Method of determining the wind speed in the rotor plane used for controlling a wind turbine

Abstract

The present invention is a method of controlling a wind turbine by determining the wind speed in the plane of a rotor (PR) of a wind turbine (1), by measuring the rotational speed of the rotor, the angle of the blades and the generated power. The method according to the invention implements a dynamic wind turbine model, a dynamic wind model and an unscented Kalman filter.

Claims

1. A method of controlling a wind turbine comprising steps of: a) measuring rotational speed of a rotor of the wind turbine, an inclination angle of at least one blade of the wind turbine and power generated by a conversion machine of the wind turbine; b) constructing a dynamic model of the wind turbine relating the rotational speed of the rotor of the wind turbine to the wind speed in a rotor plane to the inclination angle of the at least one blade of the wind turbine and to the power generated by the conversion machine of the wind turbine; c) constructing a dynamic wind model using a second-order random walk model which has a succession of random time intervals; d) determining the wind speed in the rotor plane by using an unscented Kalman filter applied to the dynamic model of the wind turbine, to the dynamic wind model, and from the measuring the rotational speed of the rotor, the inclination angle of at least one of the turbine blades and the power generated by the conversion machine of the wind turbine; and e) controlling the wind turbine according to the wind speed in the rotor plane by controlling at least one of the inclination angle of the at least one blade, electrical recovery torque of the wind turbine generator and orientation of a nacelle as a function of wind speed and direction.

2. A method of controlling a wind turbine as claimed in claim 1, wherein the dynamic wind model is expressed with a relationship: $\{\begin{array}{c}\left[\begin{array}{c}\frac{{\mathrm{dv}}_1\left(t\right)}{\mathrm{dt}}\\ \frac{{\mathrm{dv}}_2\left(t\right)}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{v}_1\left(t\right)\\ v_2\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ \eta \left(t\right)\end{array}\right]\\ v\left(t\right)=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{v}_1\left(t\right)\\ v_2\left(t\right)\end{array}\right]\end{array}$ with v.sub.1(t) being the wind speed in the rotor plane, v.sub.2(t) being a wind speed derivative in the rotor plane, and η(t) being a white noise with a zero mean and v(t)=v.sub.1(t).

3. A method of controlling a wind turbine as claimed in claim 2, wherein the dynamic model of the wind turbine is expressed with a relationship: $\frac{d\omega \left(t\right)}{\mathrm{dt}}=\frac{1}{2J}\mathrm{\pi \rho }{R}^3{C}_q\left(\beta \left(t\right),\lambda \left(t\right)\right){v\left(t\right)}^2-\frac{P_g\left(t\right)}{J\omega \left(t\right)}-\frac{1}{J}{T}_l\left(t\right)$ with ω(t) being the rotational speed of the rotor, J being a moment of inertia of a kinematic chain of the wind turbine, ρ being the air density, R being a radius of the rotor, C.sub.q being the power coefficient, β(t) being the inclination angle of the blades, λ(t) being a ratio of blade tip speed to the wind speed in the rotor plane, P.sub.g(t) being the power generated by the conversion machine of the wind turbine, v(t) being the wind speed in the rotor plane and T.sub.1(t) being the loss torque along the kinematic chain of the wind turbine.

4. A method of controlling a wind turbine as claimed in claim 3, wherein the loss torque Tl(t) is considered to be noise.

5. A method of controlling a wind turbine as claimed in claim 4, wherein the power coefficient C.sub.q is obtained by using a map of the wind turbine.

6. A method of controlling a wind turbine as claimed in claim 3, wherein the power coefficient C.sub.q is obtained by using a map of the wind turbine.

7. A method of controlling a wind turbine as claimed in claim 2, wherein the method determines a longitudinal component of an average wind speed in the rotor plane.

8. A method of controlling a wind turbine as claimed in claim 1, wherein the dynamic model of the wind turbine is expressed with a relationship: $\frac{d\omega \left(t\right)}{\mathrm{dt}}=\frac{1}{2J}\mathrm{\pi \rho }{R}^3{C}_q\left(\beta \left(t\right),\lambda \left(t\right)\right){v\left(t\right)}^2-\frac{P_g\left(t\right)}{J\omega \left(t\right)}-\frac{1}{J}{T}_l\left(t\right)$ with ω(t) being the rotational speed of the rotor, J being a moment of inertia of a kinematic chain of the wind turbine, ρ being air density, R being a radius of the rotor, C.sub.q being a power coefficient, β(t) being the inclination angle of the blades, λ(t) being a ratio of blade tip speed to the wind speed in the rotor plane, P.sub.g(t) being the power generated by the conversion machine of the wind turbine, v(t) being the wind speed in the rotor plane and T.sub.1(t) being the loss torque along the kinematic chain of the wind turbine.

9. A method of controlling a wind turbine as claimed in claim 8, wherein the loss torque Tl(t) is considered to be noise.

10. A method of controlling a wind turbine as claimed in claim 9, wherein the power coefficient C.sub.q is obtained by using a map of the wind turbine.

11. A method of controlling a wind turbine as claimed in claim 9, wherein the method determines a longitudinal component of an average wind speed in the rotor plane.

12. A method of controlling a wind turbine as claimed in claim 8, wherein the power coefficient C.sub.q is obtained by using a map of the wind turbine.

13. A method of controlling a wind turbine as claimed in claim 12, wherein the method determines a longitudinal component of an average wind speed in the rotor plane.

14. A method of controlling a wind turbine as claimed in claim 8, wherein the method determines a longitudinal component of an average wind speed in the rotor plane.

15. A method of controlling a wind turbine as claimed in claim 1, wherein the method determines a longitudinal component of an average wind speed in the rotor plane.

16. A controlling a wind turbine as claimed in claim 1, wherein the unscented Kalman filter is applied to an equation of state expressed as: $\{\begin{array}{c}\left[\begin{array}{c}\frac{{\mathrm{dx}}_1\left(t\right)}{\mathrm{dt}}\\ \frac{{\mathrm{dx}}_2\left(t\right)}{\mathrm{dt}}\\ \frac{{\mathrm{dx}}_3\left(t\right)}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{c}\frac{1}{2J}\mathrm{\pi \rho }{R}^3{C}_q\left(\beta \left(t\right),\frac{{\mathrm{Rx}}_1\left(t\right)}{x_2\left(t\right)}\right){x_2\left(t\right)}^2-\frac{P_g\left(t\right)}{{\mathrm{Jx}}_1\left(t\right)}\\ x_3\left(t\right)\\ 0\end{array}\right]+\left[\begin{array}{c}{\mu }_1\left(t\right)\\ 0\\ {\mu }_2\left(t\right)\end{array}\right]\\ y\left(t\right)=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+\xi \left(t\right)\end{array}$ with $x_1\left(t\right)=\omega \left(t\right),x_2\left(t\right)=v\left(t\right),x_3\left(t\right)=\frac{dv\left(t\right)}{dt},$ ω(t) being the rotational speed of the rotor, J being a moment of inertia of the kinematic chain of the wind turbine, ρ being the air density, R being a radius of the rotor, C.sub.q being a power coefficient, β(t) being an inclination angle of the blades, P.sub.g(t) being the power generated by the conversion machine of the wind turbine, v(t) being the wind speed in the rotor plane, μ.sub.1(t) and μ.sub.2(t) being independent white noises with zero means, and y(t) being a measured output identified at the rotor speed ω(t) corrupted by a white noise.

17. A method of controlling a wind turbine as recited in claim 1, wherein the wind speed is determined by carrying out steps of: i) initializing k=0, a state vector {circumflex over (x)}.sub.a(0|0)=m(0) and a state of a covariance matrix P(0|0)=P.sub.0, ii) at any time k different from 0, acquiring the measurements y(k); and iii) at any time k different from 0, determining wind speed v(k) in the rotor plane by using equations as follows: $K\left(k\right)=P\left(k|k-1\right){C^T\left(\mathrm{CP}\left(k|k-1\right)C^T+R\right)}^{-1}$ $\{\begin{array}{c}x\left(k|k\right)=x\left(k|k-1\right)+K\left(k\right)\left(y\left(k\right)-\mathrm{Cx}\left(k|k-1\right)\right)\\ P\left(k|k\right)=\left(I_3-K\left(k\right)C\right)P\left(k|k-1\right)\end{array}$ $v\left(k\right)=\left[\begin{array}{ccc}0& 1& 0\end{array}\right]\hat{x}$ with K being the Kalman filter gain, P being the covariance of a Gaussian noise μ, P(k|k−1) being error variance from the measurements of the time k−1, P(k|k) being error variance from the measurements of the time k, x(k|k) being an estimation of x(k) from the measurements of time k, x(k|k−1) being an estimation of x(k) from the measurements of time k−1, and R being the covariance of a Gaussian noise ξ, C=[1 0 0],l.sub.3 being a identity matrix of size 3.

18. A tangible computer program product, comprising code instructions for executing steps of the method of controlling a wind turbine as recited in claim 1, when the program is executed by one of a control and diagnosis unit of the wind turbine.

19. A wind turbine, comprising means for measuring the rotational speed of the rotor, means for measuring an inclination angle of the wind turbine blades, means for measuring power generated by a conversion machine of the wind turbine, and means for determining wind speed in a rotor plane of the wind turbine for implementing the method of controlling a wind turbine as recited in claim 1.

20. A wind turbine as claimed in claim 19, comprising a real-time control and data acquisition system including the means for measuring rotational speed of the rotor, the means for measuring the inclination angle of the wind turbine blades and the means for measuring the power generated by the conversion machine 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 according to an embodiment of the invention;

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

(4) FIG. 3 illustrates an example of a map of power coefficient C.sub.q;

(5) FIG. 4 illustrates a curve of the power generated by an (electrical) conversion machine as a function of time, measured for an application example;

(6) FIG. 5 illustrates a curve of the rotational speed of the rotor as a function of time, measured for the example of FIG. 4;

(7) FIG. 6 illustrates a curve of the inclination angle of the blades as a function of time, measured for the example of FIGS. 4 and 5; and

(8) FIG. 7 illustrates curves of the wind speed in the rotor plane as a function of time, obtained with the method according to an embodiment of the invention and by use of a LiDAR sensor, for the example of FIGS. 4 to 6.

DETAILED DESCRIPTION OF THE INVENTION

(9) The present invention relates to a method of determining in real time the wind speed in the rotor plane of a wind turbine.

(10) FIG. 1 schematically shows, by way of non-limitative example, a horizontal-axis wind turbine 1 for the method according to an embodiment of the invention. Conventionally, a wind turbine 1 converts the kinetic energy of the wind into electrical or mechanical energy. For wind energy conversion, it is made up of the following elements: 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 allowing this rotor to be positioned at a height enabling it to be 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.); 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 conversion machine. Nacelle 3 can rotate to orient the machine in the right direction; the rotor, fastened to the nacelle, comprising 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) or to any other conversion machine (hydraulic or pneumatic machine for example) that converts the energy recovered into electrical energy or any type of energy (hydraulic or pneumatic for example). The rotor is potentially provided with control systems such as a variable-angle blades or aerodynamic brakes, a transmission (not shown) having two connected shafts (mechanical shaft of the rotor and mechanical shaft of the conversion machine), thus forming a kinematic chain between the mechanical shaft of the rotor and the mechanical shaft of the conversion machine.

(11) 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. Direction y, 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 up, axis z is perpendicular to axes x and y. The rotor plane is indicated by the rectangle in dotted line PR, it is defined by directions y, z for a zero value of x.

(12) According to the invention, the method for determining the wind speed comprises the following steps: 1) measurements; 2) construction of the dynamic wind turbine model; 3) construction of the dynamic wind model; and 4) determination of the wind speed.

(13) Steps 1) and 4) can be carried out in real time. Steps 2) and 3) can be carried out beforehand and offline. These steps are described in detail in the rest of the description.

(14) FIG. 2 schematically illustrates, by way of non-limitative example, the steps of the method of determining the wind speed according to an embodiment of the invention. A dynamic wind turbine model MEO relating the rotational speed of the rotor to the wind speed in the rotor plane, the inclination angle of the blades and the power generated by the conversion machine can be constructed beforehand. Furthermore, a dynamic wind model MVE can be constructed beforehand. The method also involves a step of measuring MES the rotational speed of the rotor w, the inclination angle of the blades β and the power P.sub.g generated by the conversion machine. An unscented Kalman filter UKF is then applied to dynamic wind turbine model MEO, dynamic wind model MVE and measurements ω, β, P.sub.g. The unscented Kalman filter allows determination of the wind speed in the rotor plane v.

(15) 1. Measurements

(16) The following measurements are performed in this step: measuring rotational speed of the rotor, measuring inclination angle of the blades, and measuring the power generated by the conversion machine (in other words, the power generated by the wind turbine).

(17) According to an embodiment of the invention, at least one of the measurements can be obtained from a real-time control and data acquisition system (SCADA: Supervisory Control And Data Acquisition). A SCADA system is a large-scale remote management system providing processing in real time of a large number of remote measurements and controlling technical equipment from a distance. It is an industrial technology in the field of instrumentation whose implementations may be considered as instrumentation structures including a middleware type layer. Preferably, all the measurements can be obtained from the SCADA system, which facilitates the implementation of the method with no particular instrumentation. Furthermore, the SCADA system can account for at least one other measurement to make determination of the wind speed in the rotor plane more precise. These measurements can notably be temperatures, electrical data, vibrations, etc. Temperatures can provide information about effective mechanical losses and they therefore allow modelling of the wind turbine to be refined. Accelerometry, combined with a sufficiently fine and relevant modal and vibrational understanding of the structure, allow going back to an estimation of the wind and turbulence conditions impacting the wind turbine.

(18) Alternatively, at least one of the measurements can be obtained by a dedicated sensor. For this embodiment at least one of: a rotor angular rotation sensor used for measuring the rotational speed of the rotor; and a blade angle sensor used for measuring the inclination angle of the blades; and a known and controlled voltage sensor used for measuring the power generated by the conversion machine and an electrical current sensor used for measuring the current delivered by the generator.

(19) 2. Construction of the Dynamic Wind Turbine Model

(20) This step constructs a dynamic wind turbine model relating the rotational speed of the rotor to the wind speed in the rotor plane, the inclination angle of the wind turbine blades and the power generated by the conversion machine of the wind turbine. A dynamic wind turbine model is understood to be a model obtained by applying fundamental dynamics principles to the wind turbine.

(21) According to an embodiment of the invention, the dynamic wind turbine model can be written:

(22) $\frac{d\omega \left(t\right)}{\mathrm{dt}}=\frac{1}{2J}\mathrm{\pi \rho }{R}^3{C}_q\left(\beta \left(t\right),\lambda \left(t\right)\right){\upsilon \left(t\right)}^2-\frac{P_g\left(t\right)}{J\omega \left(t\right)}-\frac{1}{J}{T}_l\left(t\right)$
with ω(t) being the rotational speed of the rotor, J being the moment of inertia of the kinematic chain of the wind turbine, ρ being the air density, R being the radius of the rotor, C.sub.q being the power coefficient, β(t) being the inclination angle of the blades, λ(t) being the ratio of the blade tip speed to the wind speed in the rotor plane (i.e.

(23) $\lambda \left(t\right)=\frac{R\omega \left(t\right)}{v\left(t\right)}),$
P.sub.g(t) being the power generated by the conversion machine of the turbine, v(t) being the wind speed in the rotor plane and T.sub.i(t) being the torque loss along the kinematic chain of the wind turbine. Preferably, for this embodiment, loss torque T.sub.i(t) can be considered to be noise. Thus, determination of the wind speed in the rotor plane is simplified. Alternatively, loss torque T.sub.i(t) can be measured.

(24) According to an implementation of this embodiment, the power coefficient C.sub.q can be obtained from a map of the wind turbine. Such a map relates the power coefficient C.sub.q to inclination angle β of the blades and to the ratio of the blade tip speed to the wind speed in the rotor plane A. According to a non-limitative example, the map can be constructed beforehand using an aerodynamic model of the wind turbine being considered. FIG. 3 schematically illustrates, by way of non-limitative example, an example of such a map relating the power coefficient C.sub.q as a function of the inclination angle β of the blades (in degrees) and the ratio A of the blade tip speed to the wind speed in the rotor plane.

(25) Indeed, the dynamic wind turbine model according to this embodiment can be obtained from the equation of the fundamental principles of dynamics:

(26) $J\frac{d\omega \left(t\right)}{\mathrm{dt}}=T_r\left(t\right)-T_g\left(t\right)-T_l\left(t\right)$
with ω(t) being the rotational speed of the rotor, J being the moment of inertia of the kinematic chain of the wind turbine, Tr(t) being the aerodynamic torque produced by the rotor, Tg(t) being the torque generated by the conversion machine and TIM being the loss torque along the kinematic chain of the wind turbine.

(27) In this equation, the aerodynamic torque can be written:

(28) $T_r\left(t\right)=\frac{1}{2}\mathrm{\pi \rho }{R}^3{C}_q\left(\beta \left(t\right),\lambda \left(t\right)\right){\upsilon \left(t\right)}^2$
with ρ being the air density, R being the radius of the rotor, C.sub.q being the power coefficient, β(t) being the inclination angle of the blades, λ(t) being the ratio of the blade tip speed to the wind speed in the rotor plane (that is

(29) 0$\lambda \left(t\right)=\frac{R\omega \left(t\right)}{v\left(t\right)}),$
and v(t) being the wind speed in the rotor plane.

(30) Furthermore, the torque generated by the conversion machine Tg can be expressed as:

(31) $T_g\left(t\right)=\frac{P_g\left(t\right)}{\omega \left(t\right)}$
with ω(t) being the rotational speed of the rotor and P.sub.g(t) being the power generated by the conversion machine of the wind turbine.

(32) The combination of these equations allows obtaining the dynamic wind turbine model described above.

(33) The method according to the invention is not limited to this dynamic model of the wind turbine, and it can be implemented for any other dynamic model of the wind turbine.

(34) 3. Construction of the Dynamic Wind Model

(35) This step constructs a dynamic model of the wind by use of a second-order random walk model. A dynamic wind model is a model that represents the evolution of the wind as a function of time. A random walk model is a model having discrete dynamics of a succession of random time intervals. For such a model, the future of the system depends on its present state but not on the past thereof. Using a random walk model provides good wind modelling, and such a model is suitable for representing smooth curves with a squared second derivative. Such a model does not require prior knowledge of wind characteristics such as average speed, turbulence, etc.

(36) According to an embodiment of the invention, the dynamic wind model can be expressed as:

(37) $\{\begin{array}{c}\left[\begin{array}{c}\frac{{\mathrm{dv}}_1\left(t\right)}{\mathrm{dt}}\\ \frac{{\mathrm{dv}}_2\left(t\right)}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{v}_1\left(t\right)\\ v_2\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ \eta \left(t\right)\end{array}\right]\\ v\left(t\right)=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{v}_1\left(t\right)\\ v_2\left(t\right)\end{array}\right]\end{array}$
with v.sub.1(t) being the wind speed in the rotor plane, v.sub.2(t) being the wind speed derivative in the rotor plane and n (t) being a white noise with a zero mean.

(38) 4. Determination of the Wind Speed

(39) This step determines the wind speed in the rotor plane of the wind turbine by use of an unscented Kalman filter (UKF). The unscented Kalman filter is applied to the dynamic wind turbine model constructed in step 2) and to the dynamic wind model constructed in step 3), and it accounts for the measurements performed in step 1). The unscented Kalman filter is a filtering algorithm that uses a system model for estimating the current hidden state of a system, then it corrects the estimation using the available measurements. The philosophy of UKF differs from the extended Kalman filter in that it uses the unscented transform to directly approximate the mean and the covariance of the target distribution. The unscented Kalman filter can comprise the steps of state prediction and measurement correction with these two steps being preceded by a prior step of calculating the “sigma points”. The sigma points are a set of samples calculated to allow the mean and variance information to be propagated precisely through the space of a nonlinear function.

(40) Such a filter is thus well suited for rapidly determining the wind speed in the rotor plane.

(41) According to an embodiment of the invention, it is possible to determine in this step the longitudinal component of the average wind speed in the rotor plane, denoted by REWS (Rotor Equivalent Wind Speed), which corresponds to the operating and production state of the wind turbine at a given time. It is a wind speed commonly used for at least one of control and monitoring of a wind turbine.

(42) According to an implementation of the invention, the unscented Kalman filter can be applied to the following equation of state:

(43) $\{\begin{array}{c}\left[\begin{array}{c}\frac{{\mathrm{dx}}_1\left(t\right)}{\mathrm{dt}}\\ \frac{{\mathrm{dx}}_2\left(t\right)}{\mathrm{dt}}\\ \frac{{\mathrm{dx}}_3\left(t\right)}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{c}\frac{1}{2J}\mathrm{\pi \rho }{R}^3{C}_q\left(\beta \left(t\right),\frac{{\mathrm{Rx}}_1\left(t\right)}{x_2\left(t\right)}\right){x_2\left(t\right)}^2-\frac{P_g\left(t\right)}{{\mathrm{Jx}}_1\left(t\right)}\\ x_3\left(t\right)\\ 0\end{array}\right]+\left[\begin{array}{c}{\mu }_1\left(t\right)\\ 0\\ {\mu }_2\left(t\right)\end{array}\right]\\ y\left(t\right)=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+\xi \left(t\right)\end{array}$
with

(44) $x_1\left(t\right)=\omega \left(t\right),x_2\left(t\right)=v\left(t\right),x_3\left(t\right)=\frac{\mathrm{dv}\left(t\right)}{\mathrm{dt}},$
ω(t) being the rotational speed of the rotor, J being the moment of inertia of the kinematic chain of the wind turbine, ρ being the air density, R being the radius of the rotor, C.sub.q being the power coefficient, β(t) being the inclination angle of the blades, P.sub.g(t) being the power generated by the conversion machine of the wind turbine, v(t) being the wind speed in the rotor plane, μ.sub.1(t) and μ.sub.2(t) being independent white noises with a zero mean, y(t) being the measured output identified at the rotor speed ω(t) corrupted by a white noise ξ(t).

(45) In other words: y(t)=ω(t)+ξ(t).

(46) This equation of state can be obtained by combining the dynamic models of the wind turbine and of the wind respectively determined in the previous steps.

(47) With this equation of state, the problem of estimating the wind speed in the rotor plane becomes the problem of estimating the state, that is the unknown state x(t)=[x.sub.1(t) x.sub.2(t) x.sub.3(t)]T at each sampling instant by use of this equation and of measured output y(t).

(48) The unscented Kalman filter can be implemented by discretizing the equation of state by use of a Eulerian discretization method. It is then obtained a relationship written on:

(49) $\{\begin{array}{c}x\left(k\right)=f\left(x\left(k-1\right),\beta \left(k-1\right),P_g\left(k-1\right)\right)+T_s\mu \left(k-1\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+\xi \left(k\right)\end{array}$$\mathrm{with}$$x\left(k\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right],\mu \left(k\right)=\left[\begin{array}{c}{\mu }_1\left(t\right)\\ 0\\ {\mu }_2\left(t\right)\end{array}\right],C=\left[\begin{array}{ccc}1& 0& 0\end{array}\right],$$f\left(x\left(k\right),\beta \left(k\right),P_g\left(k\right)\right)=\left[\begin{array}{c}{x}_1\left(k\right)+\frac{T_s}{2J}\mathrm{\pi \rho }{R}^3{C}_q\left(\beta \left(k\right),\frac{{\mathrm{Rx}}_1\left(k\right)}{x_2\left(k\right)}\right){x_2\left(k\right)}^2-\frac{P_g\left(k\right)}{{\mathrm{Jx}}_1\left(k\right)}\\ x_2\left(k\right)+T_s{x}_3\left(k\right)\\ x_3\left(k\right)\end{array}\right]$
with T.sub.s being the sampling period.

(50) In this discretized state model, it may be assumed that μ(t) and ξ(t) are Gaussian noises with zero mean having the respective covariance matrices Q and R.

(51) It is noted:
x(k|k−1)
is the estimation of x(k) from the measurements of time k−1.
x(k|k)
is the estimation of x(k) from the measurements of time k.
P(k|k−1)
is the error variance from the measurements of time k−1.
P(k|k)
is the error variance from the measurements of time k.

(52) For the given state estimation x(k−1|k−1) and the given error variance estimation P(k−1|k−1) at the time k−1, there are two steps in the UKF which are prediction and correction.

(53) After the correction step at the time k−1, the distribution of x(k−1) can be expressed as follows:
x(k−1)˜(x(k−1|k−1),P(k−1|k−1))
with designating a Gaussian distribution.

(54) The sigma points related to the mean c(k−1|k−1) and to the covariance matrix P(k−1|k−1) can be calculated as follows:

(55) $\{\begin{array}{c}{\chi }_0=x\left(k-1|k-1\right)\\ {\chi }_i=x\left(k-1|k-1\right)+\sqrt{n+\lambda }{S}_i,i=\stackrel{\_}{1,n}\\ {\chi }_{i+n}=x\left(k-1|k-1\right)-\sqrt{n+\lambda }{S}_i,i=\stackrel{\_}{1,n}\end{array}$

(56) In this case, n=3 and Si is the i-th column of S with:
SS.sup.T=P(k−1|k−1).

(57) The sigma points are propagated in the equation of state as follows:
γ.sub.i(k)=f(x.sub.i,β(k−1),P.sub.g(k−1))
with γ.sub.i the realizations of x(k|k−1) for any i ranging from 0 to 2n.

(58) The next step calculate the predicted mean and the predicted covariance P(k|k−1) by use of:

(59) $\{\begin{array}{c}x\left(k|k-1\right)=\underset{i=0}{\overset{2n}{.Math.}}{W}_i^m{\gamma }_i,\\ P\left(k|k-1\right)=\underset{i=0}{\overset{2n}{.Math.}}{W}_i^c\left({\gamma }_i-x\left(k|k-1\right)\right){\left({\gamma }_i-x\left(k|k-1\right)\right)}^T+T_s^{2}Q\end{array}$

(60) Given that the output equation is linear, the correction step is similar to that of a linear Kalman filter. The Kalman gain can be calculated as follows:
K(k)=P(k|k−1)C.sup.T(CP(k−1)C.sup.T+R).sup.−1

(61) The state estimation x(k|k) and the covariance estimation P(k|k) at the time k can then be calculated with:

(62) $\{\begin{array}{c}x\left(k|k\right)=x\left(k|k-1\right)+K\left(k\right)\left(y\left(k\right)-\mathrm{Cx}\left(k|k-1\right)\right)\\ P\left(k|k\right)=\left(I_3-K\left(k\right)C\right)P\left(k|k-1\right)\end{array}$
with l.sub.3 the identity matrix of size 3.

(63) Once the state estimation {circumflex over (x)}=x(k|k) is determined, the wind speed in the rotor plane can be calculated by implementing: v(k)=[0 1 0]{circumflex over (x)}.

(64) The present invention also relates to a method of controlling at least one wind turbine. The following steps can be carried out for this method: determining the wind speed in the rotor plane of the wind turbine by use of the method of determining the wind speed according to any one of the above variants or variant combinations; and controlling the wind turbine according to the wind speed in the rotor plane of the wind turbine.

(65) Precise real-time prediction of the wind speed in the rotor plane of the wind turbine allows suitable wind turbine control in terms of minimization of the effects on the turbine structure and maximization of the recovered power. Indeed, this control enables adaptation of the turbine equipments so that the turbine is in the optimum configuration for this wind.

(66) According to an implementation of the invention, the inclination angle of at least one of the blades, the electrical recovery torque of the wind turbine generator and the orientation of the nacelle can be controlled as a function of the wind speed and direction. Preferably, the individual inclination angle of the blades can be controlled. Other types of regulation devices can be used. Controlling the blade inclination allows to optimize energy recovery as a function of the incident wind on the blades.

(67) According to an embodiment of the invention, at least one of the inclination angle of the blades and the electrical recovery torque can be 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 corresponding to US published patent application 2012-/0.32.1.463 can be applied.

(68) The present invention further relates to method for at least one of monitoring and diagnosis of at least one wind turbine. The following steps can be carried out for this method: determining the wind speed in the rotor plane of the wind turbine by use of the method of determining the wind speed according to any one of the above variants or variant combinations; and at least one of monitoring and diagnosing the operation of the wind turbine according to the wind speed in the rotor plane.

(69) At least one of monitoring and diagnosis can for example correspond to the mechanical strain undergone by the structure of the wind turbine according to the wind speed in the rotor plane of the wind turbine.

(70) Furthermore, the invention relates to a computer program product comprising code instructions for carrying out the steps of one of the methods described above (method of determining the wind speed, control method, diagnosis method). The program is executed on at least one of a wind turbine control and a diagnosis unit.

(71) The invention also relates to a wind turbine, notably an offshore (at sea) or an onshore (on land) wind turbine. The wind turbine is equipped for measuring the rotation of the rotor, for measuring the inclination angle of the blades, and for measuring the power generated by the conversion machine. Moreover the wind turbine comprises an apparatus for determining the wind speed in the rotor plane able to implement the method of determining the wind speed according to any one of the above variants or variant combinations. According to an embodiment, the wind turbine can be similar to the wind turbine illustrated in 1.

(72) According to an embodiment of the invention, the wind turbine can comprise a real-time control and data acquisition system (SCADA) including at least one measuring apparatus from among the apparatus for measuring the rotation of the rotor, the apparatus for measuring the inclination angle of the blades and the apparatus for measuring the power generated by the conversion machine. Preferably, the SCADA system can have all these measuring apparatus. Moreover, the SCADA system can comprise additional measuring apparatus (for example temperature, electric data, . . . ) allowing determination of the wind speed in the rotor plane to be more precise.

(73) Alternatively, the wind turbine can comprise at least one sensor for carrying out at least one of these measurements, such as: at least one of a rotor angular rotation sensor for measuring the rotational speed of the rotor; r a blade angle sensor for measuring the inclination angle of the blades; and a known and controlled voltage sensor for measuring the power generated by the conversion machine and a current sensor for measuring the current delivered by the generator.

(74) For the embodiment of the control method, the wind turbine can comprise a control, for example for control of the inclination angle (or pitch angle) of at least one blade of the wind turbine or of the electrical torque, for implementing the control method according to the invention.

(75) The invention is not limited to the embodiments of the methods described above by way of example and that it encompasses any variant embodiment.

Example

(76) The features and advantages of the method according to the invention will be clear from reading the application example hereafter.

(77) The example relates to the determination of the wind speed REWS (Rotor Equivalent Wind Speed) in the rotor plane of the wind turbine, corresponding to the operating and production state of the wind turbine at a given time. The wind turbine is equipped with a SCADA system providing measurements of the rotation of the rotor, measurements of the power generated by the conversion machine, an electrical machine, and measurements of the inclination angle of the blades.

(78) FIG. 4 illustrates the measurements of the power P.sub.g in W generated by the conversion machine (an electrical machine in this example) as a function of time Tin s.

(79) FIG. 5 shows the measurements of the rotational speed w of the rotor in rad/s as a function of time T in s.

(80) FIG. 6 shows the measurements of the inclination angle β of the blades in degrees as a function of time T in s.

(81) Applying the method according to an embodiment of the invention allows determination of wind speed REWS in the rotor plane. This speed determined by the invention is compared with the wind speed REWS in the rotor plane obtained by of a four-beam LiDAR sensor positioned on the nacelle of the wind turbine.

(82) FIG. 7 shows the two wind speed curves REWS as a function of time T in s obtained with the two methods with the invention denoted by INV and the LiDAR sensor (curve denoted by LID). It is noted that the two curves are nearly superposed, which shows that the invention, although it does not use an expensive sensor, allows determination of with precision the wind speed in the rotor plane of the wind turbine.