Method for establishing three-dimensional full wake model of wind turbine unit in yaw state

Abstract

A yaw state wind turbine three-dimensional full wake model establishment method, comprising: according to the flow field mass conservation theorem and momentum conservation theorem of yaw wind turbine, and by analogy with its normal operating state, the related parameters of yaw wind turbine wake are obtained;By solving the conservation equation of each component of wind wheel induction force, the wake inclination angle expression of the far wake area of yaw wind turbine is obtained, and combined with the empirical formula of the initial wake inclination angle at the wind wheel, the linear offset assumption of the near wake area and the definite integral according to the inclination angle of the far wake area, the wake center offset at different downstream positions of the unit is obtained;According to the related parameters of yaw wind turbine and the wake center offset model, combined with the three-dimensional wake velocity model and the turbulence intensity model of wind turbine in normal operating state, the three-dimensional full wake model of wind turbine in yaw state is constructed.The present application provides guidance for energy acquisition analysis and bearing load analysis of downstream wind turbine unit, and provides a convenient calculation method for obtaining wind field data.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wind farm wake control, and particularly relates to a method for establishing a three-dimensional full wake model of a wind turbine unit in a yaw state. BACKGROUND

[0002] Due to the environmental impact caused by the exploitation of fossil energy, the utilization of wind energy is increasingly valued. In the operation process of a wind turbine, the existence of a wake effect will affect the power output and fatigue load of a downstream wind turbine. In order to achieve the best power generation of an existing wind farm, in addition to the method of changing the micro-siting of units in the field, the wake downstream of the wind turbine can also be modified or redirected through some control strategies, and yaw control is one of the effective control strategies for optimizing the power of a wind farm. Therefore, a three-dimensional full wake model capable of accurately describing the wake distribution downstream of a wind turbine in a yaw state plays an important role in the actual operation and control of a wind farm. SUMMARY

[0003] The application provides a method for establishing a three-dimensional full wake model of a wind turbine unit in a yaw state.

[0004] To achieve the above-mentioned purpose, the following technical solutions are adopted:

[0005] A method for establishing a three-dimensional full wake model of a wind turbine unit in a yaw state, characterized in that it comprises:

[0006] According to the mass conservation law and the momentum conservation law of the flow field of the yawed wind turbine unit, and by analogy to the wind turbine unit in a normal operating state, the related parameters of the wake of the yawed wind turbine unit are obtained;

[0007] Based on the related parameters of the wake of the yawed wind turbine unit, by solving the conservation equations of each component of the wind wheel induced force, the wake inclination angle expression of the far wake area of the yawed wind turbine unit is obtained, and combined with the empirical formula of the initial wake inclination angle at the wind wheel, the wake center offset at different downstream positions of the yawed wind turbine unit is obtained by using the assumption of linear offset of the near wake area and the definite integral according to the inclination angle of the far wake area, and a wake center offset model is established;

[0008] According to the related parameters of the wake of the yawed wind turbine unit and the wake center offset model, combined with the wake velocity model and the turbulence intensity model of the wind turbine unit in a normal operating state, a three-dimensional full wake model of the wind turbine unit in a yaw state is constructed.

[0009] To optimize the above-mentioned technical solutions, the following specific measures are adopted:

[0010] Further, the calculation formula of the mass conservation law and the momentum conservation law of the flow field of the yawed wind turbine unit is as follows:

[0011]

[0012] where m1, m2 and m3 are the mass flow rates through the control volume inlet, side and outlet respectively; U0 and U w are the incoming and wake velocities respectively; F is the wind turbine induced force due to the velocity component perpendicular to the wind turbine; γ is the yaw angle of the wind turbine; θ is the wake inclination angle; ρ is the air density; dA represents the unit area.

[0013] Further, the solving process of the related parameters of the yawed wind turbine wake is as follows:

[0014] Based on the relationship between the wind turbine induced force F and the thrust coefficient C T of the wind turbine, according to the value of θ, cosθ and sinθ are set to 1 and 0 respectively, and the calculation formula is modified as follows:

[0015]

[0016] where A0 is the swept area of the wind turbine; ΔU is the wind speed difference between the incoming flow and the wake; by analogy to the wind turbine group in normal operation state, the thrust coefficient C′ T of the yawed wind turbine group is obtained T = C

[0017] Combined with the nonlinear assumption of the wake expansion of the wind turbine group, the wake radius of the yawed wind turbine group is obtained as follows:

[0018]

[0019] where r′ w is the wake radius of the yawed wind turbine group; D is the diameter of the wind turbine; I0 is the ambient turbulence intensity at the hub height; x is the downstream distance.

[0020] Further, the wake inclination angle expression of the far wake region of the yawed wind turbine group is as follows:

[0021]

[0022] where θ represents the wake inclination angle of the far wake region of the yawed wind turbine group.

[0023] Further, the establishing process of the wake center offset model is as follows:

[0024] Based on the empirical formula of the initial wake inclination angle at the wind turbine, and by using the assumption of linear offset of the wake in the near wake region, the formula of the wake center offset in the near wake region is obtained;

[0025] The equations of the initial wake angle and the far wake angle are established, the demarcation point of the wake center offset calculation is obtained, the position far from the demarcation point is obtained by integrating the wake angle, and the formula of the wake center offset in the far wake area is solved;

[0026] The wake center offsets of the yawed wind turbine at different downstream positions include the wake center offset in the near wake area and the wake center offset in the far wake area, and the specific calculation formula is as follows:

[0027]

[0028] Wherein, θ0 is the initial wake angle; x0 is the demarcation point of the wake offset calculation in the near-far wake area, and θ0 and θ are equal when calculating, θ represents the wake angle of the far wake area of the yawed wind turbine; yd(x) is the wake center offset value;

[0029] Further, the three-dimensional full wake model of the wind turbine in the yaw state includes a three-dimensional wake velocity model and a three-dimensional wake turbulence intensity model of the wind turbine in the yaw state.

[0030] Further, the three-dimensional wake velocity model is established as follows:

[0031] Based on the maximum wake loss ratio calculation formula and the Gaussian shape velocity distribution in the wake area, the wake velocity model of the wind turbine in the normal operation state is obtained by solving the mass conservation equation and the momentum conservation equation;

[0032] The three-dimensional wake velocity model of the wind turbine in the yaw state is obtained by combining the wake center offset model, the related parameters of the yawed wind turbine wake and the wake velocity model of the wind turbine in the normal operation state, and the calculation formula is as follows:

[0033]

[0034] Wherein, z h is the hub height; K is the maximum velocity loss ratio; α is the wind shear coefficient; y and z represent the longitudinal and vertical distances respectively; U represents the velocity; A g , B g and are parameters obtained by calculation as follows:

[0035]

[0036] Wherein, a g = 1.216, R is the radius of the wind wheel.

[0037] Further, the three-dimensional wake turbulence intensity model is established as follows:

[0038] Based on the wake turbulence intensity distribution of the trigonometric function shape, combined with different additional turbulence intensity models, the wake turbulence intensity model of the wind turbine group in the normal operation state is obtained;

[0039] The wake center offset model, the related parameters of the yaw wind turbine group wake and the turbulence intensity model of the wind turbine group in the normal operation state are combined, and the three-dimensional wake turbulence intensity model of the wind turbine group in the yaw state is obtained through the correction of the wake turbulence intensity below the hub height, and the calculation formula is as follows:

[0040]

[0041] Wherein, I + is the additional turbulence intensity; I +，m is the maximum additional turbulence intensity; ΔI + is the turbulence intensity correction below the hub height; I a and I w are the environmental turbulence intensity and the wake turbulence intensity respectively; R represents the wind wheel radius.

[0042] The application further provides a computer readable storage medium, which stores a computer program, and the computer program makes the computer execute the method for establishing the three-dimensional full wake model of the wind turbine group in the yaw state.

[0043] The application further provides an electronic device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor executes the computer program to realize the method for establishing the three-dimensional full wake model of the wind turbine group in the yaw state.

[0044] The three-dimensional full wake model of the wind turbine group in the yaw state provided by the application can not only accurately analyze the wake velocity distribution and the turbulence intensity distribution of the downstream entire wake area of the yaw wind turbine group, but also can provide guidance for the energy acquisition analysis and the load bearing analysis of the downstream wind turbine group, and provide a convenient calculation method for obtaining wind field data. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 It is the establishment process schematic diagram of a three-dimensional full wake model of a wind turbine group in a yaw state provided by the application.

[0046] Figure 2a 、 2bIt is a two-dimensional wake schematic diagram of the wind turbine in normal operation state and yaw operation state provided by the application.

[0047] Figure 3 It is a comparison diagram of the predicted value of the yawed wind turbine group wake center offset model in different cases, the experimental value and the predicted value of other models.

[0048] Figure 4a It is a comparison diagram of the predicted result of the yawed wind turbine group wake velocity model at low thrust coefficient, the simulation result and the predicted result of other models.

[0049] Figure 4b It is a comparison diagram of the predicted result of the yawed wind turbine group wake velocity model at high thrust coefficient, the simulation result and the predicted result of other models.

[0050] Figure 5a It is a comparison diagram of the predicted result of the yawed wind turbine group wake turbulence intensity model at low thrust coefficient, the simulation result and the predicted result of other models.

[0051] Figure 5b It is a comparison diagram of the predicted result of the yawed wind turbine group wake turbulence intensity model at high thrust coefficient, the simulation result and the predicted result of other models. DETAILED DESCRIPTION

[0052] The application will be further described in detail in combination with the drawings.

[0053] As shown in Figure 1 and Figure 2a , 2b , in an embodiment, a method for establishing a three-dimensional full wake model of a yawed wind turbine group is proposed. Due to different force conditions of the wind wheel, the wake center of the wind turbine downstream in normal operation state is generally considered to be on the axis of the wind wheel, and the wake of the wind turbine in yaw operation state deviates from the axis. The wake center offset model is extremely important for the establishment of the full wake model in the yaw state. Therefore, the specific steps of the embodiment are as follows:

[0054] Step one: according to the mass conservation law and the momentum conservation law of the flow field of the yawed wind turbine group, and by analogy with the normal operation state, the related parameters of the wake distribution of the yawed wind turbine group are obtained. In order to make the solutions of the wake in the two operation states similar, the main modified variable is the thrust coefficient.

[0055] The initial calculation formula of the mass conservation law and the momentum conservation law of the wind wheel rear control body applied in Figure 2a , 2b is as follows:

[0056]

[0057] wherein m1, m2 and m3 are the mass flow rates through the control volume inlet, side and outlet respectively; and are the mass flow rates through the control volume inlet, side and outlet respectively; is the wind turbine induced force caused by the velocity component perpendicular to the wind turbine. Substituting the specific values of the related parameters and dividing the induced force into two directions, the above equation is rewritten as follows:

[0058]

[0059] wherein U0 and U w are the incoming flow velocity and wake velocity respectively; γ is the yaw angle of the wind turbine; θ is the wake inclination angle; ρ is the atmospheric density; dA represents the unit area.

[0060] In this step, the wind turbine thrust coefficient C T is defined as follows: T is the thrust force on the wind turbine; A0 is the swept area of the wind turbine. In addition, the value of the wake inclination angle θ is small in practice, so it is assumed that cosθ and sinθ are 1 and 0 respectively, and the specific formula is modified as follows:

[0061]

[0062] By analogy with the theorem formula derivation of the wind turbine unit in the normal operating state, the thrust coefficient related to the wake of the yawed wind turbine unit is allowed to be C′ T =C T cosγ, so that the two are similar.

[0063] Combining the nonlinear assumption of the wake expansion of the wind turbine unit the wake radius expression of the yawed wind turbine unit is obtained as follows:

[0064]

[0065] wherein r w and r′ w are the normal state and the modified wake radius respectively; D is the diameter of the wind turbine; I0 is the environmental turbulence intensity at the hub height; x is the downstream distance.

[0066] Step 2: By solving the conservation equation of each component of the wind turbine induced force, the wake inclination angle expression of the far wake region of the yawed wind turbine unit is obtained, and by combining the empirical formula of the initial wake inclination angle at the wind turbine, using the assumption of linear offset of the near wake region and the definite integral according to the inclination angle of the far wake region, the wake center offset at different downstream positions of the unit, i.e. the wake center offset model described in the present application, is obtained.

[0067] Specifically, the wake skew angle expression is combined with each parameter and the expression form of the Qian & Ishihara model to obtain a wake skew angle calculation formula for the far wake region of a yawed wind turbine as follows:

[0068]

[0069] In this step, the wake offset solution is divided into two parts: the near wake region and the far wake region (the dividing point between the two is assumed to be x0). The wake offset of the near wake region is related to the initial wake skew angle θ0after the wind wheel, and the empirical formula of the skew angle is as follows:

[0070] θ0= 0.3βC T

[0071] Therefore, by assuming that the wake center offset in the near wake region is linearly increasing, the wake offset in this part is as follows:

[0072]

[0073] where y d is the wake center offset value.

[0074] Let θ0and θ be equal, and the value of the dividing point is as follows:

[0075]

[0076] Next, according to the above obtained parameter values, and the skew angle is integrated Then the wake center offset result in the far wake region is as follows:

[0077]

[0078]

[0079] where q is the abbreviation of the expression,

[0080] As shown in Figure 2a , 2b When the wind passes through the yawed wind turbine, the wake center downstream of the wind turbine appears to be offset.

[0081] Step three: based on the maximum wake loss ratio calculation formula and the Gaussian shape velocity distribution of the wake region, the wake velocity distribution of the wind turbine under normal operation is obtained by solving the mass conservation and momentum conservation equations, the wake center offset model and the corrected related parameters are combined with the normal wake velocity model, and the three-dimensional wake velocity model under the yawed state is obtained.

[0082] Specifically, by substituting the modified parameters, the maximum loss ratio K of the wind turbine wake in the yawing operation state is calculated as follows:

[0083]

[0084] In this step, the normal three-dimensional wake velocity model adopts a Gaussian distribution function, which is as follows:

[0085]

[0086] where r' is the distance from the space point to the wake center, z h is the hub height; a is the wind shear coefficient; y and z represent the longitudinal and vertical distances, respectively; U represents the velocity; A g , B g , are parameters obtained by solving, and are calculated as follows:

[0087]

[0088] where a g = 1.216, R is the radius of the wind wheel.

[0089] Step four: based on the wake turbulence intensity distribution in the shape of a trigonometric function, combined with different additional turbulence intensity models, the three-dimensional wake turbulence intensity model of the wind turbine group in the normal state is obtained, the wake center offset model and the related parameters of the yawing wind turbine group are combined with the normal wake turbulence intensity model, and the three-dimensional wake turbulence intensity model of the wind turbine group in the yawing state is obtained.

[0090] Specifically, the calculation formula of the model is as follows:

[0091]

[0092] where I + is the additional turbulence intensity; I +，m is the maximum additional turbulence intensity, which is divided into a low thrust coefficient case and a high thrust coefficient case AI + is the turbulence intensity correction amount below the hub height; I a and I w are the environmental turbulence intensity and the wake turbulence intensity, respectively, and the environmental turbulence intensity can be considered to be related to the height.

[0093] In the embodiment, the establishment process of the three-dimensional full wake model of the wind turbine set in the yaw state is divided into three parts: the wake center offset model, the three-dimensional wake velocity model and the three-dimensional wake turbulence intensity model. The three-dimensional full wake model can accurately describe the wind speed in the three-dimensional space of the wind farm, and according to the actual needs of the project, the calculation workload can be reduced and the efficiency can be improved.

[0094] In the embodiment of the application, the yaw wind turbine wake center offset is solved by the conservation theorem and the wake nonlinear expansion assumption, and then the yaw three-dimensional full wake model is established by combining the wake velocity model and the turbulence intensity model, so that the accuracy of the wake distribution in the entire wake area downstream of the yaw wind turbine can be improved, and the control strategy optimization of the wind turbine set in the wind farm can be applied.

[0095] Figure 3 The comparison chart of the predicted values of the proposed yaw wind turbine set wake offset model under different conditions and the experimental values and the predicted values of other models can be seen from which it can be seen that the wake center offset model in the embodiment is more accurate in predicting the wake offset in the near wake area and the far wake area.

[0096] Figure 4a And 4b The comparison chart of the predicted results of the proposed wake velocity model of the wind turbine set in the yaw state under different conditions and the simulation results and the predicted results of other models can be seen from which it can be seen that the wake velocity model of the wind turbine set in the embodiment can more accurately predict the velocity distribution in the wake under low thrust coefficient and high thrust coefficient.

[0097] Figure 5a And 5b The comparison chart of the predicted results of the proposed wake turbulence intensity model of the wind turbine set in the yaw state under different conditions and the simulation results and the predicted results of other models can be seen from which it can be seen that the wake turbulence intensity model of the yaw wind turbine set in the embodiment is relatively more accurate.

[0098] In another embodiment, the application provides a computer readable storage medium storing a computer program, which causes a computer to execute the method for establishing a three-dimensional full wake model of a wind turbine set in a yaw state as described in the first embodiment.

[0099] In another embodiment, the application provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the method for establishing a three-dimensional full wake model of a wind turbine set in a yaw state as described in the first embodiment.

[0100] In the embodiments disclosed in the present application, the computer storage medium can be a tangible medium which can contain or store programs for use by or in connection with an instruction execution system, apparatus or device. The computer storage medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus or device, or any suitable combination of the above. More specific examples of computer storage medium can include one or more wires, portable computer disks, hard drives, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), fiber optics, compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above.

[0101] Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed in the present application can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software manner depends on the specific application and design constraints of the technical solutions. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0102] The above is only the preferred embodiment of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical solution falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that, for ordinary skilled persons in the art, some improvements and refinements without departing from the principles of the present application shall be considered within the protection scope of the present application.

Claims

1. A method for establishing a three-dimensional full wake model of a wind farm in yaw, characterized in that, The application relates to a yawing wind turbine flow field model. According to the mass conservation law and the momentum conservation law of the yawing wind turbine flow field, and by analogy to the wind turbine in a normal operation state, relevant parameters of the wake of the yawing wind turbine are obtained; Based on the relevant parameters of the wake of the yawing wind turbine, by solving the conservation equations of each component of the wind wheel induced force, an expression of the wake angle of the far wake area of the yawing wind turbine is obtained, and by combining an empirical formula of the initial wake angle at the wind wheel, using the assumption of linear displacement of the near wake area and the definite integral of the angle in the far wake area, the wake center displacement at different downstream positions of the yawing wind turbine is obtained, and a wake center displacement model is established; the solving process of the relevant parameters of the wake of the yawing wind turbine is as follows: Based on the wind turbine induced force F and the wind turbine thrust coefficient C T Based on the relationship between θ and cosθ and sinθ, which are set to 1 and 0 respectively, the calculation formula is modified as follows: Wherein, A0 is the swept area of wind wheel; ΔU is the wind speed difference between the incoming flow and the wake flow; the thrust coefficient C ′ T = C T cosγ; U0 and U w are the incoming flow speed and the wake flow speed respectively; γ is the yaw angle of the wind turbine; θ is the wake angle; ρ is the atmospheric density; dA represents the unit area; According to the relevant parameters of the wake of the yawing wind turbine and the wake center displacement model, combined with the wake velocity model and the turbulence intensity model of the wind turbine in the normal operation state, a three-dimensional full wake model of the wind turbine in the yawing state is constructed; the establishment process of the wake center displacement model is as follows: where r w ′ is the wake radius of a yawed wind turbine; D is the wind turbine diameter; I0is the ambient turbulence intensity at hub height; x is the downstream distance; Based on the empirical formula of the initial wake angle at the wind wheel, and by using the assumption of linear displacement of the near wake area, a formula of the wake center displacement of the near wake area is obtained; An equation of the initial wake angle and the wake angle of the far wake area is established, the demarcation point for the calculation of the wake center displacement is obtained, the position far from the demarcation point is obtained by integrating the wake angle, and the formula of the wake center displacement of the far wake area is solved; The wake center displacement at different downstream positions of the yawing wind turbine includes the wake center displacement of the near wake area and the wake center displacement of the far wake area, and the specific calculation formula is as follows: The mass conservation law and the momentum conservation law of the yawing wind turbine flow field are as follows: wherein θ0 is the initial wake skew angle; x0 is the near-far wake region wake offset calculation demarcation point, calculated by equating θ0 and θ, wherein θ represents the wake skew angle of the far wake region of the yawed wind turbine; y d (x) is the wake center offset value; 2. The method for establishing a three-dimensional full wake model of a wind farm in yaw conditions according to claim 1, characterized in that: The expression of the wake angle of the far wake area of the yawing wind turbine is as follows: where m1, m2 and m3 are the mass flow rates through the control volume inlet, side and outlet respectively; U0 and U w are the free-stream and wake velocities respectively; F is the wind turbine induced force due to the velocity component normal to the wind turbine; γ is the yaw angle of the wind turbine; θ is the wake inclination angle; ρ is the atmospheric density; and dA represents the unit area.

3. The method for establishing a three-dimensional full wake model of a wind farm in yaw conditions according to claim 1, characterized in that: Wherein, theta represents the wake angle of the far wake area of the yawing wind turbine. The three-dimensional full wake model of the wind turbine in the yawing state includes a three-dimensional wake velocity model and a three-dimensional wake turbulence intensity model of the wind turbine in the yawing state.

4. The method for establishing a three-dimensional full wake model of a wind farm in yaw conditions according to claim 1, characterized in that: The establishment process of the three-dimensional wake velocity model is as follows:

5. The method for establishing a three-dimensional full wake model of a wind farm in yaw conditions according to claim 4, characterized in that: Based on the maximum wake loss ratio calculation formula and the Gaussian shape velocity distribution of the wake area, by solving the mass conservation equation and the momentum conservation equation, the wake velocity model of the wind turbine in the normal operation state is obtained; The three-dimensional wake velocity model of the wind turbine in the yawing state is obtained by combining the wake center displacement model, the relevant parameters of the wake of the yawing wind turbine and the wake velocity model of the wind turbine in the normal operation state, and the calculation formula is as follows: The establishment process of the three-dimensional wake turbulence intensity model is as follows: where z h is the hub height; K is the maximum speed deficit ratio; a is the wind shear coefficient; y, z represent the longitudinal and vertical distances, respectively; U represents the velocity; A g , B g and are parameters obtained by calculation as follows: wherein a g = 1.216, R is the wind wheel radius.

6. The method for establishing a three-dimensional full wake model of a wind farm in yaw conditions according to claim 4, characterized in that: Based on the triangular function shape of the wake turbulence intensity distribution, combined with different additional turbulence intensity models, the wake turbulence intensity model of the wind turbine in the normal operation state is obtained; The three-dimensional wake turbulence intensity model of the wind turbine in the yawing state is obtained by combining the wake center displacement model, the relevant parameters of the wake of the yawing wind turbine and the turbulence intensity model of the wind turbine in the normal operation state, and by correcting the wake turbulence intensity below the hub height, and the calculation formula is as follows: ​ where I + is the additional turbulence intensity; I +,m is the maximum additional turbulence intensity; ΔI + is the turbulence intensity correction below hub height; I a and I w are the ambient and wake turbulence intensities, respectively; R denotes the rotor radius.

7. A computer readable storage medium storing a computer program, characterized in that, The computer program enables a computer to execute the method for establishing a three-dimensional full wake model of a wind farm in yaw according to any one of claims 1-6.

8. An electronic device, comprising: The computer program product comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method for establishing a three-dimensional full wake model of a wind farm in yaw according to any one of claims 1-6 when executing the computer program.

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