Pitch control method and device for wind turbine generator set

Abstract

This invention provides a pitch control method and apparatus for wind turbine generator sets. The method includes: acquiring relevant motion parameters of the wind turbine generator set tower in the forward and backward directions; determining a damped pitch reference component for suppressing tower vibration based on the relevant motion parameters; adjusting a pitch reference for control functions using the damped pitch reference component; and using the adjusted pitch reference to control the operation of a pitch actuator. The apparatus includes: a tower monitoring unit configured to acquire relevant motion parameters of the wind turbine generator set tower in the forward and backward directions; a damping unit configured to determine a damped pitch reference component for suppressing tower vibration based on the relevant motion parameters; a pitch adjustment unit configured to adjust the pitch reference for control functions using the damped pitch reference component; and a pitch control unit configured to use the adjusted pitch reference to control the operation of a pitch actuator.

Description

Technical Field

[0001] The present application relates to the technical field of wind power generation, and in particular to a pitch control method and device for a wind generator set. Background Art

[0002] Generally, a wind turbine generator set will generate tower vibration during operation, which will cause the tower to move in the front-rear direction, which will not only affect the stable operation and power generation of the set, but also increase the load on the set. Summary of the invention

[0003] The object of the present invention is to provide a pitch control method and device for a wind turbine generator set.

[0004] According to one aspect of the present invention, there is provided a pitch control method for a wind turbine generator set, the pitch control method comprising: acquiring relevant motion parameters of a tower of the wind turbine generator set in a front-to-rear direction; determining a damped pitch reference component for suppressing vibration of the tower of the wind turbine generator set in the front-to-rear direction according to the relevant motion parameters of the tower of the wind turbine generator set in the front-to-rear direction; adjusting a pitch reference for executing a control function of the wind turbine generator set by means of the damped pitch reference component; and using the adjusted pitch reference to control the operation of a pitch actuator of the wind turbine generator set.

[0005] Preferably, the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction include at least one of the following items: the speed of the tower of the wind turbine generator set moving in the front-to-back direction; the acceleration of the tower of the wind turbine generator set moving in the front-to-back direction; the vibration frequency of the tower of the wind turbine generator set in the front-to-back direction; and the thrust borne by the tower of the wind turbine generator set in the front-to-back direction.

[0006] Preferably, the obtaining of relevant motion parameters of the tower of the wind generator set in the front-to-back direction comprises: measuring the relevant motion parameters of the tower of the wind generator set in the front-to-back direction; processing the measured relevant motion parameters using a Kalman filter or an extended Kalman filter to obtain relative true values ​​of the relevant motion parameters of the tower of the wind generator set in the front-to-back direction; and obtaining the relative true values ​​as the relevant motion parameters of the tower of the wind generator set in the front-to-back direction.

[0007] Preferably, determining a damped pitch reference component for suppressing vibration of the tower of the wind generator set in the fore-and-aft direction according to relevant motion parameters of the tower of the wind generator set in the fore-and-aft direction comprises: multiplying the relevant motion parameters of the tower of the wind generator set in the fore-and-aft direction by a tower damping gain to obtain a damped pitch reference component for suppressing vibration of the tower of the wind generator set in the fore-and-aft direction.

[0008] Preferably, the pitch control method further comprises: determining the tower damping gain based on the ambient conditions of the wind turbine generator set.

[0009] Preferably, the method of determining the damped pitch reference component for suppressing the vibration of the tower of the wind turbine in the fore-and-aft direction according to the relevant motion parameters of the tower of the wind turbine in the fore-and-aft direction comprises: inputting a plurality of state parameters of the wind turbine including the relevant motion parameters of the tower of the wind turbine in the fore-and-aft direction into the model predictive control of the wind turbine; and deriving a control sequence to be executed of the wind turbine from the model predictive control, the control sequence comprising a plurality of control functions of the wind turbine, a pitch reference for executing each of the plurality of control functions, and the damped pitch reference component.

[0010] Preferably, the adjusting the pitch reference used to execute the control function of the wind turbine generator set by the damping pitch reference component comprises: when executing each of the multiple control functions, adjusting the pitch reference used to execute the corresponding control function by the damping pitch reference component.

[0011] Preferably, deriving the control sequence to be executed of the wind turbine generator set from the model predictive control includes: constructing a cost function related to the control sequence to be executed of the wind turbine generator set; using the cost function to find the optimal control sequence to be executed of the wind turbine generator set that meets the requirements of the performance indicators of the wind turbine generator set; and determining the optimal control sequence as the control sequence to be executed of the wind turbine generator set.

[0012] Preferably, the requirements for the performance indicators of the wind turbine generator set include at least one of the following items: the rotor speed of the wind turbine generator set reaches an expected speed matching the wind speed; the output power of the wind turbine generator set reaches an expected power matching the wind speed; and the unit load of the wind turbine generator set is reduced to below an expected value.

[0013] Preferably, the pitch reference comprises at least one of: a pitch speed of the pitch actuator; and a pitch position of the pitch actuator.

[0014] Preferably, adjusting the pitch reference used to perform the control function of the wind turbine generator set by the damped pitch reference component includes: adjusting the pitch reference used to perform the control function of the wind turbine generator set by the damped pitch reference component before the pitch reference is sent to the pitch actuator.

[0015] According to another aspect of the present invention, there is provided a pitch control device for a wind turbine generator set, the pitch control device comprising: a tower monitoring unit, configured to obtain relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; a damping vibration reduction unit, configured to determine a damped pitch reference component for suppressing vibration of the tower of the wind turbine generator set in the front-to-back direction according to the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; a pitch adjustment unit, configured to adjust a pitch reference for executing a control function of the wind turbine generator set by means of the damped pitch reference component; and a pitch control unit, configured to control the operation of a pitch actuator of the wind turbine generator set using the adjusted pitch reference.

[0016] Preferably, the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction include at least one of the following items: the speed of the tower of the wind turbine generator set moving in the front-to-back direction; the acceleration of the tower of the wind turbine generator set moving in the front-to-back direction; the vibration frequency of the tower of the wind turbine generator set in the front-to-back direction; and the thrust borne by the tower of the wind turbine generator set in the front-to-back direction.

[0017] Preferably, the tower monitoring unit includes: a tower state measurement unit, configured to measure relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; a tower state estimation unit, configured to process the measured relevant motion parameters using a Kalman filter or an extended Kalman filter to obtain relative true values ​​of the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; and a tower state acquisition unit, configured to obtain the relative true values ​​as the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction.

[0018] Preferably, the damping vibration reduction unit is further configured to: multiply the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction by the tower damping gain to obtain a damping pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-to-back direction.

[0019] Preferably, the pitch control device further comprises: a gain determination unit configured to: determine the tower damping gain based on the ambient conditions of the wind turbine generator set.

[0020] Preferably, the damping vibration reduction unit includes: a model prediction control unit, configured to: input multiple state parameters of the wind turbine including relevant motion parameters of the tower of the wind turbine in the front and rear directions into the model prediction control of the wind turbine; a control sequence derivation unit, configured to: derive a control sequence to be executed of the wind turbine from the model prediction control, the control sequence including multiple control functions of the wind turbine, a pitch reference for executing each of the multiple control functions, and the damping pitch reference component.

[0021] Preferably, the pitch adjustment unit is further configured to: when executing each of the plurality of control functions, adjust the pitch reference used to execute the corresponding control function by means of the damping pitch reference component.

[0022] Preferably, the control sequence derivation unit includes: a cost function construction unit, configured to construct a cost function related to the control sequence to be executed of the wind turbine generator set; an optimal control search unit, configured to use the cost function to find the optimal control sequence to be executed of the wind turbine generator set that meets the requirements of the performance indicators of the wind turbine generator set; and an optimal control determination unit, configured to determine the optimal control sequence as the control sequence to be executed of the wind turbine generator set.

[0023] Preferably, the requirements for the performance indicators of the wind turbine generator set include at least one of the following items: the rotor speed of the wind turbine generator set reaches an expected speed matching the wind speed; the output power of the wind turbine generator set reaches an expected power matching the wind speed; and the unit load of the wind turbine generator set is reduced to below an expected value.

[0024] Preferably, the pitch reference comprises at least one of: a pitch speed of the pitch actuator; and a pitch position of the pitch actuator.

[0025] Preferably, the pitch adjustment unit is further configured to: before the pitch reference is sent to the pitch actuator, adjust the pitch reference used to perform the control function of the wind turbine generator set by means of the damping pitch reference component.

[0026] According to another aspect of the present invention, a computer-readable storage medium storing a computer program is provided. When the computer program is executed by a processor, the pitch control method for a wind turbine generator set as described above is implemented.

[0027] According to another aspect of the present invention, a computer device is provided, comprising: a processor; and a memory storing a computer program, wherein when the computer program is executed by the processor, the pitch control method for a wind turbine generator set as described above is implemented.

[0028] The pitch control method and device for a wind turbine generator set according to an exemplary embodiment of the present invention can not only effectively reduce the negative impact of tower vibration on the stable operation and power generation of the unit and reduce the load of the unit, but also further improve the accuracy of the pitch control of the wind turbine generator set. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The above objects and features of the present invention will become more apparent through the following description in conjunction with the accompanying drawings, in which:

[0030] Figure 1 A flow chart of a pitch control method for a wind turbine generator system according to an exemplary embodiment of the present invention is shown;

[0031] Figure 2 A structural block diagram of a pitch control device for a wind turbine generator set according to an exemplary embodiment of the present invention is shown;

[0032] Figure 3 A system architecture diagram for pitch control of a wind turbine generator set according to an exemplary embodiment of the present invention is shown;

[0033] Figure 4 A schematic diagram showing an interface of a tower state parameter estimator using an extended Kalman filter according to an exemplary embodiment of the present invention is shown;

[0034] Figure 5A A schematic diagram showing a system for controlling a pitch actuator of a wind turbine generator set by using a pitch control device for a wind turbine generator set according to an exemplary embodiment of the present invention; and

[0035] Figure 5B Another schematic diagram of a system for controlling a pitch actuator of a wind turbine generator set by applying a pitch control device for a wind turbine generator set according to an exemplary embodiment of the present invention is shown. DETAILED DESCRIPTION

[0036] The idea of ​​the present invention is that since the vibration of the tower in the front-to-back direction can be characterized by relevant motion parameters of the tower in the front-to-back direction (such as, but not limited to, the speed, acceleration, vibration frequency and thrust of the tower in the front-to-back direction), a damping pitch reference component for suppressing the vibration of the tower in the front-to-back direction can be generated according to the relevant motion parameters of the tower in the front-to-back direction. The damping pitch reference component can produce a damping effect to make the tower move in another direction (or in the opposite direction to the direction of movement of the tower), thereby effectively reducing various negative effects on the stable operation and power generation of the unit due to the vibration of the tower.

[0037] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[0038] Figure 1 A flow chart 100 of a pitch control method for a wind turbine generator system according to an exemplary embodiment of the present invention is shown.

[0039] Reference Figure 1 , Figure 1 The method shown may include the following steps:

[0040] In step 110, relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction may be obtained.

[0041] Here, the acquired relevant motion parameters may include, but are not limited to, one or a combination of the following items: the speed of the tower of the wind turbine generator set moving in the front-to-back direction, the acceleration of the tower of the wind turbine generator set moving in the front-to-back direction, the vibration frequency of the tower of the wind turbine generator set in the front-to-back direction, and the thrust borne by the tower of the wind turbine generator set in the front-to-back direction. Generally speaking, these relevant motion parameters can be sensed by corresponding sensors arranged on the tower of the wind turbine generator set.

[0042] Taking into account that the sensed data may include noise and interference in the system, which will affect the accuracy of subsequent adjustments to the pitch control, therefore, in the example, the relevant motion parameters of the tower of the wind turbine in the fore-and-aft direction can be measured, and the measured relevant motion parameters can be processed using a Kalman filter or an extended Kalman filter to obtain the relative true value of the relevant motion parameters of the tower of the wind turbine in the fore-and-aft direction, and the relative true value is obtained as the relevant motion parameter of the tower of the wind turbine in the fore-and-aft direction.

[0043] In step 120, a damping pitch reference component for suppressing vibration of the tower of the wind turbine generator set in the front-rear direction may be determined according to relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction.

[0044] In one example, the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction may be multiplied by the tower damping gain to obtain a damping pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-to-back direction. Here, the tower damping gain may be a set magnification, and the greater the tower damping gain, the greater the damping of the tower movement in the front-to-back direction. However, this will affect the generator rotor speed of the wind turbine generator set and cause power loss. In addition, it will also cause instability in the unit operation system because the damping effect will cause the tower to move in another direction. In order to balance the tower damping and power loss, as a feasible implementation, the tower damping gain may be determined based on the surrounding environmental conditions of the wind turbine generator set (such as wind speed, turbulence, etc.). This can make the change of the tower damping gain slower than the change of the speed of the tower in the front-to-back direction.

[0045] In another example, multiple state parameters of the wind turbine including relevant motion parameters of the tower of the wind turbine in the front-to-back direction may be input into the model predictive control (MPC) of the wind turbine, and then a control sequence to be executed of the wind turbine is derived from the MPC, which may include multiple control functions of the wind turbine, a pitch reference for executing each of the multiple control functions, and a damped pitch reference component for suppressing vibration of the tower of the wind turbine in the front-to-back direction. The damped pitch reference component obtained by the MPC is usually the optimal result, so the accuracy of subsequent pitch reference adjustment can be ensured.

[0046] In order to balance the difference requirements between the performance indicators of the wind turbine generator set, in this example, a cost function related to the control sequence to be executed by the wind turbine generator set can be constructed, and the cost function is used to find the optimal control sequence to be executed by the wind turbine generator set that meets the requirements of the performance indicators of the wind turbine generator set, and the optimal control sequence is determined as the control sequence to be executed by the wind turbine generator set. The cost function can maximize the power generation of the wind turbine generator set, minimize the generator speed error of the wind turbine generator set, and minimize the speed of the tower of the wind turbine generator set in the front and rear directions.

[0047] Here, the requirements for the performance indicators of the wind turbine generator set may include, but are not limited to, one or a combination of the following items: the rotor speed of the wind turbine generator set reaches the expected speed matching the wind speed, the output power of the wind turbine generator set reaches the expected power matching the wind speed, and the unit load of the wind turbine generator set is reduced to below the expected value.

[0048] It should be understood that although the above describes examples of determining the damping pitch reference component based on the relevant motion parameters of the tower in the fore-and-aft direction, these examples are merely exemplary and the present invention is not limited thereto. Other methods for determining the damping pitch reference component may also be applied to the present invention.

[0049] At step 130 , a pitch reference for performing a control function of the wind turbine may be adjusted by a damping pitch reference component.

[0050] Here, the pitch reference may include, but is not limited to, one or a combination of the following items: a pitch speed of a pitch actuator and a pitch position of a pitch actuator. In an example, a damping pitch reference component may be added to a pitch reference for performing a control function of a wind turbine generator set to adjust the pitch speed of the pitch actuator and / or the pitch position of the pitch actuator in the pitch reference, thereby generating a pitch reference with a damping effect.

[0051] In addition, in the case of using the model predictive control, the pitch reference used to perform the corresponding control function may be adjusted by the damping pitch reference component when each of the plurality of control functions is performed.

[0052] To ensure that the pitch reference is adjusted in time, in the above example, the pitch reference used to perform the control function of the wind turbine generator system may be adjusted by damping the pitch reference component before the pitch reference is sent to the pitch actuator.

[0053] At step 140 , the adjusted pitch reference may be used to control operation of a pitch actuator of the wind turbine.

[0054] Figure 2 A structural block diagram 200 of a pitch control device for a wind turbine generator system according to an exemplary embodiment of the present invention is shown.

[0055] Reference Figure 2 , Figure 2 The pitch control device shown may include a tower monitoring unit 210, a damping and vibration reduction unit 220, a pitch adjustment unit 230 and a pitch control unit 240, wherein the tower monitoring unit 210 may be configured to obtain relevant motion parameters of the tower of the wind turbine in the front-to-back direction; the damping and vibration reduction unit 200 may be configured to determine a damped pitch reference component for suppressing the vibration of the tower of the wind turbine in the front-to-back direction according to the relevant motion parameters of the tower of the wind turbine in the front-to-back direction; the pitch adjustment unit 230 may be configured to adjust the pitch reference used to perform the control function of the wind turbine through the damped pitch reference component; the pitch control unit 240 may be configured to use the adjusted pitch reference to control the operation of the pitch actuator of the wind turbine.

[0056] exist Figure 2 In the pitch control device shown, the tower monitoring unit 210 may include a tower state measurement unit, a tower state estimation unit, and a tower state acquisition unit (all not shown), wherein the tower state measurement unit may be configured to measure the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; the tower state estimation unit may be configured to process the measured relevant motion parameters using a Kalman filter or an extended Kalman filter to obtain the relative true value of the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; the tower state acquisition unit may be configured to obtain the relative true value as the relevant motion parameter of the tower of the wind turbine generator set in the front-to-back direction. Here, the acquired relevant motion parameters may include, but are not limited to, one of the following items or a combination thereof: the speed of the tower of the wind turbine generator set moving in the front-to-back direction, the acceleration of the tower of the wind turbine generator set moving in the front-to-back direction, the vibration frequency of the tower of the wind turbine generator set in the front-to-back direction, and the thrust borne by the tower of the wind turbine generator set in the front-to-back direction.

[0057] In one example, the damping vibration reduction unit 220 may be further configured to multiply the relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction by the tower damping gain to obtain a damping pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-rear direction. Figure 2 The pitch control device shown may further include a gain determination unit (not shown), which may be configured to determine a tower damping gain based on the surrounding environmental conditions of the wind turbine generator system (such as wind speed, turbulence, etc.).

[0058] In another example, the damping vibration reduction unit 220 may include a model prediction control unit and a control sequence derivation unit (both not shown), wherein the model prediction control unit may be configured to input various state parameters of the wind turbine including relevant motion parameters of the tower of the wind turbine in the front-rear direction to the model prediction control of the wind turbine; the control sequence derivation unit may be configured to derive a control sequence to be executed of the wind turbine from the model prediction control, the control sequence may include multiple control functions of the wind turbine, a pitch reference for executing each of the multiple control functions, and a damping pitch reference component for suppressing the vibration of the tower of the wind turbine in the front-rear direction. In this example, the control sequence derivation unit may include a cost function construction unit, an optimal control search unit, and an optimal control determination unit (all not shown), wherein the cost function construction unit may be configured to construct a cost function related to the control sequence to be executed of the wind turbine; the optimal control search unit may be configured to use the cost function to find the optimal control sequence to be executed of the wind turbine that meets the requirements of the performance index of the wind turbine; the optimal control determination unit may be configured to determine the optimal control sequence as the control sequence to be executed of the wind turbine. Here, the requirements for the performance indicators of the wind turbine generator set may include, but are not limited to, one or a combination of the following items: the rotor speed of the wind turbine generator set reaches the expected speed matching the wind speed, the output power of the wind turbine generator set reaches the expected power matching the wind speed, and the unit load of the wind turbine generator set is reduced to below the expected value.

[0059] exist Figure 2 In the pitch control device shown, the pitch adjustment unit 230 may be further configured to adjust the pitch reference used to perform the control function of the wind turbine generator set by a damped pitch reference component before the pitch reference is sent to the pitch actuator. In the case of using model predictive control, the pitch adjustment unit 230 may be further configured to adjust the pitch reference used to perform the corresponding control function by a damped pitch reference component when performing each of the multiple control functions. Here, the pitch reference may include, but is not limited to, one or a combination of the following items: the pitch speed of the pitch actuator and the pitch position of the pitch actuator.

[0060] Figure 3 A system architecture diagram 300 for pitch control of a wind turbine generator system according to an exemplary embodiment of the present invention is shown.

[0061] Reference Figure 3 , Figure 3The system architecture shown may include a pitch control device 310 for a wind turbine generator set according to an exemplary embodiment of the present invention, a wind turbine generator set 320, and a wind turbine generator set controller 330 (such as, but not limited to, a main control PLC system or a pitch control system in a wind turbine generator set). The pitch control method for a wind turbine generator set according to an exemplary embodiment of the present invention may be run as an algorithm in Figure 3 In the computing unit of the pitch control device 310 shown, and Figure 3 The pitch control device 310 shown may include Figure 2 The tower monitoring unit 210 , the damping vibration reduction unit 220 , the pitch adjustment unit 230 and the pitch control unit 240 are shown.

[0062] exist Figure 3 In the system architecture shown, a pitch reference A for executing the control function of the wind turbine generator set and a related motion parameter B of the tower of the wind turbine generator set in the front-rear direction may be input to the pitch control device 310. The pitch control device 310 may determine a damped pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-rear direction based on the input related motion parameter B, and adjust the pitch reference A by the damped pitch reference component (for example, but not limited to, adding the damped pitch reference component to the pitch reference A), and then send the adjusted pitch reference A to the wind turbine generator set 320 via the wind turbine generator set controller 330, so as to use the adjusted pitch reference A to control the operation of the pitch actuator of the wind turbine generator set 320.

[0063] It should be understood that although Figure 3 The system architecture for pitch control of a wind turbine generator set according to an exemplary embodiment of the present invention is shown, but the present invention is not limited thereto. For example, the pitch control device 310 may also be provided between the wind turbine generator set controller 330 and the wind turbine generator set 320, as long as the pitch reference A is adjusted before being sent to the pitch actuator of the wind turbine generator set 320. In addition, Figure 3 The pitch control device 310 shown can be integrated into a separate controller, or can be integrated into a wind turbine controller 330 or a background controller for scheduling wind turbines in a wind farm, or other control devices that can be connected to the wind turbine controller 330 or the wind turbine 320. The present invention is not limited to this.

[0064] Next, we will refer to Figure 4 , Figure 5A and Figure 5B The above pitch control process for a wind turbine generator set will be described in detail.

[0065] Figure 4An interface diagram 400 of a tower state parameter estimator using an extended Kalman filter according to an exemplary embodiment of the present invention is shown.

[0066] Reference Figure 4 , Figure 4 The tower state parameter estimator 401 shown may include input interfaces At_m and Ft_e and output interfaces At_e and Vt_e for Figure 2 The tower monitoring unit 210 shown in FIG. 1 is called, where At_m is the acceleration of the tower moving in the forward and backward directions measured at the sampling time k (which corresponds to a calculated below). t，m [k]); Ft_e is the thrust of the tower in the fore-aft direction estimated at sampling time k (which corresponds to Ft_e calculated below). t，e At_e is the acceleration of the tower moving in the fore-aft direction estimated at sampling time k (which corresponds to a calculated below). t，e Vt_e is the estimated velocity of the tower in the fore-aft direction at sampling time k (which corresponds to v calculated below). t，e [k]).

[0067] Figure 4 The tower state parameter estimator 401 shown can use an extended Kalman filter to remove noise from the measured acceleration At_m of the tower moving in the front-to-back direction to obtain an estimated acceleration At_e of the tower moving in the front-to-back direction, and can also use the extended Kalman filter to estimate the unmeasured speed Vt_e of the tower moving in the front-to-back direction.

[0068] Next, the data processing process of the extended Kalman filter will be described in detail.

[0069] The tower can be a model represented by a linear state space model in a discrete time domain. When the model parameters are known, the tower model can be expressed by the following equation (1):

[0070]

[0071] In formula (1), A, B, C and D are matrices with model parameters; x[k], u[k] and y[k] are the state vector, input vector and output vector of the tower model respectively.

[0072] The linear model structure of the tower model may be based on the assumption that the model parameters are known, in which case the parameters of the matrix A are uncertain.

[0073] Therefore, the state vector can be expanded to contain the estimated parameters for matrix A and the initial state.

[0074] In the current embodiment, the new nonlinear state space model can be formulated as a new enhanced state vector, which can be expressed by the following formula (2):

[0075]

[0076] In formula (2), x1[k] and x2[k] are two initial states, and A1[k], A2[k], A3[k] and A4[k] are four parameters given for the coefficients in matrix A.

[0077] The input vector u[k] can be defined as follows:

[0078]

[0079] The output vector y[k] can be defined as follows:

[0080]

[0081] Therefore, the new nonlinear state space model can be defined as follows:

[0082]

[0083] In equation (5), σ1[k-1], σ2[k-1], σ3[k-1], σ4[k-1], σ5[k-1], and σ6[k-1] are system noises that drive model parameter uncertainty applied to each state and can be included in the vector represented by the following equation (6):

[0084]

[0085] The above dynamic model can be updated to a prediction of the state vector at time k given the estimated k-1 states.

[0086] In the prediction phase of the tower state parameter estimator 401, the state estimate may be updated in the update phase of the tower state parameter estimator 401 using the estimator feedback portion. The updated state vector at time k may be represented as x ag [k|k].

[0087] Therefore, the prediction model can be defined as the following formula (7) based on the dynamic model:

[0088]

[0089] According to the above formula (7), the prediction model can also be defined as the following formula (8):

[0090] x ag [k|k-1]=f(x ag[k-1|k-1],u[k],σ[k]) (8)

[0091] In equation (8), f is the function described by the above state space model.

[0092] The above model can be extended to more tower modes by extending the state model with multiple states, each tower mode requires two states in the initial linear model, and the number of elements in the linear matrix A is the square of the number of states in the linear model.

[0093] This means that the number of states in the enhanced state vector may be calculated based on the number of tower modes.

[0094] In the current embodiment, the extended Kalman filter may include two stages, namely a prediction stage and an update stage.

[0095] 1. Prediction stage

[0096] Predicted state estimate x ag [k|k-1] can be calculated by the following formula (9):

[0097] x ag [k|k-1]=f(x ag [k-1|k-1],u[k]) (9)

[0098] In equation (9), the state can be updated based on the measured input u[k], the last state value, and a model (or prediction model) that does not include the noise portion σ[k] because the state will not be measured.

[0099] The prediction covariance estimate P[k|k-1] can be calculated by the following formula (10):

[0100] P[k|k-1]=F[k]P[k-1|k-1]F T [k]+Q[k] (10)

[0101] In equation (10), P[k-1|k-1] is the update covariance calculated in the update phase, Q[k] is the covariance of the process noise, and F[k] is the state transition matrix and can be defined as follows (11):

[0102]

[0103] (II) Update phase

[0104] Measurement residuals It can be calculated by the following formula (12):

[0105]

[0106] In formula (12), a t，e [k|k-1] can be calculated by the following formula (13):

[0107]

[0108] In formula (13), C r1 is the first row in the matrix C in the linear model.

[0109] The residual covariance S[k] can be calculated by the following formula (14):

[0110] S[k]=H[k]P[k|k-1]H T [k]+R[k] (14)

[0111] In equation (14), R[k] is the covariance of the measurement noise, H[k] is the observation matrix and can be calculated by the following equation (15):

[0112]

[0113] In formula (15), h is the function given by the above formula (13).

[0114] The near-optimal Kalman gain K[k] can be calculated by the following equation (16):

[0115] K[k]=P[k|k-1]H T [k]S -1 [k] (16)

[0116] The updated state estimate can be calculated by the following equation (17):

[0117]

[0118] The updated covariance estimate can be calculated by the following formula (18):

[0119] P[k|k]=(IK[k]H[k])P[k|k-1] (18)

[0120] Q[k] and R[k] may both be model parameters or adjustment parameters of the system and will not change during the above data processing. The initial values ​​of A1[k], A2[k], A3[k] and A4[k] may be given by the linear model parameters.

[0121] Figure 4The tower state parameter estimator 401 shown can encapsulate the above-mentioned extended Kalman filter inside it, and then call the prediction phase and update phase of the extended Kalman filter in the above-mentioned order to obtain the relative true value of the acceleration At_e of the tower moving in the front-to-back direction and / or the speed Vt_e of the tower moving in the front-to-back direction, thereby providing a more reliable and accurate data basis for the subsequent adjustment of the pitch reference.

[0122] It should be understood that although the above describes an example of using an extended Kalman filter to obtain relevant motion parameters of the tower of a wind turbine generator set, this example is only exemplary and the present invention is not limited thereto. Other nonlinear Kalman filters (such as Kalman filters) can also be used to replace the above extended Kalman filter. These filters can be packaged in Figure 4 The tower state parameter estimator 401 shown in the figure is used to obtain the relative true value of the acceleration or speed of the tower movement of the wind turbine generator set. Figure 4 The interface of the tower state parameter estimator 401 shown in FIG. Figure 4 The input interfaces At_m and Ft_e and the output interfaces At_e and Vt_e shown are also not limited. For example, as required, the measured acceleration and speed of the tower moving in the front-to-back direction can also be used as input interfaces, and the estimated vibration frequency and thrust of the tower in the front-to-back direction can be used as output interfaces.

[0123] In addition, since the Kalman filter is sensitive to the model uncertainty in the tower model, the error between the relevant motion parameters of the tower obtained by the extended Kalman filter and the true value is smaller than that of the Kalman filter. This means that the relevant motion parameters of the tower obtained by the extended Kalman filter will be more accurate, which can provide a more reliable data calculation basis for the subsequent adjustment of the pitch reference.

[0124] Figure 5A A schematic diagram 500 - 1 shows a system for controlling a pitch actuator of a wind turbine generator set by applying a pitch control device for a wind turbine generator set according to an exemplary embodiment of the present invention.

[0125] Reference Figure 5A , Figure 5A The system shown may include a wind turbine 320 and Figure 2 The tower monitoring unit 210, the damping vibration reduction unit 220, the pitch adjustment unit 230 and the pitch control unit 240 in the pitch control device for a wind turbine generator according to an exemplary embodiment of the present invention are shown.

[0126] exist Figure 5AIn the system shown in FIG. 1 , the tower monitoring unit 210 can obtain the measured acceleration B of the tower moving in the forward and backward directions from the wind turbine generator set 320, and then call Figure 4 The interface of the tower state parameter estimator 401 shown is used to process the acceleration B using an extended Kalman filter to obtain the relative true value E of the acceleration of the tower moving in the front-rear direction. The damping vibration reduction unit 220 may multiply the relative true value E of the acceleration of the tower moving in the front-rear direction by the tower damping gain to obtain a damped pitch reference component F for suppressing the vibration of the tower of the wind turbine generator set in the front-rear direction. The pitch adjustment unit 230 may add the damped pitch reference component F to the pitch reference A for the wind turbine generator set output by the pitch control unit 240 according to the state parameters such as the generator speed C of the wind turbine generator set, so that the pitch control unit 240 can use the adjusted pitch reference A to control the operation of the pitch actuator of the wind turbine generator set 320.

[0127] Figure 5A The system shown can avoid the damping pitch reference component being too small due to errors in the measurement data, so that the pitch operation can generate sufficient damping to suppress the vibration of the tower in the front-rear direction, thereby achieving optimal pitch operation.

[0128] Figure 5B Another schematic diagram 500 - 2 shows a system for controlling a pitch actuator of a wind turbine generator set by applying a pitch control device for a wind turbine generator set according to an exemplary embodiment of the present invention.

[0129] Reference Figure 5B , Figure 5B The system shown may include a wind turbine 320, a wind turbine controller 330, other monitoring units 510 for measuring or estimating other state parameters of the wind turbine, and a tower monitoring unit 210 in a pitch control device for a wind turbine according to an exemplary embodiment of the present invention, wherein a damping vibration reduction unit 220, a pitch adjustment unit 230 and a pitch control unit 240 in a pitch control device for a wind turbine according to an exemplary embodiment of the present invention may be arranged in the wind turbine controller 330.

[0130] exist Figure 5B In the system shown in FIG. 1 , the tower monitoring unit 210 can obtain the measured acceleration B of the tower moving in the forward and backward directions from the wind turbine generator set 320, and then call Figure 4The interface of the tower state parameter estimator 401 shown is used to process the acceleration B using an extended Kalman filter to obtain the relative true value E of the acceleration of the tower moving in the front-rear direction. The other monitoring unit 510 can obtain other state parameters C of the wind turbine generator set (such as generator speed, pitch angle and wind speed measurement value, etc.) from the wind turbine generator set 320, and then process these state parameters (such as denoising, or similar Kalman filter processing) to obtain the processed data D of other state parameters of the wind turbine generator set. The damping vibration reduction unit 220 set in the wind turbine generator set controller 330 can receive the relative true value E of the acceleration of the tower moving in the front-rear direction and the processed data D of other state parameters of the wind turbine generator set, and then call the model predictive control of the wind turbine generator set to derive the control sequence to be executed of the wind turbine generator set from the model predictive control, and the control sequence may include multiple control functions of the wind turbine generator set, a pitch reference for executing each control function, and a damping pitch reference component for suppressing the vibration of the tower in the front-rear direction. The pitch adjustment unit 230 provided in the wind turbine controller 330 can add the damping pitch reference component to the pitch reference used for each control function when executing each control function in the control sequence, so that the pitch control unit 240 provided in the wind turbine controller 330 can use the adjusted pitch reference A to control the operation of the pitch actuator of the wind turbine 320.

[0131] Figure 5B The system shown can also avoid the damping pitch reference component being too small due to errors in the measurement data, so that the pitch operation can generate sufficient damping to suppress the vibration of the tower in the front-rear direction, thereby achieving optimal pitch operation.

[0132] In the following, the model predictive control of wind turbines and the construction process of the cost function will be described in detail.

[0133] exist Figure 5B In the system shown, the model predictive control of the wind turbine generator set can be constructed by the following equation (19) to predict and optimize the future operation and control actions of the wind turbine generator set:

[0134] x[n+1]=f(x[n],u[n]) (19)

[0135] In formula (19), x[n] is the vector of the predicted state of the wind turbine generator set at time n, x[n+1] is the vector of the predicted state of the wind turbine generator set at the next time n+1, and u[n] is the control vector of the control sequence to be executed by the wind turbine generator set. Here, the vector of the predicted state includes not only the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction, but also other state parameters of the wind turbine generator set, such as the generator speed and generator power of the wind turbine generator set. The control sequence to be executed includes not only the pitch reference for each control function, but also the damping pitch reference component for suppressing the vibration of the tower in the front-to-back direction.

[0136] For a given prediction level N, the optimal control signal sequence associated with the cost function (which may include maximizing power generation, reducing tower speed, and other possible goals) can be calculated by the following equation (20):

[0137]

[0138] In equation (20), h(x[n],u[n]) is a cost function used to penalize the values ​​of the state signal and the control signal to balance the performance difference requirements between the various control actions of the wind turbine generator set.

[0139] The initial value of the vector x[n] of the predicted state may be set based on the input.

[0140] The damping pitch reference component for suppressing the vibration of the tower in the fore-aft direction may be included in u[n] and u[n+1] as a control vector, and the damping pitch reference component may include two parts, namely, the pitch speed u of the pitch actuator and rat [n] and the pitch position u of the pitch actuator pos [n].

[0141] Pitch position u of the pitch actuator pos [n] can be restricted in optimization to the following formula (21):

[0142]

[0143] In formula (21), Pitch min and Pitch max are the minimum pitch value and the maximum pitch value respectively, Pitch0 is the pitch position measured at the beginning of the prediction level, k is u pos The number of elements in [n].

[0144] Pitch speed u of the pitch actuator rat [n] can be restricted in optimization to the following formula (22):

[0145]

[0146] In formula (22), Rate max is the maximum pitch speed, l is u rat The number of elements in [n].

[0147] Using the above constraints and cost function, the optimal control sequence required for the wind turbine can be calculated. From the calculated control trajectory, when the controller optimization is performed for each controller sample, only the first set of values ​​is used for the next sample.

[0148] It can be seen from the above implementation process of the present invention that the pitch control method and device for a wind turbine generator set according to the exemplary embodiment of the present invention can not only effectively reduce the negative impact of tower vibration on the stable operation and power generation of the unit and reduce the load of the unit, but also further improve the accuracy of the pitch control of the wind turbine generator set.

[0149] According to an exemplary embodiment of the present invention, a computer-readable storage medium storing a computer program is also provided. The computer-readable storage medium stores a computer program that causes the processor to execute the pitch control method for a wind turbine according to the present invention when executed by the processor. The computer-readable recording medium is any data storage device that can store data read out by a computer system. Examples of computer-readable recording media include: read-only memory, random access memory, read-only optical disk, magnetic tape, floppy disk, optical data storage device, and carrier wave (such as data transmission through the Internet via a wired or wireless transmission path).

[0150] According to an exemplary embodiment of the present invention, a computer device is also provided. The computer device includes a processor and a memory. The memory is used to store a computer program. The computer program is executed by the processor so that the processor executes the computer program of the pitch control method for a wind turbine generator set according to the present invention.

[0151] While the present application has been shown and described with reference to preferred embodiments, it will be understood by those skilled in the art that various modifications and variations may be made to these embodiments without departing from the spirit and scope of the present application as defined by the appended claims.

Claims

1. A pitch control method for a wind turbine generator set, characterized in that: The pitch control method comprises: Obtain relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; Determine a damping pitch reference component for suppressing vibration of the tower of the wind turbine generator set in the front-rear direction according to relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; adjusting a pitch reference for executing a control function of the wind turbine generator set by means of the damping pitch reference component; using the adjusted pitch reference to control the operation of the pitch actuator of the wind turbine generator set, Wherein, determining the damping pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-to-back direction according to the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction comprises: The relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction are multiplied by the tower damping gain to obtain a damping pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-to-back direction, wherein the change of the tower damping gain is slower than the change of the motion speed of the tower in the front-to-back direction. Wherein, the obtaining of relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction includes: Measuring relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; Processing the measured relevant motion parameters using a Kalman filter or an extended Kalman filter encapsulated in a tower state parameter estimator to obtain relative true values ​​of relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; The relative true value is obtained as a relevant motion parameter of the tower of the wind turbine generator set in the front-rear direction. The input of the tower state parameter estimator includes the acceleration of the tower moving in the front-rear direction and the thrust borne by the tower in the front-rear direction, and the output of the tower state parameter estimator includes the acceleration of the tower moving in the front-rear direction and the speed of the tower moving in the front-rear direction; Alternatively, the input of the tower state parameter estimator includes the acceleration of the tower moving in the front-to-back direction and the speed of the tower moving in the front-to-back direction, and the output of the tower state parameter estimator includes the vibration frequency of the tower moving in the front-to-back direction and the thrust borne by the tower in the front-to-back direction.

2. The pitch control method according to claim 1, characterized in that: The relevant motion parameters of the tower of the wind turbine generator set in the front and rear directions include: The speed at which the tower of the wind turbine generator set moves in the front-rear direction; The acceleration of the tower of the wind turbine generator set moving in the front-rear direction; The vibration frequency of the tower of the wind turbine generator set in the front-to-back direction; and The tower of the wind turbine generator set is subjected to thrust in the front-rear direction.

3. The pitch control method according to claim 1, characterized in that: The pitch control method further includes: The tower damping gain is determined based on the ambient conditions of the wind turbine generator set.

4. The pitch control method according to claim 1, characterized in that: The pitch reference includes at least one of the following: a pitch speed of the pitch actuator; and The pitch position of the pitch actuator.

5. The pitch control method according to claim 1, characterized in that: The adjusting the pitch reference for executing the control function of the wind turbine generator set by the damping pitch reference component comprises: Before the pitch reference is sent to the pitch actuator, a pitch reference for performing a control function of the wind turbine is adjusted by the damping pitch reference component.

6. A pitch control method for a wind turbine generator set, characterized in that: The pitch control method comprises: Obtain relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; Determine a damping pitch reference component for suppressing vibration of the tower of the wind turbine generator set in the front-rear direction according to relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; adjusting a pitch reference for executing a control function of the wind turbine generator set by means of the damping pitch reference component; using the adjusted pitch reference to control the operation of the pitch actuator of the wind turbine generator set, Wherein, determining the damping pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-to-back direction according to the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction comprises: Inputting a plurality of state parameters of the wind turbine generator set including relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction into the model predictive control of the wind turbine generator set; deriving a control sequence to be executed of the wind turbine generator set from the model predictive control, the control sequence comprising a plurality of control functions of the wind turbine generator set, a pitch reference for executing each of the plurality of control functions, and the damping pitch reference component, Wherein, deriving the control sequence to be executed of the wind turbine generator set from the model predictive control includes: constructing a cost function associated with a control sequence to be executed for the wind turbine generator set; Using the cost function to find an optimal control sequence to be executed of the wind turbine generator set that meets the performance index requirements of the wind turbine generator set; determining the optimal control sequence as the control sequence to be executed by the wind turbine generator set, The requirements for the performance indicators of the wind turbine generator set include at least one of the following items: the rotor speed of the wind turbine generator set reaches the expected speed matching the wind speed, the output power of the wind turbine generator set reaches the expected power matching the wind speed, and the unit load of the wind turbine generator set is reduced to below the expected value.

7. The pitch control method according to claim 6, characterized in that: The adjusting the pitch reference for executing the control function of the wind turbine generator set by the damping pitch reference component comprises: When each of the plurality of control functions is executed, a pitch reference for executing the corresponding control function is adjusted by the damping pitch reference component.

8. The pitch control method according to claim 6, characterized in that: The pitch reference includes at least one of the following: a pitch speed of the pitch actuator; and The pitch position of the pitch actuator.

9. The pitch control method according to claim 6, characterized in that: The adjusting the pitch reference for executing the control function of the wind turbine generator set by the damping pitch reference component comprises: Before the pitch reference is sent to the pitch actuator, a pitch reference for performing a control function of the wind turbine is adjusted by the damping pitch reference component.

10. A pitch control device for a wind turbine generator set, characterized in that: The pitch control device comprises: A tower monitoring unit is configured to: obtain relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; The damping vibration reduction unit is configured to: determine a damping pitch reference component for suppressing vibration of the tower of the wind turbine generator set in the front-rear direction according to relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; A pitch adjustment unit, configured to: adjust a pitch reference for executing a control function of the wind turbine generator set by means of the damping pitch reference component; A pitch control unit is configured to: use the adjusted pitch reference to control the operation of the pitch actuator of the wind turbine generator set, The damping vibration reduction unit is further configured to: multiply the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction by the tower damping gain to obtain a damping pitch reference component for suppressing the vibration of the tower of the wind turbine generator set in the front-to-back direction, wherein the change of the tower damping gain is slower than the change of the movement speed of the tower in the front-to-back direction, The tower monitoring unit includes: a tower state measuring unit, configured to measure relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; a tower state estimating unit, configured to process the measured relevant motion parameters using a Kalman filter or an extended Kalman filter encapsulated in a tower state parameter estimator to obtain a relative true value of the relevant motion parameters of the tower of the wind turbine generator set in the front-to-back direction; a tower state acquiring unit, configured to acquire the relative true value as the relevant motion parameter of the tower of the wind turbine generator set in the front-to-back direction, The input of the tower state parameter estimator includes the acceleration of the tower moving in the front-rear direction and the thrust borne by the tower in the front-rear direction, and the output of the tower state parameter estimator includes the acceleration of the tower moving in the front-rear direction and the speed of the tower moving in the front-rear direction; Alternatively, the input of the tower state parameter estimator includes the acceleration of the tower moving in the front-to-back direction and the speed of the tower moving in the front-to-back direction, and the output of the tower state parameter estimator includes the vibration frequency of the tower moving in the front-to-back direction and the thrust borne by the tower in the front-to-back direction.

11. The pitch control device according to claim 10, characterized in that: The relevant motion parameters of the tower of the wind turbine generator set in the front and rear directions include: The speed at which the tower of the wind turbine generator set moves in the front-rear direction; The acceleration of the tower of the wind turbine generator set moving in the front-rear direction; The vibration frequency of the tower of the wind turbine generator set in the front-to-back direction; and The tower of the wind turbine generator set is subjected to thrust in the front-rear direction.

12. The pitch control device according to claim 10, characterized in that: The pitch control device also includes: The gain determination unit is configured to determine the tower damping gain based on the ambient conditions of the wind turbine generator set.

13. The pitch control device according to claim 10, characterized in that: The pitch reference includes at least one of the following: a pitch speed of the pitch actuator; and The pitch position of the pitch actuator.

14. The pitch control device according to claim 10, characterized in that: The pitch adjustment unit is further configured to adjust the pitch reference used to perform the control function of the wind turbine generator set by means of the damping pitch reference component before the pitch reference is sent to the pitch actuator.

15. A pitch control device for a wind turbine generator set, characterized in that: The pitch control device comprises: A tower monitoring unit is configured to: obtain relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; The damping vibration reduction unit is configured to: determine a damping pitch reference component for suppressing vibration of the tower of the wind turbine generator set in the front-rear direction according to relevant motion parameters of the tower of the wind turbine generator set in the front-rear direction; A pitch adjustment unit, configured to: adjust a pitch reference for executing a control function of the wind turbine generator set by means of the damping pitch reference component; A pitch control unit is configured to: use the adjusted pitch reference to control the operation of the pitch actuator of the wind turbine generator set, Wherein, the damping vibration reduction unit comprises: A model prediction control unit is configured to: input a plurality of state parameters of the wind generator set including relevant motion parameters of a tower of the wind generator set in a front-rear direction into a model prediction control of the wind generator set; a control sequence deriving unit, configured to: derive a control sequence to be executed of the wind turbine generator set from the model predictive control, the control sequence comprising a plurality of control functions of the wind turbine generator set, a pitch reference for executing each of the plurality of control functions, and the damping pitch reference component; Wherein, the control sequence derivation unit includes: A cost function construction unit is configured to: construct a cost function related to a control sequence to be executed by the wind turbine generator set; an optimal control search unit, configured to: use the cost function to search for an optimal control sequence to be executed of the wind turbine generator set that meets the performance index requirements of the wind turbine generator set; The optimal control determination unit is configured to: determine the optimal control sequence as the control sequence to be executed by the wind turbine generator set, The requirements for the performance indicators of the wind turbine generator set include at least one of the following items: the rotor speed of the wind turbine generator set reaches the expected speed matching the wind speed, the output power of the wind turbine generator set reaches the expected power matching the wind speed, and the unit load of the wind turbine generator set is reduced to below the expected value.

16. The pitch control device according to claim 15, characterized in that: The pitch adjustment unit is further configured to: when executing each of the plurality of control functions, adjust a pitch reference used to execute the corresponding control function by using the damping pitch reference component.

17. The pitch control device according to claim 15, characterized in that: The pitch reference includes at least one of the following: a pitch speed of the pitch actuator; and The pitch position of the pitch actuator.

18. The pitch control device according to claim 15, characterized in that: The pitch adjustment unit is further configured to adjust the pitch reference used to perform the control function of the wind turbine generator set by means of the damping pitch reference component before the pitch reference is sent to the pitch actuator.

19. A computer-readable storage medium storing a computer program, wherein: When the computer program is executed by a processor, the pitch control method for a wind turbine generator set as claimed in any one of claims 1 to 9 is implemented.

20. A computing device comprising: processor; A memory storing a computer program, which, when executed by a processor, implements the pitch control method for a wind turbine generator set as claimed in any one of claims 1 to 9.

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