CN103440541B - The joint probability density Forecasting Methodology of windy electric field short-term output power - Google Patents

Abstract

The invention discloses a kind of joint probability density Forecasting Methodology of windy electric field short-term output power, step is as follows: utilize Support vector regression forecast model to carry out One-Point-Value prediction to the output power of each wind energy turbine set, and the probability density prediction that management loading model carries out error is set up to predicated error, obtain marginal probability density function prediction expectation value and the variance of single Power Output for Wind Power Field; Statistical study is carried out to windy field output power predicated error characteristic, set up dynamic condition relevant-Multivariate autoregressive conditional different Variance model, comprehensive single wind field output power marginal probability density predicts the outcome and obtains the joint probability density function of windy field output power with correlation matrix, and forms the multidimensional scene comprising spacetime correlation characteristic by sample technique.The present invention can provide prediction average and the uncertainty in traffic information of single Power Output for Wind Power Field, can also dynamic space-time associate feature between the prediction of quantitative description windy field output power.

Description

The joint probability density Forecasting Methodology of windy electric field short-term output power

Technical field

The present invention relates to a kind of joint probability density Forecasting Methodology of windy electric field short-term output power.

Background technology

Wind-powered electricity generation large-scale grid connection alleviates China's Pressure on Energy and brings huge economy and environment benefit, is that current technology is the most ripe, the regenerative resource of on the largest scaleization exploit condition.But wind-powered electricity generation is as the power supply of a kind of intermittence and uncontrollability, and it is connected to the grid on a large scale and certainly will increases system cloud gray model and control difficulty, heavy system burden for subsequent use.Therefore, to wind energy turbine set and wind farm group output power carry out prediction tool be of great significance [thunder Asia. the research topic [J] relevant to wind-electricity integration. Automation of Electric Systems, 2003,27 (8): 84-89.].

Short-term wind-electricity power prediction is generally predict the active power of following 24h-72h blower fan or wind energy turbine set, because prediction yardstick is longer, usually better prediction effect [model Gao Feng can be obtained by numerical weather forecast, Wang Wei wins, Liu Chun, Deng. based on the wind power prediction [J] of artificial neural network. Proceedings of the CSEE, 2008,28 (34): 118-123. Wang Caixias, Lu Zongxiang, Qiao Ying, etc. the short-term wind-electricity power based on nonparametric Regression Model is predicted [J]. Automation of Electric Systems, 2010,34 (16): 78-82.].Short-term forecasting result can be used for optimizing conventional power unit and exerts oneself and system reserve configuration, improves security and the economy of system cloud gray model.According to the difference predicted the outcome, One-Point-Value can be divided into predict for short-term wind power forecast method and probabilistic type predicts two class methods.One-Point-Value Forecasting Methodology mainly contains: physical method [Feng Shuanlei, Wang Wei wins, Liu Chun, Deng. wind farm power prediction physical method research [J]. Proceedings of the CSEE, 2010, 30 (2): 1-6.], statistical method [KARINIOTAKISGN, STAVRAKAKISGS, NOGARETEF.Windpowerforecastingusingadvancedneuralnetwork smodels (utilizing higher nerve network model to predict wind power) [J] .IEEETransactiononEnergyConversion.1996, 11 (4): 762-767.FANShu, LIAOJR, YOKOYAMAR, etal.Forecastingthewindgenerationusingatwo-stagenetworkb asedonmeteorologicalinformation(predicts based on the two benches network technique wind-power electricity generation of Weather information) [J] .IEEETransactiononConversion, 2009, 24 (2): 474-482. Wang Ge are beautiful, Yang Peicai, Mao Yuqing. based on the prediction [J] of support vector machine method to nonstationary time series. Acta Physica Sinica, 2008, 57 (2): 714-719.] and combined method [Chen Ning, Sha Qian, Tang Yi, Deng. based on the wind power combination forecasting method [J] of cross entropy theory. Proceedings of the CSEE, 2012, 32 (4): 29-34.].These class methods predict certain period wind power maximum possible occurrence following, and current prediction error (mean absolute errors of 48 hours) is how between 15% and 40%.Because One-Point-Value Forecasting Methodology cannot provide the uncertain information of wind power prediction, in recent years, probabilistic type Forecasting Methodology is more and more paid attention to and is studied, main method has: Empirical rules error statistics method [PINSONP, uncertain estimation in Estimationoftheuncertaintyinwindpowerforecasting(wind power prediction) [D] .EcoledesMinesdeParis, 2006. Wang Song rock, in continuing. the combination condition probability forecasting method [J] of wind speed and wind power. Proceedings of the CSEE, 2011, 31 (7): 7-14.], quantile homing method [Li Zhi, Han Xueshan, Yang Ming, Deng. the wind power waving interval returned based on quantile analyzes [J]. Automation of Electric Systems, 2011, 35 (3): 83-87.] and probability density Forecasting Methodology [JUBANJ, SIEBERTN, probabilistic type short-term wind-electricity prediction in KARINIOTAKISGN.Probabilisticshort-termwindpowerforecasti ngfortheoptimalmanagementofwindgeneration(wind-powered electricity generation Optimal Management) [C] // .IEEELausannePowerTech, Lausanne, Switzerland, Jul1-5, 2007. Yang Ming, Fan Shu, Han Xueshan, Deng. based on the probability forecasting method [J] of the Power Output for Wind Power Field of component management loading. Automation of Electric Systems, 2012, 36 (14): 125-130, 142.].These methods can not only predict the expectation value of future time period Power Output for Wind Power Field, the distributed intelligence of predicated error can also be provided, for the operation risk assessment containing wind energy turbine set electric system and decision in the face of risk provide important references [BOUFFARDF, GALIANAFD.Stochasticsecurityforoperationsplanningwithsig nificantwindpowergeneration (containing random security in the scheduling of large-scale wind generator operation) [J] .IEEETransactiononPowerSystems, 2008, 23 (2): 306-316. Li Zhis, Han Xueshan, Yang Ming, Deng. take into account the dispatching of power netwoks model [J] receiving wind-powered electricity generation ability. Automation of Electric Systems, 2010, 34 (19): 15-19.].

Above method is only carried out by period prediction for the output power of single wind energy turbine set, does not consider the space correlation relation between associate feature between Power Output for Wind Power Field prediction period and the prediction of many Power Output for Wind Power Field.But, this spacetime correlation information is to electrical power system transmission obstructive root canal and all significant [TASTUJ of electric network reliability, PINSONP, KOTWAE, analyze and wind power prediction error modeling when etal.Spatio-temporalanalysisandmodelingofwindpowerforeca sterrors(is empty) [J] .WindEnergy, 2011, 14 (1): 43-46.GNEITINGT, LARSONK, WESTRICKK, the probabilistic type prediction of etal.CalibratedprobabilisticforecastingattheStatelinewin denergycenter:Theregime-switchingspace – timemethod(state ventilation energy calibrate: method when state transfer is empty) [J] .JournaloftheAmericanStatisticalAssociation, 2006, 101 (475): 968-979.].Document [Wang Songyan, in continuing. the combination condition probability forecasting method [J] of wind speed and wind power. Proceedings of the CSEE, 2011,31 (7): 7-14.] with present period measured value and subsequent period predicted value for combination condition, probabilistic forecasting is carried out to the wind speed of single wind energy turbine set and wind power; Document [TASTUJ, PINSONP, KOTWAE, analyze and wind power prediction error modeling when etal.Spatio-temporalanalysisandmodelingofwindpowerforeca sterrors(is empty) [J] .WindEnergy, 2011,14 (1): 43-46.] inertia analyzed due to Meteorology Forecast System causes the adjacent nearer wind farm power prediction error in position to there is space-time propagation characteristic, and achieves advanced 1h wind power prediction; Document [GNEITINGT, LARSONK, WESTRICKK, the probabilistic type prediction of etal.Calibratedprobabilisticforecastingatthestatelinewin denergycenter:Theregime-switchingspace – timemethod(state ventilation energy calibrate: method when state transfer is empty) [J] .JournaloftheAmericanStatisticalAssociation, 2006,101 (475): 968-979.] consider the spacetime correlation information between wind field, advanced 2h prediction is carried out to wind speed; Document [PINSONP, PAPAEFTHYMIOUG, KLOCKLB, the generation of etal.Generationofstatisticalscenariosofshort-termwindpow erproduction(short-term wind-power electricity generation statistics scene) [C] // .PowerTech, 2007IEEELausanne.IEEE, 2007:491-496.] using probabilistic forecasting result as input, the short-term wind-electricity power of formation statistics scene contains the associate feature between prediction period, but only studies single wind energy turbine set.Correlativity between prediction period and the spacetime correlation characteristic between the prediction of windy field output power are not all included in model simultaneously and are considered by these research work.

Summary of the invention

Object of the present invention is exactly to solve the problem, a kind of joint probability density Forecasting Methodology of windy electric field short-term output power is provided, it has the prediction average and uncertainty in traffic information that can not only provide single Power Output for Wind Power Field, can also dynamic space-time associate feature between the prediction of quantitative description windy field output power, thus prediction is tallied with the actual situation more, for providing the advantage of more abundant information containing the scheduling decision of wind energy turbine set electric system.

To achieve these goals, the present invention adopts following technical scheme:

A joint probability density Forecasting Methodology for windy electric field short-term output power, mainly comprises the steps:

Step (1): utilize Support vector regression forecast model to carry out One-Point-Value prediction to the output power of each wind energy turbine set, and the probability density prediction that management loading model carries out error is set up to predicated error, and then obtain marginal probability density function prediction expectation value and the variance of single Power Output for Wind Power Field;

Step (2): statistical study is carried out to windy field output power predicated error characteristic, according to the spacetime correlation characteristic existed between Power Output for Wind Power Field predicated error in the same area, set up dynamic condition relevant-Multivariate autoregressive conditional different Variance model, according to described dynamic condition be correlated with-the Multivariate autoregressive conditional different Variance model correlation matrix of trying to achieve can dynamic space-time correlationship between the short-term output power predicated error of quantitative description windy field;

Step (3): comprehensive single wind field output power marginal probability density predicts the outcome and obtains the joint probability density function of windy field output power with correlation matrix, and forms the multidimensional scene comprising spacetime correlation characteristic by multiple random variable sample technique.

In described step (1), Support vector regression forecast model is expressed as:

$y_{\mathrm{output}}=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{w}_{i}K(x_{\mathrm{input}},x_i)+w_0+\mathrm{\ϵ}---\left(1\right)$

In formula: y _outputfor stochastic variable to be predicted; x _inputfor input vector; x _ifor the input vector in training sample; I for identifying sample, i=1,2 ..., M; K () is kernel function, adopts gaussian kernel function form; M is training sample sum; w _iwith w ₀be weight coefficient; ε is error term.

Management loading model in described step (1) carries out on the basis of One-Point-Value prediction at SVM to Power Output for Wind Power Field, set up SBL(management loading) model, carry out the marginal probability density function prediction of error, and then obtain the distributed intelligence of future time period predicated error; The predicated error of each period is expressed as:

$e_{t+k/t}={\stackrel{\‾}{p}}_{t+k/t}-p_{t+k}---\left(2\right)$

In formula, e _t+k/tfor the predicated error of t+k period; for SVM wind power One-Point-Value predicts the outcome; p _t+kfor wind power true measurement; T is the prediction execution moment; Hop count when k is prediction.

The marginal probability density function prediction expectation value of described single Power Output for Wind Power Field and variance are respectively:

$\begin{array}{c}{\hat{p}}_{t+k/t}={\stackrel{\‾}{p}}_{t+k/t}-{\stackrel{\‾}{e}}_{t+k/t}\\ {\widehat{\mathrm{\σ}}}_{t+k/t}^2={\stackrel{\‾}{\mathrm{\σ}}}_{t+k/t}^2\end{array}---\left(3\right)$

In formula, that the t+k period is through the revised Power Output for Wind Power Field expectation value of SBL (management loading) error prediction expectation value; for the variance of Power Output for Wind Power Field; with represent SBL (management loading) error prediction expectation value and variance respectively; it is SVM wind power single-point predicted value.

In described step (2), statistical study is carried out to windy field output power predicated error characteristic:

First, cross correlation function CCF calculating is carried out to the predicated error sequence between same Power Output for Wind Power Field Different periods, correlationship intersegmental during analyses and prediction; Cross correlation function CCF computational analysis is carried out to the output power predicated error derived from without the different prediction period of wind energy turbine set.

The computing formula utilizing cross correlation function CCF to analyze correlationship between wind power prediction error sequence is between two:

${\mathrm{\ρ}}_{i,j}=\frac{{\mathrm{\Σ}}_{n-1}^N(e_{n,i}-{\mathrm{\μ}}_i)\·(e_{n,j}-{\mathrm{\μ}}_j)}{\sqrt{{\mathrm{\Σ}}_{n-1}^N(e_{n,i}-{\mathrm{\μ}}_i)}\·\sqrt{{\mathrm{\Σ}}_{n-1}^N(e_{n,j}-{\mathrm{\μ}}_j)}}---\left(4\right)$

In formula: subscript i, j are in order to identify prediction period; N scope is 1 ~ N, in order to identify sample; N represents predicated error total sample number; ρ _i,jrepresent the related coefficient between i-th period and a jth period wind power prediction error, its span is [-1,1]; μ _iand μ _jrepresent the wind power prediction error sequence average of i-th period and a jth period respectively; e _n,irepresent n-th sample of error sequence i; e _n,jrepresent n-th sample of error sequence j.

Described dynamic condition is relevant-Multivariate autoregressive conditional different Variance model: and its dynamic condition dependency structure is set as:

R _t＝diag{Q _t} ^-1/2Q _tdiag{Q _t} ^-1/2

$Q_t=[1-\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\α}}_p-\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{\mathrm{\β}}_q]\stackrel{\‾}{Q}+\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\α}}_p{\mathrm{\ϵ}}_{t-p}{\mathrm{\ϵ}}_{t-p}^T+\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{\mathrm{\β}}_q{Q}_{t-p}---\left(5\right)$

ε _t＝D _t ^-1r _t

In formula: r _tfor K × 1 dimensional vector, its element is the predicated error average of each wind energy turbine set each period; ε _tfor K × 1 dimensional vector standardized residual; R _tfor dynamic conditional correlation matrix, it is the symmetrical matrix of K × K dimension, and diagonal entry is 1, and off-diagonal element absolute value is less than 1; for K × K ties up the unconditional variance matrix of standardized residual; α _pand β _qfor the setting coefficient of DCC dynamic condition correlation model, wherein, p and q is lag order, and scope is respectively: 1 ~ P and 1 ~ Q; Q _tfor K × K ties up covariance matrix; D _tfor K × K ties up diagonal matrix, its element is that the condition standard of stochastic variable is poor, and this stochastic variable obeys unitary generilized auto regressive conditional heteroskedastic process, and unitary generilized auto regressive conditional heteroskedastic process GARCH (M, N) is:

$h_{\mathrm{it}}={\mathrm{\ω}}_i^{*}+\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{im}}^{*}{\mathrm{\ϵ}}_{\mathrm{it}-m}^2+\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\β}}_{\mathrm{in}}^{*}{h}_{\mathrm{it}-n}---\left(6\right)$

In formula: h _itrepresent the Conditional heterosedasticity of i-th stochastic variable; for model parameter, wherein, m and n is lag order, and scope is respectively: 1 ~ M and 1 ~ N.

The concrete steps of described step (3) are: the output power multivariate normal distribution in the multiple period of windy field represent, its probability density function is:

$f_{y^{*}}=\frac{1}{{\left(2\mathrm{\π}\right)}^{K/2}{\left|C\right|}^{1/2}}\exp (-\frac{1}{2}{(y^{*}-\mathrm{\η})}^T{C}^{-1}(y^{*}-\mathrm{\η}))---\left(7\right)$

In formula: represent joint probability density function; y ^*for K × 1 n-dimensional random variable n; η is K × 1 dimensional vector, and its element is the wind power prediction average of each wind energy turbine set each period; C is that K × K ties up covariance matrix; K represents stochastic variable dimension;

Find out from formula (7), only need predict that mean vector η and covariance matrix C just obtains the joint probability density function of the multi-period output power in windy field; η extracts and obtains from the probability density prediction of single Power Output for Wind Power Field, and covariance matrix C is comparatively large due to its dimension, directly predicts more difficult; But according to the character of multivariate normal distribution, covariance matrix C is necessary for positive definite symmetrical matrix, then as follows to its decomposition:

C=ARA(8)

In formula: A is that K × K ties up diagonal matrix, and its element is the standard deviation of Power Output for Wind Power Field; R is that K × K ties up correlation matrix, is also positive definite symmetrical matrix with C;

Through type (8) decomposes, the prediction of covariance matrix is converted into standard deviation prediction and the correlation matrix prediction of Power Output for Wind Power Field, and the two can obtain respectively from the marginal probability density function and DCC dynamic condition correlation regression model of Power Output for Wind Power Field;

To sum up, can predict obtain mean vector η, diagonal matrix A and correlation matrix R in conjunction with the marginal probability density prediction of single Power Output for Wind Power Field and dynamic condition correlation regression model, just can be obtained the joint probability density function of windy field output power by formula (7) and formula (8).

Beneficial effect of the present invention:

1 for above-mentioned present Research, and the present invention, on the basis analyzing actual wind energy turbine set predicated error statistical property, proposes a kind of windy field short-term output power joint probability density Forecasting Methodology considering dynamic space-time associate feature.First the method utilizes SVM(support vector machine) prediction of following 48h One-Point-Value is carried out to the output power of each wind energy turbine set, and set up SBL(management loading) model carries out probability density function prediction to predicated error, obtain the distributed intelligence of following error, and then obtain the marginal probability density function of each Power Output for Wind Power Field; Secondly, by carrying out statistical study to the historical data of predicated error, establish DCC-MGARCH(dynamic condition relevant-Multivariate ARCH) model, it predicts that the dynamic condition correlation matrix that obtains can dynamic space-time associate feature in the output power prediction of quantitative description windy field; Finally, in conjunction with single Power Output for Wind Power Field marginal probability density function and dynamic condition correlation matrix, the joint probability density function of windy field short-term output power is obtained.In order to the convenience shown and apply, by multiple random variable sample technique, joint probability density function is formed as input the multidimensional scene comprising dynamic space-time related information.To three wind energy turbine set modeling analysis in certain region, the validity of result verification the inventive method and practicality;

2 prediction average and the uncertainty in traffic information that single Power Output for Wind Power Field can not only be provided, can also dynamic space-time associate feature between the prediction of quantitative description windy field output power, thus prediction is tallied with the actual situation more, for providing more abundant information containing the scheduling decision of wind energy turbine set electric system.Sample calculation analysis utilizes actual wind power plant operation data, compares, demonstrate validity and the practicality of the inventive method to the prediction of Power Output for Wind Power Field expectation value, error forecast of distribution and scene prediction result;

3SBL has following unique advantage: (1) can provide Probability distribution prediction result; (2) without the need to setting the penalty factor balancing empiric risk and generalization ability in support vector machine; (3) the sparse degree of model and support vector machine are quite or better.

Accompanying drawing explanation

Fig. 1 is overall flow figure of the present invention;

Fig. 2 is wind energy turbine set relative position schematic diagram of the present invention;

Fig. 3 is each wind field predicated error sequence cross correlation schematic diagram of the present invention;

Fig. 4 is predicated error sequence cross correlation schematic diagram between wind field of the present invention;

Fig. 5 is probabilistic forecasting result schematic diagram of the present invention;

Fig. 6 is correlation matrix schematic diagram;

Fig. 7 is scene prediction result schematic diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

As shown in Figure 1, a kind of joint probability density Forecasting Methodology of windy electric field short-term output power, mainly comprises the steps:

Step (1): utilize Support vector regression forecast model to carry out One-Point-Value prediction to the output power of each wind energy turbine set, and the probability density prediction that management loading model carries out error is set up to predicated error, and then obtain marginal probability density function prediction expectation value and the variance of single Power Output for Wind Power Field;

Step (2): statistical study is carried out to windy field output power predicated error characteristic, according to the spacetime correlation characteristic existed between Power Output for Wind Power Field predicated error in the same area, set up dynamic condition relevant-Multivariate autoregressive conditional different Variance model, according to described dynamic condition be correlated with-the Multivariate autoregressive conditional different Variance model correlation matrix of trying to achieve can dynamic space-time correlationship between the short-term output power predicated error of quantitative description windy field;

Step (3): comprehensive single wind field output power marginal probability density predicts the outcome and obtains the joint probability density function of windy field output power with correlation matrix, and forms the multidimensional scene comprising spacetime correlation characteristic by multiple random variable sample technique.

1.1.1.11 data explanation

The present invention for research object, is expressed as wf1, wf2 and wf3 with three actual wind energy turbine set in certain region, and the relative position of wind energy turbine set as shown in Figure 2.Numerical weather forecast provides hourly average wind speed and direction data.In order to reflect that any input quantity changes the size causing output quantity to change, all data are normalized.Wherein, air speed data utilizes historical record maximal value to be normalized, and wind direction data get its sine value and cosine value, and wind power data separate wind energy turbine set installed capacity P _nbe normalized.

1.1.1.22 the probability density prediction of single Power Output for Wind Power Field

2.1 based on the wind power One-Point-Value Forecasting Methodology of support vector machine

The present invention adopts the SVM of current popular to carry out the short-term One-Point-Value prediction of Power Output for Wind Power Field.SVM is the new machine learning method of the Corpus--based Method theories of learning, and it is by Non-linear Kernel function, by input amendment spatial mappings to High-dimensional Linear feature space, has the ability of process nonlinearity regression problem.

SVM regressive prediction model can be expressed as:

$y_{\mathrm{output}}=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{w}_{i}K(x_{\mathrm{input}},x_i)+w_0+\mathrm{\ϵ}---\left(1\right)$

In formula: y _outputfor stochastic variable to be predicted; x _inputfor input vector; x _ifor the input vector in training sample; K () is kernel function, and the present invention adopts gaussian kernel function form; M is training sample sum; w _i(w ₀with) be weight coefficient; ε is error term.

The management loading Forecasting Methodology of 2.2 error distributions

SBL and SVM is all the methods building forecast model around kernel function, but, the most important feature of SBL is that its learning process is based on Bayes's framework, instead of employing structural risk minimization, this just makes SBL have following unique advantage: (1) can provide Probability distribution prediction result; (2) without the need to setting the penalty factor balancing empiric risk and generalization ability in support vector machine; (3) the sparse degree of model and support vector machine are quite or better.Same SVM, SBL regressive prediction model can be expressed as equally such as formula shown in (1).Unlike supposing error term ε Normal Distribution herein, and weight coefficient w _i(w ₀with), in management loading machine, be counted as stochastic variable, and suppose its prior distribution also Normal Distribution.Easily find out, when learning machine formula (1) Suo Shi has been trained, for any given input vector, all can obtain the probability density function of predicted amount.

In order to study the uncertainty of wind power prediction, it is significant that the Power Output for Wind Power Field predicated error obtained One-Point-Value Forecasting Methodology carries out Modeling Research.The present invention carries out, on the basis of One-Point-Value prediction, setting up SBL model to Power Output for Wind Power Field at SVM, carries out the marginal probability density function prediction of error, and then obtains the distributed intelligence of future time period predicated error.The predicated error of each period can be expressed as:

$e_{t+k/t}={\stackrel{\‾}{p}}_{t+k/t}-p_{t+k}---\left(2\right)$

In formula, e _t+k/tfor the predicated error of t+k period; for SVM wind power One-Point-Value predicts the outcome; p _t+kfor wind power true measurement.

2.3 marginal probability density function predictions

Due to SVM to the prediction of the short-term One-Point-Value of Power Output for Wind Power Field and SBL the marginal probability density function prediction to each separate periods predicated error independently carry out, so Power Output for Wind Power Field predicts that the relation between expectation value and error forecast of distribution result is separate.Therefore, the prediction expectation value of the marginal probability density function of Power Output for Wind Power Field and variance are respectively:

$\begin{array}{c}{\hat{p}}_{t+k/t}={\stackrel{\‾}{p}}_{t+k/t}-{\stackrel{\‾}{e}}_{t+k/t}\\ {\stackrel{\‾}{\mathrm{\σ}}}_{t+k/t}^2={\stackrel{\‾}{\mathrm{\σ}}}_{t+k/t}^2\end{array}---\left(3\right)$

In formula, that the t+k period is through the revised Power Output for Wind Power Field expectation value of SBL error prediction expectation value; for the variance of Power Output for Wind Power Field; e _t+k/twith represent SBL error prediction expectation value and variance respectively.

1.1.1.33 dynamic condition correlation regression model

3.1 predicated error specificity analysises

The predicated error of Power Output for Wind Power Field is mainly derived from three aspects: model error, explanatory variable Select Error and input data deviation.Model error derives from the modeling error of forecasting problem, normally unavoidable.Power Output for Wind Power Field affects by the several factors in physical environment, but, select all factors illustratively variable certainly will increase the complexity of model, usual way is the factor illustratively variable selecting influence relatively large by cross correlation analysis, such as historical power, wind speed and wind direction etc.For the present situation of current wind power prediction technology, although short-term forecasting can obtain better prediction effect by numerical weather forecast, but current numerical weather forecast system also cannot provide accurate predicted data, its data prediction error is the main source of Power Output for Wind Power Field predicated error.Meanwhile, because numerical weather forecast system has inertia characteristics, in the same area, between Power Output for Wind Power Field prediction, there is dynamic space-time associate feature.This dynamic space-time associate feature is included in forecast model and considers, the confidence level of wind power prediction can not only be improved from zone level, more advance information can also be provided for power scheduling personnel, and then make containing safer, the economic operation of wind-powered electricity generation electric system.

Cross correlation function CCF is commonly used to the correlationship between analysis two time serieses.The computing formula utilizing cross correlation function CCF to analyze correlationship between wind power prediction error sequence is between two:

${\mathrm{\ρ}}_{i,j}=\frac{{\mathrm{\Σ}}_{n-1}^N(e_{n,i}-{\mathrm{\μ}}_i)\·(e_{n,j}-{\mathrm{\μ}}_j)}{\sqrt{{\mathrm{\Σ}}_{n-1}^N(e_{n,i}-{\mathrm{\μ}}_i)}\·\sqrt{{\mathrm{\Σ}}_{n-1}^N(e_{n,j}-{\mathrm{\μ}}_j)}}---\left(4\right)$

In formula: subscript i, j are in order to identify prediction period; N scope is 1 ~ N, in order to identify sample; ρ _i,jrepresent the related coefficient between i-th period and a jth period wind power prediction error, its span is [-1,1]; μ _iand μ _jrepresent the wind power prediction error sequence average e of i-th period and a jth period respectively _n,irepresent n-th sample of error sequence i; e _n,jrepresent n-th sample of error sequence j.

First, cross correlation function CCF calculating is carried out to the predicated error sequence between same Power Output for Wind Power Field Different periods, correlationship intersegmental during analyses and prediction.This related coefficient sentenced between the predicated error sequence of first prediction period and other all period predicated error sequence is example, and result as shown in Figure 3.In figure, two dotted lines refer to 95% confidence level, and related coefficient absolute value exceedes this dotted line, illustrate to there is clear-cut correlation between two predicated error sequences, otherwise do not exist.As can be seen from the figure, along with the increase of prediction period, related coefficient declines gradually, but the once peak value again at 24h place, illustrates that wind energy turbine set has certain date periodicity.Same test is done to other period, similar conclusion can be obtained, the associate feature namely between Power Output for Wind Power Field predicated error in life period.

In order to check the correlationship between the prediction of different Power Output for Wind Power Field, cross correlation function CCF computational analysis is carried out to the output power predicated error derived from without the different prediction period of wind energy turbine set herein.For the correlation analysis between first prediction period predicated error sequence and predicated error sequence of different wind energy turbine set all periods, result as shown in Figure 4.As can be seen from the figure, between different Power Output for Wind Power Field predicated error, there is certain correlativity, and the correlativity size of different delayed duration is also not identical.Simultaneously, composition graphs 2 can be found out, relatively strong at a distance of nearlyer correlativity between wind energy turbine set, and the predicated error correlativity of the predicated error of first period of wf2 and second period of wf3 is the strongest, between the output power that wf2 and wf3 is described, latter two hour stagnant has the greatest impact.More than analyze and show to there is spacetime correlation characteristic between Power Output for Wind Power Field predicated error in the same area.

3.2 dynamic condition correlation regression models

3.1 joints have carried out CCF analysis to windy field output power predicated error in region, show that many Power Output for Wind Power Field predicated error exists spacetime correlation characteristic, meanwhile, because physical environment is moment change, so become when this incidence relation also should be.The predicated error of each period is considered as stochastic variable by the present invention, and then utilizes this dynamic space-time associate feature of dynamic condition correlation matrix quantitative description.

2002, it is relevant that Engle with Sheppard proposes a kind of new estimator-DynamicConditionalCorrelation(dynamic condition), this model has good computing velocity, can be used for the dynamic conditional correlation matrix estimated between extensive time series, so study between multiple time series time become incidence relation.DCC-MGARCH (P is set up to Power Output for Wind Power Field predicated error, Q) (dynamicconditionalcorrelation-multivariategeneralizedaut oregressiveconditionalheteroskedasticity, dynamic condition is relevant-Multivariate ARCH) and model, its dynamic condition dependency structure can be set as:

R _t＝diag{Q _t} ^-1/2Q _tdiag{Q _t} ^-1/2

$Q_t=[1-\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\α}}_p-\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{\mathrm{\β}}_q]\stackrel{\‾}{Q}+\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\α}}_p{\mathrm{\ϵ}}_{t-p}{\mathrm{\ϵ}}_{t-p}^T+\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{\mathrm{\β}}_q{Q}_{t-p}---\left(5\right)$

ε _t＝D _t ^-1r _t

In formula: r _tfor K × 1 dimensional vector, its element is the predicated error average of each wind energy turbine set each period; ε _tfor K × 1 dimensional vector standardized residual; R _tfor dynamic conditional correlation matrix, it is the symmetrical matrix of K × K dimension, and diagonal entry is 1, and off-diagonal element absolute value is less than 1; for K × K ties up the unconditional variance matrix of standardized residual; α _pand β _qfor the setting coefficient of DCC model, wherein, p and q is lag order, and scope is respectively: 1 ~ P and 1 ~ Q; Q _tfor K × K ties up covariance matrix; D _tfor K × K ties up diagonal matrix, its element is that the condition standard of stochastic variable is poor, and this stochastic variable obeys unitary generilized auto regressive conditional heteroskedastic process (GARCH process), and unitary GARCH (M, N) process is:

$h_{\mathrm{it}}={\mathrm{\ω}}_i^{*}+\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{im}}^{*}{\mathrm{\ϵ}}_{\mathrm{it}-m}^2+\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\β}}_{\mathrm{in}}^{*}{h}_{\mathrm{it}-n}---\left(6\right)$

In formula: h _itrepresent the Conditional heterosedasticity of i-th stochastic variable; for model parameter, wherein, m and n is lag order, and scope is respectively: 1 ~ M and 1 ~ N.

DCC model carrys out estimated parameter by two benches.First estimate each seasonal effect in time series single argument GARCH process, then remove residual error by the conditional variance obtained and obtain standardized residual, and then utilize maximum-likelihood method to estimate the parameter of dependency structure.By Twostep Estimation, avoid the complicacy that model calculates, meanwhile, the constraint condition in model ensure that estimates that the correlation matrix obtained is orthotropicity matrix.

1.1.1.44 windy field output power joint probability density is predicted

Based on SVM realize Power Output for Wind Power Field by period One-Point-Value prediction, and by SBL, the prediction of marginal probability density function is carried out to wind power prediction error, and then obtains single Power Output for Wind Power Field and predict by the probability density function of period.But this Forecasting Methodology does not consider the spatial and temporal association in correlationship between prediction period and the same area between wind energy turbine set, and this prediction is incomplete to a certain degree.For this reason, it is very necessary for carrying out associated prediction to many Power Output for Wind Power Field of consideration dynamic space-time associate feature.

Output power in the multiple period of windy field can use multivariate normal distribution represent, its probability density function is:

$f_{y^{*}}=\frac{1}{{\left(2\mathrm{\π}\right)}^{K/2}{\left|C\right|}^{1/2}}\exp (-\frac{1}{2}{(y^{*}-\mathrm{\η})}^T{C}^{-1}(y^{*}-\mathrm{\η}))---\left(7\right)$

In formula: y ^*for K × 1 n-dimensional random variable n; η is K × 1 dimensional vector, and its element is the wind power prediction average of each wind energy turbine set each period; C is that K × K ties up covariance matrix; The present invention predicts, so K is 144 the output power of the following 48h of three wind energy turbine set.

As can be seen from formula (7), only need predict that mean vector η and covariance matrix C just can obtain the joint probability density function of the multi-period output power in windy field.η can extract and obtain from the probability density prediction of single Power Output for Wind Power Field, and C is comparatively large due to its dimension, directly predicts more difficult.But according to the character of multivariate normal distribution, C is necessary for positive definite symmetrical matrix, then can be as follows to its decomposition:

C=ARA(8)

In formula: A is that K × K ties up diagonal matrix, and its element is the standard deviation of Power Output for Wind Power Field; R is that K × K ties up correlation matrix, is also positive definite symmetrical matrix with C.

Through type (8) decomposes, and the prediction of covariance matrix is converted into standard deviation prediction and the correlation matrix prediction of Power Output for Wind Power Field, and the two can obtain respectively from the marginal probability density function and DCC regression model of Power Output for Wind Power Field.To sum up, can predict obtain mean vector η, diagonal matrix A and correlation matrix R in conjunction with the marginal probability density prediction of single Power Output for Wind Power Field and dynamic condition correlation regression model, just can be obtained the joint probability density function of windy field output power by formula (7) and formula (8).

1.1.1.55 sample calculation analysis

The inventive method on the basis of single Power Output for Wind Power Field probability density prediction, considers dynamic space-time associate feature, to the joint probability density prediction that windy field output power is carried out.The validity of method carrys out analysis verification from three aspects: expectation value prediction, error forecast of distribution and scene prediction.

5.1 expectation value precision of predictions are analyzed

Data sample is divided into training set, test set and checking collection, and size is respectively 1200,1000 and 500.First, utilize training set for each wind energy turbine set of SVM(48 of each prediction period) train, and with the SVM trained to test set carry out looking forward to the prospect 48h by period Power Output for Wind Power Field One-Point-Value prediction, obtain prediction expectation value and predicated error; Then, predicated error and corresponding air speed data is utilized to set up management loading machine (same to SVM, each wind energy turbine set 48); Finally, utilize SVM and SBL trained checking collection to be carried out to the probability density prediction of prediction 48h, obtain the marginal probability density function of each Power Output for Wind Power Field.

Predict the outcome for expectation value, the inventive method and lasting method and traditional SVM method being predicted the outcome compares, and evaluation index is normalization mean absolute error (NMAE).The average N MAE index of prediction 48h is as shown in table 1.As can be seen from the table, the NMAE of the inventive method comparatively continues method three wind fields and on average reduces 22%, and more traditional SVM method reduces 6.2%, describes the validity of the inventive method in expectation value prediction.

The 48h average N MAE(% of table 13 kind of method) Indexes Comparison

5.2 error forecast of distribution analysis on its rationality

The prediction of Power Output for Wind Power Field probability density not only requires that its mean prediction precision is higher, also should possess certain rationality to error forecast of distribution result.The inventive method is utilized once to predict the outcome as shown in Figure 5 to wf1.In figure, red line is Power Output for Wind Power Field actual value, and zone circle black line is prediction expectation value, and the error band of two kinds of colors represents respectively error band and error band.As can be seen from the figure, the actual value overwhelming majority period drops on in error band, exceed extremely individually outside error band, it is comparatively reasonable to illustrate the forecast of distribution result of error.

In order to the error forecast of distribution effect of quantitatively evaluating the inventive method, adopt literary composition [Yang Ming, Fan Shu, Han Xueshan, Deng. based on the probability forecasting method [J] of the Power Output for Wind Power Field of component management loading. Automation of Electric Systems, 2012, 36 (14): 125-130, 142.] prediction distribution distortion rate evaluation index in, by the inventive method and literary composition [PINSONP, uncertain estimation in Estimationoftheunertaintyinwindpowerforecasting(wind power prediction) [D] .EcoledesMinesdeParis, 2006.] in, experience error statistics method compares.Interval division, the interior theoretical drop point number of interval probability and interval of prediction distribution distortion rate evaluation index are as shown in table 2.

Table 2 interval division, probability and drop point number

Table 3 gives the prediction distribution distortion rate Indexes Comparison result of the inventive method and experience error statistics method.As can be seen from the table, to wf3, the prediction distribution distortion rate of two kinds of methods is suitable, and to other two wind energy turbine set, the inventive method is all little compared with experience error statistics method, further illustrates the rationality of the inventive method to error forecast of distribution.

Table 3 prediction distribution distortion rate (%) compares

5.3 scene prediction analysis on its rationality

Utilize SVM to predict that the predicated error obtained sets up DCC-MGARCH (1,1) model to test set, prediction obtains dynamic conditional correlation matrix as shown in Figure 6.Related coefficient has just to be had negative, and fluctuation range is [-0.77 ~ 1].This correlation matrix contains the correlation information between three wind field all periods output power predicated errors.Predict the outcome in conjunction with correlation matrix and the single wind field marginal probability density by period output power, form the joint probability density function of many Power Output for Wind Power Field.Because joint probability density dimension is higher, in order to the convenience shown and apply, multiple random variable sample technique is adopted to form multidimensional scene.

Certain joint probability density is predicted the outcome as inputting the scene set (capacity is 50 scenes) of formation as shown in Figure 7.Wherein, black zone circle thick line is Power Output for Wind Power Field actual value.Form the spatial and temporal association that scene contains Power Output for Wind Power Field, as can be seen from the figure formed scene can comprise the overwhelming majority actual value.In order to verify further the effectiveness of spacetime correlation characteristic and the inventive method form the reliability of scene, the present invention adopts Energy Fraction (Es) index to compare the two class scene set comprised with not comprising spacetime correlation characteristic.Es index evaluates a kind of common counter of scene reliability, more reasonable [the GNEITINGT of value scene that less explanation is formed, STANBERRYLI, GRIMITEP, etal.Assessingprobabilisticforecastsofmultivariatequanti ties, the probabilistic type prediction and evaluation of withanapplicationtoensemblepredictionsofsurfacewinds(polytomy variable is also applied in the combined prediction of surface wind) .Test2008,17:211-235.].Es index is:

$\mathrm{Es}=\frac{1}{V}\underset{v=1}{\overset{V}{\mathrm{\Σ}}}{\left|\right|{\mathrm{\η}}^T-S^{\left(v\right)}\left|\right|}_2-\frac{1}{{2V}^2}\underset{u=1}{\overset{V}{\mathrm{\Σ}}}\underset{v=1}{\overset{V}{\mathrm{\Σ}}}{\left|\right|S^{\left(u\right)}-S^{\left(v\right)}\left|\right|}_2---\left(9\right)$

In formula: S ^(u)with S ^(v)represent u and v scene respectively; U and v represents scene, u, v=1,2 ..., V; V is scene set sizes.

It is noted that when formation does not comprise the scene set of associate feature matrix, only correlation matrix need be set to unit diagonal matrix E.To size be 2000 two class scene collection Es Indexes Comparison results as shown in table 4.Wherein, the Es index result of experience error statistics method for not comprising spacetime correlation characteristic corresponding to E, and R corresponding be the Es index result of the inventive method comprising associate feature.As seen from the table, the scene collection Es value predicted by text method is all less than the scene collection Es value of experience error statistics method prediction, illustrates and considers that the scene set that spacetime correlation characteristic is formed is more realistic.

The Es Indexes Comparison of table 4 scene

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (7)

1. a joint probability density Forecasting Methodology for windy electric field short-term output power, is characterized in that, mainly comprise the steps:

Step (1): utilize Support vector regression forecast model to carry out One-Point-Value prediction to the output power of each wind energy turbine set, and the probability density prediction that management loading model carries out error is set up to predicated error, and then obtain marginal probability density function prediction expectation value and the variance of single Power Output for Wind Power Field;

Management loading model in described step (1) carries out on the basis of One-Point-Value prediction at SVM to Power Output for Wind Power Field, set up SBL model, carry out the marginal probability density function prediction of error, and then obtain the distributed intelligence of future time period predicated error; The predicated error of each period is expressed as:

$e_{t+k/t}={\stackrel{\‾}{p}}_{t+k/t}-p_{t+k}---\left(2\right)$

In formula, e _t+k/tfor the predicated error of t+k period; for SVM wind power One-Point-Value predicts the outcome; p _t+kfor wind power true measurement, t is the prediction execution moment; Hop count when k is prediction;

Step (2): statistical study is carried out to windy field output power predicated error characteristic, according to the spacetime correlation characteristic existed between Power Output for Wind Power Field predicated error in the same area, set up dynamic condition relevant-Multivariate autoregressive conditional different Variance model, according to described dynamic condition be correlated with-the Multivariate autoregressive conditional different Variance model correlation matrix of trying to achieve can dynamic space-time correlationship between the short-term output power predicated error of quantitative description windy field;

Step (3): comprehensive single wind field output power marginal probability density predicts the outcome and obtains the joint probability density function of windy field output power with correlation matrix, and forms the multidimensional scene comprising spacetime correlation characteristic by multiple random variable sample technique.

2. the joint probability density Forecasting Methodology of a kind of windy electric field short-term output power as claimed in claim 1, is characterized in that, in described step (1), Support vector regression forecast model is expressed as:

$y_{output}=\underset{i=1}{\overset{M}{\Σ}}{w}_{i}K(x_{input},x_i)+w_0+\mathrm{\ϵ}---\left(1\right)$

In formula: y _outputfor stochastic variable to be predicted; x _inputfor input vector; x _ifor the input vector in training sample; I for identifying sample, i=1,2 ..., M; K () is kernel function, adopts gaussian kernel function form; M is training sample sum; w _iwith w ₀be weight coefficient; ε is error term.

3. the joint probability density Forecasting Methodology of a kind of windy electric field short-term output power as claimed in claim 1, is characterized in that,

The marginal probability density function prediction expectation value of described single Power Output for Wind Power Field and variance are respectively:

${\hat{p}}_{t+k/t}={\stackrel{\‾}{p}}_{t+k/t}-{\stackrel{\‾}{e_t}}_{+k/t}$

(3)

${\widehat{\mathrm{\σ}}}_{t+k/t}^2={\stackrel{\‾}{\mathrm{\σ}}}_{t+k/t}^2$

In formula, that the t+k period is through the revised Power Output for Wind Power Field expectation value of SBL error prediction expectation value; for the variance of Power Output for Wind Power Field; with represent SBL error prediction expectation value and variance respectively; it is SVM wind power single-point predicted value.

4. the joint probability density Forecasting Methodology of a kind of windy electric field short-term output power as claimed in claim 1, is characterized in that, carries out statistical study in described step (2) to windy field output power predicated error characteristic:

First, cross correlation function CCF calculating is carried out to the predicated error sequence between same Power Output for Wind Power Field Different periods, correlationship intersegmental during analyses and prediction; Cross correlation function CCF computational analysis is carried out to the output power predicated error derived from without the different prediction period of wind energy turbine set.

5. the joint probability density Forecasting Methodology of a kind of windy electric field short-term output power as claimed in claim 4, is characterized in that,

The computing formula utilizing cross correlation function CCF to analyze correlationship between wind power prediction error sequence is between two:

${\mathrm{\ρ}}_{i,j}=\frac{{\mathrm{\Σ}}_{n-1}^N(e_{n,i}-{\mathrm{\μ}}_i)\·(e_{n,j}-{\mathrm{\μ}}_j)}{\sqrt{{\mathrm{\Σ}}_{n-1}^N(e_{n,i}-{\mathrm{\μ}}_i)}\·\sqrt{{\mathrm{\Σ}}_{n-1}^N(e_{n,j}-{\mathrm{\μ}}_j)}}---\left(4\right)$

In formula: subscript i, j are in order to identify prediction period; N scope is 1 ~ N, in order to identify sample; ρ _i,jrepresent the related coefficient between i-th period and a jth period wind power prediction error, its span is [-1,1]; μ _iand μ _jrepresent the wind power prediction error sequence average of i-th period and a jth period respectively; e _n,irepresent n-th sample of error sequence i, e _n,jrepresent n-th sample of error sequence j.

6. the joint probability density Forecasting Methodology of a kind of windy electric field short-term output power as claimed in claim 1, is characterized in that,

Described dynamic condition is relevant-Multivariate autoregressive conditional different Variance model: and its dynamic condition dependency structure is set as:

R _t＝diag{Q _t} ^-1/2Q _tdiag{Q _t} ^-1/2

$Q_t=\[1-\underset{p=1}{\overset{P}{\Σ}}{\mathrm{\α}}_p-\underset{q=1}{\overset{Q}{\Σ}}{\mathrm{\β}}_q\]\stackrel{\‾}{Q}+\underset{p=1}{\overset{P}{\Σ}}{\mathrm{\α}}_p{\mathrm{\ϵ}}_{t-p}{\mathrm{\ϵ}}_{t-p}^T+\underset{q=1}{\overset{Q}{\Σ}}{\mathrm{\β}}_q{Q}_{t-q}---\left(5\right)$

ε _t＝D _t ^-1r _t

In formula: r _tfor K × 1 dimensional vector, its element is the predicated error average of each wind energy turbine set each period; ε _tfor K × 1 dimensional vector standardized residual; R _tfor dynamic conditional correlation matrix, it is the symmetrical matrix of K × K dimension, and diagonal entry is 1, and off-diagonal element absolute value is less than 1; for K × K ties up the unconditional variance matrix of standardized residual; α _pand β _qfor the setting coefficient of DCC model, wherein, p and q is lag order, and scope is respectively: 1 ~ P and 1 ~ Q; Q _tfor K × K ties up covariance matrix; D _tfor K × K ties up diagonal matrix, its element is that the condition standard of stochastic variable is poor, and this stochastic variable obeys unitary generilized auto regressive conditional heteroskedastic process, and unitary generilized auto regressive conditional heteroskedastic process GARCH (M, N) is:

$h_{it}={\mathrm{\ω}}_i^{*}+\underset{m=1}{\overset{M}{\Σ}}{\mathrm{\α}}_{im}^{*}{\mathrm{\ϵ}}_{it-m}^2+\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{in}^{*}{h}_{it-n}---\left(6\right)$

In formula: h _itrepresent the Conditional heterosedasticity of i-th stochastic variable; with for model parameter, wherein, m and n is lag order, and scope is respectively: 1 ~ M and 1 ~ N.

7. the joint probability density Forecasting Methodology of a kind of windy electric field short-term output power as claimed in claim 1, it is characterized in that, the concrete steps of described step (3) are: the output power multivariate normal distribution in the multiple period of windy field represent, its probability density function is:

$f_{y^{*}}=\frac{1}{{\left(2\mathrm{\π}\right)}^{K/2}|C{|}^{1/2}}\exp (-\frac{1}{2}{\left(y^{*}-\mathrm{\η}\right)}^T{C}^{-1}(y^{*}-\mathrm{\η}\left)\right)---\left(7\right)$

In formula: for joint probability density function; y ^*for K × 1 n-dimensional random variable n; η is K × 1 dimensional vector, and its element is the wind power prediction average of each wind energy turbine set each period; C is that K × K ties up covariance matrix;

Find out from formula (7), only need predict that mean vector η and covariance matrix C just obtains the joint probability density function of the multi-period output power in windy field; η extracts and obtains from the probability density prediction of single Power Output for Wind Power Field, and covariance matrix C is comparatively large due to its dimension, directly predicts more difficult; But according to the character of multivariate normal distribution, covariance matrix C is necessary for positive definite symmetrical matrix, then as follows to its decomposition:

C＝ARA(8)

In formula: A is that K × K ties up diagonal matrix, and its element is the standard deviation of Power Output for Wind Power Field; R is that K × K ties up correlation matrix, is also positive definite symmetrical matrix with C;

Through type (8) decomposes, and the prediction of covariance matrix is converted into standard deviation prediction and the correlation matrix prediction of Power Output for Wind Power Field, and the two can obtain respectively from the marginal probability density function and DCC regression model of Power Output for Wind Power Field;

To sum up, can predict obtain mean vector η, diagonal matrix A and correlation matrix R in conjunction with the marginal probability density prediction of single Power Output for Wind Power Field and dynamic condition correlation regression model, just can be obtained the joint probability density function of windy field output power by formula (7) and formula (8).