CN108345961A - The prediction of wind farm group output and analysis method - Google Patents
The prediction of wind farm group output and analysis method Download PDFInfo
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Abstract
The present invention relates to a kind of defeated wind farm group output predictions and analysis method, input unit to obtain each output of wind electric field history factual time series data, forms wind farm group output power measured data library；The output of wind electric field basic data that predicting unit is provided according to input unit, auto regressive moving average arma modeling, accumulating auto regressive moving average ARIMA models and ARIMA GARCH models are established respectively, and pass through the comparison of former measured data and models fitting data, the fitting effect of each prediction model is compared, and then the output variation tendency of each wind power plant is predicted；Analytic unit introduces Copula theories, establishes polynary R rattans Pair Copula models, studies the correlation between multidimensional wind farm group；Output unit is contributed dependent probability while providing between the wind farm group output predicted value and wind power plant in goal programming year.Establish the cluster wind power output mathematical model of power producing characteristics simultaneously between the fluctuation and randomness and wind power plant that can accurately reflect wind farm group output.
Description
Technical field
The present invention relates to a kind of wind power technologies, more particularly to a kind of to be based on ARIMA-GARCH-Copula scale-model investigation wind-powered electricity generations
The prediction analysis method of field group electricity output fluctuation and correlation.
Background technology
With the getting worse of energy shortages and problem of environmental pollution, clean energy resource of the wind energy as rich reserves,
As the Main way of countries in the world new energy development.However, randomness, fluctuation, uncontrollability and cluster that wind-powered electricity generation is intrinsic
Correlation so that large-scale wind power brings complicated uncertainty to power grid construction, greatly affected the peace of electric system
Full stable operation, and then constrain the sustainable and healthy development of large-scale wind power.It searches to the bottom, this is because wind power plant output work
The more difficult assurance of inherent uncertainty characteristic of rate, output power precision of prediction be also difficult to improve, so as to cause electric system from
Body power adjustment mechanism is difficult the grid-connected influence of real-time active balance large-scale wind power field cluster.In this regard, big there is an urgent need for proposing to be suitble to
The characteristics of output power of scale wind farm group is predicted and analysis method, to improve the ability that power grid receives wind-powered electricity generation, alleviates extensive
The grid-connected severe challenge brought to local area power grid of wind power plant cluster.
Through carrying out retrieval discovery to existing literature, in existing literature, Gao Yajing, Liu Dong, Cheng Hua is newly equal to exist《Chinese motor work
Journey journal》(2015,35 (11)：It is delivered on 2645-2653)《It is pre- that short-term wind-electricity output based on data-driven estimates a correction
Survey model》The relationship of wind power output historical data and meteorologic factor is analyzed, combining adaptive Dynamic Programming correction link builds base
- prediction correcting model is estimated in the wind power of wind power output data-driven, and is applied to wind turbine below rated wind speed
The short term power prediction of changeable operating point in operation area.Yu Jun, Wang Zhao, nationality daybreak etc. exist《Computing technique and automation》
(2017,36 (2)：It is delivered on 95-99)《Wind power prediction research based on mind evolutionary》Utilize convergent and alienation
Operation drastically reduces the prediction error caused by hidden layer weight threshold generates at random, and is established based on mind evolutionary
Corresponding wind power prediction model.Li Yanqing, Yuan Yan are waved, Guo Tong《Electric power system protection and control》(2017,45 (14)：
It is delivered on 113-120)《Super short-period wind power combined prediction based on AMD-ICSA-SVM》Resolution modalities are decomposed and changed
It is combined into cuckoo searching algorithm Support Vector Machines Optimized theory, chooses optimal penalty factor parameter and kernel functional parameter, it is real
Now each component of wind power output is predicted and is superimposed, to build ultrashort-term wind power combination forecasting.Sun Jianbo,
Wu little Shan, Zhang Buhan exist《HYDROELECTRIC ENERGY science》(2013,31 (9)：It is delivered on 233-235)《Estimated based on norm of nonparametric kernel density
The wind power interval prediction of meter》Wind power is calculated using nonparametric probability method based on wind power point prediction value
It predicts the probability density of error, and using the probability distribution curve of cubic spline interpolation fitting prediction error, then obtains satisfaction
The wind power prediction section of certain fiducial probability.Chen Jie, Shen Yanxia, Lu Xin etc. exist《Electric power network technique》(2016,40 (8)：
It is delivered on 2281-2287)《A kind of wind power probability interval Multiobjective Intelligent Optimization Prediction method》By improving multiple target
The probability selection of artificial bee colony algorithm acts on and strategy is deleted in constraint, utilizes the contraction-expansion factor of wavelet neural network, shift factor
It solves the problems, such as the unreasonable selection of penalty coefficient under interval prediction single object optimization model with weights, and then proposes a kind of base
In the wind power interval prediction Model for Multi-Objective Optimization of wavelet neural network.Ling Wuneng, Hang Naishan, Li Ruqi exist《Electric power is certainly
Dynamicization equipment》(2013,33 (7)：It is delivered on 34-38)《Short-term wind-electricity power prediction based on cloud supporting vector machine model》Draw
Enter the Cloud transform method of Clouds theory to excavate the stochastic behaviour of wind speed, to use the wind speed feature that cloud model indicates as supporting vector
The input of machine, and will actual measurement wind power as output, and then based on the fit correlation between wind speed feature and wind power come
Build wind power trend prediction model.Document above is carried out in advance to Wind turbines output or single output of wind electric field mostly
It surveys, does not consider interactional special complexity of contributing between multiple wind power plants.
Invention content
The problem of the present invention be directed to wind farm group output complexity and importance, it is proposed that a kind of wind farm group output is pre-
It surveys and analysis method, in conjunction with the history measured data structure reflection output of wind electric field fluctuation and randomness of output of wind electric field
ARIMA-GARCH models, and the output of wind electric field in goal programming year is predicted, ternary R rattans are established on this basis
Pair-Copula model primary studies wind power plant cluster contribute between correlation.
The technical scheme is that：A kind of wind farm group is contributed prediction and analysis method, is specifically comprised the following steps：
1) input unit：Each output of wind electric field history factual time series data are obtained, the actual measurement of wind farm group output power is formed
Database；
2) predicting unit：According to the output of wind electric field basic data that input unit provides, it is flat that autoregression movement is established respectively
Equal arma modeling, accumulating auto regressive moving average ARIMA models and ARIMA-GARCH models, and by former measured data and
The comparison of models fitting data compares the fitting effect of each prediction model, chooses optimum prediction model, and then to each wind power plant
Output variation tendency is predicted；
3) analytic unit：Each parameter value of selected optimum prediction model is estimated by output of wind electric field sample observation data,
Data information collection before the T-1 moment is recycled, the marginal probability distribution of subsequent time T is estimated, in conjunction with Copula Functional Analysis two
Then correlativity between two wind power plants recycles the interdependent journey of the entire wind farm group of R rattan Pair Copula structural analyses
Degree, the probability value for providing each wind power plant while contributing, obtains wind farm group output correlation analysis model；
4) output unit：According to wind farm group output correlation analysis obtained by the optimum prediction model and step 3) of step 2)
Model, dependent probability of contributing while providing between the wind farm group output predicted value and wind power plant in goal programming year.
ARIMA-GARCH models are mutually to tie ARIMA (p, d, q) models and GARCH (p, q) model in the step 2)
It closes, establishes the prediction model of single Power Output for Wind Power Field, wherein ARIMA (1,1,1)-GARCH (1,1) simultaneous model is as follows：
xtFor moment t Power Output for Wind Power Field data；utFor the mean value item of time series data sequence；εiFor the interference of moment t
；B moves difference operator after being；For the distracter ε of moment tiVariance；ξtTo be desired for μ, variance is constant σ2It is independent same
Distribution variables；N (μ, σ2) it is using μ as expectation, σ2For the normal distribution of variance；β0、β1、β2It is parameter to be estimated.
Method required by the step 3) marginal probability distribution：
Power Output for Wind Power Field data sequence Xt, t=1,2 ..., T-1, i.e. sequence { x1, x2..., xT-1, utilize { x1,
x2..., xT-1And best ARIMA-GARCH models estimate parameter μ, σ, β0、β1、β2It later, can be in the hope of subsequent time xT's
Marginal probability distribution：
Wherein, ΩT-1For the information collection until moment T-1；It is μ and the normal distyribution function of σ for parameter.
Analytic unit includes R rattan Pair-Copula subelements based on normal state Copula, is based on t- in the step 3)
The R rattan Pair-Copula subelements and experience Copula subelements of Copula；
R rattan Pair-Copula subelements based on normal state Copula are by normal distyribution function and polynary Copula
Pair Copula theories are combined, and build the R rattan Pair-Copula structural models based on normal state Copula, and analysis meets normal state
Group's correlation properties between the output of wind electric field of distribution；
R rattan Pair-Copula subelements based on t-Copula are by t distribution functions and polynary Copula
PairCopula theories are combined, and build the R rattan Pair-Copula structural models based on t-Copula, and analysis meets t distributions
Group's correlation properties between output of wind electric field；
Experience Copula subelements directly analyze output of wind electric field history measured data, establish the ternary warp of sample
Test Copula functions.
Output unit is as being respectively compared ternary experience Copula functions obtained by step 3) and being based on just in the step 4)
The R rattan Pair-Copula probability-distribution functions of state Copula, the R rattan Pair-Copula probability-distribution functions based on t-Copula
Close degree, choose more particularly suitable wind farm group output correlation analysis model, and provide each output of wind electric field predicted value
With the probability value contributed simultaneously.
The beneficial effects of the present invention are：The prediction of wind farm group output and analysis method, foundation of the present invention can accurately reflect
The cluster wind power output mathematical model of power producing characteristics simultaneously, pushes away between fluctuation and randomness and wind power plant that wind farm group is contributed
The access Power System Planning sustainable development of dynamic large-scale wind power, is suitable for large-scale wind power field cluster and off the net and multidimensional wind
The output of wind electric field prediction of electric field output fluctuation and wind farm group while, contribute probability analysis.
Description of the drawings
Fig. 1 is the prediction of wind farm group of the present invention output and analysis method flow diagram；
Fig. 2 is R rattan Pair-Copula tree structure diagrams；
Fig. 3 a are the wind power plant U power curve figures predicted based on arma modeling；
Fig. 3 b are the wind power plant V power curve figures predicted based on arma modeling；
Fig. 3 c are the wind power plant W power curve figures predicted based on arma modeling；
Fig. 4 a are the wind power plant U power curve figures based on ARIMA model predictions；
Fig. 4 b are the wind power plant V power curve figures based on ARIMA model predictions；
Fig. 4 c are the wind power plant W power curve figures based on ARIMA model predictions；
Fig. 5 a are the wind power plant U power curve figures based on ARIMA-GARCH model predictions；
Fig. 5 b are the wind power plant V power curve figures based on ARIMA-GARCH model predictions；
Fig. 5 c are the wind power plant W power curve figures based on ARIMA-GARCH model predictions；
Fig. 6 a are the planning year wind power plant U power curve figure based on ARIMA-GARCH model predictions；
Fig. 6 b are the planning year wind power plant V power curve figure based on ARIMA-GARCH model predictions；
Fig. 6 c are the planning year wind power plant W power curve figure based on ARIMA-GARCH model predictions；
Fig. 7 a are the marginal probability distribution functional arrangement that wind power plant U contributes；
Fig. 7 b are the marginal probability distribution functional arrangement that wind power plant V contributes；
Fig. 7 c are the marginal probability distribution functional arrangement that wind power plant W contributes.
Specific implementation mode
Wind farm group as shown in Figure 1, which is contributed, to be predicted and analysis method flow diagram, including sequentially connected input unit
1, predicting unit 2, analytic unit 3, output unit 4.
Input unit 1 obtains each output of wind electric field history factual time series data, forms wind farm group output power and surveys number
According to library；The output of wind electric field basic data that predicting unit 2 is provided according to input unit 1, establishes auto regressive moving average respectively
(Auto-regressive and Moving Average, ARMA) model, accumulating auto regressive moving average (Auto
Regression Integrated Moving Average, ARIMA) model and ARIMA-GARCH models, and pass through former actual measurement
The comparison of data and models fitting data compares the fitting effect of each prediction model, and then becomes to the variation of the output of each wind power plant
Gesture is predicted；Analytic unit 3 introduces Copula theories, establishes polynary R rattans Pair Copula models, studies multidimensional wind power plant
Correlation between group；Output unit 4 goes out while providing between the wind farm group output predicted value and wind power plant in goal programming year
Power dependent probability.
The output of wind electric field history measured data library obtained in input unit 1, including cluster it is grid-connected each wind power plant it is defeated
Go out the history measured data sequence of power.
Predicting unit 2 includes ARMA prediction models subelement 21, ARIMA prediction models subelement 22 and ARIMA-GARCH
Prediction model subelement 23.
The ARMA prediction models subelement 21 is built to stationary time series using Random time sequence regression theory
Found corresponding equation of linear regression：
Wherein, ytFor a stable time series；P is the exponent number of autoregression model；For the system undetermined of AR department patterns
Number, i=1,2 ..., p；Q is the exponent number of moving average model；atFor error；θjFor the undetermined coefficient of rolling average department pattern,
J=1,2 ..., q.
The ARIMA prediction models subelement 22 is steady firstly the need of being carried out to output of wind electric field statistical data sequence
Change is handled, and the data sequence of non-stationary is changed into the stationary random sequence that mean value is zero.Linear difference equation is main at present
Differential of sequence is become ARIMA forms and is returned by tranquilization processing mode, form and ARMA equations of linear regression after difference
Form is consistent.I.e.：
Δyt-η1Δyt-1-…-ηpΔyt-p=at-σ1at-1-…-σqat-q
Wherein, first-order difference formula can be expressed as
Δyt=yt-yt-1=(1-B) yt
One d scale sub-sequence can be written as
Δdyt=(1-B)dyt
Byt=yt-1
B moves difference operator after being.
It can be seen from above formula ARIMA (p, d, q) by the non-stationary time series of acquisition by corresponding number d into
Row difference obtains stationary sequence, and then builds ARMA (p, q) model to stationary time series, i.e., as d=0, ARIMA models become
At arma modeling.By carrying out parameter Estimation to the accumulating autoregression in time series method-sliding average (ARIMA) model
And model order, to determine a mathematical model that can describe studied energy demand total amount changing rule.
The ARIMA-GARCH prediction models subelement 23 is to be combined ARIMA models with GARCH models, structure
Fully consider the prediction model of output of wind electric field fluctuation and randomness.
By analyzing output of wind electric field time series, it can be found that the sequence obtained according to ARIMA prediction models
Residual error square or absolute value show certain correlation, while each output of wind electric field value has the wave of apparent Singular variance
Dynamic aggregation properties, and autoregression condition heteroskedasticity ARCH (Autoregression Conditional
Heteroscedasticity, ARCH) model and generilized auto regressive conditional heteroskedastic GARCH (Generalized
Autoregression Conditional Heteroscedasticity, GARCH) model just be suitble to research time series data
Wave characteristic problem.
The distracter ε of the main consideration moment t of ARCH modelstVarianceIt by moment (t-1) square error
Size and influence, i.e., it is to rely onIf time series is the autoregression of k ranks, Y can be expressed ast=α0+α1x1t+…+
αkxkt+εt
Wherein x1t..., xktIt is arranged for time series data；α0, α1, αkFor parameter to be estimated；If distracter εiVariance
The distracter ε at that neighbouring moment of early period can only be depended oni-1, then it is ARCH (1).If however, by each dry suffered by it
It disturbs item and spreads, ARCH (q) processes are：
If no auto-correlation fluctuation is present in error variance, β is just had1=β2=...=βq=0,
Wherein β1, β2..., βqFor parameter to be estimated；To predict variance, and based on previous moment information, so quilt again
Referred to as conditional variance.
May be excessive in order to avoid the exponent number q of ARCH, it is extended and improves on the basis of ARCH models, to obtain phase
GARCH (p, the q) model answered.The stability bandwidth of GARCH (p, q) model is indicated by itself lag item, and its variance equation is not
Together.GARCH models can be estimated to obtain by selecting p more than or equal to 0 or q, and variance can be written as：
Wherein, utFor the mean value item of time series data sequence；βi、γjFor parameter to be estimated, and wanted to meet stationarity
The sum of each coefficient is asked to be less than 1；Square of residual error item is interfered for the moment (t-i)；P, q is the exponent number of model.
ARIMA (p, d, q) models and GARCH (p, q) model are combined by the present invention, establish single Power Output for Wind Power Field
Prediction model.Wherein, ARIMA (1,1,1)-GARCH (1,1) simultaneous model is as follows：
Wherein xtFor moment t Power Output for Wind Power Field data；utFor the mean value item of time series data sequence；ξiTo be desired for μ,
Variance is constant σ2I.i.d. random variables；N (μ, σ2) it is using μ as expectation, σ2For the normal distribution of variance；β0、β1、β2
It is parameter to be estimated.
Utilize Power Output for Wind Power Field data sequence Xt, t=1,2 ..., T-1, i.e. formation sequence { x1, x2..., xT-1, t
For time variable, T is next determining moment value of time series t=1,2 ..., T-1 time series, is exported using wind power plant
Power data sequence { x1, x2..., xT-1And ARIMA-GARCH models estimate parameter μ, σ, β0、β1、β2It later, can be in the hope of
Next moment xTMarginal probability distribution：
Wherein, ΩT-1For the information collection until moment T-1；It is μ and the normal distyribution function of σ for parameter.
Data are observed by output of wind electric field sample to estimate each parameter value of ARIMA-GARCH models, in conjunction with XTSide
Edge distribution formula obtains the marginal probability distribution of the data information collection before the T-1 moment.
Analytic unit 3 includes the R rattan Pair-Copula subelements 31 based on normal state Copula, the R rattans based on t-Copula
Pair-Copula subelements 32 and experience Copula subelements 33.
R rattan Pair-Copula subelements 31 based on normal state Copula are by normal distyribution function and polynary Copula
Pair Copula theories are combined, and build the R rattan Pair-Copula structural models based on normal state Copula, and analysis meets normal state
Group's correlation properties between the output of wind electric field of distribution.
Copula theories are a kind of important methods of current enchancement factor correlation analysis, and essence is fixed based on Sklar
Reason is defined on multidimensional [0,1] and defines a multivariate pdf function in domain space, have do not limit each variable edge distribution,
Keep the advantageous property of consistency under monotonic transformation.N member normal state Copula distribution function expression formulas are：
C(u1, u2..., uN；ρ)=φρ[φ-1(u1), φ-1(u2) ..., φ-1(uN)]
Wherein ρ is the symmetric positive definite matrix that diagonal entry is 1, φρ(...) indicate that correlation matrix is ρ's
Standard multiple normal distyribution function, φ-1() indicates the inverse function of Standard Normal Distribution φ ().
The function Direct Modeling of polynary Copula is very difficult, so as to cause polynary Copula functions application by very big
Limitation.In addition, although the polynary Copula functions of Direct Modeling can describe the Dependence Structure of multiple variables, do not examine
Consider the correlation of different variables between any two in combination.Therefore, a kind of Pair of more flexible structure multivariate joint distribution
Copula methods are come into being.It is proposed the Pair Copula theories that binary Copula is generalized to polynary Copula first from Joe
Since, by more than ten years of Bedford, Cooke and Aas et al. over to Pair Copula structure and its parameter Estimation and data mould
Quasi- method continuously improve and it is perfect, the dependency structure gradually formed between can reflecting variable two-by-two is inconsistent and asymmetric
Etc. characteristics Pair Copula rattan models.Pair Copula rattan models think that the polytomy variable rattan structural union of n dimensions is close
Degree function can be decomposed into side n (n-1)/2 (i.e. Pair Copula density functions) according to certain rule and edge distribution is close
The product for spending function, i.e., be decomposed into multigroup different binary variable, then the Coplua between each group binary variable by polytomy variable
Correlativity is described, and finally obtains Dependence Structure between all variables.Pair Copula rattans model commonly C rattans
Pair Copula and D rattan Pair Copula.Both Pair Copula rattan structures have fixed shape, correlation analysis
Process is simply clear, but it only simplifies the correlativity considered between fixed variable two-by-two, has ignored fixed knot that may be present
Other correlativities between variable two-by-two outside structure.Therefore, the present invention uses the R rattans for the actual conditions being more in line between each variable
Pair Copula。
R rattan Pair Copula are to determine stochastic variable two-by-two according to the actual association characteristic between multiple random variables
Between dependency structure, the lowering dimension decomposition rule than C rattan Pair Copula and D rattan Pair Copula is more to a certain extent
It is accurate reasonable.Below by taking sextuple stochastic variable as an example, the tree construction decomposition rule of R rattans is introduced and based on conditional density function theory
Provide the calculation formula of polytomy variable joint density function.
R rattan Pair-Copula tree structure diagrams as shown in Figure 2, show the tree construction decomposition rule of R rattans.It can be seen that R rattans
Pair Copula determine its relational structure according to the actual influence situation between all variables, because without the tree of Uniform provisions
Planform.As shown in Fig. 2, being decomposed to sextuple R rattans Pair Copula models, 5 trees, i.e. T are shared in this structurej(j
=1,2,3,4,5), each tree TjThere is 7-j node, 6-j side is consequently formed, each edge corresponds to a Pair Copula.Root
According to the logical construction feature of R rattan Pair Copula, the n normal state R rattan Pair Copula joint density functions tieed up can be write as
Following form：
Wherein, etFor a line of figure, et={ et(1), et(2)}∈Em(m=1,2 ..., n-1, t=1,2 ..., m),
EmFor side collection, e in figuretIt is denoted as it, jt|Det；Det=Aet(1)∩ Aet(2), Aet(1)For side etIn it is related with first vertex
Set T1The set on middle vertex, Aet(2)For side etIn with the related tree T in second vertex1The set on middle vertex；it=Aet(1)-
Det；jt=Aet(2)-Det；xDet={ xq|q∈Det}；FNFor unitary normal distyribution function；fNFor unitary normal probability density function；
cNFor the marginal probability density function of normal state Copula functions.
In consideration of it, normal state R rattan Pair Copula can be used carries out modeling point to the correlation that multidimensional wind power plant cluster is contributed
Analysis.By taking three-dimensional wind power plant as an example, the joint density function of acquisition ternary normal state R rattan Pair Copula can be derived as shown in formula.
Stochastic variable can be merged two-by-two by above formula, ternary normal state R rattans are obtained using binary normal state Copula functions
The joint density function of Pair Copula calculates the probability of the three-dimensional wind power plant while power generating value that consider correlation.
The R rattan Pair-Copula subelements 32 based on t-Copula are by t distribution functions and polynary Copula
Pair Copula theories are combined, and build the R rattan Pair-Copula structural models based on t-Copula, and analysis meets t distributions
Output of wind electric field between group's correlation properties.
N member t-Copula distribution function expression formulas are：
Wherein ρ is the symmetric positive definite matrix that diagonal entry is 1, Tρ, v(...) expression correlation matrix be ρ,
Degree of freedom is the standard multiple t distribution functions of v, Tv -1() indicates that degree of freedom is the univariate t-distribution function T of vvThe inverse letter of ()
Number.
According to the logical construction feature of R rattan Pair Copula, the t distribution R rattan Pair Copula joints that can tie up n are close
Degree function is written as form：
Wherein, FtFor univariate t-distribution function；ftFor univariate t-distribution probability density function；ctIt is distributed Copula functions for t
Marginal probability density function.
By taking three-dimensional wind power plant as an example, the joint density function of acquisition ternary t distribution R rattan Pair Copula can be derived such as
Shown in formula.
Stochastic variable can be merged two-by-two by above formula, ternary t distribution R rattans Pair is obtained using binary t-Copula functions
The joint density function of Copula, the correlation contributed to three-dimensional wind power plant cluster are analyzed, and are provided and are considered the three of correlation
Tie up the probability value that wind power plant is contributed simultaneously.
The experience Copula subelements 33 refer to directly analyzing output of wind electric field history measured data, are established
The ternary experience Copula functions of sample.It is defined as follows：
If (xi, yi, zi) (i=1,2 ..., be n) to be derived from the sample of three-dimensional overall (X, Y, Z), and the experience of X, Y, Z point
Cloth function is respectively Fn(x)、Gn(y) and Hn(z), then the experience Copula functions for defining sample are as follows：
Wherein, I[·]For indicative function, work as Fn(xi≤ u) when, I[Fn(xi≤u)]Value 1, be otherwise 0；U, v, w are respectively
Obey Fn(x)、Gn(y)、Hn(z) random number being distributed.
The output unit 4 is by being respectively compared ternary experience Copula functions and based on the R rattans of normal state Copula
The close degree of Pair-Copula probability-distribution functions, R rattan Pair-Copula probability-distribution functions based on t-Copula, choosing
More particularly suitable wind farm group output correlation analysis model is taken, and provides each output of wind electric field predicted value and while contributing general
Rate value.
Ternary experience Copula functions with based on normal state Copula R rattan Pair-Copula probability-distribution functions, be based on t-
The close degree of the R rattan Pair-Copula probability-distribution functions of Copula indicates with squared euclidean distance, i.e.,
dN 2And dt 2The ternary R rattan Pair-Copula models based on normal state Copula are reflected respectively and are based on t-Copula
Ternary R rattan Pair-Copula models fitting initial data close degree, if dN 2＜ dt 2, illustrate to be based on normal state Copula
Ternary R rattan Pair-Copula models can preferably be fitted initial data；Otherwise illustrate the ternary R rattans based on t-Copula
Pair-Copula models are more particularly suitable.
Embodiment 2
This example is to carry out the year two thousand twenty output of wind electric field prediction of goal programming year and wind by taking the three-dimensional wind power plant of somewhere as an example
The analysis for correlation of contributing simultaneously between electric field.According to layout data, the year two thousand twenty this area wind power plant U, wind power plant V and wind power plant W
Installed capacity be respectively 170MW, 4311MW and 5900MW.In conjunction with each Power Output for Wind Power Field in this area in 2014 in table 1
Monthly average output (the unit of measured value：MW), be utilized respectively ARMA prediction models subelement, ARIMA prediction models subelement and
ARIMA-GARCH prediction model subelements carry out data fitting, and wind-powered electricity generation of the most suitable prediction model to the year two thousand twenty is chosen in comparison
The practical output of field U, wind power plant V and wind power plant W are predicted.
Table 1
Wind power plant U in 2014, the wind power plant V predicted using ARMA prediction model subelements is set forth in Fig. 3 a, 3b, 3c
Power curve with wind power plant W and corresponding practical power curve.Fig. 4 a, 4b, 4c are set forth predicts mould using ARIMA
Wind power plant U in 2014, the wind power plant V of the prediction of type subelement and the power curve of wind power plant W and corresponding practical power curve.
Wind power plant U in 2014, the wind power plant V predicted using ARIMA-GARCH prediction model subelements is set forth in Fig. 5 a, 5b, 5c
Power curve with wind power plant W and corresponding practical power curve.Comparison diagram is it is found that be usually used in the ARMA of stationary time series
Prediction model subelement prediction result is more smooth, poor with real data degree of fitting, does not fully demonstrate output of wind electric field
Random fluctuation characteristic；The ARIMA prediction model subelement prediction results that non-stationary series are carried out with difference tranquilization processing want excellent
In ARMA prediction model subelements, it can predict the overall variation trend of output of wind electric field, but cannot reflect output of wind electric field
Volatility clustering phenomenon；ARIMA-GARCH prediction models subelement is by square carrying out at excavation ARIMA model residual errors
Reason, meticulously features the characteristic that the variance of time series changes over time, can be fitted output of wind electric field sequence well
Fluctuation changes, and can obtain good prediction effect.
ARMA prediction models subelement, ARIMA prediction models subelement and the fitting of ARIMA-GARCH prediction model subelements
The average relative error of curve can be found in table 2.
Table 2
By upper table it can easily be seen that the average relative error of ARIMA-GARCH prediction model subelements is minimum, have preferable
Precision of prediction is suitble to the prediction of this area's output of wind electric field.
Based on this, combining target plans the statistical number of the data and existing output of wind electric field such as the wind energy turbine set installed capacity in year
According to wind power plant U, wind power plant V using the best ARIMA-GARCH prediction models subelement of precision of prediction to the year two thousand twenty this area
It is predicted with the output of wind power plant W, and obtains the unknown parameter in corresponding A RIMA-GARCH models.ARIMA-GARCH models
Fitting parameter it is as shown in table 3.Predict obtained wind power plant U, V, W power curve as shown in Fig. 6 a, 6b, 6c.
Table 3
| Stationarity parameter | Wind power plant U | Wind power plant V | Wind power plant W |
| β0 | 2.2271 | 2.9373 | 3.5082 |
| β1 | 0.2663 | 0.5865 | 0.5988 |
| β2 | 0.3392 | 0.2046 | 0.2035 |
The marginal probability distribution function curve of each wind power plant U, V, W output is obtained as shown in Fig. 7 a, 7b, 7c.Based on each wind
The marginal probability distribution function that electric field is contributed, in combination with the correlativity between Copula Functional Analysis two-by-two wind power plant, then
The interdependent degree for recycling the entire wind farm group of R rattan Pair Copula structural analyses, the probability for providing each wind power plant while contributing
Value.
Present example first passes through common binary normal state Copula functions and binary t-Copula functions to establish wind-powered electricity generation
The relationship of field between any two.Common binary normal state Copula functions can be expressed as：
Common binary t-Copula functions can be expressed as：
Marginal probability distribution function based on each output of wind electric field, can estimate binary CopThe corresponding parametric values of ula such as table
Shown in 4.
Table 4
| Binary Copula parameters | Wind power plant U, V | Wind power plant V, W | Wind power plant U, W |
| ρN | 0.3732 | 0.5643 | 0.5128 |
| ρt | 0.3767 | 0.6082 | 0.5558 |
| v | 2 | 2 | 2 |
The parameter value of table 4 is substituted into binary normal state Copula functions and binary t-Copula functions, is obtained respectively based on just
The joint density function of the ternary R rattans Pair-Copula of state Copula and ternary R rattans Pair-Copula based on t-Copula,
And calculate the ternary R rattans Pair-Copula based on the normal state Copula and ternary R rattans Pair-Copula based on t-Copula with
The Euclidean distance of experience Copula functions：dN 2=0.3710；dt 2=0.3753.Therefore, under the standard of squared euclidean distance,
It is considered that the ternary R rattan Pair-Copula models fittings this area wind farm group based on normal state Copula goes out the effect of force data
Fruit is a little better.
In conclusion present example will use the ternary R rattan Pair-Copula models based on normal state Copula to the ground
Wind power plant U, the wind power plant V in area and the monthly average of wind power plant W go out force data and are fitted, and combine its joint probability density function
The probability that wind power plant U, wind power plant V and wind power plant W contribute simultaneously is calculated, concrete outcome can be found in table 5.
Table 5
| Wind power plant U outputs/MW | Wind power plant V outputs/MW | Wind power plant W outputs/MW | Probability |
| 55.29 | 1317.94 | 2749.84 | 0.005615 |
| 71.64 | 2507.61 | 4018.96 | 0.243371 |
| 67.00 | 1514.42 | 2701.16 | 0.021208 |
| 65.53 | 2219.07 | 3743.20 | 0.501096 |
| 37.68 | 1694.77 | 1968.35 | 0.038091 |
| 74.07 | 2409.40 | 3535.40 | 0.010565 |
| 33.97 | 1700.19 | 2748.26 | 0.06983 |
| 39.00 | 2183.10 | 3030.74 | 0.035216 |
| 23.03 | 1760.43 | 1641.63 | 0.001509 |
| 28.48 | 904.35 | 1353.23 | 0.005694 |
| 54.40 | 1539.30 | 2630.87 | 0.063177 |
| 23.03 | 1219.84 | 1439.16 | 0.004627 |
Ternary R rattans Pair-Copula give when wind power plant U monthly average contribute occur when, other two wind power plant V and
The simultaneous probability of corresponding monthly average output of W, can reflect the correlation of multidimensional wind farm group to a certain extent.By table 5
As can be seen that as wind power plant U, wind power plant V and wind power plant W monthly average power generating values increase, the probability contributed simultaneously, which is presented, to be increased
The trend added, that is to say, that under this area's high speed wind regime, the correlation of each wind power plant is relatively high.
Claims (5)
- Prediction and analysis method 1. a kind of wind farm group is contributed, which is characterized in that specifically comprise the following steps：1) input unit：Each output of wind electric field history factual time series data are obtained, wind farm group output power measured data is formed Library；2) predicting unit：According to the output of wind electric field basic data that input unit provides, auto regressive moving average is established respectively Arma modeling, accumulating auto regressive moving average ARIMA models and ARIMA-GARCH models, and pass through former measured data and mould The comparison of type fitting data compares the fitting effect of each prediction model, chooses optimum prediction model, and then go out to each wind power plant Power variation tendency is predicted；3) analytic unit：Data are observed by output of wind electric field sample to estimate each parameter value of selected optimum prediction model, then profit With data information collection before the T-1 moment, the marginal probability distribution of subsequent time T is estimated, two-by-two in conjunction with Copula Functional Analysis Then correlativity between wind power plant recycles the interdependent degree of the entire wind farm group of R rattan Pair Copula structural analyses, The probability value for providing each wind power plant while contributing, obtains wind farm group output correlation analysis model；4) output unit：According to wind farm group output correlation analysis mould obtained by the optimum prediction model and step 3) of step 2) Type, dependent probability of contributing while providing between the wind farm group output predicted value and wind power plant in goal programming year.
- 2. the prediction of wind farm group output and analysis method according to claim 1, which is characterized in that in the step 2) ARIMA-GARCH models are to be combined ARIMA (p, d, q) models and GARCH (p, q) model, establish single wind power plant output The prediction model of power, wherein ARIMA (1,1,1)-GARCH (1,1) simultaneous model is as follows：xtFor moment t Power Output for Wind Power Field data；utFor the mean value item of time series data sequence；εtFor the distracter of moment t；B is After move difference operator；For the distracter ε of moment ttVariance；ξtTo be desired for μ, variance is constant σ2Independent same distribution with Machine variable；N(μ,σ2) it is using μ as expectation, σ2For the normal distribution of variance；β0、β1、β2It is parameter to be estimated.
- 3. the prediction of wind farm group output and analysis method according to claim 2, which is characterized in that the step 3) edge is general The required method of rate distribution：Power Output for Wind Power Field data sequence Xt, t=1,2 ..., T-1, i.e. sequence { x1,x2,…,xT-1, utilize { x1,x2,…, xT-1And best ARIMA-GARCH models estimate parameter μ, σ, β0、β1、β2It later, can be in the hope of subsequent time xTEdge it is general Rate is distributed：Wherein, ΩT-1For the information collection until moment T-1；It is μ and the normal distyribution function of σ for parameter.
- 4. the prediction of wind farm group output and analysis method according to claim 1, which is characterized in that analysis in the step 3) Unit includes the R rattan Pair-Copula subelements based on normal state Copula, the R rattans Pair-Copula lists based on t-Copula Member and experience Copula subelements；R rattan Pair-Copula subelements based on normal state Copula are by the Pair of normal distyribution function and polynary Copula Copula theories are combined, and build the R rattan Pair-Copula structural models based on normal state Copula, and analysis meets normal distribution Output of wind electric field between group's correlation properties；R rattan Pair-Copula subelements based on t-Copula are by the Pair Copula of t distribution functions and polynary Copula Theory is combined, and builds the R rattan Pair-Copula structural models based on t-Copula, and analysis meets the output of wind electric field of t distributions Between group's correlation properties；Experience Copula subelements directly analyze output of wind electric field history measured data, establish the ternary experience of sample Copula functions.
- 5. the prediction of wind farm group output and analysis method according to claim 4, which is characterized in that output in the step 4) Unit is as being respectively compared ternary experience Copula functions obtained by step 3) and the R rattans Pair-Copula based on normal state Copula The close degree of probability-distribution function, R rattan Pair-Copula probability-distribution functions based on t-Copula is chosen more particularly suitable Wind farm group output correlation analysis model, and provide each output of wind electric field predicted value and simultaneously output probability value.
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Application publication date: 20180731 |