CN104036121A - Wind measurement data wind speed correction method based on probability distribution transfer - Google Patents

Abstract

The invention discloses a wind measurement data wind speed correction method based on probability distribution transfer. The method comprises the steps that firstly, statistical description is carried out on wind speed through a Weibull distribution function; then, the wind speed probability distribution estimated values of an actual measurement year long-time meteorological station, an actual measurement year wind field observation station, a representative year long-time meteorological station and a representative year wind field observation station corresponding to the ith sequence number are respectively calculated; finally, the wind speed is actually measured by the actual measurement year wind field observation station corresponding to the ith sequence number according to hourly wind speed data and the probability distribution estimated values, and the correction wind speed of the representative year wind field observation station corresponding to the ith sequence number is calculated through a probability distribution identical difference value transfer method or a probability distribution identical multiple proportion transfer method. According to the probability distribution transfer method for wind speed correction, the defect that common correlation coefficients in an existing correlation analysis class method are too low and have to be used for correction is overcome, and the method can be suitable for wind speed correction under the conditions that the distance of project sites of an inshore or offshore wind plant and the like and a long-time meteorological bench-mark station is too far or the correlation of the existing method is poor.

Description

The survey wind data correction wind method shifting based on probability distribution

Technical field

The present invention relates to a kind of probability distribution transfer method of surveying wind data correction wind, belong to wind energy turbine set Evaluation of Wind Energy Resources technical field.

Background technology

According to existing country and industry standard--wind energy turbine set Evaluation of Wind Energy Resources method (GB/T18710-2002), the meteorological prospecting technique rules (DL/T5158-2012) of power engineering, in wind energy turbine set and air cooling power plant design process, need to set up certain quantitative relation according to the actual measurement wind speed and direction data of the long-term weather station in project site and near same climatic region same period, and correct accordingly try to achieve wind energy turbine set site represent year by time wind speed and direction sequence, or air cooling power plant factory site Typical Year and nearest 10 years by time wind speed and direction sequence, for wind energy turbine set Evaluation of Wind Energy Resources or the design meteorologic parameter statistical study of air cooling power plant.

For meeting wind energy turbine set Evaluation of Wind Energy Resources and the designing requirement of air cooling power plant, General Requirements project site accumulates the survey wind data of continuous a year, and within the long term, the data of this year likely higher than, lower than or be equivalent to long-term average level, i.e. actual measurement year is respectively the situation in strong wind year, little wind year and flat wind year.

According to < < wind energy turbine set Evaluation of Wind Energy Resources method > > (GB/T18710-2002) 5.3.1 bar, wind energy turbine set is surveyed the object that wind data is corrected, according near the observation data of long-term weather station (being reference station), wind data is surveyed in wind field station after checking and corrects the representative data into the long-term average level in a set of reflection site, wind energy turbine set survey on wind height, represent year (that is flat wind year) by hour wind speed and direction data.

According to meteorological prospecting technique rules > > (DL/T5158-2012) the 5.8.5 bar of < < power engineering, should be according to temperature between meteorological reference station during comparative observation and project site air cooling weather station, the variance analysis result of wind speed and direction and project site air cooling weather station temperature, the vertical change analysis result of wind speed and direction, to according to nearest 10 years of meteorological reference station by time temperature, every air cooling meteorologic parameter of wind speed and direction analysis statistics is revised, final acquisition can fully represent the air cooling meteorologic parameter of planning to build air cooling tubes condenser distributing pipe height and position actual conditions.

And existing correction wind method comprises as follows:

One. method is corrected in the correlation analysis of wind speed sector

Because wind is vector, existing size (wind speed), has again direction (wind direction), and wind speed and direction all has the randomness of height on time and space.If by two station same periods (time) the wind speed and direction sampling line correlation analysis of going forward side by side, its related coefficient is minimum and show uncorrelated, can only move back and look for second solution: by the classification of each wind direction, by time wind speed classification (in level simultaneously a wind speed average polymerization) sampling set up linear equation (correlation analysis of classify and grading polymeric linear), its related coefficient can significantly improve.

Because the survey wind data of wind field Zhan He reference station all contains wind direction, wind direction information, capable of being combined have 4 covers samplings relations, as shown in table 1, table 1 is wind field Zhan He reference station classify and grading polymerization correlation analysis sampling combination table, every cover correlationship all has 16 dependent equations, and China's regulation characterizes wind direction by 16 quadrants.

Table 1

Wherein, " field " in " relation abbreviation " hurdle represents wind field weather station, and " station " represents long-term meteorological reference station, as " field is to station speed " represents with the classification of wind field station wind direction, reference station wind speed classification.Document 1 is comparative studies [A] the > > that the < < wind energy turbine set of author Pan Xiaochun is surveyed wind data correction method. the 9th young academic meeting paper collection of CSEE [C]. and Beijing: Chinese Water Conservancy water power publishing house, 2006,1183-1189.

How to utilize the correlationship between wind field Zhan He reference station to carry out data revision, according to the suggestion of standard etc., have two class methods as shown in table 2, table 2 is surveyed wind data method table for utilizing a station correlationship to correct.

Table 2

Choose actual measurement year no matter from year border or year in wind speed profile etc. all with average very approaching for many years situation (that is actual measurement year lucky be representative year), utilize respectively 8 kinds of methods enumerating to correct actual measurement annual data above, and calculate wind-resources characteristic index, generated energy and the blower fan aspects such as impact of arranging to correcting data, analyze the situation that departs between each method achievement and flat wind year " true value " achievement, proposed the quality sequence of each method.Show that the algebraically differential technique achievement of sampling relevant with " field is to station speed " is optimum, and the algebraically differential technique achievement quality that " field is to field speed " that GB/T18710-2002 adopts samples relevant is ranked the 3rd conclusion, referring to the < < wind energy turbine set of author Pan Xiaochun, survey comparative studies [A] the > > of wind data correction method,. the 9th young academic meeting paper collection of CSEE [C]. Beijing: Chinese Water Conservancy water power publishing house, 2006,1183-1189.

Two. wind speed divides month by month correlation analysis to correct method

Take weather station by time wind speed be independent variable, take factory site observation station by time wind speed be dependent variable, set up factory site and weather station each month by time wind speed correlationship, draw each month wind speed regression equation, related coefficient, and then carry out accordingly wind speed and direction and correct with inverting and rebuild.

The degree of correlation of the wind speed and direction between long-term meteorological reference station and power plant position is generally not high, and the related coefficient of one-variable linear regression equation each month is all below 0.8, and correlativity is not remarkable, is difficult to adopt one-variable linear regression to correct method and carries out inverting reduction.

Thereby wind speed divides month by month correlation analysis to correct method and is difficult to be applied as pervasive method.

Three. method is corrected in wind vector correlation analysis

According to observation Qi Nei air cooling power plant factory site and long-term meteorological reference station by time Wind Data, take weather station by time wind vector be independent variable, take factory site observation station by time wind vector be dependent variable, set up respectively factory site observation station during observation each month by time wind vector and weather station each month by time wind vector correlationship, utilization by time wind u, v data calculate each month regression equation and related coefficient, and then carry out accordingly wind speed and direction and correct with inverting and rebuild.

The method is treated wind as vector, expectation is corrected wind speed, wind direction in the lump.Yet, according to the explanation of meteorological prospecting technique rules > > (DL/T5158-2012) the 5.8.5 clause of < < power engineering, the air speed value that the correlation analysis method inverting of employing wind vector is rebuild is less than normal as a rule, and cardinal wind may occur the situation of distortion sometimes; In addition, according to the meteorological investigation report > of < < air cooling > (Northwest Electric Power Design Institute, in March, 2010) and document 2, the < < that document 2 is Li Weilin affects several problems [J] > > of the meteorological comparative observation achievement of air cooling, Electric Power Survey design, 2008, (5): 28-31.Two places wind speed adopts vector method relevant generally, and related coefficient v component is less than 0.8, u component and is less than 0.6, and its data degree of correlation is not high yet, and after synthetic new wind, its correlated error will be larger.

Thereby wind vector correlation analysis is corrected method and is difficult to equally be applied as pervasive method.

To sum up, for wind energy turbine set site or air cooling power plant factory site and near same climatic region, long-term meteorological reference station surveys wind data the same period, no matter adopts minute month by month correlation analysis and wind vector correlation analysis to correct, even all there is the drawback of the too low distortion of related coefficient; Wind speed sector is relevant, on surface, can make related coefficient significantly improve and " looking very beautiful ", but it is a kind of wind speed " classify and grading polymerization " Linear correlative analysis in essence, not proper relevant veritably, nonetheless, in engineering practice, still may there is the too low but reality of having to correct according to it of the related coefficient of indivedual sectors.And, the object of correcting of project site being surveyed to wind data not is for carrying out real-time prediction, and be only try to achieve that data a year and a day that can represent local long-term average wind resource status maybe need to rebuild nearest 10 years wind regime data year by year, strictly relevant without the what is called of going to chase such as the wind speed of two places so-called " in the same time ", " same play ", in fact such way is also almost futile in reality.

Thereby it is too low but have to for the defect of the drawback corrected that existing correlation analysis class methods are being deposited common related coefficient.

Summary of the invention

For the deficiency existing in prior art; the present invention seeks to be to provide a kind of survey wind data correction wind method; can overcome the common related coefficient of existing correlation analysis class methods too low but have to for the drawback of correcting, be applicable to the project site of coastal waters or marine wind electric field and the situation such as long-term meteorological reference station is distant or current methods correlativity is poor under correction wind.

For solving the problems of the technologies described above, the invention provides a kind of survey wind data correction wind method shifting based on probability distribution, it is characterized in that, comprise the following steps:

1) utilize Weibull to distribute wind speed is carried out to descriptive statistics, Weibull distribution probability density function f (v) and distribution function F (v) are respectively

$f\left(v\right)=\frac{k}{C}{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^{k-1}\exp [-{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^k]---\left(1\right)$

$F\left(v\right)=1-\exp [-{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^k]---\left(2\right)$

In formula, v--stochastic variable, refers to wind speed herein; K--form parameter, dimensionless, k > 0; C--scale parameter, C > 0; δ--location parameter, δ < v _min, v _min--the minimum value in wind series deteriorates to Two-parameter Weibull distribution when δ=0.

2) utilize probability distribution to carry out correction wind with difference transfer method:

By formula (2), if wind series is pressed sort ascending v ₁≤ v ₂≤ ... v _i≤ ... ≤ v _n, the wind estimation value that i sequence number is corresponding be calculated as follows

${\hat{v}}_i=g(P_i,C,k,\mathrm{\&delta;})=C{[-\ln \left({1-P}_i\right)]}^{\frac{1}{k}}+\mathrm{\&delta;}---\left(3\right)$

In formula, the symbolic formulation of g ()--funtcional relationship; P _i--the empirical Frequency of wind series.

Have:

$\begin{array}{c}{v}_{\mathrm{df},i}=v_{\mathrm{sf},i}+({\hat{v}}_{\mathrm{dc},i}-{\hat{v}}_{\mathrm{sc},i})=v_{\mathrm{sf},i}+[g(P_i,C_{\mathrm{dc}},k_{\mathrm{dc}},{\mathrm{\&delta;}}_{\mathrm{dc}})-g(P_i,C_{\mathrm{sc}},k_{\mathrm{sc}},{\mathrm{\&delta;}}_{\mathrm{sc}})]\\ =v_{\mathrm{sf},i}+\{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}-C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}+({\mathrm{\&delta;}}_{\mathrm{dc}}-{\mathrm{\&delta;}}_{\mathrm{sc}})\}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(6\right)$

In formula, the length of n--wind series;

V _{df, i}--wind speed is corrected in representative year wind field research station corresponding to i sequence number;

V _{sf, i}--the actual measurement year wind field research station actual measurement wind speed that i sequence number is corresponding;

--the representative year long-term weather station wind speed Distribution estimation value that i sequence number is corresponding;

--the actual measurement year long-term weather station wind speed Distribution estimation value that i sequence number is corresponding;

C _dc, C _sc--represent respectively to represent the scale parameter of a year long-term weather station, actual measurement year long-term weather station wind speed probability distribution;

K _dc, k _sc--represent respectively to represent the form parameter of a year long-term weather station, actual measurement year long-term weather station wind speed probability distribution;

δ _dc, δ _sc--represent respectively to represent the location parameter of a year long-term weather station, actual measurement year long-term weather station wind speed probability distribution.

Formula (6) is reduced to Two-parameter Weibull distribution form:

$\begin{array}{c}{v}_{\mathrm{df},i}=v_{\mathrm{sf},i}+\{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}-C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}\}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(7\right)$

2) plant and with multiple proportions transfer method, carry out correction wind by probability distribution: utilize formula (9) to correct

$\begin{array}{c}{v}_{\mathrm{df},i}=\frac{{\hat{v}}_{\mathrm{dc},i}}{{\hat{v}}_{\mathrm{sc},i}}{v}_{\mathrm{sf},i}=\frac{g(P_i,C_{\mathrm{dc}},k_{\mathrm{dc}},{\mathrm{\&delta;}}_{\mathrm{dc}})}{g(P_i,C_{\mathrm{sc}},k_{\mathrm{sc}},{\mathrm{\&delta;}}_{\mathrm{sc}})}{v}_{\mathrm{sf},i}=\frac{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}+{\mathrm{\&delta;}}_{\mathrm{dc}}}{C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}+{\mathrm{\&delta;}}_{\mathrm{sc}}}{v}_{\mathrm{sf},i}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(9\right)$

Formula (9) is reduced to Two-parameter Weibull distribution form:

$v_{\mathrm{df},i}=\frac{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}}{C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}}{v}_{\mathrm{sf},i}(i=\mathrm{1,2},...,n)---\left(10\right)$

A kind of aforesaid survey wind data correction wind method shifting based on probability distribution, is characterized in that,

For two-parameter weibull, distribute, utilize 3 rank moment of the orign formula to estimate form parameter k, scale parameter c value, described 3 rank moment of the orign parameter estimation formula are as follows:

$\left\{\begin{array}{c}k=1.853{\left(\ln \frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i^3}{n\&CenterDot;{\stackrel{\&OverBar;}{V}}^3}\right)}^{-0.548}-0.35\\ c=\frac{E\left(V\right)}{\mathrm{\&Gamma;}(1+1/k)}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i}{n\&CenterDot;\mathrm{\&Gamma;}(1+1/k)}\end{array}\right.---\left(11\right)$

In formula, E (V), --represent respectively mathematical expectation and the mean value of wind series.

Gamma function Γ (y) asks calculation with the progressive progression of Stirling (Stirling) in conjunction with gamma function character:

$\mathrm{\&Gamma;}\left(y\right)={(y+1)}^{(y+0.5)}{e}^{-(y+1)}\sqrt{\frac{2\mathrm{\&pi;}}{y}}[1+\frac{1}{12(y+1)}+\frac{1}{288{(y+1)}^2}-\frac{139}{51840{(y+1)}^3}+\&CenterDot;\&CenterDot;\&CenterDot;]$

In formula, the independent variable of y--gamma function.

A kind of aforesaid survey wind data correction wind method shifting based on probability distribution, is characterized in that: for three parameter weibull, distribute, utilize following methods to estimate the value of form parameter k, scale parameter c and location parameter δ:

(1) low order is not as good as PWM method:

Form parameter k presses following formula and estimates:

$\left\{\begin{array}{c}k=\frac{0.767}{0.040\exp \left({2.277J}_M\right)-1}\\ J_M=\frac{3{\hat{M}}_{\mathrm{1,2,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}\end{array}\right.---\left(12\right)$

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

Scale parameter C, location parameter δ value are pressed following formula and are determined:

$\left\{\begin{array}{c}C=\frac{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{(1-2^{-\frac{1}{k}})\mathrm{\&Gamma;}(1+\frac{1}{k})}\\ \mathrm{\&delta;}={\hat{M}}_{\mathrm{1,0,0}}-\mathrm{C\&Gamma;}(1+\frac{1}{k})\end{array}\right.---\left(13\right)$

(2) low order surpasses PWM method:

Form parameter k presses following formula and estimates:

$\left\{\begin{array}{c}k=\frac{0.253}{0.297\exp \left({1.925L}_M\right)-1}\\ L_M=\frac{2{\hat{M}}_{\mathrm{1,0},1}-{\hat{M}}_{\mathrm{1,0,0}}}{3{\hat{M}}_{1,\mathrm{0,2}}-{\hat{M}}_{\mathrm{1,0,0}}}\end{array}\right.---\left(14\right)$

In formula, --l rank sample surpasses probability right square (l=0,1,2).

$\left\{\begin{array}{c}C=\frac{{\hat{M}}_{1,\mathrm{0,0}}-2{\hat{M}}_{\mathrm{1,0,1}}}{(1-2^{-\frac{1}{k}})\mathrm{\&Gamma;}(1+\frac{1}{k})}\\ \mathrm{\&delta;}={\hat{M}}_{\mathrm{1,0,0}}-\mathrm{C\&Gamma;}(1+\frac{1}{k})\end{array}\right.---\left(15\right)$

A kind of aforesaid survey wind data correction wind method shifting based on probability distribution, is characterized in that: sample PWM method of estimation is:

Connect order sample probability weight square computing formula:

$\left\{\begin{array}{c}{\hat{M}}_{1,j,0}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{p_i}^j\mathrm{\&Delta;}{p}_i=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{p_i}^j\\ {\hat{M}}_{\mathrm{1,0},l}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{q_i}^l\mathrm{\&Delta;}{p}_i=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{q_i}^l\end{array}\right.---\left(16\right)$

In formula, Δ p _i--corresponding to wind speed v _ifrequency, get Δ p _i=1/n;

--corresponding to wind speed v _ij rank cumulative frequency;

--corresponding to wind speed v _il rank cumulative frequency.

If series of samples is pressed sort ascending (v ₁≤ v ₂≤ ... ≤ v _n), without partially estimating calculating formula

${p_i}^j=\frac{(i-1)(i-2)\&CenterDot;\&CenterDot;\&CenterDot;(i-j)}{(n-1)(n-2)\&CenterDot;\&CenterDot;\&CenterDot;(n-j)}(i=\mathrm{1,2},...,n;j=\mathrm{1,2},...)---\left(17\right)$

Because of q=1-p, without estimator partially, be

${q_i}^l=\frac{(n-i)(n-i-1)\&CenterDot;\&CenterDot;\&CenterDot;(n-i-l+1)}{(n-1)(n-2)\&CenterDot;\&CenterDot;\&CenterDot;(n-l)}(i=\mathrm{1,2},...,n;l=\mathrm{1,2},...)---\left(18\right)$

When series of samples is pressed sort descending, with estimator exchanges.

A kind of aforesaid survey wind data correction wind method shifting based on probability distribution, is characterized in that: wind speed sample empirical Frequency computing method are:

The general type of empirical frequency formula is

$P_i=\frac{i-b}{n+c}(i=\mathrm{1,2},...,n)---\left(19\right)$

In formula, the adjustment parameter of b, c--empirical Frequency computing formula.

For making the determined n of formula (19) P _iempirical Frequency with respect to 50% is symmetric, and can prove and should meet 2b+c=1, so above formula is further write as

$P_i=\frac{i-b}{n+1-2b}(i=\mathrm{1,2},...,n)---\left(20\right)$

Research a year and a day by time mean wind speed, sample length is generally 8760h.Than choosing, the application selects extra large gloomy formula (Hazen formula) calculation of wind speed sample v by analysis ₁≤ v ₂≤ ... v _i≤ ... ≤ v _nempirical Frequency can obtain good effect,

$P_i=\frac{i-0.5}{n}(i=\mathrm{1,2},...,n)---\left(21\right)$

The beneficial effect that the present invention reaches:

The probability distribution transfer method of correction wind of the present invention, proposed with difference probability distribution transfer method with two kinds of correction wind methods of multiple proportions probability distribution transfer method, in engineering practice, can select wherein method relatively reliably according to local wind regime feature data, the representative year wind speed Weibull distribution parameter of the long-term average wind regime in location can obtain in the data such as local Wind Energy Resources Survey, without by collect meteorological reference station a large amount of by time air speed data calculate and to try to achieve, thereby probability distribution transfer method is easy and simple to handle, be easy to implement, overcome the common related coefficient of existing correlation analysis class methods too low but have to for the drawback of correcting, go for the project site such as coastal waters or marine wind electric field and the situation such as long-term meteorological reference station is distant or current methods correlativity is poor under correction wind.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, describe the present invention in detail;

Fig. 1 is that each method of the present embodiment is corrected achievement mean wind speed broken line graph month by month;

Fig. 2 is that each method of the present embodiment is corrected achievement and divided wind direction mean wind speed broken line graph;

Fig. 3 is that each method of the present embodiment is corrected achievement wind speed probability density distribution curve;

Fig. 4 is that each method of the present embodiment is corrected achievement wind power concentration and effective wind power concentration histogram;

Fig. 5 is the F wind field station wind rose map of the present embodiment;

Fig. 6 is each correction method wind energy rose of the present embodiment;

Fig. 7 is that each method of the present embodiment is corrected the average annual theoretical generated energy histogram of achievement unit;

Fig. 8 is that certain each method of 100MW wind energy turbine set of the present embodiment is corrected achievement hair electric weight histogram;

Fig. 9 is that certain each method of 100MW wind energy turbine set of the present embodiment is corrected achievement wake effect histogram.

In figure: SCN--actual measurement year; DSC_CXCS--" field is to field speed " algebraically differential technique; DSC_CXZS--" field is to station speed " algebraically differential technique; GLZY_TCZ--with difference probability distribution transfer method; GLZY_TBB--with multiple proportions probability distribution transfer method.

Embodiment

Wind is as vector, and its size and wind direction all have the randomness of height.Wind speed can be described its statistical nature by probability distribution.The probability distribution of wind speed is generally positive skewness and distributes.Weibull distributes to be generally considered and is applicable to the wind speed description that takes statistics, at aspects such as Evaluation of Wind Energy Resources, annual electricity generating capacity (AEP, Annual Energy Production) prediction, wind power generating set (WTGS) type selecting, WTGS structural design and wind-electricity integration technical research, be used widely.

It is a kind of unimodal function bunch that Weibull distributes, and its probability density function and distribution function are respectively

$f\left(v\right)=\frac{k}{C}{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^{k-1}\exp [-{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^k]---\left(1\right)$

$F\left(v\right)=1-\exp [-{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^k]---\left(2\right)$

In formula, v--stochastic variable, refers to wind speed herein; K--form parameter, dimensionless, k > 0; C--scale parameter, C > 0; δ--location parameter, δ < v _min, v _min--the minimum value in wind series deteriorates to Two-parameter Weibull distribution when δ=0.

1. probability distribution is with difference transfer method:

By formula (2), if wind series is pressed sort ascending (v ₁≤ v ₂≤ ... v _i≤ ... ≤ v _n), wind estimation value corresponding to i sequence number can be calculated as follows

${\hat{v}}_i=g(P_i,C,k,\mathrm{\&delta;})=C{[-\ln \left({1-P}_i\right)]}^{\frac{1}{k}}+\mathrm{\&delta;}---\left(3\right)$

In formula, P _i--the empirical Frequency of wind series.

Actual measurement year long-term weather station wind speed Distribution estimation value corresponding to i sequence number actual measurement year wind field research station wind speed Distribution estimation value represent a year long-term weather station wind speed Distribution estimation value and represent a year wind field research station wind speed Distribution estimation value can be calculated as follows respectively

$\left\{\begin{array}{c}{\hat{v}}_{\mathrm{sc},i}=g(P_i,C_{\mathrm{sc}},k_{\mathrm{sc}},{\mathrm{\&delta;}}_{\mathrm{sc}})\\ {\hat{v}}_{\mathrm{sf},i}=g(P_i,C_{\mathrm{sf}},k_{\mathrm{sf}},{\mathrm{\&delta;}}_{\mathrm{sf}})\\ {\hat{v}}_{\mathrm{dc},i}=g(P_i,C_{\mathrm{dc}},k_{\mathrm{dc}},{\mathrm{\&delta;}}_{\mathrm{dc}})\\ {\hat{v}}_{\mathrm{df},i}=g(P_i,C_{\mathrm{df}},k_{\mathrm{df}},{\mathrm{\&delta;}}_{\mathrm{df}})\end{array}\right.---\left(4\right)$

Actual measurement year wind field research station corresponding to i sequence number actual measurement wind speed, represent that a year wind field research station corrects wind speed and use respectively v _{sf, i}and v _{df, i}represent.

For by time air speed data and Distribution estimation value, suppose represent year and actual measurement year wind field research station with two places, weather station are identical with the algebraically difference of sequence number wind speed for a long time, that is

$v_{\mathrm{df},i}-v_{\mathrm{sf},i}={\hat{v}}_{\mathrm{df},i}-{\hat{v}}_{\mathrm{sf},i}={\hat{v}}_{\mathrm{dc},i}-{\hat{v}}_{\mathrm{sc},i}---\left(5\right)$

Thereby

$\begin{array}{c}{v}_{\mathrm{df},i}=v_{\mathrm{sf},i}+({\hat{v}}_{\mathrm{dc},i}-{\hat{v}}_{\mathrm{sc},i})=v_{\mathrm{sf},i}+[g(P_i,C_{\mathrm{dc}},k_{\mathrm{dc}},{\mathrm{\&delta;}}_{\mathrm{dc}})-g(P_i,C_{\mathrm{sc}},k_{\mathrm{sc}},{\mathrm{\&delta;}}_{\mathrm{sc}})]\\ =v_{\mathrm{sf},i}+\{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}-C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}+({\mathrm{\&delta;}}_{\mathrm{dc}}-{\mathrm{\&delta;}}_{\mathrm{sc}})\}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(6\right)$

For above formula, the computational item in brace is determined by wind speed probability distribution, is " theory " difference of probability estimate, and tool smoothness properties, adds v _{sf, i}after just can draw v _{df, i}, given the random fluctuation characteristic of wind series simultaneously.

Especially, for Two-parameter Weibull distribution, formula (6) can be reduced to

$\begin{array}{c}{v}_{\mathrm{df},i}=v_{\mathrm{sf},i}+\{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}-C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}\}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(7\right)$

2. probability distribution is with multiple proportions transfer method:

Each variable symbol implication is the same.

For by time air speed data and Distribution estimation value, suppose represent year and actual measurement year wind field research station with two places, weather station are identical with times ratio of sequence number wind speed for a long time, that is

$\frac{v_{\mathrm{df},i}}{v_{\mathrm{sf},i}}=\frac{{\hat{v}}_{\mathrm{df},i}}{{\hat{v}}_{\mathrm{sf},i}}=\frac{{\hat{v}}_{\mathrm{dc},i}}{{\hat{v}}_{\mathrm{sc},i}}---\left(8\right)$

Thereby

$\begin{array}{c}{v}_{\mathrm{df},i}=\frac{{\hat{v}}_{\mathrm{dc},i}}{{\hat{v}}_{\mathrm{sc},i}}{v}_{\mathrm{sf},i}=\frac{g(P_i,C_{\mathrm{dc}},k_{\mathrm{dc}},{\mathrm{\&delta;}}_{\mathrm{dc}})}{g(P_i,C_{\mathrm{sc}},k_{\mathrm{sc}},{\mathrm{\&delta;}}_{\mathrm{sc}})}{v}_{\mathrm{sf},i}=\frac{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}+{\mathrm{\&delta;}}_{\mathrm{dc}}}{C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}+{\mathrm{\&delta;}}_{\mathrm{sc}}}{v}_{\mathrm{sf},i}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(9\right)$

Especially, for Two-parameter Weibull distribution, formula (9) can be reduced to

$v_{\mathrm{df},i}=\frac{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}}{C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}}{v}_{\mathrm{sf},i}(i=\mathrm{1,2},...,n)---\left(10\right)$

For above formula, minute several by wind speed probability distribution, determined, be " theory " times ratio of probability estimate, tool smoothness properties, is multiplied by v _{sf, i}after just can draw v _{df, i}, given the random fluctuation characteristic of wind series simultaneously.

The wind speed field data that Weibull probability distribution parameters in formula (6), (7) and formula (9), (10) can represent year according to long-term weather station actual measurement Nian He estimates, wherein weather station represents that a year wind speed profile parameter also can obtain from local wind-resources reconnaissance information.

Will actual measurement or correct wind direction sequence dislocation to v _{sf, i}, just form the time series that wind field station represents year vector wind can supply wind field Evaluation of Wind Energy Resources, generated energy calculating etc.

Wind speed probability distribution parameters is estimated

The probability distribution transfer method computing formula of correction wind, be the parameter estimation that formula (6), formula (9) and formula (7), formula (10) relate separately to wind speed three parameter Weibull distribution and Two-parameter Weibull distribution, the following method that can draw by present inventor is respectively calculated.

Two-parameter weibull distributes

Wind speed Two-parameter Weibull distribution method for parameter estimation has multiple, can make one's options according to the different situations of Wind Data.When the continuous wind series of left and right one year, can adopt least square method (being cumulative distribution function matching Weibull distribution curve method), average and variance estimation algorithm, and minimum approach error algorithm and maximum-likelihood method etc.

According to each rank square of Two-parameter Weibull distribution, still obey this this important statistics character that distributes, drafted based on three of moment function and estimated experimental formula about k value.Through theoretical and example calculation, show: the method for parameter estimation system based on moment function follows the statistical properties of Weibull distribution and drafts, accuracy test and example all show, three apply a formula has higher precision for field of wind energy utilization, and accommodation is wide, it is easy to calculate, the excellent process of all can yet be regarded as.Wherein 3 rank moment of the orign formula wind energy indexs are very pressed close to actual measurement statistics, and what wind power was proportional to wind speed cube is this method immanent cause of " alike in spirit " the most.

In actual Wind Power Utilization work, use the formula based on moment function to estimate Weibull distribution parameter, the application utilizes 3 rank moment of the orign formula to estimate form parameter k, scale parameter c value.3 rank moment of the orign parameter estimation formula are as follows:

$\left\{\begin{array}{c}k=1.853{\left(\ln \frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i^3}{n\&CenterDot;{\stackrel{\&OverBar;}{V}}^3}\right)}^{-0.548}-0.35\\ c=\frac{E\left(V\right)}{\mathrm{\&Gamma;}(1+1/k)}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i}{n\&CenterDot;\mathrm{\&Gamma;}(1+1/k)}\end{array}\right.---\left(11\right)$

In formula, gamma function Γ (y) asks calculation with the progressive progression of Stirling (Stirling) in conjunction with gamma function character:

$\mathrm{\&Gamma;}\left(y\right)={(y+1)}^{(y+0.5)}{e}^{-(y+1)}\sqrt{\frac{2\mathrm{\&pi;}}{y}}[1+\frac{1}{12(y+1)}+\frac{1}{288{(y+1)}^2}-\frac{139}{51840{(y+1)}^3}+\&CenterDot;\&CenterDot;\&CenterDot;]$

Three parameter weibull distribute:

In recent years, China just actively carries out the development & construction of marine wind electric field, and sea wind speed generally will be higher than littoral land-based area, and its probability distribution has and is the whole phenomenon to the skew of high wind speed district.For improving the adaptability of wind speed probability model, the statistical property that adopts three parameter Weibull distribution to describe wind is necessary.

For the parameter estimation of three parameter Weibull distribution, mainly contain at present maximum-likelihood method, moments method, related coefficient optimization, gray model method and bilinear regression method etc.These methods are often more loaded down with trivial details, generally need Program, and the people who is engaged in application work is difficult for grasping, and has restricted the widespread use of three parameter Weibull distribution.

Relation based on 0,1,2 rank PWM and distribution parameter, proposes two kinds of explicit calculated relationship of low order probability right square with three Parameter Weibull Distributions estimations of degree of precision, can be conveniently used in engineering practice.

(1) low order is not as good as PWM method

Form parameter k presses following formula and estimates:

$\left\{\begin{array}{c}k=\frac{0.767}{0.040\exp \left({2.277J}_M\right)-1}\\ J_M=\frac{3{\hat{M}}_{\mathrm{1,2,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}\end{array}\right.---\left(12\right)$

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

Scale parameter C, location parameter δ value are pressed following formula and are determined.

$\left\{\begin{array}{c}C=\frac{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{(1-2^{-\frac{1}{k}})\mathrm{\&Gamma;}(1+\frac{1}{k})}\\ \mathrm{\&delta;}={\hat{M}}_{\mathrm{1,0,0}}-\mathrm{C\&Gamma;}(1+\frac{1}{k})\end{array}\right.---\left(13\right)$

(2) low order surpasses PWM method

Form parameter k presses following formula and estimates:

$\left\{\begin{array}{c}k=\frac{0.253}{0.297\exp \left({1.925L}_M\right)-1}\\ L_M=\frac{2{\hat{M}}_{\mathrm{1,0},1}-{\hat{M}}_{\mathrm{1,0,0}}}{3{\hat{M}}_{1,\mathrm{0,2}}-{\hat{M}}_{\mathrm{1,0,0}}}\end{array}\right.---\left(14\right)$

In formula, --l rank sample surpasses probability right square (l=0,1,2).

$\left\{\begin{array}{c}C=\frac{{\hat{M}}_{1,\mathrm{0,0}}-2{\hat{M}}_{\mathrm{1,0,1}}}{(1-2^{-\frac{1}{k}})\mathrm{\&Gamma;}(1+\frac{1}{k})}\\ \mathrm{\&delta;}={\hat{M}}_{\mathrm{1,0,0}}-\mathrm{C\&Gamma;}(1+\frac{1}{k})\end{array}\right.---\left(15\right)$

(3) sample PWM estimates

Connect order sample probability weight square computing formula:

$\left\{\begin{array}{c}{\hat{M}}_{1,j,0}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{p_i}^j\mathrm{\&Delta;}{p}_i=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{p_i}^j\\ {\hat{M}}_{\mathrm{1,0},l}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{q_i}^l\mathrm{\&Delta;}{p}_i=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{q_i}^l\end{array}\right.---\left(16\right)$

In formula, Δ p _ifor corresponding to wind speed v _ifrequency, desirable Δ p _i=1/n; for corresponding to v _ij rank and l rank cumulative frequency, relevant with sample sequence.

If series of samples is pressed sort ascending (v ₁≤ v ₂≤ ... ≤ v _n), without partially estimating calculating formula

${p_i}^j=\frac{(i-1)(i-2)\&CenterDot;\&CenterDot;\&CenterDot;(i-j)}{(n-1)(n-2)\&CenterDot;\&CenterDot;\&CenterDot;(n-j)}(i=\mathrm{1,2},...,n;j=\mathrm{1,2},...)---\left(17\right)$

Because of q=1-p, without estimator partially, be

${q_i}^l=\frac{(n-i)(n-i-1)\&CenterDot;\&CenterDot;\&CenterDot;(n-i-l+1)}{(n-1)(n-2)\&CenterDot;\&CenterDot;\&CenterDot;(n-l)}(i=\mathrm{1,2},...,n;l=\mathrm{1,2},...)---\left(18\right)$

When series of samples is pressed sort descending, with estimator exchanges.

Wind speed sample empirical Frequency is calculated

The probability distribution transfer method computing formula of correction wind, formula (6), (7) and formula (9), (10) relate to the empirical Frequency P of wind series _iestimation.The general type of empirical frequency formula is

$P_i=\frac{i-b}{n+c}(i=\mathrm{1,2},...,n)---\left(19\right)$

In formula, the adjustment parameter of b, c--empirical Frequency computing formula.

For making the determined n of formula (19) P _iempirical Frequency with respect to 50% is symmetric, and can prove and should meet 2b+c=1.So above formula is further write as

$P_i=\frac{i-b}{n+1-2b}(i=\mathrm{1,2},...,n)---\left(20\right)$

When b gets respectively 0,0.3,1/3,3/8,0.44 and 0.5, formula (20) corresponds respectively to mathematical expectation formula (Weibull formula), Mean Value Formula (Chegodayev formula), Tukey formula, Blom formula, Gringorten formula and extra large gloomy formula (Hazen formula).

Research a year and a day by time mean wind speed, sample length is generally 8760h.Than choosing, the application selects extra large gloomy formula (Hazen formula) calculation of wind speed sample v by analysis ₁≤ v ₂≤ ... v _i≤ ... ≤ v _nempirical Frequency can obtain good effect,

$P_i=\frac{i-0.5}{n}(i=\mathrm{1,2},...,n)---\left(21\right)$

Specific embodiment:

F wind energy turbine set site central authorities tree has a high anemometer tower of 70m, and in 70m equal altitudes, place is provided with survey wind devices.To surveying wind data, verify, arrange out a year and a day in 2005 by time survey wind data, get the 70m height wind speed and direction data computational analysis after checking.

Long-term weather station C belongs to the basic weather station of country, nearest with F wind energy turbine set, in same climatic region, as the meteorological reference station of wind energy turbine set engineering.According to the analysis of nearly 30 years of weather station C actual measurement Wind Data, within 1998, be apart from modern nearest mean wind speed and immediate time of mean wind speed for many years, can take the representative year of local wind-resources evaluation as.

Apply respectively same difference and carry out correction wind with two kinds of probability distribution transfer methods of multiple proportions, the algebraically differential technique that " field is to the station speed " of the algebraically differential technique that " field is to field speed " simultaneously providing with GB/T18710-2002 appendix A sampled relevant and literature recommendation samples relevant is corrected, and to correcting achievement by wind-resources feature and target generated output statistical study.

Algebraically differential technique is corrected:

The algebraically differential technique that the application's application " field is to station speed " is sampled relevant to " field is to field speed " is corrected, and F wind field Zhan He C reference station wind speed is carried out to the correlation analysis of classify and grading polymeric linear, and correlation analysis achievement is shown in Fig. 1 and Fig. 2 and table 1 and table 2.

Each wind direction (quadrant) related coefficient statistics is listed in table 3, and table 3 is F wind field Zhan He C reference station wind speed characteristic correlation coefficient statistical form.

Table 3

As seen from the above table, the two places wind speed correlativity of the inclined to one side southwestward of SSW～SW～WSW～W is the poorest, poor and correct wind speed for computer algebra with it, may bring the error of correcting that is difficult to precognition.

Application correlation analysis achievement is calculated the algebraic difference difference that each wind direction and wind velocity is corrected, and achievement is listed in table 4, and table 4 divides wind direction and wind velocity algebraic difference Data-Statistics table for F wind field Zhan He C reference station.

Table 4 unit: m/s

More than show data to F wind field station by time survey wind speed and impose algebraically and correct, thereby show that each method represents a year air speed data.

Probability distribution transfer method correction method:

According to analysis, adopt Two-parameter Weibull distribution to describe this example wind speed and can obtain good effect, adopt formula (11) to carry out parameter estimation, achievement is as shown in table 5, and table 5 is the actual measurement wind speed Weibull of F wind field Zhan He C reference station estimation of distribution parameters outcome table.

Table 5

By upper table parameter substitution formula (7) and formula (10).

Thereby correction wind probability distribution with difference transfer method computing formula is

$\begin{array}{c}{v}_{\mathrm{df},i}=v_{\mathrm{sf},i}+\{3.78{[-\ln (1-P_i)]}^{\frac{1}{1.823}}-3.51{[-\ln (1-P_i)]}^{\frac{1}{1.937}}\}\\ (i=\mathrm{1,2},...,8760)\end{array}---\left(22\right)$

Correction wind probability distribution with multiple proportions transfer method computing formula is

$v_{\mathrm{df},i}=1.077\frac{{[-\ln (1-P_i)]}^{\frac{1}{1.823}}}{{[-\ln (1-P_i)]}^{\frac{1}{1.937}}}{v}_{\mathrm{sf},i},(i=\mathrm{1,2},...,8760)---\left(23\right)$

Above-mentioned two formula empirical Frequency are pressed Hai Sen (Hazen) formula, and formula (21) is calculated.

Achievement comparative analysis

Reasonalbeness check:

Add up that each method is corrected extreme wind velocity and be negative and the unreasonable data bulk that is less than 0.5m/s (wind field station accuracy of instrument), list in table 6, extreme wind velocity and unreasonable data statistic that table 6 is corrected for each method.

Table 6

As can be seen here, it is maximum that " to field speed " algebraically differential technique that GB/T18710-2002 appendix A provides is corrected in data unreasonable data, with difference probability distribution transfer method, correct the unreasonable data that do not occur breaking through " border " in achievement, " field is to station speed " algebraically differential technique is roughly suitable with the unreasonable data of correcting out with multiple proportions probability distribution transfer method.

The unreasonable data that it is pointed out that table statistics are only to cross 0 and a part of data on 0.5m/s " border ", and in fact, its inside still has and is difficult in a large number the unreasonable data that detect.

For minus irrational data of correcting, directly with " 0 ", replace, participate in the below analysis of wind-resources characteristic statistics and generated energy calculating etc.

Each month and a minute wind direction and wind velocity: table 7 is corrected achievement mean wind speed achievement statistical form month by month for each method.

Table 7

Unit: m/s

The broken line graph of drawing according to upper table data as shown in Figure 1.In Fig. 1, SCN--actual measurement year; DSC_CXCS--" field is to field speed " algebraically differential technique; DSC_CXZS--" field is to station speed " algebraically differential technique; GLZY_TCZ--with difference probability distribution transfer method; GLZY_TBB--with multiple proportions probability distribution transfer method.Lower same.

From table 7, Fig. 1, average of the whole year wind speed and year interior each monthly average wind speed, with difference probability distribution transfer method achievement and " field is to station speed " algebraically differential technique achievement, approach, with multiple proportions probability distribution transfer method achievement and " field is to field speed " algebraically differential technique achievement, approach.

Table 8 is corrected achievement for each method and is divided wind direction mean wind speed achievement statistical form

Table 8 unit: m/s

Continued 8

According to upper table data, draw as shown in Figure 2.

From table 8, Fig. 2, for each wind direction mean wind speed, to compare with actual measurement year, algebraically differential technique changes greatly, wherein especially with " field is to field speed " algebraically differential technique, at the mean wind speed of the wind directions such as NE, ENE, E, SE, WSW, W and NW, changes the most remarkable.

Wind speed probability distribution parameters:

Table 9 is corrected achievement wind speed Weibull estimation of distribution parameters comparison of results table for each method

Table 9

According to upper table data, draw as shown in Figure 3.

Average wind power density computation:

Average wind power density W:

By formula (24) or by formula (25), calculate

$\stackrel{\&OverBar;}{W}=\frac{\mathrm{\&rho;}}{2n}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{v_i}^3(W/m^2)---\left(24\right)$

In formula: n--the wind speed of setting in the period records number;

ρ--atmospheric density, this example is got ρ=1.225kgm under standard state ³.

$\left.\begin{array}{c}\stackrel{\&OverBar;}{W}=\frac{1}{2}\mathrm{\&rho;}{\mathrm{EV}}^3=\frac{1}{2}\mathrm{\&rho;}\underset{0}{\overset{\&infin;}{\&Integral;}}{V}^{3}f\left(V\right)\mathrm{dV}\\ {\mathrm{EV}}^3=C^3\mathrm{\&Gamma;}(1+\frac{3}{k})+{3C}^3\mathrm{\&delta;\&Gamma;}(1+\frac{2}{k})+3C{\mathrm{\&delta;}}^2\mathrm{\&Gamma;}(1+\frac{1}{k})+{\mathrm{\&delta;}}^3\end{array}\right\}---\left(25\right)$

Wind energy can be utilized time t _e:

$t_e=T_a{\&Integral;}_{V_1}^{V_2}f\left(V\right)\mathrm{dV}=T_a\left\{\exp \right[-{\left(\frac{V_1-\mathrm{\&delta;}}{C}\right)}^k]-\exp [-{\left(\frac{V_2-\mathrm{\&delta;}}{C}\right)}^k\left]\right\}---\left(26\right)$

In formula, T _a--the T.T. in statistical time range, be 8760 hours a year and a day in non-leap year, and the leap year is 8784 hours;

V ₁, V ₂--be respectively effective upper and lower limit wind speed, generally get respectively 3m/s and 25m/s.

Average effective wind power concentration

${\stackrel{\&OverBar;}{W}}_e=\frac{1}{2}\mathrm{\&rho;}{\&Integral;}_{V_1}^{V_2}{V}^3\frac{f\left(V\right)}{F\left(V_2\right)-F\left(V_1\right)}\mathrm{dV}=\frac{T_a}{2t_e}\mathrm{\&rho;}{\&Integral;}_{V_1}^{V_2}{V}^{3}f\left(V\right)\mathrm{dV}---\left(27\right)$

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

Table 10 is corrected achievement wind energy characteristic index comparison sheet for each method.

Table 10

According to upper telogenesis fruit, draw Fig. 4.

From table 10, Fig. 4, average of the whole year wind power concentration and effectively wind power concentration, " field is to station speed " algebraically differential technique achievement is minimum, approaches with same difference probability distribution transfer method achievement; Maximum with multiple proportions probability distribution transfer method achievement, approach with " field is to field speed " algebraically differential technique achievement.

The direction distributional analysis of wind direction and wind energy:

The application does not relate to wind direction and corrects, directly divert from one use to another F wind field station actual measurement 2005 by time wind direction data, the wind direction frequency of adding up thus and drawing distributes in Table 11 and Fig. 5, table 11 is F wind field station wind direction frequency statistical form.

Table 11

Wind energy concentration D _wEbe calculated as follows:

$D_{\mathrm{WE}}=\frac{\mathrm{\&rho;}}{2}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{v_i}^3{t}_j(W\&CenterDot;h/m^2)---\left(28\right)$

In formula: m--number is recorded in wind speed interval;

T _j--the wind speed time of origin in certain sector or comprehensive j wind speed interval, h.

Calculate wind energy concentration in 16 sectors, wind energy concentration direction is distributed as the wind energy concentration of each sector and the number percent of comprehensive total wind energy concentration, referred to as " distribution of wind energy direction ".Each method is corrected achievement wind energy direction distribution achievement in Table 12, and table 12 is corrected achievement wind energy direction distribution statistics table for each method.

Table 12

Unit: %

Continued 12

According to upper table data, draw Fig. 6.

From table 12, Fig. 6, for wind energy direction, distribute, to compare with actual measurement year, algebraically differential technique changes greatly, wherein especially remarkable in the wind energy frequency shift of the wind directions such as ENE, SE with " field is to field speed " algebraically differential technique.

Annual generated energy analysis:

The average annual theoretical generated energy AEP of unit (Annual Energy Production) is calculated as follows:

$\mathrm{AEP}=T_a\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}P\left(V_i\right)f\left(V_i\right){\mathrm{\&Delta;V}}_i---\left(29\right)$

In formula, P (V _i)--wind speed V _itime the average output power of WTGS (wind power generator group, Wind Turbine Generator System); f(V _i)--wind speed V _ithe probability occurring; Δ V _i--the discrete steps of wind speed.

The subsidiary wind-powered electricity generation unit database of WAsP software of Denmark RisΦ National Laboratory research and development has collected more than 70 and has planted wind-powered electricity generation unit (WTGS) characterisitic parameter, can utilize WAsP-Turbine Editor to call it.The WTGS of tri-kinds of models of Vestas of take is example, by each method parameter achievement, by formula (29), calculates the theoretical AEP of each unit, and achievement is in Table 13, and table 13 is corrected the average annual theoretical generated energy comparison sheet of achievement unit for each method.

Table 13

According to upper telogenesis fruit, draw Fig. 7.

From table 13, Fig. 7, the theoretical AEP of tri-kinds of type units of Vestas, " field is to station speed " algebraically differential technique achievement is minimum, approaches with same difference probability distribution transfer method achievement; Maximum with multiple proportions probability distribution transfer method achievement, approach with " field is to field speed " algebraically differential technique achievement.

Wind energy turbine set generated energy and wake effect: the three kinds of WTGS of Vestas of still take are example, in a beach place that is about 10km water front, lay respectively the wind energy turbine set that total installed capacity is 100MW.Three kinds of type number of units are respectively 118,67 and 50.According to wind energy direction, distribute, the ranks spacing of three kinds of types is all got 7:5 doubly to impeller diameter.Utilize WAsP software to calculate the wake effect of respectively correcting achievement, as shown in table 14, table 14 is corrected achievement hair electric weight and wake effect comparison of results table for certain each method of 100MW wind energy turbine set.

Table 14

According to upper telogenesis fruit, draw Fig. 8, Fig. 9.

From table 14, Fig. 8 and Fig. 9, each type whole audience hair electric weight of certain 1000MW wind energy turbine set, " field is to station speed " algebraically differential technique achievement is minimum, approaches with same difference probability distribution transfer method achievement; Maximum with multiple proportions probability distribution transfer method achievement, approach with " field is to field speed " algebraically differential technique achievement; And wake effect, " field is to station speed " algebraically differential technique achievement is the highest, minimum with multiple proportions probability distribution transfer method achievement, approaching with " field is to field speed " algebraically differential technique with difference probability distribution transfer method achievement.

Table 15 is the relevant outcome table of F wind field Zhan He C reference station wind speed of " field is to field speed " sampling.

Table 15

Table 16 is the relevant outcome table of F wind field Zhan He C reference station wind speed of " field is to station speed " sampling.

Table 16

More than show and described ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that in above-described embodiment and instructions, describes 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.The claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (5)

1. the survey wind data correction wind method shifting based on probability distribution, is characterized in that, comprises the following steps:

1) utilize Weibull to distribute wind speed is carried out to descriptive statistics, Weibull distribution probability density function f (v) and distribution function F (v) are respectively

$f\left(v\right)=\frac{k}{C}{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^{k-1}\exp [-{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^k]---\left(1\right)$

$F\left(v\right)=1-\exp [-{\left(\frac{v-\mathrm{\&delta;}}{C}\right)}^k]---\left(2\right)$

In formula, v--stochastic variable, refers to wind speed herein; K--form parameter, dimensionless, k > 0; C--scale parameter, C > 0; δ--location parameter, δ < v _min, v _min--the minimum value in wind series deteriorates to Two-parameter Weibull distribution when δ=0;

2) utilize probability distribution to carry out correction wind with difference transfer method:

By formula (2), if wind series v _ipress sort ascending v ₁≤ v ₂≤ ... v _i≤ ... ≤ v _n, the wind estimation value that i sequence number is corresponding be calculated as follows

${\hat{v}}_i=g(P_i,C,k,\mathrm{\&delta;})=C{[-\ln \left({1-P}_i\right)]}^{\frac{1}{k}}+\mathrm{\&delta;}---\left(3\right)$

In formula, the symbolic formulation of g ()--funtcional relationship; P _i--the empirical Frequency of wind series;

Have:

$\begin{array}{c}{v}_{\mathrm{df},i}=v_{\mathrm{sf},i}+({\hat{v}}_{\mathrm{dc},i}-{\hat{v}}_{\mathrm{sc},i})=v_{\mathrm{sf},i}+[g(P_i,C_{\mathrm{dc}},k_{\mathrm{dc}},{\mathrm{\&delta;}}_{\mathrm{dc}})-g(P_i,C_{\mathrm{sc}},k_{\mathrm{sc}},{\mathrm{\&delta;}}_{\mathrm{sc}})]\\ =v_{\mathrm{sf},i}+\{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}-C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}+({\mathrm{\&delta;}}_{\mathrm{dc}}-{\mathrm{\&delta;}}_{\mathrm{sc}})\}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(6\right)$

In formula, the length of n--wind series;

V _{df, i}--wind speed is corrected in representative year wind field research station corresponding to i sequence number;

V _{sf, i}--the actual measurement year wind field research station actual measurement wind speed that i sequence number is corresponding;

--the representative year long-term weather station wind speed Distribution estimation value that i sequence number is corresponding;

--the actual measurement year long-term weather station wind speed Distribution estimation value that i sequence number is corresponding;

C _dc, C _sc--represent respectively to represent the scale parameter of a year long-term weather station, actual measurement year long-term weather station wind speed probability distribution;

K _dc, k _sc--represent respectively to represent the form parameter of a year long-term weather station, actual measurement year long-term weather station wind speed probability distribution;

δ _dc, δ _sc--represent respectively to represent the location parameter of a year long-term weather station, actual measurement year long-term weather station wind speed probability distribution;

Formula (6) is reduced to Two-parameter Weibull distribution form is:

$\begin{array}{c}{v}_{\mathrm{df},i}=v_{\mathrm{sf},i}+\{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}-C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}\}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(7\right)$

2) plant and with multiple proportions transfer method, carry out correction wind by probability distribution: utilize formula (9) to correct

$\begin{array}{c}{v}_{\mathrm{df},i}=\frac{{\hat{v}}_{\mathrm{dc},i}}{{\hat{v}}_{\mathrm{sc},i}}{v}_{\mathrm{sf},i}=\frac{g(P_i,C_{\mathrm{dc}},k_{\mathrm{dc}},{\mathrm{\&delta;}}_{\mathrm{dc}})}{g(P_i,C_{\mathrm{sc}},k_{\mathrm{sc}},{\mathrm{\&delta;}}_{\mathrm{sc}})}{v}_{\mathrm{sf},i}=\frac{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}+{\mathrm{\&delta;}}_{\mathrm{dc}}}{C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}+{\mathrm{\&delta;}}_{\mathrm{sc}}}{v}_{\mathrm{sf},i}\\ (i=\mathrm{1,2},...,n)\end{array}---\left(9\right)$

Formula (9) is reduced to Two-parameter Weibull distribution form:

$v_{\mathrm{df},i}=\frac{C_{\mathrm{dc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{dc}}}}}{C_{\mathrm{sc}}{[-\ln (1-P_i)]}^{\frac{1}{k_{\mathrm{sc}}}}}{v}_{\mathrm{sf},i}(i=\mathrm{1,2},...,n)---\left(10\right).$

2. the survey wind data correction wind method shifting based on probability distribution according to claim 1, is characterized in that:

For two-parameter weibull, distribute, utilize 3 rank moment of the orign formula to estimate form parameter k, scale parameter c value, described 3 rank moment of the orign parameter estimation formula are as follows:

$\left\{\begin{array}{c}k=1.853{\left(\ln \frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i^3}{n\&CenterDot;{\stackrel{\&OverBar;}{V}}^3}\right)}^{-0.548}-0.35\\ c=\frac{E\left(V\right)}{\mathrm{\&Gamma;}(1+1/k)}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i}{n\&CenterDot;\mathrm{\&Gamma;}(1+1/k)}\end{array}\right.---\left(11\right)$

In formula, E (V), --represent respectively mathematical expectation and the mean value of wind series;

Gamma function Γ (y) asks calculation with the progressive progression of Stirling (Stirling) in conjunction with gamma function character:

$\mathrm{\&Gamma;}\left(y\right)={(y+1)}^{(y+0.5)}{e}^{-(y+1)}\sqrt{\frac{2\mathrm{\&pi;}}{y}}[1+\frac{1}{12(y+1)}+\frac{1}{288{(y+1)}^2}-\frac{139}{51840{(y+1)}^3}+\&CenterDot;\&CenterDot;\&CenterDot;]$

In formula, the independent variable of y--gamma function.

3. the survey wind data correction wind method shifting based on probability distribution according to claim 1, is characterized in that: for three parameter weibull, distribute, utilize following methods to estimate the value of form parameter k, scale parameter c and location parameter δ:

(1) low order is not as good as PWM method:

Form parameter k presses following formula and estimates:

$\left\{\begin{array}{c}k=\frac{0.767}{0.040\exp \left({2.277J}_M\right)-1}\\ J_M=\frac{3{\hat{M}}_{\mathrm{1,2,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}\end{array}\right.---\left(12\right)$

In formula, --j rank sample is not as good as probability right square (j=0,1,2); J _m--intermediate variable;

Scale parameter C, location parameter δ value are pressed following formula and are determined:

$\left\{\begin{array}{c}C=\frac{2{\hat{M}}_{\mathrm{1,1,0}}-{\hat{M}}_{\mathrm{1,0,0}}}{(1-2^{-\frac{1}{k}})\mathrm{\&Gamma;}(1+\frac{1}{k})}\\ \mathrm{\&delta;}={\hat{M}}_{\mathrm{1,0,0}}-\mathrm{C\&Gamma;}(1+\frac{1}{k})\end{array}\right.---\left(13\right)$

(2) low order surpasses PWM method:

Form parameter k presses following formula and estimates:

$\left\{\begin{array}{c}k=\frac{0.253}{0.297\exp \left({1.925L}_M\right)-1}\\ L_M=\frac{2{\hat{M}}_{\mathrm{1,0},1}-{\hat{M}}_{\mathrm{1,0,0}}}{3{\hat{M}}_{1,\mathrm{0,2}}-{\hat{M}}_{\mathrm{1,0,0}}}\end{array}\right.---\left(14\right)$

In formula, --l rank sample surpasses probability right square (l=0,1,2);

$\left\{\begin{array}{c}C=\frac{{\hat{M}}_{1,\mathrm{0,0}}-2{\hat{M}}_{\mathrm{1,0,1}}}{(1-2^{-\frac{1}{k}})\mathrm{\&Gamma;}(1+\frac{1}{k})}\\ \mathrm{\&delta;}={\hat{M}}_{\mathrm{1,0,0}}-\mathrm{C\&Gamma;}(1+\frac{1}{k})\end{array}\right.---\left(15\right).$

4. a kind of survey wind data correction wind method shifting based on probability distribution according to claim 3, is characterized in that:

Sample PWM method of estimation is:

Connect order sample probability weight square computing formula:

$\left\{\begin{array}{c}{\hat{M}}_{1,j,0}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{p_i}^j\mathrm{\&Delta;}{p}_i=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{p_i}^j\\ {\hat{M}}_{\mathrm{1,0},l}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{q_i}^l\mathrm{\&Delta;}{p}_i=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{v}_i{q_i}^l\end{array}\right.---\left(16\right)$

In formula, Δ p _i--corresponding to wind speed v _ifrequency, get Δ p _i=1/n;

--corresponding to wind speed v _ij rank cumulative frequency;

--corresponding to wind speed v _il rank cumulative frequency;

If series of samples is pressed sort ascending (v ₁≤ v ₂≤ ... ≤ v _n), without partially estimating calculating formula

${p_i}^j=\frac{(i-1)(i-2)\&CenterDot;\&CenterDot;\&CenterDot;(i-j)}{(n-1)(n-2)\&CenterDot;\&CenterDot;\&CenterDot;(n-j)},(i=\mathrm{1,2},...,n;j=\mathrm{1,2},...)---\left(17\right)$

Because of q=1-p=(X>=x), without estimator partially, be

${q_i}^l=\frac{(n-i)(n-i-1)\&CenterDot;\&CenterDot;\&CenterDot;(n-i-l+1)}{(n-1)(n-2)\&CenterDot;\&CenterDot;\&CenterDot;(n-l)},(i=\mathrm{1,2},...,n;l=\mathrm{1,2},...)---\left(18\right)$

When series of samples is pressed sort descending, with estimator exchanges.

5. the survey wind data correction wind method shifting based on probability distribution according to claim 1, is characterized in that: wind speed sample empirical Frequency computing method are:

Empirical Frequency P _ithe form of computing formula is

$P_i=\frac{i-b}{n+c}(i=\mathrm{1,2},...,n)---\left(19\right)$

In formula, b, c--be the adjustment parameter of empirical Frequency computing formula;

For making the empirical Frequency P of the determined n of formula (19) wind series _iempirical Frequency with respect to 50% is symmetric, and meets 2b+c=1, so formula (19) is further write as

$P_i=\frac{i-b}{n+1-2b}(i=\mathrm{1,2},...,n)---\left(20\right)$

Select extra large gloomy formula (Hazen formula) calculation of wind speed sample v ₁≤ v ₂≤ ... v _i≤ ... ≤ v _nempirical Frequency,

$P_i=\frac{i-0.5}{n}(i=\mathrm{1,2},...,n)---\left(21\right).$