Wind turbine cluster control for improved cluster wake mixing

Abstract

Method for controlling a wind turbine cluster, wherein said wind turbine cluster is defined by a first plurality of wind turbines that are located within a predefined area, the method comprising: - providing one or more wind condition parameters indicative of a wind field upstream of said predefined area; - adjusting axial induction factors of at least a second plurality of wind turbines according to a predefined spatial, temporal or spatiotemporal pattern, wherein said second plurality of wind turbines is a subset of, or is equal to, said first plurality of wind turbines and wherein a size of the pattern corresponds to an area defined by the second plurality of wind turbines, such that the actual adjustment of the axial induction factor of each wind turbine of the second plurality of wind turbines is dependent on its geometric position within the wind turbine cluster, the time, or a combination of both, wherein the step of adjusting the axial induction factors of said second plurality of wind turbines comprises outputting a control signal for controlling the respective wind turbines of said second plurality for adjusting an operational parameter, such as a blade pitch angle, or yaw angle, of the respective wind turbine; - wherein the spatial pattern is defined by at least a first spatially periodic signal having a spatial period in the range of 100 meters to 100 kilometers, wherein the temporal pattern is defined by a first temporally periodic signal having a temporal period of 1 minute to 1 week, wherein the spatiotemporal pattern is defined by a combination of the first spatial periodic signal and / or the first temporal periodic signal and wherein said spatial and / or temporal periods are determined on the basis of the one or more condition parameters.

Description

[0001]Wind turbine cluster control for improved cluster wake mixing The current invention relates to a method for controlling a wind turbine cluster. In order to meet the ambitious goals of the Paris Agreement for limiting climate change, vast amounts of renewable energy are required in order to drive electrification processes that replace the traditional fossil powered energy sources, which traditionally lead to large carbon dioxide emissions and have shown to be one of the major, respectively the largest, contributor to the currently ongoing global warming process. Wind generated electricity, also simply known as wind power, is still one of the most promising forms of renewable energy. In order to be able to generate large amounts of wind generated electricity in an economical manner, wind turbines are typically installed in large groups of turbines, that are typically referred to as wind farms, wind turbine clusters or simply “wind clusters”. Such a wind farm, or cluster, i.e. a group of turbines, often shares a common infrastructure, such as a local power grid that is connected to one, or multiple, substation(s) for combining the power outputs of the individual turbines and, typically, feeding it into a public power grid and / or comprise shared communication means for allowing data and control commands to be send to, and received from, data centres located onshore. However, when wind turbines extract energy from the wind, a wake is generated downstream of the turbine. In the wake of a wind turbine, the (average) wind speed is reduced and the (average) turbulence is increased, which negatively affects the production of a downstream (i.e. downwind) turbine. As such, the individual turbines of a wind cluster require a minimum mutual spacing in order to reduce the wake effects of the upstream wind turbine onto the downstream wind turbine. In order to reduce these effects WO 2013 / 037374 A1 and WO 2021 / 096363 A1 propose wind turbine control methods that stimulate wake mixing downstream of the upstream (i.e. upwind) turbine in order to reduce the effect of the wake on the downstream turbine, at the expense of the power production of the upstream turbine however. Such control strategies enable to position the turbines in a more compact fashion in a single wind farm, thereby either reducing the global footprint of the wind cluster (i.e. the area of land and / or sea that is covered by the respective wind cluster), or allowing to increase the number of installed turbines in a the same area of land and / or sea, while also allowing for a more efficient use of existing infrastructure. However, with increasing amounts of wind clusters, especially offshore wind clusters in, for instance, the North Sea, it was recently noted that downstream wind clusters can be exposed to wake effects of upstream wind clusters, also in cases where these wind clusters are spaced tens of kilometres (or even more) apart, such that the downstream wind cluster is exposed to increased turbulence intensities and reduced average wind speeds that are caused by the upstream wind farm. This effect, which is also known as farm-to-farm wake interaction has been observed by various wind farm operators and is visible on satellite images. During stable atmospheric conditions with low turbulence intensities, the wakes of wind clusters can span hundreds of kilometres. Additionally, a second issue of intra-wind-farm wind speed reduction arises from the accumulation of a large number of turbines at a given location. This might either be a result of neighbouring wind farm locations or due to a large scale wind farm by itself. The accumulation of wind turbines acts as a resistance in the flow and creates an induction zone around the wind farm. This impacts the wind speed upstream and reduces it before it arrives at the wind turbines itself. As the interaction between individual turbines within a wind cluster plays at a scale of hundreds of meters, the previously proposed control strategies for controlling an individual wind turbine, work on a totally different scale and cannot be simply applied on a wind cluster level nor do they solve the cluster wake issue or the issues relating to the created induction zones. These effects thereby limit the amount of wind generated electricity that can be harvested from locations that are ideally suited therefore, such as the North Sea. It is a goal of the present disclosure to obtain a method for controlling a wind turbine cluster that reduces the wake effects downstream of the wind cluster, wherein at least one of the previously mentioned problems is at least partially alleviated. The goal may be at least partially met by a method for controlling a wind turbine cluster according to claim 1, in particular by a method for controlling a wind turbine cluster, wherein said wind turbine cluster is defined by a first plurality of wind turbines that are located within a predefined area, the method comprising: - providing one or more wind condition parameters indicative of a wind field upstream of said predefined area; - adjusting axial induction factors of at least a second plurality of wind turbines according to a predefined spatial, temporal or spatiotemporal pattern, wherein said second plurality of wind turbines is a subset of, or is equal to, said first plurality of wind turbines (and in particular wherein a size of the pattern corresponds to an area defined by the second plurality of wind turbines), such that the actual adjustment of the axial induction factor of each wind turbine of the second plurality of wind turbines is dependent on its geometric position within the wind turbine cluster, the time, or a combination of both, wherein the step of adjusting the axial induction factors of said second plurality of wind turbines comprises outputting a control signal for controlling the respective wind turbines of said second plurality for adjusting an operational parameter, such as a blade pitch angle, or yaw angle, of the respective wind turbine; - wherein the spatial pattern is defined by at least a first spatially periodic signal having a spatial period in the range of 100 meters to 100 kilometers, wherein the temporal pattern is defined by a first temporally periodic signal having a temporal period of 1 minute to 1 week, wherein the spatiotemporal pattern is defined by a combination of the first spatial periodic signal and / or the first temporal periodic signal and wherein said spatial and / or temporal periods are determined on the basis of the one or more condition parameters. It is noted that spatial period, that is in the range of 100 meters (m) to 100 kilometers (km), can also be defined according to an (average) rotor diameter of a wind turbine in the respective wind turbine cluster, which would correspond to approximately 0.4 to 1000 times the rotor diameter of a wind turbine in the respective wind turbine cluster. The spatial period may further be in the ranges of 250 m to 50 km, or 400 m to 40 km. The axial induction factor α, or simply induction factor, is generally determined by dividing the difference of the velocity of the (free) wind upstream of a rotor plane ^^and the velocity of the wind at the rotor plane (i.e. rotor disc) ^^by the velocity of the wind upstream ^^, such that: The axial induction factor is correlated to the trust force that is induced onto the wind turbine. Hence, adjusting the axial induction factor is similar (i.e. directly related to), or can be replaced by, varying the thrust force applied to the wind turbine (which is similar to, when considering action is reaction, varying the thrust force that the turbine applies to the wind). Wakes of any kind have inherent dynamic instabilities that accelerate the wake breakdown and recovery when excited. A famous example is the van Karman vortex street that forms out behind a cylinder, which was first described by Henri Benard in 1908. In the critical Reynolds Number region counter-rotating vortices are periodically shed behind the cylinder, significantly decreasing the wake length. The physics of that basic phenomenon have later been related to multiple other examples in flow physics. The examples reach from small scales like the vortex shedding behind a solid ring, up to mid-scale structures like the destruction of the Tacoma Bridge which was later related to a wind-driven torsional bending mode excited by the periodic creation of vortices. But even examples in the scale of multiple kilometres exist, like the von Karman vortex street in the stratocumulus off the island of Guadalupe. By the adjusting (e.g. varying) the induction factor according to the predefined pattern, the thrust force that is exerted onto the wind turbines of the second plurality is also adjusted (i.e. varied) according to the predetermined pattern. Secondly, the flow resistance experienced by the wind field passing through the wind cluster is also varied correspondingly with the predetermined pattern. When the thrust forces are (at a certain point in time), for instance, higher at a first side of a respective row of wind turbines (when the row is for instance positioned perpendicular to the wind direction) in the wind cluster than at a second opposite side of the wind cluster, aerodynamic structures are generated by crea^ng local imbalances in the kine^c energy. These structures appear create crosswinds that enhance the wake mixing and might also cause a deflec^on. The resulting cluster wake would, when seen from above, appear to be locally “pushed” in a sideways direction (towards the lower thrust forces), which allows to displace the resulting wake sideways downstream of the respective turbine. Assuming the same wind field now passes a row further downstream, wherein the sides with a high and low thrust force are reversed, the wake downstream of this row appears to be “pushed” in to opposite direction, by means of the same mechanism as described above. Dynamic excitations appear not to be required, as even a time-invariant, i.e. static, pattern is able to create the local imbalances in kinetic energy to enhance the wake mixing. It was found that this sequential pushing, having therein the respective spatial and / or temporal periods, leads to introducing certain aerodynamic structures in the cluster wake, which promotes a mixing process in the cluster wake and enables to excite the inherent dynamic instabilities, such that the wake tends to break up in shorter period of time, and / or distance, downstream of the wind cluster. Hereby, the wind field aerodynamic structures downstream of the wind cluster recuperates in faster manner (at least when compared to standard control approaches), such that its effects reduce faster and the average wind speeds downstream of the wind cluster increase (with respect to the case in which no mixing is stimulated). Also, with the proposed (even purely static) spatial variation of the turbine induction, secondary motions move air from higher altitudes down over turbines with high induction and up over turbines with low induction. This is a tool to excite and destabilise the blockage layer to enable vertical energy transport. Non-homogeneous induction exerted by neighbouring turbine rows represents alternating smoother / rougher streamwise roughness stripes, wherein said stripes are arranged such that they are at least partly parallel to the wind direction. These stripes are known, from experiment performed on walls having different surface roughness’s, to induce large scale secondary motions which significantly alter momentum and heat transfer properties between fluid and wall. This effect appears to, unexpectedly, also occur when “strips of turbines” having different induction factors are formed in a wind cluster. Using this, some of the economic losses can be recouped that are expected when neighbouring wind farms are erected. The size and / or shape (i.e. an equivalent surface area and / or circumferential shape thereof) of the pattern is chosen such that it corresponds to an area defined by the second plurality of wind turbines, such that an adjustment amount of the axial induction factor for each wind turbine of the second plurality of wind turbines can be interpolated from the pattern, on the basis of the geometrical coordinates of the wind turbine (if needed in combination with the time). The pattern may simply be given as a function whose output a, which may be an absolute or relative adjustment of the induction factor, is dependent on the coordinates x,y and time t, for instance in the form of ^ = ^(^, ^, ^). Typically, different wind farms (i.e. turbine clusters) are owned and operated by different entities and / or operators and have different electrical connections to a wider distribution grid, such as a public power grid. In this context a wind turbine cluster as defined here embraces a wind power plant or ‘wind farm’ in the commonly used sense. Conversely, however, a wind power plant that is owned and managed by a single operator may include more than one wind turbine cluster due to the spacing between wind turbines. In either of these contexts, a cluster of wind turbines will be embodied as a plurality of wind turbines that have a common communication structure which allows for coordinated control of those wind turbines in the assigned cluster. That assignment to the cluster may be determined on a predefined assignment based on empirical studies and / or may be based on geometric considerations about the layout of the wind turbines that make up a cluster. Typically, a wind turbine cluster will be a group of wind turbines that are closer together than another group of wind turbines. A wind turbine cluster may therefore be defined by the separation distance between one cluster and another as compared to a characteristic cluster size. The characteristic cluster size may be defined in various ways. In one example, the characteristic cluster size can be considered to be the maximum separation between any two wind turbines in the first cluster when measured in the same direction as the distance between two neighbouring clusters and / or may be defined as a collection of wind turbines whereby the nearest neighbour of an individual turbine is smaller than a predefined maximum distance that may be defined by a predefined number (for instance 5, 10 or 20) of rotor diameters of the respective wind turbines. In terms of identifying what makes a cluster, in general a wind turbine cluster is defined visually by an area that is circumscribed by an outermost circumference of wind turbines. Alternatively, the distance between clusters may be taken from a datum point defined by a geometric centre or centroid of each cluster. It should be noted that the determination of the planform shape of a cluster and the determination of a geometric centre would be within the normal abilities of a skilled person. Wind turbines within clusters may be arranged in other layouts other than rectangular. Indeed, it is known for wind turbines to be configured in layouts that appear to be irregular, but are in fact dictated by predominant wind flows, terrain features and other factors. Indeed, some clusters of wind turbines may be arranged in a relatively rounded pattern, but it is also possible for wind turbines to arranged in more linear configurations, for example twenty wind turbines arranged in two rows of ten. Rather than the cluster size being defined by the maximum distance between any two wind turbines in that cluster in a direction aligned with the direction between clusters, the characteristic cluster size may be defined in other ways, for example as the average of the sum of separation distances between wind turbines located on the perimeter of the cluster, or the maximum distance between points on the perimeter of the cluster, when taken through the geometric centre of the cluster. Also, in the current context, a wind cluster may also be defined as the collection (i.e. the first plurality) of turbines that effectively work as a combined resistance in the flow, such that an induction zone is created around the wind turbine cluster, such that the induction zone can be considered to delimit the wind turbine cluster and / or may be defined as the collection of wind turbines that jointly form a distinct wind cluster wake downstream of said wind cluster. In a preferred embodiment, said one or more wind condition parameters comprise a wind direction of the wind field and wherein a size of the wind turbine cluster is defined by an effective length, that is taken along the wind direction, and / or an effective width of the wind turbine cluster, that is taken perpendicular to the wind direction; wherein the spatial and / or temporal periods are determined on the basis of an effective width and / or effective length of the wind cluster. It was found that the effective length and width of the wind cluster are important parameters for determining the wake instabilities that can be triggered, such that it is beneficial to base the respective periods on the effective length and / or width. It is then preferred that said spatial and / or temporal periods have a positive correlation with the effective width and / or effective length of the wind cluster, in particular wherein said spatial and / or temporal periods are proportional to the effective width and / or effective length of the wind cluster. To summarize, wake mixing for a wind cluster having a larger effective width and / or length is improved if the respective periods are also chosen proportionally larger, in order to efficiently excite the instabilities in the cluster wake. Preferably, the one or more wind condition parameters comprise an average wind speed and wherein the spatial and / or temporal periods are determined on the basis of the average wind speed. The average wind speed may be the mean, or average, wind speed determined upstream of said wind cluster (which may be the free wind speed V∞), in particular determined a number of rotor diameters ahead of said wind cluster. It is then further preferred that the spatial and / or temporal periods are negatively correlated to the average wind speed, in particular wherein the spatial and / or temporal periods are inverse proportional to the average wind speed. This aids in enabling an improved wake mixing, as the instabilities can be efficiently excited. In a preferred embodiment, the spatial and / or temporal periods are further determined on the basis of a predetermined Strouhal number, wherein the characteristic length is defined by the effective width or effective length and wherein the Strouhal number is in the range of 0.001 and 2, preferably in the range of 0.01 to 1, more preferably in the range of 0.05 to 0.8, even more preferably in the range of 0.1 to 0.7, even more preferred in the range of 0.15 to 0.6, even further preferred in the range of 0.2 to 0.5, most preferably in the range of 0.25 to 0.4; and preferably wherein the spatial and / or temporal periods have a negative correlation with the Strouhal number, more preferably wherein the spatial and / or temporal periods are inversely proportional to the Strouhal number. In dimensional analysis, the Strouhal number (St) is a dimensionless number describing oscillating flow mechanisms. where f is the frequency of vortex shedding, L is the characteristic length (for example, hydraulic diameter or the airfoil thickness) and u∞ is the flow velocity. In the current disclosure, f is the inverse of the temporal period, L is the effective length, or width, of the wind cluster and u∞ is taken as the average wind speed (e.g. free wind speed), in particular the the mean, or average, wind speed determined upstream of said wind cluster as described above. The spatial period may be equal to the wavelength λ, which may be formulated as dependent on the Strouhal number: wherein the propagation speed ^^^^^is selected as a fraction of the average wind speed, in particular in the range of 0.1 to 1, more preferably in the range of 0.5 to 0.8, most preferably between 0.65 and 0.75 (e.g. around 0.7). Said fraction may be determined using appropriate linear, or non-linear, functions that may be based on the one or more wind condition parameters. It was found that, by determining the respective periods on the basis of a Strouhal number in the given ranges, an effective mixing can be obtained as is described. Preferably, the first spatial and / or temporal periodic signals are further defined by a respective amplitude for controlling an amount with which the axial induction factor is adjusted, wherein said amplitude is preferably determined on the basis of the wind condition parameters. A higher amplitude signal will lead to a stronger excitation in the wake, but will typically also lead to associated downsides, such as, for instance, reduced power production and, possibly, even increased loading for the individual wind turbines. In a preferred embodiment, the spatial pattern, or a spatial part of the spatiotemporal pattern, is defined by a first shape function along the effective width of the wind turbine cluster and a second shape function along the effective length of the wind turbine cluster, preferably wherein the respective shape functions are formed from linear, quadratic or higher-order polynomial, spline, sinusoidal, linear or non-linear sawtooth, square wave, triangle functions, combinations of these and / or absolute value functions of these and, preferably, wherein at least one of said first and second shape functions comprises a periodic signal, or a predefined fraction of the periodic signal, such that the spatial pattern, or spatial part of the spatiotemporal pattern, defines locations of (local) minima and maxima of the axial induction factor adjustment within the wind turbine cluster. The use of such shape-functions allows to efficiently define a pattern satisfying the requirements regarding the spectral and / or temporal periods and thereby to efficiently exciting the respective instabilities in the wake. Preferably, the temporal periodic signal comprises a sinusoidal temporal oscillating signal having a temporal frequency that is directly related to the temporal period, such that the axial induction factor of each wind turbine of the second plurality of wind turbines is adjusted over time between a respective maximum value and a minimum value. A sinusoidal signal enables a smooth periodic signal that can efficiently exciting the respective instabilities in the wake, as described. It is preferred that the spatiotemporal pattern is arranged such that the spatial part of the spatiotemporal pattern moves, in particular along a first translational direction, with respect to the wind turbine cluster, such that location of (local) minima and maxima of the axial induction factor adjustment within the wind turbine cluster are dependent on time. It is then further preferred that the spatial part of the spatiotemporal pattern moves with a predefined speed, in particular wherein the predefined speed is correlated to the average wind speed, even more in particular is proportional to the average wind speed; preferably wherein predefined speed is in the range of 0.01 to 2 times the average wind speed, preferably in the range of 0.1 to 1.5 times the average wind speed, more preferably in the range of 0.3 to 1 times the average wind speed, even more preferably in the range of 0.4 to 0.8 times the average wind speed, most preferably in the range of 0.5 to 0.7 times the average wind speed. It was, surprisingly, found that a moving pattern, in particular one that moves along the wind direction at a fraction of the average wind speed, leads to very effectively exciting the wake and stimulating the wake mixing. In a preferred embodiment, the method comprises the step of controlling each of wind turbines of the second plurality of wind turbines to adjust its axial induction factor according to an adjustment amount as determined from the predefined spatial, temporal or spatiotemporal pattern, wherein the adjustment amount of a respective wind turbine of the second plurality of wind turbines is determined by means of a spatial and / or temporal interpolation in the respective spatial, temporal or spatiotemporal pattern using the geometric position of the respective wind turbine and / or the actual time. This enables the individual turbines to provide the synchronized variation of the respective induction factors for simulating the enhanced cluster wake mixing. Preferably, the axial induction factor of a respective wind turbine of the second plurality is adjusted by adjusting the pitch angle of at least one of the blades, preferably collectively adjusting the pitch angle of all of the blades, of the respective turbine, and / or by adjusting the yaw angle of the respective wind turbine. An adjustment of the pitch angle and / or yaw angle leads to an adjustment of the angle of attack of the incoming wind, whereby the thrust force and axial induction factor are also adjusted. Preferably, the wind turbines are horizontal axis wind turbines (HAWTs), although it is also envisioned that the method is applicable to a wind turbine cluster comprising vertical axis wind turbines (VAWT). The control method can thereby also be implemented on existing wind farms comprising many HAWTs, such that the economic potential of area’s like the North Sea, with many already existing wind farms, can be further increased. In a second aspect, the disclosure relates to a wind turbine cluster, comprising a plurality of wind turbines, being arranged for receiving the one or more wind condition parameters and comprising means adapted for executing the steps of the method according any of the preceding embodiments. Preferably, the wind turbine cluster comprises a controlling and / or data processing system for determining the predefined spatial, temporal or spatiotemporal pattern and / or spatial and / or temporal periods by using the method according any of the preceding claims, wherein said controlling and / or data processing system further comprises communication means for providing a respective wind turbine controller of each of said second plurality of second wind turbines with a control input such that each of the wind turbines of the second plurality of wind turbines is controlled to adjust its axial induction factor, in particular by adjusting the operational parameter, such as the blade pitch angle or yaw angle, according to the predefined spatial, temporal or spatiotemporal pattern. In a third aspect, the disclosure relates to a wind turbine controller for use in a wind turbine of the wind turbine cluster according to the second aspect, wherein said wind turbine controller is arranged for receiving a control input from the controlling and / or data processing system and arranged for controlling the operational parameter, such as the blade pitch angle or yaw angle, of the respective wind turbine that the wind turbine controller is arranged to control in order to adjust its axial induction factor according to the predefined spatial, temporal or spatiotemporal pattern. In a fourth aspect, the disclosure relates to a computer program comprising instructions that, when executed by a computing device or system, cause the computing device or system to execute the steps of the method according any of the preceding embodiments. In a fifth aspect, the disclosure relates to a computer-readable medium having stored thereon the computer program of the fourth aspect. 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 shows a horizontal axis wind turbine comprising a three bladed rotor. - Figure IB schematically shows a pitched blade. - Figure 2 schematically shows a nacelle and rotor of the wind turbine comprising different components. - Figure 3 gives an overview of four different embodiments Τ1 – Τ4 of applying induction control in a spatially and temporally varying manner throughout the wind farm. - Figures 4 schematically shows, in a top view, a layout of a (fictitious) wind farm for use in simulations for demonstrating the effects of an embodiment of the method for controlling a wind turbine cluster. - Figures 5A – 5C show, at different times t1, t2 and t3, a pattern generated from a left-right block wave for controlling the axial induction factor of the wind turbines of the wind farm shown in figure 4. - Figures 6A – 6C show, at different times t1, t2 and t3, a pattern that is obtained by combining a left- right variation with a sinusoidal front-back wave for controlling the axial induction factor of the wind turbines of the wind farm shown in figure 4. - Figures 7A – 7C show, at different times t1, t2 and t3, a pattern that is obtained by combining a left- right linear variation with a sinusoidal front-back wave for controlling the axial induction factor of the wind turbines of the wind farm shown in figure 4. - Figures 8A – 8C show, at different times t1, t2 and t3, a pattern that is obtained from a sinusoidal front- back wave for controlling the axial induction factor of the wind turbines of the wind farm shown in figure 4. - Figures 9A shows the simulated wake of a second (fictitious) wind farm in a laminar flow that is controlled using a traditional “greedy” control method. - Figure 9B shows the simulated wake of the second wind farm in a laminar flow that is controlled using a control method according to the current disclosure. Figure 1 A schematically shows the layout of a typical three bladed horizontal axis wind turbine 1. The wind turbine comprises a tower 2, situated on top of a foundation 3. Note that such wind turbines can be arranged on land (e.g. onshore) and at sea (e.g. offshore). In the latter case, the foundation 3 will typically be an offshore foundation, being for instance seabed-fixed structures installed into the seabed such as monopiles, tripods, jackets, or alternatively a floating foundation, wherein a buoyant body is secured to the seabed to keep it into place. In case of an onshore turbine, such a foundation 3 is typically a so called gravity foundation comprising a heavy concrete body to keep the wind turbine 1 secured to the ground. 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 amount of blades is possible, for instance one, two or four blades can also be applied. The blades 51, 52, 53 are fixed to a hub 54. 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 yaw 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 and an angle between a central axis V of a cross section the blade 51, 52, 53 with respect to plane of rotation IV of the rotor 5 is referred to as the pitch angle. Figure IB shows the central axis V of the cross-section of the first blade 51 being pitched at a pitch angle θ1 with respect to the rotor plane IV. Figure 2 schematically shows a nacelle 4 and rotor 5 of the wind turbine 1, wherein different components arranged in the nacelle 4. The nacelle 4 houses the drive train 6, that can comprise a generator 61 for generating electrical energy, a gearbox 62 arranged between a high speed shaft 63 and low speed shaft 64, wherein the low speed shaft 64 is connected to the rotor 5 and the high-speed shaft 63 transfers the rotation from the output of gearbox 62 to the generator 61. Note that in so called direct drive wind turbines the rotor is directly connected, usually through a main shaft, or low speed shaft, to a generator. In these types of wind turbines, the gearbox 62 and high-speed shaft 63 are not needed. Furthermore, the nacelle 4 typically also comprises a yaw mechanism 7 for yawing the nacelle 4 around the tower 2, in particular the vertical axis I. The yaw mechanism 7 can comprise a number of yaw motors 71 attached to a base of nacelle 4 and comprising a gearing for reducing the rotational speed towards an output drive pinion that can be meshed with a gear rim 72 with teeth on the inner side, which in turn is connected to a top of the tower 2. Furthermore, a pitch mechanism 8 is comprised (at least partially) in the hub 54, wherein the pitch mechanism 8 is arranged for pitching the blades 51, 52, 53. In the current embodiment of the turbine 1, the pitch mechanism 8 comprises three pitch drives 81, 82, 83 that are arranged to drive the ends of blade root sections 55, 56, 57 of the respective blades 51, 52, 53. In more modern turbines the pitch drives 81, 82, 83 are typically arranged to individually drive the pitch rotations of the respective blades 51, 52, 53, such that the blades 51, 52, 53 can all have different pitch angles at any given time. Such a pitch mechanism 8 is also referred to as an individual pitch mechanism and controlling the individual pitch mechanism for minimizing the fatigue loading on a turbine is referred to as Individual Pitch Control (IPC). In older, or simpler, types of turbines the pitch mechanism 8 is often arranged such that the blades 51, 52, 53 can only pitch simultaneously, which is typically referred to as Collective Pitch. Figure 3 given an overview of four different embodiments Τ1– Τ4of applying induction control in a spatially and / or temporally varying manner throughout a first fictitious wind farm 100, comprising a plurality of wind turbines, in particular horizontal axis wind turbines 1 (left column). The second column an exemplary description if the excitation thrust CT,ethroughout the first row of turbines R1, the third column depicts an exemplary temporal evolution of CT,efor a turbine Tiand the most right column describes the advection speed of the excitation signal. Note that the concepts can also be combined, to achieve the desired flow behaviour. As described above, the cluster wake is manipulated by generating specific thrust distributions (i.e. patterns) ^ = F^,^(x^, y^, u^^^, t) over the whole wind farm, where ^ refers to the individual turbine, x^and y^on the respective position, u^the free wind speed and ^ to the time. Each turbine acts like one individual in a swarm. It contributes to the realisation of ^ by adapting its axial induction, based on the individual position. In the current examples, the spatially and temporarily varying thrust coefficient ^^is a combination of a constant ^^,^and a collection of ^ periodic function pairs ψ^and ψ^(i.e. respectively the first and second shape functions), with an amplitude ^: Each periodic functions evolves into one spatial dimension and a pair consists out of one evolving into the downwind direction ^ and one into the crosswind direction ^. The results of the periodic functions are bounded by [−1,1] ∀ ^, ^, λ, φdyn, φstat∈ ^. Their inputs are the distance ^, ^ in m, the time ^ in s, the wave length λ in m, and a dynamic and static phase offset φ in degrees. It is further noted that the excitation thrust coefficient ^^,^is a variation to a baseline thrust coefficient ^^,^that follows from applying a standard, or any suitable, wind turbine control method. Six periodic functions (ψ^- ψ^), i.e. that are suitable as the respective first and / or second shape functions, are given below as examples (whereby others and / or combinations thereof may also be applied): φdyn^ + 360 4 λ φ ^ + φ ψ ^^, ^, λ, φ , φ ^ = ^mdyn stat^ dyn statod ^^ − + λ 4 360 ψ^^^, ^, λ, φdyn, φstat, ^^ = sign^ψ^^^, ^, λ, φdyn, φstat^ − ψ^^^, ^, λ, φdyn, φstat^= 2^ψ^^^, ^, 2λ, φdyn, The function ψ^depicts a constant value, a sinusoidal wave, ψ^results in a sawtooth function, ψ^is a triangle function, ψ^a square wave, and ψ^an absolute sinusoidal function. Note that ψ^poses an exception to the other periodic functions, as it requires one additional parameter ^ to scale the length of the square plateau. The dynamic phase-shift φdyndictates the propagation speed of the pattern. In practice this would be related to the free wind speed: Solved for φdynwe get Considering wake manipulation strategies on a turbine level, the following approaches to design ^ appear promising: Static thrust distribution ^^&^Triggering gravity waves ^^: As shown in the top row of Fig 3, the thrust is constant over one turbine row R1 – R6 but varies in streamwise direction. The wavelength of the streamwise variation is the characteristic parameter, that needs to be optimized depending on the given flow conditions. This pattern doesn’t change over time. In wind farms, gravity waves occur when a mass of air is deflected upwards into the above stratification layer. Due to temperature differences, the deflected mass of air has an increased density compared to the resident air, consequently, it is accelerated downwards. This results in gravity waves, that are known to influence the blockage upstream of the wind farm and the pressure within the farm. It is expected that ^^potentially enhances gravity waves and consequently effects the vertical energy entrainment into the wind farm as well as the wind farm wake. Wake steering ^^: The second row of Figure 3 depicts a linear thrust gradient over the turbine rows, whilst the thrust over turbine columns remains constant. ^^generates a non-uniform flow deceleration over the lateral direction. The resulting velocity gradient inside the wind farm generates velocities in lateral direction, which potentially deflects the cluster wake towards the regions of increased thrust. This opens the door to steering the wind farm wake away from a downstream wind farm, to increase the collective power output. Additionally, the resulting velocity gradient between the wind farm rows generates vorticity, which is expected to increase the turbulent kinetic energy entrainment into the wind farm. Alternatively to applying ^^for wake steering purposes on the entire wind farm, potential is seen in applying it to subclusters (i.e. a second plurality of wind turbines) of turbines inside the wind farm. More specifically, applying it on small numbers of turbine columns, whilst the neighbouring subcluster applies the mirrored ^^generates multiple columns of increased and decreased induction, the combination of which can be interpreted as a single pattern. The obtained thrust distribution can be compared to regions of increased surface roughness in streamwise direction, to enable a secondary flow perpendicular to the dominant flow direction which increase the energy entrainment into the wake. Dynamic thrust distribution ^^ & ^The previous section deals with static thrust distributions, meaning that the pattern doesn’t change over time. This section presents two approaches including dynamic excitation in the farm-wide thrust distribution. Due to the high dependency on the Strouhal number observed at turbine level, we first define a Strouhal number at wind farm level as where ^^corresponds to the excitation frequency, ^^,^^to the width of the wind farm and ^^to the free wind speed (the average wind speed as specified above). Then, the thrust distribution ^ and its dynamic characteristics can be optimized in such a way, that they trigger the instabilities of the wake of the whole wind farm and thereby accelerate the breakdown. Suitable approaches could to determine such an instability triggering ^ could be Ginzburg-Landau model or a nonlinear stability analysis comparable to the one described by Batchelor and Gill. Two thrust distributions that are expected to trigger such instabilities are ^^and ^^as described in row three and four of Figure 3. However, there are multiple other ^ combined with various dynamic characteristics imaginable, not mentioned in this figure, but still falling under the scope of the appending claims. Both, ^^and ^^have in common, that the first row of the wind farm is superimposed with an unsteady thrust excitation ^^,^,^^^, ^, ^^, ^^^^^. The instantaneous thrust excitation profiles are then advected downstream with the advection speed ^^^^: where ^^^^addresses the decreased velocity inside the wind farm. Consequently, the thrust of each individual turbine oscillates periodically, but depending on the location inside the windfarm with a different phase shift and amplitude. The following gives a detailed description of ^^and ^^: A first embodiment of the dynamic thrust distribution ^^: This dynamic thrust pattern excites the thrust of the first row turbines in a substantially uniformly manner. The excitation for the first row turbines can be described as: where the excitation amplitude A second embodiment of the dynamic thrust distribution ^^: In contrast to the first embodiment given above, the second embodiment of the dynamic thrust distribution excites the first row turbines non-uniformly. This can, for instance, be achieved by applying a linear thrust distribution along the first row, with an oscillating slope: where ^^defines the lateral position of the turbine, and ^^^^the lateral position of the furthest outside turbine. It is noted that ^ = 0 is defined as the cross-stream centre of the wind farm. It is expected that this second embodiment, ^^, is to generate oscillating vortex-like structures in the wake, comparable to the van Karman vortex street. However, numerous distributions that replace the linear thrust distribution along the first row with any other distribution may result in comparable or even better results. Same as in ^^it is worth mentioning, that ^^can be applied to a subcluster of turbines, whilst the neighboring subcluster is excited with the mirrored pattern. This is of particular interest when dealing with wind farms with high aspect ratio. Note, that ^[^,^]can be superimposed or applied to any subcluster of the wind farm in order to enhance favorable effects or to adapt to local flow conditions. Simulations and implementation The proposed methods are tested using large eddy simulation (LES). LES provides insight into the temporal and spatial structure of turbulence. Combined with a model representing the wind turbine the setup enables the simulation of the interaction between a wind farm with and the turbulent atmospheric boundary layer (ABL). Assuming a turbine downwind position ^ (i.e. a coordinate along the wind direction) and a crosswind position y, where ^ = 0 m indicates the centre of the wind farm and ^ = 0 m indicates the first row, the thrust is calculated as follows: −mod(^, λ) ^^(^, ^)= ^^,^+ ^ ⋅ ^ ⋅ sin ^2π^ ^ + 2π^ λ where ^ indicates the magnitude with which the amplitude (Amp.) changes in crosswind direction, ^ indicates the time in seconds, ^ the frequency in Hz, λ is the wavelength of the actuation in meters, and ^propdenotes the propagation speed of the wave in meters per second. The term mod denotes the modulo operation. The wavelength λ can be formulated as dependent on the Strouhal number St, which we can use as tuning variable. We can further use the Strouhal number to derive the frequency: The term denotes the free wind speed, ^ a characteristic length, which we set equal to the width of the wind farm ^WF,y(note that it may also be set equal to the length). The propagation speed ^propis assumed to be a linear fraction of the free wind speed that is set to ^prop= 0.7 ^^. Figure 4 shows an exemplary wind cluster (i.e. wind farm) 200, comprising a plurality of wind turbines 1, having a staggered layout. The wind cluster 200 is seen to have, assuming the wind coming from the left side of the figure and being substantially parallel to the x-axis, as indicated by wind direction I, an effective width of 3.654 km and an effective length of 10.08 km. The individual turbines of the respective rows R1 – R16 are spaced apart, as seen along the cross wind direction II, with 4 rotor diameters D (i.e. 4D distance) . All the respective rows R1 – R16 are spaced apart 5D from the nearest row. This exemplary wind cluster 200 is used for demonstrating different types of patterns that can be used in the method of controlling a wind cluster according to the current disclosure, as shown in figures 5A – 8C. It is noted that this is a non-exhaustive and non-limiting set of examples. Figures 5A – 5C show, at different times ^^,   ^^ and ^^, wherein ^^< ^^< ^^, a pattern generated from a left-right block wave for controlling the axial induction factor of the wind turbines of the wind cluster 200 shown in figure 4. The spatial part of the pattern is thereby a combination, in particular a multiplication, of a block-wave (i.e square wave) signal with a unit amplitude as a first shape function along the effective width of the wind cluster 200, i.e. in the direction along the cross-wind direction II and a constant (unit) second shape function along the effective length of the wind cluster 200, i.e. in the direction that is parallel to the wind direction I. The spatial period is seen to be (approximately) equal to the width of the wind cluster 200, which is 3,654 km. The temporal part of the pattern is formed by a periodic function, in particular a sinusoidal function having a predetermined temporal period. This effectively leads to a periodically changing varying trust force, as seen between the left and right sides (i.e. as seen along the wind direction I) of the wind cluster 200. Aerodynamic structures are formed in the wake , as was explained earlier, which appear as being sequentially “pushed” from left, to right and back to left again. Additionally, it is expected, as was described above, that this pattern will trigger additional secondary motions that draw in additional energy from higher layers. The pattern shown in figures 6A – 6C show, again at different times ^^,  ^^ and ^^, a second version of the pattern shown in figures 5A – 5C. The first shape function is the same, but the second shape function is now a sinusoidal function having a spatial period that is substantially equal to the effective length of the wind cluster 200, which is 10,08 km. It is further seen that the pattern (translationally) moves along the direction of the wind, such that, over time, the pattern appears to shift to the back of the wind cluster 200, as was described above. The pattern shown In figures 7A – 7C show, again at different times ^^,   ^^ and ^^, a third version of the pattern, that is slightly different from the pattern shown in figures 6A – 6C. The block-wave signal that was used for the first shape function, is replaced by a linear shape function (i.e. constantly decreasing, or increasing). This results in, rows of turbines 1 having a substantially a constant thrust force (i.e. axial induction factor); at ^^this can be seen to be the case for rows R1, R8, R9, R16. The rows situated therebetween can be seen to have a variation, ranging from linear to non-linear, in the thrust force from left to right. The pattern in Figures 8A – 8C show, again at different times ^^,  ^^ and ^^, a fourth version of the pattern, that is slightly different from the pattern shown in figures 7A – 7C. In the fourth version, the first shape function is chosen to be a constant (unit) shape function. Figure 9A and 9B show comparative results of a 4 x 3 turbine array defining a second exemplary wind clusters. Figure 9A shows the resulting cluster wake 102 from using a standard control approach (often referred to as “greedy” control), wherein each turbine 1 is individually controlled to maximize its own power output. Figure 9B shows the resulting cluster wake 103 from using an embodiment of the control method according to the current disclosure, wherein a pattern similar to the pattern shown in figures 7A- 7C is applied for controlling the wind cluster. As can be seen from the accompanying legend: the darker the grey-scale, the lower the wind speed in the wake. This pattern can be defined as the following definition for the excitation thrust coefficient ^^,^: where ^^^,^denotes the maximal excitation amplitude, ^^,^^the width of the wind farm in crosswind direction, ^^ the Strouhal number with respect to ^^,^^and ^ the free wind speed. It is noted that the excitation thrust coefficient ^^,^is a variation to a baseline thrust coefficient that follows from the standard turbine control. Assuming the advection wind speed in the wake ^^^^to be 0.8^ we can calculate the wavelength λ, which defines the pattern in downstream direction. The method of controlling the wind turbine cluster is investigated in a 4 × 3 turbine array using the NREL 5MW reference turbine. A densely spaced layout with 2D spacing in crosswind direction and 3D in downstream direction was chosen to generate a pronounced cluster wake. The Strouhal number was set to ^^ = 0.4, the maximum pitch amplitude to 4∘and the free wind speed to ^^^^= 9 ^^^^, which results in an excitation period of ^^= 210 ^ for the given layout. We simulate 10 excitation periods, resolved with a timestep of ^^ = 0.5. This case is simulated with the LES toolbox for wind energy applications AMRwind. The domain extensions are 5000 × 2000 × 1000 m spatially discretized with 256 × 104 × 48 cells. One refinement level is added in the area of 1D around the wind farm to obtain a cell size of 9.77 × 9.62 × 10.42 m. For this study, laminar inflow conditions have been selected. The difference as shown in the respective figures is striking: in the baseline case, a significant velocity deficit can be observed in the region directly downstream of the turbine cluster until the breakdown of the cluster wake initiates at 2000 ^ < ^ < 3000 ^. The wind turbine cluster control method according to the current disclosure reduces the near wake area significantly by shifting the breakdown upstream to 1000 ^ < ^ < 1500 ^. At ^ = 3000  ^ the mean velocity calculated over the width of the cluster is ≈   19.0 % higher than in the baseline case of figure 9A, at ≈ ^ = 4000  ^ the mean velocity is 9.4  % higher. Additionally, a periodic crosswind deflection of the wake fitting the excitation frequency is observed. A characteristic vortex structure can be identified at the peak of each deflection. The present disclosure is not limited to the embodiment shown, but extends also to other embodiments falling within the scope of the appended claims.

Claims

Claims 1. Method for controlling a wind turbine cluster, wherein said wind turbine cluster is defined by a first plurality of wind turbines that are located within a predefined area, the method comprising: - providing one or more wind condition parameters indicative of a wind field upstream of said predefined area; - adjusting axial induction factors of at least a second plurality of wind turbines according to a predefined spatial, temporal or spatiotemporal pattern, wherein said second plurality of wind turbines is a subset of, or is equal to, said first plurality of wind turbines and wherein a size of the pattern corresponds to an area defined by the second plurality of wind turbines, such that the actual adjustment of the axial induction factor of each wind turbine of the second plurality of wind turbines is dependent on its geometric position within the wind turbine cluster, the time, or a combination of both, wherein the step of adjusting the axial induction factors of said second plurality of wind turbines comprises outputting a control signal for controlling the respective wind turbines of said second plurality for adjusting an operational parameter, such as a blade pitch angle, or yaw angle, of the respective wind turbine; - wherein the spatial pattern is defined by at least a first spatially periodic signal having a spatial period in the range of 100 meters to 100 kilometers, wherein the temporal pattern is defined by a first temporally periodic signal having a temporal period of 1 minute to 1 week, wherein the spatiotemporal pattern is defined by a combination of the first spatial periodic signal and / or the first temporal periodic signal and wherein said spatial and / or temporal periods are determined on the basis of the one or more condition parameters.

2. Method for controlling a wind turbine cluster according to claim 1, wherein said one or more wind condition parameters comprise a wind direction of the wind field and wherein a size of the wind turbine cluster is defined by an effective length, that is taken along the wind direction, and / or an effective width of the wind turbine cluster, that is taken perpendicular to the wind direction; wherein the spatial and / or temporal periods are determined on the basis of an effective width and / or effective length of the wind cluster.

3. Method for controlling a wind turbine cluster according to claim 2, wherein said spatial and / or temporal periods have a positive correlation with the effective width and / or effective length of the wind cluster, in particular wherein said spatial and / or temporal periods are proportional to the effective width and / or effective length of the wind cluster.

4. Method for controlling a wind turbine cluster according to any of the preceding claims, wherein said one or more wind condition parameters comprise an average wind speed and wherein the spatial and / or temporal periods are determined on the basis of the average wind speed.

5. Method for controlling a wind turbine cluster according to claim 4, wherein the spatial and / or temporal periods are negatively correlated to the average wind speed, in particular wherein the spatial and / or temporal periods are inverse proportional to the average wind speed.

6. Method for controlling a wind turbine cluster according to any of the preceding claims 2 - 5, wherein the spatial and / or temporal periods are further determined on the basis of a predetermined Strouhal number, wherein the characteristic length is defined by the effective width or effective length and wherein the Strouhal number is in the range of 0.001 and 2, preferably in the range of 0.01 to 1, more preferably in the range of 0.05 to 0.8, even more preferably in the range of 0.1 to 0.7, even further preferred in the range of 0.2 to 0.6, most preferably in the range of 0.3 to 0.5; and preferably wherein the spatial and / or temporal periods have a negative correlation with the Strouhal number, more preferably wherein the spatial and / or temporal periods are inversely proportional to the Strouhal number.

7. Method for controlling a wind turbine cluster according to any of the preceding claims, wherein the first spatial and / or temporal periodic signals are further defined by a respective amplitude for controlling an amount with which the axial induction factor is adjusted, wherein said amplitude is preferably determined on the basis of the wind condition parameters.

8. Method for controlling a wind turbine cluster according to any of the preceding claims, as far as depending on claim 2, wherein the spatial pattern, or a spatial part of the spatiotemporal pattern, is defined by a first shape function along the effective width of the wind turbine cluster and a second shape function along the effective length of the wind turbine cluster, preferably wherein the respective shape functions are formed from linear, quadratic or higher-order polynomial, spline, sinusoidal, linear or non- linear sawtooth, square wave, triangle functions, combinations of these and / or absolute value functions of these and wherein at least one of said first and second shape functions comprises a periodic signal, such that the spatial pattern, or spatial part of the spatiotemporal pattern, defines locations of (local) minima and maxima of the axial induction factor adjustment within the wind turbine cluster.

9. Method for controlling a wind turbine cluster according to any of the preceding claims, wherein said temporal periodic signal comprises a sinusoidal temporal oscillating signal having a temporal frequency that is directly related to the temporal period, such that the axial induction factor of each wind turbine of the second plurality of wind turbines is adjusted over time between a respective maximum value and a minimum value.

10. Method for controlling a wind turbine cluster according to any of the preceding claims, wherein the spatiotemporal pattern is arranged such that the spatial part of the spatiotemporal pattern moves, in particular along a first translational direction, with respect to the wind turbine cluster, such that locationof (local) minima and maxima of the axial induction factor adjustment within the wind turbine cluster are dependent on time.

11. Method for controlling a wind turbine cluster according to claim 10, wherein the spatial part of the spatiotemporal pattern moves with a predefined speed, in particular wherein the predefined speed is correlated to the average wind speed, even more in particular is proportional to the average wind speed; preferably wherein predefined speed is in the range of 0.01 to 2 times the average wind speed, preferably in the range of 0.1 to 1.5 times the average wind speed, more preferably in the range of 0.3 to 1 times the average wind speed, even more preferably in the range of 0.4 to 0.8 times the average wind speed, most preferably in the range of 0.5 to 0.7 times the average wind speed.

12. Method for controlling a wind turbine cluster according to any of the preceding claims, wherein the method comprises the step of controlling each of wind turbines of the second plurality of wind turbines to adjust its axial induction factor according to an adjustment amount as determined from the predefined spatial, temporal or spatiotemporal pattern, wherein the adjustment amount of a respective wind turbine of the second plurality of wind turbines is determined by means of a spatial and / or temporal interpolation in the respective spatial, temporal or spatiotemporal pattern using the geometric position of the respective wind turbine and / or the actual time.

13. Method for controlling a wind turbine cluster according to any of the preceding claims, wherein axial induction factor of a respective wind turbine of the second plurality is adjusted by adjusting the pitch angle of at least one of the blades, preferably collectively adjusting the pitch angle of all of the blades, of the respective turbine, and / or by adjusting the yaw angle of the respective wind turbine.

14. Method for controlling a wind turbine cluster according to any of the preceding claims, wherein said wind turbines are horizontal axis wind turbines.

15. Wind turbine cluster, comprising a plurality of wind turbines, being arranged for receiving the one or more wind condition parameters and comprising means adapted for executing the steps of the method according any of the preceding claims.

16. Wind turbine cluster according to claim 15, comprising a controlling and / or data processing system for determining the predefined spatial, temporal or spatiotemporal pattern and / or spatial and / or temporal periods by using the method according any of the preceding claims, wherein said controlling and / or data processing system further comprises communication means for providing a respective wind turbine controller of each of said second plurality of second wind turbines with a control input such that each of the wind turbines of the second plurality of wind turbines is controlled to adjust its axial inductionfactor, in particular by adjusting the operational parameter, such as the blade pitch angle or yaw angle, according to the predefined spatial, temporal or spatiotemporal pattern.

17. Wind turbine controller for use in a wind turbine of the wind turbine cluster according to claim 16, wherein said wind turbine controller is arranged for receiving a control input from the controlling and / or data processing system and arranged for controlling the operational parameter, such as the blade pitch angle or yaw angle, of the respective wind turbine that the wind turbine controller is arranged to control in order to adjust its axial induction factor according to the predefined spatial, temporal or spatiotemporal pattern.

18. A computer program comprising instructions that, when executed by a computing device or system, cause the computing device or system to execute the steps of the method according any of the preceding claims 1 - 14.

19. A computer-readable medium having stored thereon the computer program of claim 18.

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