Calibrating a wind direction sensor of a wind turbine

Abstract

The invention relates to calibrating a wind direction sensor of a wind turbine. The invention involves retrieving a measured relative power output between a downwind wind turbine and the wind turbine, as a function of absolute wind direction at the wind turbine. The invention involves determining predicted relative power output as a function of absolute wind direction, wherein the predicted relative power output is a predicted power output of the further wind turbine relative to the predicted power output of the wind turbine, the further wind turbine power output being based on wake flow generated by the wind turbine. The invention involves comparing the measured relative power output against the predicted relative power output to determine an error in terms of absolute wind direction, and updating defined wind turbine yaw offset based on the determined error. The invention involves calibrating the wind direction sensor based on the determined error.

Description

[0001] CALIBRATING A WIND DIRECTION SENSOR OF A WIND TURBINE

[0002] TECHNICAL FIELD

[0003] The invention relates to calibrating a wind direction sensor of a wind turbine. In particular, the invention involves comparing measured and predicted relative power outputs between the wind turbine and a downwind wind turbine, and using an error in terms of absolute wind direction obtained from the comparison to calibrate the wind direction sensor.

[0004] BACKGROUND

[0005] Wind turbines are used to capture energy in the wind as it flows past them, and to generate electrical power from the captured energy, e.g. to be supplied to an electrical grid. Often, several wind turbines are located in relatively close proximity to one another in a geographical area, where such a group of wind turbines may be referred to collectively as forming a wind park or wind farm.

[0006] The amount of wind energy that may be captured by a wind turbine varies in dependence on various environmental factors, such as wind speed and wind direction. For instance, a wind turbine may in general be most efficient at capturing wind energy when a rotor or nacelle of the turbine faces directly into the incoming wind direction, i.e. when the wind turbine is ‘aligned’ with the wind.

[0007] It may in some cases be desired to orient the wind turbine rotor or nacelle at an angle to the incoming wind direction, i.e. such that the wind turbine is ‘misaligned’ with the wind. For instance, this may be performed to account for the influence of the incoming wind flow on another wind turbine in the wind farm. The angle between the incoming wind direction and the nacelle / rotor direction may be referred to as a yaw offset or yaw misalignment.

[0008] Typically, a wind turbine has one or more wind direction sensors for measuring incoming wind direction or relative wind direction, with a desired yaw offset being implemented based on the wind direction sensor measurement. These sensors provide point measurements of the wind field, which can lead to inaccurate measurements that do not account for different types of flow in the incoming wind field, e.g. vortices, eddies, etc. Incorrect calibration of the wind direction sensors can also lead to measurement inaccuracies. There is a need to increase the accuracy of wind direction measurements at a wind turbine. This can ensure that yaw offsets are implemented in a desired manner, for instance. It is against this background to which the present invention is set.

[0009] SUMMARY OF THE INVENTION

[0010] According to an aspect of the invention there is provided a method of calibrating a wind direction sensor of a wind turbine. The method comprises retrieving measurement data to determine measured relative power output indicative of power output of a further wind turbine relative to power output of the wind turbine, as a function of absolute wind direction at the wind turbine. The further wind turbine is downwind of the wind turbine.

[0011] The method comprises the following iteratively repeated steps: determining predicted power output of the wind turbine as a function of absolute wind direction at the wind turbine; determining predicted wake flow generated by the wind turbine, using a defined wake flow model, as a function of defined yaw offset of the wind turbine; determining predicted power output of the further wind turbine, based on the predicted wake flow generated by the wind turbine, as a function of absolute wind direction; determining predicted relative power output as a function of absolute wind direction, wherein the predicted relative power output is the predicted power output of the further wind turbine relative to the predicted power output of the wind turbine; comparing the measured relative power output against the determined predicted relative power output to determine an error in terms of absolute wind direction; and, updating the defined yaw offset of the wind turbine based on the determined error. These steps are repeated iteratively until a stop condition is satisfied.

[0012] The method comprises calibrating the wind direction sensor of the wind turbine based on the determined error.

[0013] The stop condition may be satisfied if a difference between the determined error of successive iterations is less than a defined value.

[0014] The stop condition may be satisfied if a defined number of iterations has been performed. Optionally, the defined number of iterations may be greater than or equal to one. Comparing the measured relative power output against the determined predicted relative power output may comprise: identifying a minimum value of the measured relative power output; and, identifying a minimum value of the determined predicted relative power output. The error may be determined as a difference between the respective minimum values.

[0015] Comparing the measured relative power output against the determined predicted relative power output may comprise: fitting a curve to the measured relative power output; and, matching the fitted curve to a curve describing determined predicted relative power output as a function of absolute wind direction. The error may be determined based on the curve matching.

[0016] The measurement data may comprise data points of power output of the further wind turbine divided by power output of the wind turbine as a function of absolute wind speed. The determined predicted relative power output may comprise data points of the predicted power output of the further wind turbine divided by the predicted power output of the wind turbine.

[0017] The defined wake flow model may comprise a defined velocity deficit model configured to determine a wind velocity deficit downwind of the wind turbine as a result of the generated wake flow.

[0018] The defined wake flow model may comprise a defined wake deflection model configured to determine a lateral deflection of the generated wake flow, based on the defined yaw offset of the wind turbine.

[0019] The defined yaw offset may be set to zero for a first iteration of the iteratively repeated steps.

[0020] The measured relative power output and the determined predicted relative power output may be obtained for a defined sub-range of possible absolute wind directions.

[0021] The defined sub-range may include absolute wind directions in which the further wind turbine is predicted to experience wake flow effects as a result of the generated wake flow at the wind turbine. The method may comprise retrieving second measurement data to determine second measured relative power output indicative of power output of a second wind turbine relative to power output of the wind turbine, as a function of absolute wind direction. The second wind turbine may be downwind of the wind turbine. The second measurement data may be obtained for a defined second sub-range of possible absolute wind directions different from the defined sub-range. The method may comprise iteratively repeated steps, for absolute wind direction values in the defined second sub-range, as follows: determining predicted power output of the wind turbine as a function of absolute wind direction at the wind turbine; determining predicted wake flow generated by the wind turbine, using the defined wake flow model, as a function of defined yaw offset of the wind turbine; determining predicted power output of the second wind turbine, based on the predicted wake flow generated by the wind turbine, as a function of absolute wind direction; determining second predicted relative power output as a function of absolute wind direction, wherein the second predicted relative power output is the predicted power output of the second wind turbine relative to the predicted power output of the wind turbine; comparing the second measured relative power output against the determined second predicted relative power output to determine a second error in terms of absolute wind direction; and, updating the defined yaw offset of the wind turbine based on the determined second error. The iteratively repeated steps may be repeated until a second stop condition is satisfied. The method may comprise calibrating the wind direction sensor of the wind turbine based on the determined second error.

[0022] The method may comprise using the calibrated wind sensor to determine relative wind direction at the wind turbine.

[0023] The method may comprise adjusting an actual yaw offset applied to the wind turbine in accordance with determined relative wind direction.

[0024] In accordance with another aspect of the invention there is provided a non-transitory, computer-readable storage medium storing instructions thereon that when executed by one or more processors cause the one or more processors to perform a method as defined above.

[0025] In accordance with another aspect of the invention there is provided a controller for a wind turbine. The controller is configured to retrieve measurement data to determine measured relative power output indicative of power output of a further wind turbine relative to power output of the wind turbine, as a function of absolute wind direction. The further wind turbine is downwind of the wind turbine. The controller is configured to iteratively repeat steps of: determine predicted power output of the wind turbine as a function of absolute wind direction at the wind turbine; determine predicted wake flow generated by the wind turbine, using a defined wake flow model, as a function of defined yaw offset of the wind turbine; determine predicted power output of the further wind turbine, based on the predicted wake flow generated by the wind turbine, as a function of absolute wind direction; determine predicted relative power output as a function of absolute wind direction, wherein the predicted relative power output is the predicted power output of the further wind turbine relative to the predicted power output of the wind turbine; compare the measured relative power output against the determined predicted relative power output to determine an error in terms of absolute wind direction; and, update the defined yaw offset of the wind turbine based on the determined error. The iterative steps are repeated until a stop condition is satisfied. The controller is configured to calibrate a wind direction sensor of the wind turbine based on the determined error.

[0026] In accordance with another aspect of the invention there is provided a wind turbine comprising a controller as defined above.

[0027] In accordance with another aspect of the invention there is provided a wind park comprising a controller as defined above. The wind park comprises the wind turbine and the further wind turbine.

[0028] BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Examples of the invention will now be described with reference to the accompanying drawings, in which:

[0030] Figure 1 schematically illustrates a wind park / farm including a plurality of wind turbines in accordance with an aspect of the present invention;

[0031] Figure 2(a) schematically illustrates wake generated downstream of one of the wind turbines of Figure 1 when the wind turbine is aligned with the incoming wind direction, and Figure 2(b) schematically illustrates the generated wake when the wind turbine of Figure 2(a) is misaligned relative to the incoming wind direction; Figure 3 shows the steps of a method performed by a controller of a wind turbine of Figure 1 in accordance with an aspect of the invention;

[0032] Figure 4 shows a plot of measured power output of an upwind turbine of Figure 1 divided by measured power output of a downwind turbine of Figure 1 , against absolute wind direction;

[0033] Figure 5 shows the plot of Figure 4, as well as predicted power output of the upwind turbine of Figure 1 divided by predicted power output of the downwind turbine of Figure 1 , against absolute wind direction, for zero yaw offset of the upwind turbine;

[0034] Figure 6 shows the plots of Figures 4 and 5, as well as predicted power output of the upwind turbine of Figure 1 divided by predicted power output of the downwind turbine of Figure 1 , against absolute wind direction, for non-zero yaw offset of the upwind turbine; and,

[0035] Figure 7 shows a schematic representation of a controller, in accordance with an aspect of the invention, of one of the wind turbines of Figure 1 that generates wake downstream thereof.

[0036] DETAILED DESCRIPTION

[0037] Figure 1 shows a schematic illustration of a wind park or wind farm 10 comprising a plurality of wind turbines 12. Each wind turbine 12 includes a tower 121 , a nacelle disposed at the apex of, or atop, the tower, and a rotor operatively coupled to a generator housed inside the nacelle. In addition to the generator, the nacelle houses other components required for converting wind energy into electrical energy and various components needed to operate, control, and optimise the performance of the wind turbine 12. The rotor of each wind turbine 12 includes a central hub and three rotor blades 122 that project outwardly from the central hub.

[0038] Each wind turbine 12 includes a control system or controller (not shown in Figure 1). The controller may be placed inside the nacelle, in the tower or distributed at a number of locations inside (or externally to) the turbine 12 and communicatively connected to one another. In addition, the wind park 10 may include a (central) controller that is communicatively connected to the wind turbine controllers. Each wind turbine 12 may include one or more sensors for measuring wind direction at the wind turbine 12. Relative wind direction may be regarded as a difference between absolute wind direction and nacelle heading, i.e. a direction in which the nacelle is oriented. The wind direction sensors may be of any suitable type, such as a wind vane anemometer, cup anemometer, laser doppler anemometer, ultrasonic anemometer, etc. Each wind turbine 12 will typically include other types of sensors, such as accelerometers, gyroscopes, etc. The wind turbine sensors may be located in or on the rotor or nacelle of the wind turbines 12.

[0039] Each wind turbine 12 may be configured to adjust a yaw offset, also referred to as yaw angle, yaw error or yaw misalignment. The yaw offset is a difference between the incoming wind direction at a wind turbine and a direction in which the nacelle or rotor of the wind turbine is oriented. Each wind turbine 12 may comprise a yaw system between the tower 121 and nacelle, which allows for rotational motion of the nacelle (and attached components, including the rotor and rotor blades 122) relative to the tower 121 in order to adjust the yaw offset of the wind turbine 12 relative to the wind, i.e. rotation about a tower axis of the turbine 12. The control system / controller of the respective wind turbine 12 may determine a desired yaw offset for the wind turbine 12, and output a control signal to control a yaw drive mechanism of the turbine 12 to rotate the nacelle relative to the tower 121 via the yaw bearing in accordance with the desired yaw angle.

[0040] In some operating conditions, it may be desired to orient the nacelle / rotor (directly) into the incoming wind direction, i.e. zero yaw offset, e.g. to maximise energy capture by the wind turbine from the wind. In some other operating conditions, it may be desired to offset the nacelle / rotor direction from the incoming wind direction, e.g. to reduce loading on one or more wind turbine components or to account for disturbances in the incoming wind flow, e.g. turbulence, whirl, etc.

[0041] Figure 1 schematically illustrates a direction 14 of wind flow in the wind park 10. As the wind flows past a first one of the turbines 12a in the wind park 10, wake is generated downstream of the wind turbine 12a. This means that wind flow downstream of the wind turbine 12a is perturbed or disturbed relative to upstream of the wind turbine 12a, resulting in a reduction in the speed of the wind flow and / or an increase in the turbulence of the wind flow. Depending on the positioning of the other wind turbines 12b, 12c in the wind park 10 relative to the (first) wind turbine 12a, the wind flow past one or more of the other wind turbines 12b, 12c may include wake effects caused by the wind flow past the first wind turbine 12a. The wind turbine that generates I causes the wake may be referred to as the upstream or upwind wind turbine 12a, and the one or more wind turbines that experience effects of the generated wake may be referred to as downstream or downwind wind turbines 12b, 12c.

[0042] It will be appreciated that while three wind turbines 12 are shown in Figure 1 , any suitable number of (upwind and downwind) wind turbines may be present in the wind farm in different examples. Indeed, it will also be understood that any given wind turbine in a wind farm may be upwind of one or more other wind turbines in the wind farm, and downwind of one or more other wind turbines in the wind farm, depending on the wind direction.

[0043] Wake effects from upwind wind turbines results in reduced wind speed and increased turbulence in the vicinity of the downwind wind turbines relative to the upwind wind turbines. This tends to reduce the amount of energy that can be captured from the wind by downwind wind turbines, which reduces the power output of these wind turbines. Controlling yaw offset of an upstream wind turbine adjusts the generated wake downwind, and can be used to reduce the effects of the wake on one or more wind turbines downwind of the upwind wind turbine. This may be performed by misaligning the upwind wind turbine relative to the incoming wind direction. This type of control may be referred to as yaw steering.

[0044] Figure 2 schematically illustrates how controlling yaw offset adjusts the wake generated by a wind turbine. In particular, Figure 2(a) shows a case in which the upwind wind turbine 12a is aligned with the incoming wind direction 14. In this case, it is seen that the wake 20 generated downwind of the upwind wind turbine 12a is directed towards another wind turbine 12b downwind of the upwind wind turbine 12a. As the downwind wind turbine 12b experiences the effects of the generated wake 20, then this reduces the amount of wind energy that may be captured by the downwind wind turbine 12b. Figure 2(b) shows a case in which the upwind wind turbine 12a is misaligned relative to the incoming wind direction 14, e.g. a yaw offset of the upwind wind turbine 12a is adjusted relative to Figure 2(a). It is seen that this changes the direction of the generated wake 20 such that the downwind wind turbine 12b does not experience the effects of the generated wake 20, or at least experiences reduced effects thereof. A desired yaw offset of a particular wind turbine 12 may be determined based on relative wind direction at the wind turbine 12 as measured by a wind direction sensor of the wind turbine 12. However, wind direction as measured by such wind direction sensors may be inaccurate, which can result in a yaw offset being implemented that is not in line with a desired or intended control strategy for the relevant wind turbine. In particular, a wind direction sensor typically provides a point measurement of the incoming wind field, and so does not account for certain dynamics that may be present in the wind field, e.g. turbulence, whirl, etc.

[0045] The present invention is advantageous in that it calibrates a wind direction sensor of a wind turbine - or corrects the measurements obtained from such a wind direction sensor

[0046] - to account for measurement inaccuracies. This allows for an accurate determination of relative wind direction at a wind turbine (assuming accurate knowledge of nacelle heading), which in turn allows for the yaw offset of the wind turbine to be controlled in a manner that is accurate and in line with a desired control strategy. The invention benefits from not needing any additional hardware to implement the calibration.

[0047] The invention achieves these benefits by making use of the fact that wake flow experienced at a wind turbine that is downwind of a wind turbine that generates the wake flow may be predicted based on (absolute) wind direction and a yaw offset of the upwind wind turbine. In particular, the power output of the downwind wind turbine may be predicted based on the predicted wake flow. Then, an error between measured and predicted relative power outputs between the upwind and downwind wind turbines may be used to correct the yaw offset at the upwind wind turbine in order to account for errors in the measured relative wind direction at the upwind wind turbine. It is further noted that the invention is more generally applicable to wind turbine operation beyond yaw offset control, i.e. the invention can be used to calibrate a wind direction sensor (of a wind turbine) to be used in any appropriate manner by the wind turbine. This will be described in greater detail below.

[0048] Compared to some previous approaches, the present invention beneficially does not ‘overshoot’ in its correction of yaw offset, and does not require new experimental / testing data sets from field measurements - which could take weeks or months to acquire / collect

[0049] - in order to perform subsequent corrections as part of an iterative process. This is because the invention beneficially uses physics-based models or engineering models to model the generated wake flow / deflections and the wind turbine power production / output, and iterates on the models - rather than iterating on ‘real-life’ / measurement data - in order to correct yaw offset. In this sense, the invention is more precise than some previous approaches. The invention also benefits from being able to be performed offline because no real-time data is needed. These and other benefits will become apparent in the following description.

[0050] Figure 3 shows the steps of a method 30 performed by a controller of one of the wind turbines 12 in the wind park 10. In particular, the method 30 is for calibrating a wind direction sensor of said one of the wind turbines 12. The method 30 is for calibrating the wind direction sensor of a wind turbine that generates wake flow that is experienced by one or more further wind turbines that are downwind of said wind turbine. As such, in the following an example is described in which the method 30 is for calibrating the wind direction sensor of the upwind wind turbine 12a.

[0051] At step 301 , the method 30 involves retrieving measurement data related to the power output of the upwind wind turbine 12a, and also related to the power output of at least one (further) wind turbine downwind of the upwind wind turbine 12a. In the described example, measurement data relating to the downwind wind turbine 12b is retrieved. The measurement data in particular relates to power output of the wind turbines 12a, 12b as a function of absolute wind direction (at the respective wind turbines 12a, 12b).

[0052] The measurement data may be obtained by monitoring operation of the wind turbines 12a, 12b over a certain time period, e.g. several weeks or months, at least until measurements of a sufficient large range of wind directions at both sides of a full wake angle have been obtained. In particular, the power output at each wind turbine 12a, 12b may be measured in conjunction with absolute wind direction, e.g. to obtain data points of power output against absolute wind direction. Absolute wind direction may be measured using an appropriate sensor that is part of, or near to, the relevant wind turbine, e.g. one of the wind direction sensors mentioned above. Here and throughout, absolute wind direction may refer to the absolute wind direction at an upwind wind turbine - of a pair of wind turbines - under consideration. Absolute wind direction may be obtained as an angle relative to (true) north. Wind turbine power output may be measured in a known manner, e.g. directly using a power meter / sensor of the wind turbine. Wind turbine power output may be measured when a defined yaw offset of the wind turbine is zero. The retrieved measurement data is used to determine measured relative power output between the upwind and downwind wind turbines 12a, 12b as a function of absolute wind direction. In particular, this may be determined by calculating measured power output at the downwind wind turbine 12b divided by measured power output at the upwind wind turbine 12a, for values of absolute wind direction.

[0053] Figure 4 shows an example plot 40 of measured relative power output as a function of absolute wind direction, obtained from field measurements over a certain time period. In particular, Figure 4 shows data points 401 of measured power output of a downwind wind turbine divided by measured power output of an upwind wind turbine, at given values of absolute wind direction measured by the upwind turbine across a relatively wide range of absolute wind directions. Figure 4 also shows a curve 402 describing the median values of the data points as a function of absolute wind direction. Figure 4 further indicates a confidence level interval 403 for the median curve 402. It is noted that the median curve 402 has a minimum value 404 at a given absolute wind direction value wlm. This may be regarded as corresponding to the absolute wind direction at which the wake flow generated by the upwind wind turbine is centred on the rotor of the downwind wind turbine.

[0054] Although in the described example, measured values of power output are used to determine the measured relative power output it will be understood that different measurement values indicative of power output at the relevant wind turbines may instead be used in different examples, i.e. parameter values that may be regarded as proxies for wind turbine power output / production may be used. For instance, in some examples the measured relative power output - indicative of power output of the downwind wind turbine 12b relative to power output of the upwind wind turbine 12a - may be based on measured wind speed values.

[0055] The collected / acquired measurement data may be stored in suitable data storage or memory storage, e.g. locally at one or more of the wind turbines 12, in a memory module of the wind farm 10, or centrally at a remote (Cloud) server. The measurement data may then be retrieved by the wind turbine controller when needed to perform the described method 30. The measurement data only needs to be collected once, i.e. no further measurement data needs to be collected for subsequent iterations of the following process. In some examples, the method 30 may be regarded as including the step of collecting the measurement data using appropriate sensors. Referring back to Figure 3, at step 302 the method 30 involves determining predicted power output of the upwind wind turbine 12a as a function of absolute wind direction (at the wind turbine 12a). Wind turbine power output may be predicted in a known manner, e.g. using a power curve for the wind turbine, i.e. a defined curve describing power output as a function of wind speed for the specific wind turbine. The predicted power output may alternatively be determined using a defined engineering (or physics-based) model. In the described example, it may be assumed that the upwind turbine 12a does not experience any wake flow effects from other wind turbines upwind of said turbine 12a. As such, it may be assumed in the described example that the incoming wind at the upwind turbine 12a is substantially free-flow, undisturbed flow, i.e. without significant effects from turbulence, etc. It will be understood, however, that in different examples the incoming wind flow at the upwind turbine 12a may be assumed to be disrupted by one or more wind field factors, e.g. wake flow, that may be taken into account in the wind turbine power output prediction for the upwind turbine 12a. The predicted power output may be determined based on the yaw offset of the (upwind) wind turbine 12a, i.e. the yaw offset is taken into account in the engineering model used to predict power output. Typically, the yaw offset will initially be set to be zero.

[0056] At step 303, the method 30 involves determining predicted wake flow generated by the upwind wind turbine 12a as a function of defined yaw offset of the upwind wind turbine 12a. As mentioned above, the defined yaw offset may initially be set to zero. The wake flow prediction is performed using a defined wake flow model. In particular, the wake flow model may predict a deflection angle and / or a velocity of the flow generated downwind of the upwind wind turbine 12a. It will be understood that a number of different wake flow models may be used to predict the wake flow generated by the upwind wind turbine 12a.

[0057] The wake flow model may for instance include a defined velocity deficit model configured to determine a wind velocity deficit downwind of the upwind wind turbine 12a as a result of the generated wake flow. Such a velocity deficit model determines or predicts a ‘lack of wind’ downwind of the upwind wind turbine 12a as a result of the wake flow generated by the upwind wind turbine 12a. Expressed differently, the velocity deficit model predicts a reduction in wind velocity downwind of the upwind wind turbine 12a as a result of the generated wake flow. It will be understood that different known velocity deficit models may be used. An example of such a velocity deficit model is described in ‘Analytical Modeling of Wind Farms: A New Approach for Power Prediction’, Niayifar et al., Energies, 2016, 9, 741. The output of the velocity reduction model is a wind speed / velocity of the wake flow downwind of the upwind wind turbine 12a. The velocity reduction model may assume a self-similar Gaussian profile for the wake, and may depend on a thrust coefficient of the (upwind) wind turbine, a turbulence intensity, a distance / direction from the (upwind) wind turbine, a height of the wind turbine hub, wind turbine diameter, the undisturbed wind velocity / speed, etc. The velocity reduction model typically assumes a conservation of mass and momentum. An alternative velocity reduction model may assume a ‘top hat’ shape / profile.

[0058] The defined wake flow model may include a defined wake deflection model for determining / predicting a lateral and / or vertical deflection of the wake flow generated by the upwind wind turbine 12a. In particular, the angle of deflection is determined based on the defined yaw offset of the upwind wind turbine 12a, i.e. the wake deficit deflection angle resulting from the yaw angle of the upwind wind turbine 12a. It will be understood that different known wake deflection models may be used. An example of such a wake deflection model is described in ‘Control-Oriented Model for Secondary Effects of Wake Steering’, King eta / ., Wind Energ. Sci., 6, 701-714, 2021. The output of the wake deflection model is an angle of the generated wake flow downwind of the upwind wind turbine 12a. The wake deflection model may depend on the thrust coefficient of the (upwind) wind turbine as well as the yaw misalignment of the wind turbine.

[0059] Implementation of the wake flow model may be performed using suitable software on the wind turbine / farm controller. For instance, the known FLORIS (Flow Redirection and Induction in Steady State) software package may be used for this purpose.

[0060] Referring again to Figure 3, at step 304 the method 30 involves determining predicted power output of one or more of the wind turbines 12b, 12c downwind of the (upwind) wind turbine 12a. In the described example, the predicted power output of the wind turbine 12b is considered. The predicted power output of the downwind wind turbine 12b is in particular determined based on the predicted wake flow - as determined at step 303 - generated by the upwind wind turbine 12a. Specifically, the predicted power output of the downwind wind turbine 12b is determined as a function of absolute wind direction. A power curve model, or other defined engineering model, for the downwind wind turbine 12b may be used to predict power output, or a proxy thereof, based on the incoming wind flow as predicted by the wake flow model. It will be understood that parameters such as the geographical positioning (distance, angle, etc.) of the downwind turbine 12b relative to the upwind turbine 12a will be known, and can be used to determine the effects of the wake flow generated by the upwind turbine 12a on the downwind turbine 12b for various absolute wind directions (and for the specific yaw offset of the upwind turbine 12a).

[0061] At step 305, the method 30 includes determining predicted relative power output as a function of absolute wind direction. In particular, the predicted relative power output is the relative power output between the (pair of) upwind and downwind wind turbines 12a, 12b, i.e. the predicted power output of the downwind wind turbine 12b - from step 304 - relative to the predicted power output of the upwind wind turbine 12a - from step 302 - or vice versa. In the described example, the predicted relative power output is determined as the predicted power output of the downwind wind turbine 12b divided by the predicted power output of the upwind wind turbine 12a.

[0062] Figure 5 shows an example plot 50 of relative power output against absolute wind direction. In particular, Figure 5 includes the data points 401 and curve 402 of Figure 4, showing measured relative power output (between the downwind and upwind turbines 12b, 12a) against absolute wind direction (from method step 301). In addition, Figure 5 shows data points 501 , and a curve 502 fitted to the data points 501 , showing predicted relative power output (between the downwind and upwind turbines 12b, 12a) against absolute wind direction (from method step 305). The predicted power output curve 502 has a (global) minimum value 504 at a given absolute wind direction value wlp. This corresponds to the absolute wind direction at which the centre of the wake flow generated by the upwind wind turbine 12a is predicted to overlap with the centre (i.e. rotor) of the downwind wind turbine 12b (predicted geo-positional centre wake).

[0063] It is apparent from Figure 5 that the predicted wake flow centre value wlpis different from the measured wake flow centre value wlm. More generally, it may be seen that the predicted curve 502 is offset from the measured curve 402. This offset can be indicative of an error in the wind direction sensor used to obtain the measurement data.

[0064] Referring back to Figure 3, step 306 of the method 30 involves comparing the measured relative power output - from step 301 - against the determined predicted relative power output - from step 305 - to determine an error or delta in terms of absolute wind direction. In the described example, the error is calculated as the difference between the measured and predicted / expected wake flow centre values, i.e. wlp- wlm. In the example illustrated in Figure 5, the error wlm- wlp= 249 - 259 = -10°. The error may be determined in a different manner in different examples. For instance, in another example the error may be determined based on curve matching / shifting the predicted curve 502 to the measured curve 501 in order to calculate the offset in absolute wind direction.

[0065] At step 307, the method 30 involves updating the defined yaw offset of the upwind wind turbine 12a based on the error / delta determined at step 306. As mentioned above, in the described example the defined yaw offset of the upwind turbine 12a is set to zero initially, and the calculated error is -10°. As such, in the described example the defined yaw offset is updated to be -10°.

[0066] The updated yaw offset is fed back to step 302 of the method 30 to update the predicted wake flow generated by the upwind wind turbine 12a as a function of this updated yaw offset. Indeed, steps 302-307 of the method 30 are repeated with the updated value of the defined yaw offset of the upwind wind turbine 12a. This change in yaw offset of the upwind wind turbine 12a will change the predicted wake flow generated by the upwind turbine 12a, and so will change the predicted wake flow experienced by the downwind turbine 12b. In turn, this will change the predicted relative power output determined at step 305.

[0067] Figure 6 shows a plot 60 of relative power output against absolute wind direction. In particular, Figure 6 shows the measured data points 401 and median curve 402 of Figures 4 and 5, and the predicted points 501 and curve 502 of Figure 5. In addition, Figure 6 shows updated predicted points 601 and an updated predicted curve 602, determined by performing the method steps with the updated yaw offset for the upwind turbine 12a. It is apparent from Figure 6 that the updated predicted wake flow centre value w2pis offset / shifted compared to the (initial) predicted wake flow centre value wlp. Specifically, in the described example the minimum value, i.e. predicted centre wake, has shifted by one degree from 259° to 258°. This means that the updated error determined at step 306 iswim ~w2p = 249 - 258 = -9°. At step 307, the yaw offset is therefore (further) updated to be set at -9°.

[0068] Steps 302-307 of the method 30 may be repeated in an iterative manner for any suitable number of iterations until a stop condition is satisfied. In the described example, these method steps may be repeated iteratively until convergence is reached, e.g. to within a defined number of significant figures, i.e. the stop condition is a certain level of convergence of the calculated error. Alternatively, the stop condition may be that the repeated steps have been performed a prescribed number of times in an iterative manner. Indeed, in some examples the method steps may be performed only once, i.e. one iteration, in order to provide a sufficiently accurate correction.

[0069] Referring back to Figure 3, once the stop condition has been satisfied, at step 308 the method 30 involves calibrating the wind direction sensor of the upwind wind turbine 12a. In particular, this involves calibrating the wind direction sensor to account for the calculated error (obtained in the most recent I final iteration of the method). The calibrated wind direction sensor may then be used to measure relative wind direction in a more accurate manner. As relative wind direction is used to control various control routines (e.g. yaw offset control, also called yaw steering) of the wind turbine 12a to, for instance, maximise energy capture I power production of the wind farm or minimise component loading on downwind turbines, then such control routines can be implemented such that the wind turbine 12a is controlled according to a desired strategy. It is noted, however, that the described method is also applicable during regular operation of a wind turbine (that is not intended for yaw steering) in which a wind sensor of the turbine is poorly calibrated or needs recalibrated.

[0070] Figure 7 schematically illustrates elements of a controller 70 of the upstream wind turbine 12a. The controller 70 may be located in a nacelle of the turbine 12a, for instance. The controller 70 includes one or more computer processors 701 , and may include a data storage or memory 702. The controller 70 is configured to receive input signals 704, e.g. via an input of the controller 70. The controller 70 is configured to output / transmit control signals 705, via an output of the controller 70. The output signals 705 can include a correction / calibration to be applied to a wind direction sensor of the wind turbine 12a.

[0071] The described controller 70 may be in the form of any suitable computing device, for instance one or more functional units or modules implemented on one or more computer processors. Such functional units may be provided by suitable software running on any suitable computing substrate using conventional or customer processors and memory. The one or more functional units may use a common computing substrate (for example, they may run on the same server) or separate substrates, or one or both may themselves be distributed between multiple computing devices. A computer memory may store instructions for performing the methods performed by the controller, and the processor(s) may execute the stored instructions to perform the method. Many modifications may be made to the described examples without departing from the scope of the appended claims.

[0072] In the above-described example, the measured and predicted / estimated relative power output between a pair of wind turbines is considered for a relatively wide range of absolute wind direction values. It may be that wake flow generated by the upwind wind turbine (of the pair of turbines) influences, or is experienced by, the downwind wind turbine (of the pair of wind turbines) for a certain (defined) range / sector of (absolute) wind directions. The analysis performed in the above-described method may in some examples therefore only be performed for a defined range of wind directions in which the downwind turbine is expected to experience the wake flow generated by the upwind turbine.

[0073] As mentioned above, the wake flow generated by a wind turbine may be experienced by a plurality of other wind turbines downwind thereof. Indeed, it may be that for different wind directions, different downwind wind turbines experience the wake flow generated by the upwind wind turbine. For instance, in one example a first downwind turbine may experience wake flow generated by the upwind turbine for a first range of wind directions, and a second downwind turbine may experience wake flow generated by the upwind turbine for a second range of wind directions different from the first range. In some examples, therefore, the above-described method steps may be performed for the first downwind turbine for wind directions in the first range of values and the above-described method steps may be performed for the second downwind turbine for wind directions in the second range of values. It may be that different error values are obtained for the different analyses performed for the first and second downwind turbines. In such a case, the different errors may be combined in a suitable manner, e.g. averaged, in order to obtain an overall error value to be used to calibrate the wind direction sensor of the upwind turbine. This can result in a more accurate calibration of the wind direction sensor.

Claims

CLAIMS1. A method of calibrating a wind direction sensor of a wind turbine, the method comprising: retrieving measurement data to determine measured relative power output indicative of power output of a further wind turbine relative to power output of the wind turbine, as a function of absolute wind direction at the wind turbine, the further wind turbine being downwind of the wind turbine; iteratively repeating steps of: determining predicted power output of the wind turbine as a function of absolute wind direction at the wind turbine; determining predicted wake flow generated by the wind turbine, using a defined wake flow model, as a function of defined yaw offset of the wind turbine; determining predicted power output of the further wind turbine, based on the predicted wake flow generated by the wind turbine, as a function of absolute wind direction; determining predicted relative power output as a function of absolute wind direction, wherein the predicted relative power output is the predicted power output of the further wind turbine relative to the predicted power output of the wind turbine; comparing the measured relative power output against the determined predicted relative power output to determine an error in terms of absolute wind direction; and, updating the defined yaw offset of the wind turbine based on the determined error, until a stop condition is satisfied; and, calibrating the wind direction sensor of the wind turbine based on the determined error.

2. A method according to Claim 1 , wherein the stop condition is satisfied if a difference between the determined error of successive iterations is less than a defined value.

3. A method according to Claim 1 or Claim 2, wherein the stop condition is satisfied if a defined number of iterations has been performed.

4. A method according to any previous claim, wherein comparing the measured relative power output against the determined predicted relative power output comprises: identifying a minimum value of the measured relative power output; and, identifying a minimum valueof the determined predicted relative power output, wherein the error is determined as a difference between the respective minimum values.

5. A method according to any previous claim, wherein comparing the measured relative power output against the determined predicted relative power output comprises: fitting a curve to the measured relative power output; and, matching the fitted curve to a curve describing determined predicted relative power output as a function of absolute wind direction, wherein the error is determined based on the curve matching.

6. A method according to any previous claim, wherein the defined wake flow model comprises a defined velocity deficit model configured to determine a wind velocity deficit downwind of the wind turbine as a result of the generated wake flow.

7. A method according to any previous claim, wherein the defined wake flow model comprises a defined wake deflection model configured to determine a lateral deflection of the generated wake flow, based on the defined yaw offset of the wind turbine.

8. A method according to any previous claim, wherein the defined yaw offset is set to zero for a first iteration of the iteratively repeated steps.

9. A method according to any previous claim, wherein the measured relative power output and the determined predicted relative power output are obtained for a defined sub-range of possible absolute wind directions.

10. A method according to Claim 9, wherein the defined sub-range includes absolute wind directions in which the further wind turbine is predicted to experience wake flow effects as a result of the generated wake flow at the wind turbine.11 . A method according to Claim 9 or Claim 10, the method comprising: retrieving second measurement data to determine second measured relative power output indicative of power output of a second wind turbine relative to power output of the wind turbine, as a function of absolute wind direction, the second wind turbine being downwind of the wind turbine, wherein the second measurement data is obtained for a defined second sub-range of possible absolute wind directions different from the defined sub-range;iteratively repeating steps of, for absolute wind direction values in the defined second subrange: determining predicted power output of the wind turbine as a function of absolute wind direction at the wind turbine; determining predicted wake flow generated by the wind turbine, using the defined wake flow model, as a function of defined yaw offset of the wind turbine; determining predicted power output of the second wind turbine, based on the predicted wake flow generated by the wind turbine, as a function of absolute wind direction; determining second predicted relative power output as a function of absolute wind direction, wherein the second predicted relative power output is the predicted power output of the second wind turbine relative to the predicted power output of the wind turbine; comparing the second measured relative power output against the determined second predicted relative power output to determine a second error in terms of absolute wind direction; updating the defined yaw offset of the wind turbine based on the determined second error, until a second stop condition is satisfied; and, calibrating the wind direction sensor of the wind turbine based on the determined second error.

12. A method according to any previous claim, the method comprising using the calibrated wind sensor to determine relative wind direction at the wind turbine.

13. A method according to Claim 12, the method comprising adjusting an actual yaw offset applied to the wind turbine in accordance with determined relative wind direction.

14. A controller for a wind turbine, the controller being configured to: retrieve measurement data to determine measured relative power output indicative of power output of a further wind turbine relative to power output of the wind turbine, as a function of absolute wind direction, the further wind turbine being downwind of the wind turbine; iteratively repeat steps of: determine predicted power output of the wind turbine as a function of absolute wind direction at the wind turbine;determine predicted wake flow generated by the wind turbine, using a defined wake flow model, as a function of defined yaw offset of the wind turbine; determine predicted power output of the further wind turbine, based on the predicted wake flow generated by the wind turbine, as a function of absolute wind direction; determine predicted relative power output as a function of absolute wind direction, wherein the predicted relative power output is the predicted power output of the further wind turbine relative to the predicted power output of the wind turbine; compare the measured relative power output against the determined predicted relative power output to determine an error in terms of absolute wind direction; update the defined yaw offset of the wind turbine based on the determined error, until a stop condition is satisfied; and, calibrate a wind direction sensor of the wind turbine based on the determined error.

15. A wind turbine comprising a controller according to Claim 14; or, a wind park comprising a controller according to Claim 14, the wind park comprising the wind turbine and the further wind turbine.

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