CN103020423A - Copula-function-based method for acquiring relevant characteristic of wind power plant capacity - Google Patents

Abstract

The invention discloses a copula-function-based method for acquiring relevant characteristics of wind power plant capacities. The method comprising the following steps: acquiring M cumulative distribution functions and cumulative distribution function values of the wind power plant capacity according to a wind power plant capacity sample; acquiring parameters of copula functions by using a maximum likelihood method; determining each copular function according to the parameters; acquiring experience copula function values according to the cumulative distribution functions and the cumulative distribution function values; calculating copula function values corresponding to the cumulative distribution function values according to each copula function; acquiring the Euclidean distances between the copula function values and the experience copula function values according to the copula function values and the experience copula function values; determining a copula function corresponding to the smallest Euclidean distance so as to describe the relevance of the wind power plant capacities; and calculating four relevance coefficients among the wind power plant capacities according to the copula functions and subsequently acquiring the relevance characteristics among the wind power plant capacities.

Description

Obtain the method for output of wind electric field correlation properties based on the copula function

Technical field

The invention belongs to wind-power electricity generation distribution technique field, more specifically, relate to a kind of method of obtaining the output of wind electric field correlation properties based on the copula function.

Background technology

Along with the scale development and use of China's wind energy, wind-powered electricity generation continues fast development, the installed capacity rapid growth.According to statistics, the newly-increased wind-powered electricity generation installation of China ratio that accounts for the newly-increased installation in the whole world from less than 10% in 2006 rise to 2010 49%.By in June, 2012, national grid connected wind power capacity has had 5,258 ten thousand kilowatts.The operation characteristic of the uncertainty of wind-resources and wind-powered electricity generation unit itself makes the output power of wind energy turbine set have intermittence and undulatory property, the access of large-scale wind power certainly will bring difficulty to the safe and stable operation of electric system, the technical barrier of wind-electricity integration, operation difficulty, bottleneck progressively manifest, and the wind-electricity integration difficulty becomes a focus.Between rationally the windy electric field of portrayal is exerted oneself correlation properties and the random variation rule, to improving the precision of prediction of output of wind electric field, and then raising operation of power networks level, thereby reduce the consumption of non-regeneration energy, ensure power system safety and stability, improve power system economy, reduce greenhouse gas emission and be significant.At present, only adopt linearly dependent coefficient to be described to the correlativity of output of wind electric field.Yet in many cases, the correlativity of output of wind electric field presents nonlinear relationship, only is difficult to correlationship between the accurate description output of wind electric field with linearly dependent coefficient.And there is no and find that exerting oneself of wind energy turbine set meets some specific distributions, the joint probability distribution function of a plurality of output of wind electric field is difficult to structure especially, and therefore, the correlationship of how describing exactly between a plurality of output of wind electric field is a difficulties.

Summary of the invention

Defective for prior art, the object of the present invention is to provide a kind of method of obtaining the output of wind electric field correlation properties based on the copula function, be intended to solve in the situation of a plurality of wind energy turbine set joint probability distribution the unknown, describe more accurately the problem of output of wind electric field correlativity from multi-angles such as Spearman rank correlation coefficient, Kendall rank correlation coefficient, upper tail dependence coefficient and lower tail related coefficients.

The invention provides and a kind ofly obtain the method for output of wind electric field correlation properties based on the copula function, comprise the steps:

S1: probability density function and the cumulative distribution function of calculating M output of wind electric field according to the historical data sample of output of wind electric field;

S2: the described cumulative distribution function of historical data sample substitution of M output of wind electric field is obtained corresponding cumulative distribution function value;

S3: with described cumulative distribution function value respectively in a plurality of copula functions of substitution and obtain the parameter of copula function by maximum likelihood method; Determine respectively each copula function according to described parameter again;

S4: obtain experience copula functional value according to cumulative distribution function and cumulative distribution function value;

S5: according to copula functional value corresponding to each copula function calculation cumulative distribution function value among the step S3;

S6: according to described copula functional value and described experience copula functional value acquisition Euclidean space distance between the two;

S7: with described Euclidean space apart from the corresponding copula function of minimum as the copula function of describing the output of wind electric field correlativity;

S8: according to the correlation properties that obtain after the Spearman rank correlation coefficient between the copula function calculation output of wind electric field of selecting among the step S7, Kendall rank correlation coefficient, upper tail dependence coefficient and the lower tail related coefficient between the described wind energy turbine set.

Further, before step S3, also comprise copula function selection step:

S30: select the copula function according to the cumulative distribution function value.

Further, described step S30 is specially:

S301: obtain frequency histogram according to any two wind energy turbine set cumulative distribution function values;

S302: shape and related coefficient according to frequency histogram are selected the copula function.

Further, step S302 is specially:

When frequency histogram has symmetrical afterbody and tail dependence coefficient when being 0, select binary normal state Copula function and Frank copula function;

When frequency histogram has symmetrical afterbody and tail dependence coefficient when being not 0, select the t-Copula function;

When the upper tail height of frequency histogram and lower tail are low, select Gumbel Copula function;

When the high and upper tail of the lower tail of frequency histogram is low, select Clayton Copula function.

Further, in step S8, when being binary normal state copula function, described Kendall rank order correlation coefficient Described Spearman rank order correlation coefficient

Described lower tail related coefficient is λ ^Low=0; Described upper tail dependence coefficient is λ ^Up=0, ρ is correlation parameter.

Further, in step S8, when being the t-copula function, described Kendall rank order correlation coefficient Described Spearman rank order correlation coefficient Described lower tail related coefficient is

Described upper tail dependence coefficient is

ρ is correlation parameter, and k is the degree of freedom parameter, t _K+1For degree of freedom is that the t of k+1 distributes.

Further, in step S8, when being the Gumbel-copula function, described Kendall rank order correlation coefficient

Described lower tail related coefficient is λ ^Low=0; Described upper tail dependence coefficient is λ ^Up=2-2 ^1/aA is correlation parameter.

Further, in step S8, when being the Clayton-copula function, described Kendall rank order correlation coefficient Described lower tail related coefficient is λ ^Low=2 ^-1/aDescribed upper tail dependence coefficient is λ ^Up=0; The a correlation parameter.

Further, in step S8, when being the Frank-copula function, described Kendall rank order correlation coefficient

Described Spearman rank order correlation coefficient

Described lower tail related coefficient is λ ^Low=0; Described upper tail dependence coefficient is λ ^Up=0; The a correlation parameter,

Be debye function, m is the exponent number of debye function, D ₁And D ₂Represent respectively 1 rank and 2 rank debye functions, x is argument of function, and y is integration variable.

The present invention adopts the correlativity between the adjacent output of wind electric field in Copula function representation space, the method edge distributes without limits, can be with marginal distribution function and the separately research of their dependency structure of stochastic variable, avoid this difficult point of direct structure of multiple random variable joint distribution function, can catch non-linear between the variable, asymmetry and tail dependence relation, thereby provide more valuable wind power information for electric system.To the precision of prediction of raising output of wind electric field, and then improve the operation of power networks level, thereby reduce the consumption of non-regeneration energy, ensure power system safety and stability, improve power system economy, the minimizing greenhouse gas emission is significant.

Description of drawings

Fig. 1 is a kind of method realization flow figure that obtains correlation properties between the output of wind electric field based on the copula function that the embodiment of the invention provides;

Fig. 2 is the cumulative distribution function synoptic diagram that wind energy turbine set WF1 exerts oneself;

Fig. 3 is the cumulative distribution function synoptic diagram that wind energy turbine set WF2 exerts oneself;

Fig. 4 is the frequency Nogata synoptic diagram of two wind energy turbine set WF1 and the WF2 cumulative distribution function of exerting oneself;

Fig. 5 is correlation parameter ρ=0.9697 o'clock binary normal state copula function synoptic diagram;

T-copula function synoptic diagram when Fig. 6 is correlation parameter ρ=0.9697 and degree of freedom parameter k=3.9612;

Fig. 7 is the experience copula function synoptic diagram that two wind energy turbine set WF1 and WF2 exert oneself.

Embodiment

In order to make purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, is not intended to limit the present invention.

In order to solve the technical matters that correlativity is difficult to portray between the output of wind electric field, with reference to shown in Figure 1, the invention provides a kind of based on the copula function portray windy electric field exert oneself between the method for correlativity, specifically comprise following steps:

(1) determine the probability distribution function of each output of wind electric field, computing method are as follows:

If x _i(i=1,2 ..., N) be the historical data sample of an output of wind electric field, calculate probability density function f (x) and the cumulative distribution function F (x) at x place, arbitrfary point according to formula (1)-(4); $f\left(x\right)=\frac{1}{\mathrm{Nh}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{x-x_i}{h}\right)---\left(1\right),$ $f\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{x-x_i}{h}\right)---\left(2\right),$ $K\left(\frac{x-x_i}{h}\right)=\frac{1}{\sqrt{2\mathrm{\π}}}\exp (-\frac{1}{2}\×{\left(\frac{x-x_i}{h}\right)}^2)---\left(3\right),$ H=1.06Sn ^-0.2(4), in the formula, K is called kernel function, and h is called window width, and S is sample standard deviation, and n is total sample number.

Suppose to have M wind energy turbine set, can obtain the cumulative probability function of each output of wind electric field by above-mentioned calculating, be designated as respectively: (F ₁(x), F ₂(x) ..., F _j(x) ..., F _M(x)).

(2) data sample (X that exerts oneself that M wind energy turbine set is observed ₁, X ₂..., X _j..., X _M), X _j=(x _J1..., x _JN) ^TDifference substitution wind energy turbine set cumulative distribution function (F ₁(x), F ₂(x) ..., F _j(x) ..., F _M(x)), obtain corresponding cumulative distribution function value, be designated as (U ₁, U ₂..., U _j..., U _M), U _j=(U _J1, U _J2..., U _Jn..., U _JN) ^T

(3) select the copula function according to the cumulative distribution function value, for example: make any two wind energy turbine set cumulative distribution function value (U _i, U _j), U _i=(U _I1, U _I2..., U _In..., U _IN) ^T, U _j=(U _J1, U _J2..., U _Jn..., U _JN) ^TFrequency histogram, choose according to the histogrammic shape of binary and to select suitable copula function, specific as follows:

Rule 1: be 0 if frequency histogram has symmetrical afterbody and tail dependence coefficient, then select binary normal state Copula function and Frank copula function;

Rule 2: be not 0 if frequency histogram has symmetrical afterbody and tail dependence coefficient, then select the t-Copula function;

Rule 3: be " J " font if frequency histogram resembles, upper tail is high, lower tail is low, then selects the GumbelCopula function;

Rule 4: be " L " font if frequency histogram resembles, lower tail is high, and upper tail is low, then selects the ClaytonCopula function.

(4) utilize the data obtained (U ₁, U ₂..., U _j..., U _M), obtain parameter in the selected copula function by maximum likelihood method.Approximating method is as follows:

The expression formula of given first binary Gumbel Copula function, Clayton Copula function, Frank copula function, t-copula function and normal state copula function:

(4.1) Gumbel Copula function:

$C_{\mathrm{Gum}}(u,v;a)=\exp \{-{[{(-\log u)}^{\frac{1}{a}}+{(-\log v)}^{\frac{1}{a}}]}^a\},0<a\&le;1\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\left(5\right),$ A ∈ in the formula (0,1] be correlation parameter, when a=1, stochastic variable u, v is independent, and as a=0 stochastic variable u, v is tending towards complete dependence.

(4.2) Clayton Copula function:

$C_{\mathrm{cl}}(u,v;a)=\max \{{(u^{-a}+v^{-a}-1)}^{\frac{1}{a}},0\},a>0\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\left(6\right),$ A ∈ in the formula (0, ∞) be correlation parameter, when a → 0, stochastic variable u, v trends towards independence, and as a → 1 stochastic variable u, v is tending towards complete dependence.

(4.3) Frank Copula function:

$C_F(u,v;a)=-\frac{1}{a}\log (1+\frac{(e^{-\mathrm{au}}-1)(e^{-\mathrm{av}}-1)}{e^{-a}-1}),a>0\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\left(7\right),$ A is correlation parameter in the formula, a ≠ 0, a〉0 stochastic variable u, v positive correlation, as a → 0 stochastic variable u, it is independent that v is tending towards, a＜0 stochastic variable u, v negative correlation.

(4.4) t-Copula function:

$C_t(u,v;\mathrm{\&rho;},\mathrm{\&tau;})={\&Integral;}_{-\&infin;}^{T_{\mathrm{\&tau;}}^{-1}\left(u\right)}{\&Integral;}_{-\&infin;}^{T_{\mathrm{\&tau;}}^{-1}\left(v\right)}\frac{1}{2\mathrm{\&pi;}\sqrt{1-{\mathrm{\&rho;}}^2}}{(1+\frac{s^2-2\mathrm{\&rho;st}+t^2}{\mathrm{\&tau;}(1-{\mathrm{\&rho;}}^2)})}^{\frac{-(\mathrm{\&tau;}+2)}{2}}\mathrm{dsdt}\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\left(8\right),$ Wherein-and 1≤ρ≤1 is interdependent parameter, τ is the degree of freedom parameter, T _ZWith

Being respectively degree of freedom is student t-distribution and the inverse function thereof of τ.

(4.5) normal state Copula function (Gauss Copula function):

Wherein-1≤ρ≤1 is interdependent parameter, Φ and Φ ^-1Be respectively standardized normal distribution and inverse function thereof.

Wherein (5), (6), (7) are called Archimedes's contiguous function, (8), (9) are called the elliptical-type contiguous function.

The probability density function of supposing to treat the Copula function of match is expressed as c (u ₁, u ₂..., u _n| θ), wherein θ is for needing the parameter of estimation: the structure likelihood function

Get the logarithm of likelihood function $\ln L\left(\mathrm{\&theta;}\right)=\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\ln f({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1,i},u_{2,i},\&CenterDot;\&CenterDot;\&CenterDot;,u_{n,i}|\mathrm{\&theta;});$ Order $\frac{\&PartialD;\ln L}{\&PartialD;\mathrm{\&theta;}}=0;$ Separate the maximum likelihood estimator that likelihood equation gets parameter θ

(5) obtain experience copula functional value according to cumulative distribution function and cumulative distribution function value;

Utilizing cumulative distribution function is (F ₁(x), F ₂(x) ..., F _j(x) ..., F _MAnd (U (x)) ₁, U ₂..., U _j..., U _M), calculate experience copula functional value, computing method are as follows:

$C_n({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{I}_{F_1(x_{1,i}\&le;u_1)}\&CenterDot;\&CenterDot;\&CenterDot;I_{F_M(x_{M,i}\&le;u_M)}$

Wherein, I _[]Be indicative function, work as F _n(x _{M, i})≤u _mThe time,

Otherwise

(6) with (U ₁, U ₂..., U _j..., U _M) substitution match the copula function and the experience copula function that obtain, the Euclidean space distance of the copula function of digital simulation and experience copula function is selected the minimum copula function of distance as describing the exert oneself copula function of correlativity of windy electric field.Computing method are as follows:

(6.1) the Euclidean distance computing formula of Gauss copula function and experience copula function: $d_{\mathrm{Ga}}^2=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{|C_{\mathrm{Ga}}({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)-C_n({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)|}^2$

(6.2) the Euclidean distance computing formula of t-copula function and experience copula function: $d_t^2=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{|C_t({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)-C_n({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)|}^2$

(6.3) the Euclidean distance computing formula of Gumbel Copula function and experience copula function: $d_{\mathrm{Gum}}^2=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{|C_{\mathrm{Gum}}({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)-C_n({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)|}^2$

(6.4) the Euclidean distance computing formula of Clayton Copula function and experience copula function: $d_{\mathrm{Cla}}^2=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{|C_{\mathrm{Cla}}({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)-C_n({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)|}^2$

(6.5) the Euclidean distance computing formula of Frank copula function and experience copula function: $d_F^2=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{|C_F({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)-C_n({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002442517500022.png,HDA00002442517500031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M)|}^2$

(7) utilize the copula function that calculates, calculate Spearman rank correlation coefficient, Kendall rank correlation coefficient, upper tail dependence coefficient and lower tail related coefficient that windy electric field is exerted oneself.

Various copula function calculation method is as follows:

(7.1) normal state copula function: Kendall rank correlation coefficient

The Spearman rank correlation coefficient

Lower tail related coefficient λ ^Low=0; Upper tail dependence coefficient lambda ^Up=0; In the formula, ρ is correlation parameter.

(7.2) t-copula function: Kendall rank correlation coefficient

The Spearman rank correlation coefficient ${\mathrm{\&rho;}}_s=\frac{6\arcsin \frac{\mathrm{\&rho;}}{2}}{\mathrm{\&pi;}};$ The lower tail related coefficient ${\mathrm{\&lambda;}}^{\mathrm{low}}=2-2t_{k+1}\left(\frac{\sqrt{k+1}\sqrt{1-\mathrm{\&rho;}}}{\sqrt{1+\mathrm{\&rho;}}}\right);$ Upper tail dependence coefficient

ρ is correlation parameter in the formula, t _K+1For degree of freedom is that the t of k+1 distributes.

(7.3) Gumbel-copula function: Kendall rank correlation coefficient

Lower tail related coefficient λ ^Low=0; Upper tail dependence coefficient lambda ^Up=2-2 ^1/a, a correlation parameter.

(7.4) Clayton-copula function: Kendall rank correlation coefficient

Lower tail related coefficient λ ^Low=2 ^-1/aUpper tail dependence coefficient lambda ^Up=0, a correlation parameter.

(7.5) Frank-copula function: Kendall rank correlation coefficient The Spearman rank correlation coefficient Lower tail related coefficient λ ^Low=0; Upper tail dependence coefficient lambda ^Up=0, a correlation parameter, Be debye function, m is the exponent number of debye function, D ₁And D ₂Represent respectively 1 rank and 2 rank debye functions, x is argument of function, and y is integration variable.

The present invention adopts the correlativity between the adjacent wind energy turbine set in Copula function (contiguous function) description space, the method edge distributes without limits, can be with marginal distribution function and the separately research of their dependency structure of stochastic variable, avoid this difficult point of direct structure of multiple random variable joint distribution function, can catch non-linear between the variable, asymmetry and tail dependence relation, thereby provide more valuable wind power information for electric system.To the precision of prediction of raising output of wind electric field, and then improve the operation of power networks level, thereby reduce the consumption of non-regeneration energy, ensure power system safety and stability, improve power system economy, the minimizing greenhouse gas emission is significant.

A kind ofly obtain the method for output of wind electric field correlation properties based on the copula function for what illustrate further that the embodiment of the invention provides, details are as follows with reference to the accompanying drawings and in conjunction with instantiation:

The for convenience of explanation principle of the invention and step, embodiment take the Texas history in 1 year of adjacent two wind energy turbine set observed value (representing with W1 and W2) of exerting oneself study as example, the basic geography information of wind energy turbine set WF1 and WF2 as shown in Table 1:

Wind field

The position

Height above sea level (m)

Wind density

Wind speed

Capacity

?	?	?	（W/m2）	(m/s)	(MW)
						WF1	（31.19N，102.24W）	850	401.3	7.6	30
WF2	（31.19N，102.21W）	850	419	7.8	31.3
						WF3	（31.23N，102.21W）	850	427.8	8.1	33.6

Table one

(1) determines the distribution function of each output of wind electric field.

Adopt method of the present invention, obtain two output of wind electric field cumulative distribution function F shown in accompanying drawing 2 and accompanying drawing 3 ₁(x) and F ₂(x).As seen, though the distribution function that calculates and empirical distribution function are incomplete same, but both difference are very small from accompanying drawing.

(2) the cumulative distribution function U of two output of wind electric field of drafting ₁=F ₁(x) and U ₂=F ₂(x) frequency histogram, as shown in Figure 4, can find out that from accompanying drawing 4 two output of wind electric field have symmetrical afterbody, the dependency structure that therefore can select binary normal state Copula function or binary t-Copula function representation wind energy turbine set W1 and wind energy turbine set W2 to exert oneself.

(3) utilize method of the present invention, the parameter of match binary normal state copula and binary t-Copula function, the result as shown in Table 2, binary normal state copula function, binary t-Copula function and the experience distribution copula function that match obtains such as accompanying drawing 5, Fig. 6 and shown in Figure 7:

Table two

(4) method of setting forth according to the present invention is calculated the copula function of gained and the theorem in Euclid space distance of experience copula function, thereby selects best copula function.More as can be known, the Euclidean distance of binary normal state Copula and experience Copula square is 0.2074 by the Euclidean distance duplicate ratio, and the Euclidean distance of binary t-Copula and experience Copula square is 0.2314.Therefore, under Euclidean distance square index instructs, can think binary normal state Copula and better match wind energy turbine set of experience Copula model W1 and the W2 correlativity between exerting oneself.

With correlation matrix ρ=0.9697 substitution normal state copula function

Obtain describing the exert oneself function of correlativity of wind energy turbine set W1 and W2:

(5) utilize the copula function, try to achieve the joint probability distribution function that windy electric field is exerted oneself:

(6) utilize the copula function of gained, the Spearman rank correlation coefficient that the windy electric field in zoning is exerted oneself, Kendall rank correlation coefficient, upper tail dependence coefficient and lower tail related coefficient; Wherein, Kendall rank correlation coefficient

The Spearman rank correlation coefficient

Lower tail related coefficient λ ^Low=0; Upper tail dependence coefficient lambda ^Up=0.

Upper tail dependence coefficient and lower tail related coefficient are 0, illustrate that two output of wind electric field have symmetrical afterbody.

Those skilled in the art will readily understand; the above only is preferred embodiment of the present invention; not in order to limiting the present invention, all any modifications of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., all should be included within protection scope of the present invention.

Claims (9)

1. one kind is obtained the method for output of wind electric field correlation properties based on the copula function, it is characterized in that, comprises the steps:

S1: probability density function and the cumulative distribution function of calculating M output of wind electric field according to the historical data sample of output of wind electric field;

S2: the described cumulative distribution function of historical data sample substitution of M output of wind electric field is obtained corresponding cumulative distribution function value;

S3: with described cumulative distribution function value respectively in a plurality of copula functions of substitution and obtain the parameter of copula function by maximum likelihood method; Determine respectively each copula function according to described parameter again;

S4: obtain experience copula functional value according to cumulative distribution function and cumulative distribution function value;

S5: according to copula functional value corresponding to each copula function calculation cumulative distribution function value among the step S3;

S6: according to described copula functional value and described experience copula functional value acquisition Euclidean space distance between the two;

S7: with described Euclidean space apart from the corresponding copula function of minimum as the copula function of describing the output of wind electric field correlativity;

S8: according to the correlation properties that obtain after the Spearman rank correlation coefficient between the copula function calculation output of wind electric field of selecting among the step S7, Kendall rank correlation coefficient, upper tail dependence coefficient and the lower tail related coefficient between the described wind energy turbine set.

2. the method for claim 1 is characterized in that, also comprises copula function selection step before step S3:

S30: select the copula function according to the cumulative distribution function value.

3. method as claimed in claim 2 is characterized in that, described step S30 is specially:

S301: obtain frequency histogram according to any two wind energy turbine set cumulative distribution function values;

S302: shape and related coefficient according to frequency histogram are selected the copula function.

4. method as claimed in claim 3 is characterized in that, step S302 is specially:

When frequency histogram has symmetrical afterbody and tail dependence coefficient when being 0, select binary normal state Copula function and Frank copula function;

When frequency histogram has symmetrical afterbody and tail dependence coefficient when being not 0, select the t-Copula function;

When the upper tail height of frequency histogram and lower tail are low, select Gumbel Copula function;

When the high and upper tail of the lower tail of frequency histogram is low, select Clayton Copula function.

5. method as claimed in claim 4 is characterized in that, in step S8, and when being binary normal state copula function, described Kendall rank order correlation coefficient

Described Spearman rank order correlation coefficient

Described lower tail related coefficient is λ ^Low=0; Described upper tail dependence coefficient is λ ^Up=0, ρ is correlation parameter.

6. method as claimed in claim 4 is characterized in that, in step S8, and when being the t-copula function, described Kendall rank order correlation coefficient

Described Spearman rank order correlation coefficient ${\mathrm{\&rho;}}_s=\frac{6\arcsin \frac{\mathrm{\&rho;}}{2}}{\mathrm{\&pi;}};$ Described lower tail related coefficient is ${\mathrm{\&lambda;}}^{\mathrm{low}}=2-2t_{k+1}\left(\frac{\sqrt{k+1}\sqrt{1-\mathrm{\&rho;}}}{\sqrt{1+\mathrm{\&rho;}}}\right);$ Described upper tail dependence coefficient is ρ is correlation parameter, and k is the degree of freedom parameter, t _K+1For degree of freedom is that the t of k+1 distributes.

7. method as claimed in claim 4 is characterized in that, in step S8, and when being the Gumbel-copula function, described Kendall rank order correlation coefficient

Described lower tail related coefficient is λ ^Low=0; Described upper tail dependence coefficient is λ ^Up=2-2 ^1/aA is correlation parameter.

8. method as claimed in claim 4 is characterized in that, in step S8, and when being the Clayton-copula function, described Kendall rank order correlation coefficient Described lower tail related coefficient is λ ^Low=2 ^-1/aDescribed upper tail dependence coefficient is λ ^Up=0; The a correlation parameter.

9. method as claimed in claim 4 is characterized in that, in step S8, and when being the Frank-copula function, described Kendall rank order correlation coefficient

Described Spearman rank order correlation coefficient

Described lower tail related coefficient is λ ^Low=0; Described upper tail dependence coefficient is λ ^Up=0; The a correlation parameter,

Be debye function, m is the exponent number of debye function, D ₁And D ₂Represent respectively 1 rank and 2 rank debye functions, x is argument of function, and y is integration variable.

Images