CN104834793A - Simulation generation method for wind speed data of multiple wind power farms - Google Patents

Abstract

The invention provides a simulation generation method for wind speed data of multiple wind power farms. The method includes the steps that according to historical data of wind speeds of the multiple wind power farms, delay time among the wind speeds is determined; a model for the wind speeds of the multiple wind power farms is constructed through a Copula function theory, and the constructing step includes the substeps that marginal distribution of all the wind speeds is determined, the suitable Copula function model is selected, model parameters are estimated, and the model is evaluated; the wind speeds of the multiple wind power farms are generated according to the constructed Copula function model; the wind speeds generated in a simulation mode are reconstructed and adjusted in the aspect of the time sequence through a stochastic differential equation and a delay relation. The simulation generation method for the wind speed data of the multiple wind power farms can meet fluctuation characteristics of the respective wind speeds of the wind power farms and the cross correlation among the wind speeds of the multiple wind power farms.

Description

A kind of simulation-generation method of windy field gas velocity data

Technical field

The present invention relates to renewable energy power generation field, be specifically related to a kind of simulation-generation method of windy field gas velocity data.

Background technology

In recent years, China's wind-power electricity generation development rapidly, in succession build up and come into operation by the wind power base of existing multiple ten million multikilowatt.Although wind speed has very strong randomness and uncertainty, windy electric field, because geographic position is at a distance of comparatively near, is substantially in same wind band, can has stronger correlativity between wind speed.Consider the Changing Pattern of windy field gas velocity, set up the Wind speed model of windy electric field, significant to research large-scale wind power connecting system.

At present, large quantifier elimination is carried out to the method for single wind farm wind velocity and wind power data genaration both at home and abroad, according to the difference of model and principle, mainly can be divided into regretional analysis modeling and the large class of stochastic differential equation modeling two.Regretional analysis modeling normally sets up regression analysis model by after original wind speed standardization, as AR, MA, ARMA, ARIMA model etc., obtains wind speed by modeling, then obtains wind speed time series by average corresponding to each point and variance reduction.The modeling of stochastic differential equation is then the change of wind speed seen being a kind of Markov process, simulates wind speed change, obtain corresponding wind speed time series by the stochastic differential equation built about wind speed.

For the generation of windy field gas velocity data, except will meeting the Changing Pattern of respective wind farm wind velocity, also to consider the cross correlation between windy field gas velocity and time delay relation.At present, a lot of scholar is had to use Copula function to study the correlativity of many output of wind electric field both at home and abroad.But these methods have ignored the time delay relation between windy electric field on the one hand, reduce the fitting effect of model; On the other hand, the wind series generated by Copula function only meets statistical property and cross correlation, have ignored the wave characteristic of wind farm wind velocity.

Summary of the invention

Ignore the time delay relation of each wind energy turbine set for field gas velocity modeling windy in prior art, ignore the problem of the fluctuations in wind speed characteristic of each wind energy turbine set, the present invention proposes a kind of simulated data generation method considering windy field gas velocity Changing Pattern.

Above-mentioned purpose of the present invention is realized by the technical characteristic of independent claims, and dependent claims develops the technical characteristic of independent claims with alternative or favourable mode.

For reaching above-mentioned purpose, the present invention proposes a kind of simulation-generation method of windy field gas velocity data, comprises the following steps:

Steps A, historical data according to windy field gas velocity, determine the delay time between wind speed;

Step B, built the model of windy field gas velocity by Copula function theory;

Step C, according to build Copula function model simulation generate windy field gas velocity; And

Step D, the reconstruct that the wind speed to simulation generation carries out in sequential by stochastic differential equation and time delay relation adjust.

In the example that some are concrete, abovementioned steps A, according to the historical data of windy field gas velocity, determines the delay time between wind speed, and its realization comprises following process:

Assuming that within a period of time, windy electric field affects by same wind band, and wind direction is substantially constant, for the wind series (X of any given one group of wind energy turbine set _t, Y _t) cross-correlation coefficient R under decay time T _xY, computing formula is as follows:

$R_{\mathrm{XY}}=\frac{C_{\mathrm{xy}}\left(T\right)}{\sqrt{C_{\mathrm{xx}}\left(0\right)X_{\mathrm{yy}}\left(0\right)}}$

Wherein

$C_{\mathrm{xy}}\left(T\right)=\left\{\begin{array}{cc}\frac{1}{n-T}\underset{t=1}{\overset{n-T}{\mathrm{\&Sigma;}}}(X_t-X_M)(Y_{(t+T)}-T_M)& T\&GreaterEqual;0\\ \frac{1}{n+T}\underset{t=1}{\overset{n+T}{\mathrm{\&Sigma;}}}(X_{(t-T)}-X_M)(Y_t-Y_M)& T<0\end{array}\right.$

In formula: T is delay time, X _m, Y _mfor wind series X _tand Y _tmean value, n is wind series total sample number;

The curve that the cross-correlation coefficient that can obtain windy field gas velocity according to above formula changes with delay time, determines their maximum cross-correlation coefficient R then _xYwith delay time T, mobile adjustment wind series being carried out to sequential obtains new sequence (X _t, Y _t+T).

In the example that some are concrete, abovementioned steps B, builds the model of windy field gas velocity by Copula function theory, and its realization comprises following process:

Step B-1: the marginal distribution function determining each stochastic variable

Parametric method is adopted to process wind speed, assuming that wind speed obeys following Two-parameter Weibull Distribution:

$f_1\left(v_1\right)=\frac{k_1}{c_1}{\left(\frac{v_1}{c_1}\right)}^{k_1-1}\exp (-{\left(\frac{v_1}{c_1}\right)}^{k_1})$

In formula: k ₁for Weibull Distribution Form Parameter; c ₁for scale parameter,

Integration is carried out to above formula, the cumulative distribution function of wind speed can be obtained:

$F_1\left(v_1\right)=1-\exp (-{\left(\frac{v_1}{c_1}\right)}^{k_1})$

Step B-2: choose suitable Copula function model

To the wind series (X after time delay adjustment _t, Y _t+T) make bivariate frequency histogram after, the Copula function then chosen according to respective shapes;

Step B-3: the estimation of model parameter

Adopt Maximum Likelihood Estimation Method to estimate correlation parameter, model parameter estimation comprises two parts: one is the unknown parameter contained in marginal distribution, and another is the unknown parameter contained in the Copula function model chosen;

If the marginal distribution function of two wind farm wind velocity stochastic variables (X, Y) is respectively F ₁(x; θ ₁) and F ₂(y; θ ₂), density function is respectively f ₁(x; θ ₁) and f ₂(y; θ ₂), wherein θ ₁, θ ₂for the unknown parameter in marginal distribution function, if the Copula distribution function chosen is C (u, v; α), Copula density function

Wherein α is the unknown parameter in Copula function;

Then the joint distribution function of (X, Y) is:

F(x,y；θ ₁,θ ₂,α)＝C[F ₁(x；θ ₁),F ₂(y；θ ₂)；α]

The joint density function of (X, Y) is:

f(x,y；θ ₁,θ ₂,α)＝c[F ₁(x；θ ₁),F ₂(y；θ ₂)；α]×f ₁(x；θ ₁)f ₂(y；θ ₂)

Sample (X can be obtained _i, Y _i) (i=1,2 ..., likelihood function n) is:

$L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}f(x,y;{\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}c[F_1(x_i;{\mathrm{\&theta;}}_1),F_2(y_i;{\mathrm{\&theta;}}_2);\mathrm{\&alpha;}]f_1(x_i;{\mathrm{\&theta;}}_1)f_2(y_i;{\mathrm{\&theta;}}_2)$

So obtain log-likelihood function:

$\ln L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln c[F_1(x_i;{\mathrm{\&theta;}}_1),F_2(y_i;{\mathrm{\&theta;}}_2);\mathrm{\&alpha;}]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln f_1(x_i;{\mathrm{\&theta;}}_1)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln f_2(y_i;{\mathrm{\&theta;}}_2)$

Solve the maximum of points of log-likelihood function, unknown parameter θ in marginal distribution and Copula function can be obtained ₁, θ ₂, the maximal possibility estimation of α:

${\widehat{\mathrm{\&theta;}}}_1,{\widehat{\mathrm{\&theta;}}}_2,\widehat{\mathrm{\&alpha;}}=\arg \max \ln L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;});$

Step B-4: the evaluation of model

Introducing experience Copula function is evaluated relevant Copula function;

If (x _i, y _i) (i=1,2 ..., n) for taking from the sample of population of two dimension (X, Y), the empirical distribution function of note X, Y is respectively F ₁and F (X) ₂(Y) the experience Copula, defining sample is as follows:

${\hat{C}}_n(u,v)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{I}_{[F_1\left(x_i\right)\&le;u]}{I}_{[F_2\left(y_i\right)\&le;v]}u,v\&Element;\left[\mathrm{0,1}\right]$

Wherein, I _[]for indicative function, work as F _n(x _iduring)≤u, otherwise

Utilize experience Copula function investigate the squared euclidean distance of each Copula function and experience Copula:

$d^2=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{|{\hat{C}}_n(u_i,v_i)-C_{\mathrm{copula}}(u_i,v_i)|}^2$

Wherein, u _i=F ₁(x _i), v _i=F ₂(y _i) (i=1,2 ..., n), C _copula(u _i, v _i) represent Copula function, d ²represent squared euclidean distance, d ²the situation of less expression matching raw data is better.

In the example that some are concrete, abovementioned steps C, the Copula function model simulation according to building generates windy field gas velocity, and its realization comprises following process:

After matching obtains suitable Copula function model, utilize Copula function model to generate the marginal distribution random series meeting cross correlation, the inverse function of recycling following formula wind speed Cumulative Distribution Function, can obtain corresponding wind series:

$v_1=F^{-1}\left(u\right)={c_1}^{k_1}\sqrt{\ln \frac{1}{1-u}}.$

In the example that some are concrete, abovementioned steps D, adjusted the reconstruct that the wind speed that simulation generates carries out in sequential by stochastic differential equation and time delay relation, its realization comprises following process:

Step D-1: random differential equation models adjusts

Wind speed increment be distributed as f (x), if probability density function f (x) is at its field of definition (l, u) non-negative in, continuously and variance is limited, its mathematical expectation E (x)=μ, then stochastic differential equation can be expressed as:

${\mathrm{dX}}_t=-\mathrm{\&theta;}(X-\mathrm{\&mu;})\mathrm{dt}+\sqrt{v\left(X_t\right)}d{W}_t,t\&GreaterEqual;0$

Wherein x _tfor wind speed amplitude, θ>=0, W _tfor Brownian movement, v (X _t) be the nonnegative function be defined on (l, u):

$v\left(x\right)=\frac{2\mathrm{\&theta;}}{f\left(x\right)}\underset{l}{\overset{u}{\&Integral;}}(\mathrm{\&mu;}-y)f\left(y\right)\mathrm{dy\; x}\&Element;(l,u)$

If p (t, x, z) represents that initial time gustiness is x, after elapsed time t, amplitude has changed the probability density of z, then it meets following Kolmogorov's forward equations:

$\frac{\&PartialD;p(t,x,z)}{\&PartialD;t}=\frac{1}{2}\frac{{\&PartialD;}^2\left(v\left(z\right)p(t,x,z)\right)}{\&PartialD;z^2}+\frac{\&PartialD;\left(\mathrm{\&theta;}(z-\mathrm{\&mu;})p(t,x,z)\right)}{\&PartialD;z}$

After solving p (t, x, z), the time series Δ x of one group of typical wind speed variable quantity can be generated according to maximum probability principle on each time point ₁, Δ x ₂..., Δ x _n, by the average v of wind series sample _μas wind speed initial value v ₀, the wind series meeting this variation tendency can be generated by variable quantity sequence;

Original wind series generated by Copula function is carried out the reconstruct adjustment in sequential, make the deviator of itself and canonical trend sequence wind speed minimum, can obtain the wind series meeting typical change trend, the wind series of all the other wind energy turbine set is adjusted accordingly according to corresponding sequential relationship;

Step D-2: windy electric field time delay relation adjustment

According to the delay time between the windy electric field that steps A is determined, the windy field gas velocity sequence generated is carried out to the translation adjustment in sequential, obtain the random fluctuation temporal model of final windy electric field.

From the above technical solution of the present invention shows that, the simulation-generation method of the windy field gas velocity data that the present invention proposes, can describe each wind energy turbine set self and Changing Pattern each other.It considers the time delay relation of each wind farm wind velocity in advance, improves the fitting effect of Copula function model.The present invention is reconstructed adjustment by random differential equation models and time delay relation after the windy field gas velocity sequence of generation, can on the basis of guaranteeing windy electric field cross correlation and each wind farm wind velocity probability distribution, take into account the sequential wave characteristic of time delay relation between windy electric field and each wind energy turbine set.The windy field gas velocity simulated data generated by the inventive method can be widely used in the simulation analysis containing wind-powered electricity generation electric system, has good future in engineering applications.

As long as should be appreciated that aforementioned concepts and all combinations of extra design described in further detail below can be regarded as a part for subject matter of the present disclosure when such design is not conflicting.In addition, all combinations of theme required for protection are all regarded as a part for subject matter of the present disclosure.

The foregoing and other aspect of the present invention's instruction, embodiment and feature can be understood by reference to the accompanying drawings from the following description more all sidedly.Feature and/or the beneficial effect of other additional aspect of the present invention such as illustrative embodiments will be obvious in the following description, or by learning in the practice of the embodiment according to the present invention's instruction.

Accompanying drawing explanation

Accompanying drawing is not intended to draw in proportion.In the accompanying drawings, each identical or approximately uniform ingredient illustrated in each figure can represent with identical label.For clarity, in each figure, not each ingredient is all labeled.Now, the embodiment of various aspects of the present invention also will be described with reference to accompanying drawing by example, wherein:

Fig. 1 is the process flow diagram of the simulation-generation method of the windy field gas velocity data illustrated according to certain embodiments of the invention.

Fig. 2 is the illustrative diagram of the two wind farm wind velocity sequence datas illustrated according to certain embodiments of the invention.

Fig. 3 illustrates according to two wind energy turbine set cross-correlation coefficients of the certain embodiments of the invention illustrative diagram with time delay change curve.

Fig. 4 a-4e is the distribution plan of the common Copula function probability density illustrated according to certain embodiments of the invention.

Fig. 5 a, 5b are the illustrative diagram illustrated according to the raw data of certain embodiments of the invention and the frequency histogram of Copula function generation data respectively.

Fig. 6 illustrates the illustrative diagram generating windy field gas velocity sequence according to the Copula function model of certain embodiments of the invention.

Fig. 7 a, 7b and 7c illustrate the schematic diagram according to the random differential equation models of certain embodiments of the invention, wind farm wind velocity being reconstructed to adjustment.

Fig. 8 illustrates the schematic diagram according to the time delay relation of certain embodiments of the invention, wind farm wind velocity sequence being carried out to translation adjustment.

Fig. 9 a, 9b illustrate the illustrative diagram according to the generation of certain embodiments of the invention windy field gas velocity train wave dynamic characteristic.

Embodiment

In order to more understand technology contents of the present invention, institute's accompanying drawings is coordinated to be described as follows especially exemplified by specific embodiment.

Each side with reference to the accompanying drawings to describe the present invention in the disclosure, shown in the drawings of the embodiment of many explanations.Embodiment of the present disclosure must not be intended to comprise all aspects of the present invention.Be to be understood that, multiple design presented hereinbefore and embodiment, and describe in more detail below those design and embodiment can in many ways in any one is implemented, this is because design disclosed in this invention and embodiment are not limited to any embodiment.In addition, aspects more disclosed by the invention can be used alone, or otherwisely anyly appropriately combinedly to use with disclosed by the invention.

According to embodiments of the invention, as shown in Figure 1, a kind of simulation-generation method of windy field gas velocity data, comprises the following steps: first, according to the historical data of windy field gas velocity, determines the delay time between wind speed; Then, the model of windy field gas velocity is built by Copula function theory; Then, windy field gas velocity is generated according to the Copula function model simulation built; Finally, by stochastic differential equation and time delay relation, the reconstruct that the wind speed that simulation generates carries out in sequential is adjusted.

Below in conjunction with accompanying drawing and some concrete examples, to the concrete enforcement of the simulation-generation method of aforementioned windy field gas velocity data in addition more detailed description.

The simulation-generation method of these windy field gas velocity data, comprises the following steps generally:

Steps A: according to the historical data of windy field gas velocity, determine the delay time between wind speed, concrete steps are as follows:

Assuming that within a period of time, each wind energy turbine set affects by same wind band, and wind direction is substantially constant.For the wind series (X of any given one group of wind energy turbine set _t, Y _t) as shown in Figure 2 (Fig. 2 exemplary give one group of two wind farm wind velocity data), the cross-correlation coefficient R under decay time T _xY, computing formula is as follows:

$R_{\mathrm{XY}}=\frac{C_{\mathrm{xy}}\left(T\right)}{\sqrt{C_{\mathrm{xx}}\left(0\right)C_{\mathrm{yy}}\left(0\right)}}$

Wherein

$C_{\mathrm{xy}}\left(T\right)=\left\{\begin{array}{cc}\frac{1}{n-T}\underset{t=1}{\overset{n-T}{\mathrm{\&Sigma;}}}(X_t-X_M)(Y_{(t+T)}-T_M)& T\&GreaterEqual;0\\ \frac{1}{n+T}\underset{t=1}{\overset{n+T}{\mathrm{\&Sigma;}}}(X_{(t-T)}-X_M)(Y_t-Y_M)& T<0\end{array}\right.$

In formula: T is delay time, X _m, Y _mfor wind series X _tand Y _tmean value, n is wind series total sample number.

The curve that the cross-correlation coefficient that just can obtain windy field gas velocity according to above formula changes with delay time as shown in Figure 3, determines their maximum cross-correlation coefficient R then _xYas shown in table 1 with delay time T, mobile adjustment wind series being carried out to sequential obtains new sequence (X _t, Y _t+T);

Table 1 liang wind farm wind velocity cross-correlation coefficient

Wind energy turbine set	During T=0, cross-correlation coefficient	Maximum cross-correlation coefficient	Delay time T	Leading wind energy turbine set
					(A,B)	0.7941	0.8243	-140min	Wind energy turbine set B

Step B: the model being built windy field gas velocity by Copula function theory, concrete steps are as follows:

Step B-1: the marginal distribution function determining each stochastic variable.The present invention adopts parametric method to process wind speed, assuming that wind speed obeys following Two-parameter Weibull Distribution:

$f_1\left(v_1\right)=\frac{k_1}{c_1}{\left(\frac{v_1}{c_1}\right)}^{k_1-1}\exp (-{\left(\frac{v_1}{c_1}\right)}^{k_1})$

In formula: k ₁for Weibull Distribution Form Parameter; c ₁for scale parameter.Integration is carried out to above formula, the cumulative distribution function of wind speed can be obtained:

$F_1\left(v_1\right)=1-\exp (-{\left(\frac{v_1}{c_1}\right)}^{k_1})$

Step B-2: choose suitable Copula function model.Common Copula function model mainly contains 5 kinds, be respectively Normal-Copula (Fig. 4 a), t-Copula (Fig. 4 b), Gumbel-Copula (Fig. 4 c), Clayton-Copula (Fig. 4 d) and Frank-Copula (Fig. 4 e), as shown in figs. 4a-4e.Wherein Normal-Copula function and Frank-Copula function are applicable to having symmetrical afterbody, and the two-dimensional random of afterbody asymptotic independence is vectorial; T-Copula function is applicable to having symmetrical afterbody, and the two-dimensional random vector that afterbody is relevant; Gumbel-Copula and Clayton-Copula function is applicable to the binary random vector with Asymmetric Tail, and wherein on Gumbel-Copula, tail is correlated with, lower tail asymptotic independence, and Clayton-Copula function lower tail is correlated with, upper tail asymptotic independence.

To the wind series (X after time delay adjustment _t, Y _t+T) make bivariate frequency histogram raw data as shown in Figure 5 a, just can choose suitable Copula function according to respective shapes.

Step B-3: the estimation of model parameter.Parameter estimation mainly contains two parts.One is the unknown parameter contained in marginal distribution, and another is the unknown parameter contained in the Copula function model chosen.The present invention adopts Maximum Likelihood Estimation Method to estimate correlation parameter.

If the marginal distribution function of two wind farm wind velocity stochastic variables (X, Y) is respectively F ₁(x; θ ₁) and F ₂(y; θ ₂), density function is respectively f ₁(x; θ ₁) and f ₂(y; θ ₂), wherein θ ₁, θ ₂for the unknown parameter in marginal distribution function.If the Copula distribution function chosen is C (u, v; α), Copula density function

Wherein α is the unknown parameter in Copula function.Then the joint distribution function of (X, Y) is

F(x,y；θ ₁,θ ₂,α)＝C[F ₁(x；θ ₁),F ₂(y；θ ₂)；α]

The joint density function of (X, Y) is

f(x,y；θ ₁,θ ₂,α)＝c[F ₁(x；θ ₁),F ₂(y；θ ₂)；α]×f ₁(x；θ ₁)f ₂(y；θ ₂)

Sample (X can be obtained _i, Y _i) (i=1,2 ..., likelihood function n) is

$L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}f(x,y;{\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}c[F_1(x_i;{\mathrm{\&theta;}}_1),F_2(y_i;{\mathrm{\&theta;}}_2);\mathrm{\&alpha;}]f_1(x_i;{\mathrm{\&theta;}}_1)f_2(y_i;{\mathrm{\&theta;}}_2)$

So obtain log-likelihood function

$\ln L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln c[F_1(x_i;{\mathrm{\&theta;}}_1),F_2(y_i;{\mathrm{\&theta;}}_2);\mathrm{\&alpha;}]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln f_1(x_i;{\mathrm{\&theta;}}_1)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln f_2(y_i;{\mathrm{\&theta;}}_2)$

Solve the maximum of points of log-likelihood function, unknown parameter θ in marginal distribution and Copula function can be obtained ₁, θ ₂, the maximal possibility estimation of α

${\widehat{\mathrm{\&theta;}}}_1,{\widehat{\mathrm{\&theta;}}}_2,\widehat{\mathrm{\&alpha;}}=\arg \max \ln L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})$

In conjunction with two wind farm wind velocity data of exemplary example, the parameter of Weibull parameter and Copula function model that identification obtains two wind farm wind velocities is as shown in table 2, table 3.

Table 2 liang wind energy turbine set Weibull parameter value

	Scale parameter c	Form parameter k
			Wind energy turbine set A	7.0255	2.3154
Wind energy turbine set B	7.6994	2.1913

Table 3 each Copula function parameter value

Step B-4: the evaluation of model.Introducing experience Copula function is evaluated relevant Copula function.If (x _i, y _i) (i=1,2 ..., n) for taking from the sample of population of two dimension (X, Y), the empirical distribution function of note X, Y is respectively F ₁and F (X) ₂(Y) the experience Copula, defining sample is as follows:

${\hat{C}}_n(u,v)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{I}_{[F_1\left(x_i\right)\&le;u]}{I}_{[F_2\left(y_i\right)\&le;v]}u,v\&Element;\left[\mathrm{0,1}\right]$

Wherein, I _[]for indicative function, work as F _n(x _iduring)≤u, otherwise

There is experience Copula function afterwards, the squared euclidean distance of each Copula function and experience Copula can just be investigated

$d^2=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{|{\hat{C}}_n(u_i,v_i)-C_{\mathrm{copula}}(u_i,v_i)|}^2$

Wherein, u _i=F ₁(x _i), v _i=F ₂(y _i) (i=1,2 ..., n), C _copula(u _i, v _i) represent Copula function, d ²represent Euclidean squared-distance, d ²the situation of less expression matching raw data is better, as shown in table 4.

Square Euclidean distance of table 4 each Copula Function Fitting raw data

Copula function	Normal	t-Copula	Gumbel	Clayton	Frank
						Square Euclidean distance	0.1174	0.0830	0.3864	2.6111	0.2918

Can think that binary t-Copula model can the cross-correlation model of better matching two wind farm wind velocity sequence thus.Table 5 compares before and after time-delay analysis, t-Copula function model fitting effect, result shows, after consideration time-delay analysis, no matter be linear correlation parameter, Spearman rank correlation coefficient, Kendall rank correlation coefficient or Euclidean squared-distance, had certain improvement.

In table 5 two kinds of situations, the inspection of t-Copula function is compared

Step C: simulation generates windy field gas velocity.After matching obtains suitable Copula function model, utilize Copula function model just can generate the marginal distribution random series meeting cross correlation, generation data as shown in Figure 5 b, the inverse function of recycling following formula wind speed Cumulative Distribution Function, corresponding wind series can be obtained, as shown in Figure 6.

$v_1=F^{-1}\left(u\right)={c_1}^{k_1}\sqrt{\ln \frac{1}{1-u}}.$

Step D: the reconstruct adjustment in wind series sequential.Simulate by Copula function model the wind series generated and meet cross correlation between windy field gas velocity and respective probability distribution, but there is a lot of unordered change and oscillation on large scale process in this wind series, need the reconstruct adjustment carried out in sequential, make it meet variation characteristic in time domain, concrete steps are as follows:

Step D-1: random differential equation models adjusts.Wind speed increment be distributed as f (x), if probability density function f (x) is at its field of definition (l, u) non-negative in, continuously and variance is limited, its mathematical expectation E (x)=μ, then stochastic differential equation can be expressed as:

${\mathrm{dX}}_t=-\mathrm{\&theta;}(X-\mathrm{\&mu;})\mathrm{dt}+\sqrt{v\left(X_t\right)}d{W}_t,t\&GreaterEqual;0$

Wherein x _tfor wind speed amplitude, θ>=0, W _tfor Brownian movement, v (X _t) be the nonnegative function be defined on (l, u):

$v\left(x\right)=\frac{2\mathrm{\&theta;}}{f\left(x\right)}\underset{l}{\overset{u}{\&Integral;}}(\mathrm{\&mu;}-y)f\left(y\right)\mathrm{dy\; x}\&Element;(l,u)$

If p (t, x, z) represents that initial time gustiness is x, after elapsed time t, amplitude has changed the probability density of z, then it meets following Kolmogorov's forward equations:

$\frac{\&PartialD;p(t,x,z)}{\&PartialD;t}=\frac{1}{2}\frac{{\&PartialD;}^2\left(v\left(z\right)p(t,x,z)\right)}{\&PartialD;z^2}+\frac{\&PartialD;\left(\mathrm{\&theta;}(z-\mathrm{\&mu;})p(t,x,z)\right)}{\&PartialD;z}$

After solving p (t, x, z), the time series Δ x of one group of typical wind speed variable quantity can be generated according to maximum probability principle on each time point ₁, Δ x ₂..., Δ x _n.By the average v of wind series sample _μas wind speed initial value v ₀, the wind series meeting this variation tendency can be generated by variable quantity sequence.

Original wind series generated by Copula function is carried out the reconstruct adjustment in sequential, make the deviator of itself and canonical trend sequence wind speed minimum, the wind series meeting typical change trend can be obtained, the wind series of all the other wind energy turbine set is adjusted accordingly according to corresponding sequential relationship, as shown in Fig. 7 a, 7b, 7c, wherein 7a represent reconstruct before single wind farm wind velocity, 7b represent reconstruct after single wind farm wind velocity, 7c represent reconstruct after multiple wind farm wind velocity.

Step D-2: windy electric field time delay relation adjustment.According to the delay time between the windy electric field that steps A is determined, the windy field gas velocity sequence generated is carried out to the translation adjustment in sequential, obtain the random fluctuation temporal model of final windy electric field, as shown in Figure 8.

Utilize the present invention to simulate the generation air speed data of month, the cross correlation coefficient obtained before and after time delay adjustment is as shown in table 6.Result shows, generates the cross correlation that data can meet raw data.

Table 6 compares the cross correlation generating data and raw data

Type	(X t,Y t)	Time delay adjustment direction	(X t,Y t+T)
				Raw data	0.7941	→	0.8243
Generate data	0.8032	←	0.8267

Fig. 9 a, 9b give the probability distribution of two wind farm wind velocity increments, and wherein 9a represents the probability density distribution of wind energy turbine set A, and 9b represents the probability density distribution of wind energy turbine set B.The wind speed of wind energy turbine set A is by reconstruct, and wave characteristic can agree with the wave characteristic of original wind speed preferably.The wind speed of wind energy turbine set B by with wind energy turbine set A wind series one to one principle be reconstructed, wave characteristic also agrees with original air speed data substantially.

In sum, the simulation-generation method of the windy field gas velocity data that the present invention proposes, can describe each wind energy turbine set self and Changing Pattern each other.It considers the time delay relation of each wind farm wind velocity in advance, improves the fitting effect of Copula function model.The present invention is reconstructed adjustment by random differential equation models and time delay relation after the windy field gas velocity sequence of generation, can on the basis of guaranteeing windy electric field cross correlation and each wind farm wind velocity probability distribution, take into account the sequential wave characteristic of time delay relation between windy electric field and each wind energy turbine set.

Although the present invention with preferred embodiment disclose as above, so itself and be not used to limit the present invention.Persond having ordinary knowledge in the technical field of the present invention, without departing from the spirit and scope of the present invention, when being used for a variety of modifications and variations.Therefore, protection scope of the present invention is when being as the criterion depending on those as defined in claim.

Claims (5)

1. a simulation-generation method for windy field gas velocity data, is characterized in that, comprise the following steps:

Steps A, historical data according to windy field gas velocity, determine the delay time between wind speed;

Step B, built the model of windy field gas velocity by Copula function theory;

Step C, according to build Copula function model simulation generate windy field gas velocity; And

Step D, the reconstruct that the wind speed to simulation generation carries out in sequential by stochastic differential equation and time delay relation adjust.

2. the simulation-generation method of windy field gas velocity data according to claim 1, is characterized in that, abovementioned steps A, according to the historical data of windy field gas velocity, determines the delay time between wind speed, and its realization comprises following process:

Assuming that within a period of time, windy electric field affects by same wind band, and wind direction is substantially constant, for the wind series (X of any given one group of wind energy turbine set _t, Y _t) cross-correlation coefficient R under decay time T _xY, computing formula is as follows:

$R_{\mathrm{XY}}=\frac{C_{\mathrm{xy}}\left(T\right)}{\sqrt{C_{\mathrm{xx}}\left(0\right)C_{\mathrm{yy}}\left(0\right)}}$

Wherein

$C_{\mathrm{xy}}\left(T\right)=\left\{\begin{array}{cc}\frac{1}{n-T}\underset{t=1}{\overset{n-T}{\mathrm{\&Sigma;}}}(X_t-X_M)(Y_{(t+T)}-Y_M)& T\&GreaterEqual;0\\ \frac{1}{n+T}\underset{t=1}{\overset{n+T}{\mathrm{\&Sigma;}}}(X_{(t-T)}-X_M)(Y_t-Y_M)& T<0\end{array}\right.$

In formula: T is delay time, X _m, Y _mfor wind series X _tand Y _tmean value, n is wind series total sample number;

The curve that the cross-correlation coefficient that can obtain windy field gas velocity according to above formula changes with delay time, determines their maximum cross-correlation coefficient R then _xYwith delay time T, mobile adjustment wind series being carried out to sequential obtains new sequence (X _t, Y _t+T).

3. the simulation-generation method of windy field gas velocity data according to claim 2, be is characterized in that, abovementioned steps B, is built the model of windy field gas velocity by Copula function theory, and its realization comprises following process:

Step B-1: the marginal distribution function determining each stochastic variable

Parametric method is adopted to process wind speed, assuming that wind speed obeys following Two-parameter Weibull Distribution:

$f_1\left(v_1\right)=\frac{k_1}{c_1}{\left(\frac{v_1}{c_1}\right)}^{k_1-1}\exp (-{\left(\frac{v_1}{c_1}\right)}^{k_1})$

In formula: k ₁for Weibull Distribution Form Parameter; c ₁for scale parameter,

Integration is carried out to above formula, the cumulative distribution function of wind speed can be obtained:

$F_1\left(v_1\right)=1-\exp (-{\left(\frac{v_1}{c_1}\right)}^{k_1})$

Step B-2: choose suitable Copula function model

To the wind series (X after time delay adjustment _t, Y _t+T) make bivariate frequency histogram after, the Copula function then chosen according to respective shapes;

Step B-3: the estimation of model parameter

Adopt Maximum Likelihood Estimation Method to estimate correlation parameter, model parameter estimation comprises two parts: one is the unknown parameter contained in marginal distribution, and another is the unknown parameter contained in the Copula function model chosen;

If the marginal distribution function of two wind farm wind velocity stochastic variables (X, Y) is respectively F ₁(x; θ ₁) and F ₂(y; θ ₂), density function is respectively f ₁(x; θ ₁) and f ₂(y; θ ₂), wherein θ ₁, θ ₂for the unknown parameter in marginal distribution function, if the Copula distribution function chosen is C (u, v; α), Copula density function

Wherein α is the unknown parameter in Copula function;

Then the joint distribution function of (X, Y) is:

F(x,y；θ ₁,θ ₂,α)＝C[F ₁(x；θ ₁),F ₂(y；θ ₂)；α]

The joint density function of (X, Y) is:

f(x,y；θ ₁,θ ₂,α)＝c[F ₁(x；θ ₁),F ₂(y；θ ₂)；α]×f ₁(x；θ ₁)f ₂(y；θ ₂)

Sample (X can be obtained _i, Y _i) (i=1,2 ..., likelihood function n) is:

$L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}f(x,y;{\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}c[F_1(x_i;{\mathrm{\&theta;}}_1),F_2(y_i;{\mathrm{\&theta;}}_2);\mathrm{\&alpha;}]f_1(x_i;{\mathrm{\&theta;}}_1)f_2(y_i;{\mathrm{\&theta;}}_2)$

So obtain log-likelihood function:

$\ln \mathrm{}L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln \mathrm{}c[F_1(x_i;{\mathrm{\&theta;}}_1),F_2(y_i;{\mathrm{\&theta;}}_2);\mathrm{\&alpha;}]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln \mathrm{}{f}_1(x_i;{\mathrm{\&theta;}}_1)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\ln \mathrm{}{f}_2(y_i;{\mathrm{\&theta;}}_2)$

Solve the maximum of points of log-likelihood function, unknown parameter θ in marginal distribution and Copula function can be obtained ₁, θ ₂, the maximal possibility estimation of α:

${\widehat{\mathrm{\&theta;}}}_1,{\widehat{\mathrm{\&theta;}}}_2,\widehat{\mathrm{\&alpha;}}=\arg \mathrm{}\max \mathrm{}\ln \mathrm{}L({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,\mathrm{\&alpha;});$

Step B-4: the evaluation of model

Introducing experience Copula function is evaluated relevant Copula function;

If (x _i, y _i) (i=1,2 ..., n) for taking from the sample of population of two dimension (X, Y), the empirical distribution function of note X, Y is respectively F ₁and F (X) ₂(Y) the experience Copula, defining sample is as follows:

$\begin{array}{cc}{\hat{C}}_n(u,v)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{I}_{[F_1\left(x_i\right)\&le;u]}{I}_{[F_2\left(y_i\right)\&le;v]}& u,v\&Element;\left[\mathrm{0,1}\right]\end{array}$

Wherein, I _[]for indicative function, work as F _n(x _iduring)≤u, otherwise

Utilize experience Copula function investigate the squared euclidean distance of each Copula function and experience Copula:

$d^2=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{|{\hat{C}}_n(u_i,v_i)-C_{\mathrm{copula}}(u_i,v_i)|}^2$

Wherein, u _i=F ₁(x _i), v _i=F ₂(y _i) (i=1,2 ..., n), C _copula(u _i, v _i) represent Copula function, d ²represent squared euclidean distance, d ²the situation of less expression matching raw data is better.

4. the simulation-generation method of windy field gas velocity data according to claim 3, is characterized in that, abovementioned steps C, and the Copula function model simulation according to building generates windy field gas velocity, and its realization comprises following process:

After matching obtains suitable Copula function model, utilize Copula function model to generate the marginal distribution random series meeting cross correlation, the inverse function of recycling following formula wind speed Cumulative Distribution Function, can obtain corresponding wind series:

$v_1=F^{-1}\left(u\right)={c_1}^{k_1}\sqrt{\ln \frac{1}{1-u}}.$

5. the simulation-generation method of windy field gas velocity data according to claim 4, is characterized in that, abovementioned steps D, and adjusted the reconstruct that the wind speed that simulation generates carries out in sequential by stochastic differential equation and time delay relation, its realization comprises following process:

Step D-1: random differential equation models adjusts

Wind speed increment be distributed as f (x), if probability density function f (x) is at its field of definition (l, u) non-negative in, continuously and variance is limited, its mathematical expectation E (x)=μ, then stochastic differential equation can be expressed as:

$d{X}_t=-\mathrm{\&theta;}(X-\mathrm{\&mu;})\mathrm{dt}+\sqrt{v\left(X_t\right)}d{W}_t,t\&GreaterEqual;0$

Wherein x _tfor wind speed amplitude, θ>=0, W _tfor Brownian movement, v (X _t) be the nonnegative function be defined on (l, u):

$\begin{array}{cc}v\left(x\right)=\frac{2\mathrm{\&theta;}}{f\left(x\right)}\underset{l}{\overset{u}{\&Integral;}}(\mathrm{\&mu;}-y)f\left(y\right)\mathrm{dy}& x\&Element;(l,u)\end{array}$

If p (t, x, z) represents that initial time gustiness is x, after elapsed time t, amplitude has changed the probability density of z, then it meets following Kolmogorov's forward equations:

$\frac{\&PartialD;p(t,x,z)}{\&PartialD;t}=\frac{1}{2}\frac{{\&PartialD;}^2\left(v\left(z\right)p(t,x,z)\right)}{{\&PartialD;z}^2}+\frac{\&PartialD;\left(\mathrm{\&theta;}(z-\mathrm{\&mu;})p(t,x,z)\right)}{\&PartialD;z}$

After solving p (t, x, z), the time series Δ x of one group of typical wind speed variable quantity can be generated according to maximum probability principle on each time point ₁, Δ x ₂..., Δ x _n, by the average v of wind series sample _μas wind speed initial value v ₀, the wind series meeting this variation tendency can be generated by variable quantity sequence;

Original wind series generated by Copula function is carried out the reconstruct adjustment in sequential, make the deviator of itself and canonical trend sequence wind speed minimum, can obtain the wind series meeting typical change trend, the wind series of all the other wind energy turbine set is adjusted accordingly according to corresponding sequential relationship;

Step D-2: windy electric field time delay relation adjustment

According to the delay time between the windy electric field that steps A is determined, the windy field gas velocity sequence generated is carried out to the translation adjustment in sequential, obtain the random fluctuation temporal model of final windy electric field.