A method for establishing a three-dimensional time-based full wake model for a horizontal axis wind turbine

Abstract

The present invention relates to the technical field of wind field data analysis, and in particular to a method for establishing a three-dimensional time full wake model of a horizontal axis wind turbine. The method comprises the following steps: constructing a three-dimensional super-Gaussian full wake model, obtaining an incoming flow wind speed u0(t), substituting the incoming flow wind speed u0(t) into the three-dimensional super-Gaussian full wake model, and obtaining an initial three-dimensional time full wake model; calculating a delay time τ of the incoming flow wind speed u0(t), solving for an arrival time T of the incoming flow wind speed u0(t) based on the delay time τ and an inflow time t of the incoming flow wind speed u0(t), substituting the arrival time T of the incoming flow wind speed u0(t) into the initial three-dimensional time full wake model for calculation, and obtaining the three-dimensional time full wake model.

Description

Technical Field

[0001] The present invention relates to the technical field of wind field data analysis, and in particular to a method for establishing a three-dimensional time-based full wake model of a horizontal axis wind turbine. Background Art

[0002] For actual wind farms, in order to reduce the interference of wake, most downstream wind turbines are arranged in the far wake, and the far wake is about 3D-5D away from the upstream wind turbine. This data means that most of the wind speed flowing in from the upstream wind turbine must travel at least 3D to reach the downstream wind turbine. Therefore, the wind speed flowing into the upstream wind turbine generally needs a delay time of more than 1 minute to affect the downstream wind turbine. This one-minute delay time determines the speed, pitch angle and other power adjustment methods of the downstream wind turbine, which not only affects the control of the wind turbine, but also easily leads to problems in the control, efficiency and safety of the entire site. In order to further understand the time-varying characteristics of the wake profile caused by the change of the upstream wind turbine flow, we proposed a method for establishing a three-dimensional time full wake model of the horizontal axis wind turbine to study the spatiotemporal inhomogeneity of the wake profile. Summary of the invention

[0003] The object of the present invention is to provide a method for establishing a three-dimensional time-based full wake model of a horizontal-axis wind turbine, which is used to solve the above-mentioned technical problems.

[0004] The embodiments of the present invention are implemented by the following technical solutions:

[0005] A method for establishing a three-dimensional time-based full wake model of a horizontal axis wind turbine, characterized by comprising the following contents:

[0006] A three-dimensional super-Gaussian full wake model is constructed to obtain the incoming wind speed u0(t), and the incoming wind speed u0(t) is substituted into the three-dimensional super-Gaussian full wake model to obtain an initial three-dimensional time full wake model;

[0007] The delay time τ of the incoming wind speed u0(t) is calculated, and the arrival time T of the incoming wind speed u0(t) is solved according to the delay time τ and the inflow time t of the incoming wind speed u0(t). The arrival time T of the incoming wind speed u0(t) is substituted into the initial three-dimensional time full wake model for calculation, and the three-dimensional time full wake model considering the delay is obtained.

[0008] Optionally, the calculation formula of the initial three-dimensional time full wake model is as follows:

[0009]

[0010] Among them, u hub is the incoming wind speed at the center of the wind turbine hub; hubis the center height of the wind turbine hub; z+z hub is the height from the ground; α is the wind shear index; y is the distance from the center of the hub on the horizontal plane; σ y is the standard deviation of the horizontal Gaussian distribution.

[0011] Optionally, the calculation formula of the delay time τ is as follows:

[0012]

[0013] Among them, u(x, y, z, t) is the initial three-dimensional time full wake model, and τ is the delay time.

[0014] Optionally, the calculation formula for the arrival time T of the incoming wind speed u0(t) is as follows:

[0015] T=t+τ

[0016] Among them, T is the arrival time of the incoming wind speed u0(t), t is the inflow time of the incoming wind speed u0(t), and τ is the delay time.

[0017] Optionally, the calculation formula of the three-dimensional time full wake model is as follows:

[0018]

[0019] Among them, z hub is the center height of the wind turbine hub, C is an unknown parameter, t is the inflow time of the incoming wind speed u0(t), and T is the arrival time of the incoming wind speed u0(t).

[0020] Optionally, the construction process of the three-dimensional super-Gaussian full wake model is as follows:

[0021] Obtain wind field data, calculate the wind field data based on the preset Jensen wake model, super Gaussian function and mass conservation algorithm, and obtain the initial vertical height full wake wind speed distribution;

[0022] The incoming wind speed data is obtained to generate a wind shear curve, and the mass loss is calculated based on the wind shear curve. The initial vertical height wake wind speed distribution is corrected by the mass loss to obtain the corrected vertical height full wake wind speed distribution;

[0023] The horizontal plane full wake wind speed distribution is solved according to the corrected vertical height full wake wind speed distribution, and a three-dimensional super-Gaussian full wake model is constructed by combining the corrected vertical height wake wind speed distribution and the horizontal plane full wake wind speed distribution.

[0024] Optionally, the calculation formula of the super Gaussian function is as follows:

[0025]

[0026]

[0027] Among them, x i is the horizontal coordinate of the maximum value of the super-Gaussian function, σ i is the standard deviation of the super-Gaussian function, the coefficient a is the ordinate of the maximum value of the super-Gaussian function, n is the exponent of the super-Gaussian function, and c1 and c2 are both parameters.

[0028] Optionally, the calculation formula for the initial vertical height full wake wind speed distribution is as follows:

[0029]

[0030] Among them, σ z is the standard deviation of the Gaussian function in the vertical direction; u hub is the incoming wind speed at the center of the wind turbine hub; axial induction factor r z is the vertical wake radius; r0 is the initial wake radius; n is the exponent of the super Gaussian function.

[0031] Optionally, the calculation formula for the modified vertical height full wake wind speed distribution is as follows:

[0032]

[0033] Among them, Δu is the speed difference between the shear wind and the center flow of the hub; r0 is the initial wake radius; u0(x,z) is the initial vertical height full wake wind speed distribution; a is the axial induction factor.

[0034] Optionally, the calculation formula of the three-dimensional super-Gaussian full wake model is as follows:

[0035]

[0036] Among them, u hub is the incoming wind speed at the center of the wind turbine hub; hub is the center height of the wind turbine hub; z+z hub is the height from the ground; α is the wind shear index; y is the distance from the center of the hub on the horizontal plane; σ y is the standard deviation of the horizontal Gaussian distribution.

[0037] The technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects:

[0038] The invention has a reasonable design and a simple structure. By calculating the delay time to introduce the time variable, the wake change in time and space can be better predicted. The wake wind speed downstream of the wind turbine can be predicted in combination with the free stream wind speed prediction model, and the power of the downstream wind turbine can be predicted. The downstream wind turbine can control the speed, pitch angle, etc. in advance, which can effectively reduce the impact of the wake on the downstream unit and increase the power generation of the wind farm. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic flow chart of a method for establishing a three-dimensional time-based full wake model of a horizontal axis wind turbine provided by the present invention;

[0040] Figure 2 A three-dimensional coordinate system diagram provided by the present invention;

[0041] Figure 3 A schematic diagram of a super-Gaussian function provided by the present invention;

[0042] Figure 4 A schematic diagram of the wake wind speed distribution at a vertical height without considering the influence of shear wind provided by the present invention;

[0043] Figure 5 A vertical profile prediction diagram of the three-dimensional full wake model provided by the present invention;

[0044] Figure 6 A schematic diagram of the prediction results of the three-dimensional time full wake model considering delay provided by the present invention;

[0045] Figure 7 A schematic diagram of a system for establishing a three-dimensional time-based full wake model of a horizontal-axis wind turbine provided by the present invention. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0047] like Figure 1 As shown, the present invention provides one embodiment: firstly, a three-dimensional super-Gaussian full wake model is proposed, and the establishment process thereof is as follows:

[0048] Step 1: Based on the preset Jensen wake model, super Gaussian function and the law of conservation of mass, a prediction is made to obtain the full wake wind speed distribution at the vertical height without considering the influence of shear wind.

[0049] Among them, the Jensen wake model and the super Gaussian function (super Gaussian in the near wake area and Gaussian in the far wake area) are preset.

[0050] In order to accurately describe the wind speed distribution in the three-dimensional space of the entire wake area, the wake model proposed in this embodiment assumes that the wake velocity U is a three-dimensional function of space, that is, U = U (x, y, z), such as Figure 2 As shown, a three-dimensional coordinate system is established with the center of the wind turbine hub as the coordinate origin: the x direction represents the axis direction of the wake area, which is ideally the direction of the incoming wind speed; the y direction represents the horizontal direction lateral to the wake axis; the z direction is perpendicular to the wake axis and vertically upward.

[0051] like Figure 3 As shown, the expression of the super Gaussian function is Note that when n = 2, the super-Gaussian function is transformed into a Gaussian function, where x i Determines the horizontal coordinate of the maximum value of the super-Gaussian function, σ i is the standard deviation of the super-Gaussian function, the coefficient a determines the ordinate of the maximum value of the super-Gaussian function, and n is the exponent of the super-Gaussian function. According to the standard density function curve of the two-dimensional Gaussian distribution, 2.81 standard deviations (2.81σ) of the distance from the mean of each dimension can satisfy the probability of 99% in each dimension.

[0052] In this step, we first predict the vertical height near wake wind speed as super-Gaussian distribution and far wake area as Gaussian distribution. The calculation formula is as follows: A is an unknown parameter, z represents the vertical height from the center of the wheel hub, σ z is the standard deviation of the super-Gaussian function in the vertical direction. At the same time, we adopt the assumption of linear expansion of the wake in the Jensen wake model, and the wake radius r z Linear relationship with downwind distance x: r z =k z x+r0,k z is the vertical wake expansion coefficient, r0 is the initial wake radius (the initial wake radius refers to the wake radius after the free wind passes the wind turbine), and the super-Gaussian function exponent The parameter c1 is determined by the size of the wake loss at x=0, and the parameter c2 is determined by the speed at which the wake changes from a super-Gaussian type to a single Gaussian type and the position of the maximum wake loss on the hub centerline in the flow direction.

[0053] Then, we assume that the mass flux of the three-dimensional full wake model is the same as that of the Jensen wake model:

[0054]

[0055] in For the Jensen wake model in -r z≤z≤r z The mass flux, axial induction factor From the thrust coefficient C T Determine (can be found in the wind turbine manufacturer's technical manual). The expression of the obtained parameter A and the standard deviation of the Gaussian distribution is:

[0056]

[0057] Vertical wake expansion coefficient Finally, the value of A and the standard deviation of the super-Gaussian distribution are substituted into the predicted vertical height full wake wind speed distribution to obtain the vertical height full wake wind speed distribution without considering the shear wind effect. The calculation formula for the vertical height full wake wind speed distribution without considering the shear wind effect is as follows:

[0058]

[0059] like Figure 4 As shown in the figure, after the wind passes through the wind turbine, the wind speed presents a super-Gaussian distribution in the near wake area and a Gaussian distribution in the far wake area.

[0060] Step 2: Obtain the wind shear curve of the incoming wind speed, introduce the wind shear wind speed and the wind speed difference between the hub center, obtain the mass loss, and obtain the corrected vertical height wake wind speed distribution of the entire wake field, that is, the corrected vertical height full wake wind speed distribution described in the present invention, wherein the incoming wind speed refers to undisturbed wind, also called free wind.

[0061] Specifically, the formula for the wind shear curve is as follows: The speed difference between the shear wind and the hub center flow is Δu=u(z)-u hub .

[0062] Among them, z hub is the center height of the wind turbine hub, z+z hub is the height from the ground, α is the wind shear index, which is determined by the topography and atmospheric environment of the area where the wind farm is located. The typical value of the wind shear index α on land in the project is 0.14 or the formula Calculate, v1 and v2 are the measured wind speeds at known heights z1 and z2.

[0063] Next, we consider the mass difference caused by the introduction of shear wind inflow. The mass difference Δm is calculated as:

[0064]

[0065]

[0066] like Figure 5 As shown, the wake velocity distribution of the vertical section considering the shear wind is: u* Represents the wake velocity of the Jensen wake model.

[0067] Step 3: predict the wake velocity on the horizontal plane to obtain the wake wind speed distribution on the horizontal plane of the entire wake field, that is, the horizontal plane full wake wind speed distribution described in the present invention, and establish a three-dimensional super-Gaussian full wake model based on the wake wind speed distribution of the corrected vertical height of the entire wake field and the horizontal plane wake wind speed distribution.

[0068] According to the full wake wind speed distribution of the corrected vertical height, it is assumed that the full wake speed distribution in the horizontal direction of the wake area is:

[0069]

[0070] Where y represents the distance from the center of the wheel hub on the horizontal plane, σ y is the standard deviation of the horizontal super-Gaussian distribution, and the horizontal wake radius r y =k y x+r0=2.81σ y Horizontal wake expansion coefficient

[0071] Note that the mass difference formula in the above is solved for the xz plane when y=0, so we can get u(x,0,z)=u(x,z), and solve for the parameter C:

[0072]

[0073] Therefore, the expression of the three-dimensional super-Gaussian full wake model is as follows:

[0074]

[0075] Step 4: Based on the three-dimensional super-Gaussian full wake model obtained above, we add the time factor and construct a three-dimensional time full wake model.

[0076] The time-varying wake region can be regarded as the set of trajectories of air particles in the wind with different wind speeds flowing from the upstream to the downstream of the turbine. It is assumed that the particles in the wind are independent and do not interact with each other. It is assumed that at any time, the set of moving trajectories of particles at the same windward distance conforms to the three-dimensional super-Gaussian full wake model.

[0077] In our establishment process: the first step is to obtain the wake time series expression without considering the delay time through the three-dimensional super Gaussian full wake model: the ordinary three-dimensional super Gaussian full wake model takes the constant incoming flow as the input condition, but when the incoming flow wind speed changes with time, the wake wind speed will also change with time. Let this incoming flow wind speed be u0(t), and substitute it into the three-dimensional super Gaussian full wake model to obtain the three-dimensional time full wake model that changes with time: (Delay time is not taken into account);

[0078] The second step is to calculate the delay time: because it takes a certain amount of time for the free wind speed particles to enter the wind turbine and reach a certain position downstream of the wind turbine, this time is recorded as the delay time τ. The calculation formula is as follows:

[0079]

[0080] The third step is to obtain a three-dimensional time-based full wake model that takes into account the delay time: at time t (the time when the wind speed particles flow into the wind turbine), the time when the wind speed particles flowing into the wind turbine arrive at a certain position downstream of the wind turbine is calculated as T = t + τ (the time when the wind speed particles arrive at a certain position downstream of the wind turbine). Substitute time T into the initial three-dimensional time-based full wake model u (x, y, z, t) to obtain a three-dimensional time-based full wake model that takes into account the delay:

[0081]

[0082] z hub represents the center height of the wind turbine hub, C is an unknown parameter, t is the time for the wind speed particles to flow into the wind turbine, and T is the time for the wind speed particles to reach a certain position downstream of the wind turbine. Figure 6 As shown, the predictions of the three-dimensional time-wide wake model fit the experimental data well.

[0083] In this embodiment, firstly, a prediction is made based on the preset Jensen wake model, super Gaussian function and the law of conservation of mass, and the vertical height full wake wind speed distribution without considering the influence of shear wind is obtained, and then the wind shear curve of the incoming wind speed is obtained, and then the mass loss caused by the difference between the shear wind and the wind speed of the hub center is calculated, and the vertical height wake wind speed distribution without considering the influence of shear wind is corrected to obtain the corrected vertical height full wake wind speed distribution, and then the horizontal plane full wake speed is predicted to obtain the horizontal plane full wake wind speed distribution, and a three-dimensional super Gaussian full wake model is established according to the corrected vertical height full wake wind speed distribution and the horizontal plane full wake wind speed distribution. Finally, on the basis of the three-dimensional super Gaussian full wake model, the delay time is calculated, and the time variable is introduced to obtain the three-dimensional time full wake model considering the delay.

[0084] Based on the present embodiment, the present invention introduces a time variable by calculating the delay time, which can better predict the changes in wake in time and space, and can be combined with the free stream wind speed prediction model to predict the wake wind speed downstream of the wind turbine, that is, to predict the power of the downstream wind turbine. The downstream wind turbine can control the speed, pitch angle, etc. in advance, which can effectively reduce the impact of the wake on the downstream unit and increase the power generation of the wind farm. Note that the wake model for calculating the delay time can also use other wake models. The more accurate the wake model used, the more accurate the corresponding delay time calculation, and the more accurate the prediction of the wake.

[0085] like Figure 7 As shown, the present invention also provides another embodiment, which is a system for establishing a three-dimensional time full wake model, including: a vertical height full wake wind speed distribution acquisition module without considering the influence of shear wind, which is used to predict based on a preset Jensen wake model and a super Gaussian function and the law of conservation of mass, and obtain the vertical height full wake wind speed distribution without considering the influence of shear wind, wherein the preset includes the Jensen wake model and the super Gaussian function; a mass loss calculation module, which is used to obtain the wind shear curve of the incoming wind speed and calculate the mass loss caused by the wind shear; a vertical height full wake wind speed distribution acquisition module for correcting the vertical height The invention discloses a module for obtaining a full wake wind speed distribution at a vertical height without considering the influence of shear wind, and obtains a full wake wind speed distribution at a corrected vertical height; a module for obtaining a full wake wind speed distribution at a horizontal plane, and predicts the full wake speed at a horizontal plane, and obtains a full wake wind speed distribution at a horizontal plane; a module for establishing a three-dimensional super-Gaussian full wake model, and a module for establishing a three-dimensional full wake model based on the full wake wind speed distribution at a corrected vertical height and the full wake wind speed distribution at a horizontal plane; and a module for establishing a three-dimensional time full wake model considering delay, and a module for establishing a three-dimensional time full wake model considering delay based on a three-dimensional super-Gaussian full wake model.

[0086] The three-dimensional time wake model provided in this embodiment can effectively describe the spatial distribution and time-varying characteristics of the wake expansion, provide a reference for the dynamic load analysis of downstream wind turbines considering the dynamic adjustment process of wind turbine control strategy, and further improve the wake model for optimizing the control strategy of wind turbines and improving the revenue of wind farms.

[0087] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for establishing a three-dimensional time-based full wake model of a horizontal axis wind turbine, characterized in that: It includes the following: Construct a three-dimensional super-Gaussian full wake model to obtain the incoming wind speed , future wind speed Substitute it into the three-dimensional super-Gaussian full wake model to obtain the initial three-dimensional time full wake model; Convection wind speed Delay time Calculate the delay time , and the incoming wind speed Inflow time Solve for the incoming wind speed Arrival time , future wind speed Arrival time Substitute it into the initial three-dimensional time full wake model for calculation to obtain the three-dimensional time full wake model; The calculation formula of the initial three-dimensional time full wake model is as follows: in, is the incoming wind speed at the center of the wind turbine hub; is the center height of the wind turbine hub; is the height from the ground; is the wind shear index; is the distance from the center of the hub on the horizontal plane; is the standard deviation of the Gaussian distribution in the horizontal direction; The construction process of the three-dimensional super-Gaussian full wake model is as follows: Obtain wind field data, calculate the wind field data based on the preset Jensen wake model, super Gaussian function and mass conservation algorithm, and obtain the initial vertical height full wake wind speed distribution; The incoming wind speed data is obtained to generate a wind shear curve, and the mass loss is calculated based on the wind shear curve. The initial vertical height wake wind speed distribution is corrected by the mass loss to obtain the corrected vertical height full wake wind speed distribution; The horizontal plane full wake wind speed distribution is solved according to the modified vertical height full wake wind speed distribution, and a three-dimensional super-Gaussian full wake model is constructed by combining the modified vertical height wake wind speed distribution and the horizontal plane full wake wind speed distribution. The calculation formula of the three-dimensional super-Gaussian full wake model is as follows: in, is the incoming wind speed at the center of the wind turbine hub; is the center height of the wind turbine hub; is the height from the ground; is the wind shear index; is the distance from the center of the hub on the horizontal plane; is the standard deviation of the Gaussian distribution in the horizontal direction; The calculation formula of the three-dimensional time full wake model is as follows: in, is the center height of the wind turbine hub, is an unknown parameter, Incoming wind speed The inflow time, Incoming wind speed Arrival time.

2. The method according to claim 1, characterized in that The delay time The calculation formula is as follows: in, is the initial three-dimensional time full wake model, is the delay time.

3. The method according to claim 2, characterized in that The incoming wind speed Arrival time The calculation formula is as follows: in, Incoming wind speed Arrival time, Incoming wind speed The inflow time, is the delay time.

4. The method according to claim 3, characterized in that The calculation formula of the super Gaussian function is as follows: in, is the horizontal coordinate of the maximum value of the super-Gaussian function, is the standard deviation of the super-Gaussian function, and the coefficient is the ordinate of the maximum value of the super-Gaussian function, is the exponent of the super-Gaussian function, , All are parameters.

5. The method according to claim 4, characterized in that The calculation formula of the initial vertical height full wake wind speed distribution is as follows: in, is the standard deviation of the Gaussian function in the vertical direction; is the incoming wind speed at the center of the wind turbine hub; axial induction factor ; is the wake radius in the vertical direction; is the initial wake radius; is the exponent of the super-Gaussian function.

6. The method according to claim 5, characterized in that The calculation formula of the modified vertical height full wake wind speed distribution is as follows: in, The speed difference between the shear wind and the center flow of the hub; is the initial wake radius; is the full wake wind speed distribution at the initial vertical height; is the axial induction factor.

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