CN105939026A - Hybrid Laplace distribution-based wind power fluctuation quantity probability distribution model building method - Google Patents

Abstract

The invention discloses a hybrid Laplace distribution-based wind power fluctuation quantity probability distribution model building method. The method comprises the steps of firstly, calculating a wind power fluctuation quantity sequence according to actually measured wind power data of a wind farm and a default time scale; building a hybrid Laplace distribution model; and determining a parameter of the hybrid Laplace distribution model according to the wind power fluctuation quantity sequence, thereby obtaining a wind power probability distribution model. By the wind power probability distribution model obtained by the method, the wind power fluctuation characteristics can be accurately described; especially, the accuracy of heavy-tailed characteristic description of wind power fluctuation distribution is improved; and aiming at the description problem of wind power fluctuation of different temporal and spatial scale levels, the model can also reach the satisfactory accuracy.

Description

Wind power undulate quantity probability Distribution Model based on mixing Laplace distribution is set up Method

Technical field

The invention belongs to wind power swing specificity analysis technical field, more specifically, relate to a kind of based on mixing The wind power undulate quantity probability Distribution Model method for building up of Laplace distribution.

Background technology

Along with the fast development of generation of electricity by new energy technology, the grid-connected demand of large-scale wind power strengthens further, and wind power Undulatory property, intermittence not only affect the quality of power supply, add the difficulty of Electric Power Network Planning and scheduling, also give the safety and stability of electrical network Operation causes potential risks.The control performance of minute level yardstick influence of fluctuations power system AGC；Hour level yardstick influence of fluctuations Power system in a few days Real-Time Scheduling；Daily fluctuation affects the arrangement of power system peak regulation method；Influence of fluctuations power system on days electricity Power electric quantity balancing, accurately analyzes wind power wave characteristic, is the basis solving these problems, is also that research wind-powered electricity generation is extensive also The important step of net generating.Set up effectively reliably model, can be applied not only to wind power prediction assessment, generation schedule is repaiied Just, it is also applied for spinning reserve to estimate.

The method of traditional description wind power wave characteristic, generally has three kinds of different directions.One is with the time for dimension Degree, sets up wind power random seriation model, i.e. Time series analysis method, as at document: " Chen P, Pedersen T, Bak-Jensen B, et al.ARIMA-based time series model of stochastic wind power Generation.IEEE Trans.on Power Systems, Vol.25 (2), 2010, pp.667 676 " in, wind-powered electricity generation is gone out Power sequence regards non-stationary series as, establishes autoregression integration moving average model based on wind power fluctuation.One is false Subduing the wind syndrome electrical power does not also meet certain prior probability distribution, and uses Nonparametric Estimation to build the probability nature of wind-powered electricity generation Mould, as document " Yang Nan, Cui Jiazhan, Zhou Zheng, etc. based on Fuzzy Ordered optimize wind power probability model nonparametric probability Method. electric power network technique, Vol.40 (2), 2016, pp.335 340 " in, using Gaussian function as wind power Multilayer networks Kernel function, build wind power nonparametric estimation model.Also one is, based on certain prior probability distribution, right Pdf model carries out Parameterization estimate, as document " woods satellite, Wen Jingyu, Ai little Meng, etc. wind power wave characteristic Probability distribution research. Proceedings of the CSEE, Vol.32 (1), 2012, pp.38 46 " in, utilize band translocation factor with flexible The t-distribution t location-scale distribution of coefficient, describes wind field power minute level component fluctuation situation.

Owing to the randomness of wind power change is strong, on different spatial and temporal scales, wind power fluctuation pattern difference is big, The Time series analysis method of single spatial and temporal scales is difficult to accurately describe the wave characteristic of wind power.And utilize non-parametric estmation Method describes the wave characteristic of wind power, generally requires the sample data of magnanimity, and it turned out wind-powered electricity generation by available data The probability distribution of power swing presents clear and definite regularity, and therefore Nonparametric Estimation is not optimal case.Wind power The probability distribution of fluctuation, presents the strongest heavy-tailed property, for Parameterization estimate method, traditional distributed model, is difficult to accurately Reflection wind power fluctuation crest probability near average.

Summary of the invention

It is an object of the invention to overcome the deficiencies in the prior art, it is provided that a kind of wind-powered electricity generation based on mixing Laplace distribution Power waves momentum probability Distribution Model method for building up, it is provided that wind power fluctuation under a kind of energy accurate description different time and space scales Probability Distribution Model, is being to describe at the heavy-tailed property of distribution especially, is being effectively improved fitting precision.

For achieving the above object, present invention wind power undulate quantity probability distribution based on mixing Laplace distribution Method for establishing model comprises the following steps:

S1: according to wind power data and the default time scale Δ t of wind energy turbine set actual measurement, calculate wind power undulate quantity Sequence P=[p₁, p₂, p₃,···,p_M]^T, wherein M represents the dimension of wind power undulate quantity sequence；

S2: build and mix Laplace distributed model:

$f\left(P\right|\mathrm{\α},\mathrm{\μ},\mathrm{\δ})=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\α}}_i{f}_i\left(p\right|{\mathrm{\μ}}_i,{\mathrm{\δ}}_i)$

Wherein, α={ α₁,α₂,···,α_NRepresent weight parameter collection, α_iThe weight being distributed for i-th Laplace, andμ={ μ₁,μ₂,···,μ_NRepresent Mean Parameters collection, μ_iRepresent the distribution of i-th Laplace Middle wind power undulate quantity serial variance, δ={ δ₁,δ₂,···,δ_NRepresent variance parameter collection, δ_iRepresent i-th Laplace Wind power undulate quantity serial mean in distribution；N is that Laplace is distributed number, N ＞ 1；f_i(p|μ_i,δ_i) represent the single M of i-th The probability density function of dimension Laplace distribution；

S3: according to wind power undulate quantity sequence P=[p₁, p₂, p₃,···,p_M]^TThe mixing that step S2 is obtained Laplace distributed model solves, and obtains its weight parameter collection α, Mean Parameters collection μ and variance parameter collection δ, thus obtains wind The probability Distribution Model of electrical power undulate quantity.

Present invention wind power undulate quantity probability Distribution Model method for building up based on mixing Laplace distribution, first root Wind power data and the time scale preset according to wind energy turbine set actual measurement calculate wind power undulate quantity sequence, build mixing Laplace distributed model, solves the parameter obtaining mixing Laplace distributed model according to wind power undulate quantity sequence, thus Obtain wind power probability Distribution Model.Use the wind power probability Distribution Model obtained by the present invention, can accurate description wind Power swing characteristic, in particular improves the degree of accuracy that the heavy-tailed property of wind power swing distribution describes；For the different time On scale level, and the description problem of different spaces scale level wind power swing, this model also can reach satisfied precision, For the assessment of power system peak regulation nargin, wind power prediction assessment, generation schedule correction, probabilistic load flow and balance of electric power and ener The problems such as analysis provide reliable base reference.

Accompanying drawing explanation

Fig. 1 is present invention wind power undulate quantity probability Distribution Model method for building up based on mixing Laplace distribution Flow chart；

Fig. 2 be mixing Laplace distributed model solve flow chart；

Fig. 3 is the present invention and the wind power undulate quantity probability distribution graph of contrast model in the present embodiment；

Fig. 4 is the different time scales present invention and the wind power undulate quantity probability distribution of contrast model in the present embodiment Figure；

Fig. 5 is the different spaces yardstick present invention and the wind power undulate quantity probability distribution of contrast model in the present embodiment Figure.

Detailed description of the invention

Below in conjunction with the accompanying drawings the detailed description of the invention of the present invention is described, in order to those skilled in the art is preferably Understand the present invention.Requiring particular attention is that, in the following description, when known function and design detailed description perhaps When can desalinate the main contents of the present invention, these are described in and will be left in the basket here.

Embodiment

Fig. 1 is present invention wind power undulate quantity probability Distribution Model method for building up based on mixing Laplace distribution Flow chart.As it is shown in figure 1, present invention wind power undulate quantity probability Distribution Model foundation side based on mixing Laplace distribution Method comprises the following steps:

S101: calculating wind power undulate quantity:

Wind power data according to wind energy turbine set actual measurement and default time scale Δ t, calculate wind power undulate quantity sequence Row P=[p₁,p₂,p₃,···,p_M]^T, wherein M represents the dimension of wind power undulate quantity sequence.

In the prior art, it is common that (t+ Δ t)-P (t) is as wind for the first-order difference Δ P=P of employing wind power data Electrical power undulate quantity, it is also possible to wind power output rate of change P_v=[P (t+ Δ t)-P (t)]/P_NAs wind power undulate quantity, its (t+ Δ t), P (t) represent moment t+ Δ t and the wind power of moment t, P to middle P respectively_NRepresent specified installed capacity.Due to wind speed Size directly affects wind power output, although after first-order difference, weakens the non-stationary of wind power fluctuation, but if selects Time scale Δ t time span is big, wind power there will be in Δ t larger fluctuation or present regular poor.Therefore, in order to The natural fluctuation situation of energy accurate response wind power, weakens volatility series average and the coupling of variance and the Singular variance of sequence Property, wind power output is first carried out natural logrithm conversion by the present embodiment, then does first-order difference, describe wind power undulate quantity, Wind power undulate quantity p of i.e. moment t_tComputing formula be:

p_t=lnP (t+ Δ t)-lnP (t)

Obviously, as a length of L of the wind power data sequence of wind energy turbine set actual measurement, M=L-Δ t.

S102: build and mix Laplace distributed model:

Laplace distributed model is widely used in Speech processing, is two parameter probabilistic models.Single The mathematic(al) representation of Laplace distribution density function can be designated as:

$f\left(x\right|\mathrm{\μ},\mathrm{\δ})=\frac{1}{\sqrt{2}\mathrm{\δ}}\exp (-\frac{\sqrt{2}}{\mathrm{\δ}}|x-\mathrm{\μ}\left|\right)$

Wherein, exp represents exponential function.

Proving after deliberation, single distribution can not accurately describe wind power fluctuation pattern.Therefore the present invention is single On the basis of Laplace distribution, derive finite element mixing Laplace distributed model.Assuming that wind power undulate quantity sequence P= [p₁, p₂, p₃,···,p_M]^TObey the distribution after the weighting of N number of Laplace distribution, then its mathematic(al) representation is:

$\begin{array}{c}f\left(P\right|\mathrm{\α},\mathrm{\μ},B)={\mathrm{\α}}_1{f}_1\left(P\right|{\mathrm{\μ}}_1,B_1)+{\mathrm{\α}}_2{f}_2\left(P\right|{\mathrm{\μ}}_2,B_2)+\mathrm{...}+{\mathrm{\α}}_N{f}_N\left(P\right|{\mathrm{\μ}}_N,B_N)\\ =\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\α}}_i{f}_i\left(P\right|{\mathrm{\μ}}_i,B_i)\end{array}$

Wherein, f (P | α, μ, B) represents mixing Laplace distributed model distribution probability density function；α={ α₁, α₂,···,α_NRepresent weight parameter collection, andα_iThe weight being distributed for i-th Laplace, i=1,2 ..., N； μ={ μ₁,μ₂,···,μ_NRepresent Mean Parameters collection, B={B₁,B₂,···,B_NRepresent covariance matrix parameter set；N is Laplace is distributed number, N ＞ 1, in general, considers complexity and the model accuracy of model, and the span of N is 2≤ N≤5；f_i(P|μ_i,B_i) be single M dimension Laplace distribution probability density function, its expression formula is:

$f_i\left(P\right|{\mathrm{\μ}}_i,B_i)=\frac{1}{2^{\frac{M}{2}}{B_i}^{\frac{1}{2}}}\exp \{-\sqrt{2}|P-{\mathrm{\μ}}_i\left|{B_i}^{-\frac{1}{2}}\right\}$

μ_iFor f_i(P|μ_i,B_i) the corresponding equal value sequence of wind power undulate quantity, μ_i=[μ_i,1,μ_i,2,···μ_i,M]^T；B_i For f_i(P|μ_i,B_i) covariance matrix, after natural logrithm difference processing, vector P be regarded as separate, therefore Can obtain:

$B_i=\left[\begin{array}{cccc}{{\mathrm{\δ}}_{i,1}}^2& & & \\ & {{\mathrm{\δ}}_{i,2}}^2& & \\ & & \mathrm{...}& \\ & & & {{\mathrm{\δ}}_{i,M}}^2\end{array}\right]$

In order to simplify calculating, present invention assumes that M dimension wind power undulate quantity sequence has identical average and variance, can :

μ_i=[μ_i,1,μ_i,2,···μ_i,M]^T=[μ_i,μ_i,···μ_i]^T=μ_iE

$B_i=\left[\begin{array}{cccc}{{\mathrm{\δ}}_{i,1}}^2& & & \\ & {{\mathrm{\δ}}_{i,2}}^2& & \\ & & \mathrm{...}& \\ & & & {{\mathrm{\δ}}_{i,M}}^2\end{array}\right]={{\mathrm{\δ}}_i}^2\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & \mathrm{...}& \\ & & & 1\end{array}\right]={{\mathrm{\δ}}_i}^{2}E={{\mathrm{\δ}}_i}^2$

Visible now μ={ μ₁,μ₂,···,μ_NRepresent Mean Parameters collection, μ_iRepresent i-th Laplace distribution apoplexy Electrical power undulate quantity serial variance, δ={ δ₁,δ₂,···,δ_NRepresent variance parameter collection, δ_iRepresent the distribution of i-th Laplace Middle wind power undulate quantity serial mean.

Therefore mean vector and covariance matrix can be expressed as a constant and a unit matrix product, then single The probability density function of one M dimension Laplace distribution is represented by:

$f\left(p\right|{\mathrm{\μ}}_i,{\mathrm{\δ}}_i)=\frac{1}{2^{\frac{M}{2}}{\mathrm{\δ}}_i}\exp \{-\sqrt{2}\frac{\left|p-{\mathrm{\μ}}_i\right|}{{\mathrm{\δ}}_i}\}$

Wherein, p represents wind power undulate quantity.

Mixing Laplace distributed model is represented by:

$f\left(P\right|\mathrm{\α},\mathrm{\μ},\mathrm{\δ})=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\α}}_i{f}_i\left(p\right|{\mathrm{\μ}}_i,{\mathrm{\δ}}_i)$

Visible, Θ={ α_i,μ_i,δ_iIt is the parameter set that finite element mixes Laplace, i.e. Θ={ α₁,α₂,···, α_N；μ₁,μ₂,···,μ_N；δ₁,δ₂,···,δ_N}

S103: solve and mix Laplace distributed model:

The mixing Laplace distributed model obtaining step S102 solves, and obtains its weight parameter collection α, average ginseng Manifold μ and variance parameter collection δ, thus obtain wind power probability Distribution Model.

The present embodiment use the EM algorithm for mixing Laplace distribution solve mixing Laplace distribution Model.Fig. 2 be mixing Laplace distributed model solve flow chart.As in figure 2 it is shown, mix solving of Laplace distributed model Process comprises the following steps:

S201: order solves number of times d=1.

S202: initiation parameter:

Initialize weight parameter collectionMean Parameters collectionAnd variance Parameter setIt is usually random assignment.Make iterations t=1.

S203: calculating posterior probability:

To wind power undulate quantity sequence P=[p₁,p₂,p₃,···p_M]^TIn each undulate quantity p_j, j=1,2 ..., M, calculates its posterior probability generated in the t time iteration by the distribution of kth Laplace according to Bayes theoremMeter Calculation formula is:

$\begin{array}{c}{\mathrm{\η}}_k^t\left(p_j\right)={\mathrm{\π}}^{t-1}\left(k\right|p_j)=\frac{{\mathrm{\π}}^{t-1}\left(k\right){\mathrm{\π}}^{t-1}\left(p_j\right|k)}{{\mathrm{\π}}^{t-1}\left(p_j\right)}\\ =\frac{{\mathrm{\π}}^{t-1}\left(k\right){\mathrm{\π}}^{t-1}\left(p_j\right|k)}{{\mathrm{\α}}_1^{t-1}\mathrm{\π}\left(p_j\right|{\mathrm{\α}}_1)+{\mathrm{\α}}_2^{t-1}\mathrm{\π}\left(p_j\right|{\mathrm{\α}}_2)+\mathrm{...}+{\mathrm{\α}}_N^{t-1}\mathrm{\π}\left(p_j\right|{\mathrm{\α}}_N)}\\ =\frac{{\mathrm{\α}}_k^{t-1}f\left(p_j\right|{\mathrm{\μ}}_k^{t-1},{\mathrm{\δ}}_k^{t-1})}{\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\α}}_i^{t-1}f\left(p_j\right|{\mathrm{\μ}}_i^{t-1},{\mathrm{\δ}}_i^{t-1})}\end{array}$

Wherein, k=1,2 ..., N, π^t-1X () is for representing the mixing Laplace distributed model obtained according to the t-1 time iteration The probability that event x obtained occurs.Represent p_jWithSingle M for parameter ties up Laplace Probability in distribution.Obviously,Weight parameter α obtained when representing the t-1 time iteration_k, mean μ_kAnd side Difference δ_k。

S204: calculate each Laplace distribution parameter:

P is determined according to step S203_jPosterior probability η generated by the distribution of kth Laplace_k ^t(p_j), a demand solution The parameter of k Laplace distribution.

Set up wind power swing vector P=[p₁,p₂,p₃,···,p_m]^TMaximum likelihood function:

$H\left(\mathrm{\Θ}\right)=ln\left(\underset{j=1}{\overset{M}{\Π}}f\right(P|\mathrm{\Θ}\left)\right)=\underset{j=1}{\overset{M}{\Σ}}ln\[\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\α}}_{i}f\left(p_i\right|{\mathrm{\μ}}_i,{\mathrm{\δ}}_i)\]$

Wherein, Θ is the parameter set of mixing Laplace distributed model；

Introduce variable Φ (Θ), it is assumed that after certain step iteration, obtain parameter setAlways need to find out new Θ, makeThus can obtain:

$H\left(\mathrm{\Θ}\right)-H\left(\widetilde{\mathrm{\Θ}}\right)\≥\mathrm{\Φ}\left(\mathrm{\Θ}\right)$

$H\left(\mathrm{\Θ}\right)-H\left(\widetilde{\mathrm{\Θ}}\right)=\underset{j=1}{\overset{M}{\Σ}}ln\[\frac{\underset{k=1}{\overset{N}{\Σ}}{\mathrm{\α}}_{k}f\left(p_j\right|{\mathrm{\μ}}_k,{\mathrm{\δ}}_k)}{\underset{k=1}{\overset{N}{\Σ}}{\widetilde{\mathrm{\α}}}_{k}f\left(p_j\right|{\widetilde{\mathrm{\μ}}}_k,{\widetilde{\mathrm{\δ}}}_k)}\]\≥\underset{j=1}{\overset{M}{\Σ}}\[\underset{k=1}{\overset{N}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)ln\frac{{\mathrm{\α}}_{k}f\left(p_j\right|{\mathrm{\μ}}_k,{\mathrm{\δ}}_k)}{\underset{k=1}{\overset{N}{\Σ}}{\widetilde{\mathrm{\α}}}_{k}f\left(p_j\right|{\widetilde{\mathrm{\μ}}}_k,{\widetilde{\mathrm{\δ}}}_k){\mathrm{\η}}_k\left(p_j\right)}\]$

Wherein:And for concrete p_j,For constant；Order

$\mathrm{\Φ}\left(\mathrm{\Θ}\right)=\underset{j=1}{\overset{M}{\Σ}}\[\underset{k=1}{\overset{N}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)ln\frac{{\mathrm{\α}}_{k}f\left(p_j\right|{\mathrm{\μ}}_k,{\mathrm{\δ}}_k)}{\underset{i=1}{\overset{N}{\Σ}}{\widetilde{\mathrm{\α}}}_{k}f\left(p_j\right|{\widetilde{\mathrm{\μ}}}_k,{\widetilde{\mathrm{\δ}}}_k){\mathrm{\η}}_k\left(p_j\right)}\]$

Thus, when as Φ (Θ) ＞ 0 and constantly increasing, H (Θ) will continue to increase, and Φ (Θ) need only be asked to obtain maximum Time Θ.

Φ (Θ) is asked for μ_k、δ_kDerivative, can obtain:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\Φ}\left(\mathrm{\Θ}\right)}{\∂{\mathrm{\δ}}_k}=\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)(-\frac{1}{{\mathrm{\δ}}_k}+\frac{\sqrt{2}\left|p_j-{\mathrm{\μ}}_k\right|}{{{\mathrm{\δ}}_k}^2})\\ \frac{\∂\mathrm{\Φ}\left(\mathrm{\Θ}\right)}{\∂{\mathrm{\μ}}_k}=\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)\frac{\sqrt{2}\mathrm{sgn}({\mathrm{\μ}}_k-p_j)}{{\mathrm{\δ}}_k}\end{array}\right.$

In formula, sgn () represents sign function.

OrderCan obtain:

$\left\{\begin{array}{c}{\mathrm{\μ}}_k=\frac{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)p_j}{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)}\\ {\mathrm{\δ}}_k=\sqrt{2}\frac{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)\left|p_j-{\mathrm{\μ}}_k\right|}{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)}\end{array}\right.$

By Lagrangian method, can obtain:

${\mathrm{\α}}_k=\frac{1}{M}\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k\left(p_j\right)$

In summary, the posterior probability obtained according to step S202Calculate kth Laplace in the t time iteration The parameter calculation formula of distribution is:

$\left\{\begin{array}{c}{\mathrm{\μ}}_k^t=\frac{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)p_j}{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)}\\ {\mathrm{\α}}_k^t=\frac{1}{M}\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)\\ {\mathrm{\δ}}_k^t=\sqrt{2}\frac{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)\left|p_j-{\mathrm{\μ}}_k^t\right|}{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)}\end{array}\right.$

S205: judge whether | Θ^t-Θ^t-1|≤ε, wherein Θ^t、Θ^t-1Represent the t time and the t-1 time iteration gained respectively The parameter set arrived, will weight parameter collection, Mean Parameters collection and variance parameter concentrate all parameters together with the vector that constitutes, ε table Show default error threshold.If it is not, enter step S206, otherwise enter step S207.

S206: make t=t+1, returns step S203.

S207: obtain this solve mixing Laplace distributed model parameter:

The mixing Laplace distributed model parameter the t time iteration obtained is as the ginseng of mixing Laplace distributed model Number.

S208: judge whether that d ＜ D, D represent the default total degree that solves, D >=1, if it is, enter step S209, otherwise Enter step S210.

S209:d=d+1, returns step S202.

S210: calculate and finally mix Laplace distributed model parameter:

Owing in solution procedure, initial parameter value is randomly provided, therefore to avoid iteration local convergence, this enforcement Example arranges the initial parameter value that D group is different, carries out D time solving, and solves the right of the mixing Laplace distributed model that obtains by D time Parameter is answered to be averaged, using meansigma methods as the final parameter mixing Laplace distributed model.I.e.Wherein α_i(d)、μ_i(d) and δ_i(d) table respectively Show the d time and solve the parameter obtained.

In summary, the present invention is by building mixing Laplace distributed model, and is asked by actual measurement wind power data Solution obtains its parameter, thus obtains wind power probability Distribution Model, can draw according to this model and obtain wind power probability Distribution curve, thus show the wind power wave characteristic of wind energy turbine set.

In order to the wind power probability Distribution Model effectiveness to wind power wave characteristic obtained by the present invention is described, adopt Carrying out index contrast by four wind power probability Distribution Model, four contrast models are that normal distribution model, logistic divide Cloth model, GMM (Gaussian Mixture Model, Gaussian mixtures) model and t Location-Scale model.Institute Index is used to attach most importance to exponential tail ψ (X), mean absolute error MAE, residual standard deviation RSD, goodness of fit R²Four indexs.Institute's base In the measured power data that wind power data are Sichuan Province's wind power plant cluster 10min level, each wind field 47520 sampling Data.The present embodiment arranges quantity N=2 of Laplace in mixing Laplace distributed model.Table 1 is that the present invention is right with four Table is contrasted than the index of model.

Model	MAE	RSD	R2	ψ
					Normal distribution model	3.1793×10-3	9.3728×10-3	0.73963	1.7320
Logistic distributed model	1.8137×10-3	6.7692×10-3	0.86092	2.6544
					GMM model	1.2561×10-3	5.2273×10-3	0.91387	3.7683
T Location-Scale model	1.0637×10-3	4.5494×10-3	0.93452	4.3506
					Mixing Laplace distributed model	8.4161×10-4	3.0110×10-3	0.97157	5.5092

Table 1

As shown in Table 1, MAE and RSD of mixing Laplace distributed model is minimum, R²Closer to 1, show mixing Laplace distributed model more can accurately reflect wind power swing rule, it can be seen that mix from the ψ index of each distribution Laplace distributed model has obvious advantage on heavy-tailed property describes.

Arranging time scale Δ t=10min, the wind power undulate quantity probability drawing the present invention and four contrast models divides Butut.Fig. 3 is the present invention and the wind power undulate quantity probability distribution graph of contrast model in the present embodiment.As it is shown on figure 3, In 10min level time scale, when wind power swing is bigger, GMM distributed model and t Location-Scale model can be preferable Ground matching wind power fluctuation, but wind power fluctuation is less or when more open steady, both models fail to Describe well.And the mixing Laplace distributed model of the present invention can closer to the probability histogram of wind power undulate quantity, Particularly in the case of wind power fluctuation is little, the mixing Laplace distributed model of the present invention is than other contrast models more Tool advantage.

The time scale close ties of the undulate quantity of wind power and selection, the ripple of different time scale correspondence wind power Dynamic characteristic differs greatly.In actual electric network is run, usual wind power at the fluctuation characteristic of second (s) level and point (min) level is High frequency and secondary high frequency provide foundation, and time (h) level and the wave characteristic of sky (d) level, for wind-powered electricity generation scheduling, rationally dissolve Wind power provides reference, is also the evaluation index of wind power prediction simultaneously.Therefore, in order to verify that the present invention mixes Laplace The effectiveness that wind power wave characteristic is embodied under different time and space scales by distributed model, to the actual measurement under different time and space scales Power data builds mixing Laplace distributed model.

Fig. 4 is the different time scales present invention and the wind power undulate quantity probability distribution of contrast model in the present embodiment Figure.As shown in Figure 4, on the mixing Laplace distributed model of the present invention, on different time scales, degree of accuracy is higher than other models, And the heavy-tailed property of distribution can be accurately reflected, therefore mixing Laplace distributed model is applicable to the wind-powered electricity generation merit of different time scales Rate fluctuation pattern describes.

Fig. 5 is the different spaces yardstick present invention and the wind power undulate quantity probability distribution of contrast model in the present embodiment Figure.As it is shown in figure 5, for the wind power fluctuation distribution of different spaces yardstick, mixing Laplace distributed model also can accurately be intended Close.

In summary, the wind power undulate quantity probability distribution mould based on mixing Laplace distribution obtained by the present invention Type can accurately realize the description to wind power fluctuation pattern under different time and space scales.

Although detailed description of the invention illustrative to the present invention is described above, in order to the technology of the art Personnel understand the present invention, the common skill it should be apparent that the invention is not restricted to the scope of detailed description of the invention, to the art From the point of view of art personnel, as long as various change limits and in the spirit and scope of the present invention that determine in appended claim, these Change is apparent from, and all utilize the innovation and creation of present inventive concept all at the row of protection.

Claims (4)

1. a wind power undulate quantity probability Distribution Model method for building up based on mixing Laplace distribution, it is characterised in that Comprise the following steps:

S1: according to wind power data and the default time scale Δ t of wind energy turbine set actual measurement, calculate wind power undulate quantity sequence P=[p₁,p₂,p₃,···,p_M]^T, wherein M represents the dimension of wind power undulate quantity sequence；

S2: build and mix Laplace distributed model:

$f\left(P\right|\mathrm{\α},\mathrm{\μ},\mathrm{\δ})=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\α}}_i{f}_i\left(p\right|{\mathrm{\μ}}_i,{\mathrm{\δ}}_i)$

Wherein, α={ α₁,α₂,···,α_NRepresent weight parameter collection, α_iThe weight being distributed for i-th Laplace, andμ={ μ₁,μ₂,···,μ_NRepresent Mean Parameters collection, μ_iRepresent wind power ripple in the distribution of i-th Laplace Momentum serial variance；δ={ δ₁,δ₂,···,δ_NRepresent variance parameter collection, δ_iRepresent i-th Laplace distribution apoplexy electric work Rate undulate quantity serial mean；N is that Laplace is distributed number, N ＞ 1；f_i(p|μ_i,δ_i) represent i-th single Laplace distribution Probability density function；

S3: according to wind power undulate quantity sequence P=[p₁,p₂,p₃,···,p_M]^TThe mixing Laplace that step S2 is obtained Distributed model solves, and obtains its weight parameter collection α, Mean Parameters collection μ and variance parameter collection δ, thus obtains wind power The probability Distribution Model of undulate quantity.

Wind power probability Distribution Model method for building up the most according to claim 1, it is characterised in that in described step S1 The computational methods of wind power undulate quantity are:

p_t=lnP (t+ Δ t)-lnP (t)

Wherein, p_tRepresenting the wind power undulate quantity of moment t, (t+ Δ t), P (t) represent moment t+ Δ t and the wind of moment t to P respectively Electrical power.

Wind power probability Distribution Model method for building up the most according to claim 1, it is characterised in that in described step S2 The span of Laplace distribution number N is 2≤N≤5.

Wind power probability Distribution Model method for building up the most according to claim 1, it is characterised in that in described step S3 The method for solving of mixing Laplace distributed model is:

S3.1: order solves number of times d=1.

S3.2: initialize weight parameter collectionMean Parameters collectionAnd variance Parameter setMake iterations t=1；

S3.3: to wind power undulate quantity sequence P=[p₁,p₂,p₃,···p_M]^TIn each undulate quantity p_j, calculate it The posterior probability generated by the distribution of kth Laplace in t iterationComputing formula is:

${\mathrm{\η}}_k^t\left(p_j\right)=\frac{{\mathrm{\α}}_k^{t-1}f\left(p_j\right|{\mathrm{\μ}}_k^{t-1},{\mathrm{\δ}}_k^{t-1})}{\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\α}}_i^{t-1}f\left(p_j\right|{\mathrm{\μ}}_i^{t-1},{\mathrm{\δ}}_i^{t-1})}$

Wherein, k=1,2 ..., N；

S3.4: calculate respectively each Laplace distribution parameter:

$\left\{\begin{array}{c}{\mathrm{\μ}}_k^t=\frac{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)p_j}{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)}\\ {\mathrm{\α}}_k^t=\frac{1}{M}\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)\\ {\mathrm{\δ}}_k^t=\sqrt{2}\frac{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)\left|p_j-{\mathrm{\μ}}_k^t\right|}{\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\η}}_k^t\left(p_j\right)}\end{array}\right.$

S3.5: if | Θ^t-Θ^t-1|≤ε, wherein Θ^t、Θ^t-1Represent respectively the t time and parameter obtained by the t-1 time iteration Collection vector, ε represents default error threshold, obtains the parameter of this mixing Laplace distributed model solved, otherwise makes t=t + 1, return step S3.3；

S3.6: if d is ＜ D, makes d=d+1, returns step S3.2, the mixing Laplace distributed model otherwise solved D time Parameter is averaged, using meansigma methods as the final parameter mixing Laplace distributed model.