CN105354636A - Wind power fluctuation probability density modeling method based on nonparametric kernel density estimation - Google Patents

Abstract

The present invention provides a wind power fluctuation probability density modeling method based on nonparametric kernel density estimation. The method comprises the following steps: 1, extracting a fluctuation amount of wind power sample data by wavelet decomposition; 2, establishing a corresponding nonparametric kernel density estimation model based on a fluctuation amount sample, and then aiming at the model bandwidth selection problem, constructing a constrained bandwidth optimization model which uses a goodness-of-fit test as a constraint condition; and 3, solving the optimization model by using a constrained sequence optimization algorithm. According to the present invention, due to adoption of the wavelet decomposition method, a wind power fluctuation component can be more precisely extracted; moreover, a probability characteristic modeling method of the extracted fluctuation component is entirely driven by the sample data without performing prior subjective assumption on the probability density model, so that the method has higher modeling accuracy and applicability; and an improvement strategy aiming at the nonparametric kernel density estimation method also enables modeling accuracy and computing efficiency of the method to be effectively improved.

Description

A kind of wind power swing probability density modeling method based on nonparametric probability

Technical field

The invention belongs to wind power swing quantity research field, be specifically related to the extraction of a kind of wind power waves momentum and the probability density modeling method based on nonparametric probability thereof.

Background technology

In recent years along with China's Wind Power Generation Industry fast development, wind-electricity integration installed capacity sustainable growth, ended for the end of the year 2014, and China adds up installed capacity and reaches 114.6GW.Although the large-scale grid connection of wind-powered electricity generation can alleviate environmental pressure and energy crisis to a certain extent, the feature such as undulatory property, randomness of wind power output also can reduce the reliability of Operation of Electric Systems, brings difficulty to Electric Power Network Planning and scheduling.Therefore, be necessary to study the undulatory property of wind power, grasp its inherent probability nature, solve the difficult problem that is incorporated into the power networks of large-scale wind power.

At present, the probability distribution under wind power different time sequence is mainly concentrated on to the research of wind power output characteristic, wind power prediction error, the aspects such as Wind turbines current harmonics, less to the wave characteristic research of wind power.The existing study general for wind power swing probability density is the wave component adopting running mean method to extract wind power, and then adopts method for parameter estimation to carry out probabilistic Modeling to wave component.But, on the one hand, because moving average method is not thorough with being separated of high fdrequency component for Low-frequency continuous component, in the process extracting undulate quantity, likely comprises sustained component, thus impact is formed on modeling accuracy; On the other hand, modelling method of probabilistic based on parameter estimation depends on and defines the priori of model, once prior model hypothesis has error, then sample size is much all cannot ensure that estimation model finally converges on real sample distribution, and the wind power swing characteristic of different geographical likely obeys different probability density forms, thus need to determine different prior models, which in turn reduces the general applicability of wind power probability modeling method.China's wind energy turbine set is widely distributed, is difficult to carry out priori to the undulate quantity distributed model of all wind energy turbine set and defines when studying different wind energy turbine set undulatory property, therefore needs the wind power swing analytical approach that a kind of applicability is higher badly.

Summary of the invention

The present invention proposes a kind of wind power swing probability density modeling method based on nonparametric probability, the method take Gaussian distribution as kernel function, does not need to determine which kind of canonical parameter form wind power probability density is followed and directly carry out modeling to it.For promoting the applicability of nonparametric probability in this particular problem of wind power swing modeling, it take the test of fitness of fot as the bandwidth optimization model of constraint condition that the present invention constructs a kind of, efficiently solve the problem that in bandwidth selection process, model exactness and flatness are coordinated, then propose a kind of constraint sequence optimized algorithm to solve model, thus improve the counting yield of nonparametric probability method.Embodiment based on two province's two places wind energy turbine set actual operating data demonstrate the present invention put forward correctness and the validity of modeling method, compared to traditional wind power swing probability density modeling method, institute of the present invention extracting method has higher modeling accuracy and general applicability.

The technical solution adopted in the present invention is:

Based on a wind power swing probability density modeling method for nonparametric probability, comprise the following steps:

Step 1: utilize wavelet decomposition to be separated with the carrying out of low frequency signal wind power high frequency signal.Suppose that f (x) is for certain wind energy turbine set wind power signal, then the expression formula of its continuous wavelet transform is:

$\left(W_{\mathrm{\ψ}}f\right)(a,b)=|a{|}^{-\frac{1}{2}}\∫f(x\left)\mathrm{\ψ}\right(\frac{x-b}{a})dx---\left(1\right)$

In formula: a is scale factor, b is translation parameters, and ψ () allows small echo.

Make a=2 ^-m, b=2 ^-mn, m, n ∈ Z, just can obtain wavelet transform by a, b discretize:

(DW _ψf)(m,n)＝[f(t),ψ _m,n(t)](2)

Its decomposition result is as Fig. 1, and expression formula is:

f(x)＝a3+d1+d2+d3(3)

In formula: a3 is wind power low frequency part, and d1, d2, d3 are HFS.

Using wind power low frequency component a3 as its sustained component, residue high fdrequency component is carried out cumulative as its undulate quantity.

Step 2: utilize sample data structure based on the pdf model of kernel function.Suppose x ₁, x ₂..., x _nfor n sample of wind power waves momentum, then the nonparametric probability of wind power waves momentum probability density function is:

$\hat{f}\left(x\right)=\frac{1}{nh}\underset{i=1}{\overset{n}{\Σ}}K\left(\frac{x-x_i}{h}\right)---\left(4\right)$

In formula: h is bandwidth, also referred to as smoothing factor, K () is kernel function.

Select Gaussian function as the kernel function of wind power waves momentum Multilayer networks, from formula (4), the nonparametric probability of wind power swing pdf model can be rewritten as:

$\hat{f}(x,h)=\frac{1}{\sqrt{2\mathrm{\π}}nh}\underset{i=1}{\overset{n}{\Σ}}\exp \[-\frac{1}{2}{\left(\frac{x-x_i}{h}\right)}^2\]---\left(5\right)$

In nonparametric probability model, the selection of bandwidth h is the key factor affecting Density Estimator accuracy, and therefore the present invention is by goodness of fit χ ²inspection, as constraint condition, is brought bandwidth optimization model into, is proposed a kind of bandwidth optimization model of belt restraining:

$\begin{array}{cc}\min & R_{ise}\left(f_h\right)=\∫{\[{\hat{f}}_h\left(x\right)-f\left(x\right)\]}^{2}dx\\ s.t.& {{\mathrm{\χ}}_h}^2\≤{{\mathrm{\χ}}_{m-1}}^2\left(\mathrm{\α}\right)\end{array}---\left(6\right)$

In formula: f (x) is the trues probability density function of wind power waves momentum, when the unknown of undulate quantity trues probability density, generally substitute by the discrete statistics based on historical data; χ _h ²for the χ of nonparametric probability ²test statistics; χ _m-1 ²(α) for degree of freedom under level of signifiance α is the χ of m-1 ²distribution.

Step 3: utilize constraint sequence optimization method to be optimized the parameter to be asked (bandwidth) in model and solve.

Comprise the following steps in step 3:

Step 3.1: in the solution space of bandwidth h, extracts N number of bandwidth value form solution room Ω according to being uniformly distributed, the number of N and the size of solution space closely related, be less than 10 in solution space ⁸time, the number of N generally selects 1000.

Step 3.2: utilize formula (5) to determine the probability density function of wind power waves momentum.

Step 3.3: utilize formula (7) to determine to observe the number s separated in disaggregation S.

$\begin{array}{c}\mathrm{Pr}ob\left(\left|\mathrm{\Θ}\∩S\right|\≥k\right)\\ =\underset{j=k}{\overset{\min \left(g,s\right)}{\Σ}}\underset{i=0}{\overset{s-j}{\Σ}}\frac{\left(\begin{array}{c}g\\ j\end{array}\right)\left(\begin{array}{c}N-g\\ s-i-j\end{array}\right)}{\left(\begin{array}{c}N\\ s-i\end{array}\right)}\\ \×\left(\begin{array}{c}s\\ i\end{array}\right)q^{s-i}{\left(1-q\right)}^i\≥\mathrm{\η}\end{array}---\left(7\right)$

In formula: Prob () is for aiming at probability, g is true number of separating, s is the number of separating in observation disaggregation S, k represents in selected set to have k true enough good solution at least, η represents the probability containing k enough good solution in observation disaggregation S, usual η get 0.95, q be in solution space real observation to the probability of feasible solution.

Step 3.4: with goodness of fit χ ²verify as rough model, in Ω, ask for individual being deconstructed into of the s meeting this test condition observe disaggregation S, its concrete method of inspection is:

According to given wind power swing sample data, be divided into m group, calculated χ under different bandwidth respectively by group result ²test statistics.

${\mathrm{\χ}}^2=\underset{i=1}{\overset{m}{\Σ}}\left(\frac{t_i-{\mathrm{np}}_i}{{\mathrm{np}}_i}\right)---\left(8\right)$

In formula: t _irepresent the sample actual frequency falling into i-th group, n is the number of sample, p _ifor theoretical probability value.

Judge the feasibility of different bandwidth, when sample size is enough large, this statistic is similar to and obeys degree of freedom is the χ of m-1 ²distribution.If χ _h ²> χ _m-1 ²a (), then mean the hypothesis distribution of wind power swing be false, upcheck; On the contrary, if χ _h ²≤ χ _m-1 ²a (), then suppose to set up, inspection is not passed through.

Step 3.5: the objective function of (6) is accurate model with the formula, carries out sequence to the solution in disaggregation S and compares, and chooses front k and separates as true enough good solution.

Compared with the conventional method, a kind of wind power swing probability density modeling method based on nonparametric probability of the present invention, has the following advantages and beneficial effect:

1) the present invention utilizes wavelet decomposition to extract wind power waves momentum, and compared to traditional running mean method, the sustained component that wavelet decomposition can effectively be rejected in wind power swing component is remaining, and accuracy is higher.

2) the belt restraining bandwidth optimization model that builds of the present invention can the making overall plans and coordinate of implementation model accuracy and flatness, promote the modeling accuracy of Nonparametric Estimation in wind power swing probabilistic Modeling problem, and improve the counting yield of Nonparametric Estimation based on the bandwidth optimization model solution algorithm retraining sequence optimization.

3) the nonparametric probability method of the wind power waves momentum pdf model of the present invention's proposition is driven by sample data completely, do not need to carry out priori subjectivity hypothesis to pdf model, thus more traditional modeling method based on parameter estimation has higher accuracy and applicability.

Accompanying drawing explanation

Fig. 1 is wavelet decomposition structural drawing of the present invention.

Fig. 2 is that embodiment of the present invention apoplexy power continues amount and measured data.

Fig. 3 is the wind power waves momentum in the embodiment of the present invention.

Fig. 4 is the spectrum distribution of the undulate quantity in the embodiment of the present invention.

Fig. 5 is that in the embodiment of the present invention, A economizes certain wind energy turbine set wind power swing probability density function curve map.

Fig. 6 is that in the embodiment of the present invention, B economizes certain wind energy turbine set wind power swing probability density function curve map.

Embodiment

A kind of wind power swing probability density modeling method based on nonparametric probability, this method propose the method adopting wavelet decomposition to extract wind power waves momentum, utilize carry a kind of to carry out matching based on the probability distribution of nonparametric probability method to wind power waves momentum, specifically comprise the following steps:

Step 1: utilize wavelet decomposition to be separated with the carrying out of low frequency signal wind power high frequency signal.Suppose that f (x) is for certain wind energy turbine set wind power signal, then the expression formula of its continuous wavelet transform is:

$\left(W_{\mathrm{\ψ}}f\right)(a,b)=|a{|}^{-\frac{1}{2}}\∫f(x\left)\mathrm{\ψ}\right(\frac{x-b}{a})dx---\left(1\right)$

In formula: a is scale factor, b is translation parameters, and ψ () allows small echo.

Make a=2 ^-m, b=2 ^-mn, m, n ∈ Z, just can obtain wavelet transform by a, b discretize:

(DW _ψf)(m,n)＝[f(t),ψ _m,n(t)](2)

Its decomposition result is as Fig. 1, and expression formula is:

f(x)＝a3+d1+d2+d3(3)

In formula: a3 is wind power low frequency part, and d1, d2, d3 are HFS.

Using wind power low frequency component a3 as its sustained component, residue high fdrequency component is carried out cumulative as its undulate quantity.

Step 2: utilize sample data structure based on the pdf model of kernel function.Suppose x ₁, x ₂..., x _nfor n sample of wind power waves momentum, then the nonparametric probability of wind power waves momentum probability density function is:

$\hat{f}\left(x\right)=\frac{1}{nh}\underset{i=1}{\overset{n}{\Σ}}K\left(\frac{x-x_i}{h}\right)---\left(4\right)$

In formula: h is bandwidth, also referred to as smoothing factor, K () is kernel function.

Select Gaussian function as the kernel function of wind power waves momentum Multilayer networks, from formula (4), the nonparametric probability of wind power swing pdf model can be rewritten as:

$\hat{f}(x,h)=\frac{1}{\sqrt{2\mathrm{\π}}nh}\underset{i=1}{\overset{n}{\Σ}}\exp \[-\frac{1}{2}{\left(\frac{x-x_i}{h}\right)}^2\]---\left(5\right)$

In nonparametric probability model, the selection of bandwidth h is the key factor affecting Density Estimator accuracy, and therefore the present invention is by goodness of fit χ ²inspection, as constraint condition, is brought bandwidth optimization model into, is proposed a kind of bandwidth optimization model of belt restraining:

$\begin{array}{cc}\min & R_{ise}\left(f_h\right)=\∫{\[{\hat{f}}_h\left(x\right)-f\left(x\right)\]}^{2}dx\\ s.t.& {{\mathrm{\χ}}_h}^2\≤{{\mathrm{\χ}}_{m-1}}^2\left(\mathrm{\α}\right)\end{array}---\left(6\right)$

In formula: f (x) is the trues probability density function of wind power waves momentum, when the unknown of undulate quantity trues probability density, generally substitute by the discrete statistics based on historical data; χ _h ²for the χ of nonparametric probability ²test statistics; χ _m-1 ²(α) for degree of freedom under level of signifiance α is the χ of m-1 ²distribution.

Step 3: utilize constraint sequence optimization method to be optimized the parameter to be asked (bandwidth) in model and solve.

Comprise the following steps in step 3:

Step 3.1: in the solution space of bandwidth h, extracts N number of bandwidth value form solution room Ω according to being uniformly distributed, the number of N and the size of solution space closely related, be less than 10 in solution space ⁸time, the number of N generally selects 1000.

Step 3.2: utilize formula (5) to determine the probability density function of wind power waves momentum.

Step 3.3: utilize formula (7) to determine to observe the number s separated in disaggregation S.

$a\begin{array}{c}\mathrm{Pr}ob\left(\left|\mathrm{\Θ}\∩S\right|\≥k\right)\\ =\underset{j=k}{\overset{\min \left(g,s\right)}{\Σ}}\underset{i=0}{\overset{s-j}{\Σ}}\frac{\left(\begin{array}{c}g\\ j\end{array}\right)\left(\begin{array}{c}N-g\\ s-i-j\end{array}\right)}{\left(\begin{array}{c}N\\ s-i\end{array}\right)}\\ \×\left(\begin{array}{c}s\\ i\end{array}\right)q^{s-i}{\left(1-q\right)}^i\≥\mathrm{\η}\end{array}---\left(7\right)$

In formula: Prob () is for aiming at probability, g is true number of separating, s is the number of separating in observation disaggregation S, k represents in selected set to have k true enough good solution at least, η represents the probability containing k enough good solution in observation disaggregation S, usual η get 0.95, q be in solution space real observation to the probability of feasible solution.

Step 3.4: with goodness of fit χ ²verify as rough model, in Ω, ask for individual being deconstructed into of the s meeting this test condition observe disaggregation S, its concrete method of inspection is:

According to given wind power swing sample data, be divided into m group, calculated χ under different bandwidth respectively by group result ²test statistics.

${\mathrm{\χ}}^2=\underset{i=1}{\overset{m}{\Σ}}\left(\frac{t_i-{\mathrm{np}}_i}{{\mathrm{np}}_i}\right)---\left(8\right)$

In formula: t _irepresent the sample actual frequency falling into i-th group, n is the number of sample, p _ifor theoretical probability value.

Judge the feasibility of different bandwidth, when sample size is enough large, this statistic is similar to and obeys degree of freedom is the χ of m-1 ²distribution.If χ _h ²> χ _m-1 ²a (), then mean the hypothesis distribution of wind power swing be false, upcheck; On the contrary, if χ _h ²≤ χ _m-1 ²a (), then suppose to set up, inspection is not passed through.

Step 3.5: the objective function of (6) is accurate model with the formula, carries out sequence to the solution in disaggregation S and compares, and chooses front k and separates as true enough good solution.

Embodiment:

Simulation example of the present invention economizes certain wind energy turbine set by A and B economizes based on certain wind energy turbine set measured data, and emulation experiment is programming realization under Matlab environment.

1) the wind power waves momentum, based on wavelet decomposition extracts:

Choose the meritorious data analysis of exerting oneself of actual measurement that A economizes certain 1-January 31 January wind energy turbine set year, the sampling period of these data is 10min, and the total rated power of wind electric field blower is 13.6MW.Carry out wavelet decomposition to meritorious the exerting oneself of wind-powered electricity generation, select compact schemes biorthogonal wavelet db10 as wavelet basis through test, carry out three layers of decomposition, its data result as shown in Figure 2,3.

For checking is based on the correctness of the wind power waves momentum extracting method of wavelet decomposition, the present invention also adopts moving average method to extract undulate quantity, and carries out FFT conversion to two kinds of results, analyzes its spread spectrum scenarios, the window value of running mean elects 15 as, and result as shown in Figure 4.As shown in Figure 4, after utilizing wavelet decomposition, the amplitude of wind power low frequency part (0-50Hz) is 0, spectrum distribution and the running mean of other parts are similar, visible, wavelet decomposition effectively can reject continuation component wherein while accurately extracting wind power swing component, then may there are the remnants of sustained component, thus affect the effect of wind power swing analysis in the wind power waves momentum utilizing running mean method to extract.

2), the bandwidth of nonparametric probability model solves:

Adopt institute of the present invention extracting method, build the above-mentioned nonparametric probability model being extracted undulate quantity probability density, and to obtain model bandwidth be 59.2.Result of calculation is as shown in table 1.

Table 1 bandwidth optimizing result table

As shown in Table 2, in this example, model of the present invention have passed χ ²inspection, and integrated square error is all less, modeling accuracy is desirable, introduces χ ²after the constraint condition of inspection as bandwidth optimization model, improve the optimizing effect of bandwidth solving model, accuracy and the flatness of nonparametric probability function curve can be ensured simultaneously.

3), based on the efficiency analysis of the bandwidth derivation algorithm of constraint sequence optimization:

For analyzing the counting yield of the constraint sequence optimized algorithm that the present invention proposes, genetic algorithm, particle cluster algorithm and constraint sequence optimized algorithm is adopted to solve bandwidth optimization model of the present invention respectively, correlation computations is all at Intel Duo i3-3240 processor/3.40GHz, 4G memory computer completes, and its result of calculation is as shown in table 3.

Table 2 bandwidth optimizing result table

As shown in Table 2, the derivation algorithm that the present invention proposes effectively can reduce the computation complexity of wind power waves momentum pdf model nonparametric probability method, is that genetic algorithm all more traditional in computational accuracy and counting yield and particle cluster algorithm have obvious advantage.

4), the efficiency analysis of nonparametric probability modeling method:

For the correctness of the wind power swing probability density nonparametric probability method that checking the present invention proposes, utilize modeling method that the present invention puies forward respectively, the method for parameter estimation of t-locationscale distribution and normal distribution, for Hubei wind energy turbine set example, set up the pdf model of its wind power swing, undetermined parameter in parameter estimation calculates by Maximum Likelihood Estimation and tries to achieve, and its probability density curve as shown in Figure 5.

As shown in Figure 5, the pdf model utilizing normal distyribution function to build has comparatively big error, cannot the probability density of accurate description wind power swing, visible for method for parameter estimation, the determination of prior model directly can have influence on last modeling accuracy, once prior model selection is improper, then can directly cause built probability model cannot meet modeling accuracy requirement.And the method for parameter estimation adopting t to distribute and the model constructed by the inventive method all effectively can simulate the probability density of Hubei wind energy turbine set wind power waves momentum, for assessing the modeling accuracy of said method further, adopt integrated square error carry out quantitative test, its parameter and error criterion as shown in table 3.

The integrated square error of table 3 wind power swing pdf model

As shown in Table 3, the integrated square error of institute of the present invention established model is less, shows higher fitting precision.

5), the applicability analysis of nonparametric probability modeling method:

For checking the inventive method is for applicability during different wind energy turbine set sample, certain wind energy turbine set day breeze power historical service data on annual 1-January 31 in January is economized for sample again with B, sampling period is 10min, adopt the inventive method respectively, method for parameter estimation based on t-locationscale distribution and normal distribution carries out modeling to the probability density that B economizes wind energy turbine set wind power waves momentum, and its result as shown in Figure 6.

As shown in Figure 6, the Nonparametric Estimation that the present invention proposes is economized in wind energy turbine set example at B, still achieve good modeling accuracy, and economize in example based on the method for parameter estimation of t-locationscale distribution and normal distribution at B, modeling error increases all to some extent, and its detailed results is as shown in table 4.

The integrated square error of table 4 wind power swing pdf model

As shown in Table 4, wind energy turbine set is economized compared to A, the modeling error that method for parameter estimation economizes for B the pdf model that wind energy turbine set example builds all is significantly increased, wherein the error of t-locationscale distributed model increases particularly evident, its reason is, B province local climate changes comparatively A and economizes more violent, wind power swing is also larger, the potential probability distribution that its undulate quantity is followed also is economized with A and is not quite similar, and method for parameter estimation can only adopt fixing prior density function to carry out probability density modeling when the unknown of sample data prior model, thus modeling accuracy in some example may be caused to meet the requirements, but in the situation that other example medial error are larger.And the Nonparametric Estimation that the present invention proposes is because without the need to determining the prior distribution model of sample data, therefore also would not occur above-mentioned situation, Comparatively speaking, the applicability of the wind power swing probability density modeling method that the present invention proposes is stronger.

Claims (2)

1., based on a wind power swing probability density modeling method for nonparametric probability, it is characterized in that comprising the following steps:

Step 1: utilize wavelet decomposition to be separated with the carrying out of low frequency signal wind power high frequency signal, suppose that f (x) is for certain wind energy turbine set wind power signal, then the expression formula of its continuous wavelet transform is:

$\left(W_{\mathrm{\ψ}}f\right)(a,b)={\left|a\right|}^{-\frac{1}{2}}\∫f\left(x\right)\mathrm{\ψ}\left(\frac{x-b}{a}\right)dx---\left(1\right)$

In formula: a is scale factor, b is translation parameters, and ψ () allows small echo;

Make a=2 ^-m, b=2 ^-mn, m, n ∈ Z, just can obtain wavelet transform by a, b discretize:

(DW _ψf)(m,n)＝[f(t),ψ _m,n(t)](2)

Its decomposition result is as Fig. 1, and expression formula is:

f(x)＝a3+d1+d2+d3(3)

In formula: a3 is wind power low frequency part, and d1, d2, d3 are HFS;

Using wind power low frequency component a3 as its sustained component, residue high fdrequency component is carried out cumulative as its undulate quantity;

Step 2: utilize sample data structure based on the pdf model of kernel function, suppose x ₁, x ₂..., x _nfor n sample of wind power waves momentum, then the nonparametric probability of wind power waves momentum probability density function is:

$\hat{f}\left(x\right)=\frac{1}{nh}\underset{i=1}{\overset{n}{\Σ}}K\left(\frac{x-x_i}{h}\right)---\left(4\right)$

In formula: h is bandwidth, also referred to as smoothing factor, K () is kernel function;

Select Gaussian function as the kernel function of wind power waves momentum Multilayer networks, from formula (4), the nonparametric probability of wind power swing pdf model can be rewritten as:

$\hat{f}(x,h)=\frac{1}{\sqrt{2\mathrm{\π}}nh}\underset{i=1}{\overset{n}{\Σ}}\exp \[-\frac{1}{2}{\left(\frac{x-x_i}{h}\right)}^2\]---\left(5\right)$

In nonparametric probability model, the selection of bandwidth h is the key factor affecting Density Estimator accuracy, and therefore the present invention is by goodness of fit χ ²inspection, as constraint condition, is brought bandwidth optimization model into, is proposed a kind of bandwidth optimization model of belt restraining:

$\min R_{ise}\left(f_h\right)=\∫{\[{\hat{f}}_h\left(x\right)-f\left(x\right)\]}^{2}dx---\left(6\right)$

s.t.χ _h ²≤χ _m-1 ²(α)

In formula: f (x) is the trues probability density function of wind power waves momentum, when the unknown of undulate quantity trues probability density, generally substitute by the discrete statistics based on historical data; χ _h ²for the χ of nonparametric probability ²test statistics; χ _m-1 ²(α) for degree of freedom under level of signifiance α is the χ of m-1 ²distribution;

Step 3: utilize constraint sequence optimization method to be optimized the bandwidth to be asked in model and solve.

2. the approximating method that distributes of a kind of power probability of leeward in the same time based on Fourier series according to claim 1, it is characterized in that, step 3 concrete steps are as follows:

Step 3.1: in the solution space of bandwidth h, extracts N number of bandwidth value form solution room Ω according to being uniformly distributed, the number of N and the size of solution space closely related, be less than 10 in solution space ⁸time, the number of N generally selects 1000;

Step 3.2: utilize formula (5) to determine the probability density function of wind power waves momentum;

Step 3.3: utilize formula (7) to determine to observe the number s separated in disaggregation S;

$\begin{array}{c}\mathrm{Pr}ob\left(\right|\mathrm{\Θ}\∩S|\≥k)\\ =\underset{j=k}{\overset{\min (g,s)}{\mathrm{\Σ}}}\underset{i=0}{\overset{s-j}{\mathrm{\Σ}}}\frac{\left(\begin{array}{c}g\\ j\end{array}\right)\left(\begin{array}{c}N-g\\ s-i-j\end{array}\right)}{\left(\begin{array}{c}N\\ s-j\end{array}\right)}\\ \×\left(\begin{array}{c}s\\ i\end{array}\right)q^{s-i}{(1-q)}^i\≥\mathrm{\η}\end{array}---\left(7\right)$

In formula: Prob () is for aiming at probability, g is true number of separating, s is the number of separating in observation disaggregation S, k represents in selected set to have k true enough good solution at least, η represents the probability containing k enough good solution in observation disaggregation S, usual η get 0.95, q be in solution space real observation to the probability of feasible solution;

Step 3.4: with goodness of fit χ ²verify as rough model, in Ω, ask for individual being deconstructed into of the s meeting this test condition observe disaggregation S, its concrete method of inspection is:

According to given wind power swing sample data, be divided into m group, calculated χ under different bandwidth respectively by group result ²test statistics;

${\mathrm{\χ}}^2=\underset{i=1}{\overset{m}{\Σ}}\left(\frac{t_i-{\mathrm{np}}_i}{{\mathrm{np}}_i}\right)---\left(8\right)$ In formula: t _irepresent the sample actual frequency falling into i-th group, n is the number of sample, p _ifor theoretical probability value;

Judge the feasibility of different bandwidth, when sample size is enough large, this statistic is similar to and obeys degree of freedom is the χ of m-1 ²distribution, if χ _h ²> χ _m-1 ²a (), then mean the hypothesis distribution of wind power swing be false, upcheck; On the contrary, if χ _h ²≤ χ _m-1 ²(a), then suppose to set up, inspection is not passed through;

Step 3.5: the objective function of (6) is accurate model with the formula, carries out sequence to the solution in disaggregation S and compares, and chooses front k and separates as true enough good solution.