CN102609397B - Based on the wind velocity distributing paremeter method for parameter estimation of low order probability right square - Google Patents

Abstract

The invention discloses the wind velocity distributing paremeter method for parameter estimation based on low order probability right square, dependent variable and independent variable is adopted to exchange, Luo Jisidi curve is utilized to draft the explicit algorithm relational expression of wind speed form parameter, solve the problem that low order probability right square method for parameter estimation is not easily applied, by accuracy test and example display, what can obtain three parameters of the wind speed three-parameter weibull distribution parameter estimation with degree of precision solves relational expression, thus improves the precision of wind velocity distributing paremeter parameter estimation.Two kinds of low order probability-weighted moment that the present invention proposes have higher precision in the scope that Wind Power Utilization relates to, and all can be used as the effective ways of wind speed three-parameter weibull distribution parameter estimation.

Description

Based on the wind velocity distributing paremeter method for parameter estimation of low order probability right square

Technical field

The present invention relates to the wind velocity distributing paremeter method for parameter estimation based on low order probability right square, belong to Evaluation of Wind Energy Resources and utilize field.

Background technology

Wind has the randomness of height, probability model can be utilized to describe its statistical nature, Weibull distribution is generally considered and surveys the good probability model of wind speed profile matching, be used widely in Evaluation of Wind Energy Resources, generated energy calculating, Wind turbines type selecting etc., in recent years, China just actively carries out the development & construction of marine wind electric field, and ocean surface wind speed is generally higher than littoral land-based area, and its probability distribution has in the overall phenomenon to the skew of high wind speed district.For improving the adaptability of wind speed probability model, the statistical property adopting wind speed three-parameter weibull distribution to describe wind is necessary, for the parameter estimation of wind speed three-parameter weibull distribution, at present, mainly contain maximum-likelihood method, moments method, correlation coefficient method, gray forecast approach and bilinear regression method etc., but these methods are often more loaded down with trivial details, generally need Program, the people being engaged in application work not easily grasps, and constrains the widespread use of wind speed three-parameter weibull distribution.

At present, a kind of probability right square is also had to be a kind of new square of Greenwood definition in 1979.It is multiplied by stochastic variable to calculate using the probability containing power as weight, and the proposition of probability right square, the parameter estimation for multiparameter probability distribution provides a kind of new approach.Three parameters distributed for asking Weibull, the parameter relationship formula of 3 probability right squares connection solution is needed to draw the distribution parameter relational expression represented with probability right square, and probability right square can also be estimated by sample probability weight square, thus the value just can carrying out three parameters is estimated.Because low order probability right square method for parameter estimation is not easily applied to engineering practice, and traditional order Probability weight square needs to utilize high-order to exceed probability right square, three parameters drawn solve relational expression, but now there are some researches show that sample order Probability weight square exists higher " ask square poor ", the precision using it to the wind velocity distributing paremeter parameter of estimation is not high.

Summary of the invention

In order to solve the problem adopting high-order to exceed the not high and low order probability right square method for parameter estimation of the precision of the wind velocity distributing paremeter parameter estimation that probability-weighted moment obtains not easily to apply, the present invention proposes and adopt dependent variable and independent variable to exchange, Luo Jisidi curve is utilized to draft the explicit algorithm relational expression of form parameter, solve the problem that low order probability right square is not easily applied, and can obtain three parameters of the wind speed three-parameter weibull distribution parameter estimation with degree of precision solve relational expression, thus improve the precision of wind velocity distributing paremeter parameter estimation.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

Based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability-weighted moment, it is characterized in that: comprise the following steps,

Step (1), lists probability distribution function and the probability density function of wind speed three-parameter weibull distribution, namely

$F\left(x\right)=1-\exp [-{\left(\frac{x-\mathrm{\δ}}{\mathrm{\β}}\right)}^{\mathrm{\α}}]---\left(1\right)$

$f\left(x\right)=\frac{\mathrm{\α}}{\mathrm{\β}}{\left(\frac{x-\mathrm{\δ}}{\mathrm{\β}}\right)}^{\mathrm{\α}-1}\exp [-{\left(\frac{x-\mathrm{\δ}}{\mathrm{\β}}\right)}^{\mathrm{\α}}]---\left(2\right)$

Wherein x is stochastic variable, α is the form parameter of wind speed, β is the scale parameter of wind speed, δ is the location parameter of wind speed, the probability distribution function of the wind speed three-parameter weibull distribution that F (x) is stochastic variable x, the probability density function of the wind speed three-parameter weibull distribution that f (x) is stochastic variable x;

Step (2), according to wind speed probability distribution, calculating probability right square is:

$M_{i,j,k}=E\left\{x^i{\left[F\left(x\right)\right]}^j{[1-F\left(x\right)]}^k\right\}=\underset{0}{\overset{1}{\∫}}{\left[x\left(F\right)\right]}^i{F}^j{(1-F)}^k\mathrm{dF}---\left(3\right)$

In formula, E{} is the mathematical expectation of certain probability distribution or the combination distribution that probability statistics represents; F ≡ F (x)=P (x ∈ X), X is the set of stochastic variable x, the definition that P (x ∈ X) is the probability statistics of distribution function F (x), for meeting the probability of set (x ∈ X); X ≡ x (F)=P ^-1(F), P ^-1(F) be the inverse function of the distribution function of stochastic variable x, i, j, k are real parameter;

Step (3), if the real parameter k=0 in step (2), not as good as probability right square is then,

$M_{i,j,0}=\underset{0}{\overset{1}{\∫}}{x}^i{F}^j\mathrm{dF}=\underset{\mathrm{\δ}}{\overset{\∞}{\∫}}{x}^i{\left[\underset{\mathrm{\δ}}{\overset{x}{\∫}}f\left(t\right)\mathrm{dt}\right]}^{j}f\left(x\right)\mathrm{dx}---\left(4\right)$

In formula, M _{i, j, 0}for j rank are not as good as probability right square;

Step (4), according to the formula of the too late probability right square that step (3) draws, the probability distribution function of wind speed three-parameter weibull distribution step (1) listed and probability density function substitute in formula (4), and get i=1, j=0,1,2,0 ~ 2 rank of deriving wind speed three-parameter weibull distribution are not as good as the relation of probability right square and distribution parameter, and relational expression is:

$M_{\mathrm{1,0,0}}=\mathrm{\δ}+\mathrm{\β\Γ}(1+\frac{1}{\mathrm{\α}})---\left(5\right)$

$M_{1,\mathrm{1,0}}=\frac{\mathrm{\δ}}{2}+\mathrm{\β\Γ}(1+\frac{1}{\mathrm{\α}})[1-2^{-(1+\frac{1}{\mathrm{\α}})}]---\left(6\right)$

$M_{1,2,0}=\frac{\mathrm{\δ}}{3}+\mathrm{\β\Γ}(1+\frac{1}{\mathrm{\α}})[1-2^{1-(1+\frac{1}{\mathrm{\α}})}+3^{-(1+\frac{1}{\mathrm{\α}})}]---\left(7\right)$

In formula, Γ (*) is gamma function;

Step (5), connection 0 ~ 2 rank of separating the wind speed three-parameter weibull distribution in step (4), not as good as the relational expression (5) of probability right square and distribution parameter, (6), (7), obtain,

$\frac{3M_{\mathrm{1,2,0}}-M_{\mathrm{1,0,0}}}{2M_{\mathrm{1,1,0}}-M_{\mathrm{1,0,0}}}=2-\frac{3^{\frac{1}{\mathrm{\α}}}-2^{\frac{1}{\mathrm{\α}}}}{6^{\frac{1}{\mathrm{\α}}}-3^{\frac{1}{\mathrm{\α}}}}---\left(8\right)$

Step (6), setting form parameter α variation range is 0.45 ~ 8.0, and the sample value of α is got by step-length 0.01, substitute into item on the right of formula formula (8) equal sign, adopt Luo Jisidi curve to go out form parameter α value and low order not as good as the empirical relationship of probability right square, draw the explicit relation formula of form parameter α as dependent variable:

$\left.\begin{array}{c}{J}_M=\frac{3M_{\mathrm{1,2,0}}-M_{\mathrm{1,0,0}}}{2M_{\mathrm{1,1,0}}-M_{\mathrm{1,0,0}}}\≅\frac{3{\hat{M}}_{\mathrm{1,2,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}\\ \mathrm{\α}=\frac{0.767}{0.040\exp \left(2.277J_M\right)-1}\end{array}\right\}---\left(9\right)$

In formula, for jth rank sample is not as good as probability right square, j=0,1,2, represent the sign of operation calculated via estimator;

Step (7), according to the relational expression (5) in step (4), (6), (7), draws the relational expression of the scale parameter that the sample value of choosing α is corresponding and location parameter β, δ value:

$\left.\begin{array}{c}\mathrm{\β}\≅\frac{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{(1-2^{\frac{-1}{\mathrm{\α}}})\mathrm{\Γ}(1+\frac{1}{\mathrm{\α}})}\\ \mathrm{\δ}\≅{\hat{M}}_{\mathrm{1,0,0}}-\mathrm{\β\Γ}(1+\frac{1}{\mathrm{\α}})\end{array}\right\}---\left(10\right)$

In formula, for jth rank sample is not as good as probability right square, j=0,1,2.

Aforesaid based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability-weighted moment, it is characterized in that: described wind speed form parameter α >0, wind speed scale parameter β >0, wind speed location parameter δ < x _min, wherein x _minfor the minimum value of stochastic variable.

Aforesaidly it is characterized in that: when δ=0 based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability-weighted moment, described step (4) only need derive the relation of 0 ~ 1 rank not as good as probability right square and distribution parameter.

Aforesaid based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability-weighted moment, it is characterized in that: the characteristic index envelope average wind power density of described step (8) wind energy, effectively wind power concentration, wind energy can utilize time and the theoretical annual electricity generating capacity of unit.

Exceed a wind velocity distributing paremeter method for parameter estimation for probability-weighted moment based on low order, it is characterized in that: comprise the following steps,

Step (1), lists probability distribution function and the probability density function of wind speed three-parameter weibull distribution, namely

$F\left(x\right)=1-\exp [-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}]---\left(1\right)$

$f\left(x\right)=\frac{\mathrm{\&alpha;}}{\mathrm{\&beta;}}{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}-1}\exp [-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}]---\left(2\right)$

Wherein x is stochastic variable, α is the form parameter of wind speed, β is the scale parameter of wind speed, δ is the location parameter of wind speed, the probability distribution function of the wind speed three-parameter weibull distribution that F (x) is stochastic variable x, the probability density function of the wind speed three-parameter weibull distribution that f (x) is stochastic variable x; Step (2), according to wind speed probability distribution, calculates and exceedes probability right square and be:

$M_{i,j,k}=E\left\{x^i{\left[F\left(x\right)\right]}^j{[1-F\left(x\right)]}^k\right\}=\underset{0}{\overset{1}{\&Integral;}}{\left[x\left(F\right)\right]}^i{F}^j{(1-F)}^k\mathrm{dF}---\left(3\right)$

In formula, E{} is the mathematical expectation of certain probability distribution or the combination distribution that probability statistics represents; F ≡ F (x)=P (x ∈ X), X is the set of stochastic variable x, the definition that P (x ∈ X) is the probability statistics of distribution function F (x), for meeting the probability of set (x ∈ X); X ≡ x (F)=P ^-1(F), P ^-1(F) be the inverse function of the distribution function of stochastic variable x, i, j, k are real parameter;

Step (3), if the real parameter j=0 in step (2), then exceeding probability right square is,

$M_{i,0,k}=\underset{0}{\overset{1}{\&Integral;}}{x}^i{(1-F)}^k\mathrm{dF}=\underset{\mathrm{\&delta;}}{\overset{\&infin;}{\&Integral;}}{x}^i{[1-\underset{\mathrm{\&delta;}}{\overset{x}{\&Integral;}}f\left(t\right)\mathrm{dt}]}^{k}f\left(x\right)\mathrm{dx}---\left(11\right)$

In formula, M _{i, 0, k}for k rank exceed probability right square;

Step (4), the formula exceeding probability right square is drawn according to step (3), the probability distribution function of wind speed three-parameter weibull distribution step (1) listed and probability density function substitute in formula (11), and get i=1, k=1,2,3,1 rank, rank ~ 3 of deriving wind speed three-parameter weibull distribution exceed the relation of probability right square and distribution parameter, and relational expression is:

$M_{\mathrm{1,0},1}=\frac{\mathrm{\&delta;}}{2}+\frac{\mathrm{\&beta;}}{2^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(12\right)$

$M_{\mathrm{1,0},2}=\frac{\mathrm{\&delta;}}{3}+\frac{\mathrm{\&beta;}}{3^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(13\right)$

$M_{\mathrm{1,0},3}=\frac{\mathrm{\&delta;}}{4}+\frac{\mathrm{\&beta;}}{4^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(14\right)$

In formula, Γ (*) is gamma function;

Step (5), 1 rank, rank ~ 3 of the wind speed three-parameter weibull distribution that connection is separated in step (4) exceed relational expression (12), (13), (14) of probability right square and distribution parameter, obtain,

$\frac{2M_{1,0,1}-M_{\mathrm{1,0,0}}}{3M_{1,0,2}-M_{\mathrm{1,0,0}}}=\frac{6^{\frac{1}{\mathrm{\&alpha;}}}-3^{\frac{1}{\mathrm{\&alpha;}}}}{6^{\frac{1}{\mathrm{\&alpha;}}}-2^{\frac{1}{\mathrm{\&alpha;}}}}---\left(15\right)$

Step (6), setting form parameter α variation range is 0.45 ~ 8.0, and the sample value of α is got by step-length 0.01, substitute into item on the right of formula formula (13) equal sign, adopt Luo Jisidi curve to go out form parameter α value and the empirical relationship exceeding probability right square, draw the explicit relation formula of α as dependent variable:

$\left.\begin{array}{c}{K}_M=\frac{2M_{\mathrm{1,0},1}-M_{\mathrm{1,0,0}}}{3M_{\mathrm{1,0,2}}-M_{\mathrm{1,0,0}}}\&cong;\frac{2{\hat{M}}_{1,0,1}-{\hat{M}}_{\mathrm{1,0,0}}}{3{\hat{M}}_{\mathrm{1,0,2}}-{\hat{M}}_{\mathrm{1,0,0}}}\\ \mathrm{\&alpha;}=\frac{0.253}{0.297\exp \left(1.925K_M\right)-1}\end{array}\right\}---\left(16\right)$

In formula, for kth rank sample exceedes probability right square, k=0,1,2, represent the sign of operation calculated via estimator;

Step (7), according to the relational expression (12) in step (4), (13), (14), draws the relational expression of the scale parameter that the sample value of choosing α is corresponding and location parameter β, δ value:

$\left.\begin{array}{c}\mathrm{\&beta;}\&cong;\frac{{\hat{M}}_{\mathrm{1,0,0}}-2{\hat{M}}_{\mathrm{1,0},1}}{(1-2^{\frac{-1}{\mathrm{\&alpha;}}})\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})}\\ \mathrm{\&delta;}\&cong;{\hat{M}}_{\mathrm{1,0,0}}-\mathrm{\&beta;\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})\end{array}\right\}---\left(17\right)$

In formula, for kth rank sample exceedes probability right square, k=0,1,2.

The aforesaid wind velocity distributing paremeter method for parameter estimation exceeding probability-weighted moment based on low order, it is characterized in that: described wind speed form parameter α >0, wind speed scale parameter β >0, wind speed location parameter δ < x _min, wherein x _minfor the minimum value of stochastic variable.

The aforesaid wind velocity distributing paremeter method for parameter estimation exceeding probability-weighted moment based on low order, is characterized in that: when δ=0, and described step (4) only need derive the relation that 0 ~ 1 rank exceed probability right square and distribution parameter.

The aforesaid wind velocity distributing paremeter method for parameter estimation exceeding probability-weighted moment based on low order, is characterized in that: the characteristic index envelope average wind power density of described step (8) wind energy, effectively wind power concentration, wind energy can utilize time and the theoretical annual electricity generating capacity of unit.

Beneficial effect of the present invention: the present invention proposes probability right square method for parameter estimation at a low price and carry out the parameter estimation of wind speed three-parameter weibull distribution, what obtain three parameters of the wind speed three-parameter weibull distribution parameter estimation with degree of precision solves relational expression, adopt dependent variable and independent variable exchanges and Luo Jisidi curve drafts the explicit algorithm relational expression of form parameter, solve the problem that low order probability right square method for parameter estimation is not easily applied, by accuracy test and example display, improve the precision of wind velocity distributing paremeter parameter estimation, two kinds of low order probability-weighted moment that the present invention proposes have higher precision in the scope that Wind Power Utilization relates to, all can be used as the effective ways of three-parameter weibull distribution parameter estimation.

Accompanying drawing explanation

Fig. 1 is the fit error curve figure of the experimental formula α value that low order probability right square method for parameter estimation of the present invention draws.

Embodiment

Below in conjunction with Figure of description, the present invention is further illustrated.

The present invention is based on the relation of the low order probability-weighted moment on 0,1,2 rank and the distribution parameter of wind speed, the low order probability-weighted moment that two kinds have the three-parameter weibull distribution parameter estimation of degree of precision is proposed, what draw three parameters solves relational expression, two kinds of low order probability-weighted moment are that low order exceedes probability-weighted moment not as good as probability-weighted moment and low order respectively, the too late probability right square of same order and exceed between probability right square and there is linear relationship, can derive each other.Thus, the factor that there are differences of fitting precision of removing empirical relationship, two kinds of low order probability-weighted moment that the present invention proposes are consistent in essence, have equal precision level in theory, below just introduce lower two kinds of low order probability-weighted moment respectively.

The first, based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability-weighted moment, comprises the following steps,

The first step: probability distribution function and the probability density function of listing wind speed three-parameter weibull distribution, namely

$F\left(x\right)=1-\exp [-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}]---\left(1\right)$

$f\left(x\right)=\frac{\mathrm{\&alpha;}}{\mathrm{\&beta;}}{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}-1}\exp [-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}]---\left(2\right)$

Wherein x is stochastic variable, α > 0, is the form parameter of wind speed, and β >0 is the scale parameter of wind speed, δ < x _min, be the location parameter of wind speed, wherein x _minfor the minimum value of stochastic variable, the probability distribution function of the wind speed three-parameter weibull distribution that F (x) is stochastic variable x, the probability density function of the wind speed three-parameter weibull distribution that f (x) is stochastic variable x;

Second step: according to wind speed probability distribution, calculating probability right square is:

$M_{i,j,k}=E\left\{x^i{\left[F\left(x\right)\right]}^j{[1-F\left(x\right)]}^k\right\}=\underset{0}{\overset{1}{\&Integral;}}{\left[x\left(F\right)\right]}^i{F}^j{(1-F)}^k\mathrm{dF}---\left(3\right)$

In formula, E{} is the mathematical expectation of certain probability distribution or the combination distribution that probability statistics represents; F ≡ F (x)=P (x ∈ X), X is the set of stochastic variable x, the definition that P (x ∈ X) is the probability statistics of distribution function F (x), for meeting the probability of set (x ∈ X); X ≡ x (F)=P ^-1(F), P ^-1(F) be the inverse function of the distribution function of stochastic variable x, i, j, k are real parameter;

3rd step: establish the real parameter k=0 in second step, then not as good as probability right square be,

$M_{i,j,0}=\underset{0}{\overset{1}{\&Integral;}}{x}^i{F}^j\mathrm{dF}=\underset{\mathrm{\&delta;}}{\overset{\&infin;}{\&Integral;}}{x}^i{\left[\underset{\mathrm{\&delta;}}{\overset{x}{\&Integral;}}f\left(t\right)\mathrm{dt}\right]}^{j}f\left(x\right)\mathrm{dx}---\left(4\right)$

In formula, M _{i, j, 0}for j rank are not as good as probability right square;

4th step: according to the formula of the too late probability right square that the 3rd step draws, the probability distribution function of wind speed three-parameter weibull distribution step (1) listed and probability density function substitute in formula (4), and get i=1, j=0,1,2,0 ~ 2 rank of deriving wind speed three-parameter weibull distribution are not as good as the relation of probability right square and distribution parameter, and relational expression is:

$M_{\mathrm{1,0,0}}=\mathrm{\&delta;}+\mathrm{\&beta;\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(5\right)$

$M_{1,\mathrm{1,0}}=\frac{\mathrm{\&delta;}}{2}+\mathrm{\&beta;\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})[1-2^{-(1+\frac{1}{\mathrm{\&alpha;}})}]---\left(6\right)$

$M_{1,2,0}=\frac{\mathrm{\&delta;}}{3}+\mathrm{\&beta;\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})[1-2^{1-(1+\frac{1}{\mathrm{\&alpha;}})}+3^{-(1+\frac{1}{\mathrm{\&alpha;}})}]---\left(7\right)$

In formula, Γ (*) is gamma function;

5th step: 0 ~ 2 rank of the wind speed three-parameter weibull distribution in connection solution the 4th step, not as good as the relational expression (5) of probability right square and distribution parameter, (6), (7), obtain,

$\frac{3M_{\mathrm{1,2,0}}-M_{\mathrm{1,0,0}}}{2M_{\mathrm{1,1,0}}-M_{\mathrm{1,0,0}}}=2-\frac{3^{\frac{1}{\mathrm{\&alpha;}}}-2^{\frac{1}{\mathrm{\&alpha;}}}}{6^{\frac{1}{\mathrm{\&alpha;}}}-3^{\frac{1}{\mathrm{\&alpha;}}}}---\left(8\right)$

6th step: setting form parameter α variation range is 0.45 ~ 8.0, and get α sample value by step-length 0.01, substitute into item on the right of formula formula (8) equal sign, adopt Luo Jisidi curve to go out form parameter α value and the empirical relationship not as good as probability right square, draw the explicit relation formula of form parameter α as dependent variable:

$\left.\begin{array}{c}{J}_M=\frac{3M_{\mathrm{1,2,0}}-M_{\mathrm{1,0,0}}}{2M_{\mathrm{1,1,0}}-M_{\mathrm{1,0,0}}}\&cong;\frac{3{\hat{M}}_{\mathrm{1,2,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}\\ \mathrm{\&alpha;}=\frac{0.767}{0.040\exp \left(2.277J_M\right)-1}\end{array}\right\}---\left(9\right)$

In formula, for jth rank sample is not as good as probability right square (j=0,1,2), represent the sign of operation calculated via estimator;

7th step: according to the relational expression (5) in the 4th step, (6), (7), draws the relational expression of the scale parameter that the sample value of choosing α is corresponding and location parameter β, δ value:

$\left.\begin{array}{c}\mathrm{\&beta;}\&cong;\frac{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{(1-2^{\frac{-1}{\mathrm{\&alpha;}}})\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})}\\ \mathrm{\&delta;}\&cong;{\hat{M}}_{\mathrm{1,0,0}}-\mathrm{\&beta;\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})\end{array}\right\}---\left(10\right)$

In formula, for jth rank sample is not as good as probability right square (j=0,1,2).

Especially, when δ=0, wind speed three-parameter weibull distribution is just wind speed Two-parameter Weibull distribution, described 4th step only need derive the relation of 0 ~ 1 rank not as good as probability right square and distribution parameter of Weibull distribution, then obtains other two parameter relationship formulas according to the five to eight follow-up step execution.

The second exceedes the wind velocity distributing paremeter method for parameter estimation of probability-weighted moment based on low order, comprises the following steps:

The first step: probability distribution function and the probability density function of listing wind speed three-parameter weibull distribution, namely

$F\left(x\right)=1-\exp [-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}]---\left(1\right)$

$f\left(x\right)=\frac{\mathrm{\&alpha;}}{\mathrm{\&beta;}}{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}-1}\exp [-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}]---\left(2\right)$

Wherein x is stochastic variable, α is the form parameter of wind speed, β is the scale parameter of wind speed, δ is the location parameter of wind speed, the probability distribution function of the wind speed three-parameter weibull distribution that F (x) is stochastic variable x, the probability density function of the wind speed three-parameter weibull distribution that f (x) is stochastic variable x; Second step: according to wind speed probability distribution, calculates and exceedes probability right square and be:

$M_{i,j,k}=E\left\{x^i{\left[F\left(x\right)\right]}^j{[1-F\left(x\right)]}^k\right\}=\underset{0}{\overset{1}{\&Integral;}}{\left[x\left(F\right)\right]}^i{F}^j{(1-F)}^k\mathrm{dF}---\left(3\right)$

In formula, E{} is the mathematical expectation of certain probability distribution or the combination distribution that probability statistics represents; F ≡ F (x)=P (x ∈ X), X is the set of stochastic variable x, the definition that P (x ∈ X) is the probability statistics of distribution function F (x), for meeting the probability of set (x ∈ X); X ≡ x (F)=P ^-1(F), P ^-1(F) be the inverse function of the distribution function of stochastic variable x, i, j, k are real parameter;

3rd step: establish the real parameter j=0 in second step, then exceeding probability right square is,

$M_{i,0,k}=\underset{0}{\overset{1}{\&Integral;}}{x}^i{(1-F)}^k\mathrm{dF}=\underset{\mathrm{\&delta;}}{\overset{\&infin;}{\&Integral;}}{x}^i{[1-\underset{\mathrm{\&delta;}}{\overset{x}{\&Integral;}}f\left(t\right)\mathrm{dt}]}^{k}f\left(x\right)\mathrm{dx}---\left(11\right)$

In formula, M _{i, 0, k}for k rank exceed probability right square;

4th step: draw the formula exceeding probability right square according to the 3rd step, the probability distribution function of wind speed three-parameter weibull distribution step (1) listed and probability density function substitute in formula (11), and get i=1, k=1,2,3,1 rank, rank ~ 3 of deriving wind speed three-parameter weibull distribution exceed the relation of probability right square and distribution parameter, and relational expression is:

$M_{\mathrm{1,0},1}=\frac{\mathrm{\&delta;}}{2}+\frac{\mathrm{\&beta;}}{2^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(12\right)$

$M_{\mathrm{1,0},2}=\frac{\mathrm{\&delta;}}{3}+\frac{\mathrm{\&beta;}}{3^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(13\right)$

$M_{\mathrm{1,0},3}=\frac{\mathrm{\&delta;}}{4}+\frac{\mathrm{\&beta;}}{4^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(14\right)$

In formula, Γ (*) is gamma function;

5th step: 1 rank, rank ~ 3 of the wind speed three-parameter weibull distribution in connection solution the 4th step exceed relational expression (12), (13), (14) of probability right square and distribution parameter, obtain,

$\frac{2M_{1,0,1}-M_{\mathrm{1,0,0}}}{3M_{1,0,2}-M_{\mathrm{1,0,0}}}=\frac{6^{\frac{1}{\mathrm{\&alpha;}}}-3^{\frac{1}{\mathrm{\&alpha;}}}}{6^{\frac{1}{\mathrm{\&alpha;}}}-2^{\frac{1}{\mathrm{\&alpha;}}}}---\left(15\right)$

6th step: setting form parameter α variation range is 0.45 ~ 8.0, and the sample value of α is got by step-length 0.01, substitute into item on the right of formula formula (13) equal sign, adopt Luo Jisidi curve to go out form parameter α value and the empirical relationship exceeding probability right square, draw the explicit relation formula of α as dependent variable:

$\left.\begin{array}{c}{K}_M=\frac{2M_{\mathrm{1,0},1}-M_{\mathrm{1,0,0}}}{3M_{\mathrm{1,0,2}}-M_{\mathrm{1,0,0}}}\&cong;\frac{2{\hat{M}}_{1,0,1}-{\hat{M}}_{\mathrm{1,0,0}}}{3{\hat{M}}_{\mathrm{1,0,2}}-{\hat{M}}_{\mathrm{1,0,0}}}\\ \mathrm{\&alpha;}=\frac{0.253}{0.297\exp \left(1.925K_M\right)-1}\end{array}\right\}---\left(16\right)$

In formula, for kth rank sample exceedes probability right square (k=0,1,2);

7th step: according to the relational expression (12) in the 4th step, (13), (14), draws the relational expression of the scale parameter that the sample value of choosing α is corresponding and location parameter β, δ value:

$\left.\begin{array}{c}\mathrm{\&beta;}\&cong;\frac{{\hat{M}}_{\mathrm{1,0,0}}-2{\hat{M}}_{\mathrm{1,0},1}}{(1-2^{\frac{-1}{\mathrm{\&alpha;}}})\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})}\\ \mathrm{\&delta;}\&cong;{\hat{M}}_{\mathrm{1,0,0}}-\mathrm{\&beta;\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})\end{array}\right\}---\left(17\right)$

In formula, for kth rank sample exceedes probability right square (k=0,1,2).

Especially, when δ=0, wind speed three-parameter weibull distribution is just wind speed Two-parameter Weibull distribution, 0 ~ 1 rank that described 4th step only need derive Weibull distribution exceed the relation of probability right square and distribution parameter, then obtain other two parameter relationship formulas according to the five to eight follow-up step execution.

As shown in Figure 1, in the wind velocity distributing paremeter method for parameter estimation of two kinds of low order probability right squares, the scope of form parameter α is between 0.45 ~ 8.0, the error of formula (9) and formula (16) can be made so all less, be only-0.023 ~ 0.021; When α two formula errors of fitting between 2.9 ~ 3.6 are all very little, and the common interval of 2.9 ~ 3.6 intervals form parameter α value of wind velocity distributing paremeter just.

Final step namely the 8th step of the wind velocity distributing paremeter method for parameter estimation of two kinds of above-mentioned low order probability right squares, according to the Weibull distribution parameter that the 7th step draws, determine the characteristic index of wind energy, the characteristic index of wind energy comprises average wind power density, effectively wind power concentration, wind energy and the characteristic indexs such as time can be utilized can to try to achieve easily according to formula (18) ~ (21)

Average wind power density

$\left.\begin{array}{c}\stackrel{\&OverBar;}{W}=\frac{1}{2}\mathrm{\&rho;E}{V}^3=\frac{1}{2}\mathrm{\&rho;}\underset{0}{\overset{\&infin;}{\&Integral;}}{V}^{3}f\left(V\right)\mathrm{dV}\\ E{V}^3={\mathrm{\&beta;}}^3\mathrm{\&Gamma;}(1+\frac{3}{\mathrm{\&alpha;}})+3{\mathrm{\&beta;}}^2\mathrm{\&delta;\&Gamma;}(1+\frac{2}{\mathrm{\&alpha;}})+3\mathrm{\&beta;}{\mathrm{\&delta;}}^2\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})+{\mathrm{\&delta;}}^3\end{array}\right\}---\left(18\right)$

In formula, ρ is atmospheric density, ρ=1.225kg/m under standard state ³.

Wind energy can utilize time t _e:

$t_e=T_a{\&Integral;}_{V_1}^{V_2}f\left(V\right)\mathrm{dV}=T_a\left\{\exp \right[-{\left(\frac{V_1-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}]-\exp [-{\left(\frac{V_2-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}\left]\right\}---\left(19\right)$

In formula, T _afor the T.T. in statistical time range, a year and a day in non-leap year is 8760 hours, and the leap year is 8784 hours; V ₁, V ₂for being respectively effective upper and lower limit wind speed, generally get 3m/s and 25m/s respectively.

Average effective wind power concentration

$\stackrel{\&OverBar;}{W_e}=\frac{1}{2}\mathrm{\&rho;}{\&Integral;}_{V_1}^{V_2}{V}^3\frac{f\left(V\right)}{F\left(V_2\right)-F\left(V_1\right)}\mathrm{dV}=\frac{T_a}{2t_e}\mathrm{\&rho;}{\&Integral;}_{V_1}^{V_2}{V}^{3}f\left(V\right)\mathrm{dV}---\left(20\right)$

In formula, be incomplete gamma functions under the sign of integration, direct solution is more difficult, can be solved by MonteCarlo, also discretize can ask calculation.

The theoretical annual electricity generating capacity AEP of unit:

$\mathrm{AEP}=T_a\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}P\left(V_i\right)f\left(V_i\right)\mathrm{\&Delta;}{V}_i---\left(21\right)$

In formula, P (V _i) be wind speed V _itime Wind turbines average output power.

Probability right square needs to replace continuous probability-weighted moment with the sample probability weight square of Discrete Finite and form, thus exist " ask square poor " that comprise " terraced square is poor " and " end moment is poor ", and exponent number is higher, also more very, it is similar that this and traditional moments method exist error " ask square poor ".Probability-weighted moment contains the probability of power as weight by introduction, objectively serves the effect of " depression of order ", improves the precision of parameter estimation.Therefore the precision that order Probability weight square Parameter Estimation Method obtains parameter is lower than low order probability right square Parameter Estimation Method of the present invention, below with regard to the concrete testing result of somewhere, northern Suzhou COASTAL SURFACE illustratively:

Table 1 be somewhere, northern Suzhou COASTAL SURFACE 70m height anemometer tower, Coastal beach 70m height anemometer tower each a year and a day by time wind speed series each rank probability right square.

Somewhere, table 1 northern Suzhou COASTAL SURFACE, Coastal beach wind speed each rank probability right square are added up

Tab.1Thestat.resultswitheach-orderprobability-weightedmomentsofwindspeed

According to somewhere, the northern Suzhou COASTAL SURFACE 70m height anemometer tower that table 1 provides, along seabeach 70m height anemometer tower each a year and a day by time wind speed series each rank probability right square, estimate that Weibull three parameters that distribute are as shown in table 2 with order Probability weight moments method and low order probability-weighted moment of the present invention respectively, and utilize wind power features Index Formula (18) ~ (21) accordingly, calculate wind power features index, table 3 gives each characteristic index directly counted by air speed data, and the Wind turbines database utilizing WASP software subsidiary summarizes more than 70 plants Wind turbines (WTGS) characterisitic parameter, for the WTGS of Vestas tri-kinds of models, each method parameter achievement calculates the theoretical annual electricity generating capacity AEP value of each unit, as shown in table 4, for more each method precision with good and bad.

Table 2 the inventive method and order Probability weight moments method parameter estimation achievement

Table 3 the inventive method and order Probability weight moments method parameter calculate wind power features index achievement

The average annual theoretical generated energy of table 4 each method unit compares

From table 2, the form parameter α that order Probability weight Moment method estimators goes out, scale parameter β are bigger than normal, and location parameter δ is less than normal a lot of, form parameter α, the scale parameter β of two kinds of low order probability-weighted moment provided by the invention and the value of location parameter δ or quite reasonable by contrast; From table 3 and table 4, low order exceedes the wind power features index Result Precision of the parameter calculating that probability-weighted moment is estimated all higher than order Probability weight moments method not as good as probability-weighted moment and low order, in general, the theoretical annual electricity generating capacity AEP value of theoretical unit of three kinds of WTGS, the low order probability-weighted moment Result Precision of COASTAL SURFACE is higher than order Probability weight moments method.

In sum, the present invention adopts dependent variable and independent variable to exchange, Luo Jisidi curve is utilized to draft the explicit algorithm relational expression of form parameter, solve the problem that low order probability-weighted moment is not easily applied, by accuracy test and example display, what can obtain three parameters of the wind speed three-parameter weibull distribution parameter estimation with degree of precision solves relational expression, thus improve the precision of wind velocity distributing paremeter parameter estimation, two kinds of low order probability-weighted moment that the present invention proposes have higher precision in the scope that Wind Power Utilization relates to, all can be used as the effective ways of wind speed three-parameter weibull distribution parameter estimation.

The calculating that described Luo Jisidi curve and sample exceed probability right square not as good as probability right square, sample is the known technology that those skilled in the art grasp, therefore does not introduce in detail.

More than show and describe ultimate principle of the present invention, principal character and advantage.The technician of the industry should understand; the present invention is not restricted to the described embodiments; what describe in above-described embodiment and instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.Application claims protection domain is defined by appending claims and equivalent thereof.

Claims (8)

1., based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability right square, it is characterized in that: comprise the following steps:

Step (1), lists probability distribution function and the probability density function of wind speed three-parameter weibull distribution, namely

$F\left(x\right)=1-\exp \&lsqb;-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}\&rsqb;---\left(1\right)$

$f\left(x\right)=\frac{\mathrm{\&alpha;}}{\mathrm{\&beta;}}{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}-1}\exp \&lsqb;-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}\&rsqb;---\left(2\right)$

Wherein x is stochastic variable, α is the form parameter of wind speed, β is the scale parameter of wind speed, δ is the location parameter of wind speed, the probability distribution function of the wind speed three-parameter weibull distribution that F (x) is stochastic variable x, the probability density function of the wind speed three-parameter weibull distribution that f (x) is stochastic variable x; Step (2), according to wind speed probability distribution, calculating probability right square is:

$M_{i,j,k}=E\left\{x^i{\&lsqb;F\left(x\right)\&rsqb;}^j{\&lsqb;1-F\left(x\right)\&rsqb;}^k\right\}=\underset{0}{\overset{1}{\&Integral;}}{\&lsqb;x\left(F\right)\&rsqb;}^i{F}^j{(1-F)}^{k}dF---\left(3\right)$

In formula, E{} is the mathematical expectation of certain probability distribution or the combination distribution that probability statistics represents; F ≡ F (x)=P (x ∈ X), X is the set of stochastic variable x, the definition that P (x ∈ X) is the probability statistics of distribution function F (x), for meeting the probability of set (x ∈ X); X ≡ x (F)=P ^-1(F), P ^-1(F) be the inverse function of the distribution function of stochastic variable x, i, j, k are real parameter;

Step (3), if the real parameter k=0 in step (2), not as good as probability right square is then,

$M_{i,j,0}=\underset{0}{\overset{1}{\&Integral;}}{x}^i{F}^{j}dF=\underset{\mathrm{\&delta;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}{x}^i{\&lsqb;\underset{\mathrm{\&delta;}}{\overset{x}{\&Integral;}}f\left(t\right)dt\&rsqb;}^{j}f\left(x\right)dx---\left(4\right)$

In formula, M _{i, j, 0}for j rank are not as good as probability right square;

Step (4), according to the formula of the too late probability right square that step (3) draws, the probability distribution function of wind speed three-parameter weibull distribution step (1) listed and probability density function substitute in formula (4), and get i=1, j=0,1,2,0 ~ 2 rank of deriving wind speed three-parameter weibull distribution are not as good as the relation of probability right square and distribution parameter, and relational expression is:

$M_{1,0,0}=\mathrm{\&delta;}+\mathrm{\&beta;}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(5\right)$

$M_{1,1,0}=\frac{\mathrm{\&delta;}}{2}+\mathrm{\&beta;}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})\&lsqb;1-2^{-(1+\frac{1}{\mathrm{\&alpha;}})}\&rsqb;---\left(6\right)$

$M_{1,2,0}=\frac{\mathrm{\&delta;}}{3}+\mathrm{\&beta;}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})\&lsqb;1-2^{1-(1+\frac{1}{\mathrm{\&alpha;}})}+3^{-(1+\frac{1}{\mathrm{\&alpha;}})}\&rsqb;---\left(7\right)$

In formula, Γ (*) is gamma function;

Step (5), connection 0 ~ 2 rank of separating the wind speed three-parameter weibull distribution in step (4), not as good as the relational expression (5) of probability right square and distribution parameter, (6), (7), obtain,

$\frac{3M_{1,2,0}-M_{1,0,0}}{2M_{1,1,0}-M_{1,0,0}}=2-\frac{3^{\frac{1}{\mathrm{\&alpha;}}}-2^{\frac{1}{\mathrm{\&alpha;}}}}{6^{\frac{1}{\mathrm{\&alpha;}}}-3^{\frac{1}{\mathrm{\&alpha;}}}}---\left(8\right)$

Step (6), setting form parameter α variation range is 0.45 ~ 8.0, and the sample value of α is got by step-length 0.01, substitute into item on the right of formula (8) equal sign, adopt Luo Jisidi curve to go out form parameter α value and low order not as good as the empirical relationship of probability right square, draw the explicit relation formula of α as dependent variable:

$\left.\begin{array}{c}{J}_M=\frac{3M_{1,2,0}-M_{1,0,0}}{2M_{1,1,0}-M_{1,0,0}}\&cong;\frac{3{\hat{M}}_{1,2,0}-{\hat{M}}_{1,0,0}}{2{\hat{M}}_{1,1,0}-{\hat{M}}_{1,0,0}}\\ \mathrm{\&alpha;}=\frac{0.767}{0.040\exp \left(2.277J_M\right)-1}\end{array}\right\}---\left(9\right)$

In formula, for the too late probability right square that jth rank sample is corresponding, j=0,1,2, represent the sign of operation calculated via estimator;

Step (7), according to the relational expression (5) in step (4), (6), (7), draws the relational expression of the scale parameter that the value of choosing α is corresponding and location parameter β, δ value:

$\left.\begin{array}{c}\mathrm{\&beta;}\&cong;\frac{2{\hat{M}}_{1,1,0}-{\hat{M}}_{1,0,0}}{(1-2^{\frac{-1}{\mathrm{\&alpha;}}})\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})}\\ \mathrm{\&delta;}\&cong;{\hat{M}}_{1,0,0}-\mathrm{\&beta;}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})\end{array}\right\}---\left(10\right)$

In formula, for jth rank sample is not as good as probability right square, j=0,1,2;

Step (8), according to the Weibull distribution parameter that step (7) draws, determines the characteristic index of wind energy.

2. according to claim 1 based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability right square, it is characterized in that: described wind speed form parameter α >0, wind speed scale parameter β >0, wind speed location parameter δ < x _min, wherein x _minfor the minimum value of stochastic variable.

3. according to claim 1 and 2 based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability right square, it is characterized in that: when δ=0, described step (4) only need derive the relation of 0 ~ 1 rank not as good as probability right square and distribution parameter.

4. according to claim 1 based on the wind velocity distributing paremeter method for parameter estimation of low order not as good as probability right square, it is characterized in that: the characteristic index of described step (8) wind energy comprises average wind power density, effectively wind power concentration, wind energy can utilize the time and the theoretical annual electricity generating capacity of unit.

5. exceed the wind velocity distributing paremeter method for parameter estimation of probability right square based on low order, it is characterized in that: comprise the following steps:

Step (1), lists probability distribution function and the probability density function of wind speed three-parameter weibull distribution, namely

$F\left(x\right)=1-\exp \&lsqb;-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}\&rsqb;---\left(1\right)$

$f\left(x\right)=\frac{\mathrm{\&alpha;}}{\mathrm{\&beta;}}{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}-1}\exp \&lsqb;-{\left(\frac{x-\mathrm{\&delta;}}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}\&rsqb;---\left(2\right)$

Wherein x is stochastic variable, α is the form parameter of wind speed, β is the scale parameter of wind speed, δ is the location parameter of wind speed, the probability distribution function of the wind speed three-parameter weibull distribution that F (x) is stochastic variable x, the probability density function of the wind speed three-parameter weibull distribution that f (x) is stochastic variable x; Step (2), according to wind speed probability distribution, calculates and exceedes probability right square and be:

$M_{i,j,k}=E\left\{x^i{\&lsqb;F\left(x\right)\&rsqb;}^j{\&lsqb;1-F\left(x\right)\&rsqb;}^k\right\}=\underset{0}{\overset{1}{\&Integral;}}{\&lsqb;x\left(F\right)\&rsqb;}^i{F}^j{(1-F)}^{k}dF---\left(3\right)$

In formula, E{} is the mathematical expectation of certain probability distribution or the combination distribution that probability statistics represents; F ≡ F (x)=P (x ∈ X), X is the set of stochastic variable x, the definition that P (x ∈ X) is the probability statistics of distribution function F (x), for meeting the probability of set (x ∈ X); X ≡ x (F)=P ^-1(F), P ^-1(F) be the inverse function of the distribution function of stochastic variable x, i, j, k are real parameter;

Step (3), if the real parameter j=0 in step (2), then exceeding probability right square is,

$M_{i,0,k}=\underset{0}{\overset{1}{\&Integral;}}{x}^i{(1-F)}^{k}dF=\underset{\mathrm{\&delta;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}{x}^i{\&lsqb;1-\underset{\mathrm{\&delta;}}{\overset{x}{\&Integral;}}f\left(t\right)dt\&rsqb;}^{k}f\left(x\right)dx---\left(11\right)$

In formula, M _{i, 0, k}for k rank exceed probability right square;

Step (4), the formula exceeding probability right square is drawn according to step (3), the probability distribution function of wind speed three-parameter weibull distribution step (1) listed and probability density function substitute in formula (11), and get i=1, k=1,2,3,1 rank, rank ~ 3 of deriving wind speed three-parameter weibull distribution exceed the relation of probability right square and distribution parameter, and relational expression is:

$M_{1,0,1}=\frac{\mathrm{\&delta;}}{2}+\frac{\mathrm{\&beta;}}{2^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(12\right)$

$M_{1,0,2}=\frac{\mathrm{\&delta;}}{3}+\frac{\mathrm{\&beta;}}{3^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(13\right)$

$M_{1,0,3}=\frac{\mathrm{\&delta;}}{4}+\frac{\mathrm{\&beta;}}{4^{1+\frac{1}{\mathrm{\&alpha;}}}}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})---\left(14\right)$

In formula, Γ (*) is gamma function;

Step (5), 1 rank, rank ~ 3 of the wind speed three-parameter weibull distribution that connection is separated in step (4) exceed relational expression (12), (13), (14) of probability right square and distribution parameter, obtain,

$\frac{2M_{1,0,1}-M_{1,0,0}}{3M_{1,0,2}-M_{1,0,0}}=\frac{6^{\frac{1}{\mathrm{\&alpha;}}}-3^{\frac{1}{\mathrm{\&alpha;}}}}{6^{\frac{1}{\mathrm{\&alpha;}}}-2^{\frac{1}{\mathrm{\&alpha;}}}}---\left(15\right)$

Step (6), setting form parameter α variation range is 0.45 ~ 8.0, and the sample value of α is got by step-length 0.01, substitute into item on the right of formula (13) equal sign, the empirical relationship adopting Luo Jisidi curve to go out form parameter α value and low order to exceed probability right square, draws the explicit relation formula of α as dependent variable:

$\left.\begin{array}{c}{K}_M=\frac{2M_{1,0,1}-M_{1,0,0}}{3M_{1,0,2}-M_{1,0,0}}\&cong;\frac{2{\hat{M}}_{1,0,1}-{\hat{M}}_{1,0,0}}{3{\hat{M}}_{1,0,2}-{\hat{M}}_{1,0,0}}\\ \mathrm{\&alpha;}=\frac{0.253}{0.297\exp \left(1.925K_M\right)-1}\end{array}\right\}---\left(16\right)$

In formula, for kth rank sample exceedes probability right square, k=0,1,2, represent the sign of operation calculated via estimator;

Step (7), according to the relational expression (12) in step (4), (13), (14), draws the relational expression of the scale parameter that the sample value of choosing α is corresponding and location parameter β, δ value:

$\left.\begin{array}{c}\mathrm{\&beta;}\&cong;\frac{{\hat{M}}_{1,0,0}-2{\hat{M}}_{1,0,1}}{(1-2^{\frac{-1}{\mathrm{\&alpha;}}})\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})}\\ \mathrm{\&delta;}\&cong;{\hat{M}}_{1,0,0}-\mathrm{\&beta;}\mathrm{\&Gamma;}(1+\frac{1}{\mathrm{\&alpha;}})\end{array}\right\}---\left(17\right)$

In formula, for kth rank sample exceedes probability right square, k=0,1,2;

Step (8), according to the Weibull distribution parameter that step (7) draws, determines the characteristic index of wind energy.

6. the wind velocity distributing paremeter method for parameter estimation exceeding probability right square based on low order according to claim 5, it is characterized in that: described wind speed form parameter α >0, wind speed scale parameter β >0, wind speed location parameter δ < x _min, wherein x _minfor the minimum value of stochastic variable.

7. the wind velocity distributing paremeter method for parameter estimation exceeding probability right square based on low order according to claim 5 or 6, it is characterized in that: when δ=0, described step (4) only need derive the relation that 0 ~ 1 rank exceed probability right square and distribution parameter.

8. the wind velocity distributing paremeter method for parameter estimation exceeding probability right square based on low order according to claim 5, is characterized in that: the characteristic index of described step (8) wind energy comprises average wind power density, effectively wind power concentration, wind energy can utilize the time and the theoretical annual electricity generating capacity of unit.