with an helix phase and a deflection; - Figure 8 shows a flow chart comprising different steps of a method of controlling a wind turbine according to an embodiment; - Figure 9 shows a flow chart comprising different steps of a method according to an embodiment using a Kalman filter as estimator of Figure 8; - Figure 10 shows a flow chart comprising different steps of a method according to Figure 9 applied to an helix control; - Figure 11 shows a flow chart comprising different steps of a method according to another embodiment using a Recursive least Squares Estimator applied to an helix control; - Figures 12A and 12B schematically show the wakes of wind turbines in an array of three turbines, wherein in Figure 12A the second wind turbine is controlled like in Fig.5 and the third turbine is controlled according to a greedy scheme like fig.2A, and in Figure 12B, the second and third turbines are controlled according to a greedy control scheme like Fig.2A; - Figure 13A shows the difference in power generated by the second turbine between the scenarios of Fig.12A and 12B according to the phase shift of the second turbine with respect to the first turbine; - Figure 13B shows the difference in power generated the third turbine between the scenarios of Fig.12A and 12B according to the phase shift of the second turbine with respect to the first turbine. Figure 1A schematically shows the layout of a typical bladed horizontal axis wind turbine 1. The wind turbine 1, situated on top of a foundation 3. Note that such wind turbines can be arranged on land and at sea. In the latter case, the foundation 3 will typically be an offshore foundation, being for instance seabed-fixed structures installed into the seabed. A nacelle 4, which is coupled to a rotor 5, is arranged on top of the tower 2. The rotor 5 comprises three blades 51, 52, 53, although any number of blades is possible, for instance one, two or four blades can also be envisaged. The blades 51, 52, 53 are fixed to a hub. A rotation of the nacelle 4 around the vertical axis I, which is substantially parallel, or coincides, with the tower 2 and which is substantially perpendicular to the ground plane, is referred to as a yaw rotation. The yaw angle can be defined in dependence of a wind direction, in which case a non-zero yam angle means that there is a misalignment between the direction of the rotor axis II and the wind direction W. The rotor 5 is arranged to rotate around the rotor axis II, this rotation is often referred to as the azimuth rotation. The blades 51, 52, 53 are furthermore arranged to rotate around their respective longitudinal axis III, which rotation is referred to as the pitch rotation. An angle between a central axis V of a cross section of a blade 51, 52, 53 with respect to a plane of rotation IV of the rotor 5 is referred to as pitch angle. Figure 1B shows the central axis V of the cross-section of the first blade 51 being pitches at a pitch angle θ1with respect to the rotor plane IV. A blade root moment sensor may be arranged on each blade, to sense a blade root moment. A blade root moment sensor 55 is typically a resistance-based strain gauge (SG) attach to the surface of rotor blade root. A plurality of such sensors are typically arranged at the root of the blade to measure the blade root moment. Figure 2A, 2B and 2C schematically show graphs representing average wake velocities at different distances behind a turbine controlled according to three different control schemes, with Figure 2A corresponding to a traditional greedy control, Fig 2B corresponding to a DIC control or ‘pulse’ control and Fig 2C corresponding to a DIPC control or helix control. Figure 2A shows a baseline situation in which a turbine is controlled according to a greedy control scheme creating a wake downstream of the turbine which is stable and may be defined as normal. By comparison the wake of Figure 2B is a result of the ‘pulse’ method and shows a periodically shedding vortex ring. Finally, the wake of Figure 2C is the result of the ‘helix’ method and follows a helical pattern. The darker parts indicate an iso surface for a wind velocity, while the lighter parts are the absolute wind velocity. The distance is further scaled by the rotor diameter. It is noted that both the ‘pulse’ and ‘helix’ approach qualify as wake mixing control scheme. These have been more effective for wind speeds below the rated regime. This is because above rated regime, the power losses of downstream turbines are significantly lower. Figure 3 schematically shows an array of two wind turbines, wherein the second wind turbine is arranged downstream in a wake of the first wind turbine. The wind direction W is such that the second wind turbine 102 is positioned downstream in a wake of the first wind turbine 101. The wake can be considered a region, as indicated between dashed lines 103, 104 of reduced (average) wind speeds with an increased turbulence. The wake caused by the wind turbine 101 will slowly mix with the surrounding (unaffected) wind field and due to this mixing, the wake effects will reduce with increasing distance from the turbine. Turbines 101, 102 are typically placed at mutual distances d of three to ten times the rotor diameter (3D-10D), wherein a mutual distance of ten times the rotor diameter will obviously lead to lower wake effects, such as a reduced power output and reduced vibrations, and thereby reduced fatigue loading on different wind turbine components, than a mutual distance of only three times the distance. Figures 4A, 4B and 4C schematically shows graph representing average wake velocities at different distances behind an array of two wind turbines like Figure 3, wherein the upstream turbine is controlled respectively according to Figure 2A, Fig.2B, or Fig 2C, while the downstream turbine is controlled according to Fig.2A. These figures show how the different wake mixing control schemes reduce the wake effect and, in particular, improve the power output. The Figures show a power amount increasing respectively from 6.1MW for a greedy control, to 7.2MW for a ‘pulse’ control and finally to 8.2MW for a ’helix’ control. Nonetheless, as already described above, a wind farm typically must be developed within a limited space, such that the longer mutual distances might lead to a reduced power output of the entire farm and thereby a higher cost of the generated energy. It is thus beneficial to reduce wake effects such that turbines can be placed at smaller distances while optimizing the power output and reducing their fatigue loading. Figure 5 shows a flow chart comprising different steps of a method of controlling a wind turbine according to the helix approach of Figure 2C. Figure 5 shows a block chart, or flow chart 200, of steps of a control method for controlling the wind turbine according to the ‘helix’ wake mixing control scheme. In step 201 periodic tilt and yaw functions 2011, 2012 are defined, wherein the periodic tilt and yaw functions 2011, 2012 are defined as sinusoidal function with a common predefined frequency f, and wherein the periodic tilt and yaw functions 2011, 2012 have a certain phase offset of preferably 90º or 270º. Hence, in this specific embodiment, called Helix method, both tilt and yaw degrees-of-freedom are excited, but with a phase offset of π / 2 rad (90º). This will in a moment on the rotor disc (as seen in the non-rotating frame) that rotates over time, completing one rotation every T = 1 / f seconds, and leading to a helix-shaped wake, as is seen in Figure 4C. The predetermined frequency f of the periodic tilt and yaw functions 2011, 2012 can be determined with respect to the inflow wind speed U∞ and the turbine rotor diameter D on the basis of a dimensionless number called the Strouhal number: An optimal Strouhal number is and 1.0, more preferably between 0.15 and 0.55 and even more preferably between 0.2 and 0.3, most preferably around 0.25. An estimation of this optimum has been obtained by doing a grid search in a simulation program, Simulator fOr Wind Farm Applications (SOWFA), for different frequencies in laminar flow conditions as explained in the previous patent application WO2021 / 096363. The Strouhal number can be chosen for determining the excitation frequency. Furthermore, a pitch amplitude ^ is preferably 15º or less, more preferably 10º or less, even more preferably 5º or less, most preferably between 2º and 4º, as a too large pitch amplitude of the (preferably) sinusoidal pitch variations will lead to increased loading on the turbine. An inverse multiblade coordinate (MBC) transformation step (203) is applied for obtaining the periodic variation of the pitch angles θ1, θ2, θ3 of the respective blades 51, 52, 53. A MBC transformation decouples, or stated differently: projects, the blade loads in a non-rotating reference frame and is a transformation used in for instance Individual Pitch Control approaches that aim at lowering fatigue loading of the wind turbine. The rotor speed dependent n-times-per-revolution (nP) load harmonic is transferred to a steady-state contribution, simplifying controller design. The equations effectuating the transformation are summarized. The measured out-of-plane blade root bending moments M(t)∈ RBare supplied to forward transformation, transforming the rotating blade moments into a non-rotating reference frame in equation A below (as also shown in for instance step 207): with 0,5 0,5 0,5^^ = 2 / ^ ^cos(^^1) cos(^^2) cos(^^3)^sin(^^1) sin(^^2) sin(^^3)in which n⊂ Z+is the harmonic number, B∈ Z+the total amount of blades, and ψb⊂ R the azimuth angle for blade b⊂ Z+, where ψ = 0º indicates the vertical upright position. collective mode M0 represents the cumulative out-of-plane rotor moment, and Mtand Myrepresent the fixed frame and azimuth-independent tilt- and yaw-moments (2071, 2072), respectively. The latter two mentioned components are typically used for the purpose of fatigue load reductions. By applying the reverse MBC transformation to the non-rotating signals (of step 201), this yields implementable individual pitch contributions in the rotating (i.e., blade) frame. with where θ0,n, and ψo,nis the azimuth offset for each harmonic. possibilities of individually driving the pitch of the rotor blades, using for instance pitch drives are now employed for increasing the wake recovery effects, or in other words to increase the wake mixing. By pitching the blades individually, the thrust force, and subsequently the power production, of the turbine can be controlled close to the greedy optimum (step 205). In the control method according to the ‘helix’ wake mixing control scheme, individually pitching the blades according to the periodic variation of the pitch angles θ1, θ2, θ3is used to stimulate wake mixing by individually varying the induction factors of a blade and thereby of the yaw angle of attack of a turbine. The method of control enables imposing yaw and tilt moments on the rotor, as seen in step 207, by applying the MBC transformation, as explained above. These yaw and tilt moments 207 can subsequently lead to a forced wake mixing, with minor variations in power and wake velocity. This is achieved by superimposing the periodic variation of the pitch angles θ1, θ2, θ3(step 204) on the collective blade pitch angles of a wind turbine. These projected load signals are first into the rotating frame by using the MBC transformation explained above to obtain the implemented pitch angles. For identical sinusoidal tilt and yaw signals, wherein the yaw signal has a phase delay of 90º, this results according to the common trigonometry formulas in a sinusoidal pitch signal β with a different frequency: with ψb the and φb the phase offset of blade b. It can thus be determined that fh= f +fr, where fris the rotation frequency of the rotor. Alternative solutions are, for instance, found if the periodic tilt function 2011 is set to zero (Yaw IPC), or instead the periodic yaw function 2012 is set to zero (Tilt IPC). In that case the inverse MBC (step 203) and common trigonometry formulas lead to periodic variation of the pitch angles θ1, θ2, θ3 wherein the periodic variation then becomes a superposition of two sinusoidal signals, the first sinusoidal signal with a first frequency fh= f +frand the second sinusoidal signal with a second frequency fh= fr- f. Figure 6 schematically shows the wakes of two wind turbines 301 and 302, wherein the second wind turbine 302 is positioned downstream in a wake of the first wind turbine 301 and is controlled according to an embodiment of the method of controlling a wind turbine in an array of two wind turbines. The first wind turbine 301 is controlled according to an ‘helix’ wake mixing control scheme as described in Figure 5. The first wind turbine 301 generates a downstream helical wake 401 with a first helical pattern having a predefined frequency and a given phase at the location of the second turbine. The second wind turbine 302 is also controlled according to an ‘helix’ wake mixing control scheme creating thus as well a downstream helical wake 402 with a second helical pattern. The second helical pattern has the same frequency as the first helical pattern and is phase shifted with a phase shift φowith respect to the first pattern at the location of the second turbine 302. In particular the phase shift φomay be set to zero in order to synchronize the wake 402 of the second turbine 302 with the wake 401 of the first turbine 301 or it could be set to an value optimizing power production, for instance 270 ^ . The second helical pattern may further have the same or an opposite direction as the first pattern. CW is typically better for minimizing pitch bearing loads, but CCW may yield stronger power increase. Both directions may be used in the present method. The directions may also be used in combination for the upstream and the downstream turbine. Figure 7 schematically shows a helical wake with an helix phase ϕ and a deflection d. The phase of the helical wake ϕ (x, t) may be defined as the angle of deflection at an arbitrary position x downstream of the turbine at an instant in The phase ϕ (x, t) is in other words the angle at the time t between the location of a point in the wake of the center of the rotor with the vertical axis (z axis in Figure 7, equivalent to axis I in Figure 1A) in a section plane at the distance x (i.e. in a plane perpendicular to the main direction of propagation of the wake downstream the wind turbine). The amount of deflection d is the distance between the location of a point in the wake of the center of the rotor and the rotor axis (x axis in Figure 7, equivalent to II axis of figure 1A). Figure 8 shows a flow chart comprising different steps of a method of controlling a wind turbine according to an embodiment. The flow chart is oversimplified for explanation purposes. The incoming wake 501 is modelled as an input disturbance Vk with a known frequency ωe and an unknown phase ϕ acting on the control input signal uk. Both the control input ukand the input disturbance Vkare input to the linear time-variant (LTI) wind turbine system 502. The output of the wind turbine system 502 is fed to an estimator 503 which produces an estimate of the phase ˆϕ of the input disturbance 501. The estimated phase ˆϕ is then fed to a synchronisation controller 504 generating the control input signal uk. By feeding the estimated phase of the incoming wake 501 to the wind turbine system 502, the downstream wake created by the wind turbine may thus be phase- shifted with the incoming wake 501. For instance, in-phase helix synchronization or helix wake rejection may be envisaged. The estimation performed by the estimator 503 may take different forms. Figures 9 and 10 explore the use of a Kalman filter as estimator, while Figure 111 shows the use of a Recursive Least Square Estimator. The same reference signs will be given to similar elements in Figures 8-11. Figure 9 shows a flow chart comprising different steps of a method according to an embodiment using a Kalman filter as the estimator 503 of Figure 8. Like in Figure 8, the wake 501 is modelled as a periodic wake disturbance upkwith a known frequency ωe and an unknown phase ϕ acting on the control input channel uck. A load disturbance wk also acts on this channel (via the adder 602) to form the input disturbance ukucontaining a noise sequence capturing variances of the non-periodic input disturbances, such as the wind speed The inverse MBC 604 (also called reverse MBC) similar to element 203 of Figure 5, the wind turbine control system 605 and a forward MBC (also called MBC) similar to element 206 of Figure 5 form together the wind turbine system 502 of Figure 8. The MBC transformation is used to go from a rotating framework of the rotor blades to a non-rotating framework of the rotor and vice versa via a projection. The output of the wind turbine system 502 is disturbed by vk and fed to the Kalman filter estimator together with the control input ukc. The Kalman filter takes thus both the blade tilt and yaw bending moments and tilt and yaw control pitch angles as input. The Kalman filter contains the discrete-time linearized state-space of the wind turbine required to estimate the periodic wake disturbance upk. In other words, the Kalman filter is model based. The wake frequency ωe is a known quantity used in the augmented system, which produces an estimate ˆupkused phase synchronization by the controller. The control input ukcis then fed back to adder 603 receiving also the input disturbance ukuas input to wind turbine system. Figure 10 shows a flow chart comprising different steps of a method according to Figure 9 applied to a helix control. In the case of a ‘helix’ control scheme, the estimate ˆupkoutput by the Kalman filter 608 is transformed with block 709 (Tdq(ωet)) to remove the ωe component. The resulting quantity contains information about the phase of the helical disturbance. The phase is then computed using the inverse tangent in block 710 (atan2(y,x)). The advantage of the Kalman filter lies thus in the direct estimation of the phase of the helical wake. Figure 11 shows a flow chart comprising different steps of a method according to another embodiment using a Recursive least Squares Estimator applied to a helix control. Contrary to the model-based Kalman estimation, the RLS estimator is model-free. The RLS estimator uses the fact that the phase information of the incoming helical wake is contained in the DC offset of the resulting tilt and yaw moments of equation (A) established in the context of the ‘helix’ method. These DC offsets can be estimated using filtering methods like a recursive least square adaptive filter. The RLS estimator has thus the advantage of being easy to implement while being adaptative to changes in dynamics of the wind turbine. One downside is the fact that it does not directly estimate the phase of the helical wake but rather the combined phase of the wake inflow and the controller effort. As illustrated in Figure 10, a summation (via adder 803) of the Park and Clarke (via blocks 801 and 802) transformed output ykis used as input to the square-root RLS estimator 804. The resulting estimate is filtered through a low-pass filter 805, after which the phase ϕ is computed (block 806, atan2(y,x) function). To correct for coupling and actuator delays the optimal azimuth offset ψo is then added (via adder 807) before the phase estimate is used for employing the ‘helix’ Figures 12A and 12B schematically show the wakes of wind turbines in an array of three turbines, wherein in Figure 12A the second wind turbine is controlled like in Fig.5 and the third turbine is controlled according to a greedy control scheme like fig.2A, and in Figure 12B, the second and third turbines are controlled according to a greedy control scheme like Fig.2A. In figure 12A, the first turbine 301 generates a helical wake 401, the second turbine 302 generates a helical wake 402, while the third turbine 303 controlled according to a greedy control generates a (standard / non- periodic) wake 403. In figure 12B, a baseline situation is considered in which the first turbine 301 generates a helical wake 401, the second turbine 302 is controlled according to a greedy control and generates a (standard / non-periodic) wake 402, while the third turbine 303 controlled according to a greedy control generates a wake 403. Figure 13A shows the difference in percentages for the power generated by the second turbine 302 between the scenarios of Fig.12A and 12B according to a phase shift of the second turbine with respect to the first turbine. The percentages with respect to the baseline case of the same turbine row. Figure 13B shows the difference in percentages for the power generated by third turbine 303 between the scenarios of Fig.12A and 12B according to a phase shift of the second turbine with respect to the first turbine. From Figure 12A and 12B, in-phase helix wake synchronization in turbine 302 did not result in an increase in power for the three-turbine system. The second turbine 302 was able to coordinate / synchronise with the incoming helical with minimal power loss. However, on average the third turbine 303 had a reduced power output with respect to the baseline case. However, an optimum in the power of the third and second turbine could be found when the second turbine 302 was phase shifted with a phase shift around -π / 2 with respect to the first turbine 301. In this setting, the third turbine 303 produced on average +9,79 % more power compared to a baseline case while the phase shift did not cause any power losses in the second turbine, implying thus an increase of power generation for the three-turbine system. More generally, it can thus be seen that the selection of the respective phase angles between the wakes of several turbines downstream of each other may improve the power generation of the whole system comprising said turbines. Whilst the principles of the invention have been set out above in connection with specific embodiments, it is understood that this description is merely made by way of example and not as a limitation of the scope of protection which is determined by the appended claims.

Claims

1. Method for controlling a wind turbine comprising at least a first blade, the method comprising the steps of: - Monitoring a periodic component of an air stream incoming on the at least first blade; - Controlling periodically and dynamically a pitch angle of the at least first blade of the wind turbine over time according to a wake mixing control scheme on the basis of the monitored periodic component.

2. Method according to claim 1, wherein controlling the pitch on the basis of the monitored periodic component comprises coordinating at least one of a frequency, a direction and / or a phase shift of the wake created downstream of the wind turbine with the monitored periodic component.

3. Method according to the preceding claim, wherein the at least one of a frequency, a direction and / or a phase shift of the wake created downstream is further set according to a desired objective of power production and / or load mitigation.

4. Method according to any of the above claims, wherein controlling the pitch on the basis of the monitored periodic component comprises synchronising in frequency and with a predetermined phase shift the wake created downstream of the wind turbine with the monitored periodic component.

5. Method according to the preceding claim, wherein the predetermined phase shift is set to zero, such that the wind turbine is in phase with the incoming air stream.

6. Method according to any of the above claims, wherein the wake mixing control scheme is a dynamic individual pitch control scheme, wherein the pitch of each blade of the wind turbine is controlled independently to periodically vary in time such as to create an helical wake downstream of the wind turbine.

7. Method according to any of the above claims, wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises monitoring a phase φ of an incoming periodical wake.

8. Method according to any of the above wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises monitoring at least one parameter of an incoming periodical wake modelled as up(t)=^ℎ^^1αi sin(ωit + φi) where αi, φi, ωi are the amplitude, phase shift and frequencies of each periodic component, and h is the number of periodic components, wherein preferably the at least one parameter comprises a phase shift φo of a fundamental component of an incoming periodical wake.

9. Method according to any of the above claims, wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises measuring at least one state of the turbine, and preferably deriving an estimation of the periodic component on the basis of the measured state.

10. Method according to the previous claim, wherein measuring at least one state of the turbine comprises measuring at least a root blade moment on the at least first blade.

11. Method according to any of the above claims, wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises estimating and tracking the periodic component of the air stream incoming on the at least first blade.

12. Method according to the previous claim and any of claims 9 or 10, wherein estimating and tracking the periodic component comprises processing at least one measured state of the turbine through a Kalman filter or a recursive least squares method.

13. Method according to any of the above claims, wherein the wake mixing control scheme is configured for controlling the amplitude, location, frequency, phase shift and / or direction of a wake formed downstream of the wind turbine.

14. Method according to any of the above claims, wherein the wind turbine comprises at least two blades, and wherein controlling the wind turbine comprises periodically and dynamically changing a pitch angle of each blade independently over time.

15. Method for controlling an array of at least a first wind turbine and a second wind turbine, wherein, for a given wind direction, the second wind turbine is arranged at least partiallydownstream in a wake of the first wherein each wind turbine comprises at least a first blade, comprising the steps of: - Controlling the first wind turbine such that the wake formed downstream of the first wind turbine follows a first periodic pattern with a first frequency and a first phase shift, - applying the method according to any of the above claims for controlling the second wind turbine such that the wake formed by the second turbine follows a second periodic pattern, wherein at least one of a frequency, a direction and / or a phase shift of the second periodic pattern is coordinated with the first pattern.

16. Wind turbine controller for controlling a wind turbine comprising at least a first blade, said wind controller being configured for: - receiving data related to a periodic component of an air stream incoming on the at least first blade, - monitoring the periodic component on the basis of the received data, - generating control signals for controlling dynamically and periodically over time a pitch angle of the at least one blade of the wind turbine according to a wake mixing control scheme and on the basis of the monitored periodic component.

17. Wind turbine controller according to any of the previous claim controlling the pitch on the basis of the monitored periodic component comprises coordinating at least one of a frequency, a direction and / or a phase shift of the wake created downstream of the wind turbine with the monitored periodic component.

18. Wind turbine controller according to any of the above controller claims, wherein the at least one of a frequency, a direction and / or a phase shift of the wake created downstream is set according to a desired objective of power production and / or load mitigation.

19. Wind turbine controller according to any of the above controller claims, wherein controlling the pitch on the basis of the monitored periodic component comprises synchronising in frequency and with a predetermined phase shift the wake created downstream of the wind turbine with the monitored periodic component.

20. Wind turbine controller according to preceding claim, wherein the predetermined phase shift is zero, such that the wake downstream the wind turbine is in phase with the incoming air stream.

21. Wind turbine controller according to any of the above controller claims, wherein the wake mixing control scheme is a dynamic individual pitch control scheme, wherein the pitch of each blade of the wind turbine is controlled independently to periodically vary in time such as to create an helical wake downstream of the wind turbine.

22. Wind turbine controller according to any of the above controller claims, wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises monitoring a phase φ of an incoming periodical wake.

23. Wind turbine controller according to any of the above controller claims, wherein monitoring a periodic component of an air stream incoming on the at least first blade comprises monitoring at least one parameter of an incoming periodical wake modelled as up(t)= ^ℎ^^1αi sin(ωit + φi) amplitude, phase shift and frequencies of each periodiccomponent, and h is the number of periodic components, wherein preferably the at least one parameter comprises a phase shift φo of a fundamental component of an incoming periodical wake.

24. Wind turbine controller according to any of the above controller claims, wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises measuring at least one state of the turbine and preferably deriving an estimation of the periodic component on the basis of the measured state.

25. Wind turbine controller according to the previous claim, wherein the at least one state of the turbine comprises a root blade moment.

26. Wind turbine controller according to any of the above controller claims, wherein monitoring the periodic component of an air stream incoming on the at least first blade comprises estimating and tracking the periodic component of the air stream incoming on the at least first blade.

27. Wind turbine controller according to previous claim and any of the above claims 24 or 25, wherein estimating and tracking the periodic component comprises processing the at least one measured state of the turbine through a Kalman filter or a recursive least squares method.

28. Wind turbine controller according to any of the above controller claims, wherein the wake mixing control scheme is configured for controlling the amplitude, location, frequency, phase shift and / or direction of a wake formed downstream of the wind turbine.

29. Wind turbine controller according to any of the above controller claims, wherein controller is for a wind turbine with at least two blades, and wherein controlling the wind turbine comprises periodically and dynamically changing a pitch angle of each blade independently over time.

30. Wind turbine comprising at least a first blade, further comprising a wind turbine controller according to any of the above wind turbine controller claims.

31. Wind turbine according to the previous claims, wherein the wind turbine comprises at least two blades, preferably three blades, wherein controlling the wind turbine comprises periodically and dynamically changing a pitch angle of each blade independently over time.

32. Array of at least two wind turbines, wherein, for a given wind direction, a second wind turbine is arranged at least partially downstream in a wake of a first wind turbine, wherein the first and second wind turbine each comprise at least a first blade, and wherein at the second turbine comprises a wind turbine controller according to any of the above wind turbine controller claims.

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