Method for estimating a wind speed at a wind turbine

Abstract

A fast-converging and reliable method for estimating a wind speed at, for example, a wind turbine comprising a rotor carrying a set of variable pitch angle wind turbine blades. The estimated wind speed is iteratively derived using a wind turbine rotor rotational speed, a turbine blade pitch angle, and a derived initial estimated wind speed. The initial estimated wind speed is based on the rotational speed and an initial tip speed ratio. The initial tip speed ratio is selected to be a value greater than a minimum tip speed ratio, wherein the minimum tip speed ratio defines a control region stability limit as a function of the pitch angle. Thus, for a given pitch angle, a minimum tip speed ratio is derived as a limit or boundary point between a stable control region and an unstable control region.

Claims

1. A method for estimating a wind speed at a wind turbine, the wind turbine comprising a rotor carrying a set of wind turbine blades, each wind turbine blade having a variable pitch angle, the method comprising: obtaining a rotational speed of the rotor; obtaining a pitch angle of the wind turbine blades; deriving a minimum tip speed ratio based on the obtained pitch angle, the minimum tip speed ratio defining an upper limit of a stable control region; selecting an initial tip speed ratio that is greater than the minimum tip speed ratio; deriving an initial estimated wind speed based on the initial tip speed ratio and the obtained rotational speed; iteratively deriving an estimated wind speed based on the obtained rotational speed and the obtained pitch angle, and using the derived initial estimated wind speed as a starting point; and using the estimated wind speed to control the wind turbine, wherein stability of the control region is based on a stability of the estimated wind speed.

2. The method according to claim 1, further comprising controlling the wind turbine in accordance with the estimated wind speed.

3. The method according to claim 1, wherein deriving a minimum tip speed ratio further comprises using a minimum tip speed ratio look-up table comprising interrelated values of pitch angle and minimum tip speed ratio.

4. The method according to claim 1, wherein the selected initial tip speed ratio exceeds the minimum tip speed ratio at least by a predefined amount.

5. The method according to claim 1, further comprising: calculating an estimated tip speed ratio based on the obtained rotational speed and the estimated wind speed; setting a flag, indicating that the estimated wind speed is unreliable, when the estimated wind speed results in the estimated tip speed ratio being lower than the minimum tip speed ratio; and controlling the wind turbine in accordance with an alternate estimated wind speed, the alternate estimated wind speed corresponding to the minimum tip speed ratio and in accordance with the flag.

6. The method according to claim 5, further comprising: removing the flag and controlling the wind turbine in accordance with the estimated wind speed when the estimated tip speed ratio increases above the minimum tip speed ratio.

7. The method according to claim 1, wherein iteratively deriving an estimated wind speed further comprises using a look-up table comprising interrelated values of rotational speed, wind speed, pitch angle, and power coefficient.

8. The method according to claim 1, wherein iteratively deriving an estimated wind speed further comprises: estimating a power output of the wind turbine and forming a power error signal by comparing the estimated power output to a measured power output of the wind turbine.

9. The method according to claim 8, further comprising adjusting the power error signal by applying a gain factor and integrating the adjusted power error signal to form a new estimated wind speed feedback.

10. The method according to claim 1, wherein the defined limit is such that when the wind turbine is operated at tip speed ratios below the minimum tip speed ratio, the estimated wind speed is unstable, and when the wind turbine is operated at tip speed ratios above the minimum tip speed ratio the estimated wind speed is stable.

11. The method according to claim 1, wherein the upper limit of the stable control region is determined in part by where, for a given pitch angle, a partial derivative of a power output with respect to the wind speed is positive.

12. A wind turbine comprising: a rotor carrying a set of wind turbine blades, each wind turbine blade having a variable pitch angle; and a controller configured to implement an operation for estimating a wind speed at a wind turbine, the operation comprising: obtaining a rotational speed of the rotor; obtaining a pitch angle of the wind turbine blades; deriving a minimum tip speed ratio based on the obtained pitch angle, the minimum tip speed ratio defining a boundary between a stable control region and an unstable control region; selecting an initial tip speed ratio that is greater than the minimum tip speed ratio; deriving an initial estimated wind speed based on the selected initial tip speed ratio and the obtained rotational speed; and iteratively deriving an estimated wind speed based on the obtained rotational speed and the obtained pitch angle and using the derived initial estimated wind speed as a starting point; wherein stability of the control region is based on a stability of the estimated wind speed.

13. A computer program product comprising computer executable code on a non-transitory computer readable storage medium which, when executed by one or more processors, implements an operation for estimating a wind speed at a wind turbine, the wind turbine comprising a rotor carrying a set of wind turbine blades, each wind turbine blade having a variable pitch angle, the operation comprising: obtaining a rotational speed of the rotor; obtaining a pitch angle of the wind turbine blades; deriving a minimum tip speed ratio based on the obtained pitch angle, the minimum tip speed ratio defining an upper limit of a stable control region; selecting an initial tip speed ratio that is greater than the minimum tip speed ratio; deriving an initial estimated wind speed based on the initial tip speed ratio and the obtained rotational speed; iteratively deriving an estimated wind speed based on the obtained rotational speed and the obtained pitch angle, and using the derived initial estimated wind speed as a starting point; and using the estimated wind speed to control the wind turbine, wherein stability of the control region is based on a stability of the estimated wind speed.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will now be described in further detail with reference to the accompanying drawings in which

(2) FIG. 1 is a block diagram illustrating a method according to an embodiment of the invention,

(3) FIG. 2 is a graph illustrating power coefficient, c.sub.P, as a function of tip speed ratio, , for a fixed pitch angle,

(4) FIG. 3 is graph illustrating power output as a function of wind speed for three different pitch angles, and

(5) FIG. 4 is a flow chart illustrating a method according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE DRAWINGS

(6) FIG. 1 is a block diagram illustrating a method according to an embodiment of the invention, in the form of a closed loop approximation process. A rotational speed, , of the rotor of a wind turbine, and a pitch angle, , of the wind turbine blades of the wind turbine are measured and supplied to an estimating block 1. Furthermore, a previously estimated wind speed, v.sub.est, is also supplied to the estimating block 1.

(7) In the estimating block 1, an estimated power output, P.sub.est, is calculated, based on the supplied parameters, , and v.sub.est. This includes deriving a power coefficient, c.sub.P, e.g. by means of a c.sub.P look-up table, based on an estimated tip speed ratio, .sub.est, and the pitch angle, .

(8) The estimated power output, P.sub.est, is compared to a measured power output, P.sub.meas, at a comparator 2. This results in an error signal, P.sub.err. If the error signal, P.sub.err, is zero, then P.sub.est=P.sub.meas, indicating that the estimated wind speed, v.sub.est, supplied to the estimator block 1 is equal to or close to the actual wind speed prevailing at the wind turbine.

(9) If the error signal, P.sub.err, is positive, then the measured power output, P.sub.meas, is larger than the estimated power output, P.sub.est, indicating that the expected power output at the estimated wind speed, v.sub.est, is lower than the actual power output. This indicates that the estimated wind speed, v.sub.est, is lower than the actual wind speed prevailing at the wind turbine, and the estimated wind speed, v.sub.est, should therefore be increased.

(10) Similarly, if the error signal, P.sub.err, is negative, then the measured power output, P.sub.meas, is smaller than the estimated power output, P.sub.est, indicating that the expected power output at the estimated wind speed, v.sub.est, is higher than the actual power output. This indicates that the estimated wind speed, v.sub.est, is higher than the actual wind speed prevailing at the wind turbine, and the estimated wind speed, v.sub.est, should therefore be decreased.

(11) The adjustments to the estimated wind speed, v.sub.est, described above, are performed in the following manner. The error signal, P.sub.err, is multiplied by a gain factor, k.sub.est, at multiplier 3, and the resulting signal is supplied to an integrator 4. At the integrator 4 the signal received from the multiplier 3 is integrated, resulting in a new estimated wind speed, v.sub.est, which is supplied to the estimating block 1 for the next iteration.

(12) Thus, the estimation process described above is an iterative process. In order to start the iterative process, an initial wind speed, v.sub.init, is supplied to the estimating block 1. The initial wind speed, v.sub.init, is derived in the following manner.

(13) A minimum tip speed ratio, .sub.min, is derived, based on the measured pitch angle, . The minimum tip speed ratio, .sub.min, defines a limit between a stable and an unstable control region, at the measured pitch angle, . Thus, at tip speed ratios above the minimum tip speed ratio, .sub.min, the wind speed is estimated in a stable manner, and at tip speed ratios below the minimum tip speed ratio, .sub.min, the wind speed is potentially estimated in an unstable manner.

(14) An initial tip speed ratio, .sub.init, is selected, in such a manner that .sub.init>.sub.min. Accordingly, the selected initial tip speed ratio, .sub.init, is well within the stable control region. The initial estimated wind speed, v.sub.init, is then derived, based on the measured rotational speed, , of the rotor and the selected initial tip speed ratio, .sub.init. Thus, the initial wind speed, v.sub.init, which is used as a starting point for the iterative process described above, corresponds to the initial tip speed ratio, .sub.init, and is therefore also well within the stable control region at the measured pitch angle, . This ensures that the iterative process converges in a fast and reliable manner, i.e. a reliable estimate for the wind speed is reached fast.

(15) FIG. 2 is a graph illustrating power coefficient, c.sub.P, as a function of tip speed ratio, , for a fixed pitch angle. The graph of FIG. 2 illustrates how a minimum tip speed ratio, .sub.min, can be determined.

(16) The power output, P, of the wind turbine is given as:

(17) $P=\frac{}{2}{\mathrm{Ac}}_P\left(,\right)v^3,$
where P is the power output, is the air density, A is an area swept by the rotor, c.sub.P(,) is the power coefficient, depending on the tip speed ratio, , and the pitch angle, , and v is the wind speed.

(18) It can be assumed that the wind turbine is operated within a stable control region as long as the partial derivative of the power output with respect to the wind speed is positive. The partial derivative of the power output with respect to wind speed is given as:

(19) $\frac{P}{v}=\frac{}{2}A\left(3v^2{c}_P+v^3\frac{c_P}{v}\right).$

(20) The partial derivative of the rotor power coefficient is given as:

(21) $\begin{array}{c}\frac{c_p}{v}=\frac{c_P}{}\frac{}{v^{}}\\ \mathrm{where}\\ =\frac{R}{v}.Math.\frac{}{v}=-\frac{R}{v^2}.\end{array}$

(22) Inserting this in the equation above regarding the partial derivative of the power output results in:

(23) $\frac{P}{v}=\frac{}{2}A\left(3v^2{c}_P-Rv\frac{c_P}{}\right)=\frac{}{2}{\mathrm{Av}}^2\left(3c_P-\frac{c_P}{}\right).$

(24) Hence, the wind turbine is operated within a stable control region if:

(25) $\frac{c_P}{}<\frac{3c_P}{}.$

(26) This sets a restriction on the gradient of the power coefficient, c.sub.P, versus the tip speed ratio, . This is illustrated in the graph of FIG. 2, where a tangent of the curve is shown in a point corresponding to a specific tip speed ratio, . If the tangent intersects the ordinate axis at a point, .sub.s>, then the equation above will be violated, and the wind turbine will be operated in an unstable control region. Based on this, a minimum tip speed ratio, .sub.min, can be derived, which defines a limit between a stable and an unstable control region. Minimum tip speed ratios, .sub.min, for various pitch angles, , can be derived in this manner, and inserted into a look-up table, which can be consulted during operation of the wind turbine.

(27) FIG. 3 is graph illustrating power output as a function of wind speed for three different pitch angles, =4, =0, and =4. All three curves represent that the wind turbine is operated at nominal rotational speed, . It can be seen that some of the curves have portions with a negative gradient,

(28) $\frac{P}{v},$
i.e. portions where the wind speed estimation would not converge. These portions are all in a region where the power output is above the rated power output. However, for other pitch angles and/or for other rotors, such regions may occur below rated power, in which case it is necessary to establish the minimum tip speed ratio, in the manner described above, in order to ensure stable wind speed estimation.

(29) FIG. 4 is a flow chart illustrating a method according to an embodiment of the invention. The process is started at step 5. At step 6 the rotational speed, , of the rotor of the wind turbine and the pitch angle, , of the wind turbine blades of the wind turbine are measured, or obtained in another suitable manner.

(30) At step 7 a minimum tip speed ratio, .sub.min, is derived, based on the measured pitch angle, . The minimum tip speed ratio, .sub.min, defines a limit between a stable and an unstable control region for the wind speed estimation. The minimum tip speed ratio, .sub.min, may, e.g., be derived in the manner described above with reference to FIG. 2.

(31) Thus, when the wind turbine is operated at tip speed ratios which are above the minimum tip speed ratio, .sub.min, the wind speed estimation is within a stable control region. When the wind turbine is operated at tip speed ratios which are below the minimum tip speed ratio, .sub.min, the wind speed estimation is within an unstable control region.

(32) At step 8 an initial tip speed ratio, .sub.init, is selected in such a manner that .sub.in>.sub.min. Thus, the initial tip speed ratio, .sub.init, is selected in such a manner that it is well within the stable control region.

(33) At step 9 an initial estimated wind speed, v.sub.init, is derived, based on the selected initial tip speed ratio, .sub.init. Thus, the derived initial estimated wind speed, v.sub.init, corresponds to the initial tip speed ratio, .sub.init, and therefore the initial estimated wind speed, v.sub.init, is also well within the stable control region. Therefore the initial estimated wind speed, v.sub.init, is a good starting point for an iterative process for estimating the wind speed prevailing at the wind turbine.

(34) Accordingly, at step 10, an iterative process is started, in which a new estimated wind speed, v.sub.est, is derived, based on the initial estimated wind speed, v.sub.init, the measured rotational speed, , and the measured pitch angle, .

(35) At step 11 the rotational speed, , and the pitch angle, , are measured, and at step 12 the wind turbine is operated in accordance with the estimated wind speed, v.sub.est, the measured rotational speed, , and the measured pitch angle, . Then the process is returned to step 10, where a new estimated wind speed, v.sub.est, is derived, based on the previous estimated wind speed, v.sub.est, the measured rotational speed, , and the measured pitch angle, . Accordingly, an iterative process is performed in order to obtain an estimated wind speed, v.sub.est, which is close to the actual wind speed prevailing at the wind turbine.

(36) Since the initial estimated wind speed, v.sub.init, which is used as a starting point for the iterative process, is selected in such a manner that it is well within the stable control region, it is ensured that the iterative process converges fast and reliably. Thus, a reliable estimate for the wind speed is reached fast.

(37) While embodiments of the invention have been shown and described, it will be understood that such embodiments are described by way of example only. Numerous variations, changes and substitutions will occur to those skilled in the art without departing from the scope of the present invention as defined by the appended claims. Accordingly, it is intended that the following claims cover all such variations or equivalents as fall within the spirit and the scope of the invention.