CN113312739B - Correlation wind speed generation method based on mixed semi-cloud model - Google Patents

Correlation wind speed generation method based on mixed semi-cloud model Download PDF

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CN113312739B
CN113312739B CN202010122779.XA CN202010122779A CN113312739B CN 113312739 B CN113312739 B CN 113312739B CN 202010122779 A CN202010122779 A CN 202010122779A CN 113312739 B CN113312739 B CN 113312739B
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蒋海峰
张曼
王宝华
王冰冰
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Abstract

The invention discloses a correlation wind speed generation method based on a hybrid semi-cloud model, which comprises the following steps: respectively constructing wind speed mixed semi-cloud models of a plurality of wind power plants based on historical wind speed data; calculating a correlation coefficient matrix and a covariance matrix of wind speeds among a plurality of wind fields based on historical wind speed data, and decomposing the covariance matrix to obtain a lower triangular matrix; respectively sampling wind power plants, generating wind speed cloud droplets with multidimensional and uncorrelated characteristics based on a mixed semi-cloud model of each wind field, subtracting a wind speed average value and dividing by a wind speed variance to obtain a sampled data column vector; and obtaining a group of wind speed vectors with associated characteristics through matrix transformation. According to the method, the mixed semi-cloud model and the correlation matrix method are combined, and the requirement that the wind speed is subjected to normal distribution by the correlation matrix method is considered, so that the generated correlation wind speed is closer to the real data.

Description

Correlation wind speed generation method based on mixed semi-cloud model
Technical Field
The invention belongs to the technical field of wind power plants, and particularly relates to a correlation wind speed generation method based on a hybrid semi-cloud model.
Background
Wind energy has strong randomness and fluctuation, and for a single wind field, model descriptions such as two-parameter Weibull distribution, normal distribution, rayleigh distribution and the like are commonly used for wind speed distribution. For a plurality of wind power plants with similar geographical positions, the wind speeds have strong correlation, and the force output of each wind power plant also has obvious regional correlation.
The correlation matrix method is a conventional method of generating a correlation wind speed, but the correlation matrix method is applicable only to a normal distribution. When a multidimensional wind speed random variable with correlation is generated conventionally, the wind speed distribution is assumed to obey normal distribution, matrix transformation is carried out by random sampling, or a Weibull distribution model is used for a correlation matrix method, and the wind speed obeying Weibull probability distribution is generated based on Monte Carlo. However, the correlation matrix method is used for generating the non-normally distributed correlation wind speed samples, and the correlation matrix method has a large error with real data, so that the obtained reliability analysis result deviates from the actual situation.
Disclosure of Invention
The invention aims to provide a correlation wind speed generation method based on a mixed semi-cloud model, which considers the requirement that a correlation matrix method is subject to normal distribution on wind speed and overcomes the defect that a traditional method generates a wind speed sample.
The technical solution for realizing the purpose of the invention is as follows: a correlation wind speed generation method based on a hybrid semi-cloud model comprises the following steps:
step 1, respectively constructing a mixed semi-cloud model of a plurality of wind power plants based on historical wind speed data;
step 2, calculating a correlation coefficient matrix and a covariance matrix of wind speeds among a plurality of wind fields based on historical wind speed data, and decomposing the covariance matrix to obtain a lower triangular matrix;
step 3, respectively sampling the wind power plants, generating multi-dimensional wind speed cloud droplets without correlation characteristics based on the mixed semi-cloud model of each wind field, subtracting a wind speed average value and dividing by a wind speed variance to obtain a sampled data column vector;
and 4, obtaining a group of wind speed vectors with correlation characteristics through matrix transformation.
Compared with the prior art, the invention has the remarkable advantages that: on the basis of generating the correlation wind speed by the traditional correlation matrix method, the requirements of the correlation matrix method on a wind speed probability distribution model are considered, a mixed semi-cloud model is introduced, the wind speed probability distribution is divided into two semi-normal distribution models, the requirements of the correlation matrix method are met, errors caused by the models are reduced in the correlation wind speed generation process, and the generated correlation wind speed is closer to real data.
Drawings
FIG. 1 is a flow chart of a correlation wind speed generation method based on a hybrid semi-cloud model.
FIG. 2 is a wind speed probability distribution diagram of the wind farm in embodiment A.
FIG. 3 is a wind speed probability distribution diagram of the wind farm in the embodiment B.
Detailed Description
The invention provides a correlation wind speed generation method based on a mixed semi-cloud model, aiming at the requirement that the wind speed probability distribution is required to be subjected to normal distribution when a traditional correlation matrix method generates correlation wind speed, the mixed semi-cloud model is introduced, the wind speed probability distribution is divided into two intervals which are subjected to the normal distribution, the wind speed sampling is carried out on the semi-normal cloud model, the matrix conversion is carried out, and the wind speed with the correlation is generated; the method comprises the following specific steps:
step 1, respectively constructing a mixed semi-cloud model of a plurality of wind power plants based on historical wind speed data;
step 2, calculating a correlation coefficient matrix and a covariance matrix of wind speeds among a plurality of wind fields based on historical wind speed data, and decomposing the covariance matrix to obtain a lower triangular matrix;
step 3, respectively sampling the wind power plants, generating multi-dimensional wind speed cloud droplets without correlation characteristics based on the mixed semi-cloud model of each wind field, subtracting a wind speed average value and dividing by a wind speed variance to obtain a sampled data column vector;
and 4, obtaining a group of wind speed vectors with correlation characteristics through matrix transformation.
Further, the step 1 of respectively constructing the hybrid semi-cloud models of the plurality of wind power plants based on the historical wind speed data includes the steps of partitioning and standardizing the irregularly distributed wind speed samples and solving cloud parameters, and specifically includes the following steps:
step 1-1, obtaining probability density distribution of each wind speed interval according to historical wind speed, and distributing peak load P according to probability max Dividing the wind speed probability distribution into a left half area V and a right half area V L And V R And wind speed left half area: v L ＝{v l |v≤V pmax V ∈ V }, right half of wind speed: v R ＝{v r |v＞V pmax And V belongs to V, and a symmetrical mapping sample of two half areas is constructed, wherein the left half area of the wind speed is symmetrically mapped: v L ′＝{v′ l |v′ l ＝2V pmax -v l ，v l ∈V L And symmetrically mapping a right half area of the wind speed: v R ′＝{v′ r |v＇ r ＝2V pmax -v r ，v r ∈V R }
Integrating each half-area sample with the symmetrical mapping sample to obtain a left half-area sample and a right half-area sample with symmetry;
V l ＝V L ∪V L V r ＝V R ∪V R
step 1-2, carrying out standardization processing on the wind speed probability distribution to obtain a sample conforming to normal distribution;
V left ＝{x′ l |x′ l ＝[x l -E(V l )/δ(V l )]，x l ∈V l }
V right ＝{x＇ r |x＇ r ＝[x r -E(V r )/δ(V r )]，x r ∈V r }
in the formula, E (V) l ) And E (V) r ) Respectively the expectations of the left and right halves of the area sample; delta (V) l ) And δ (V) r ) The standard deviations of the samples in the left and right halves are shown.
Step 1-3, a reverse cloud generator is used for solving the characteristic parameter E of the probability density distribution of the wind speed sample after each half area is standardized xL 、E nL 、H eL 、E xR 、E nR 、H eR ：
Wind speed sample expectation:
Figure BDA0002393492080000031
sample second order center distance:
Figure BDA0002393492080000032
sample fourth-order center distance:
Figure BDA0002393492080000033
entropy:
Figure BDA0002393492080000034
super entropy:
Figure BDA0002393492080000035
/>
further, in step 2, a correlation coefficient matrix and a covariance matrix of wind speeds among a plurality of wind farms are calculated based on historical wind speed data, and the covariance matrix is decomposed to obtain a lower triangular matrix, wherein the specific calculation formula is as follows:
the calculation formula for calculating the correlation coefficient of the wind speeds among the plurality of wind fields based on the historical wind speed data is as follows:
Figure BDA0002393492080000036
in the formula: e (v) i )、E(v j ) Is the wind speed v i 、v j Desired wind speed; var (v) i )、var(v j ) Is the wind speed v i 、v j The variance of the wind speed of (2); e (v) i v j ) Is the wind speed v i 、v j Product expectation.
The correlation coefficient matrix is:
Figure BDA0002393492080000041
in the formula: and n is the number of wind power plants.
The covariance matrix is:
Figure BDA0002393492080000042
in the formula: sigma 1 ，σ 2 ，…，σ n Is the standard deviation of wind speed distribution probability of 1,2, \ 8230;, n.
The lower triangular matrix L is obtained by decomposing the covariance matrix C: c = LL T 。
Further, the wind power plants are respectively sampled in the step 3, and wind speed cloud droplets with multidimensional and uncorrelated characteristics are generated on the basis of the mixed semi-cloud models of the wind power plants, and the steps are as follows:
step 3-1, randomly generating a sample by using a forward cloud generator, firstly generating the sample by E n In the interest of expectation,
Figure BDA0002393492080000043
normal random entropy E 'of variance' n (ii) a Is then randomly generated with E x Is desired to>
Figure BDA0002393492080000044
Is a normal random sample x 'of variance' i ；
Step 3-2, carrying out inverse standardization treatment on the generated wind speed cloud droplets,
x i ＝x＇ i ×δ(V l )+E(V l )orx i ＝x＇ i ×δ(V r )+E(V r )
in the formula, delta (V) l ) And δ (V) r ) Left and right half-area variances, E (V), with symmetry for the wind speed sample V l ) And E (V) r ) The left and right half-zone expectation values of the wind speed sample v with symmetry.
Wind speed cloud droplets x of the wind field are obtained after the wind speeds of all the half areas are subjected to inverse standardization i Subtract the average value of wind speed E (v) i ) And divided by the variance of wind speed var (v) i ) Obtaining the sampled data
Figure BDA0002393492080000045
Sampled data column vector z = [ z ] 1 ，z 2 …，z n ] T 。
Further, in step 4, a group of wind speed vectors with correlation characteristics are obtained through matrix transformation, and a formula is calculated:
v＝Lz+E
in the formula: e is the expected vector of the wind field, E = [ E (v) 1 )，…，E(v n )] T . v is a multi-dimensional wind velocity vector with correlation
The technical solution of the present invention will be described in detail with reference to the accompanying drawings and examples.
Examples
As shown in fig. 1, the invention provides a correlation wind speed generation method based on a hybrid semi-cloud model, comprising the following steps:
step 1, respectively constructing a mixed semi-cloud model of a plurality of wind power plants based on historical wind speed data;
taking historical wind speed data of A and B wind power plants in Huaian places as an example, obtaining probability density distribution of each wind speed interval according to historical wind speeds, wherein the wind speed of the A wind power plantThe probability distribution diagram is shown in FIG. 2, wherein A is the wind speed probability distribution peak load P of the wind power plant maxA =0.0559, corresponding wind speed V pmaxA =6m/s; the wind speed probability distribution diagram of the wind power plant B is shown in FIG. 3, and the wind speed probability distribution peak load P of the wind power plant B maxB =0.0727, corresponding wind speed V pmaxB ＝6m/s。
For A and B wind power plants, peak load P is distributed according to probability max The wind speed probability distribution is divided into a left half area and a right half area, wherein the left half area of the wind speed is as follows: v L ＝{v l |v≤V pmax V ∈ V }, right half of wind speed: v R ＝{v r |v＞V pmax And V belongs to V, and a symmetrical mapping sample of two half areas is constructed, wherein the left half area of the wind speed is symmetrically mapped: v L ′＝{v′ l |v′ l ＝2V pmax -v l ，v l ∈V L And symmetrically mapping a right half area of the wind speed: v R ′＝{v′ r |v＇ r ＝2V pmax -v r ，v r ∈V R }
Integrating each half-area sample with the symmetrical mapping sample to obtain a left half-area sample and a right half-area sample with symmetry;
V l ＝V L ∪V L V r ＝V R ∪V R
carrying out standardization processing on the wind speed probability distribution to obtain a sample conforming to normal distribution;
V left ＝{x′ l |x＇ l ＝[x l -E(V l )/δ(V l )]，x l ∈V l }
V right ＝{x′ r |x′ r ＝[x r -E(V r )/δ(V r )]，x r ∈V r }
in the formula, E (V) l ) And E (V) r ) Respectively the expectations of the left and right halves of the area sample; delta (V) l ) And δ (V) r ) The standard deviations of the samples in the left and right halves are shown.
Applying a reverse cloud generator to obtain a characteristic parameter E of the probability density distribution of the wind speed sample after each half area is standardized xL 、E nL 、H eL 、E xR 、E nR 、H eR ：
Wind speed sample expectation:
Figure BDA0002393492080000051
sample second order center distance:
Figure BDA0002393492080000061
sample fourth-order center distance:
Figure BDA0002393492080000062
entropy:
Figure BDA0002393492080000063
super entropy:
Figure BDA0002393492080000064
A. the calculation results of the characteristic parameters of the left and right half areas of the two wind fields B are shown in Table 1:
TABLE 1A, B wind farm wind speed probability distribution characteristic parameter results
Figure BDA0002393492080000065
Step 2, calculating a correlation coefficient matrix and a covariance matrix of wind speeds among a plurality of wind fields based on historical wind speed data, and decomposing the covariance matrix to obtain a lower triangular matrix;
the calculation formula for calculating the correlation coefficient of the wind speed between the wind fields A and B based on the historical wind speed data is as follows:
Figure BDA0002393492080000066
in the formula: e (v) A )、E(v B ) The expected wind speeds of the wind fields A and B; var (v) A )、var(v B ) The wind speed variance of the wind field A and the wind field B is obtained; e (v) A v B ) Is the wind speed v A 、v B Product expectation.
The correlation coefficient matrix is:
Figure BDA0002393492080000067
the covariance matrix is:
Figure BDA0002393492080000068
in the formula: sigma 1 And σ 2 The standard deviation of the wind speeds of the A wind field and the B wind field is respectively.
The covariance matrix C is decomposed, C = LL T To obtain a lower triangular matrix
Figure BDA0002393492080000071
Step 3, respectively sampling the wind power plants, generating multi-dimensional wind speed cloud droplets without correlation characteristics based on the mixed semi-cloud model of each wind field, subtracting a wind speed average value and dividing by a wind speed variance to obtain a sampled data column vector;
randomly generating samples using a forward cloud generator, first with E n In the interest of expectation,
Figure BDA0002393492080000072
normal random entropy E 'of variance' n (ii) a Is then randomly generated with E x To expect->
Figure BDA0002393492080000073
Normal random sample x 'being variance' i (ii) a Carrying out inverse standardization processing on the generated wind speed cloud droplets, x i ＝x＇ i ×δ(V l )+E(V l )orx i ＝x＇ i ×δ(V r )+E(V r )
In the formula, delta (V) l ) And δ (V) r ) Left and right half-area variances, E (V), with symmetry for the wind speed sample V l ) And E (V) r ) Left and right half-area expectation with symmetry for wind speed sample vThe value is obtained.
Wind speed cloud droplets x of the wind field are obtained after the wind speeds of all the half areas are subjected to inverse standardization i Subtract the average value of wind speed E (v) i ) And divided by the variance of wind speed var (v) i ) Obtaining the sampled data
Figure BDA0002393492080000074
Sampled data column vector z = [ z ] 1 ，z 2 …，z n ] T 。
Step 4, obtaining a group of wind speed vectors with correlation characteristics through matrix transformation, and calculating a formula:
v＝Lz+E
in the formula: e is the expected vector of the wind field, E = [ E (v) 1 )，…，E(v n )] T . v is the multidimensional wind velocity vector with correlation.
After generating 87600 correlated wind speeds for ten years, the expectation, variance and correlation coefficient between data samples are calculated and compared with the real data, and the result is shown in table 2. The results in table 2 show that the proposed correlation wind speed generation method is accurate and effective in result.
TABLE 2 correlation wind speed results generated based on the hybrid semi-cloud model compared to the real data
Figure BDA0002393492080000075
/>

Claims (3)

1. A correlation wind speed generation method based on a hybrid semi-cloud model is characterized by comprising the following steps:
step 1, respectively constructing a mixed semi-cloud model of a plurality of wind power plants based on historical wind speed data, wherein the mixed semi-cloud model comprises the steps of partitioning and standardizing irregularly distributed wind speed samples and solving cloud parameters, and the specific steps are as follows:
step 1-1, obtaining probability density distribution of each wind speed interval according to historical wind speed, and distributing peak load P according to probability max Is divided into a left half area V and a right half area V L And V R And wind speed left half area:V L ＝{v l |v≤V pmax v ∈ V }, right half of wind speed: v R ＝{v r |v＞V pmax And V belongs to V, and a symmetrical mapping sample of two half areas is constructed, wherein the left half area of the wind speed is symmetrically mapped: v L '＝{v′ l |v′ l ＝2V pmax -v l ,v l ∈V L And (4) symmetrically mapping the right half area of the wind speed: v R '＝{v' r |v' r ＝2V pmax -v r ,v r ∈V R }；
Integrating each half-area sample with the symmetrical mapping sample to obtain a left half-area sample and a right half-area sample with symmetry;
V l ＝V L ∪V′ L V r ＝V R ∪V′ R
step 1-2, carrying out standardization processing on the wind speed probability distribution to obtain a sample conforming to normal distribution;
V left ＝{x′ l |x′ l ＝[x l -E(V l )/δ(V l )],x l ∈V l }
V right ＝{x' r |x' r ＝[x r -E(V r )/δ(V r )],x r ∈V r }
in the formula, E (V) l ) And E (V) r ) Respectively the expectations of the left and right halves of the area sample; delta (V) l ) And δ (V) r ) Respectively taking the standard deviation of the samples of the left half area and the right half area;
step 1-3, a reverse cloud generator is applied to obtain a characteristic parameter E of the probability density distribution of the wind speed sample after each half area is standardized xL 、E nL 、H eL 、E xR 、E nR 、H eR ：
Wind speed sample expectation:
Figure FDA0004013183900000011
sample second order center distance:
Figure FDA0004013183900000012
sample fourth-order center distance:
Figure FDA0004013183900000013
entropy:
Figure FDA0004013183900000014
super entropy:
Figure FDA0004013183900000021
in the formula, v i For the ith sample of the wind speed,
Figure FDA0004013183900000022
is the average number of samples, and N is the total number of samples;
step 2, calculating a correlation coefficient matrix and a covariance matrix of wind speeds among a plurality of wind farms based on historical wind speed data, and decomposing the covariance matrix to obtain a lower triangular matrix;
step 3, respectively sampling the wind power plants, generating multi-dimensional wind speed cloud droplets without correlation characteristics based on the mixed semi-cloud model of each wind power plant, subtracting a wind speed average value and dividing by a wind speed variance to obtain a sampled data column vector; the step of drawing a wind speed sample comprises:
step 3-1, randomly generating a sample by using a forward cloud generator, and firstly generating the sample by using E n In the interest of expectation,
Figure FDA0004013183900000023
normal random entropy E 'of variance' n (ii) a Is then randomly generated with E x To expect->
Figure FDA0004013183900000024
Is a normal random sample x 'of variance' i ；
Step 3-2, carrying out inverse standardization treatment on the generated wind speed cloud droplets:
x i ＝x′ i ×δ(V l )+E(V l )orx i ＝x′ i ×δ(V r )+E(V r )
in the formula, delta (V) l ) And δ (V) r ) Left and right half-area variances, E (V), with symmetry for the wind speed sample V l ) And E (V) r ) The expected values of the left half area and the right half area with symmetry of the wind speed sample v are obtained;
wind speed cloud droplets x of the wind field are obtained after the wind speeds of all the half areas are subjected to inverse standardization i Subtract the average value of wind speed E (v) i ) And divided by the variance of wind speed var (v) i ) Obtaining the sampled data
Figure FDA0004013183900000025
Sampled data column vector z = [ z ] 1 ,z 2 …,z n ] T ；
And 4, obtaining a group of wind speed vectors with correlation characteristics through matrix transformation.
2. The correlation wind speed generation method based on the hybrid semi-cloud model according to claim 1, wherein the calculation formula for calculating the correlation coefficient of the wind speeds among the plurality of wind farms based on the historical wind speed data is as follows:
Figure FDA0004013183900000026
in the formula: e (v) i )、E(v j ) Is the wind speed v i 、v j Desired wind speed; var (v) i )、var(v j ) Is the wind speed v i 、v j The variance of wind speed of (c); e (v) i v j ) Is the wind speed v i 、v j (ii) an expectation of product;
the correlation coefficient matrix is:
Figure FDA0004013183900000031
in the formula: n is the number of wind power plants;
the covariance matrix is:
Figure FDA0004013183900000032
in the formula: sigma 1 ,σ 2 ,…,σ n The wind power plant is 1,2, \ 8230, the standard deviation of n wind speed distribution probability;
the lower triangular matrix L is obtained by decomposing the covariance matrix C: c = LL T 。
3. The correlation wind speed generation method based on the hybrid semi-cloud model of claim 2, wherein a set of wind speed vectors with correlation characteristics is obtained through matrix transformation:
v＝Lz+E
in the formula: e is the expected vector of the wind field, E = [ E (v) 1 ),…,E(v n )] T (ii) a v is the multidimensional wind velocity vector with correlation.
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