CN113536686B - Modeling method of probability model of wind speed - Google Patents

Modeling method of probability model of wind speed Download PDF

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CN113536686B
CN113536686B CN202110835160.8A CN202110835160A CN113536686B CN 113536686 B CN113536686 B CN 113536686B CN 202110835160 A CN202110835160 A CN 202110835160A CN 113536686 B CN113536686 B CN 113536686B
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wind speed
interval
frequency component
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frequency
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CN113536686A (en
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张家安
王军燕
王向伟
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Hebei Branch Of Huaneng New Energy Co ltd
Hebei University of Technology
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Hebei Branch Of Huaneng New Energy Co ltd
Hebei University of Technology
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Abstract

The invention relates to a modeling method of a probability model of wind speed, which comprises the following steps: obtaining a plurality of wind speed components with different frequencies, and then reconstructing the plurality of wind speed components into wind speed low-frequency components and wind speed high-frequency components; the modeling of the wind speed is divided into a low-frequency component model with strong regularity and a high-frequency component model with strong randomness, and the volatility and the randomness of the model are respectively considered during modeling, and the relation between the wind speed variation and the wind speed is quantitatively analyzed, so that the modeling precision can be effectively improved; a wind speed-variable quantity combined probability density model of the low-frequency wind speed component and a general description model of the high-frequency wind speed component are established. The method is particularly suitable for the situation of wind speed with strong uncertainty, and improves the accuracy of wind speed modeling.

Description

Modeling method of probability model of wind speed
Technical Field
The invention belongs to the field of wind power generation, and particularly relates to a novel modeling method of a wind speed probability model.
Background
Wind power generation is an important component of the energy structure in China at present, accurate wind energy prediction has important significance on safe and stable operation of a power system, and a power grid makes a scheduling plan and adjusts the frequency of the power grid according to a wind speed prediction result to ensure the stability of the power grid and the power supply quality; and the wind power plant adjusts the fans according to the wind speed prediction result to improve the power generation benefit.
The accurate establishment of the wind speed model is the basis of wind speed prediction, the wind speed has the characteristic of uncertainty, the modeling of the wind speed is difficult due to randomness and volatility of the wind speed, and in order to simplify the model and improve the accuracy of the model, the decomposed and reconstructed wind speed components can be respectively established into the model. For this purpose, decomposing and reconstructing the wind speed into a low-frequency component with a certain rule and a high-frequency component with strong randomness, and then respectively establishing models to describe the volatility and the randomness of the wind speed; modeling can be simplified, and model accuracy can be improved.
The conventional wind speed probability modeling method is to analyze and count a large amount of historical wind speed data and directly analyze the probability distribution of the historical wind speed data, and the accuracy and the integrity of the historical data influence the accuracy of wind speed modeling to a great extent.
Disclosure of Invention
The probability model provided by the invention represents the distribution situation of the wind speed variation along with the change of the wind speed.
The invention aims to provide a probability model of wind speed. The method comprises the steps of firstly decomposing a large amount of historical wind speed data to obtain a plurality of modal components, solving the frequency of each component by using Fast Fourier Transform (FFT), reconstructing the plurality of modal components of the wind speed into a high-frequency component and a low-frequency component of the wind speed according to the frequency from high to low, wherein the high-frequency component mainly reflects random factors in a wind speed time sequence and is poor in regularity, and the low-frequency component describes the basic trend of fluctuation and has certain regularity; then, the fluctuation characteristics of the wind speed are described by considering the relation between the wind speed variation and the wind speed according to the low-frequency component of the wind speed, and the probability density function of the wind speed variation is obtained by respectively fitting under the wind speed of each numerical value; and further quantifying the relation between the wind speed variable quantity and the wind speed, and establishing a wind speed-variable quantity combined probability density model. Aiming at the high-frequency component of the wind speed, a general description model is established based on a particle swarm algorithm.
In order to realize the purpose, the invention adopts the following technical scheme:
a method of modelling a probabilistic model of wind speed, the method comprising:
decomposing years of historical wind speed data of the wind power plant by applying a VMD algorithm to obtain a plurality of wind speed components with different frequencies, and reconstructing the plurality of wind speed components into a wind speed low-frequency component and a wind speed high-frequency component;
aiming at the low-frequency components of the wind speed, calculating the wind speed variation of two adjacent wind speed points in the time sequence of the wind speed to obtain the variation delta V of the wind speedt(ii) a Dividing the continuous wind speed low-frequency component data into multiple sections, recording the number of the divided sections as m, and taking the midpoint V of the section ast_jAs the interval wind speed value, then the variation quantity delta V is addedtSorting the interval wind speeds from small to large; respectively counting the number of wind speed change quantities under each interval of wind speed, generating a frequency distribution histogram of the wind speed change quantity, and then taking a point in a histogram to generate a frequency distribution broken line graph so as to obtain the frequency distribution histogram and the broken line graph of the wind speed change quantity; obtaining a distribution model of the variation under each interval wind speed through the frequency distribution histogram and the broken line graph, fitting a probability density function of the variation under each interval wind speed through the distribution model, and further obtaining the interval wind speed V from Vt_1To Vt_mGenerating a wind speed-variable quantity combined probability density three-dimensional graph;
the probability density function under each interval wind speed has parameter items, and a power function model is adopted to fit all parameters of the interval wind speed and the current probability density functionObtaining the trend of the power function curve of each parameter, and realizing the interval wind speed from V according to the probability density curve under the corresponding interval wind speedt_1To Vt_nExtrapolation of (2); further obtaining a generalized wind speed-variable combined probability density model, and expressing an expression of a generalized wind speed-variable combined probability density three-dimensional graph, namely a generalized wind speed-variable combined probability density function;
aiming at the high-frequency component of the wind speed, because the randomness is strong, the high-frequency component corresponding to the interval wind speed of each low-frequency component is found out, and the maximum value and the minimum value of the high-frequency component are counted; fitting the relation between the maximum value of the high-frequency component and the interval wind speed and the relation between the minimum value of the high-frequency component and the interval wind speed based on a particle swarm algorithm; then, establishing a general description model of the wind speed high-frequency component by using the two maximum values of the wind speed high-frequency component;
and constructing the generalized wind speed-variable quantity combined probability density model and the general description model of the wind speed high-frequency component to obtain a final wind speed model.
Further, parameters of the power function curve need to be optimized through a particle swarm algorithm, the optimized parameters are substituted into the generalized wind speed-variable quantity combined probability density model, and the optimized generalized wind speed-variable quantity combined probability density model is obtained; and when the optimized generalized wind speed-variable quantity combined probability density model exists, combining the optimized generalized wind speed-variable quantity combined probability density model and the general description model of the wind speed high-frequency component to serve as a final wind speed model.
Further, the distribution model approximately follows Gaussian distribution, so that probability density functions f under wind speeds in each interval are respectively fitted by adopting the Gaussian distributionjFurther, the interval wind speed V can be obtainedt_1To Vt_mA probability density curve within a range of (a);
probability density function f at each interval wind speedjCorresponding to a set of Gaussian parameters including a mean parameter
Figure GDA0003837007040000031
And standard deviation parameter
Figure GDA0003837007040000032
Using power function model to measure interval wind speed and mean value parameter
Figure GDA0003837007040000033
Interval wind speed and standard deviation parameter
Figure GDA0003837007040000034
Fitting to obtain corresponding function expression and mean value parameter
Figure GDA0003837007040000035
Standard deviation parameter
Figure GDA0003837007040000036
The trend of the power function curve of the wind speed sensor, and then the interval wind speed V is realized according to the probability density curve under the corresponding interval wind speedt_1To Vt_nExtrapolation of (2); and further obtaining a generalized wind speed-variable quantity combined probability density model.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the method, modeling of the wind speed is divided into a low-frequency component model with strong regularity and a high-frequency component model with strong randomness, and during modeling, volatility and randomness of the low-frequency component model and the high-frequency component model are respectively considered and the relation between the wind speed variable quantity and the wind speed is quantitatively analyzed, so that modeling accuracy can be effectively improved; a wind speed-variable quantity combined probability density model of the low-frequency wind speed component is established, the fluctuation characteristic of the wind speed can be described through the model, and a time sequence of the low-frequency wind speed component can be continuously generated; meanwhile, the method of the invention also establishes a general description model of the high-frequency components of the wind speed to reflect the random factors in the wind speed sequence.
(2) In the method, a power function model is adopted to describe each parameter (mean value parameter) in the wind speed and distribution model
Figure GDA0003837007040000037
Standard deviation parameter
Figure GDA0003837007040000038
) And the extrapolation of the data volume is realized. Compared with the existing general extrapolation methods (a linear extrapolation method, an exponential curve method and a growth curve method), the power function can more accurately describe the function relation of the curve and improve the extrapolation precision.
(3) And a particle swarm optimization algorithm is adopted to optimize the power function curve of the parameters obtained by the power function model fitting, so that the precision is further improved.
(4) The method is particularly suitable for the situation of wind speed with strong uncertainty, has strong adaptability, is suitable for extrapolation of wind speed occasions, and improves the accuracy of wind speed modeling.
Drawings
FIG. 1 VMD decomposed wind speed component vIMFAnd the frequency obtained by Fourier transform, wherein the left graph is the wind speed component, and the right graph is the frequency.
FIG. 2 illustrates the low frequency components and high frequency components of wind speed obtained by decomposing the original wind speed, wherein the top is the original wind speed, the middle is the low frequency components of wind speed, and the bottom is the high frequency components of wind speed.
FIG. 3 is a partial variation frequency distribution histogram and a frequency distribution broken line diagram, wherein the partial variation frequency distribution histogram and the frequency distribution broken line diagram correspond to the interval wind speed V from top to bottom respectivelytFrequency distribution histograms and frequency distribution broken lines of 3.5m/s, 6m/s and 11.5m/s, wherein the horizontal axis represents wind speed variation, the vertical axis represents frequency, and the broken line in the graph represents frequency distribution broken line.
FIG. 4 is a three-dimensional (Gaussian distribution) plot of wind speed-variance joint probability density for low frequency components of wind speed.
FIG. 5 is a scattergram of the relationship between the mean parameter and the standard deviation parameter of the Gaussian distribution and the wind speed of the interval, wherein the upper graph is the scattergram of the mean parameter, and the lower graph is the scattergram of the standard deviation parameter.
Fig. 6 is a fitting curve obtained by performing particle swarm optimization on the two parameters in fig. 5 by using a power function model.
FIG. 7 is a schematic flow chart of a wind speed modeling method according to the present invention.
FIG. 8 is a flow chart of a particle swarm optimization algorithm in the present invention.
Detailed Description
The present invention is further explained with reference to the following examples and drawings, but the scope of the present invention is not limited thereto.
The invention provides a modeling method of a wind speed probability model (see fig. 7), which comprises the following steps:
the method comprises the following steps: the method comprises the steps of decomposing two-year historical wind speed data (the general acquisition period is 10-15 min) of a wind power plant into a plurality of wind speed components v with different frequencies by applying a VMD algorithmIMFAs shown in formula (1);
v＝vIMF1+vIMF2+vIMF3...+vIMFn (1)
in the formula (1), n is the number of wind speed components, n is not less than 3, and the number of the wind speed components can be set according to different wind conditions.
Step two: respectively calculating the wind speed components v decomposed in the step one by using Fast Fourier Transform (FFT)IMFThe wind speed components are accumulated from high to low according to the frequency, the wind speed components v decomposed in the step one are subjected to normal distribution as a criterion, and the wind speed components v are obtainedIMFThe wind speed low-frequency component and the completely random wind speed high-frequency component are reconstructed to be two parts with a certain rule, and the volatility and the randomness of the wind speed are respectively reflected.
Figure GDA0003837007040000041
ω＝max_Y-1(ω) (3)
In the formula, Y (ω) is an image function of Y (t), Y (t) is an image primitive function of Y (ω), Y (t) represents a time series of wind speeds, ω =2 π f, f is a center frequency of a wind speed component, and ω is a center angular frequency of the wind speed component.
A t test with a confidence level alpha is performed on the mathematical expectation of the high-frequency component of the wind speed by using the central limit theorem, and an x test with a confidence level alpha is performed on the variance of the high-frequency component of the wind speed2And the detection can more accurately ensure that the extraction of high-frequency components is satisfied. Sequentially accumulating the wind speed components according to frequency, and utilizing the t test sum chi of normal distribution after accumulating one wind speed component each time2Checking outThe group closest to the normal distribution is the high-frequency component of the wind speed, and the rest of the sum is the low-frequency component of the wind speed:
v＝Vt+Vf (4)
in the formula (4), V is the wind speed, VtIs a low-frequency component of wind speed, VfIs a high frequency component of wind speed.
Step three: establishing a wind speed-variable quantity combined density model:
the low-frequency components of wind speed are processed as follows
1 respectively calculating the wind speed variation delta V between two adjacent wind speeds in the time sequence of the low-frequency components of the wind speedst：ΔVt_i＝Vt_i+1-Vt_i(I =1,2 \ 8230l, I), I being the total data volume of wind speed;
2 dividing the continuous wind speed value into m sections according to the low-frequency wind speed component, taking the wind speed value of which the middle point represents the section, and recording as the section wind speed, namely Vt_j＝0.5[0.25,0.75],1[0.75,1.25],1.5[1.25,1.75]"\8230; (j =1,2 \8230; m), in m/s, where 0.5, 0.25,0.75]Indicates that the wind speed interval is [0.25,0.75 ]]The interval wind speed value of (2) is 0.5m/s;
3 with a variation Δ VtSorting the interval wind speeds from small to large;
4, respectively counting the number of wind speed change quantities in wind speeds of corresponding intervals of different wind speed intervals, and generating a wind speed change quantity frequency distribution histogram and a frequency distribution broken line graph;
5 obtaining a wind speed variation frequency distribution histogram and a frequency distribution broken line diagram from the wind speed variation frequency distribution histogram and the frequency distribution broken line diagram;
6 selecting a certain distribution model to fit the probability density curve f of the variation under the wind speed of each interval according to the shapes of the frequency distribution histogram and the frequency distribution broken line graphjJ =1,2,3 \8230 \8230m, where the horizontal axis of the probability density curve is the value of variation and the vertical axis is the probability density, and the interval wind speed is obtained from Vt_1To Vt_mA probability density function within a range of (a).
7 selecting different distribution models corresponding to parameters of a group of distribution models at each interval of wind speed, wherein the parameters are different, for exampleIf the distribution model is Gaussian distribution, the parameters of the Gaussian distribution are mean parameters respectively
Figure GDA0003837007040000051
And standard deviation parameter
Figure GDA0003837007040000052
And respectively fitting the two parameters of the interval wind speed and the distribution model by adopting a power function model to obtain corresponding function expressions.
Figure GDA0003837007040000061
(x>0 and x ≠ 1) (5)
Equation (5) is an expression of a power function model; wherein g (x) is a dependent variable, x is an independent variable (interval wind speed), cq、kqThe method is characterized in that the parameters of the model are q =0,1, 2\8230, N and N are the number of power functions in the power function model, p =1,2 \8230, M and M are the number of the parameters in the selected distribution model.
And (3) fitting the interval wind speed and the parameters of the distribution model by the power function model of the formula (5) to obtain a corresponding function expression when the wind speed is not 1.
When x =1, obtaining parameters of a distribution model under the condition of actual wind speed by using a large amount of historical data, wherein the corresponding expression is as follows:
gp(x)＝ap(x＝1) (6)
in the formula, apIs constant, p =1,2 \8230, 8230M is the number of parameters in the selected distribution model, apThe values of (c) vary with different wind conditions and with parameters in different distribution models.
According to the change condition of the low-frequency wind speed component, a Gaussian distribution model is selected to fit a probability density curve of the variable quantity in each interval of wind speed, and the wind speed-variable quantity combined probability density model of the low-frequency wind speed component is obtained through the following processing:
Figure GDA0003837007040000062
(0m/s≤Vtnot more than 18m/s and Vt≠1) (7)
Figure GDA0003837007040000063
In the formula, a1 and a2 are constants and are calculated from actual wind conditions, c1, c2, k1 and k2 are parameters of a power function curve expression, and delta VtIs the variation of the wind speed.
Step four: optimization of wind speed-variable quantity combined density model of wind speed low-frequency component
Parameters c1, c2, k1 and k2 in the formula (7) are optimized by using a particle swarm optimization, and a fitness function E is as follows:
Figure GDA0003837007040000064
in the formula, wrIn order to be the weight, the weight is,
Figure GDA0003837007040000071
corresponding to the r-th particle
Figure GDA0003837007040000072
Or
Figure GDA0003837007040000073
Predicted value of (a), yrCorresponds to the r-th particle
Figure GDA0003837007040000074
Or
Figure GDA0003837007040000075
N is the population number.
The flow chart of the particle swarm algorithm is shown in fig. 8.
When V istWhen the average value is not equal to 1, obtaining optimized interval wind speed and average value parameters through a particle swarm algorithm
Figure GDA0003837007040000076
Interval wind speed parameter and standard deviation parameterNumber of
Figure GDA0003837007040000077
Fitting to obtain a corresponding power function expression:
Figure GDA0003837007040000078
in the formula, c1 'and c2' are parameters in the power function expression optimized by the particle swarm, respectively.
When V istWhen =1, the parameter value can be directly obtained from historical data of wind speed:
Figure GDA0003837007040000079
in the above formula, a1 and a2 are both constants,
Figure GDA00038370070400000710
respectively representing low-frequency components of wind speed as VtGaussian mean and standard deviation parameters.
And the extrapolation method of the power function is utilized to realize the extrapolation of the data quantity by the power function expression of the formula (10), namely the range of the wind speed in the interval V can be obtainedt_1To Vt_nMean and standard deviation parameters of.
Further, a generalized wind speed-variable combined probability density model of the low-frequency wind speed component can be obtained:
Figure GDA00038370070400000711
(0m/s≤Vtv is less than or equal to 34m/st≠1) (12)
Figure GDA00038370070400000712
Step five: establishing a general description model of the high-frequency components of the wind speed:
1 Low frequency component v after VMD decomposition obtainable from equation (4)tAnd a high frequency component vf；
2 dividing the continuous wind speed value into m sections according to the low frequency component of the wind speed, taking the wind speed value of which the middle point represents the section and recording as the section wind speed, namely Vt_j＝0.5[0.25,0.75],1[0.75,1.25],1.5[1.25,1.75]\8230; (j =1,2 \8230m) in m/s, where 0.5[ 2 ], [0.25,0.75]Indicates that the wind speed interval is [0.25,0.75 ]]The wind speed value of (2) is recorded as 0.5m/s;
3 with high-frequency component VfSorting the interval wind speeds from small to large;
4, counting the maximum and minimum values of the high-frequency components of the wind speed at each interval, and fitting based on a particle swarm algorithm to obtain the functional relationship between the maximum value of the high-frequency components of the wind speed and the interval wind speed;
Figure GDA0003837007040000081
in the formula, Vf_minIs the minimum value of the high frequency component of the wind speed, Vf_maxIs the maximum value of the high frequency component of the wind speed, h1(Vt)、h2(Vt) Is expressed as a variable VtIs measured as a function of (c).
5, converting the wind speed high-frequency component V under each interval wind speedfIs unified to [0,1 ]]；
Figure GDA0003837007040000082
Remember h3(Vt)＝Vf_max-Vf_min，
Figure GDA0003837007040000083
Since these two values are functions of Vt, the low frequency component of the wind speed is of a certain magnitude h3(Vt)、h4(Vt) If the value is constant, equation (15) can be rewritten as:
Figure GDA0003837007040000084
wherein the content of the first and second substances,
Figure GDA0003837007040000085
is the wind speed high-frequency component after per unit.
Equation (16) is a general description model of the high frequency components of the wind speed.
Example 1
The embodiment is a wind speed probability model:
the method comprises the following steps: the historical wind speed data (the general acquisition period is 10 min-15 min) of the wind power plant for two years is decomposed into 11 wind speed components v with different frequencies by applying a VMD algorithmIMFAs shown in formula (1);
v＝vIMF1+vIMF2+vIMF3...+vIMF11 (1)
in the formula (1), n is the number of wind speed components, n is not less than 3, and the number of the wind speed components can be set according to different wind conditions.
Step two: respectively calculating the wind speed components v decomposed in the step one by using Fast Fourier Transform (FFT)IMFThe wind speed components are accumulated from high to low according to the frequency, the wind speed components v decomposed in the step one are subjected to normal distribution as a criterion, and the wind speed components v are obtainedIMFThe wind speed is reconstructed into a wind speed low-frequency component with a certain rule and a completely random wind speed high-frequency component, and the volatility and the randomness of the wind speed are respectively reflected.
Figure GDA0003837007040000091
ω＝max_Y-1(ω) (3)
In the formula, Y (ω) is an image function of Y (t), Y (t) is an image primitive function of Y (ω), Y (t) represents a time series of wind speeds, ω =2 π f, f is the center frequency of the wind speed component.
A t-test with a confidence level alpha is performed on the mathematical expectation of the high frequency component of the wind speed by using the central limit theorem, and a chi-test with a confidence level alpha is performed on the variance of the high frequency component of the wind speed2Checking to ensure the fluctuation quantity extraction. Sequentially accumulating the wind speed components according to frequency, and utilizing the t test sum chi of normal distribution after accumulating one wind speed component each time2And (3) one group which is found out by the test and is closest to the normal distribution is the high-frequency component of the wind speed, and the rest sum is the low-frequency component of the wind speed:
v＝Vt+Vf (4)
in the formula (4), V is the wind speed, VtIs a low-frequency component of wind speed, VfIs a high frequency component of wind speed.
Step three: the low frequency components of wind speed are processed as follows
1 calculating the wind speed variation delta V between two adjacent wind speeds in the time sequence of the low-frequency wind speed componentst：ΔVt_i＝vt_i+1-vt_i(I =1,2 \ 8230l, I), I being the total data volume of wind speed;
2 dividing the continuous wind speed value into m sections according to the low-frequency component of the wind speed, and taking the midpoint of the section to represent the wind speed value of the section, namely Vt_j＝0.5[0.25,0.75],1[0.75,1.25],1.5[1.25,1.75]\8230; (j =1,2 \8230m) in m/s, where 0.5[ 2 ], [0.25,0.75]Representing a wind speed interval of [0.25,0.75]The wind speed value of (2) is 0.5m/s;
3 when Vt_j＝0.5[0.25,0.75],[0.75,1.25]8230shows a variation Δ VtSorting the wind speed trend quantity from small to large;
4, respectively counting the number of wind speed change quantities in wind speeds of corresponding intervals of different wind speed intervals, and generating a wind speed change quantity frequency distribution histogram and a frequency distribution broken line graph;
5, obtaining a wind speed variation frequency distribution histogram and a frequency distribution broken line diagram from the wind speed variation frequency distribution histogram and the frequency distribution broken line diagram;
6 according to the frequency distribution histogram and the frequency distribution broken line graph, gaussian distribution is selected to fit the probability density curve f of the variation under the wind speed of each intervaljJ =1,2,3 \ 8230a \ 8230m, wherein the horizontal axis of the probability density curve is the value of the variation, the vertical axis is the probability density, and the interval wind speed is obtained from Vt_1To Vt_mA probability density function within a range of (a).
And 7, corresponding to a group of Gaussian parameters under each interval wind speed, namely a mean parameter mu and a standard deviation parameter sigma, and fitting the interval wind speed and the mean parameter mu and the interval wind speed and the standard deviation parameter sigma by adopting a power function to obtain corresponding function expressions.
Figure GDA0003837007040000101
(x>0 and x ≠ 1) (5)
Equation (5) is an expression of a power function model; wherein g (x) is a dependent variable, x is an independent variable (interval wind speed), cq、kqThe method is characterized in that q =0,1, 2\8230, N and p =1,2 \8230, M and M are parameters of the selected model, and N and p =1,2 \8230areparameters of the model.
The interval wind speed and the mean value parameter are paired by the model of the formula (5)
Figure GDA00038370070400001016
Interval wind speed and standard deviation parameter
Figure GDA0003837007040000102
Fitting to obtain a corresponding function expression when the wind speed is not 1, wherein the function expression is as follows:
Figure GDA0003837007040000103
(0m/s≤Vtnot more than 18m/s and Vt≠1) (17)
When V istWhen the wind speed is not less than 1, the mean value parameter under the condition of actual wind speed is obtained by using a large amount of historical data
Figure GDA0003837007040000104
Sum standard deviation parameter
Figure GDA0003837007040000105
The corresponding expression is:
Figure GDA0003837007040000106
obtaining a wind speed-variable quantity combined probability density model of the low-frequency wind speed component through the processing:
Figure GDA0003837007040000107
(0m/s≤Vtnot more than 18m/s and Vt≠1) (19)
Figure GDA0003837007040000108
Step four: optimization of wind speed-variation combined probability density model
And (3) optimizing the parameters in the formula (6) by utilizing a particle swarm algorithm, wherein the fitness function is as follows:
Figure GDA0003837007040000109
in the formula, wrIn order to be the weight, the weight is,
Figure GDA00038370070400001010
for the r-th particle
Figure GDA00038370070400001011
Or
Figure GDA00038370070400001012
Predicted value of (a), yrCorresponds to the r-th particle
Figure GDA00038370070400001013
Or
Figure GDA00038370070400001014
N is the population number.
Obtaining optimized interval wind speed and mean value parameters through particle swarm optimization
Figure GDA00038370070400001015
Interval wind speed and standard deviation parameter
Figure GDA0003837007040000111
Fitting to obtain a corresponding functional expression:
Figure GDA0003837007040000112
(0m/s≤Vtv is less than or equal to 34m/st≠1) (21)
When V istIf =1, the functional expression is unchanged and remains as the expression (18).
And the extrapolation of the data quantity is realized by the power function expression of the formula (21) by using a power function extrapolation method, so that the interval wind speed range in V can be obtainedt_1To Vt_nMean and standard deviation parameters of.
Further, a generalized wind speed-variable combined probability density model of the low-frequency wind speed component can be obtained:
Figure GDA0003837007040000113
(0m/s≤Vtv is less than or equal to 34m/st≠1) (22)
Figure GDA0003837007040000114
Step five: establishing a general description model of the high-frequency components of the wind speed:
1 Low frequency component v after VMD decomposition obtainable from equation (4)tAnd a high frequency component vf；
2 dividing the continuous wind speed value into m sections according to the low-frequency wind speed component, taking the wind speed value of which the middle point represents the section, and recording as the section wind speed, namely Vt_j＝0.5[0.25,0.75],1[0.75,1.25],1.5[1.25,1.75]"\8230; (j =1,2 \8230; m), in m/s, where 0.5, 0.25,0.75]Indicates that the wind speed interval is [0.25,0.75 ]]The wind speed value of (2) is recorded as 0.5m/s;
3 when Vt_j＝0.5[0.25,0.75],[0.75,1.25]82300 deg.C, with high-frequency component VfSorting the interval wind speeds from small to large;
4, counting the maximum and minimum values of the wind speed fluctuation amount under each interval wind speed, and fitting based on a particle swarm algorithm to obtain the functional relation between the maximum value of the wind speed fluctuation amount and the interval wind speed;
selecting a power function to describe the functional relation according to the relation between the interval wind speed and the fluctuation amount, and optimizing by utilizing a particle swarm algorithm;
Figure GDA0003837007040000115
Figure GDA0003837007040000121
in the formula, Vf_minIs the minimum value of the high frequency component of the wind speed, Vf_maxIs the maximum of the high frequency components of the wind speed.
5, converting the wind speed high-frequency component V under each interval wind speedfIs unified to [0,1 ]]；
Figure GDA0003837007040000122
Remember h3(Vt)＝Vf_max-Vf_min，
Figure GDA0003837007040000123
When the size of the low-frequency component of the wind speed is determined h3(Vt)、h4(Vt) If the value is constant, equation (13) can be rewritten as:
Figure GDA0003837007040000124
wherein the content of the first and second substances,
Figure GDA0003837007040000125
equation (16) is a general description model of the high frequency components of the wind speed.
Nothing in this specification is said to apply to the prior art.

Claims (6)

1. A method of modelling a probabilistic model of wind speed, the method comprising:
decomposing years of historical wind speed data of a wind power plant to obtain a plurality of wind speed components with different frequencies, and reconstructing the plurality of wind speed components into a wind speed low-frequency component and a wind speed high-frequency component;
aiming at the low-frequency components of the wind speed, calculating the wind speed variation of two adjacent wind speed points in the time sequence of the wind speed to obtain the variation delta V of the wind speedt(ii) a Dividing the data of the continuous wind speed low-frequency components into multiple sections, wherein the number of the divided sections is marked as m, and the midpoint V of each section is usedt_jAs the interval wind speed value, then with the variation Δ VtSequencing the interval wind speeds from small to large; respectively counting the number of wind speed change quantities under each interval of wind speed, generating a frequency distribution histogram of the wind speed change quantity, and then taking a point in a histogram to generate a frequency distribution broken line graph so as to obtain the frequency distribution histogram and the broken line graph of the wind speed change quantity; obtaining a distribution model of the variation under each interval wind speed through the frequency distribution histogram and the broken line graph, fitting a probability density function of the variation under each interval wind speed through the distribution model, and further obtaining the interval wind speed V from Vt_1To Vt_mObtaining a wind speed-variation combined density model by using the probability density curve of the variation in the range of (1);
the probability density function under each interval wind speed has parameter items, each parameter of the interval wind speed and the current probability density function is subjected to function fitting to obtain the trend of the function curve of each parameter, and the interval wind speed is realized from V according to the probability density curve under the corresponding interval wind speedt_1To Vt_nThe generalized wind speed-variable quantity combined probability density model is obtained through extrapolation;
aiming at the high-frequency component of the wind speed, finding out the corresponding high-frequency component of the wind speed in the interval of the low-frequency component of each wind speed, and counting the maximum value and the minimum value of the high-frequency component; fitting the relation between the maximum value of the high-frequency component and the interval wind speed and the relation between the minimum value of the high-frequency component and the interval wind speed based on a particle swarm algorithm; and then establishing a universal description model of the high-frequency wind speed component by using the two maximum values of the high-frequency wind speed component.
2. The modeling method according to claim 1, wherein a power function model is adopted to fit each parameter of the interval wind speed and the current probability density function to obtain the trend of a power function curve of each parameter; parameters of the power function curve need to be optimized through a particle swarm algorithm, and the optimized parameters are substituted into the generalized wind speed-variable quantity combined probability density model to obtain the optimized generalized wind speed-variable quantity combined probability density model; and when the optimized generalized wind speed-variable quantity combined probability density model exists, combining the optimized generalized wind speed-variable quantity combined probability density model and the general description model of the wind speed high-frequency component to serve as a final wind speed model.
3. The modeling method of claim 2, wherein the distribution model approximately follows a gaussian distribution, and the probability density function f at each interval wind speed is fitted with the gaussian distribution respectivelyjFurther obtaining the interval wind speed Vt_1To Vt_mA probability density curve within a range of (a);
probability density function f at each interval wind speedjCorresponding to a set of Gaussian parameters including a mean parameter
Figure FDA0003842203590000021
Sum standard deviation parameter
Figure FDA0003842203590000022
Using power function model to measure interval wind speed and mean value parameters
Figure FDA0003842203590000023
Interval wind speed and standard deviation parameter
Figure FDA0003842203590000024
Fitting to obtain corresponding function expression and mean value parameter
Figure FDA0003842203590000025
Standard deviation parameter
Figure FDA0003842203590000026
According to the probability density curve under the corresponding interval wind speed, the interval wind speed is Vt_1To Vt_nAnd (4) extrapolating to obtain a generalized wind speed-variable quantity combined probability density model.
4. A modeling method according to claim 1, characterized in that the process of wind speed component reconstruction is: wind speed decomposition is carried out by applying a VMD algorithm, and a decomposed wind speed component v is obtained by utilizing fast Fourier transformIMFUsing the central limit theorem to perform a t test with a confidence level alpha on the mathematical expectation of the high-frequency component of the wind speed, and to perform a chi test with a confidence level alpha on the variance of the high-frequency component of the wind speed2Checking, accumulating wind speed components from high to low according to frequency, accumulating one wind speed component each time, and utilizing t-check sum chi of normal distribution2And (3) testing and finding out a group which is closest to normal distribution as a high-frequency component of the wind speed, and the sum of the rest parts is a low-frequency component of the wind speed:
v＝Vt+Vf (4)
in the formula (4), V is the wind speed, VtIs a low-frequency component of wind speed, VfIs the high frequency component of the wind speed.
5. A modeling method according to claim 3, wherein the wind speed-delta joint density model is:
Figure FDA0003842203590000027
Figure FDA0003842203590000028
in the formula, a1 and a2 are constants and are calculated from actual wind conditions, c1, c2, k1 and k2 are parameters of a power function curve expression, and delta VtIs the variation of the wind speed.
6. The modeling method of claim 1, wherein the generic description model is built by:
after the low-frequency component and the high-frequency component of the wind speed are determined, the continuous wind speed value is divided into m sections according to the low-frequency component of the wind speed, the wind speed value of the section represented by the middle point of the section is taken and recorded as the section wind speed, namely Vt_j＝0.5[0.25,0.75],1[0.75,1.25],1.5[1.25,1.75]\8230hasunit of m/s, wherein 0.5[0.25 ] 0.75]Indicates that the wind speed interval is [0.25,0.75 ]]The wind speed value of (1) is recorded as 0.5m/s, j =1,2 \8230m;
with high-frequency components VfSorting the interval wind speeds from small to large;
counting the maximum and minimum values of the high-frequency components of the wind speed at each interval of wind speed, and fitting based on a particle swarm algorithm to obtain the function relationship between the maximum value of the high-frequency components of the wind speed and the interval of wind speed;
Figure FDA0003842203590000031
in the formula, Vf_minIs the minimum value of the high frequency component of the wind speed, Vf_maxIs the maximum value of the high frequency component of the wind speed, h1(Vt)、h2(Vt) Is expressed as a variable VtA function of (a);
the wind speed high-frequency component V under each interval wind speed is measuredfIs unified to [0,1 ]]；
Figure FDA0003842203590000032
Note the book
Figure FDA0003842203590000033
Since these two values relate to low frequenciesComponent VtH when the magnitude of the low-frequency component of the wind speed is determined3(Vt)、h4(Vt) If the value is constant, equation (15) is rewritten as:
Figure FDA0003842203590000034
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003842203590000035
is the wind speed high-frequency component after per unit;
equation (16) is a general description model of the high frequency component of the wind speed.
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