Method of determining an induction factor for a wind turbine equipped with a lidar sensor

Abstract

The present invention is a method of determining an induction factor of the wind for a wind turbine (1) equipped with a LiDAR sensor (2). For this method, wind speed measurements are performed in measurement planes (PM) by use of LiDAR sensor (2), then induction factors between measurement planes (PM) are determined by use of the measurements and of a first linear Kalman filter, and the induction factor between a measurement plane (PM) and the rotor plane (PR) of wind turbine (1) is determined by a second linear Kalman filter.

Claims

1. A method of controlling a wind turbine equipped with a LiDAR sensor performing a measurement relative to wind speed in at least three measurement planes separated in space from the wind turbine, comprising: A. determining an induction factor of wind between a measurement plane and a rotor plane of a wind turbine equipped with a LiDAR sensor, the induction factor of the wind representing a wind deceleration coefficient defined as a ratio of wind speeds between two separate points upstream from the wind turbine resulting from deceleration of the wind in the planes caused by operation of the wind turbine in a wind field, by: a) measuring the wind speed in at least three measurement planes separated in space from the wind turbine by use of the LiDAR sensor; b) determining at least two induction factors of the wind between two of the measurement planes by providing the wind speed measurements as inputs to a first linear Kalman filter to produce an output of the linear induction factors in the two measurement planes; and c) determining the induction factor of the wind between of one at least two of the measurement planes and the rotor plane of the wind turbine by using the output of the determined induction factors from the first linear Kalman filter as inputs to a second linear Kalman filter to produce an output of the induction factor from the second linear Kalman filter; B. determining the wind speed in the rotor plane as a function of the induction factor of the wind between one of the at least two of the measurement planes and the rotor plane of the wind turbine by using wind speed measurements in the measurement plane relative to the induction factor of the wind between one of the at least two of the measurement planes and the rotor plane; and C. controlling the wind turbine as a function of the wind speed in the rotor plane.

2. A method as claimed in claim 1, wherein the at least two induction factors of the wind are determined between the measurement planes having known spacings which are equal to a distance between the rotor plane and a measurement plane closest to the rotor plane.

3. A method as claimed in claim 2, wherein the wind speed measurement is performed in at least four measurement planes and at least three induction factors of the wind are determined between two measurement planes.

4. A method as claimed in claim 1, wherein the wind speed measurement is performed in at least four measurement planes and at least three induction factors of the wind are determined between two measurement planes.

5. A method as claimed in claim 1, wherein the wind speed in the rotor plane corresponds to multiplication of the induction factor of the wind between a measurement plane and the rotor plane of a wind turbine by the wind speed in the measurement plane relative to the induction factor of the wind.

6. A computer program product comprising code instructions stored on a tangible storage medium which when executed by a processor of the LiDAR sensor which performs steps of the method of claim 1 when the program is executed on a processor of the LiDAR sensor.

7. A LiDAR sensor for a wind turbine, comprising a processor implementing the method of claim 1.

8. A wind turbine comprising the LiDAR sensor recited in claim 7 in which the LiDAR sensor is located on the nacelle of the wind turbine.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the method according to the invention will be clear from reading the description hereafter of embodiments given by way of non-limitative example, with reference to the accompanying drawings wherein:

(2) FIG. 1 illustrates a wind turbine equipped with a LiDAR sensor according to an embodiment of the invention;

(3) FIG. 2 illustrates the steps of the method of determining an induction factor of the wind according to an embodiment of the invention;

(4) FIG. 3 illustrates the steps of the method of determining the wind speed according to an embodiment of the invention;

(5) FIG. 4 illustrates the steps of the wind turbine control method according to an embodiment of the invention;

(6) FIG. 5 illustrates the steps of a wind turbine diagnosis method according to an embodiment of the invention;

(7) FIG. 6 illustrates the evolution over time of three induction factors between measurement planes obtained by use of the method according to an embodiment of the invention;

(8) FIG. 7 illustrates the evolution of the induction factor as a function of the distance to the rotor plane for a given time obtained by use of the method according to an embodiment of the invention;

(9) FIG. 8 illustrates the evolution over time of the induction factor of the wind in the rotor plane obtained by use of the method according to an embodiment of the invention; and

(10) FIG. 9 illustrates the evolution of the induction factor as a function of the distance to the rotor plane for a given time obtained by use of the method according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

(11) The invention relates to a method of measuring the resource of wind turbines: wind, in particular with turbine control (orientation, torque and speed regulation) and at least one of diagnosis and monitoring objectives, wherein the wind turbine is at least one of controlled and monitored according to a determination of an induction factor of the wind with the turbine being equipped with a LiDAR sensor to perform this estimation.

(12) The induction factor is a wind deceleration coefficient in the induction zone of the wind turbine. Indeed, the wind is decelerated in the upstream part of the turbine due to the presence of the wind turbine and to the operation thereof. The power drawn by the turbine from the wind causes deceleration of the wind upstream from the turbine. Thus, the induction factor is representative of a physical phenomenon and it gives an indication of the operation of the wind turbine. The induction factor is calculated between two planes upstream from the wind turbine. By definition, it corresponds to the speed ratio between these planes. If a denotes the induction factor, u the wind speed, and d1 and d2 the respective distances of the two planes considered to the rotor plane, the induction factor between the planes located at distances d1 and d2 from the rotor plane can be expressed as:

(13) $a_{d1,d2}=\frac{u_{d1}}{u_{d2}}$

(14) When one of the planes is being considered is the rotor plane, d1=0.

(15) According to the invention, the LiDAR sensor allows measurement of the wind speed in (at least three) measurement planes upstream from the wind turbine. There are several types of LiDAR sensors, which for example are scanning LiDAR, continuous wave LiDAR or pulsed LiDAR sensors. Within the context of the invention, a pulsed LiDAR is preferably used. However, the other LiDAR technologies may also be used while remaining within the scope of the invention.

(16) LiDAR sensors allow fast measurement. Therefore, using such a sensor enables fast and continuous determination of the induction factor of the wind. For example, the sampling rate of the LiDAR sensor can range between 1 and 5 Hz, and it can be 4 Hz.

(17) FIG. 1 schematically shows, by way of non-limitative example, a horizontal-axis wind turbine 1 equipped with a LiDAR sensor 2 for the method according to an embodiment of the invention. LiDAR sensor 2 is used to measure the wind speed at a given distance in measurement planes PM (only two measurement planes are shown). Knowing the wind measurement in advance a priori provides much information. This figure also shows axes x, y and z. The reference point of this coordinate system is the center of the rotor. Direction x is the longitudinal direction corresponding to the direction of the rotor axis, upstream from the wind turbine, this direction also corresponds to the measurement direction of LiDAR sensor 2. Direction y, which is perpendicular to direction x, is the lateral direction located in a horizontal plane (directions x, y form a horizontal plane). Direction z is the vertical direction (substantially corresponding to the direction of tower 4) pointing of this axis that points up. The z axis is perpendicular to axes x and y. The rotor plane is indicated by the rectangle in dotted line PR and is defined by directions y, z for a zero value of x. Measurement planes PM are planes formed by directions y, z at a distance from rotor plane PR (for a non-zero value of x). Measurement planes PM are parallel to rotor plane PR.

(18) Conventionally, a wind turbine 1 converts the kinetic energy of the wind into electrical or mechanical energy. To convert the wind energy into electrical energy, it is made up of the following elements:

(19) a tower 4 allowing a rotor (not shown) to be positioned at a sufficient height to enable motion thereof (necessary for horizontal-axis wind turbines) or this rotor positioned at a height enables being driven by a stronger and more regular wind than at ground level 6. Tower 4 generally houses part of the electrical and electronic components (modulator, control, multiplier, generator, etc.),

(20) a nacelle 3 mounted at the top of tower 4, housing mechanical, pneumatic and some electrical and electronic components (not shown) necessary for operating the machine. Nacelle 3 can rotate to orient the machine in the correct direction,

(21) the rotor, fastened to the nacelle, comprises several blades 7 (generally three) and the hub of the wind turbine. The rotor is driven by the energy from the wind and it is connected by a mechanical shaft, directly or indirectly (via a gearbox and mechanical shaft system), to an electrical machine (electrical generator) (not shown) that converts the energy recovered to electrical energy. The rotor is potentially provided with control systems such as variable-angle blades or aerodynamic brakes,

(22) a transmission made up of two shafts (mechanical shaft of the rotor and mechanical shaft of the electric machine) connected by a transmission (gearbox) (not shown).

(23) As can be seen in FIG. 1, which is an example embodiment of a pulsed LiDAR sensor, the LiDAR sensor 2 used comprises four beams or measurement axes (b1, b2, b3, b4). By way of non-limitative example, the method according to the invention also operates with a LiDAR sensor comprising one or more beams. The LiDAR sensor performs a punctual measurement at each intersection point of a measurement plane PM and a beam (b1, b2, b3, b4). These measurement points are represented by black circles in FIG. 1. Processing the measurements at these measurement points allows determination of the wind speed in measurement planes PM. The wind modelling method which is described in French patent application FR-1,755,675 can therefore notably be applied.

(24) Preferably, LiDAR sensor 2 can be mounted on nacelle 3 of wind turbine 1.

(25) According to the invention, the method of determining an induction factor of the wind between a measurement plane and the rotor plane of a wind turbine comprises the following steps:

(26) 1) measuring the wind speed;

(27) 2) determining induction factors between measurement planes; and

(28) 3) determining the induction factor between a measurement plane and the rotor plane.

(29) FIG. 2 schematically illustrates, by way of non-limitative example, the steps of the method according to the invention. The first step is a step (MES) measures the wind speed in measurement planes. The second step uses the measurements and a first linear Kalman filter (KAL1) to determine the induction factors between measurement planes denoted by a.sub.PM. The third step uses the induction factors between measurement planes a.sub.PM to determine, by use of a second linear Kalman filter (KAL2), the induction factor of the wind between a measurement plane and the rotor plane denoted by α.sub.PR.

(30) 1. Wind Speed Measurement

(31) In this step, the wind speed is continuously measured in at least three measurement planes distant from the wind turbine, by use of the LiDAR sensor. Thus, the wind speed can be known upstream from the wind turbine in three measurement planes located at different distances from the wind turbine. In other words, the wind speed can be known at three distances from the rotor plane of the wind turbine. For this step, the three wind components (longitudinal, lateral and vertical), as well as the wind speed variations in the measurement plane (the wind speed increases with height for example) are considered.

(32) According to an embodiment of the invention, the wind speed is measured in at least four measurement planes to improve the wind knowledge precision upstream from the wind turbine and, therefore, the precision in estimation of the induction factor of the wind in the rotor plane.

(33) According to an implementation of the invention, the measurement planes can be spaced out by a longitudinal distance (along axis x in FIG. 1) ranging between 50 and 400 m from the rotor plane. It is thus possible to determine the evolution of the wind speed over a long distance upstream from the wind turbine, which also allows increasing the precision in estimation of the induction factors of the wind.

(34) According to a non-limitative example, the LiDAR sensor can perform measurements for ten measurement planes, which can notably be located at distances of 50, 70, 90, 100, 110, 120, 140, 160, 180 and 200 m from the rotor plane respectively.

(35) 2. Determining the Induction Factors Between Measurement Planes

(36) This step determines in real time at least two induction factors of the wind between two measurement planes. In other words, at a minimum, a first induction factor is determined between a first measurement plane and a second measurement plane, and a second induction factor is determined between a third measurement plane and a fourth measurement plane (at maximum one of the third and fourth measurement planes corresponds to one of the first and second measurement planes). In a simplified manner, these induction factors are referred to as induction factors between measurement planes in the description hereafter.

(37) According to the invention, the induction factors between measurement planes are determined by use of the wind speed measurements and of a Kalman filter, notably a linear Kalman filter.

(38) Advantageously, for this step and for the embodiment where the measurement is performed for at least four measurement planes, at least three induction factors of the wind between measurement planes are determined. It is thus possible to increase the precision of the wind deceleration phenomenon upstream from the wind turbine and, therefore, the precision in estimation of the induction factor of the wind in the rotor plane.

(39) According to an embodiment of the invention, an induction factor between measurement planes can be determined for the measurement plane closest to the rotor plane, to have information relative to the wind field as close as possible to the rotor plane.

(40) According to an implementation of the invention, the induction factors of the wind between measurement planes can be determined for measurement planes having the same spacing. For example, the spacing can be 50 m and a first induction factor can be determined for measurement planes located at 70 and 120 m, and a second induction factor for measurement planes located at 90 and 140 m.

(41) Preferably, the spacing between the measurement planes used for the induction factors of the wind between measurement planes can be identical to the distance between the rotor plane and the closest measurement plane. Thus, the induction factor model is simplified, which notably facilitates solution of the Kalman filter.

(42) For example, by combining the variants described above, if the first measurement plane is located 50 m from the rotor plane, a first induction factor can be determined for measurement planes located at 50 and 100 m, a second induction factor for measurement planes located at 70 and 120 m, and a third induction factor for measurement planes located at 90 and 140 m.

(43) According to an embodiment of the invention, the Kalman filter can be used with the different steps described hereafter. The steps are described for an embodiment where a first induction factor a.sub.50,100 is determined for measurement planes located at 50 and 100 m, a second induction factor a.sub.70,120 for measurement planes located at 70 and 120 m, and a third induction factor a.sub.90,140 for measurement planes located at 90 and 140 m.

(44) Below, it is only shown how to estimate a.sub.50,100 in real time. a.sub.70,120 and a.sub.90,140 are obtained exactly in the same way. Since u.sub.50, u.sub.100 are available in real time, the induction factor definition equation could be directly used to determine a.sub.50,100. However, this method involves two drawbacks. On the one hand, the information on the standard deviation of the estimated wind speeds u.sub.50, u.sub.100 is not used. The standard deviation of estimation a.sub.50,100 can therefore not be known. On the other hand, a calculation stability problem may occur for low speeds, i.e. when u.sub.100 is close to zero.

(45) The induction factor at the time k is denoted by a.sub.50,100(k). It is clear that the variation a.sub.50,100(k)-a.sub.50,100(k−1) is relatively small, therefore it can be expressed as:
a.sub.50,100(k)=a.sub.50,100(k−1)+η(k−1)
where η(k−1) is used to describe the variation of a.sub.50,100(k) over time.

(46) The first induction factor definition equation is rewritten as:
u.sub.100(k)a.sub.50,100(k)=u.sub.50(k).

(47) Since estimations u.sub.50(k), u.sub.100(k) contain noise. A more realistic model of the above equation is:
(u.sub.100(k)+∈.sub.100(k))a.sub.50,100(k)=u.sub.50(k)+∈.sub.50(k)
where ε.sub.50(k), ε.sub.100(k) are the noises for u.sub.50(k), u.sub.100(k) respectively. The previous equation can then be rewritten as follows:
u.sub.100(k)a.sub.50,100(k)=u.sub.50(k)+∈.sub.50(k)−∈.sub.100(k)a.sub.50,100(k)

(48) By combining the previous equations, the following equation of state is obtained:

(49) $\{\begin{array}{cc}{a}_{50,100}\left(k\right)& =a_{50,100}\left(k-1\right)+\eta \left(k-1\right),\\ u_{50}\left(k\right)& =u_{100}\left(k\right)a_{50,100}\left(k\right)+\mu \left(k\right)\end{array}\mu \left(k\right)={ϵ}_{100}\left(k\right)a_{50,100}\left(k\right)-{ϵ}_{50}\left(k\right)$

(50) One way of estimating the unknown state vector a.sub.50,100(k) that accounts for information on ε(k) and μ(k) applies a Kalman filtering algorithm referred to as Kalman filter. In practice. This filter provides the solution to the following problem:

(51) $\underset{a_{50,100}\left(k\right)}{\min }J\left(k\right)$
with

(52) $J\left(k\right)={\left(a_{50,100}\left(0\right)-{\stackrel{\_}{a}}_{50,100}\left(0\right)\right)}^T{P}_0^{-1}\left(a_{50,100}\left(0\right)-{\stackrel{\_}{a}}_{50,100}\left(0\right)\right)+\underset{j=1}{\overset{k}{.Math.}}\left({\eta \left(j-1\right)}^T{Q}^{-1}\eta \left(k-1\right)+{\mu \left(j\right)}^T{R}^{-1}\mu \left(j\right)\right)$
where P.sub.0, Q, R are weighting matrices of suitable dimension, a.sub.50,100(0). An overbar is the mean value of initial state a.sub.50,100(0).

(53) In order to solve the optimization problem using the Kalman filtering algorithm, the following assumptions are made. These assumptions mainly relate to a mathematical interpretation for P.sub.0, Q, R. a.sub.50,100(0) is a random vector which is not correlated with noises ε(k) and μ(k), a.sub.50,100(0) has a known mean with P0 being the covariance matrix, expressed as:
P.sub.0=E[(a.sub.50,100(0)−ā.sub.50,100(0))(a.sub.50,100(0)−ā.sub.50,100(0)).sup.T] with ā.sub.50,100(0) the mean value of the initial state, ε(k) and μ(k) are white noises with zero mean which are not correlated with covariance matrices Q and R respectively:

(54) $E\left[\eta \left(k\right){\eta \left(j\right)}^T\right]=\{\begin{array}{c}Q,\mathrm{if}k=j,\\ 0,\mathrm{if}k\ne j\end{array}E\left[\mu \left(k\right){\mu \left(j\right)}^T\right]=\{\begin{array}{c}R,\mathrm{if}k=j,\\ 0,\mathrm{if}k\ne j\end{array}E\left[\eta \left(k\right){\mu \left(j\right)}^T\right]=0,\mathrm{for}\mathrm{all}k,j$

(55) It is noted that this assumption also implies that Q and R are positive semi-definite symmetric matrices.

(56) The following notations are adopted: â.sub.50,100(k|k−1) is the estimation of a.sub.50,100(k) given the time measurements k−1 â.sub.50,100(k|k) is the estimation of a.sub.50,100(k) given the time measurements k P(k|k−1) is the covariance matrix of a.sub.50,100(k) given the time measurements k−1 P(k|k) is the covariance matrix of a.sub.50,100(k) given the time measurements k.

(57) The Kalman filtering algorithm can then be summarized as follows: Time update equation:

(58) $\{\begin{array}{cc}{\hat{a}}_{50,100}\left(k.Math.k-1\right)& ={\hat{a}}_{50,100}\left(k-1.Math.k-1\right)\\ P\left(k.Math.k-1\right)& =P\left(k-1.Math.k-1\right)+Q\end{array}\hspace{1em}$ Measurement update equation:

(59) $\{\begin{array}{cc}K\left(k\right)& =P\left(k.Math.k-1\right){u_{100}\left(k\right)}^T{\left(P\left(k.Math.k-1\right)+u_{100}\left(k\right){{\mathrm{Ru}}_{100}\left(k\right)}^T\right)}^{-1}\\ {\hat{a}}_{50,100}\left(k.Math.k\right)& ={\hat{a}}_{50,100}\left(k.Math.k-1\right)+K\left(k\right)\left(u_{50}\left(k\right)-u_{100}\left(k\right)\hat{x}\left(k.Math.k-1\right)\right),\\ P\left(k.Math.k\right)& =\left(I-K\left(k\right)\right)P\left(k.Math.k-1\right)\end{array}\hspace{1em}$

(60) By carrying out these steps, induction factor a.sub.50,100 can be determined. These steps can be repeated to determine induction factors a.sub.70,120 and a.sub.90,140.

(61) FIG. 6 illustrates, by way of non-limitative example, induction factors between measurement planes a.sub.50,100 (dark grey), a.sub.70,120 (dotted medium grey) and a.sub.90,140 (dashed light grey) as a function of time T in seconds. These induction factors are obtained with the method according to the invention. The wind deceleration phenomenon can be seen on the one hand as the closer to the wind turbine, the lower the induction factor between measurement planes. On the other hand, it is observed that the induction factor is variable over time.

(62) FIG. 7 illustrates, by way of non-limitative example, the evolution of the induction factor between measurement planes a as a function of distance D in meters of the first measurement plane for a given time. The wind deceleration phenomenon and the non-linearity of the induction factor as a function of distance are also observed.

(63) 3. Determining the Induction Factor Between a Measurement Plane and the Rotor Plane

(64) This step determines in real time the induction factor of the wind between one of the measurement planes and the rotor plane. Thus, the evolution of the wind at the rotor can be represented by accounting for the physical phenomena, in particular the wind deceleration. According to the invention, the induction factor of the wind between a measurement plane and the rotor plane is determined by use of the induction factors determined in the previous step and using a Kalman filter, notably a linear Kalman filter. To simplify, this induction factor is referred to as induction factor in the rotor plane in the description hereafter.

(65) Preferably, the induction factor of the wind can be determined between the measurement plane closest to the rotor and the rotor plane.

(66) For example, in this step, the induction factor can be determined between a measurement plane located 50 m from the rotor and the rotor plane.

(67) According to an embodiment of the invention, the Kalman filter can be used by applying the various steps described below. The steps are described for an embodiment for which a.sub.50,100, a.sub.70,120 and a.sub.90,140 have been determined and for which a.sub.0,50 is determined, which is the induction factor between a measurement plane located at 50 m and the rotor plane.

(68) Using a.sub.50,100, a.sub.70,120 and a.sub.90,140, the main idea of the estimation of a.sub.0,50 is to assume that a.sub.0,50, a.sub.50,100, a.sub.70,120 and a.sub.90,140 depend on distance. The following relation is therefore assumed:

(69) $\{\begin{array}{cc}{a}_{0,50}& =0_{x_1}+x_2,\\ a_{50,100}& =50x_1+x_2,\\ a_{70,120}& =70x_1+x_2,\\ a_{90,140}& =90x_1+x_2\end{array}\hspace{1em}$
where x.sub.1, x.sub.2 are unknown parameters that need to be determined. Since a.sub.50,100, a.sub.70,120 and a.sub.90,140 change slowly over time, the same applies to x.sub.1, x.sub.2. Therefore, they are expressed as:

(70) $\{\begin{array}{c}{x}_1\left(k\right)=x_1\left(k-1\right)+{\zeta }_1\left(k-1\right),\\ x_2\left(k\right)=x_2\left(k-1\right)+{\zeta }_2\left(k-1\right)\end{array}\hspace{1em}$
where ζ1(k), ζ2(k) are used to characterize the variation of x.sub.1(k), x.sub.2(k). Therefore, the variation is expressed as:

(71) 0$x\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\end{array}\right],\zeta \left(k\right)=\left[\begin{array}{c}{\zeta }_1\left(k\right)\\ {\zeta }_2\left(k\right)\end{array}\right]$

(72) They can be expressed in compact form:
x(k)=x(k−1)+ζ(k−1).

(73) A more realistic model taking account of the noises is:

(74) $\{\begin{array}{c}{a}_{50,100}\left(k\right)=[\begin{array}{cc}50& 1]\end{array}x\left(k\right)+{ϵ}_1\left(k\right),\\ a_{70,120}\left(k\right)=[\begin{array}{cc}70& 1]\end{array}x\left(k\right)+{ϵ}_2\left(k\right),\\ a_{50,100}\left(k\right)=[\begin{array}{cc}50& 1]\end{array}x\left(k\right)+{ϵ}_1\left(k\right),\end{array}\hspace{1em}$
where ε1, ε2, ε3 are the noises of estimations a.sub.50,100(k), a.sub.70,120(k) and a.sub.90,140(k). They can be expressed as:

(75) $y\left(k\right)=\left[\begin{array}{c}{a}_{50,100}\left(k\right)\\ a_{70,120}\left(k\right)\\ a_{50,100}\left(k\right)\end{array}\right],C=\left[\begin{array}{cc}50& 1\\ 70& 1\\ 90& 1\end{array}\right],ϵ\left(k\right)=\left[\begin{array}{c}{ϵ}_1\left(k\right)\\ {ϵ}_2\left(k\right)\\ {ϵ}_3\left(k\right)\end{array}\right]$

(76) They can be expressed in compact form:
y(k)=Cx(k)+ε(k).

(77) By combining the previous equations, the equation of state is obtained as follows:

(78) $\{\begin{array}{c}x\left(k\right)=x\left(k-1\right)+\zeta \left(k-1\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+ϵ\left(k\right)\end{array}\hspace{1em}$

(79) As for a.sub.50,100(k), a.sub.70,120(k) and a.sub.90,140(k), one way of obtaining x(k) that takes account for noises ζ(k), ε(k) uses the linear Kalman filter technique. The same steps as those described for the previous step are therefore applied.

(80) Once x(k) estimated, induction factor a.sub.0,50 can be calculated as follows:
a.sub.0,50(k)=[0 1]x(k).

(81) FIG. 8 illustrates, by way of a non-limitative example, the induction factor in the rotor plane a.sub.0,50 as a function of time T in seconds. This induction factor is obtained with the method according to the invention from the induction factors of FIG. 6. The wind deceleration phenomenon (induction) can be seen on the one hand with the induction factor at the rotor (FIG. 8) being lower than the induction factors between measurement planes (FIG. 6). On the other hand, it is observed that the induction factor is variable over time. Besides, the evolutions from one induction factor to another are different.

(82) FIG. 9 is a curve similar to FIG. 7 showing, by way of non-limitative example, the evolution of induction factor a as a function of distance D in meters from the first measurement plane for a given time. The wind deceleration phenomenon and the non-linearity of the induction factor as a function of distance are also observed.

(83) Thus, the method according to the invention determines the induction factor of the wind between a measurement plane and the rotor plane in real time.

(84) Applications

(85) Furthermore, the invention relates to a method of determining the wind speed in the rotor plane of a wind turbine equipped with a LiDAR sensor. The following steps are carried out for this method: determining an induction factor of the wind between a measurement plane and the rotor plane of the wind turbine by use of the method according to any one of the variant combinations described above; and determining the wind speed in the rotor plane of the wind turbine as a function of the induction factor of the wind determined in the previous step, and by use of at least one wind speed measurement used in the previous step with the wind speed measurement corresponding to the wind speed in the measurement plane relative to the measurement plane used for the induction factor.

(86) In other words, if the induction factor between a measurement plane located at distance d2 from the rotor plane is determined in the first step, the measurement of the wind speed in the measurement plane located at distance d2 from the rotor plane is used in the step of determining the wind speed in the rotor plane.

(87) The method according to the invention allows determination online of the wind speed in the rotor plane, in a simple and precise manner (since it takes account of the physical phenomena in the induction zone).

(88) According to an embodiment, the wind speed in the rotor plane can be determined by multiplying (product) the induction factor of the wind by the relative wind speed. The induction factor definition equation can then be expressed as follows:
u.sub.0=u.sub.d2×a.sub.0,d2
with speed u.sub.d2 being measured and the induction factor a.sub.0,d2 being determined by the induction factor determination method.

(89) FIG. 3 schematically illustrates, by way of non-limitative example, the steps of the method of determining the wind speed in the rotor plane. The first steps are identical to the steps of FIG. 2. The first step is a step (MES) of measuring the wind speed in several measurement planes. The second step uses the measurements and a Kalman filter (KAL1) to determine the induction factors between measurement planes denoted by a.sub.PM. The third step uses the induction factors between measurement planes a.sub.PM to determine, by means of a Kalman filter (KAL2), the induction factor of the wind between a measurement plane and the rotor plane denoted by a.sub.PR. The fourth step (VIV) determines the wind speed in the rotor plane u.sub.0 from the induction factor between a measurement plane and rotor plane a.sub.PR, and a measurement of the wind speed in the measurement plane considered.

(90) The present invention also relates to a method of controlling a wind turbine equipped with a LiDAR sensor. The following steps are carried out for this method: determining the wind speed in the rotor plane by use of the method of determining the wind speed according to any one of the above variants; and controlling the wind turbine according to the wind speed in the rotor plane.

(91) Precise real-time knowledge of the wind speed in the rotor plane allows suitable wind turbine control in terms of minimization of the effects on the wind turbine structure and maximization of the recovered power. Indeed, by use of this control, the LiDAR allows reduction of loads on the structure, with the blades and the tower representing 54% of the cost. Therefore, using a LiDAR sensor allows optimizing the wind turbine structure and thus decreasing the costs and maintenance.

(92) According to an implementation of the invention, at least one of the inclination angle of the blades and the electrical recovery torque of the wind turbine generator can be controlled as a function of the wind speed. Other types of regulation devices can also be used.

(93) According to an embodiment of the invention, at least one of the inclination angle of the blades and the electrical recovery torque are determined by use of wind turbine maps as a function of the wind speed at the rotor. For example, the control method described in French patent application FR-2,976,630 A1 which corresponds to US 2012-0,321,463 can be applied.

(94) FIG. 4 schematically illustrates, by way of non-limitative example, the steps of the wind turbine control determination method. The first steps are identical to the steps of FIG. 3. The first step is a step (MES) of measuring the wind speed in several measurement planes. The second step uses the measurements and a Kalman filter (KAL1) to determine the induction factors between measurement planes denoted by a.sub.PM. The third step uses the induction factors between measurement planes a.sub.PM to determine, by use of a Kalman filter (KAL2), the induction factor of the wind between a measurement plane and the rotor plane denoted by a.sub.PR. The fourth step (VIV) determines the wind speed in the rotor plane u.sub.0 from the induction factor between a measurement plane and rotor plane a.sub.PR, and a measurement of the wind speed in the measurement plane being considered. The fifth step (CON) relates to the wind turbine control as a function of wind speed u.sub.0 in the rotor plane.

(95) Furthermore, the invention relates to at least one of a diagnosis and monitoring for a wind turbine equipped with a LiDAR sensor, wherein the following steps are carried out: determining an induction factor of the wind between a measurement plane and the rotor plane of the wind turbine by use of the induction factor determination method according to any one of the variant combinations described above; determining the aerodynamic power drawn from the wind by the wind turbine by use of the induction factor determined in the previous step; and at least one of diagnosing monitoring the operation of the wind turbine according to the aerodynamic power determined in the previous step.

(96) By use of the induction factor expressing the wind deceleration due to the presence of the wind turbine in the wind field, it is possible to determine from this induction factor the aerodynamic power drawn from the wind by the wind turbine. According to an embodiment, the aerodynamic power drawn P.sub.aéro expressed by the relationship below can be determined by use of induction factor a, the speed of the free wind flow V.sub.inf, the air density Ro and the surface area of the wind turbine A.sub.d,
P.sub.aéro=2RoA.sub.dV.sub.inf.sup.3a(1−a).sup.2

(97) The aerodynamic power drawn provides information on the operation of the wind turbine, which enables at least one diagnosis and monitoring of the wind turbine operation. The fundamental operation compares the electrical power produced by the wind turbine with the theoretical electrical power given by the previous equation.

(98) The ratio of the two powers allows performing at least one of diagnosis and monitoring of the operation and of the effective aerodynamic yield of the wind turbine.

(99) Real-time update of the induction factor also allows to quantify the aerodynamic thrust loads applied on the wind turbine and to deduce therefrom an estimation of the cumulative fatigue damage. According to an implementation of the invention, this can be done using the relation that connects the thrust coefficient C.sub.T to the induction factor (Burton, Wind Energy Handbook, ch. 3.2), which can be written as follows: C.sub.T=4a(1−a).

(100) Furthermore, online estimation of the induction factor can allow development and updating in real time simplified wind turbine wake models. This allows performing operation diagnoses at a wind farm scale including identifying risk zones with wake interaction between neighboring wind turbines.

(101) FIG. 5 schematically illustrates, by way of non-limitative example, the steps of the method of determining the wind speed in the rotor plane. The first steps are identical to the steps of FIG. 2. The first step is a step (MES) of measuring the wind speed in several measurement planes. The second step uses the measurements and a Kalman filter (KAL1) to determine the induction factors between measurement planes denoted by a.sub.PM. The third step uses the induction factors between measurement planes a.sub.PM to determine, by use of a Kalman filter (KAL2), the induction factor of the wind between a measurement plane and the rotor plane denoted by a.sub.PR. The fourth step (PUI) determines the aerodynamic power drawn from the wind P.sub.aéro from the induction factor between a measurement plane and rotor plane a.sub.PR, and a wind speed measurement in the measurement plane. The fifth step (DIA) performs diagnosis or monitoring of the wind turbine according to the aerodynamic power drawn P.sub.aéro.

(102) Furthermore, the invention relates to a computer program product comprising code instructions designed to carry out the steps of one of the methods described above for an induction factor determination method, speed determination in the rotor plane, control method, including at least one of diagnosis and monitoring method. The program is executed on a unit for processing the LiDAR sensor, or on any similar medium connected to the LiDAR sensor or to the wind turbine.

(103) According to an aspect, the present invention also relates to a LiDAR sensor for a wind turbine, comprising a processing unit configured to implement one of the methods described above (induction factor determination method, speed determination in the rotor plane, control method, and at least one of diagnosis and monitoring).

(104) According to an implementation of the 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.

(105) The invention also relates to a wind turbine, notably for an offshore or an onshore wind turbine equipped with a LiDAR sensor as described above. According to an embodiment of the invention, the LiDAR sensor can be arranged on the nacelle of the wind turbine. The LiDAR sensor is so oriented to perform a measurement of the wind upstream from the wind turbine (that is before the wind turbine and along the longitudinal axis thereof, designated by axis x in FIG. 1). According to an embodiment, the wind turbine can be similar to the wind turbine illustrated in FIG. 1.

(106) For the embodiment of the control method, the wind turbine can comprise a control use, for example for control of the pitch angle of a wind turbine blade or of the electrical torque, for implementing the method according to the invention.

(107) For the embodiment of at least one of the diagnosis and monitoring method, the wind turbine can comprise at least one of wind turbine operation diagnosis and monitoring use.