Monitoring of wind direction measurements in wind parks

FIELD OF THE INVENTION

The present invention relates to a method for monitoring the validity of a calibration of a system parameter by each of a plurality of spatially associated wind turbines. It further relates to a computer program for performing such method and a control system configured to carry out such method.

BACKGROUND

It is important to have an accurate absolute wind direction measurement on each wind turbine in a wind park for the con trol of the wind park and in particular for wake or noise control. Wake effects within wind parks decrease the power production and increase the cost of electricity and, thus, it is important to keep wake effects at a low level. Noise emis sion of wind parks has to be reduced to a minimum volume or directed away from nearby urban areas. The efficiency of both the noise control and the wake control strongly depends on the accuracy of absolute wind direction measurement. The ac curacy of the absolute wind direction measurements has there fore to be maximized in order to ensure that negative wake effects and noise emission can be reduced significantly.

A calibration can be performed in order to improve the accu racy of the detection of the absolute wind direction. Figure 1 shows a set of schematic diagrams illustrating data plots related to such a calibration method. The calibration method is based on an alignment of wake profiles generated by a measured power ratio 103 and a respective predicted power ra tio 104. The predicted power ratio 104 is predicted by a wake model based on information of the layout of the wind park and measured data, e.g. the non-calibrated absolute wind direc tion. The first data plot of figure 1 shows the wake profiles before calibration 110 and the second data plot shows the wake profiles after calibration 120. The vertical axis 101 of the first and second data plots represents the power ratio of the production power of two spatially associated wind tur bines and the horizontal axis 102 represents the absolute wind direction from 0 to 360 degrees. For the calibration, the wake profile generated by the predicted power ratio 104 is shifted by the application of an optimization or brute force method to approximately align it with the wake profile generated by the measured power ratio 103. The measured dips 105 and the predicted dips 106 are aligned therefor by adapt ing a correction value which is added to the non-calibrated absolute wind direction. The required data for the measured power ratio 103 enabling such a calibration method has to be collected over a time period of several weeks (at least 60 days). After an initial calibration, the measured absolute calibrated wind direction of a respective wind turbine can abruptly become invalid again during its operation. From this moment, new data has to be collected over the time period of several weeks in order to be able to detect such a change and to recalibrate and correct the absolute wind direction. Dur ing this time period of several weeks, the absolute wind di rection is inaccurate and neither a reliable wake control nor noise control, nor wind park analysis can be performed.

As indicated by the above explanations, the calibration meth od requires a complex modelling of the wake model, rather high computation power for aligning the measured and predict ed wake profiles by an optimization method, and collecting data over a long period of time, which results in a long time required for detecting an invalid calibration and, hence, a long reaction time until the invalid calibration is correct ed.

The document US 2015/0345476 A1 relates to a method for re calibrating nacelle-positions of a plurality of wind turbines in a wind park. The method includes identifying two associat ed wind turbines included within the wind park, determining a plurality of predicted wake features for the associated wind turbines, determining a plurality of current wake features based on historical performance data that is related to the associated wind turbines, identifying a variance between the predicted and the current wake features, and determining a recalibration factor based on the identified variance for at least one of the associated wind turbines.

SUMMARY

Accordingly, there is the need to mitigate at least some of the drawbacks mentioned above and to provide a method for monitoring the validity of a calibration of a system parame ter in a fast, reliable and efficient way.

This need is met by the features of the independent claims. The dependent claims describe embodiments of the invention.

According to an embodiment of the invention, a method for monitoring the validity of a calibration of a system parame ter is provided. A calibrated system parameter is generated based on the calibration by each of a plurality of spatially associated wind turbines of a wind park. The plurality of spatially associated wind turbines comprises a first wind turbine and a second wind turbine. The method comprises sub tracting from a first signal representing the calibrated sys tem parameter measured at the first wind turbine a second signal representing the calibrated system parameter measured by the second wind turbine in order to generate a difference signal, processing the difference signal by a function based on a stochastic model to generate a decision data signal and determining, based on the decision data signal, if the cali brated system parameter of at least one of the first wind turbine and the second wind turbine is based on an invalid calibration .

Preferably, the first signal and the second signal represent the same calibrated system parameter. Such method may allow, based on the generated decision data signal, to immediately detect an invalid calibration of the calibrated system parameter, which may be the measured abso lute wind direction, of one or more wind turbines and to cor rect such a corruption. A delay or a reaction time of several weeks does not occur since collection of data over a longer time period is not necessary. The method may be fully data driven, it may be an automatic software solution requiring no additional hardware, e.g. additional sensors in order to pro vide a redundant measurement of the calibrated system parame ter. Since less data has to be processed by the proposed so lution and no optimization method may need to be applied, performing the method may also require less computation pow er. Detecting an incorrectly calibrated system parameter in such a fast and efficient way has consequently a positive ef fect on the wake control resulting in a higher annual energy production, on the noise control resulting in a more effi cient noise adaption, which is in particular demanded for on shore locations, and on the data analysis on wind park level, e.g. for the validation of wind turbine loads in wake condi tions.

It should be clear that the calibrated system parameter is not limited to the measured absolute wind direction. The herein described methods may be applied to monitor other sys tem parameters and may, accordingly, be applied to monitor the validity of the respective calibration. The examples dis closed herein are related to the system parameter 'wind di rection'. However, the method may be performed corresponding ly with respect to any calibrated system parameter that is available at at least two wind turbines of the plurality of spatially associated wind turbines and that is based on the calibration that is to be monitored. A system parameter may be a parameter that has an influence on the (underlying) sys tem, e.g. a parameter that has an influence on a wind turbine or a wind park. A system parameter may in particular be an environmental parameter. For example, the calibrated system parameter may be a system parameter that is representative of an environmental influence, e.g. air humidity or wind speed. As a further example, the calibrated system parameter may be a system parameter related to the mechanics of structurally identical wind turbines and that is relevant for the motion control of the structurally identical wind turbines (e.g. a miscalibrated mechanical system parameter in the control ar chitecture of a first wind turbine may respond with a differ ent motion to a respective motion command than a second wind turbine controlled by a control architecture comprising the correctly calibrated system parameter).

It should further be clear, that the calibrated system param eter that is generated based on the calibration by each of the plurality of spatially associated wind turbines of the wind park may be the same calibrated system parameter for at least a portion or all of the plural spatially associated wind turbines.

In an embodiment, the method may further comprise measuring for each of at least two or all of the plural associated wind turbines a signal that represents the calibrated system pa rameter at the respective wind turbine.

The stochastic model may be based on stochastic characteris tics generated from empirical and/or historical data of the difference signal, e.g. the expected value, the standard de viation and/or the variance. The stochastic model may further involve the stochastic characteristics in a mathematical rep resentation of an assumed probability distribution, e.g. the mathematical representation of the normal distribution.

A plurality of spatially associated wind turbines may be a group of spatially associated wind turbines. The wind tur bines of the group may be positioned such that effects on a single wind turbine affect at least a portion of the other wind turbines of the group in a similar or same way. An exam ple is that the wind turbines of the group are positioned so close to each other that approximately the same wind direc tion is measured by each wind turbine.

The method may be performed for each wind turbine of the group by forming a pair of this wind turbine with another wind turbine of the group.

The group of spatially associated wind turbines may comprise a wind turbine of the group and n-1 wind turbines of the wind park closest to the wind turbine, wherein n is the number of wind turbines in the group. This means the n-1 wind turbines of the wind park are positioned in the smallest distance rel ative to the n-th wind turbine.

The group of spatially associated wind turbines may alterna tively comprise a wind turbine of the group and n-1 wind tur bines of the wind park, wherein n is the number of wind tur bines in the group, and wherein the measured absolute wind direction of the n-th turbine correlates best to the measured absolute wind directions of the n-1 wind turbines of the wind park. Preferably, the measured absolute wind direction of the n-th turbine correlates best to the measured absolute wind directions of the n-1 wind turbines of the wind park, wherein the n-1 wind turbines have the smallest absolute expected value for the measured absolute wind direction difference relative to the n-th turbine or, wherein the n-1 wind tur bines have the smallest standard deviation for the measured absolute wind direction relative to the n-th turbine.

The calibrated system parameter may be an absolute wind di rection that is based on a measurement and a calibration. The calibration may be a directional calibration, e.g. a North calibration. The measured calibrated absolute wind direction of a wind turbine may be based on a measurement of the wind direction and on a measured nacelle angular position of that wind turbine. A sensor for measuring the wind direction may for example be mounted to the nacelle. The absolute wind direction may be the wind direction rela tive to North. The wind direction (relative wind direction) may be measured for a wind turbine relative to the orienta tion (angular position) of the nacelle thereof, and the abso lute wind direction may be derived from such measurement. The absolute wind direction is measured in accordance with the meteorological wind direction, wherein the meteorological wind direction counts in clockwise direction starting from North and comprises a range from 0 to 360 degrees.

The measuring of the calibrated system parameter may be per formed such that the parameter is directly measured or indi rectly measured and further processed in order to generate the parameter. It is in particular possible that a relative measured signal is used to approximate the respective abso lute signal by adding an offset to the relative measured sig nal, which may generate the parameter. For example, a meas ured relative wind direction may be measured (e.g. in de grees) by a wind turbine and added to the angular position (e.g. in degrees) of the nacelle of the wind turbine in order to generate an absolute wind direction.

The stochastic model may comprise an expected value for a difference of the calibrated system parameter measured at the first wind turbine and the second wind turbine. Processing the difference signal by the function based on the stochastic model may comprise comparing the difference signal to the ex pected value.

The decision data signal may comprise an indication if one of the first wind turbine or the second wind turbine is based on an invalid calibration. It may for example comprise a result of the comparison. In a simple example, it may comprise a Boolean data type which is true to indicate that the first or second wind turbine is based on an invalid calibration or is false if not, or it may comprise a deviation derived from the comparison. It may further comprise corresponding information about other pairs of wind turbines from the plurality of the spatially associated wind turbines.

The stochastic model may further comprise a limit for an al lowable deviation from the expected value. Comparing the dif ference signal to the expected value may comprise determining if the deviation of the difference signal from the expected value exceeds the limit.

The limit may define a confidence interval and the confidence interval may include a range of values of the difference sig nal, in which a value of the difference signal is expected (assuming a correct calibration).

The decision data signal may comprise information indicating if the deviation of the difference signal from the expected value exceeds the limit.

In particular, if the decision data signal indicates that the deviation of the difference signal from the expected value exceeds the limit, it is determined that the calibration of the system parameter of at least one of the first wind tur bine and the second wind turbine is invalid.

In an embodiment, the expected value is generated by monitor ing the difference of the calibrated system parameter meas ured at the first wind turbine and the second wind turbine over a predetermined period of time and averaging the moni tored difference over the period of time. For generating the expected value, the system parameter is measured at the first wind turbine and the second wind turbine, e.g. when both are correctly calibrated. The monitored difference may comprise historically monitored difference signal data. The predeter mined period is preferably 0.5 to 3 months, e.g. 1 to 2 months.

Generating the expected value in such a way allows a high ro bustness of the detection of an invalid calibration since the empirical data contains system information of the correlation of the first and second wind turbine in a correctly calibrat ed state.

The limit may be determined based on a standard deviation of the difference signal around the expected value. It should be clear that the standard deviation is generated from the same data as the expected value. The expected value and the stand ard deviation associated with the first and second wind tur bines, which form a first pair of wind turbines, are a first pair of stochastic characteristics being comprised by a set of stochastic characteristics, wherein the set of stochastic characteristics comprises further pairs of stochastic charac teristics, wherein each is associated with a combination of two wind turbines of the plurality of spatially associated wind turbines, the combinations forming further pairs of wind turbines. Preferably the number of combinations forming fur ther pairs of wind turbines is n(n-l) or n(n-l)/2, wherein n is the number of single wind turbines of the plurality of spatially associated wind turbines.

The limit may further be determined by multiplying the stand ard deviation by a predetermined scaling factor. The scaling factor is preferably selected from the range of 1 to 4, pref erably 1.2 to 3, e.g. 1.5 to 2. The scaling factor may be de rived from a probability value, wherein the probability value represents the probability of a value of the difference sig nal of being or not being in the limit assuming a normal dis tribution. Such a conversion from the probability value to the scaling factor allows a tuning of the limit.

The limit may comprise an upper limit and a lower limit. The upper limit may be determined by the formula m + zs and the lower limit may be determined by the formula m - zs, wherein m is the expected value of the difference signal, s is the standard deviation of the difference signal and z is a scal ing factor. Considering a scaled standard deviation around the expected value allows a more precise configuration of the limit and accordingly reduces incorrectly detected invalid calibra tions, for example due to measured outlier values. Using a scaling factor further increases the flexibility of the meth od.

According to an embodiment, processing the difference signal by the function based on the stochastic model further com prises applying a filter to the difference signal to generate a filtered difference signal, wherein the filtered signal is compared to the expected value. It should be clear that ap plying a filter to the difference signal may also be per formed by applying the filter to the measured signals and forming the difference thereafter, resulting in the filtered difference signal.

The filter may be a low-pass filter. The low-pass filter is preferably a moving average filter. The applying of the mov ing average filter may calculate a moving average over a pre determined time period and in particular over a time period of 1 day. The filter may also be a simple gain element scal ing the input signal by a given factor and the given factor may even be equal 1, it is however preferably smaller or larger than 1.

According to an embodiment, it is determined that at least for one of the first and second wind turbines, the calibrated system parameter of which is based on an invalid calibration, the method further comprises identifying for which of the first and the second wind turbines the calibrated system pa rameter is based on an invalid calibration, i.e. is an inval- idly calibrated system parameter.

The determining if the calibrated system parameter is based on an invalid calibration may be performed for each of plural pairs of said wind turbines. The method may further comprise identifying, based on said determining, a reference wind tur- bine the calibration of the system parameter of which is not invalid. The method may further comprise, if for at least one of the first and second wind turbine it is determined that the calibration of the system parameter is invalid, comparing the measured calibrated system parameter of at least one of the first and second wind turbine to the measured calibrated system parameter of the reference wind turbine to determine for which of the first and second wind turbine the calibra tion is invalid.

It should by clear that said determining may also include said subtracting for generating the difference signal and said processing for generating the decision data signal for each of the plural pairs of wind turbines.

Said plural pairs of wind turbines may comprise for each wind turbine of a group of wind turbines pairs of the wind turbine with each other wind turbine of the group. Identifying the reference wind turbine may comprise determining for which wind turbine of the group the decision data signal indicates for the largest number of pairs that the calibrated system parameter is not based on an invalid calibration.

For example for a group of three wind turbines, one of which has an invalid calibration, the decision data signal may in dicate for two of them that the calibration is valid, and ei ther one of them or both may be selected as the reference wind turbine. The decision data signal of the other wind tur bine might then indicate an invalid calibration when compared to the reference wind turbine (i.e. for the respective pair), so that it can be determined that it is this wind turbine for which the calibration is invalid.

Alternatively or additionally, identifying the reference wind turbine may comprise determining for which wind turbine of the group the decision data signal indicates for the largest number of pairs that the calibrated system parameter is based on an invalid calibration and selecting a different wind tur bine of the group as the reference wind turbine.

The group of wind turbines may comprise such a wind turbine as indicated above.

Doing so, the validity of the calibration of the system pa rameter of each wind turbine from the plurality of spatially associated wind turbines is monitored. As soon as an invalid ity of a calibration is determined for one or more wind tur bine pairs, the reference wind turbine can be used in order to identify which wind turbine of each pair is based on an invalid calibration.

According to another embodiment, the method further compris es, if it is determined that the calibrated system parameter of at least one of the first wind turbine and the second wind turbine is based on an invalid calibration, i.e. is an inval- idly calibrated system parameter, the recalibrating of the invalidly the calibrated system parameter. For example, the recalibrating may comprise for each invalidly calibrated sys tem parameter, correcting the invalidly calibrated system pa rameter by applying a correction value based on an average of a series of deviations. The series of deviations may comprise at least one deviation between the invalidly calibrated sys tem parameter and a calibrated system parameter of at least one of the plurality of wind turbines the calibration of the system parameter of which is not invalid.

Recalibrating may additionally or alternatively comprise re setting a reference for the calibrated system parameter based on a deviation between the invalidly calibrated system param eter and a calibrated system parameter of at least one of the plurality of wind turbines the calibration of which is not invalid. For example, a value of a certain angle of the wind sensor may be set (e.g. relative to North or relative to the nacelle), and/or a value of a certain angle of nacelle angu lar position may be set, e.g. relative to North. Recalibrating may for example comprise for each invalidly calibrated system parameter applying the correction factor to a yaw controlling system of the respective first or second wind turbine. Preferably, applying the correction factor to the yaw controlling system comprises applying the correction factor to the yaw encoder signal.

The method may further comprise outputting a series of moni tored calibrated system parameters, wherein one monitored calibrated system parameter is associated with one of the plurality of spatially associated wind turbines and providing the series of monitored calibrated system parameters to a wind park control and in particular to a wake control or noise control.

According to an embodiment of the invention, a computer pro gram for monitoring the validity of a calibration of a system parameter individually generated by a plurality of spatially associated wind turbines is provided. The computer program comprises control instructions which, when executed by a pro cessing unit, cause the processing unit to perform any of the herein described methods for monitoring the validity of a calibration of a system parameter individually generated by a plurality of spatially associated wind turbines. The computer program may be provided on a volatile or non-volatile storage medium or data carrier.

According to an embodiment of the invention, a control system for monitoring the validity of a calibration of a system pa rameter individually generated by a plurality of spatially associated wind turbines is provided. The control system is configured to perform any of the herein described methods. By such control system, advantages similar to the one outlined further above may be achieved. The control system may include respective sensors for measuring the system parameter, e.g. a wind sensor and/or an encoder of the yaw drive of a wind tur- bine. The control system may further include any of the ele ments described herein with respect to the method.

The control system may for example include a processor and a memory, the memory storing control instructions which when executed by the processor of the control system, cause the control system to perform any of the methods described here in.

It is to be understood that the features mentioned above and those yet to be explained below can be used not only in the respective combinations indicated, but also in other combina tions or in isolation, without leaving the scope of the pre sent invention. In particular, the features of the different aspects and embodiments of the invention can be combined with each other unless noted to the contrary.

BRIEF DESCRIPTION OF THE DRAWINGS

The forgoing and other features and advantages of the inven tion will become further apparent from the following detailed description read in conjunction with the accompanying draw ings. In the drawings, like reference numerals refer to like elements.

Fig. 1 is a set of schematic diagrams illustrating data plots related to a calibration method that uses a wake pro file for calibration.

Fig. 2 is a schematic drawing illustrating nacelle posi tion measurements of a group of spatially associated wind turbines of a wind park before and after absolute wind direc tion calibrations. Fig. 3 is a schematic flow diagram describing a method of monitoring the validity of a calibrated system parameter ac cording to an embodiment.

Fig. 4 composed by figures 4a and 4b is a set of schematic diagrams illustrating difference signals of measured nacelle positions of pairs of wind turbines from a group of spatially associated wind turbines.

Fig. 4a is the first part of figure 4.

Fig. 4b is the second part of figure 4.

Fig. 5 is a schematic drawing showing a control system for monitoring the validity of a calibrated system parameter ac cording to an embodiment.

DETAILED DESCRIPTION

In the following, embodiments of the invention will be de scribed in detail with reference to the accompanying draw ings. It is to be understood that the following description of the embodiments is given only for the purpose of illustra tion and is not to be taken in a limiting sense. It should be noted that the drawings are to be regarded as being schematic representations only, and elements in the drawings are not necessarily to scale with each other. Rather, the representa tion of the various elements is chosen such that their func tion and general purpose become apparent to a person skilled in the art. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, un less the context clearly indicates otherwise. The terms "com prising," "having," "including," and "containing" are to be construed as open-ended terms (i.e., meaning "including, but not limited to,") unless otherwise noted.

Figure 2 is a schematic drawing illustrating nacelle position measurements 210, 220 of a group 200 of spatially associated wind turbines of a wind park before and after absolute wind direction calibrations. The calibration of the absolute wind direction aims at providing the respective wind turbine with an absolute measure of the wind direction with respect to the geographical orientation (e.g. North is 0 degrees). Both states of the nacelle position measurements 210, 220 are de picted in a respective diagram comprising a horizontal east ing axis 205 and a vertical northing axis 204. Both axes are scaled in kilometers. The group 200 of spatially associated wind turbines is comprised in a wind park. It should be clear that the wind park may comprise a second or further of such groups of wind turbines. Each wind turbine 203 of the group 200 of spatially associated wind turbines is associated with a wind turbine controller 202 controlling the respective wind turbine 203 and the wind park comprises a wind park control ler 201 controlling the wind park (see figure 5). However, for the sake of simplicity, figure 2 shows only one wind tur bine controller 202. The wind turbine controller 202 compris es a control system, e.g. a yaw control system, which is able to rotate the nacelle of a respective wind turbine towards a direction based on the measured (calibrated) absolute wind direction. Since the measured (calibrated) absolute wind di rection of a single wind turbine is based on its measured na celle position, the quality of the North calibration can be derived from the conformity of the nacelle position measure ments of the group 200. It can be seen in the right diagram 220 of figure 2 that after performing an initial North cali bration of the measured absolute wind direction by each wind turbine 203 in the group 200, the nacelle position measure ments are generally better aligned with each other. Accord ingly, the measured calibrated absolute wind directions are also better aligned. It can also be seen by comparing the na celle position measurements of the wind turbines after cali bration 220 and the nacelle position measurements of the wind turbines before calibration 210 that the variation of the na celle position measurements of the wind turbines after cali bration 220 is significantly reduced, but is still existent. The difference between the calibrated absolute wind direction is measured by each of a pair of wind turbines 203 of the group 200 and can be stochastically characterized. For each pair from the group 200 a 'bias' (regarded as expected value m) and variance s ^L 2 /standard deviation s can be derived to stochastically model the respective measurement difference. Figure 2 shows a number n=ll wind turbines 203 and indicates exemplarily three pairs 233, 234, 235 from a total of 55 pos sible pairs (n(n-l)/2). In the right-hand drawing, the sto chastic characteristics 230, 231, 232 describing the differ ence signal between each pair 233, 234, 235 are indicated by arrows. Pair 233 comprises a first wind turbine 241 and a second wind turbine 242. The stochastic characteristics 230, 231, 232 are mΐ and ol for the first pair 233, m2 and o2 for the second pair 234, and m3 and o3 for the third pair 235. If the sequence of the two values to be subtracted is taken into account, the stochastic characteristics of n(n-l) pairs may be calculated, which is 110 pairs in the given example. The expected value for this difference is related to the average non-uniformity of the inflow of wind into the wind park, and possibly remaining small offsets in the North calibration.

The variance may be related to a local turbulence and/or oth er spatial and temporal variation of the wind field.

The variance and the expected value of such a difference sig nal typically increase with the distance that wind turbines from each other. The difference signal can be compared to a limit in which the difference is expected. Such comparison can be used in order to detect an invalid calibration. The limit of the difference signal is therefor based on the sto chastic characteristics defining a range of values (confi dence interval) in which a value of a respective difference signal is expected. As outlined above, the stochastic charac teristics for one pair from the group of spatially associated wind turbines differ from those of another pair and thus the stochastic characteristics may be generated individually for each pair from the group 200. The stochastic characteristics are derived from empirical da ta sets. The expected value of the difference signal of the measured absolute wind directions of one pair (mean differ ence of the measured absolute wind direction) is estimated by averaging the difference between two measured correctly cali brated absolute wind directions over a determined longer pe riod, e.g. 1-2 months. Based on the same data set, variance and standard deviation can be derived. This is for example performed by calculating the mean absolute deviation from the mean difference of the measured calibrated absolute wind di rection. The initial calibration may for example be performed as described above with respect to figure 1.

Figure 3 is a schematic flow diagram describing a method 300 for monitoring the validity of a calibrated system parameter of the group 200 of spatially associated wind turbines ac cording to an embodiment. Each of the n wind turbines 203 of the plurality 200 of spatially associated wind turbines (re ferring to figure 2, n is equal to 11) individually measures and provides the calibrated system parameter. The n calibrat ed system parameters 301, 302, 30N, which are associated with the first, second and n-th wind turbine 203, are indicated in figure 3 using the solid line arrows. The calibrated system parameter is in the shown example the measured absolute cali brated wind direction. The n measured absolute calibrated wind directions are combined to a set of calibrated system parameters 304. It should be clear that the invention is not limited to such implementation using a set or array. In this case the sets are only used for the ease of the explanation of figure 3 and to emphasize that a portion of the depicted signal flow is multidimensional and not for scalars or one dimensional numbers only. A set is generally represented in figure 3 by using a dashed line arrow. The set of calibrated system parameters 304 comprises n elements.

In step S310, for each pair from the set of calibrated system parameters 304 the difference signal is generated by sub tracting the measured calibrated system parameter of one tur- bine from that of the other. If the sequence of two signals to be subtracted is considered, the result is a set of dif ference signals 311 comprising n(n-l) elements. If for exam ple a group consists of 5 spatially associated wind turbines, the set of calibrated system parameters 304 comprises 5 ele ments and the set of difference signals 311 comprises 20 ele ments (each of the 5 elements combined with the 4 other ele ments). It should by clear that it is not necessary to use each possible pair, but the method may equally be used with a subset of possible pairs.

In step S320 the set of difference signals 311 is processed by a function based on a stochastic model and generates a de cision data signal 321. The decision data signal 321 compris es the information if at least one of the wind turbines of each pair is based on an invalid calibration. In a simple ex ample, the decision data signal may comprise a set of true/false values, e.g. represented as an array of Booleans. Each true/false value of the set may be associated with one respective element from the set of difference signals 311 and, accordingly, is associated with the respective pair of wind turbines. Further, each true/false value may represent a true value if at least one of the respective pair of wind turbines is based on an invalid calibration or a false value if not.

In order to generate the decision data signal 321, each dif ference signal of the set of the difference signals is com pared to a limit which is individually generated based on em pirical data for the respective pair of wind turbines. Each limit defines a confidence interval in which a value of the difference signal of a pair of wind turbines is expected. If it is determined S330 based on the decision data signal 321 that the deviation of a difference signal exceeds such a lim it, it is determined that the calibration of the system pa rameter of at least one of the wind turbines of a respective pair of wind turbines is invalid. In order to determine the limit for each pair of wind tur bines, the expected value and standard deviation of the re spective difference signal is calculated based on monitored data of the respective difference signal. The monitored data is generated by monitoring the difference signal of a wind turbine pair in operation over a period which for example lasts for 1-2 months. It is ensured during the period that the calibrated system parameter measured by each of the pair of wind turbines is correctly calibrated (e.g. by performing the measurement directly after a calibration carried out in accordance with the method of figure 1). The result is a set of expected values 313 and a set of standard deviations 314 which can be stored and later be provided by a data source 391. The data source may be a data base, preferably stored on a wind park server comprised by the wind park. The limit for each pair is then determined based on the standard deviation of the difference signal around the expected value.

The mathematical representations of the limit described here inafter are exemplary given for the first wind turbine 241 and the second wind turbine 242 forming pair 233. It should be clear that the equations can be applied to any other pair of wind turbines from the group of spatially associated wind turbines in a corresponding way. The mathematical representa tion of the limit can be given for pair 233 by m12 - s12 < cspl - csp2 < m12 + s12, (eq. 1).

In equation 1 m12 is the expected value of the calibrated system parameter 2 (csp2) measured at the first wind turbine 241 subtracted from the calibrated system parameter 1 (cspl) measured at the second wind turbine 242 and ol2 is the stand ard deviation of the measured calibrated system parameter 2 (csp2) subtracted from the measured calibrated system parame ter 1 (cspl). In an embodiment, the standard deviation may further be multiplied by a scaling factor z which leads to m!2 - s!2*z < cspl - csp2 < m!2 + s12*z, (eq. 2). Such scaling factor may be the same for all pairs of wind turbines or determined individually. Scaling factor z allows a more specific tuning of the confidence interval. In another embodiment, each of the difference signals may further be shifted by the respective expected value and normalized by the respective standard deviation. It is then determined if each shifted and normalized difference signal exceeds its re spective scaling factor. This leads for the given example of the confidence interval to

-z < ((cspl - csp2) - m12)/ s12 < +z, (eq. 3).

The mathematical representation of the limit according to equation 3 is advantageous since the expected value and standard deviation differs between the single pairs of wind turbines. The process of shifting and normalizing however re stricts the limit of each pair to the scaling factor z chosen for that pair. As outlined above, the scaling factor z may be chosen individually for each pair of wind turbines.

However, in order to provide representation of scaling factor z that is more easily understood, it is also conceivable that a function 392 may be used which converts a probability value p to scaling factor z. The probability value may represent the probability p that a value of the difference signal does not exceed the limit, or the probability q=l-p that a value of the difference signal exceeds the limit assuming a normal distribution. The limit is then set by scaling factor z such that it comprises or does not comprise a value of the differ ence signal for the given probability. Such function 392 may be based on the inverse function of the cumulative distribu tion function ifcdf of the normal distribution and be imple mented by the equation z = 2*ifcdf((p+1)/2) = 2*ifcdf(l-q/2), (eq. 4).

Table 1 shows z values derived by equation 4 and given p, q. Table 1: exemplary values for z, p and q

P q z

0.50 0.50 0.674

0.90 0.10 1.645

0.99 0.01 2.576

It can thus be seen how the probability changes with changing the scaling factor z, and the scaling factor z may be chosen in accordance with the desired probability.

In another embodiment, a filter is applied to the difference signal to generate a filtered difference signal and the fil tered signal is compared to the limit. Starting for example from equation 2 this leads to m12 - s12*z < F(cspl - csp2) < m12 + s12*z, (eq. 4), wherein F represents the filtering. Such filter may be a low- pass filter in order to smooth out outlier of the difference signal which are not due to an invalid calibration. The low- pass filter is preferably a moving average filter. The apply ing of the moving average filter calculates a moving average over a predetermined time period and in particular over a time period of 0.5-2 days, e.g. 1 day. The filter may also be a simple gain element scaling its input signal by a given factor and the given factor may even be equal to 1.

The input data of the filter may be restricted to such data which passes a given condition, e.g. a wind direction sensor status which is non-faulty or a wind turbine that is operat ing without error mode.

It is also possible that it is not the difference which is filtered but both calibrated system parameters measured by a pair of wind turbines before generating the difference sig nal. In such embodiment the difference of the filtered meas ured calibrated system parameters is compared to the limit, which is represented by equation 5. 11 < FI(cspl) F2(csp2) < 12, (eq. 5), wherein 11 is the lower limit and 12 is the upper limit. Such filters FI and F2 may be but are not limited to a low-pass filter. However, if the same low-pass filter is used for fil tering the first and second signal (FI and F2 are equal to F) it can be shown that

11 <

Fl(cspl) - F2(csp2) = F(cspl) - F(csp2) = F(cspl - csp2)

£ 12, (eq. 6).

Thus, if 11 and 12 are aligned in accordance with equation 4, equation 6 is equal to equation 4.

If the difference signal of a pair of wind turbines exceeds the respective limit according to any of the outlined embodi ments, information of such exceeding is stored in the deci sion data signal 321.

After it is determined (S330) based on the decision data sig nal that at least one of the measured calibrated system pa rameters of a pair of wind turbines is based on an invalid calibration, it is identified (S340) for which wind turbine of the pair the calibration is invalid. Such identifying S340 is necessary, since an exceeding of the limit of the differ ence signal associated with a pair of wind turbines does not reveal which of both turbines is based on an invalid calibra tion or if even both turbines are based on an invalid cali bration. In a first step, a reference wind turbine the cali bration of the system parameter of which is not invalid is identified.

In an embodiment, the reference wind turbine is determined by determining for which wind turbine of the group of wind tur bines the decision data signal indicates for the largest num ber of pairs that the calibrated system parameter is not based on an invalid calibration (difference does not exceed the limit). For example, it may be counted for each wind tur bine in the group the number of wind turbines a wind turbine is consistent with (i.e. for which the measured difference signal is within limits). The wind turbine which is con sistent with most other wind turbines is identified as the reference wind turbine. If there are a plurality of reference wind turbine candidates all having a calibration that is con sistent with the greatest number of other wind turbines, a random choice may be applied. The identifying S340 further comprises a second step of comparing the measured calibrated system parameter of both wind turbines of the determined pair to the measured calibrated system parameter of the reference wind turbine to determine for which of both wind turbines of the determined pair the calibration is invalid. For example, if the first (or second) wind turbine of the determined pair is consistent with the reference wind turbine (difference does not exceed the limit) or is in fact the reference wind turbine itself, then the system parameter measured by the first (or second) wind turbine is most likely not corrupted. If the first (or second) wind turbine of the determined pair is not consistent with the reference wind turbine (difference exceeds the limit), the first (or second) wind turbine is likely based on an invalid calibration.

The above determination of which wind turbine has an invalid calibration may be improved by involving information about that wind turbine which is inconsistent with most other wind turbines and/or by identifying at least a second reference wind turbine (chosen by the second greatest number of wind turbines that wind turbine is consistent with) the system pa rameter of which may be additionally compared to those of the determined pair of wind turbines.

The result of the identifying S340 is a set of identified wind turbines 341 the measured system parameter of which is based on an invalid calibration, i.e. is an invalidly cali brated system parameter. It should be clear that such a set 341 may comprise only one identified wind turbine. Such set 341 may be communicated in one embodiment to the wind park controller 201 and further processed, e.g. displayed via a human machine interface. In another embodiment, step S350 is further performed. In step S350, for each wind turbine from the set of identified wind turbines 341, the invalidly cali brated system parameter is recalibrated. The calibrated sys tem parameter may be corrected by applying a correction fac tor based on an average of a series of deviations between the measured invalidly calibrated system parameter and the meas ured correctly calibrated system parameters. The correction factor may for example be applied to the yaw controlling sys tem of that turbine the measured calibrated system parameter of which is invalid. Since the yaw controller system rotates the position of the nacelle in a direction based on the wind direction relative to the position of the nacelle the correc tion factor may in particular be added to the yaw encoder signal. Additionally or alternatively, the correction factor may also be applied to the measured wind direction measured by a wind sensor relative to the yaw drive, or to a wind di rection measured by a wind sensor independent of any yaw drive (e.g. a wind sensor not mounted to the nacelle). In serting the correction factor in such almost non-invasive way allows implementing the method in a running control system with low effort and by a simple retrofitting process.

Before applying the correction factor, additional conditions may be checked in order to prevent an undesired yaw misalign ment, e.g. if the North calibration offset was manually changed or the sensor might be twisted. In the case of a twisted sensor, a warning might rather be output than an au tomatic correcting performed. An alternative implementation may in addition or instead of applying a correction factor reset the reference for the invalidly calibrated system pa rameter, e.g. by setting a certain angle of the wind sensor that corresponds to North. The set of corrected calibrated system parameters 351 may be further processed and is for example communicated to the wind park controller 201.

Figure 4 is a set of twenty schematic diagrams illustrating difference signals of the measured nacelle positions of pairs of wind turbines from a group of spatially associated wind turbines. Figure 4 is composed by figures 4a and 4b, wherein both figure 4a and figure 4b are aligned to each other by the vertical dashed line. The measured absolute wind direction of a wind turbine may be derived from the position of the na celle of the wind turbine, which is why the usage of the na celle position is possible. However, it is more efficient to compare wind direction signals in order to allow yaw offsets for e.g. wake steering control. Referring to figure 3, the depicted set of difference signals 311 in figure 4 is an ex ample for the result of method step 310. In the given exam ple, the group comprises five spatially associated wind tur bines. The sequence of two signals to be subtracted from each other is considered and thus the set of difference signals comprises n(n-l) = 20 signals. The monitored pairs of wind turbines generating the set of difference signals 311 can al so be seen in table 2. By the use of symmetry, the infor mation contained in the n(n-l) difference signals may also be derived from the n(n-l)/2 difference signals associated only with unique pairs (no consideration of the subtraction se quence) of turbines. The position in the table corresponds to the position of the respective diagram showing the respective signal.

Table 2: Possible combinations for generating a set of dif ference signals given a group of five spatially associated wind turbines (Wl, W2, W3, W4, W5)

W3-W4 W3-W2 W3-W5 W3-W1

W4-W3 W4-W2 W4-W5 W4-W1

W2-W3 W2-W4 W2-W5 W2-W1

W5-W3 W5-W4 W5-W2 W5-W1

W1-W3 W1-W4 W1-W2 W1-W5 Each diagram in figure 4 shows a difference signal shifted by the respective expected value and normalized by the respec tive standard deviation according to equation 3. The expected value and the standard deviation of each pair are individual ly derived based on the respective empirical data for each pair. The scaling factor z is set in this example equal to the value which corresponds to a value p 0.95 and a value q 0.05. The horizontal axis describes the time and is shown over a period of one year which is indicated by four quar ters. The vertical axis represents the value for the respec tive shifted (i.e. the expected value is subtracted) and nor malized (by the standard deviation) difference signal; a unit of the values of the vertical axis can thus not be given (per unit). Although wind turbine W5 is based on an invalid cali bration, it can be seen that not all difference signals based on the invalid calibrated system parameter of wind turbine W5 are detected. The detected rising edges 401 exceeded the up per limit (positive number two), the detected falling edges 402 exceeded the lower limit (negative number two) but the change of the undetected rising edge 401a and the undetected falling edge 402a does not exceed the upper and lower limit, respectively. The detected difference signals do not indicate which turbine is based on an invalid calibration. However, the result of applying the step of identifying S340 clearly indicates that wind turbine W5 is based on an invalid cali bration.

Figure 5 is a schematic drawing showing a control system ac cording to an embodiment and illustrating a signal flow chart for an implementation of the method of figure 3 for monitor ing the validity of a calibrated system parameter according. The control system may include the wind park controller 201, which may be implemented as a wind park server 523. It may communicate with or include the wind turbine controllers 202. The wind park controller may for example comprise a processor and a memory that stores control instructions which when car ried out by the processor cause the wind park controller to perform any of the methods described herein. The processor may be any kind of processor, such as a microprocessor, an application specific integrated circuit, a digital signal processor or the like. The memory may include volatile and non-volatile memory, in particular RAM, ROM, FLASH-memory, hard disc drives and the like.

The method may for example be implemented on the wind park server 523. The wind park server 523 receives by an upload process 525 at North calibration upload user interface 520 a North calibration configuration file 524 comprising data for an initial calibration. The data for the initial calibration is generated by a data-driven North calibration tool 526 com prised by a PC/VDI application 529. The data-driven North calibration tool 526 exchanges information with wake model 527 and receives data from wind farm data base 528. Generat ing the data for the initial calibration may be based on the prior art calibration method as outlined in the background section. The PC/VDI application may form part of the control system.

After the initial calibration is applied the method for moni toring is enabled. The wind park North calibration monitor 516 continuously collects, e.g. one time per 10 minutes, a set of wind direction statistical data 521 for each pair of wind turbines being monitored. The statistical data 521 com prises the set of calibrated system parameters measured for that sample. The statistical data may be stored in the wind park server data base 522 but can also be received directly from each monitored wind turbine. The wind park North cali bration monitor 516 further receives a set of last yaw encod er reset times 514 and a set of monitor parameters 519. The set of last yaw encoder reset times may be used in order to detect a manually changed calibration or a twisted sensor. Based on the received information, the wind park North cali bration monitor 516 determines the validity status of the measured calibrated absolute wind direction signals and out puts a North calibration validity status from a set of North calibration validity status 513 to the respective yaw encoder 511 of a wind turbine controller 202 from the set of wind turbine controllers 500. Each wind turbine controller 202 from the set of wind turbine controllers 500 is associated with one wind turbine from the group of spatially associated wind turbines. The calibration validity status may be provid ed to a wind turbine. Optionally or additionally, the cali bration validity status is provided to other wind park appli cations, which can use the calibration validity status to de termine whether the respective measured absolute wind direc tion on a particular wind turbine is useable for wake con trol, noise control or wind park data analysis.

Further, the wind park North calibration monitor 516 gener ates a set of North calibration corrections 517 comprising a North calibration correction for each wind turbine the wind direction measurement of which is based on an invalid cali bration. Thus, a North calibration correction from the set of North calibration corrections 517 can be used to correct the calibration of the respective wind turbine. The set of North calibration corrections 517 is provided to a wind park North calibration interface 515 which also receives a set of up loaded North calibration offsets 518 from the North calibra tion upload user interface 520. The wind park North calibra tion interface 515 generates a set of corrected North cali bration offsets 512 based on the input signals thereof and provides it to the set of wind turbines 500. A corrected North calibration offset from the set of North calibration offsets 512 is provided to the respective yaw encoder 511 in order to recalibrate the measured calibrated absolute wind direction of the respective wind turbine.

By such control system, a fast and precise detection of an invalid calibration becomes possible. In particular, based on the difference signals, it can be identified quite quickly is the calibration has become invalid for one of the wind tur bines, as illustrated in figure 4. The calibration can fur ther be corrected efficiently. It is not necessary to collect data for several weeks for detecting such miscalibration and for correcting it. Correct operation of noise control and wake control can thereby be achieved. It should be clear that for implementing the method, it is not necessary to monitor each possible pair of the group of wind turbines, but a pre- determined number of pairs may be monitored that allows a re liable detection of an invalid calibration. Also, implementa tions other than adding a correction factor to a yaw drive encoder are conceivable for correcting an invalid calibra tion.

While specific embodiments are disclosed herein, various changes and modifications can be made without departing from the scope of the invention. The present embodiments are to be considered in all respects as illustrative and non- restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.