Methods and systems for determining surface condition of wind turbine blades and wind turbine control

Abstract

To provide methods and systems for controlling and operating wind turbines or for determining a surface condition of one or more wind turbine blades of a wind turbine.SOLUTION: A method comprises: rotating a wind turbine rotor under the influence of a wind in predetermined rotation conditions, where the predetermined rotation conditions include at least a predetermined pitch angle of additional wind turbine blades; determining a current value of one or more parameters of the wind turbine when rotating in the predetermined rotation conditions; and comparing the current value of the one or more parameters of the wind turbine with one or more reference values to determine a surface condition of the wind turbine blades.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present disclosure relates to methods for controlling and operating a wind turbine, and more particularly to a method for determining or detecting the roughness of a wind turbine blade and a method for operating a wind turbine, as well as a wind turbine controller and a wind turbine. [Background technology]

[0002] Today, wind turbines are commonly used to supply power to the power grid. This type of wind turbine generally includes a tower and a rotor disposed on the tower. The rotor typically includes a hub and a number of blades and is configured to rotate under the influence of wind on the blades. This rotation generates torque that is typically transmitted to a generator through the rotor shaft, either directly ("direct drive" or "gearless") or through the use of a gearbox. In this way, the generator generates electricity that can be supplied to the power grid.

[0003] The wind turbine hub may be rotatably coupled to the front of the nacelle. The wind turbine hub may be connected to a rotor shaft, which may then be rotatably mounted within the nacelle using one or more rotor shaft bearings located within a frame within the nacelle. The nacelle is a housing located at the top of the wind turbine tower that may contain and protect the gearbox (if present) and generator (if not located outside the nacelle), and, depending on the wind turbine, may also include additional components and auxiliary systems, such as power converters.

[0004] During wind turbine operation, the exterior surfaces of wind turbine blades, particularly the leading edge and adjacent surface areas, can become fouled. For example, dust, pollen, insects, salt, or ice can accumulate on the exterior surfaces of wind turbine blades. Wind turbine blades can also be corroded by, for example, rain, hail, or wind-borne particles striking the blades. Dirty and / or eroded blades have a more irregular surface than clean blades, which can significantly affect airflow around the blades. Rough blades generally produce less lift and more drag for a given wind flow, reducing the power generated by the wind turbine. For example, blade roughness can reduce annual energy production (AEP) by 2% to 5%, a significant loss.

[0005] Blade roughness may be monitored to determine whether corrective action, such as blade cleaning or repair, is necessary, or whether increased wind turbine output is indicated, such as after rainfall has removed dirt from the blades. Blade inspections can be time-consuming and expensive and generally require the presence of one or more operators. Furthermore, access to potentially affected blade areas can be difficult, and monitoring equipment can be sensitive to external conditions. In some instances, drones may be used. In these or other instances, images may be taken, for example, with an infrared camera, although in such cases, extensive post-processing of the images may be required.

[0006] The present disclosure aims to provide improved identification or detection of blade roughness. Summary of the Invention [Problem to be solved by the invention]

[0007] In an aspect of the present disclosure, a method is provided for determining a surface condition of one or more wind turbine blades of a wind turbine including a rotor including a first wind turbine blade and one or more additional wind turbine blades. The method includes rotating the wind turbine rotor under the influence of wind at predetermined rotational conditions, the predetermined rotational conditions including at least predetermined pitch angles of the additional (other) wind turbine blades. The method further includes determining current values ​​of one or more parameters of the wind turbine when rotating at the predetermined rotational conditions. The method further includes comparing the current values ​​of the one or more parameters of the wind turbine to one or more reference values ​​to determine the surface condition of the one or more wind turbine blades.

[0008] According to this aspect, while the wind turbine rotor is rotating at a predetermined rotational condition, one or more values ​​of one or more parameters can be determined and compared to corresponding reference values, where the reference values ​​of the parameters are known, e.g., they may have been previously determined for a particular wind turbine rotor configuration.

[0009] Comparing the current values ​​of one or more wind turbine parameters determined under a predetermined rotational condition, where the predetermined rotational condition includes at least a predetermined pitch angle of a wind turbine blade other than the first wind turbine blade, with a reference value can help detect the blade surface condition, in particular an indication of roughness, without using a blade sensor or drone. This can avoid the presence of an operator. Also, photography can be omitted, which can eliminate time-consuming post-processing. Therefore, a faster and more autonomous detection of blade roughness can be provided.

[0010] Throughout this disclosure, the pitch angle of a wind turbine blade may be understood as the angle that may be measured in a cross section between a datum line and the chord of the blade, which in some instances may be substantially parallel to the plane of the wind turbine rotor, e.g., may be contained within the wind turbine rotor.

[0011] In this disclosure, blade roughness can refer to the degree to which the outer surface of a blade, or a particular region of the outer surface of a blade, is irregular. Here, a rough blade may refer to a blade whose surface differs from the surface of the blade when it was clean or cleaner, and the effects of the roughness are noticeable in wind turbine performance. That is, the airflow around the blade is affected to a different extent at a given angle of attack and a given wind speed by the blade's lift and / or drag. For example, a rough blade may contain irregularities, such as protrusions and / or depressions, that the blade did not contain when the cleanliness baseline was achieved, and these irregularities may affect the power generated by the wind turbine, generally in a negative direction. For example, the irregularities may create, for example, a more turbulent flow, a larger wake, or different points that separate the airflow from the blade.

[0012] Throughout this disclosure, a clean blade can be understood as a smooth blade, i.e., a blade whose outer surface has not yet been affected, or at least not significantly affected, by material accumulation and / or erosion. Material accumulation can include, for example, dirt and ice. The surface of a clean blade can be the designed and manufactured surface. A clean blade can be installed at the top of a wind turbine tower, for example, during installation of the wind turbine. Because a clean blade is at the beginning of its service life, it may not yet have accumulated dirt, ice, or other material and / or may not have been eroded in a significant way. It is understood that a clean blade can provide maximum power output according to design specifications under optimal conditions. During installation of a blade, it may accumulate some dirt and / or it may be slightly eroded, but this generally does not have a significant effect, and therefore, a blade in the context of this disclosure is considered to be a clean blade. The clean blades can be used to obtain a baseline value for comparison with values ​​determined over a period of time after the wind turbine has begun operation, for example, days, weeks, or months after the wind turbine has begun operation.

[0013] Throughout this disclosure, a semi-clean blade may refer to a blade that has an outer surface that is different from the blade surface when it was new, i.e., "clean," due to, for example, erosion or the fact that the blade may have been repaired and its surface may be slightly different than when it was new. A semi-clean blade may be, for example, a washed blade or a repaired blade. A semi-clean blade may also be used for determining a baseline value for one or more parameters.

[0014] Throughout this disclosure, a wind turbine may be understood to be in operation (running) when its rotor is rotating fast enough to generate energy and the wind turbine's generator is producing electrical power.

[0015] In a further aspect of the present disclosure, a wind turbine controller is provided, the controller including a communications module, a processor, and a memory, the memory including instructions that, when executed by the processor, cause the processor to perform one or more of the method steps disclosed herein.

[0016] In yet another aspect of the present disclosure, a method for controlling a wind turbine is provided. The method includes determining one or more reference values ​​of one or more wind turbine parameters for an idle wind turbine rotor with a first blade positioned at a first pitch angle reference value and the remaining blades positioned at a second pitch angle reference value before the wind turbine begins operation. The method further includes initiating wind turbine operation. Then, after a period of time, initiating idling of the wind turbine rotor with the first blade positioned at the first pitch angle reference value and the remaining blades positioned at the second pitch angle reference value. The method further includes determining one or more current values ​​of the one or more wind turbine parameters and comparing them to the corresponding reference values. The method further includes adapting wind turbine operation based on the comparison. [Brief explanation of the drawings]

[0017] [Figure 1] 1 illustrates a perspective view of an embodiment of a wind turbine. [Figure 2] 2 shows a simplified internal view of an embodiment of a nacelle of the wind turbine of FIG. 1. [Figure 3] 1 illustrates a schematic diagram of an embodiment of a controller for a wind turbine. [Figure 4] 1 shows a flow chart of an embodiment of a method for operating a wind turbine to detect blade roughness. [Figure 5] 5A, 5B and 5C illustrate schematically different pitch angles of a wind turbine blade according to one embodiment. [Figure 6]1 illustrates a schematic front view of an embodiment of a wind turbine in which a first blade is positioned at a first pitch angle, and a second blade and a third blade are positioned at a second pitch angle, the first pitch angle value being higher than the second pitch angle value. [Figure 7] 1 shows a set of reference values ​​schematically. [Figure 8] 2 shows a schematic representation of an example of the evolution of the reference wind turbine rotor speed as a function of wind speed and an example of a determined current value of the rotor speed; [Figure 9] 1 shows a flow chart of an embodiment of a method for controlling a wind turbine. DETAILED DESCRIPTION OF THE INVENTION

[0018] Reference will now be made in detail to the embodiments of the present disclosure, one or more examples of which are illustrated in the drawings. Each example is provided by way of illustration only, and not by way of limitation. Indeed, it will be apparent to those skilled in the art that various modifications and variations can be made in the present disclosure. For example, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. It is therefore intended that the present disclosure cover such modifications and variations as come within the scope of the appended claims and their equivalents.

[0019] FIG. 1 is a perspective view of an example wind turbine 10. In this example, wind turbine 10 is a horizontal axis wind turbine. Alternatively, wind turbine 10 may be a vertical axis wind turbine. In this example, wind turbine 10 includes a tower 15 extending from a support system 14 on ground 12, a nacelle 16 mounted on tower 15, and a rotor 18 coupled to nacelle 16. Rotor 18 includes a rotatable hub 20 and at least one rotor blade 22 coupled to the hub and extending outward from hub 20. In this example, rotor 18 has three rotor blades 22. In other embodiments, rotor 18 includes more or less than three rotor blades 22. Tower 15 may be fabricated from tubular steel to define a cavity (not shown in FIG. 1 ) between support system 14 and nacelle 16. In alternative embodiments, tower 15 is any suitable type of tower having any suitable height. Alternatively, the tower may be a hybrid tower including a concrete section and a tubular steel section. The tower can also be a partial or full lattice tower.

[0020] Rotor blades 22 are spaced about hub 20 and facilitate rotation of rotor 18, allowing for the transfer of kinetic energy from wind into usable mechanical energy and then electrical energy. Rotor blades 22 are mated to hub 20 by coupling blade root regions 24 to hub 20 at a plurality of load transfer regions 26. The load transfer regions 26 may include hub load transfer regions and blade load transfer regions (neither of which are shown in FIG. 1 ). Loads induced on rotor blades 22 are transferred to hub 20 through the load transfer regions 26.

[0021] In embodiments, rotor blades 22 may have lengths ranging from approximately 15 meters (m) to approximately 90 meters or more. Rotor blades 22 may have any suitable length that enables wind turbine 10 to function as described herein. For example, non-limiting examples of blade lengths include lengths of 20 m or less, 37 m, 48.7 m, 50.2 m, 52.2 m, or greater than 91 m. When wind impinges on rotor blades 22 from wind direction 28, rotor 18 rotates about rotor axis 30. As rotor blades 22 rotate and experience centrifugal forces, rotor blades 22 also experience various forces and moments. In this manner, rotor blades 22 may deflect and / or rotate from a neutral or unbiased position to a biased position.

[0022] Additionally, the pitch angles of the rotor blades 22, e.g., the angles that determine the orientation of the rotor blades 22 relative to the wind direction, may be varied by the pitch system 32 to control the load and power generated by the wind turbine 10 by adjusting the angular position of at least one rotor blade 22 relative to the wind vector. A pitch axis 34 of the rotor blades 22 is shown. During operation of the wind turbine 10, the pitch system 32 may vary the pitch angles of the rotor blades 22, among other things, to reduce the angle of attack of (some of) the rotor blades, facilitate a reduction in rotational speed, and / or facilitate a stall of the rotor 18.

[0023] In this example, the blade pitch of each rotor blade 22 is individually controlled by the wind turbine controller 36 or pitch control system 80. Alternatively, the blade pitch of all rotor blades 22 may be simultaneously controlled by the control system.

[0024] Additionally, in this embodiment, as wind direction 28 changes, the yaw orientation of nacelle 16 may rotate about yaw axis 38 to position rotor blades 22 relative to wind direction 28 .

[0025] In the example embodiment, wind turbine controller 36 is shown as being centralized within nacelle 16, but wind turbine controller 36 may be a distributed control system throughout wind turbine 10, on support system 14, within a wind farm, and / or at a remote control center. Wind turbine controller 36 includes one or more processors 40 configured to perform the steps and / or methods described herein. See also FIG. 3. Additionally, many of the other components described herein include one or more processors.

[0026] 2 is an enlarged cross-sectional view of a portion of wind turbine 10. In one embodiment, wind turbine 10 includes a nacelle 16 and a rotor 18 rotatably coupled to nacelle 16. Specifically, a hub 20 of rotor 18 is rotatably coupled to a generator 42 located within nacelle 16 by a main shaft 44, a gearbox 46, a high-speed shaft 48, and a coupling 50. In this example, main shaft 44 is disposed at least partially coaxially with a longitudinal axis (not shown) of nacelle 16. Rotation of main shaft 44 drives a gearbox 46, which converts the relatively slow rotational motion of rotor 18 and main shaft 44 into relatively faster rotational motion of high-speed shaft 48, thereby driving high-speed shaft 48. The latter is connected to generator 42 for producing electrical energy with the aid of coupling 50. Additionally, a transformer 90 and / or appropriate electronics, switches and / or inverters may be disposed within the nacelle 16 to convert the electrical energy generated by the generator 42, e.g., having a voltage between 400V and 1000V, into electrical energy having a medium voltage (e.g., 10-35KV). Offshore wind turbines may have a generator voltage between 650V and 3500V, for example, and the transformer voltage may be between 30kV and 70kV, for example. This electrical energy is conducted from the nacelle 16 to the tower 15 via a power cable.

[0027] In some examples, the wind turbine 10 may include one or more shaft sensors 51. The shaft sensors may be configured to monitor at least one of a torque load acting on the main shaft 44 and / or the high speed shaft 48 and the rotational speed of the shafts 44, 48. In some examples, the wind turbine 10 may include one or more generator sensors 53. The generator sensors may be configured to monitor at least one of a rotational speed of the generator 42 and a generator torque. The shaft sensors 51 and / or the generator sensors 53 may include, for example, one or more torque sensors (e.g., strain gauges or pressure sensors), optical sensors, accelerometers, magnetic sensors, speed sensors, and micro inertial measurement units (MIMUs).

[0028] The gearbox 46, generator 42, and transformer 90 may be supported by a main support structure frame of the nacelle 16, optionally embodied as a main frame 52. The gearbox 46 may include a gearbox housing connected to the main frame 52 by one or more torque arms 103. In an embodiment, the nacelle 16 also includes a main forward support bearing 60 and a main aft support bearing 62. Furthermore, the generator 42 may be mounted to the main frame 52 by a decoupling support means 54, particularly to prevent vibrations of the generator 42 from being introduced into the main frame 52 and creating a source of noise emissions. The generator 42 may be mounted to the main frame 52 by a decoupling support means 54 to prevent vibrations of the generator 42 from being introduced into the main frame 52 and creating a source of noise emissions.

[0029] Optionally, main frame 52 is configured to carry the weight of rotor 18 and components of nacelle 16, as well as all loads caused by wind and rotational loads, and to introduce these loads into tower 15 of wind turbine 10. Rotor shaft 44, generator 42, gearbox 46, high speed shaft 48, coupling 50, and associated fastening, supporting, and / or securing devices, including, but not limited to, supports 52, forward support bearing 60, and aft support bearing 62, may be referred to as drive train 64.

[0030] In some examples, the wind turbine may be a direct drive wind turbine without a gearbox 46. The generators 42 operate at the same rotational speed as the rotor 18 of the direct drive wind turbine. Therefore, they generally have a much larger diameter than the generators used in wind turbines with gearboxes 46 to provide equivalent power to wind turbines with gearboxes.

[0031] The nacelle 16 may also include a yaw drive mechanism 56 that is used to rotate the nacelle 16, and thereby the rotor 18, about the yaw axis 38 to control the proximity of the rotor blades 22 to the wind direction 28.

[0032] To properly position the nacelle 16 relative to the wind direction 28, the nacelle 16 may also include at least one meteorological measurement system, which may include a wind vane and an anemometer. The meteorological measurement system 58 may provide information including the wind direction 28 and / or wind speed to the wind turbine controller 36.

[0033] In this example, pitch system 32 is at least partially disposed within hub 20 as a pitch assembly 66. Pitch assembly 66 includes one or more pitch drive systems 68 and at least one sensor 70. Each pitch drive system 68 is coupled to a respective rotor blade 22 (shown in FIG. 1 ) to modulate the pitch angle of rotor blade 22 along pitch axis 34. Only one of the three pitch drive systems 68 is shown in FIG. 2 .

[0034] In this example, pitch assembly 66 includes at least one pitch bearing 72 coupled to hub 20 and each rotor blade 22 (shown in FIG. 1 ) to rotate each rotor blade 22 about pitch axis 34. Pitch drive system 68 includes a pitch drive motor 74, a pitch drive gearbox 76, and a pitch drive pinion 78. Pitch drive motor 74 is coupled to pitch drive gearbox 76 such that pitch drive motor 74 imparts mechanical power to pitch drive gearbox 76. Pitch drive gearbox 76 is coupled to pitch drive pinion 78 such that pitch drive pinion 78 is rotated by pitch drive gearbox 76. Pitch bearing 72 is coupled to pitch drive pinion 78 such that rotation of pitch drive pinion 78 rotates pitch bearing 72.

[0035] Pitch drive system 68 is coupled to wind turbine controller 36 to adjust the pitch angle of rotor blades 22 upon receiving one or more signals from wind turbine controller 36. In examples, pitch drive motor 74 is any suitable motor driven by an electric and / or hydraulic system that enables pitch assembly 66 to function as described herein. Alternatively, pitch assembly 66 may include any suitable structure, configuration, arrangement, and / or components, such as, but not limited to, hydraulic cylinders, springs, and / or servo mechanisms. In certain embodiments, pitch drive motor 74 is driven by the rotational inertia of hub 20 and / or energy extracted from a stored energy source (not shown) that provides energy to components of wind turbine 10.

[0036] Pitch assembly 66 may also include one or more pitch control systems 80 for controlling pitch drive systems 68 according to control signals from wind turbine controller 36 for certain prioritized conditions and / or during overspeed of rotor 18. In this example, pitch assembly 66 includes at least one pitch control system 80 communicatively coupled to each pitch drive system 68 for controlling pitch drive systems 68 independently from wind turbine controller 36. In this example, pitch control system 80 is coupled to pitch drive systems 68 and sensors 70. During normal operation of wind turbine 10, wind turbine controller 36 may control pitch drive systems 68 to adjust the pitch angle of rotor blades 22.

[0037] According to one embodiment, a generator 84, including, for example, a battery and an electrical capacitor, is located within or within the hub 20 and is coupled to the sensors 70, the pitch control system 80, and the pitch drive system 68 to provide a source of electrical power to these components. In an example embodiment, the wind generator 84 provides a continuous source of electrical power to the pitch assembly 66 during operation of the wind turbine 10. In another embodiment, the generator 84 supplies electrical power to the pitch assembly 66 only during a power loss event of the wind turbine 10. A power loss event may include a loss or dip in the power grid, a malfunction of the electrical system of the wind turbine 10, and / or a failure of the wind turbine controller 36. During a power loss event, the generator 84 operates to provide electrical power to the pitch assembly 66 so that the pitch assembly 66 can operate during the power loss event.

[0038] In this example, pitch drive system 68, sensor 70, pitch control system 80, cables, and generator 84 are each disposed within a cavity 86 defined by an inner surface 88 of hub 20. In another embodiment, these components may be disposed relative to and directly or indirectly coupled to an outer surface of hub 20.

[0039] 3 illustrates a schematic diagram of one embodiment of a wind turbine controller 36 or control system 36. The controller 36 may be configured to perform one or more of the methods, steps, decisions, etc. disclosed herein. As used herein, the term "processor" is not limited to integrated circuits referred to in the art as computers, but rather refers broadly to controllers, microcontrollers, microcomputers, programmable logic controllers (PLCs), application specific integrated circuits, and other programmable circuits, and these terms are used interchangeably herein.

[0040] The control system 36 may also include a memory 41, such as one or more memory devices. The memory 41 may include memory elements, including, but not limited to, computer-readable media (e.g., random access memory (RAM)), computer-readable non-volatile media (e.g., flash memory), floppy disks™, compact disk read-only memories (CD-ROMs), magneto-optical disks (MDs), digital versatile disks (DVDs), and / or other suitable memory elements. Such memory devices 41 may generally be configured to store appropriate computer-readable instructions that, when executed by the processor 40, configure the controller 36 to perform or trigger the execution of the various steps disclosed herein. The memory 41 may also be configured to store data, for example, from measurements and / or calculations.

[0041] Additionally, the control system 36 may also include a communications module 43 that facilitates communication between the controller 36 and various components of the wind turbine 10. For example, the communications module 43 may function as an interface that allows the turbine controller 36 to send control signals to the pitch drive system 66 for controlling the pitch angle of the rotor blades 22. The communications module 43 may be configured to communicatively connect the control system 36 to other elements of the wind turbine 10. The connection may be via a wired connection and / or via a wireless connection, e.g., using any suitable wireless communication protocol known in the art. Additionally, the communications module 43 may include a sensor interface 49, e.g., one or more analog-to-digital converters, that allow signals transmitted from the one or more sensors 51, 53, 58 to be converted into signals that can be understood and processed by the processor 40.

[0042] A method diagram 100 is provided for determining a surface condition of one or more wind turbine blades 22 of a wind turbine 10 including a rotor 18 including a first wind turbine blade 221 and one or more additional wind turbine blades 222, 223. The method is illustrated generally in the flow chart of FIG. 4. The method includes, at block 110, rotating the wind turbine blade rotor 18 under the influence of wind at predetermined rotation conditions. The predetermined rotation conditions include at least predetermined pitch angles 252 of the one or more additional wind turbine blades 222, 223. The method further includes, at block 120, determining current values ​​of one or more parameters of the wind turbine 10 as it rotates at the predetermined rotation conditions. The method further includes, at block 130, comparing the current values ​​of the one or more parameters of the wind turbine 10 with one or more reference values ​​37 to determine a surface condition (particularly a roughness index or condition) of the one or more wind turbine blades 221, 222, 223.

[0043] Here, a parameter may be understood to be a characteristic that helps define or describe the operation of a wind turbine at a predetermined rotational condition. As used herein, a parameter may include control settings (i.e., set points for actuators or pitch angles, generator torque, or other factors) and / or measured variables (e.g., rotor speed). Note that "predetermined" may mean that the rotational conditions are predetermined, i.e., before rotation of the rotor 18 at a certain condition is initiated. "Predetermined" should not necessarily be interpreted as a constant condition, e.g., a constant parameter value, remaining constant throughout the entire period during which rotor rotation occurs. In some instances, this may be as described above (e.g., one or more pitch angles 25 may be held substantially constant while performing method 100), but in other instances this may not be the case (e.g., even if a particular rotor speed is set for rotation, this speed may vary over time due to blade roughness).

[0044] Throughout this disclosure, the pitch angle of a wind turbine blade 22 may be understood as an angle 25 that may be measured in a cross section between a reference line 26 and the chord of the blade 27 (see FIGS. 5A, 5B, and 5C). The reference line 26, shown as a dotted line in FIGS. 5A, 5B, and 5C, may be substantially parallel to the rotor plane of the wind turbine 10. FIGS. 5A, 5B, and 5C schematically show the blade 22 in cross section. In these figures, the wind (see arrow "TW") may be blowing from left to right. The wind turbine blade 22 rotates in the plane of the rotor 18 and moves in a downward direction in this figure, resulting in an apparent wind flow (see arrow "AW"). The apparent wind AW is composed of wind due to the rotation of the blade and wind blowing axially TW against the blade 22.

[0045] The right side of the profile shown in FIG. 5 may be understood as the negative pressure side of the blade, and the left side as the pressure side of the blade.

[0046] In Figure 5A, the blade is in a reference position at pitch angle 25. In the reference position, the blade chord 27 is substantially parallel to the reference line 26. In Figure 5A, the blade chord 27 and the reference line 26 overlap. Thus, pitch angle 25 may be 0° or a "default pitch angle." The default pitch angle, or "reference position," may be a position where the wind turbine blade 22 maintains a low wind speed range, for example, a sub-nominal wind speed.

[0047] In FIG. 5B, the blades are tilted away from the reference position. Therefore, the pitch angle 25 in FIG. 5B is greater than in FIG. 5A. In FIG. 5C, the pitch angle 25 is even greater relative to the reference position. Increasing the pitch angle 25 generally slows down the wind turbine rotor, i.e., the wind turbine blades are positioned to generate less lift and more drag to reduce the aerodynamic torque of the wind turbine rotor. Pitching the blades 22 approximately 90° from the reference position can place the wind turbine in a feathered position, potentially stopping the wind turbine or at least significantly reducing its rotational speed. The feathered position of the blades is the position at which the blades can be placed when the wind turbine is stopped. Similarly, decreasing the pitch angle 25, for example, from the feathered position, can increase the rotational speed of the wind turbine rotor 18.

[0048] Thus, pitching the blades 22 can accelerate and decelerate the rotation of the rotor 18. Rotating the wind turbine rotor 18 under the influence of wind and at a predetermined rotational condition, e.g., rotating all but one blade at a known pitch angle 25, can help determine whether one or more blades 22 have a roughened surface. For example, the first blade 221 can be positioned at a first pitch angle 251 that is greater than the second pitch angles 252 of the other blades 222 and 223, e.g., the other two blades. Thus, in this example, the predetermined rotational condition includes the predetermined first pitch angle 251 and the predetermined second pitch angle 252. As the rotor rotates, the first blade 221 tends to slow down the rotor 18 of the wind turbine 10, while the other blades, e.g., the second blade 222 and the third blade 223, tend to accelerate the rotor 18. A schematic diagram of such an example is shown in FIG. 6. 6, the first wind turbine blade 221 has a pitch angle 251 that is greater than the pitch angle 252 of the second blade 222 and the third blade 223. Thus, the second blade 222 and the third blade 223 tend to accelerate the rotation of the rotor 118, and the first blade 221 tends to break this rotation, i.e., to slow down the rotation of the rotor 118.

[0049] By determining one or more current values ​​of one or more parameters and comparing the one or more determined values ​​to corresponding known reference values, it can be checked whether the roughness of the blades 22 has increased after some operating time of the wind turbine 10, for example, due to a first blade being positioned at a predetermined first pitch angle 251 that is greater than a predetermined second pitch angle 252 at which the remaining blades are positioned. Determining the current values ​​generally includes both direct and indirect measurements. Instead of attaching sensors to the blades 22, method 100 can be used using drones, cameras, or other methods that require additional equipment and / or operators to check whether the blades have become rough during operation. This method makes checking the roughness of the blades faster, more convenient, and less expensive.

[0050] A parameter may be assigned one or more values. When parameter values ​​are determined for certain known reference conditions, e.g., a clean blade and a blade positioned at a first pitch angle greater than a second pitch angle of the remaining blades, these values ​​may be referred to as reference values. Thus, in some examples, the reference values ​​correspond to clean blades. A set of reference values ​​37 is shown schematically in FIG. 7. In the example of FIG. 7, first pitch angle 251 has a reference value of approximately 70°, and second pitch angle 252 has a reference value of approximately 10°. The set of reference values ​​37 further includes multiple values ​​of rotational speed of rotor 18 at multiple values ​​of wind speed. A curve of such data is represented in FIG. 7B as rs=f(ws).

[0051] In some examples, the predetermined rotational condition can include a predetermined pitch angle 251 of the first blade 221, and the wind turbine parameter can include rotational speed. That is, a current value of the speed of the wind turbine rotor 18 can be determined and then compared to a reference value of the wind turbine rotor speed. This determination can be made at a certain wind speed, and the comparison can then be to a reference value of the rotor speed at substantially the same wind speed. For example, the first blade 221 can be positioned at a reference value of the first pitch angle 251, and the remaining blades 222, 223 can be positioned at a reference value of the second pitch angle 252. The current wind speed can be measured by a meteorological measurement system 58, such as an anemometer. The current value of the rotor speed can be determined by, for example, the shaft sensor 51 or the generator sensor 53. The current value of the wind turbine rotor speed at a current wind speed can be compared to a reference value of the wind turbine rotor speed at a corresponding wind speed.

[0052] FIG. 8 schematically illustrates an example of a reference curve (dashed line 45) of the speed of a wind turbine rotor 18, measured, for example, in revolutions per minute (rpm), as a function of wind speed, measured, for example, in meters per second (m / s). The rotor speed data (black circles) can be fitted according to an appropriate equation, for example, a linear equation, to obtain intermediate values ​​of the data. The dashed line 45 represents the fit to the rotor speed data. FIG. 8 also illustrates an example of a current rotor speed value at a current wind speed, labeled 47. In this example, the current value of rotor speed 47 is lower than the corresponding reference rotor speed 55, so it can be concluded that the blades are rougher than before.

[0053] Comparing the rotor speed values ​​indicates whether the current value is substantially the same as a reference value, which may indicate an absence of irregularities on the blades 22, or whether it is lower than the reference speed, which may indicate that the blades 22 have roughened. Operation of the wind turbine can be adjusted depending on the results of the comparison.

[0054] In some examples, the predetermined rotational condition may include a predetermined pitch angle 251 of the first blade 22, and the measured or otherwise determined parameter of the wind turbine 10 may include a tip speed ratio (TSR). That is, in this case, a current value of the tip speed ratio may be determined and compared to a reference value of the TSR. The first blade 221 may be positioned at a reference first pitch angle 251, and the remaining blades 222, 223 may be positioned at a reference second pitch angle 252. In some of these examples, the TSR may be determined by first measuring the current (e.g., angular) rotor speed (rs) and the current wind speed (ws), measured, for example, by a nacelle anemometer, and then calculating the current tip speed by considering the length (L) of the blade 22. This value may be divided by the measured current wind speed (ws) to determine the TSR. The current speed of the wind turbine rotor 18 may be measured, for example, in some examples, in revolutions per minute (rpm). Other methods of determining the TSR are also possible. The determined current TSR can be compared to a baseline TSR.

[0055] TSR is the ratio of blade tip speed to wind speed. Determining TSR and comparing it to a reference TSR value may be less restrictive than determining rotor speed and comparing it to a corresponding reference value. The slope of rotor speed reference curve 45 may be related to the value of reference TSR; in particular, TSR and slope may be related by a proportionality constant that includes blade length. FIG. 8 also shows that the slope of a possible current curve of rotor speed as a function of wind speed 57, and therefore the value of current TSR, may be less than the slope of reference curve 45 and therefore the value of reference TSR.

[0056] In some examples, the predetermined rotational condition can include a predetermined rotor speed, and the wind turbine parameters can include a pitch angle 251 of the first blade 221 to maintain the predetermined rotor speed. In some of these examples, the remaining blades 222, 223 can be positioned at a reference second pitch angle 252, and optionally, the first blade 221 can be positioned at a reference first pitch angle 251, before the determination is made. In other examples, such positioning can be omitted. The controller 36 can determine that a constant speed of the rotor 18 can be achieved at a selected configuration of pitch angles 251, 252 with clean or semi-clean blades 22. During a blade roughness check, the first pitch angle 251 can be varied to reach and maintain a specific reference rotor speed. The pitch angle 251 required to maintain a specific rotor speed can indicate whether the blades maintain a regular surface or whether irregularities, such as depressions and / or protrusions, are present on the blade surface.

[0057] For example, if the required current value of first pitch angle 251 is substantially the same as the corresponding reference value of first pitch angle 251, it can be concluded that the blades remain clean or semi-clean. However, if the value of first pitch angle 251 required to maintain a substantially constant rotor speed is lower than the corresponding reference value, this may indicate that the blade surface of one or more blades has been modified, adversely affecting wind turbine performance. According to the discussion of FIGS. 5A-6 , a current value of first pitch angle 251 lower than the reference value of first pitch angle indicates that the rotation of rotor 18 must be favored to maintain a constant rotor speed. That is, if a blade, particularly the remaining blade 222 or 223, becomes rough, the first pitch angle 251 must be decreased to increase the rotational speed, thereby reaching the reference rotational speed.

[0058] Additionally, a roughness check may be performed using the blades 222, 223 with the second pitch angle 252 as the reference pitch angle 25. In some examples, the pitch angle 252, 253 of one of the remaining blades 222, 223 may be varied to maintain a substantially constant rotational speed, while the first pitch angle 251 of the first blade 221 and the second pitch angle 252 of the other blade may be maintained substantially constant.

[0059] In some examples, the predetermined rotational conditions can include a pitch angle 251 of the first blade 221 and a predetermined rotor speed, and the wind turbine parameters can include a generator torque to maintain the predetermined rotor speed. That is, a torque value provided by the wind turbine generator 42 to maintain a known speed of the wind turbine rotor 18, such as a reference speed, can be determined and then compared to the reference torque value. The first blade 221 can be positioned at a reference first pitch angle 251, and the remaining blades 222, 223 can be positioned at a reference second pitch angle 252. For example, with clean or semi-clean blades, it is known that a constant rotor 18 speed can be achieved at a selected configuration of pitch angles 251, 252. A constant value of generator torque may be required to maintain that rotor speed. During a roughness check, the torque can be varied to reach and maintain the predetermined rotor speed. If the current value of the required torque is substantially the same as the corresponding reference torque value, it can be concluded that the blades remain clean or semi-clean. However, if the torque required to maintain a substantially constant rotor speed is lower than the torque reference value, this may mean that the surface roughness of one or more blades is increasing.

[0060] In some examples, the predetermined rotational condition may include idling the wind turbine 10. That is, in some examples, the method may further include idling the wind turbine rotor 18 before determining the current value of one or more parameters. Here, idle or idling refers to the wind turbine blades 22 rotating (slowly) but not generating energy, i.e., the generator 42 is not connected to the grid. An idling rotor 18 may facilitate observing changes in blade roughness and measuring related parameters. The rotor 18 may be set to idle before determining the current values ​​of, for example, the rotational rotor speed, the tip speed ratio, or one or more pitch angles 25. In some examples, a power converter and the grid may be used to vary the generator torque, while in other examples, other power sources may be used. For example, one or more auxiliary or additional power sources may be used to use the wind turbine generator 42 as a motor. If the determination of the current values ​​is performed during idling, the reference values ​​may also be determined during idling to make direct comparison more meaningful.

[0061] For values ​​of the second pitch angle 252, and optionally for the first pitch angle 251, at a given rotational condition, the pitch angle 251 of the first blade 221 may be higher than the pitch angles 252, 253 of the other blades 222, 223. These predetermined values, as well as the optional reference value for the first pitch angle 251, as well as the reference value for the second pitch angle 252, may be selected such that the effect of roughness on one or more of the determined parameters is maximized, or at least increased, for other values ​​of the pitch angle 252.

[0062] In some examples, the predetermined and / or reference value for second pitch angle 252 may be near the stall position. That is, in this case, second pitch angle 252 may be less than, but close to, the pitch angle at which stall occurs. At such a pitch angle, the effect of a rough blade surface can be more easily measured. In some examples, the predetermined and / or reference value for second pitch angle 252 may be between 0° and 30°, more specifically between 5° and 15°. In some of these examples, the reference value for second pitch angle 252 is approximately 10°.

[0063] The predetermined and / or reference value of the first pitch angle 251 can be selected to optimize measurement conditions. For example, the first pitch angle can be selected to accommodate the rotational speed of the rotor 18. If the rotor rotates too fast, over-rotation can damage the wind turbine blades. The first pitch angle 251 can also be selected so that the determined value distinguishes between the accuracy of the measurement, e.g., so that variations in the parameter of interest due to blade roughness are increased relative to other possible values ​​of the first pitch angle 251. In some examples, the predetermined and / or reference value of the first pitch angle 251 can be between 45° and 90°, or more specifically, between 60° and 80°. In some of these examples, the reference value of the first pitch angle 252 is approximately 70°.

[0064] In some examples, the pitch angle 251 of the first blade 221 may be in the range of 45° to 90°, specifically in the range of 60° to 80°, and the pitch angles 252 of the other blades 222, 223 may be in the range of 0° to 30°, specifically in the range of 5° to 15°.

[0065] In most implementations it may be sufficient to determine the blade roughness generally, i.e. without distinguishing between individual blades. In most cases it can be assumed that material accumulation or erosion occurs at a similar rate on all blades of a wind turbine rotor.

[0066] However, different blades may roughen at different rates. To account for this, in some examples, the method may further include repeating the steps of rotating, determining, and comparing one or more, e.g., all, of the other blades 222, 223 acting as first blades. Repeatedly determining the current value of one or more parameters and comparing the determined current value to a corresponding reference value for each rotor configuration, i.e., a configuration in which a particular blade 221 is positioned at a particular first pitch angle 251 and the remaining blades 222, 223 are positioned at a particular second pitch angle 252, can help distinguish which blades 22 are more irregular (rough) when they experience different roughness changes.

[0067] For illustrative purposes, assume that the first blade 221 is rougher than the remaining blades 222 and 223, and the current value of the first pitch angle for maintaining a substantially constant rotor speed is compared to a reference value of the first pitch angle. In this situation, when the current value of the first pitch angle is determined for each rotor configuration, it is found that the current value for the rotor configuration in which the pitch angle of the first blade 221 is changed is different from the current value for the other rotor configurations in which the pitch angles of the remaining blades are changed.

[0068] It should be noted that these example methods may be performed at the current wind speed regardless of the selected predetermined rotational conditions, i.e., avoiding waiting for specific wind conditions to perform these methods.

[0069] In some examples, any of the above methods may be implemented as part of a method of operating a wind turbine 10. Such a method of operating a wind turbine 10 may include operating the wind turbine with default control settings. The method may further include performing the above-described method 100. The method may further include adjusting operation of the wind turbine if the current value of the parameter differs from the reference value by or more than a predetermined threshold.

[0070] In some examples, the wind turbine 10 may be operated with default control settings at the start of operation after installation and commissioning. Appropriate control settings may be based on prototype testing, simulations, and so forth. The baseline values ​​used in the method for determining blade roughness may be determined during installation or commissioning of the wind turbine after all blades have been installed. Additionally or alternatively, the baseline values ​​may be determined after an event occurs after the start of operation of the wind turbine in other examples, such as after a blade 22 has been cleaned, replaced, or repaired. For example, if the wind turbine has already been operating for some time, the blades may be cleaned, and then the baseline values ​​for the cleaned blades may be determined. It is also possible to replace one or more wind turbine blades and determine the baseline values ​​for the new rotor 18. Replaced blades may be considered clean blades. Washed or cleaned blades may be considered semi-clean blades.

[0071] In some embodiments, the method of operation may further include determining a reference curve 45 of the speed of the wind turbine rotor as a function of wind speed, for example, for a clean or semi-clean blade, a first blade 221 positioned at a reference value of the first pitch angle 251, and the remaining blades 222, 223 positioned at a reference value of the second pitch angle 252. For example, a curve 45 similar to the one shown schematically in FIG.

[0072] The wind speed and rotor 18 speed values ​​may be determined over a period of time and then averaged. In some examples, they may be measured over a period of 1 minute, 5 minutes, 10 minutes, or more. In some examples, they may be measured over a period during which the wind speed is substantially constant or can be considered substantially constant. In some of these examples, the wind speed is considered to be substantially constant over a period of time if the wind speed value remains within an interval defined by the mean value of the wind speed plus or minus 10%, i.e., an interval [0.9: mean wind speed, 1.1: mean wind speed]. This description may apply to any directly measured values, such as any suitable reference value and any suitable current value. For example, the current value of a parameter of a set of parameters may be determined as the average of multiple values ​​measured over a period of time, e.g., 10 minutes.

[0073] If the blades 22 are clean, they should all perform equally well. Therefore, it may be sufficient to have one set of reference values ​​37 for a single rotor configuration. It therefore does not matter which clean blade has the larger reference pitch angle 251, as the resulting reference values ​​may be the same. However, it is not excluded and possible to determine several sets of reference values ​​37, for example, N sets of reference values, where N is equal to the number of blades 22 of the wind turbine 10. This can be done, for example, when using semi-clean blades to determine the reference values.

[0074] In some examples, adjusting the operation of the wind turbine 10 may include one or more of changing control settings, outputting a status message, and initiating a corrective action. In some examples, the message may indicate whether a particular blade, or generally all blades, are as clean as before or rougher. A level of roughness may be indicated. For example, a variation in the current value of a parameter relative to the parameter's corresponding reference value may be linked to a degree of roughness. Different thresholds may be created, either for absolute values ​​(e.g., parameter X reaches value Y) or relative values ​​(e.g., parameter X has changed by more than Y%). Different messages may be configured or different actions may be performed depending on how much the current value differs from the reference value. If blade roughness, for example, blade roughness exceeding a predetermined threshold, is detected, a corrective action may be triggered. The corrective action may be aimed at reducing blade roughness and / or increasing the wind turbine's power output if the roughness has reduced the power output. Corrective actions may include one or more of repairing, replacing, cleaning, defrosting, pitching, and varying a TSR of one or more blades. Other corrective actions are possible. The status message may also recommend specific corrective actions.

[0075] In examples, control settings may be changed to continue operation of the wind turbine taking into account the actual condition of the wind turbine blades, for example PID settings, and / or generator torque control and / or aerodynamic actuator settings may be changed after detecting different surface roughness of the blades.

[0076] In some examples, the method may be performed at regular, predetermined intervals, such as daily, weekly, or monthly. In other examples, the method may be performed after manual instruction or request, such as by an operator. In some examples, the method may be triggered after the occurrence of a particular environmental condition, such as the occurrence of rain, a storm, or snow.

[0077] According to a further aspect, a controller 36 for a wind turbine 10 is provided. As described with respect to Figure 3, the controller 36 includes a communications module 43, a processor 40, and a memory 41. The memory 41 includes instructions that, when executed by the processor 40, cause the processor to perform the methods disclosed herein. A wind turbine 10 may be provided with such a controller 36.

[0078] In a further aspect of the present disclosure, a method 200 for controlling a wind turbine 10 is provided. The method is illustrated in the flow chart of Figure 9. Aspects and discussions relating to method 100 may be applied in combination to method 200 and vice versa.

[0079] At block 210, the method 200 includes determining one or more reference values ​​of one or more wind turbine parameters 35 for an idle wind turbine rotor 18 before the wind turbine begins operation 10, with a first blade 221 positioned at a reference first pitch angle 251 and the remaining blades 222, 223 positioned at a reference second pitch angle 252. Determining the one or more reference values ​​may, in some examples, include measuring a reference curve of wind turbine rotor speed as a function of wind speed. Determining the reference values ​​may occur after all wind turbine blades 22 are installed on the wind turbine 10 during installation or commissioning of the wind turbine. In some examples, the reference values ​​for the first pitch angle 251 and the second pitch angle 252 may be between 60° and 80°, and between 5° and 20°, respectively. For example, the reference values ​​may be set to approximately 70° for the first pitch angle 251 and approximately 10° for the second pitch angle.

[0080] The method further includes initiating wind turbine operation at blocks 220 and 230. After a period of time, the wind turbine rotor 18 begins idling, positioning the first blade 221 at a reference first pitch angle 251 and the remaining blades 222, 223 at a reference second pitch angle 252.

[0081] The method further includes determining one or more current values ​​of the one or more wind turbine parameters and comparing those values ​​to corresponding reference values ​​at block 240. In some examples, one or more reference values ​​and one or more current values ​​are obtained for at least one of rotor speed and tip speed ratio.

[0082] The method further includes adapting wind turbine operation based on the comparison at block 250. Adapting wind turbine operation may include outputting one or more status messages and triggering corrective action or operational changes as described above if blade roughness is detected. Corrective action may include one or more of repairing, replacing, cleaning, defrosting, pitching, and changing the tip speed ratio of one or more blades.

[0083] In some examples, after corrective action has been implemented, steps 230 and 240 may be performed again to check whether the corrective action was successful. For example, if blade roughness due to the presence of ice on one or more blades 22 is detected, the wind turbine 10 may be shut down. The blades may be de-iced, and the rotor 18 may then be idled and the blades 22 may be pitched to an appropriate pitch angle (step 230). The current values ​​of one or more of the parameters may be determined and compared to the corresponding reference values ​​(step 240). This may confirm whether the de-icing was successful. If successful, the wind turbine 10 may be restarted.

[0084] The description set forth herein uses examples to disclose the teachings, including preferred embodiments, and to enable one of ordinary skill in the art to practice the teachings, including making and using any devices or systems and performing any incorporated methods. The patentable scope is defined by the claims and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they contain equivalent structural elements that do not differ substantially from the literal language of the claims. Aspects from the various described embodiments, as well as other known equivalents to each such aspect, can be mixed and matched by one of ordinary skill in the art to construct additional embodiments and techniques in accordance with the principles of the present application. Where reference signs relating to the drawings are placed in parentheses in the claims, they are intended only to enhance comprehension of the claims and should not be construed as limiting the scope of the claims. [Explanation of symbols]

[0085] 10: Wind turbine 12: Ground 14: Support system 15: Tower 16: Nacelle 18: Rotor 20: Hub 22: Rotor blade 24: Blade root 26: Load transfer area 25: Pitch angle 26: Reference line 27: Chord 28: Wind direction 30: Rotor axis 32: Pitch system 34: Pitch axis 36: Wind turbine controller 37: Reference value 38: Yaw axis 40: Processor 41: Memory 42: Generator 43: Communication module 44: Main shaft 45: Rotor speed reference curve 46: Gearbox 48: High speed shaft 49: Sensor interface 50: Coupling 51: Shaft sensor 52: Main frame 53: Generator sensor 54: Decoupling support means 56: Yaw drive mechanism 58: Meteorological measurement system 60: Main forward support bearing 62: Aft support bearing 64: Drive train 66: Pitch assembly 68: Pitch drive system 70: Sensor 72: Pitch bearing 74: Pitch drive motor 76: Pitch drive gearbox 78: Pitch drive pinion 80: Pitch control system 84: Generator 86: Cavity 88: Inner surface 90: Transformer 103: Torque arm 221: First blade 222: Second blade 223: Third blade 251: First pitch angle 252: Second pitch angle

Claims

1. 1. A method (100) for determining a surface condition of one or more wind turbine blades (22) of a wind turbine (10) including a rotor (18) including a first wind turbine blade (221) and one or more further wind turbine blades (222, 223), comprising: Rotating (110) the wind turbine rotor (18) under the influence of wind under predetermined rotation conditions, the predetermined rotation conditions including at least a predetermined constant pitch angle (252) of the remaining wind turbine blades (222, 223); Determining (120) current values ​​of one or more parameters of the wind turbine when rotating at a predetermined rotation condition; comparing (130) current values ​​of one or more parameters of the wind turbine with one or more reference values ​​(37) to determine a surface condition of the wind turbine blades (22); Including, the predetermined rotational conditions include a predetermined pitch angle (251) of the first blade (221), and the determined parameters of the wind turbine include a rotational speed; Or, the predetermined rotational conditions include a predetermined rotor speed, and the determined parameters of the wind turbine include a pitch angle of the first blade (221) to maintain the predetermined rotor speed; Or, The method, wherein the predetermined rotational conditions include a pitch angle of the first blade (221) and a predetermined rotor speed, and the determined parameters of the wind turbine include a generator torque to maintain the predetermined rotor speed.

2. 2. The method of claim 1, wherein the reference value (37) corresponds to a clean blade.

3. The method of claim 1 , wherein the predetermined rotation condition comprises idling the wind turbine.

4. 2. The method of claim 1, wherein the pitch angle (251) of the first blade (221) at a given rotational condition is greater than the pitch angle (252) of the other blades (222, 223).

5. 5. The method according to claim 4, wherein the pitch angle (251) of the first blade (221) is in the range of 45 to 90°, in particular in the range of 60 to 80°, and the pitch angles (252) of the other blades (222, 223) are in the range of 0 to 30°, in particular in the range of 5 to 15°.

6. 2. The method of claim 1, further comprising repeating the steps of rotating (110), determining (120), and comparing (130) with one or more other blades (222, 223) acting as the first blade (221).

7. A method of operating a wind turbine (10), comprising: operating the wind turbine with default control settings; Executing a method (100) according to any one of claims 1 to 6; adjusting the operation of the wind turbine if the current value of the parameter differs from the reference value (37) by more than a predetermined threshold; A method comprising:

8. The method of claim 7, further comprising determining one or more reference values ​​(37) of one or more wind turbine parameters at predetermined rotational conditions prior to operation of the wind turbine.

9. 9. The method of claim 8, further comprising positioning a first blade (221) at a reference value of a first pitch angle (251) and positioning the remaining blades (222, 223) at a reference value of a second pitch angle (252) to determine a reference curve (45) of speed of the wind turbine rotor (18) as a function of wind speed.

10. 10. A control device (36) for a wind turbine, comprising: a communications module (43); a processor (40); and a memory (41), the memory (41) containing instructions that, when executed by the processor (40), cause the processor (40) to perform a method according to any one of claims 1 to 6.

11. A wind turbine (10) comprising a control device (36) according to claim 10.

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