Wind speed prediction method based on mixed binary Copula function

Abstract

The invention discloses a wind speed prediction method based on a hybrid binary Copula function, and the method comprises the steps: firstly collecting the wind speed historical data and geographic position data of each wind turbine generator in a wind power plant, and then selecting the adjacent wind turbine generators of each wind turbine generator; then, multiple Copula functions are sampled to be combined to construct optimal mixed binary Copula functions of adjacent fan sets at different sampling moments, and parameters of the optimal mixed binary Copula functions are estimated through an EM algorithm; finally, the wind speed prediction of the wind turbine generator is realized based on the optimal mixed binary Copula function, and the wind speed prediction precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric power systems, and more specifically, relates to a wind speed prediction method based on a hybrid binary Copula function. Background Art

[0002] In recent years, due to the increasing depletion of fossil energy and the intensification of environmental pollution, wind energy, as a classic clean and renewable energy, has received widespread attention from the energy industry. The installed capacity of wind power has increased rapidly, and the proportion of wind power in the power grid has also increased significantly. Wind power generation has become one of the strategic directions of the energy industry. However, the uncertainty, volatility and anti-peak characteristics of wind power generation have brought huge challenges to wind power grid connection.

[0003] As the proportion of domestic wind power continues to increase, the power industry has begun to pay attention to the impact of the correlation between multiple wind speeds on the power system. At present, the methods used to describe correlation mainly include the constant coefficient method, the Copula function method, neural networks, and mutual correlation coefficients. Among them, the most commonly used constant coefficient method refers to the use of linear correlation coefficients to perform linear correlation analysis on historical data of wind turbines, and use this to describe wind speed correlation. However, the constant coefficient method only performs a simple linear analysis of the variables, without considering the spatial distribution factors, and is difficult to apply to complex wind farms in real scenarios. However, the Copula function rule uses the Copula function to fit the wind speed data, solves the dependence coefficient of the Copula function to describe the correlation, and makes full use of the Copula function to describe the complex correlation between variables. However, the existing Copula analysis method is usually based on a single type of Copula function, which can only characterize one correlation between variables and cannot accurately describe multiple correlations that exist simultaneously between variables; while the correlation structure of the mixed Copula function is more flexible than that of a single Copula function, and can accurately describe more complex correlations between wind speeds.

[0004] Therefore, how to realize wind speed prediction of multiple wind turbines based on historical wind speed data and make full use of the excellent characteristics of Copula function to describe complex correlations has very important engineering value for wind power grid connection and increasing the proportion of wind power. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a wind speed prediction method based on a hybrid binary Copula function, which can accurately describe the correlation between multiple wind speeds and realize wind speed prediction of multiple wind turbines through multiple iterations and cluster analysis, which is helpful to solve the problem that large-scale wind power grid connection affects the operation planning of the power system.

[0006] To achieve the above object of the invention, the present invention provides a wind speed prediction method based on a mixed binary Copula function, characterized in that it comprises the following steps:

[0007] (1) Collect historical wind speed data and geographic location data of each wind turbine in the wind farm;

[0008] (2) Select the adjacent wind turbines of each wind turbine;

[0009] (3) Construct the optimal mixed binary Copula function of adjacent wind turbine groups at different sampling times;

[0010] (4) Estimate the parameters to be estimated of the optimal mixed binary Copula function by using the EM algorithm;

[0011] (5) Realize wind speed prediction of wind turbines based on the optimal hybrid binary Copula function.

[0012] The object of the invention of the present invention is achieved in this way:

[0013] The wind speed prediction method of the present invention is based on a hybrid binary Copula function. First, the wind speed historical data and geographical location data of each wind turbine in a wind farm are collected, and then the adjacent wind turbines of each wind turbine are selected; then, a plurality of Copula functions are sampled and combined to construct the optimal hybrid binary Copula function of the adjacent wind turbines at different sampling times, and the parameters of the optimal hybrid binary Copula function are estimated by using an EM algorithm; finally, the wind speed prediction of the wind turbine is realized based on the optimal hybrid binary Copula function, thereby improving the wind speed prediction accuracy.

[0014] At the same time, the wind speed prediction method based on the mixed binary Copula function of the present invention also has the following beneficial effects:

[0015] (1) The hybrid Copula function model constructed by the present invention for wind speed sequences with complex correlation characteristics can better describe the linear correlation, nonlinear correlation, upper tail correlation and lower tail correlation of the wind speed sequence, and there is no need to determine the correlation coefficient matrix in the traditional method;

[0016] (2) The present invention constructs a mixed Copula function with different structures as a wind speed correlation model in each time period, which can capture the change of correlation characteristics between variables over time in real time and effectively improve the fitting accuracy of the wind speed correlation model;

[0017] (3) The present invention constructs a hybrid Copula function for adjacent units in pairs according to the geographical location characteristics of the units in the wind farm, and again selects the best among the hybrid Copula functions constructed with several adjacent units. Under the premise of effectively controlling the amount of calculation, it ensures that the optimal hybrid Copula function of each unit is selected, which can improve the fitting accuracy and reflect the spatial correlation characteristics of wind speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the distribution of wind turbines in a wind farm;

[0019] Figure 2 It is a flow chart of the wind speed prediction method based on the mixed binary Copula function of the present invention;

[0020] Figure 3 It is the optimal mixed Copula distribution function diagram of wind turbines 1 and 2;

[0021] Figure 4 is the joint distribution probability cloud diagram of wind turbines 1 and 2;

[0022] Figure 5 These are the four typical predicted wind speed values ​​and their probability distribution diagrams for wind turbine 1;

[0023] Figure 6 These are the four typical predicted wind speed values ​​of wind turbine 2 and their probability distribution diagrams;

[0024] Figure 7 It is a box plot of the wind speed prediction curve of wind turbine 1 and the actual data during the prediction period;

[0025] Figure 8 It is a box plot of the wind speed prediction curve of wind turbine 2 and the actual data during the prediction period;

[0026] Fig. 9 are the 90%, 95%, and 99% confidence intervals of the predicted wind speed and the actual wind speed of wind turbine 1;

[0027] Fig.10 It is the 90%, 95%, and 99% confidence interval of the predicted wind speed and the actual wind speed of wind turbine 2. DETAILED DESCRIPTION

[0028] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0029] Example

[0030] In this embodiment, if Figure 1 As shown, taking the 8015 wind turbine 1 with longitude and latitude coordinates (102.126°, 30.74232°), the 8034 wind turbine 2 with coordinates (102.463°, 30.73763°), the 8095 wind turbine 3 with coordinates (102.383°, 30.7794°), and the 9014 wind turbine 4 with coordinates (102.1°, 31.39647°) in a certain wind farm as examples, the historical data are the actual operating data of each wind turbine from March to May, and 15456 data are selected for each wind turbine.

[0031] Next we combine Figure 1 A wind speed prediction method based on a mixed binary Copula function of the present invention is described in detail. Figure 2 As shown, the specific steps include:

[0032] S1. Collect historical wind speed data and geographic location data of each wind turbine in the wind farm;

[0033] S1.1. Collect the historical wind speed data of M wind turbines in the wind farm and obtain the wind speed data of each wind turbine in one day T. * The wind speed data at sampling time is recorded as follows: Where i = 1, 2, ..., M, t = 1, 2, ..., T * , represents the pth wind speed sampling data of wind turbine i at the tth sampling time, and m represents the sampling times of wind turbine i at the tth sampling time;

[0034] In this embodiment, M=4, T * =24, m=644;

[0035] The wind speed data of each wind turbine at each sampling time is normalized to the range of [0,1] through cumulative distribution to obtain the normalized variable in, express The normalized value of

[0036] S1.2. Collect the geographical location data of M wind turbines in the wind farm, where the geographical location data of the i-th wind turbine is recorded as S i =(Lat i ,Lng i ), Lat i ,Lng i Indicates the longitude and latitude of the location of the i-th wind turbine;

[0037] S2, selecting the adjacent wind turbines of each wind turbine;

[0038] S2.1. Taking wind turbine i as the reference, calculate the distance between any wind turbine j and wind turbine i in the wind farm:

[0039]

[0040] Where i≠j, i,j∈[1,M], R=6371;

[0041] S2.2. Select the wind turbine closest to wind turbine i in the wind farm and record it as wind turbine j. The variable after normalizing the wind speed data of wind turbine j at each sampling time is recorded as

[0042] S2.3, traverse each wind turbine in the wind farm, and then process according to steps S2.1 to S2.2 to obtain the adjacent wind turbines of each wind turbine.

[0043] In this embodiment, wind turbine set 1 is taken as an example. Wind turbine set 2 is adjacent to wind turbine set 1. Hereinafter, the following steps will be described by taking adjacent wind turbine sets 1 and 2 as an example.

[0044] S3. Constructing the optimal mixed binary Copula function of wind speeds of adjacent wind turbines at different sampling times; S3.1. Constructing the basic binary Copula function of wind speeds of adjacent wind turbines at different sampling times;

[0045] In this embodiment, we select the following five typical basic binary Copula functions:

[0046] Gaussian Copula Function:

[0047] Clayton Copula Function:

[0048] Gumbel Copula Function:

[0049] Frank Copula Function:

[0050] T Copula function:

[0051] Among them, s, t are integral variables, φ -1 (·) is the inverse function of the standard normal distribution function, is the inverse function of the univariate student distribution function with κ degrees of freedom, and They represent the parameters to be estimated in the basic binary Copula function at t sampling moments respectively;

[0052] S3.2. Estimate the relevant parameters of each basic binary Copula function based on the maximum likelihood estimation method and

[0053] S3.3, calculate the evaluation index and select the basic binary Copula function to form the optimal mixed binary Copula function;

[0054] S3.3.1. Sample each basic binary Copula function m times to obtain the sampling value sequence of each basic binary Copula function Among them, k = 1, 2, 3, 4, 5 represents the number of the basic binary Copula function, represents the mth sampling value of wind turbine i at the tth sampling time in the kth basic binary Copula function;

[0055] S3.3.2, substitute the sampling values ​​at different sampling times into the basic binary Copula function, substitute the normalized wind speed values ​​at different sampling times into the empirical Copula function, and then calculate the sum of squares of the Euclidean distances between the basic binary Copula function and the empirical Copula function of adjacent wind turbines at different sampling times;

[0056]

[0057] S3.3.3. Calculate the normalized wind speed values ​​of adjacent wind turbines at each sampling time and the sampled values ​​of each basic binary Copula function The correlation coefficient between

[0058]

[0059] in, and Sequence and The mean of

[0060] Similarly, calculate the correlation coefficient of wind turbine j at each sampling time

[0061] S3.3.4. Filter out the sum of squared Euclidean distances Less than 0.05*m and correlation coefficient r i t；k , The basic binary Copula functions are all greater than 0.9 at the same time; then the selected basic binary Copula functions are combined into the optimal mixed binary Copula function;

[0062]

[0063] in, is the optimal mixed binary Copula function between wind turbines i and j at the tth sampling moment, ρ t Indicates the number of basic binary Copula functions screened at time t, and is the parameter to be estimated in the optimal mixed binary Copula function;

[0064] S4, estimating the parameters to be estimated of the optimal mixed binary Copula function by using the EM algorithm;

[0065] S4.1. Construct the likelihood function corresponding to the optimal mixed binary Copula function:

[0066]

[0067] in,

[0068] S4.2, use the EM algorithm to iterate the likelihood function for ξ steps and obtain the parameters and

[0069] Among them, the parameters of iterative solution The iterative equation is:

[0070]

[0071] in, and is the result of the nth iteration; The initial value is

[0072] parameter The iterative equation is:

[0073]

[0074] The above formula cannot be solved directly, and the parameters are solved by the BFGS algorithm in the quasi-Newton method The iterative equation is Initial value of The parameter values ​​estimated for each basic binary copula function in step S3.2;

[0075] Finally, the iterative solution of step ξ is is the estimated parameter of the optimal mixed binary Copula function

[0076] S5. Wind speed prediction of wind turbines;

[0077] S5.1. The parameter values ​​estimated in step S4 are Substitute the optimal mixed binary Copula function, and then perform Monte Carlo sampling on the optimal mixed binary Copula function to obtain the sampling sequence of wind turbine i at each sampling time

[0078] S5.2. Establishing a mapping relationship between wind speed and wind speed normalization value Through Perform the inverse transformation, Map out the wind speed prediction value sequence of wind turbine i at each sampling time

[0079] S5.3, using K-means algorithm Perform cluster reduction to obtain the four typical wind speed prediction values ​​of wind turbine i at the tth sampling time and its probability

[0080] Finally, the typical wind speed value of wind turbine i at each sampling time is obtained and its probability

[0081] S5.4. Yes and The wind speed forecast result of wind turbine i at T sampling moments in the next cycle is obtained by weighted calculation in, is the predicted value of wind turbine i at the tth sampling time in the next cycle,

[0082] In this embodiment, taking adjacent wind turbines 1 and 2 as examples, the mixed Copula function distribution diagram of the wind speed data of wind turbines 1 and 2 and their joint distribution probability cloud diagram are obtained by the optimal mixed binary Copula function, as shown in FIG. Figure 3 and Figure 4 As shown. Among them, Figure 3 and Figure 4 The 12th sampling period The wind speed of wind turbine 1 and wind turbine 2 is Figure 3 and Figure 4 There is a strong correlation on the diagonal line, indicating The correlation between the wind speeds of wind turbine group 1 and wind turbine group 2 can be accurately described.

[0083] In addition, according to the above method, four typical wind speed prediction values ​​and their probabilities of wind turbine 1 and wind turbine 2 in each period can be obtained, as shown in the following figure: Figure 5 and Figure 6 shown.

[0084] Secondly, the box plots of the wind speed prediction curves of wind turbine 1 and wind turbine 2 obtained according to the above method and the actual wind speed data during the prediction period are as follows: Figure 7 and Figure 8 In the two figures, box plots are drawn based on the actual wind speed data of the forecast period. The solid line in the box plot is the median of the actual wind speed data, and the circle is the wind speed forecast value of each period. It can be seen that the wind speed forecast value obtained by the present invention has good accuracy.

[0085] Finally, we plot the wind speed forecast curves for wind turbine 1 and wind turbine 2 and the 90%, 95% and 99% confidence intervals of the actual wind speed data during the forecast period as follows: Fig. 9 and Fig.10 In the two figures, different confidence intervals of the actual wind speed data in the prediction period are plotted, wherein the dark broken line is the wind speed prediction value in the prediction period, and the broken line is basically within the 99% confidence interval, which shows that the wind speed prediction value obtained by the present invention has good accuracy.

[0086] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A wind speed prediction method based on a mixed binary Copula function, characterized in that: The following steps are involved: (1) Collect historical wind speed data and geographic location data of each wind turbine in the wind farm; (1.1) Collect the historical wind speed data of M wind turbines in the wind farm and obtain the wind speed of each wind turbine in one day T. * The wind speed data at sampling time is recorded as follows: Where i = 1, 2, ..., M, t = 1, 2, ..., T * , represents the pth wind speed sampling data of wind turbine i at the tth sampling time, and m represents the sampling times of wind turbine i at the tth sampling time; The wind speed data of each wind turbine at each sampling time is normalized to the range of [0,1] through cumulative distribution to obtain the normalized variable in, express The normalized value of (1.2) Collect the geographical location data of M wind turbines in the wind farm, where the geographical location data of the i-th wind turbine is recorded as S i =(Lat i ,Lng i ), Lat i ,Lng i Indicates the longitude and latitude of the location of the i-th wind turbine; (2) Select the adjacent wind turbines of each wind turbine; (3) Construct the optimal mixed binary Copula function of adjacent wind turbine groups at different sampling times; (4) Estimate the parameters to be estimated of the optimal mixed binary Copula function by using the EM algorithm; (4.1) Construct the likelihood function corresponding to the optimal mixed binary Copula function: in, (4.2) The likelihood function is solved by ξ-step iteration using the EM algorithm to obtain the parameter and Among them, the parameters of iterative solution The iteration equation is: in, and is the result of the nth iteration; The initial value is parameter The iterative equation is: The above formula cannot be solved directly, and the parameters are solved by the BFGS algorithm in the quasi-Newton method The iterative equation is Initial value of The estimated parameter values ​​of each basic binary Copula function in step (3.2); Finally, the iterative solution of step ξ is is the estimated parameter of the optimal mixed binary Copula function (5) Wind speed prediction for wind turbines; (5.1), the parameter values ​​estimated in step (4) Substitute the optimal mixed binary Copula function, and then perform Monte Carlo sampling on the optimal mixed binary Copula function to obtain the sampling sequence of wind turbine i at each sampling time (5.2) Establish a mapping relationship between wind speed and wind speed normalization value Through Perform the inverse transformation, Map out the wind speed prediction value sequence of wind turbine i at each sampling time (5.3) Using K-means algorithm Perform cluster reduction to obtain the four typical wind speed prediction values ​​of wind turbine i at the tth sampling time and its probability Finally, the typical wind speed value of wind turbine i at each sampling time is obtained and its probability (5.4) and The wind speed forecast result of wind turbine i at T sampling moments in the next cycle is obtained by weighted calculation in, is the predicted value of wind turbine i at the tth sampling time in the next cycle, 2. The wind speed prediction method based on the mixed binary Copula function according to claim 1, characterized in that: The method for selecting adjacent wind turbines is as follows: (2.1) Taking wind turbine i as the reference, calculate the distance between any wind turbine j and wind turbine i in the wind farm: Where i≠j, i,j∈[1,M], R is a constant coefficient; (2.2) Select the wind turbine closest to wind turbine i in the wind farm and record it as wind turbine j. The variable after normalizing the wind speed data of wind turbine j at each sampling time is recorded as (2.3) Traverse each wind turbine in the wind farm, and then process according to steps (2.1) and (2.2) to obtain the adjacent wind turbines of each wind turbine.

3. The wind speed prediction method based on the mixed binary Copula function according to claim 1, characterized in that: The method for constructing the optimal mixed binary Copula function of the adjacent wind turbine groups at different sampling times is: (3.1) Construct the basic binary Copula function of the wind speed of adjacent wind turbines at different sampling times; Gaussian Copula Function: Clayton Copula Function: Gumbel Copula Function: Frank Copula Function: T Copula function: Among them, s, t are integral variables, φ -1 (·) is the inverse function of the standard normal distribution function, is the inverse function of the univariate student distribution function with κ degrees of freedom, and They represent the parameters to be estimated in the basic binary Copula function at t sampling moments respectively; (3.2) Estimate the relevant parameters of each basic binary Copula function according to the maximum likelihood estimation method and (3.3) Calculate the evaluation index and select the basic binary Copula function to form the optimal mixed binary Copula function; (3.3.1) Sample each basic binary Copula function m times to obtain the sampling value sequence of each basic binary Copula function Among them, k = 1, 2, 3, 4, 5 represents the number of the basic binary Copula function, represents the mth sampling value of wind turbine i at the tth sampling time in the kth basic binary Copula function; (3.3.2) Substitute the sampling values ​​at different sampling times into the basic binary Copula function, substitute the normalized wind speed values ​​at different sampling times into the empirical Copula function, and then calculate the sum of squares of the Euclidean distances between the basic binary Copula function and the empirical Copula function of adjacent wind turbines at different sampling times; (3.3.3) Calculate the normalized wind speed values ​​of adjacent wind turbines at each sampling time and the sampled values ​​of each basic binary Copula function The correlation coefficient between in, and Sequence and The mean of Similarly, calculate the correlation coefficient of wind turbine j at each sampling time (3.3.4) Filter out the sum of squared Euclidean distances Less than 0.05*m and the correlation coefficient The basic binary Copula functions are all greater than 0.9 at the same time; then the selected basic binary Copula functions are combined into the optimal mixed binary Copula function; in, is the optimal mixed binary Copula function between wind turbines i and j at the tth sampling moment, ρ t Indicates the number of basic binary Copula functions screened at time t, and is the parameter to be estimated in the optimal mixed binary Copula function.

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