A wind farm power generation evaluation method based on uncertainty and wake model

Abstract

This invention discloses a wind farm power generation assessment method based on uncertainty and wake model. Specifically, it involves: statistically analyzing long-term reference wind speed data to obtain the input annual average wind speed for Monte Carlo simulation; extrapolating wind speed using the long-term corrected MCP method to obtain the wind speed at the reference height of the meteorological tower; obtaining the wind speed at the hub height of the meteorological tower based on vertical extrapolation; obtaining the wind speed at the hub height of each wind turbine in the wind farm based on horizontal extrapolation using the wind flow model; considering the wake effect to obtain the wake-reduced wind speed; obtaining a probabilistic model of air density versus power curves; calculating the average energy per unit area (AEP) of each wind turbine in the wind farm; and after 1000 iterations, obtaining the uncertainty of the AEP of each wind turbine in the wind farm, ultimately obtaining the uncertainty of the wind farm's power generation. This invention can obtain the AEP and uncertainty of the entire wind farm and each wind turbine, providing guidance and reference for the evaluation standards of operating wind farms.

Description

Technical Field

[0001] This invention belongs to the field of wind resource assessment technology, and in particular relates to a method for assessing the power generation of wind farms based on uncertainty and wake models. Background Technology

[0002] Wind energy, with its large reserves, wide distribution, and high degree of commercialization, has become a key focus of the current energy transition. Wind farms are the primary sites for wind energy utilization, and their site selection relies heavily on wind resource assessment. Estimated Annual Power Generation (AEP) is a crucial statistical indicator for wind resource assessment and a vital basis for wind farm construction. Generally, wind resource assessments and AEP calculations do not consider the uncertainties of wind farms; however, in reality, every step involved involves uncertainty. The existence of uncertainty leads to significant differences in AEP obtained from different deterministic estimation schemes, which is detrimental to investment decisions. Accurately estimating the uncertainties at each stage, thereby obtaining a more reliable AEP, is becoming increasingly important.

[0003] There are two main categories of methods for studying AEP uncertainty: the first is the uncertainty combination method, which first determines the uncertainty of each component and then quantifies the total uncertainty using a combination criterion (usually a sum of squares); the second is the Monte Carlo simulation method, which considers the uncertainty of each component through Monte Carlo simulations of parameters such as wind speed. Both the uncertainty combination method and the IEC standard are based on the fundamental assumption that each component is independent. However, in reality, components are correlated and interact with each other, and the combined uncertainty may be incorrect if the uncertainty of a certain component deviates from a normal distribution. Monte Carlo simulation can compensate for the analyst's experience and maintain the correlation between components and the non-Gaussianity of the probability distribution, ultimately obtaining a reliable and reasonable AEP uncertainty. However, existing Monte Carlo simulation-based methods, such as those by Kwon, Jung, and Hrafnkelsson, only obtain AEP results for a single location at the in-situ anemometer tower, and cannot accurately provide the AEP for the entire wind farm. Amirinia et al. used data from 550 locations. In actual engineering projects, a wind farm often only has a few or even just one wind measurement tower. It is necessary to consider the differences in wind speed distribution in space and perform horizontal extrapolation. At the same time, the influence of wake effect was not taken into account. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for evaluating wind farm power generation based on an uncertainty and wake model.

[0005] The present invention provides a wind farm power generation assessment method based on an uncertainty and wake model, specifically as follows:

[0006] Step 1: Perform statistical analysis on long-term reference wind speed data to obtain the input annual average wind speed for Monte Carlo simulation.

[0007] Step 2: Extrapolate the wind speed based on the long-term corrected measurement-correlation-prediction (MCP) method to obtain the wind speed at the reference height of the meteorological tower.

[0008] Step 3: Based on vertical extrapolation, obtain the wind speed at the height of the wind measuring tower hub.

[0009] Step 4: Based on the horizontal extrapolation of the wind flow model, obtain the wind speed at the hub height of each wind turbine in the wind farm.

[0010] Step 5: Consider the wake effect to obtain the wind speed after wake reduction.

[0011] Step 6: Obtain the probabilistic model of the air density versus power curve.

[0012] Step 7: Calculate the AEP of each wind turbine in the wind farm.

[0013] Step 8: After repeating steps 1 to 7 1000 times, the uncertainty of AEP of each wind turbine in the wind farm is obtained, and finally the uncertainty of the wind farm's power generation is obtained.

[0014] Furthermore, the probability density function of the long-term reference wind speed data in step 1 is:

[0015]

[0016] Where V>0; k is a dimensionless shape factor; c is a scaling factor. Parameters k and c are estimated using the method of moments and both follow a normal distribution. Their mean expressions are as follows:

[0017]

[0018]

[0019] Where Γ is the gamma function.

[0020] The standard deviations of k and c need to be obtained from the statistical results of long-term reference wind speeds.

[0021] Furthermore, step 2 specifically involves:

[0022] The formula for the MCP method based on the standard deviation ratio is expressed as follows:

[0023]

[0024] in, U represents the long-term wind speed time history estimated by the anemometer tower, and U represents the reference long-term wind speed time history. S and V SThese are the short-term wind speed time histories at the reference location and the reference height of the meteorological tower, respectively, for the corresponding time period; the symbol () represents the mean, and σ represents the standard deviation.

[0025] When the MCP method is used with short-term measured data, there is a certain residual between the measured wind speed and the estimated wind speed, as shown below:

[0026]

[0027] According to equations (4) and (5), the mean and standard deviation of the residuals can be expressed as follows:

[0028]

[0029] Where n is V S The number of discrete points of wind speed included; It is the correlation coefficient between the reference location and the short-term wind speed of the meteorological tower.

[0030] Furthermore, step 3 specifically involves:

[0031] The wind speed at the height of the wind turbine hub of the meteorological tower is obtained by vertical extrapolation from the wind speed at the reference height of the meteorological tower, using the following exponential function:

[0032]

[0033] in, The z-shaped wind measurement tower is obtained based on vertical extrapolation. hub Wind speed at altitude The anemometer tower z is obtained based on the MCP method r Wind speed at altitude, z hub Z represents the height of the wind turbine hub. r For reference height, α is the ground roughness index and is assumed to follow a normal distribution.

[0034] Furthermore, step 4 specifically involves:

[0035] Wind speed time history from the wind measurement tower Find the wind speed time history at any wind turbine location i. Based on the airflow model, it is assumed that the following conditions are met. Where S i As the acceleration effect factor, and the acceleration factor S in the wind flow model i R, the ratio of the measured wind speed i The error model is expressed as follows:

[0036]

[0037] Among them, S i R represents the ratio of wind speeds at two locations in the wind flow model. iExpressed as the ratio of the true wind speeds at two locations; the acceleration effect error satisfies a mean of 0 and a standard deviation, i.e., the combined uncertainty, of u. i The normal distribution is given by:

[0038]

[0039] in,

[0040]

[0041]

[0042] in, This represents the uncertainty related to distance, where λ is the asymptotic value of the uncertainty and takes the value of 10%. L1 represents the distance between the wind measurement tower and wind turbine i, where L1 is the distance factor and has a value of 1km; This represents the uncertainty related to the acceleration factor; first, the acceleration effect factor S at the location of each wind turbine in the wind farm is obtained. i Then, based on the above distance uncertainty and acceleration factor uncertainty, the combined uncertainty and error are obtained, and the true ratio R is calculated. i Thus, the wind speed time history at each wind turbine is obtained.

[0043] Furthermore, step 5 specifically involves:

[0044] The wind speed loss rate in the Jensen model is expressed as:

[0045]

[0046] Where, ΔV ij This represents the wind speed loss rate of wind turbine j affected by wind turbine i; D is the thrust coefficient of wind turbine i; i x is the diameter of the impeller of wind turbine i; ij The distance between fan i and fan j; ξ, the wake descent coefficient, is expressed as:

[0047]

[0048] Where z hub z0 and z0 represent the height of the wind turbine hub and the height of the ground roughness, respectively.

[0049] If wind turbine j is affected by n wind turbines, the linear superposition criterion and the wind speed after loss are:

[0050]

[0051]

[0052] Where, ΔV j This represents the total loss rate of the wind turbine at wind speed j; V represents the usable wind speed of wind turbine j after wake loss. zhub,j This represents the wind speed j of the fan, obtained based on the flow field model.

[0053] Furthermore, step 6 specifically involves:

[0054] The normalized air density follows a uniform distribution and is expressed as:

[0055]

[0056] The expressions for the mean and standard deviation of the fan output power are as follows:

[0057]

[0058]

[0059] Furthermore, step 7 specifically involves:

[0060] The wind direction data is divided into 12 sectors, and wind turbine i is in sector θ. d The available wind energy for d = 1, 2, 3... 12 is expressed as:

[0061]

[0062] in, It is sector θ d The number of hours, and It is wind speed The corresponding fan output power, at the same time It is wind speed In sector θ d The probability density is given below.

[0063] Substituting the power curve expression and discretizing its integral, the wind turbine i in sector θ d The AEP under the following formula can be expressed as:

[0064]

[0065] in, The wind speed at hour j Corresponding output power; It is the normalized air density. By superimposing the results of all 12 sectors, the AEP of fan i can be finally obtained.

[0066] The beneficial technical effects of this invention are as follows:

[0067] This invention proposes a wind farm power generation assessment method based on uncertainty and wake model, which can obtain the AEP (Advanced Power Estimation) and its uncertainty of the wind farm. The proposed method has the following advantages: First, based on the uncertainty of the flow field model, the wind speed level at the anemometer tower is extrapolated to each wind turbine in the wind farm; second, considering the influence of wake effect, the wind speed of each wind turbine after being affected by the wake is obtained by determining the wind speed loss rate of each wind turbine. Finally, the AEP and its uncertainty of each wind turbine in the wind farm, as well as the AEP and its uncertainty of the entire wind farm, can be obtained. The uncertainty of the AEP of wind turbines in the wind farm obtained by the method proposed in this invention has certain guiding and reference significance for the evaluation criteria of operating wind farms. In addition, the proposed method is verified through a wind farm example, and the results show the effectiveness of the proposed method. Attached Figure Description

[0068] Figure 1 This is a wind farm layout diagram according to the present invention.

[0069] Figure 2 The AEP scatter plot of the wind turbine 2 obtained in the example is shown.

[0070] Figure 3 The AEP scatter plot of the fan 7 obtained in the example is shown.

[0071] Figure 4 The probability density comparison diagram of wind turbine 2 obtained in the example is shown.

[0072] Figure 5 The probability density comparison diagram of the wind turbine 7 obtained in the example is shown. Detailed Implementation

[0073] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0074] Step 1: Perform statistical analysis on long-term reference wind speed data to obtain the input annual average wind speed for Monte Carlo simulation.

[0075] The probability density function of long-term reference wind speed data is:

[0076]

[0077] Where V>0; k is a dimensionless shape factor; c is a scaling factor. Parameters k and c are estimated using the method of moments and both follow a normal distribution. Their mean expressions are as follows:

[0078]

[0079]

[0080] Where Γ is the gamma function.

[0081] The standard deviations of k and c need to be obtained from the statistical results of long-term reference wind speeds.

[0082] Step 2: Extrapolate the wind speed based on the long-term corrected measurement-correlation-prediction (MCP) method to obtain the wind speed at the reference height of the meteorological tower.

[0083] The formula for the MCP method based on the standard deviation ratio is expressed as follows:

[0084]

[0085] in, U represents the long-term wind speed time history estimated by the anemometer tower, and U represents the reference long-term wind speed time history. S and V S σ represents the short-term wind speed time history at the reference location and the reference height of the meteorological tower, respectively, within the corresponding time period; the symbol (-) represents the mean, and σ represents the standard deviation.

[0086] When the MCP method is used with short-term measured data, there is a certain residual between the measured wind speed and the estimated wind speed, as shown below:

[0087]

[0088] According to equations (4) and (5), the mean and standard deviation of the residuals can be expressed as follows:

[0089]

[0090] Where n is V S The number of discrete points of wind speed included; It is the correlation coefficient between the reference location and the short-term wind speed of the meteorological tower.

[0091] Step 3: Based on vertical extrapolation, obtain the wind speed at the height of the wind measuring tower hub.

[0092] The wind speed at the height of the wind turbine hub of the meteorological tower is obtained by vertical extrapolation from the wind speed at the reference height of the meteorological tower, using the following exponential function:

[0093]

[0094] in, The z-shaped wind measurement tower is obtained based on vertical extrapolation. hub Wind speed at altitude The anemometer tower z is obtained based on the MCP method r Wind speed at altitude, z hub Z represents the height of the wind turbine hub. r For reference height, α is the ground roughness index and is assumed to follow a normal distribution.

[0095] Step 4: Based on the horizontal extrapolation of the wind flow model, obtain the wind speed at the hub height of each wind turbine in the wind farm.

[0096] Wind speed time history from the wind measurement tower Find the wind speed time history at any wind turbine location i. Based on the airflow model, it is assumed that the following conditions are met. Where S i As the acceleration effect factor, and the acceleration factor S in the wind flow model i R, the ratio of the measured wind speed i The error model is expressed as follows:

[0097]

[0098] Among them, S i R represents the ratio of wind speeds at two locations in the wind flow model. i Expressed as the ratio of the true wind speeds at two locations; the acceleration effect error satisfies a mean of 0 and a standard deviation, i.e., the combined uncertainty, of u. i The normal distribution is given by:

[0099]

[0100] in,

[0101]

[0102]

[0103] in, This represents the uncertainty related to distance, where λ is the asymptotic value of the uncertainty and takes the value of 10%. L1 represents the distance between the wind measurement tower and wind turbine i, where L1 is the distance factor and has a value of 1km; This represents the uncertainty related to the acceleration factor; first, the acceleration effect factor S at the location of each wind turbine in the wind farm is obtained. i Then, based on the above distance uncertainty and acceleration factor uncertainty, the combined uncertainty and error are obtained, and the true ratio R is calculated. i Thus, the wind speed time history at each wind turbine is obtained.

[0104] Step 5: Consider the wake effect to obtain the wind speed after wake reduction.

[0105] The wind speed loss rate in the Jensen model is expressed as:

[0106]

[0107] Where, ΔV ij This represents the wind speed loss rate of wind turbine j affected by wind turbine i; D is the thrust coefficient of wind turbine i; i x is the diameter of the impeller of wind turbine i; ij The distance between fan i and fan j; ξ, the wake descent coefficient, is expressed as:

[0108]

[0109] Where z hub z0 and z0 represent the height of the wind turbine hub and the height of the ground roughness, respectively.

[0110] If wind turbine j is affected by n wind turbines, the linear superposition criterion and the wind speed after loss are:

[0111]

[0112]

[0113] Where, ΔV j This represents the total loss rate of the wind turbine at wind speed j; This represents the usable wind speed of fan j after the wake loss. This represents the wind speed j of the fan, obtained based on the flow field model.

[0114] Step 6: Obtain the probabilistic model of the air density versus power curve.

[0115] The normalized air density follows a uniform distribution and is expressed as:

[0116]

[0117] The expressions for the mean and standard deviation of the fan output power are as follows:

[0118]

[0119]

[0120] Step 7: Calculate the AEP of each wind turbine in the wind farm.

[0121] The wind direction data is divided into 12 sectors, and wind turbine i is in sector θ. d The available wind energy for d = 1, 2, 3... 12 is expressed as:

[0122]

[0123] in, It is sector θ d The number of hours, and It is wind speed The corresponding fan output power, at the same time It is wind speed In sector θd The probability density is given below.

[0124] Substituting the power curve expression and discretizing its integral, the wind turbine i in sector θ d The AEP under the following formula can be expressed as:

[0125]

[0126] in, The wind speed at hour j Corresponding output power; It is the normalized air density. By superimposing the results of all 12 sectors, the AEP of fan i can be finally obtained.

[0127] Step 8: After repeating steps 1 to 7 1000 times, the uncertainty of AEP of each wind turbine in the wind farm is obtained, and finally the uncertainty of the wind farm's power generation is obtained.

[0128] Example:

[0129] To verify the effectiveness of the proposed method, a calculation was performed on a wind farm. The wind farm is located in a flat area, and its layout is shown in the diagram below. Figure 1 As shown.

[0130] The results for long-term reference wind speeds k and c are as follows: σ k =0.04andσ c =0.34.

[0131] The mean and standard deviation of the exponent α in vertical extrapolation are as follows: in

[0132] S in horizontal extrapolation i The vast majority are close to 1, R i The wind speeds of each fan are obtained after considering wake reduction. Then, combined with normalized air density and output power, the average efficiency (AEP) of each fan is obtained. After 1000 cycles, the AEP scatter plots for fans 2 and 7 are as follows: Figure 2 , Figure 3 The probability density maps for wind turbines 2 and 7 are obtained as follows: Figure 4 , Figure 5 .

[0133] from Figure 2-5The results show that the mean and standard deviation of AEP for wind turbines 2 and 7 are very close. This is because the wind turbines are located in the same terrain area, and the effects of roughness and obstacles are almost identical. Furthermore, the mean AEP of wind turbine 2 is larger than that of wind turbine 7, consistent with the influence of the wake effect. The uncertainty of AEP for all eight wind turbines is 9.0%, consistent with previous research statistics.

Claims

1. A method for evaluating the power generation of a wind farm based on an uncertainty and wake model, characterized in that, Specifically: Step 1: Perform statistical analysis on long-term reference wind speed data to obtain the input annual average wind speed for Monte Carlo simulation; Step 2: Extrapolate the wind speed based on the long-term corrected measurement-correlation-prediction (MCP) method to obtain the wind speed at the reference height of the meteorological tower; Step 3: Based on vertical extrapolation, obtain the wind speed at the height of the wind tower hub; Step 4: Based on the horizontal extrapolation of the wind flow model, obtain the wind speed at the hub height of each wind turbine in the wind farm; Wind speed time history from the wind measurement tower Find the wind speed time history at any wind turbine location i. Based on the airflow model, it is assumed that the following conditions are met. Where S i As the acceleration effect factor, and the acceleration factor S in the wind flow model i R, the ratio of the measured wind speed i The error model is expressed as follows: Among them, S i R represents the ratio of wind speeds at two locations in the wind flow model. i Expressed as the ratio of the true wind speeds at two locations; the acceleration effect error satisfies a mean of 0 and a standard deviation, i.e., the combined uncertainty, of u. i The normal distribution is given by: in, in, This represents the uncertainty related to distance, where λ is the asymptotic value of the uncertainty and takes the value of 10%. L1 represents the distance between the wind measurement tower and wind turbine i, where L1 is the distance factor and has a value of 1km; This represents the uncertainty related to the acceleration factor; first, the acceleration effect factor S at the location of each wind turbine in the wind farm is obtained. i Then, based on the above distance uncertainty and acceleration factor uncertainty, the combined uncertainty and error are obtained, and the true ratio R is calculated. i Thus, the wind speed time history at each wind turbine is obtained; Step 5: Considering the wake effect, obtain the wind speed after wake reduction; The wind speed loss rate in the Jensen model is expressed as: Where, ΔV ij This represents the wind speed loss rate of wind turbine j affected by wind turbine i; D is the thrust coefficient of wind turbine i; i x is the diameter of the impeller of wind turbine i; ij The distance between fan i and fan j; ξ, the wake descent coefficient, is expressed as: Where z hub z0 and z0 represent the height of the wind turbine hub and the height of the ground surface roughness, respectively; If wind turbine j is affected by n wind turbines, the linear superposition criterion and the wind speed after loss are: Where, ΔV j This represents the total loss rate of the wind turbine at wind speed j; This represents the usable wind speed of fan j after the wake loss. This represents the wind speed j of the fan, obtained based on the flow field model. Step 6: Obtain a probabilistic model of the air density versus power curve; Step 7: Calculate the AEP of each wind turbine in the wind farm; Step 8: After repeating steps 1 to 7 1000 times, the uncertainty of AEP of each wind turbine in the wind farm is obtained, and finally the uncertainty of the wind farm's power generation is obtained.

2. The wind farm power generation assessment method based on uncertainty and wake model according to claim 1, characterized in that, The probability density function of the long-term reference wind speed data in step 1 is: Where V>0; k is a dimensionless shape factor; c is a scaling factor. Parameters k and c are estimated using the method of moments and both follow a normal distribution. Their mean expressions are as follows: Where Γ is the gamma function; The standard deviations of k and c need to be obtained from the statistical results of long-term reference wind speeds.

3. The wind farm power generation assessment method based on uncertainty and wake model according to claim 1, characterized in that, Step 2 specifically involves: The formula for the MCP method based on the standard deviation ratio is expressed as follows: in, U represents the long-term wind speed time history estimated by the anemometer tower, and U represents the reference long-term wind speed time history. S and V S These represent the short-term wind speed time histories at the reference location and the reference height of the meteorological tower, respectively, for the corresponding time periods; (symbols omitted). σ represents the mean, and σ represents the standard deviation. When the MCP method is used with short-term measured data, there is a certain residual between the measured wind speed and the estimated wind speed, as shown below: According to equations (4) and (5), the mean and standard deviation of the residuals can be expressed as follows: Where n is V S The number of discrete points of wind speed included; It is the correlation coefficient between the reference location and the short-term wind speed of the meteorological tower.

4. The wind farm power generation assessment method based on uncertainty and wake model according to claim 1, characterized in that, Step 3 specifically involves: The wind speed at the height of the wind turbine hub of the meteorological tower is obtained by vertical extrapolation from the wind speed at the reference height of the meteorological tower, using the following exponential function: in, The z-shaped wind measurement tower is obtained based on vertical extrapolation. hub Wind speed at altitude The anemometer tower z is obtained based on the MCP method r Wind speed at altitude, z hub Z represents the height of the wind turbine hub. r For reference height, α is the ground roughness index and is assumed to follow a normal distribution.

5. The wind farm power generation assessment method based on an uncertainty and wake model according to claim 4, characterized in that, Step 6 specifically involves: The normalized air density follows a uniform distribution and is expressed as: The expressions for the mean and standard deviation of the fan output power are as follows:

6. The wind farm power generation assessment method based on an uncertainty and wake model according to claim 5, characterized in that, Step 7 specifically involves: The wind direction data is divided into 12 sectors, and wind turbine i is in sector θ. d The available wind energy for d = 1, 2, 3... 12 is expressed as: in, It is sector θ d The number of hours, and It is wind speed The corresponding fan output power, at the same time It is wind speed In sector θ d The probability density is as follows; Substituting the power curve expression and discretizing its integral, the wind turbine i in sector θ d The AEP under the following formula can be expressed as: in, The wind speed at hour j Corresponding output power; It is the normalized air density. By superimposing the results of all 12 sectors, the AEP of fan i can be finally obtained.

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