Method of determining a vertical profile of wind speed upstream of a wind turbine equipped with a lidar sensor

Abstract

The invention relates to a method of determining a vertical profile of the wind speed upstream of a wind turbine (1), wherein the wind speed measurement is performed by a LiDAR sensor (2), then the exponent alpha of a power law is determined by an unscented Kalman filter and the measurement, and the exponent alpha is applied to the power law to determine the vertical wind speed profile.

Description

Technical Field

[0001] The present invention relates to the field of renewable energy, and in particular to measuring the resource (ie wind) of a wind turbine for wind prediction, turbine control (orientation, torque and speed regulation) and / or diagnostic and / or monitoring purposes.

[0002] A wind turbine allows the kinetic energy from the wind to be converted into electrical or mechanical energy. To convert wind energy into electrical energy, the wind turbine is composed of the following elements:

[0003] - A tower that allows the rotor to be placed at a sufficient height to enable its movement (required for horizontal axis wind turbines) and / or to be placed at a height that allows it to be driven by stronger and more regular winds than at ground level. The tower usually houses part of the electrical and electronic components (modulators, control devices, multipliers, generators, etc.)

[0004] - A nacelle mounted on top of the tower that houses the mechanical, pneumatic, and some electrical and electronic components necessary to operate the machine. The nacelle can be rotated to orient the machine in the correct direction.

[0005] - A rotor fixed to the nacelle, which includes several blades (usually three) of the wind turbine and the wheel shaft. The rotor is driven by the wind and is connected directly or indirectly (via a gearbox and mechanical shaft system) to a motor (generator) through a mechanical shaft, which converts the recovered energy into electrical energy. The rotor is potentially equipped with a control system, such as a variable angle blade control system or a pneumatic brake control system,

[0006] - A gearbox, which consists of two shafts (the mechanical shaft of the rotor and the mechanical shaft of the electric motor) connected by a gearbox (gearbox).

[0007] Since the early 1990s, there has been a renewed interest in wind power, particularly in the European Union, where annual growth rates are approximately 20%. This growth is attributed to the inherent potential of carbon-free electricity generation. To sustain this growth, the energy yield of wind turbines must continue to increase. The prospect of increased wind power production requires the development of efficient production tools and advanced control tools to improve machine performance. Wind turbines are designed to generate electricity at the lowest possible cost. Therefore, they are typically constructed to achieve maximum performance at wind speeds of approximately 15 m / s. It is uncommon for wind turbines to be designed to maximize their output at higher wind speeds. At wind speeds above 15 m / s, some of the additional energy contained in the wind must be discarded to avoid damage to the wind turbine. Therefore, all wind turbines are designed with power conditioning systems.

[0008] For this power regulation, controllers have been designed for variable speed wind turbines. The controllers aim to maximize the recovered power, minimize rotor speed fluctuations, and minimize fatigue and ultimate moments of the structure (blades, tower, and platform). Background Art

[0009] To optimize control, it is important to know the wind speed at the rotor of a wind turbine. Various techniques have been developed for this purpose.

[0010] According to the first technique, the wind speed at a certain point can be estimated using an anemometer, but this imprecise technique cannot measure the entire wind field, nor can it know the three-dimensional components of the wind speed or the vertical wind speed profile.

[0011] According to the second technology, LiDAR (Light Detection and Ranging) sensors can be used. LiDAR is a remote sensing or optical measurement technology based on analyzing the characteristics of a light beam returning from a transmitter. This method is particularly used to determine the distance to an object using pulsed laser light. Unlike radar, which is based on a similar principle, LiDAR sensors use visible or infrared light instead of radio waves. The distance to an object or surface is determined by measuring the delay between the pulse and the detection of the reflected signal.

[0012] In the field of wind turbines, LiDAR sensors have been declared indispensable for the proper operation of large wind turbines, especially as their size and power continue to increase (offshore wind turbines are now 5 MW and will soon reach 12 MW). This sensor allows remote wind speed measurement, first allowing the wind turbine to be calibrated so that it can deliver maximum power (power curve optimization). For this calibration phase, the sensor can be placed on the ground and oriented vertically (profiler), allowing the wind speed and direction as well as the wind speed gradient to be measured depending on the altitude. This application is particularly critical because it allows the resource used to generate energy to be known. This is important for wind turbine projects because it determines the project's financial viability. However, this approach may seem expensive because, in addition to providing the wind turbine with the LiDAR sensor for the application described below, it also requires the LiDAR sensor to be fixedly arranged on the ground or at sea and oriented vertically.

[0013] A second application involves placing the sensor on the nacelle of a wind turbine to measure the wind field in front of the turbine when oriented nearly horizontally. Measuring the wind field in front of the turbine a priori allows for advance knowledge of the turbulence the wind turbine will encounter shortly thereafter. However, current wind turbine control and monitoring technology does not allow for the use of LiDAR sensors to accurately estimate the wind speed at the rotor (i.e., in the rotor plane). This application is specifically described in patent application FR-3-013,777 (US-2015-145,253).

[0014] Wind speed varies with altitude: Wind is stronger at high altitudes than at ground level. Knowing the vertical wind speed profile, in other words the wind speed gradient as a function of altitude, is useful in various wind turbine control applications. Wagner, Rozenn & Antoniou, Ioannis & M. Pedersen, &Courtney,Michael& Hans's paper, "The Influence of the Wind Speed ​​Profile on Wind Turbine Performance Measurements," published in Wind Energy 12.348-362.10.1002 / we.297, specifically describes the relationship between wind speed profiles and wind turbine performance. According to various examples, the vertical wind speed profile can be used for wind turbine energy assessment or to control the pitch angle of the turbine blades.

[0015] Conventionally, vertical wind speed profiles used by LiDAR sensor manufacturers are obtained using offline batch-based methods. These methods are therefore not suitable for estimating vertical wind speed profiles in real time.

[0016] Additionally, other methods for determining the vertical wind speed profile use its mathematical representation, including logarithmic profiles or power laws.

[0017] The logarithmic wind profile was created by Prandtl based on a turbulent boundary layer model on a flat plate. It was subsequently found to be valid in its unmodified form in the atmospheric boundary layer near the ground or sea surface under strong wind conditions. On the surface, the logarithmic wind profile is then given by:

[0018]

[0019] where v z is the longitudinal wind speed at height z, V * is the friction velocity, k = 0.41 is the von Karman constant, z0 is the surface roughness, ψ m is an adiabatic correction to the vertical wind speed profile. This logarithmic profile depends only on a constant, is inaccurate at high altitudes, and is difficult to calibrate. Furthermore, this logarithmic profile is not as accurate as the power law.

[0020] The power law is written as follows:

[0021]

[0022] v zis the longitudinal wind speed at height z, z0 is the reference height, Vz0 is the longitudinal wind speed at the reference height z0, and α is the exponent of the power law.

[0023] This power law is commonly used in wind energy assessments where the wind speed at wind turbine height needs to be estimated based on wind speed observations near the surface, or when wind speed data at different heights need to be adjusted to a standard height. As with the logarithmic law, the power law can be easily integrated over one height. This profile is widely used for engineering purposes due to its simplicity. Assuming neutral atmospheric conditions, it is known that the power law produces more accurate wind speed predictions than the logarithmic law in the range from 100 m to the upper atmospheric boundary layer. For normal wind conditions at offshore sites (offshore), the exponent α is set to 1 / 7. However, when a constant exponent is used, it does not take into account changes in surface roughness that vary with time. Furthermore, it does not take into account the displacement of the wind from the surface due to the presence of obstacles (such as wind turbines in this case). Therefore, using a constant exponent will produce a rather erroneous estimate of the vertical wind speed profile.

[0024] The present invention is particularly aimed at determining an accurate vertical wind speed profile in real time and in a simple manner. The present invention therefore relates to a method for determining a vertical wind speed profile upstream of a wind turbine, wherein wind speed measurements are performed by a LiDAR sensor, an exponent α of a power law is then determined by an unscented Kalman filter and the measurements, and this exponent α is applied to the power law to determine the vertical wind speed profile. Summary of the Invention

[0025] The present invention relates to a method for determining a vertical profile of the wind speed upstream of a wind turbine, said wind turbine being equipped with a LiDAR sensor facing upstream of said wind turbine, wherein the following steps are performed:

[0026] a) measuring the wind speed at at least two measuring points located at different heights in at least one measuring plane upstream of the wind turbine by means of the LiDAR sensor,

[0027] b) The vertical wind speed profile is modeled using a power law of the following form:

[0028]

[0029] v z is the longitudinal wind speed at height z, z0 is the reference height, Vz0 is the longitudinal wind speed at the reference height z0, and α is the exponent of the power law.

[0030] c) determining the exponent α of the power law by means of an unscented Kalman filter using the wind speed measurements at the two measurement points, and

[0031] d) determining the vertical wind speed profile by applying the determined exponent α to the model of the vertical wind speed profile.

[0032] According to an embodiment of the present invention, the unscented Kalman filter is applied to a state model containing additive noise and multiplicative noise.

[0033] Advantageously, the state model is written as:

[0034]

[0035] x(k)=α(k) is the state variable at time k, y(k)=v1(k) is the output of the state model corresponding to the longitudinal wind speed measured at measurement point 1 at time k, η(k-1) is the variance of the exponent α at time k-1, v2(k) is the longitudinal wind speed measured at measurement point 2 at time k, z1 is the height of measurement point 1, z2 is the height of measurement point 2, ε1(k) is the noise of velocity v1 at time k, and ε2(k) is the noise of velocity v2 at time k.

[0036] Preferably, to apply the Kalman filter, an increasing random variable x is considered a :

[0037]

[0038] x(k)=α(k) is the state variable at time k, and ε2(k) is the noise of velocity v2 at time k.

[0039] According to one aspect, the exponent α of the power law is determined by performing the following steps:

[0040] i) Initialize k=0, state vector And the state of the covariance matrix P(0|0)=P0,

[0041] ii) at any time k, the wind speed measurements v1(k) and v2(k) are collected at measurement points 1 and 2, with y(k) = v1(k), and

[0042] iii) At any time k, the exponent α of the power law is determined by:

[0043]

[0044] K is the Kalman filter gain, P xy is the state measurement cross-covariance, P yy is the predicted measurement covariance, m y is the predicted output mean, and v1(k) is the longitudinal wind speed measured at measurement point 1 at time k.

[0045] Furthermore, the present application relates to a method of controlling a wind turbine equipped with a LiDAR sensor, wherein the following steps are performed:

[0046] a) determining the vertical wind speed profile upstream of the wind turbine by means of a method according to one of the above features, and

[0047] b) controlling the wind turbine in accordance with the vertical wind speed profile upstream of the wind turbine.

[0048] The present application also relates to a computer program product comprising code instructions designed to perform the steps of a method according to one of the above features when this program is executed on a unit for processing the LiDAR sensor.

[0049] Furthermore, the present application also relates to a LiDAR sensor for a wind turbine. It comprises a processing unit implementing a method according to one of the above features.

[0050] Furthermore, the present application relates to a wind turbine comprising a LiDAR sensor according to one of the above features, the LiDAR sensor being preferably arranged on the nacelle of the wind turbine or in the hub of the wind turbine. BRIEF DESCRIPTION OF DRAWINGS

[0051] Other features and advantages of the method according to the present application will appear clearly on reading the following description of embodiments given by way of non-limiting examples, with reference to the annexed drawings in which:

[0052] Figure 1 is shown a wind turbine equipped with a LiDAR sensor according to an embodiment of the present application,

[0053] Figure 2 is shown the steps of a method of determining a vertical wind speed profile according to an embodiment of the present application,

[0054] Figure 3 is shown the steps of a wind turbine control method according to a second embodiment of the present application,

[0055] Figure 4 is a plot of the radial wind speed 200 meters upstream of the wind turbine as a function of time for one example measured at two heights,

[0056] Figure 5 is a plot of the longitudinal wind speed 200 meters upstream of the wind turbine as a function of time for the example of Figure 4

[0057] Figure 6 Figure 4 ​​An example of a curve showing the exponent α changing with time, and

[0058] Figure 7 is estimated by the method according to an embodiment of the present invention (according to Figure 4 Graph of the longitudinal wind speed as a function of time measured 100 meters upstream of the wind turbine (measurements in the example of ). DETAILED DESCRIPTION

[0059] The present invention relates to a method for determining the vertical wind speed profile upstream of a wind turbine (the concept of "upstream" being defined with respect to the direction of the wind blowing toward the turbine). The vertical wind speed profile is understood to be the wind speed gradient as a function of altitude. The determined vertical wind speed profile allows the determination of vertical wind variations upstream of the wind turbine and in the turbine rotor plane. According to the invention, the wind turbine is equipped with a LiDAR sensor, which is arranged substantially horizontally, for measuring the wind speed upstream of the turbine.

[0060] According to the present invention, a LiDAR sensor allows for measurement of wind speed in at least one measurement plane upstream of a wind turbine. Several types of LiDAR sensors exist, such as scanning LiDAR sensors, continuous wave LiDAR sensors, or pulsed LiDAR sensors. Within the context of the present invention, pulsed LiDAR is preferably used. However, other LiDAR technologies may also be used while remaining within the scope of the present invention.

[0061] LiDAR sensors allow for rapid measurements. Therefore, using this sensor enables rapid, continuous, and real-time determination of the vertical wind speed profile. For example, the sampling rate of a LiDAR sensor can range from 1 to 5 Hz (or even higher in the future), and this sampling rate can be 4 Hz. Furthermore, LiDAR sensors allow for the acquisition of information related to the wind upstream of the wind turbine, which is related to the wind flowing toward the turbine. LiDAR sensors can therefore be used to determine the vertical wind speed profile.

[0062] Figure 1By way of non-limiting example, a horizontal-axis wind turbine 1 equipped with a LiDAR sensor 2 for use in a method according to an embodiment of the present invention is schematically illustrated. The LiDAR sensor 2 is used to measure wind speed at a given distance in multiple measurement planes PM (only two are shown). Knowing the wind measurements a priori allows for a wealth of information. The figure also shows axes x, y, and z. The reference point of this coordinate system is the rotor center. Direction x is the longitudinal direction corresponding to the direction of the rotor axis upstream of the wind turbine, which also corresponds to the measurement direction of the LiDAR sensor 2. Direction y, perpendicular to direction x, is a transverse direction lying in the horizontal plane (directions x and y form the horizontal plane). Direction z is a vertical direction pointing upward (essentially corresponding to the direction of tower 4), with axis z perpendicular to axes x and y. The rotor plane is indicated by a dashed rectangle PR, which is defined by directions y and z (x is zero). Measurement plane PM is the plane formed by directions y and z at a certain distance from rotor plane PR (for non-zero values ​​of x). Measurement plane PM is parallel to rotor plane PR.

[0063] Conventionally, a wind turbine 1 allows the kinetic energy of the wind to be converted into electrical or mechanical energy. To convert the wind energy into electrical energy, the wind turbine 1 is composed of the following elements:

[0064] - a tower 4 which allows placing the rotor (not shown) at a sufficient height to enable its movement (required for horizontal axis wind turbines) and / or allows placing the rotor at a height where it can be driven by stronger and more regular winds than at ground level 6. The tower 4 usually houses part of the electrical and electronic components (modulators, control devices, multipliers, generators, etc.)

[0065] - A nacelle 3 mounted at the top of a tower 4, which houses the mechanical, pneumatic and some electrical and electronic components (not shown) necessary to operate the machine. The nacelle 3 can be rotated to orient the machine in the correct direction,

[0066] - A rotor fixed to the nacelle, comprising a number of blades 7 (usually three) of the wind turbine and a wheel shaft. The rotor is driven by wind energy and is connected via a mechanical shaft directly or indirectly (via a gearbox and mechanical shaft system) to a motor (generator) (not shown), which converts the recovered energy into electrical energy. The rotor is potentially equipped with a control system, such as a variable angle blade control system or a pneumatic brake control system,

[0067] - a gearbox consisting of two shafts (the mechanical shaft of the rotor and the mechanical shaft of the electric motor) connected by a gearbox (gearbox) (not shown).

[0068] As an example embodiment of a pulsed LiDAR sensor Figure 1As can be seen in FIG, the LiDAR sensor 2 used comprises four beams or measurement axes (b1, b2, b3, b4). As a non-limiting example, the method according to the invention can also operate with a LiDAR sensor comprising any number of beams. The LiDAR sensor performs a punctual measurement at each measurement point (PT1, PT2, PT3, PT4), which is the intersection of the measurement plane PM with the beams (b1, b2, b3, b4). These measurement points (PT1, PT2, PT3, PT4) are Figure 1 denoted by black circles in the figure. Processing the measurements at the measurement points (PT1, PT2, PT3, PT4) allows the determination of wind speeds in the measurement plane PM at several altitudes: measurement points PT1 and PT2 are at altitudes higher than measurement points PT3 and PT4. The wind modeling method described in French patent application FR-3,068,139 (WO-2018 / 234,409) can therefore be particularly applied.

[0069] Preferably, the LiDAR sensor 2 may be mounted on the nacelle 3 of the wind turbine 1 or in the hub of the wind turbine 1 .

[0070] According to the present invention, a method for determining a vertical wind speed profile upstream of a wind turbine comprises the following steps:

[0071] 1) Measure wind speed,

[0072] 2) Constructing a vertical wind speed profile model

[0073] 3) Determine the index α

[0074] 4) Determine the vertical wind speed profile.

[0075] These steps are performed in real time. The step of building the vertical wind speed profile model can be performed offline in advance.

[0076] Figure 2 The steps of a method for determining a vertical wind speed profile according to an embodiment of the present invention are schematically illustrated by way of non-limiting example. The first step is a step (MES) of measuring wind speeds v1 and v2 at two different heights and in at least one measurement plane using a LiDAR sensor. A vertical wind speed profile model (MOD) is constructed. The next step comprises determining an exponent α of the vertical wind speed profile model (MOD) using an unscented Kalman filter (UKF) and the wind speed measurements v1 and v2. The exponent α thus determined is used together with the vertical wind speed profile model (MOD) to determine (PRO) a vertical profile of the wind speed v(z).

[0077] 1. Wind speed measurement

[0078] In this step, the wind speed in at least one measurement plane away from the wind turbine is continuously measured by a LiDAR sensor at at least two measurement points at different heights. Thus, the wind speed upstream of the wind turbine in at least one measurement plane at two different heights is known. The height of the measurement point is considered to be the vertical axis relative to the ground or sea level ( Figure 1 In this step, the wind speed can be, for example, Figure 1 The measurement is performed at the measuring point PT1 (“upper” point) and the measuring point PT3 (“lower” point).

[0079] According to an implementation of the invention, the measuring plane may be located at a longitudinal distance (along the Figure 1 The x-axis in FIG. 2 is preferably between 50 and 400 m. Thus, the wind speed evolution over a long distance upstream of the wind turbine can be determined, which also allows to improve the accuracy of determining the vertical wind speed profile.

[0080] Alternatively, the measurement plane may be closer or further away than the preferred range.

[0081] According to a non-limiting example embodiment, the LiDAR sensor may perform measurements for ten measurement planes which may in particular be located at distances of 50, 70, 90, 100, 110, 120, 140, 160, 180 and 200 meters from the rotor plane, respectively.

[0082] According to one embodiment of the present invention, at each altitude, wind speed measurements can be performed at several measurement points. For example, wind speed can be measured at two measurement points PT1 and PT2 ("upper" points) and two measurement points PT3 and PT4 ("lower" points). In this case, the wind speed measured at a certain altitude can be a combination (e.g., an average) of the wind speed measurements at that altitude.

[0083] To increase the accuracy of subsequent steps, the wind speed can be measured in several measurement planes.

[0084] According to an implementation of the invention, the LiDAR sensor may allow the measurement of radial velocity (along the axis of the LiDAR sensor measurement beam). In this case, the method may comprise the steps of determining the longitudinal velocity (along the axis of the beam) from the radial velocity by any known method, in particular by projecting the radial velocity onto the longitudinal axis or by a wind reconstruction method such as that described in patent application FR-3,068,139 (WO-2018 / 234,409). Figure 1 x-axis).

[0085] 2. Building a wind speed model

[0086] This step involves modeling the vertical wind speed profile by a power law (or any equivalent law) of the form:

[0087]

[0088] v z is the longitudinal wind speed at height z, z0 is the reference height, Vz0 is the longitudinal wind speed at the reference height z0, and α is the exponent of the power law.

[0089] The method according to the present invention allows determining the variation of the exponent α over time so that the wind speed model is accurate. One advantage of the power law is its simplicity. In addition, the power law produces more accurate wind speed predictions than the logarithmic law, especially at altitudes ranging from 100 meters to the upper atmospheric boundary layer.

[0090] 3. Determine the exponent α

[0091] This step consists of determining the exponent α of the power law by means of an unscented Kalman filter (UKF) and wind speed measurements performed at the measurement points. An unscented Kalman filter is a filtering algorithm that uses a system model to estimate the current hidden state of the system and then corrects this estimate using available sensor measurements. The principle of the UKF differs from that of the extended Kalman filter in that it uses an unscented transform to directly approximate the mean and covariance of the target distribution. An unscented Kalman filter may comprise a state prediction and a measurement correction step, both following a preceding step of calculating a "sigma point". A sigma point is a set of samples calculated so as to allow the mean and covariance information to be accurately propagated through the space of nonlinear functions.

[0092] Therefore, this filter is very suitable for quickly determining the exponent α of the power law.

[0093] According to one embodiment of the present invention, an unscented Kalman filter is applied to a state model containing additive and multiplicative noise. The additive and multiplicative noise come from wind speed measurements at different altitudes. Noise is called additive because it appears to be a term added to the state model. Noise is called multiplicative because it appears to be a term multiplied by the inputs of the state model. This embodiment allows for the precise determination of the power law exponent α.

[0094] Advantageously, the state model can be written as:

[0095]

[0096] x(k)=α(k) is the state variable at time k, y(k)=v1(k) is the output of the state model corresponding to the longitudinal wind speed measured at measurement point 1 at time k, η(k-1) is the variance of the exponent α at time k-1, v2(k) is the longitudinal wind speed measured at measurement point 2 at time k, z1 is the height of measurement point 1, z2 is the height of measurement point 2, ε1(k) is the noise of velocity v1 at time k, and ε2(k) is the noise of velocity v2 at time k. For this state model, ε1(k) is additive noise, while ε2(k) is multiplicative noise.

[0097] To determine the exponent α by using the unscented Kalman filter, consider the increasing random variable x a :

[0098]

[0099] x(k)=α(k) is the state variable at time k, and ε2(k) is the noise of velocity v2 at time k.

[0100] According to an implementation of the present invention, the exponent α of the power law can be determined by performing the following steps:

[0101] i) Initialize k=0, state vector And the state of the covariance matrix P(0|0)=P0,

[0102] ii) at any time k, the wind speed measurements v1(k) and v2(k) are collected at measurement points 1 and 2, with y(k) = v1(k), and

[0103] iii) At any time k, the exponent α of the power law is determined by:

[0104]

[0105] K is the Kalman filter gain, P xy is the state measurement cross-covariance, P yy is the predicted measurement covariance, m y is the predicted output mean, and v1(k) is the longitudinal wind speed measured at measurement point 1 at time k.

[0106] According to one embodiment of the present invention, the unscented Kalman filter can be used by the following steps:

[0107] x(k|k-1) is the estimate of x(k) based on the measurement at time k-1.

[0108] x(k|k) is the estimate of x() based on the measurement at time k.

[0109] P(k|k-1) is the error variance of the measurement from time k-1.

[0110] P(k|k) is the error variance of the measurement from time k.

[0111] Q is the variance of the system noise η(k).

[0112] Since the equation is linear, the prediction step can be written as:

[0113] x(k|k-1)=x(k-1|k-1)

[0114] P(k|k-1)=P(k-1|k-1)+Q

[0115] The correction step becomes more complicated due to the presence of additive and multiplicative noise. To overcome this problem, the following increasing random variables can be considered:

[0116]

[0117] After the prediction step, the incremented random variable x a The distribution of (k) can be given as a normal distribution denoted by N:

[0118] x a (k|k-1)~N(m xa , P xa )

[0119] and:

[0120]

[0121] R2(k) is the variance of the noise ε2(k) of velocity v2 at time k.

[0122] By and mean m xa and the covariance matrix P xa Associated X0, X i 、X i+n The sigma point represented by can be calculated as follows:

[0123]

[0124] Where n=2, S is P xa The square root of

[0125] λ=μ 2 (n+κ)-n

[0126] μ is a scalar parameter that determines the dispersion of the sigma points, and κ is a secondary resizing parameter.

[0127] X i，x and X i，εThen it can be defined as X i For any i in the range 1 to 2n, the sigma points are propagated through the measurement model as follows:

[0128]

[0129] The next step consists in calculating the predicted mean m y , the predicted measurement covariance P yy and the state measurement cross-covariance P xy .

[0130]

[0131] R1(k) is the variance of the noise ε1(k) of the velocity v1 at time k, W i m 、W i c is the weight defined by:

[0132]

[0133]

[0134]

[0135]

[0136] ξ is a random variable x used to incorporate the increment a without any prior knowledge of the distribution's parameters.

[0137] The Kalman filter gains, state estimates, and covariance matrix at time k can then be expressed as:

[0138]

[0139] Given x(k)=α, these equations allow determining the exponent α of the power law, which varies with time.

[0140] 4. Determine the vertical wind speed profile

[0141] This step comprises determining the vertical profile of the wind speed upstream of the wind turbine using the vertical wind speed profile model constructed in step 2) and the exponent α determined in step 3). Thus, the method according to the invention allows determining the wind speed at any point in space upstream of the wind turbine.

[0142] Preferably, the method according to the invention allows determining the longitudinal wind speed at any point in space upstream of the wind turbine.

[0143] According to one embodiment of the present invention, in the power law, the reference height z0 can be considered to be the height of any measurement point of the LiDAR sensor (which can be different from the measurement point used in step 1), and the speed Vz0 can be considered to be the wind speed measured at the measurement point in question. The vertical wind speed profile can thus be determined in the measurement plane by applying the power law.

[0144] Alternatively, any reference point z0 (e.g., a point in the rotor plane) can be considered in the power law and the speed Vz0 can be considered to be the estimated (reconstructed) wind speed at the point considered. It is thus possible to determine the wind speed in any plane in space, including the rotor plane. To reconstruct the wind speed, any wind reconstruction method can be applied, in particular the method described in patent application FR-3,068,139 (WO-2018 / 234,409), the main steps of which are hereinafter recalled:

[0145] Gridding the space upstream of the LiDAR sensor, the grid including estimation points and measurement points,

[0146] Measure wind amplitude and direction at each measuring point,

[0147] using a recursive least squares method for a cost function (also called an objective function) to estimate the wind magnitude and direction for all estimation points at any time, and

[0148] • Reconstruct the incident wind field in three dimensions at all discrete points in real time.

[0149] The present invention also relates to a method for controlling a wind turbine equipped with a LiDAR sensor. The method comprises the following steps:

[0150] - determining a vertical wind speed profile upstream of the wind turbine by a method for determining a vertical wind speed profile according to any of the above variants, and

[0151] - Controlling the wind turbine according to the vertical wind speed profile upstream of the wind turbine.

[0152] Real-time, accurate predictions of the vertical profile of wind speed upstream of a wind turbine allow for appropriate wind turbine control, minimizing impacts on the turbine structure and maximizing recovered power. Indeed, LiDAR allows for these predictions to predict the wind speed approaching the turbine, thereby enabling early phase adjustment of the turbine equipment so that the turbine is optimally configured for the wind at the estimated arrival time. Furthermore, LiDAR sensors allow for a reduction in structural loads, with blades and towers accounting for 54% of costs. Thus, the use of LiDAR sensors allows for optimization of wind turbine structures, thereby reducing costs and maintenance.

[0153] According to the present invention, the pitch angle of the blades and / or the power recovery torque of the wind turbine generator can be controlled based on wind speed. Preferably, the pitch angle of each blade can be controlled individually. Other types of adjustment devices can also be used. Controlling the blade pitch angle allows for optimizing energy recovery as a function of the incident wind on the blades.

[0154] According to an embodiment of the present invention, the pitch angle of the blades and / or the power recovery torque can be determined as a function of the wind speed at the rotor using a wind turbine map. For example, the control method described in patent application FR-2,976,630 A1 (US 2012-0,321,463) can be applied.

[0155] Figure 3 The steps of a wind turbine control method according to an embodiment of the present invention are schematically illustrated by way of non-limiting example. The first step is a step (MES) of measuring wind speeds v1, v2 at two different heights and in at least one measurement plane using a LiDAR sensor. A vertical wind speed profile model (MOD) is constructed. The next step involves determining an exponent α of the vertical wind speed profile model (MOD) using an unscented Kalman filter (UKF) and the wind speed measurements v1, v2. The exponent α thus determined is used together with the vertical wind speed profile model (MOD) to determine (PRO) a vertical profile of the wind speed v(z). The vertical profile of the wind speed v(z) is then used to control (CON) the wind turbine.

[0156] Furthermore, the present invention relates to a computer program product comprising code instructions designed to perform the steps of one of the above-described methods (method for determining a vertical wind speed profile, control method). The program is executed on a unit for processing a LiDAR sensor or on any similar medium connected to a LiDAR sensor or a wind turbine.

[0157] According to one aspect, the invention also relates to a LiDAR sensor for a wind turbine, comprising a processing unit configured to implement one of the above-mentioned methods (method of determining a vertical wind speed profile, control method).

[0158] According to the implementation of the present invention, the LiDAR sensor can be a scanning LiDAR, a continuous wave LiDAR or a pulsed LiDAR sensor. Preferably, the LiDAR sensor is a pulsed LiDAR sensor.

[0159] The present invention also relates to a wind turbine, in particular an offshore (sea) or onshore (land) wind turbine equipped with a LiDAR sensor as described above. According to one embodiment of the present invention, the LiDAR sensor may be arranged on the nacelle of the wind turbine or in the wheel shaft of the wind turbine. The LiDAR sensor is oriented so that it performs measurements of the wind upstream of the wind turbine (i.e. in front of the wind turbine and along its axis). Figure 1 According to one embodiment, a wind turbine may be similar to Figure 1 Wind turbine shown.

[0160] For an embodiment of the control method, a wind turbine may comprise a control device, eg for controlling the pitch angle or the electrical torque of at least one blade of the wind turbine for implementing the method according to the invention.

[0161] Example

[0162] The features and advantages of the method according to the invention will become clear by reading the application examples below.

[0163] In this example, the wind speed estimated at a point upstream of the wind turbine is compared with a vertical wind speed profile determined using a method according to an embodiment of the present invention. For a distance of 200 meters upstream of the wind turbine, wind speeds are measured at two measurement points at different heights to estimate the power law exponent α in real time using a method according to an embodiment of the present invention. Then, for a distance of 100 meters upstream of the wind turbine, the exponent α is applied to the determined vertical wind speed profile to determine the longitudinal wind speed at a predetermined height from the longitudinal wind speed measurement at a known height.

[0164] For this example a 4-beam pulsed LiDAR is considered that performs measurements in measurement planes at 100 meters and 200 meters from the wind turbine.

[0165] Figure 4 The two measurement points (corresponding to Figure 1 The dependent variables measured at the measurement points PT1 and PT3) are 10 4 Radial wind speed RWS in meters per second (i.e., in the direction of the measurement beam) at time T in seconds. This radial wind speed was measured in a measurement plane 200 meters upstream of the wind turbine. The measured light-gray speed v1 corresponds to the speed measured at the lowest measurement point. The measured dark-gray speed v2 corresponds to the speed measured at the highest measurement point. As expected, the speed measured at the highest measurement point is greater than the speed measured at the lowest measurement point. In this figure, note that the LiDAR sensor does not provide measurements at all times due to blade obstruction effects.

[0166] Figure 5 is dependent on the 10 corresponding to the single day measurement 4 The longitudinal wind speed wx in meters per second at the time T in seconds (i.e., Figure 1 The longitudinal wind speed wx is based on Figure 4 The longitudinal wind speed is estimated from the radial wind speed RWS in the wind turbine. The longitudinal wind speed is estimated in a measurement plane 200 meters upstream of the wind turbine. The light grey longitudinal speed wx1 corresponds to the longitudinal speed estimated at the lowest measurement point. The dark grey longitudinal speed wx2 corresponds to the longitudinal speed estimated at the highest measurement point.

[0167] The exponent α of the power law is determined from these velocities by the method according to the invention. Figure 6 Is due to 10 4 Graph of the exponent α of the power law with time T in seconds. It can be seen that the exponent α varies significantly, so the prior art assumption of considering a constant exponent α is unrealistic and does not allow to accurately determine the vertical profile of the wind speed.

[0168] The LiDAR sensor also measures the wind speed at two known heights in a measurement plane located 100 meters upstream of the wind turbine. In order to demonstrate the precise characteristics of the method according to the invention, on the one hand the wind speed measurement at the highest point of 100 meters is considered as a reference and on the other hand the wind speed is measured according to the method according to the invention. Figure 6 The wind speed at the lowest measuring point at 100 meters is determined by the wind speed measurement at 200 meters and the exponent α is used to estimate the wind speed at the highest measuring point at 100 meters. Figure 7 Is due to 10 4 The longitudinal wind speed wx in meters per second at the highest measurement point at a time T of 10 seconds (i.e., Figure 1 The longitudinal wind speed is estimated in a measurement plane 100 meters upstream of the wind turbine. The curve REF corresponds to the reference defined above, and the curve EST corresponds to the estimate using the method according to the present invention as defined above. It can be noted that these curves are very close, which shows that the method according to the present invention enables precise determination of the wind speed.

Claims

1. A method for determining a vertical profile of wind speed upstream of a wind turbine, said wind turbine being equipped with a LiDAR sensor facing upstream of said wind turbine, wherein the following steps are performed: a) measuring the wind speed at at least two measuring points located at different heights in at least one measuring plane upstream of the wind turbine by means of the LiDAR sensor, b) modeling the vertical profile by a power law of the form: v z is the longitudinal wind speed at height z, z0 is the reference height, Vz0 is the longitudinal wind speed at the reference height z0, and a is the exponent of the power law, c) determining the exponent a of the power law by means of an unscented Kalman filter using the wind speed measurements at the two measurement points, and d) determining the vertical profile by applying the determined exponent a to the model.

2. The method according to claim 1, wherein The unscented Kalman filter is applied to a state model including additive noise and multiplicative noise.

3. The method according to claim 2, wherein The state model is written as: x(k)=α(k) is the state variable at time k, y(k)=v1(k) is the output of the state model corresponding to the longitudinal wind speed measured at measurement point 1 at time k, η(k-1) is the variance of the exponent a at time k-1, v2(k) is the longitudinal wind speed measured at measurement point 2 at time k, z1 is the height of measurement point 1, z2 is the height of measurement point 2, ε1(k) is the noise of velocity v1 at time k, and ε2(k) is the noise of velocity v2 at time k.

4. The method according to any one of claims 2 or 3, characterized in that To apply the Kalman filter, consider an increasing random variable x a : x(k)=α(k) is the state variable at time k, and ε2(k) is the noise of velocity v2 at time k.

5. The method according to claim 1, wherein The exponent a of the power law is determined by performing the following steps: i) Initialize k=0, state vector And the state of the covariance matrix P(0|0)=P0, ii) at any time k, taking the wind speed measurements v1(k) and v2(k) at measurement points 1 and 2, with y(k) = v1(k), and iii) At any time k, the exponent a of the power law is determined by: K is the Kalman filter gain, P xy is the state measurement cross-covariance, P yy is the predicted measurement covariance, x(k|k) is the estimate of x(k) based on the measurement at time k, x(k|k-1) is the estimate of x(k) based on the measurement at time k-1, and m y is the predicted output mean, v1(k) is the longitudinal wind speed measured at measurement point 1 at time k, P(k|k-1) is the error variance of the measurement from time k-1, and P(k|k) is the error variance of the measurement from time k.

6. A method of controlling a wind turbine equipped with a LiDAR sensor, wherein the following steps are performed: a) determining the vertical profile upstream of the wind turbine by a method as claimed in any one of the preceding claims, and b) controlling the wind turbine according to the vertical profile upstream of the wind turbine.

7. A computer program product, characterized in that The program comprises code instructions designed to execute the steps of the method according to any one of the preceding claims when the program is executed on a unit for processing the LiDAR sensor.

8. A LiDAR sensor for a wind turbine, characterized in that Comprising a processing unit implementing the method according to any one of claims 1 to 6.

9. A wind turbine, characterized in that: The LiDAR sensor according to claim 8 is arranged on a nacelle of the wind turbine or in a wheel hub of the wind turbine.

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