CN103440541A - Joint probability density prediction method of short-term output power of plurality of wind power plants - Google Patents

Abstract

The invention discloses a joint probability density prediction method of short-term output power of a plurality of wind power plants. The method comprises the following steps: carrying out single point value prediction on output power of each wind power plant by using a support vector machine regression prediction model; building a sparse bayesian learning model as to a prediction error to carry out probability density prediction of the error, so as to obtain an expected value and a variance of marginal probability density function prediction of the output power of a single wind power plant; carrying out statistic analysis on the prediction error characteristics of the output power of the plurality of wind power plants, building a dynamic conditional correlation-multivariate generalized autoregressive condition heteroscedasticity model, and integrating a marginal probability density prediction result of the output power of the single wind power plant and a correlation coefficient matrix to obtain a joint probability density function of the output power of the plurality of wind power plants; forming a multidimensional scene including space-time correlation characteristics by using a sampling technique. By adopting the joint probability density prediction method, a mean prediction value and prediction uncertainty information of the output power of the single wind power plant can be provided; the dynamic space-time correlation characteristics between output power prediction of the plurality of wind power plants also can be quantitatively described.

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 is extensive grid-connectedly have been alleviated China's Pressure on Energy and has brought huge economy and environment benefit, is the most ripe, the on the largest scale regenerative resource that melts the clockwork spring part of current technology.Yet wind-powered electricity generation is as the power supply of a kind of intermittence and uncontrollability, it is connected to the grid on a large scale and certainly will the operation of increase system controls difficulty, the standby burden of heavy system.Therefore, to wind energy turbine set and wind farm group output power predicted tool be of great significance [the thunder Asia. the research topic relevant to wind-electricity integration [J]. Automation of Electric Systems, 2003,27 (8): 84-89.].

The short-term wind-electricity power prediction is predicted the active power of following 24h-72h blower fan or wind energy turbine set, because the prediction yardstick is longer, usually can access better prediction effect [model Gao Feng by numerical weather forecast, Wang Wei's victory, Liu Chun, Deng. the wind power prediction [J] based on artificial neural network. Proceedings of the CSEE, 2008,28 (34): the 118-123. Wang Caixia, Lu Zongxiang, Qiao Ying, etc. the short-term wind-electricity power prediction [J] based on nonparametric Regression Model. Automation of Electric Systems, 2010,34 (16): 78-82.].The short-term forecasting result can be used for optimizing conventional unit output and system reserve configuration, security and the economy of the operation of raising system.According to the difference predicted the outcome, the short-term wind-electricity power Forecasting Methodology can be divided into the One-Point-Value prediction and probabilistic type is predicted two class methods.The One-Point-Value Forecasting Methodology mainly contains: physical method [Feng Shuanlei, Wang Wei's victory, Liu Chun, Deng. wind farm power prediction physical method research [J]. Proceedings of the CSEE, 2010, 30 (2): 1-6.], statistical method [KARINIOTAKISG N, STAVRAKAKIS G S, NOGARET E F.Wind power forecasting using advanced neuralnetworks models (utilizing higher nerve network model prediction wind power) [J] .IEEE Transaction on Energy Conversion.1996, 11 (4): 762-767.FAN Shu, LIAO J R, YOKOYAMA R, the two stages network technique wind-power electricity generation prediction of et al.Forecasting the wind generation using a two-stage network based on meteorological information(based on Weather information) [J] .IEEE Transaction on Conversion, 2009, 24 (2): 474-482. Wang Ge is beautiful, Yang Peicai, Mao Yuqing. the prediction [J] based on 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. the wind power combination forecasting method [J] based on the cross entropy theory. Proceedings of the CSEE, 2012, 32 (4): 29-34.].These class methods are following certain period wind power maximum possible to be gone out to present worth predicted, current predicated error (mean absolute errors of 48 hours) is many between 15% and 40%.Because the One-Point-Value Forecasting Methodology can't provide the uncertain information of wind power prediction, in recent years, the probabilistic type Forecasting Methodology is more and more paid attention to and is studied, main method has: Empirical rules error statistics method [PINSON P, uncertain estimation in the prediction of Estimation of the uncertainty in wind power forecasting(wind power) [D] .Ecole des Mines de Paris, 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 fluctuation interval analysis [J] returned based on quantile. Automation of Electric Systems, 2011, 35 (3): 83-87.] and probability density Forecasting Methodology [JUBAN J, SIEBERT N, probabilistic type short-term wind-electricity prediction in KARINIOTAKIS G N.Probabilistic short-term wind power forecasting for the optimal management of wind generation(wind-powered electricity generation Optimal Management) [C] // .IEEE Lausanne Power Tech, Lausanne, Switzerland, Jul1-5, 2007. Yang Ming, the model timely rain, Han Xueshan, Deng. the probability forecasting method [J] of the Power Output for Wind Power Field based on the study of component sparse Bayesian. Automation of Electric Systems, 2012, 36 (14): 125-130, 142.].These methods not only can predict future period Power Output for Wind Power Field expectation value, can also provide the distributed intelligence of predicated error, for operation risk assessment and the decision in the face of risk that contains the wind energy turbine set electric system provides important references [BOUFFARD F, GALIANA F D.Stochastic security for operations planning with significant wind power generation (containing random safety in the scheduling of large-scale wind generator operation) [J] .IEEE Transaction on Power Systems, 2008, 23 (2): 306-316. Li Zhi, Han Xueshan, Yang Ming, Deng. take into account the dispatching of power netwoks model [J] of receiving the wind-powered electricity generation ability. Automation of Electric Systems, 2010, 34 (19): 15-19.].

Above method is only pursued period prediction for the output power of single wind energy turbine set, does not consider associate feature between the Power Output for Wind Power Field prediction period and the space correlation relation between the prediction of windy electric field output power.Yet, this spacetime correlation information is controlled the electric system transmission blocking and electric network reliability significant [TASTU J all, PINSON P, KOTWA E, when et al.Spatio-temporal analysis and modeling of wind power forecast errors(is empty, analyze and the modeling of wind power predicated error) [J] .Wind Energy, 2011, 14 (1): 43-46.GNEITING T, LARSON K, WESTRICK K, the probabilistic type prediction of et al.Calibrated probabilistic forecasting at the Stateline wind energy center:The regime-switching space – time method(state ventilation energy calibrate: method when state transitions is empty) [J] .Journal of the American Statistical Association, 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.] take current period measured value and next period predicted value is combination condition, and wind speed and the wind power of single wind energy turbine set carried out to probabilistic forecasting; Document [TASTU J, PINSON P, KOTWA E, when et al.Spatio-temporal analysis and modeling of wind power forecast errors(is empty, analyze and the modeling of wind power predicated error) [J] .Wind Energy, 2011,14 (1): 43-46.] inertia of having analyzed due to Meteorology Forecast System causes the adjacent nearer wind farm power prediction error in position to have the space-time propagation characteristic, and has realized leading 1h wind power prediction; Document [GNEITING T, LARSON K, WESTRICK K, the probabilistic type prediction of et al.Calibrated probabilistic forecasting at the stateline wind energy center:The regime-switching space – time method(state ventilation energy calibrate: method when state transitions is empty) [J] .Journal of the American Statistical Association, 2006,101 (475): 968-979.] consider the spacetime correlation information between wind field, wind speed is carried out to leading 2h prediction; Document [PINSON P, PAPAEFTHYMIOU G, KLOCKL B, the generation of et al.Generation of statistical scenarios of short-term wind power production(short-term wind-power electricity generation statistics scene) [C] // .Power Tech, 2007IEEE Lausanne.IEEE, 2007:491-496.] using the probabilistic forecasting result as input, the short-term wind-electricity power statistics scene formed has comprised the associate feature between prediction period, but only single wind energy turbine set is studied.These research work are not all included the spacetime correlation characteristic between the correlativity between prediction period and the output power prediction of windy field in model in and are considered simultaneously.

Summary of the invention

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

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

A kind of joint probability density Forecasting Methodology of windy electric field short-term output power, mainly comprise the steps:

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

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

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

In described step (1), the support vector machine regressive prediction model is expressed as:

$y_{\mathrm{output}}=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{i}K(x_{\mathrm{input}},x_i)+{\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="HDA0000384364320000021.png,HDA0000384364320000031.png"\; state="\{\{state\}\}">w</figure-callout>}}_0+\mathrm{\&epsiv;}---\left(1\right)$

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

Sparse Bayesian learning model in described step (1) is Power Output for Wind Power Field to be carried out on the basis of One-Point-Value prediction at SVM, set up the study of SBL(sparse Bayesian) model, carry out the marginal probability density function prediction of error, and then obtain the distributed intelligence of following period predicated error; The predicated error of each period is expressed as:

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

In formula, e _t+k/tpredicated error for the t+k period;

for SVM wind power One-Point-Value predicts the outcome; p _t+kfor the wind power true measurement; T carries out constantly for prediction; Hop count when k is prediction.

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

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

In formula,

that the t+k period is through the revised Power Output for Wind Power Field expectation value of SBL (sparse Bayesian study) error prediction expectation value;

variance for Power Output for Wind Power Field; with

mean respectively SBL (sparse Bayesian study) error prediction expectation value and variance;

it is SVM wind power single-point predicted value.

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

At first, when different to same Power Output for Wind Power Field, intersegmental predicated error sequence is carried out cross correlation function CCF calculating, intersegmental correlationship during analyses and prediction; Carry out cross correlation function CCF computational analysis to deriving from without the output power predicated error of the different prediction periods of wind energy turbine set.

Utilize cross correlation function CCF to analyze in twos the computing formula of correlationship between wind power predicated error sequence to be:

${\mathrm{\&rho;}}_{i,j}=\frac{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,i}-{\mathrm{\&mu;}}_i)\&CenterDot;(e_{n,j}-{\mathrm{\&mu;}}_j)}{\sqrt{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,i}-{\mathrm{\&mu;}}_i)}\&CenterDot;\sqrt{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,j}-{\mathrm{\&mu;}}_j)}}---\left(4\right)$

In formula: subscript i, j is in order to identify prediction period; The n scope is 1～N, in order to identify sample; N means the predicated error total sample number; ρ _i,jmean the related coefficient between i period and j period wind power predicated error, its span is [1,1]; μ _iand μ _jrepresent respectively the wind power predicated error serial mean of i period and j period; e _n,in the sample that means error sequence i; e _n,jn the sample that means error sequence j.

Described dynamic correlation-Multivariate autoregressive conditional different Variance model: its dynamic correlation structure is set as:

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

$Q_t=[1-\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_p-\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_q]\stackrel{\&OverBar;}{Q}+\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_p{\mathrm{\&epsiv;}}_{t-p}{\mathrm{\&epsiv;}}_{t-p}^T+\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_q{Q}_{t-p}---\left(5\right)$

ε _t＝D _t ^-1r _t

In formula: r _tfor K * 1 dimensional vector, the predicated error average that its element is each each period of wind energy turbine set; ε _tfor K * 1 dimensional vector standardized residual; R _tfor the dynamic conditional correlation matrix, its symmetrical matrix that is K * K dimension, diagonal entry is 1, and the off-diagonal element absolute value is less than 1;

unconditional variance matrix for K * K dimension standardized residual; α _pand β _qfor the setting coefficient of DCC dynamic correlation model, wherein, p and q are the hysteresis exponent number, 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, the condition standard deviation that its element is stochastic variable, this stochastic variable is obeyed monobasic broad sense ARCH process, and monobasic broad sense ARCH process GARCH (M, N) is:

$h_{\mathrm{it}}={\mathrm{\&omega;}}_i^{*}+\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{im}}^{*}{\mathrm{\&epsiv;}}_{\mathrm{it}-m}^2+\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{in}}^{*}{h}_{\mathrm{it}-n}---\left(6\right)$

In formula: h _itthe different variance of condition that means i stochastic variable;

for model parameter, wherein, m and n are the hysteresis exponent number, and scope is respectively: 1～M and 1～N.

The concrete steps of described step (3) are: windy interior output power multivariate normal distribution of a plurality of periods mean, its probability density function is:

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

In formula:

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

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

C=ARA (8)

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

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

To sum up, can predict and obtain mean vector η, diagonal matrix A and correlation matrix R in conjunction with the prediction of the marginal probability density of single Power Output for Wind Power Field and dynamic correlation regression model, just can be accessed 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 of analyzing actual wind energy turbine set predicated error statistical property, has proposed a kind of windy short-term output power joint probability density Forecasting Methodology considering the dynamic space-time associate feature.At first the method utilizes the SVM(support vector machine) output power of each wind energy turbine set is carried out to following 48h One-Point-Value prediction, and set up SBL(sparse Bayesian study) model carries out the 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, carry out statistical study by the historical data to predicated error, set up DCC-MGARCH(dynamic correlation-Multivariate ARCH) model, the dynamic space-time associate feature in can quantitative description windy output power prediction of the dynamic correlation matrix that its prediction obtains; Finally, in conjunction with single Power Output for Wind Power Field marginal probability density function and dynamic correlation matrix, obtain the joint probability density function of windy short-term output power.For the convenience of showing and applying, by the multiple random variable sample technique, joint probability density function is formed to the multidimensional scene that comprises the dynamic space-time related information as input.To certain the zone interior three wind energy turbine set modeling analysis, result verification validity and the practicality of the inventive method;

2 not only can provide prediction average and the uncertainty in traffic information of single Power Output for Wind Power Field, dynamic space-time associate feature between can also quantitative description windy output power prediction, thereby prediction is tallied with the actual situation more, for the scheduling decision containing the wind energy turbine set electric system provides abundanter information.Sample calculation analysis utilizes actual wind energy turbine set service data, and the prediction of Power Output for Wind Power Field expectation value, error forecast of distribution and scene prediction result are compared, and has verified validity and the practicality of the inventive method;

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

The 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 the 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 comprise the steps:

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

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

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

1.1.1.11 data declaration

The present invention take certain the zone interior three actual wind energy turbine set be research object, be expressed as respectively wf1, wf2 and wf3, the relative position of wind energy turbine set is 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 that causes that output quantity changes, and carries out normalized to all data.Wherein, air speed data utilizes the historical record maximal value to carry out normalization, and the wind direction data are got its sine value and cosine value, and the wind power data are utilized wind energy turbine set installed capacity P _ncarry out normalization.

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

2.1 the wind power One-Point-Value Forecasting Methodology based on 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 based on the new machine learning method of Statistical Learning Theory, and it,, by the Non-linear Kernel function, will be inputted sample space and be mapped to the High-dimensional Linear feature space, has the ability of processing the nonlinearity regression problem.

The SVM regressive prediction model can be expressed as:

$y_{\mathrm{output}}=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{i}K(x_{\mathrm{input}},x_i)+{\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="HDA0000384364320000021.png,HDA0000384364320000031.png"\; state="\{\{state\}\}">w</figure-callout>}}_0+\mathrm{\&epsiv;}---\left(1\right)$

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 the gaussian kernel function form; M is the training sample sum; w _i(w ₀with) be weight coefficient; ε is error term.

2.2 the sparse Bayesian that error distributes study Forecasting Methodology

SBL and SVM are all the methods of forecast model that build around kernel function, yet, the most important characteristics of SBL are that its learning process is based on Bayes's framework, rather than the employing structural risk minimization, this just makes SBL have following unique advantage: (1) can provide the Probability distribution prediction result; (2) without the penalty factor to balance empiric risk and generalization ability in support vector machine, set; (3) the sparse degree of model and support vector machine are quite or better.Same SVM, the SBL regressive prediction model can be expressed as equally suc as formula shown in (1).Different is to suppose error term ε Normal Distribution herein, and weight coefficient w _i(w ₀with), be counted as stochastic variable in the sparse Bayesian learning machine, and suppose also Normal Distribution of its prior distribution.Easily find out, when shown in formula (1), learning machine 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 that the One-Point-Value Forecasting Methodology is obtained is carried out Modeling Research.The present invention carries out Power Output for Wind Power Field at SVM, on the basis of One-Point-Value prediction, setting up the SBL model, carries out the marginal probability density function prediction of error, and then obtains the distributed intelligence of following period predicated error.The predicated error of each period can be expressed as:

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

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

2.3 marginal probability density function prediction

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

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

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;

variance for Power Output for Wind Power Field; e _t+k/twith

mean respectively SBL error prediction expectation value and variance.

1.1.1.33 dynamic correlation regression model

3.1 predicated error specificity analysis

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 is affected by the several factors in physical environment, yet, select all factors certainly will increase the complexity of model as explanatory variable, usually way is to select the relatively large factor of influence as explanatory variable by the cross correlation analysis, such as historical power, wind speed and wind direction etc.Present situation for current wind power forecasting techniques, although short-term forecasting can obtain better prediction effect by numerical weather forecast, but current numerical weather forecast system also can't provide accurate predicted data, its data prediction error is the main source of Power Output for Wind Power Field predicated error.Simultaneously, because the numerical weather forecast system has inertia characteristics, in the same area, between the Power Output for Wind Power Field prediction, there is the dynamic space-time associate feature.This dynamic space-time associate feature is included in forecast model and considered, not only can improve from zone level the confidence level of wind power prediction, can also be for the power scheduling personnel provide more advance information, and then make containing safer, the economic operation of wind-powered electricity generation electric system.

Cross correlation function CCF is commonly used to analyze two correlationships between time series.Utilize cross correlation function CCF to analyze in twos the computing formula of correlationship between wind power predicated error sequence to be:

${\mathrm{\&rho;}}_{i,j}=\frac{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,i}-{\mathrm{\&mu;}}_i)\&CenterDot;(e_{n,j}-{\mathrm{\&mu;}}_j)}{\sqrt{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,i}-{\mathrm{\&mu;}}_i)}\&CenterDot;\sqrt{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,j}-{\mathrm{\&mu;}}_j)}}---\left(4\right)$

In formula: subscript i, j is in order to identify prediction period; The n scope is 1～N, in order to identify sample; ρ _i,jmean the related coefficient between i period and j period wind power predicated error, its span is [1,1]; μ _iand μ _jrepresent respectively the wind power predicated error serial mean e of i period and j period _n,in the sample that means error sequence i; e _n,jn the sample that means error sequence j.

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

In order to check the correlationship between different Power Output for Wind Power Field predictions, carry out cross correlation function CCF computational analysis to deriving from without the output power predicated error of the different prediction periods of wind energy turbine set herein.The correlation analysis of take between first prediction period predicated error sequence and predicated error sequence of all periods of different wind energy turbine set is example, and result as shown in Figure 4.As can be seen from the figure, between different Power Output for Wind Power Field predicated errors, have certain correlativity, and the correlativity size of different hysteresis durations is also not identical.Simultaneously, in conjunction with Fig. 2, can find out, relatively strong at a distance of nearlyer correlativity between wind energy turbine set, and the predicated error correlativity of second period of the predicated error of first period of wf2 and wf3 is the strongest, illustrates between the output power of wf2 and wf3 that stagnant latter two hour has the greatest impact.More than the analysis showed that, in the same area, between the Power Output for Wind Power Field predicated error, have the spacetime correlation characteristic.

3.2 dynamic correlation regression model

3.1 joint has carried out the CCF analysis to windy output power predicated error in zone, show that there is the spacetime correlation characteristic in windy electric field output power predicated error, simultaneously, and because physical environment is constantly to change, so become when this incidence relation should be also.The present invention is considered as stochastic variable by the predicated error of each period, and then utilizes this dynamic space-time associate feature of dynamic correlation matrix quantitative description.

2002, Engle and Sheppard have proposed a kind of new estimator-Dynamic Conditional Correlation(dynamic correlation), this model has good computing velocity, can be used for estimating the dynamic conditional correlation matrix between extensive time series, so study between a plurality of time serieses the time become incidence relation.The Power Output for Wind Power Field predicated error is set up to DCC-MGARCH (P, Q) (dynamic conditional correlation-multivariate generalized auto regressive conditional heteroskedasticity, dynamic correlation-Multivariate ARCH) model, its dynamic correlation structure can be set as:

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

$Q_t=[1-\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_p-\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_q]\stackrel{\&OverBar;}{Q}+\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_p{\mathrm{\&epsiv;}}_{t-p}{\mathrm{\&epsiv;}}_{t-p}^T+\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_q{Q}_{t-p}---\left(5\right)$

ε _t＝D _t ^-1r _t

In formula: r _tfor K * 1 dimensional vector, the predicated error average that its element is each each period of wind energy turbine set; ε _tfor K * 1 dimensional vector standardized residual; R _tfor the dynamic conditional correlation matrix, its symmetrical matrix that is K * K dimension, diagonal entry is 1, and the off-diagonal element absolute value is less than 1;

unconditional variance matrix for K * K dimension standardized residual; α _pand β _qfor the setting coefficient of DCC model, wherein, p and q are the hysteresis exponent number, 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, the condition standard deviation that its element is stochastic variable, this stochastic variable is obeyed monobasic broad sense ARCH process (GARCH process), and monobasic GARCH (M, N) process is:

$h_{\mathrm{it}}={\mathrm{\&omega;}}_i^{*}+\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{im}}^{*}{\mathrm{\&epsiv;}}_{\mathrm{it}-m}^2+\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{in}}^{*}{h}_{\mathrm{it}-n}---\left(6\right)$

In formula: h _itthe different variance of condition that means i stochastic variable;

for model parameter, wherein, m and n are the hysteresis exponent number, and scope is respectively: 1～M and 1～N.

The DCC model is by two stage estimated parameters.At first estimate each seasonal effect in time series single argument GARCH process, then by the conditional variance obtained, remove residual error and obtain standardized residual, and then utilize maximum-likelihood method to estimate the parameter of dependency structure.By Twostep Estimation, the complicacy of having avoided model to calculate, simultaneously, the constraint condition in model has guaranteed to estimate that the correlation matrix obtained is the orthotropicity matrix.

1.1.1.44 windy output power joint probability density prediction

Realize predicting by the period One-Point-Value of Power Output for Wind Power Field based on SVM, and by SBL, the wind power predicated error is carried out to the prediction of marginal probability density function, and then obtain the probability density function prediction of single Power Output for Wind Power Field by the period.Yet this Forecasting Methodology is not considered the spacetime correlation relation between wind energy turbine set in correlationship between prediction period and the same area, this prediction is from being incomplete to a certain degree.For this reason, it is very necessary the windy electric field output power of considering the dynamic space-time associate feature being carried out to associated prediction.

Windy interior output power of a plurality of periods can be used multivariate normal distribution

mean, its probability density function is:

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

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

Can find out from formula (7), only need prediction mean vector η and covariance matrix C just can obtain the joint probability density function of windy multi-period output power.η can extract and obtain from the probability density prediction of single Power Output for Wind Power Field, and C is larger due to its dimension, and directly prediction is more difficult.Yet, according to the character of multivariate normal distribution, C is necessary for the positive definite symmetrical matrix, can be as follows to its decomposition:

C=ARA (8)

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

Through type (8) decomposes, and the prediction of covariance matrix is converted into standard deviation prediction and the correlation matrix of Power Output for Wind Power Field and predicts, and the two can be respectively obtains from the marginal probability density function of Power Output for Wind Power Field and DCC regression model.To sum up, can predict and obtain mean vector η, diagonal matrix A and correlation matrix R in conjunction with the prediction of the marginal probability density of single Power Output for Wind Power Field and dynamic 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 is to consider the dynamic space-time associate feature on the basis of single Power Output for Wind Power Field probability density prediction, the joint probability density prediction that windy output power carried out.The validity of method is carried out analysis verification from three aspects: expectation value prediction, error forecast of distribution and scene prediction.

5.1 the expectation value precision of prediction is analyzed

Data sample is divided into training set, test set and checking collection, and size is respectively 1200,1000 and 500.At first, utilize training set 48 of each wind energy turbine set of SVM(for each prediction period) trained, and with the SVM trained to test set the predicting by period Power Output for Wind Power Field One-Point-Value of 48h of being looked forward to the prospect, obtain predicting expectation value and predicated error; Then, utilize predicated error and corresponding air speed data to set up sparse Bayesian learning machine (same SVM, 48 of each wind energy turbine set); Finally, utilize the SVM and the SBL that train checking to be collected to the probability density prediction of the 48h that looked forward to the prospect, 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 are predicted the outcome and compare, 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 continues three wind fields of method and has on average reduced by 22%, and more traditional SVM method has reduced by 6.2%, and the validity of the inventive method in the expectation value prediction has been described.

The 48h average N MAE(% of table 13 kind of method) index relatively

5.2 error forecast of distribution analysis on its rationality

The prediction of Power Output for Wind Power Field probability density not only requires its mean prediction precision higher, to error forecast of distribution result, also should possess certain rationality.Utilize the inventive method once predicting the outcome as shown in Figure 5 to wf1.In figure, red line is the Power Output for Wind Power Field actual value, and the zone circle black line is the 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, surpass extremely individually outside error band, it is comparatively reasonable to illustrate the forecast of distribution result of error.

Error forecast of distribution effect for quantitatively evaluating the inventive method, adopt literary composition [Yang Ming, the model timely rain, Han Xueshan, Deng. the probability forecasting method [J] of the Power Output for Wind Power Field based on the study of component sparse Bayesian. Automation of Electric Systems, 2012, 36 (14): 125-130, 142.] middle prediction distribution distortion rate evaluation index, by the inventive method and literary composition [PINSON P, uncertain estimation in the prediction of Estimation of the unertainty in wind power forecasting(wind power) [D] .Ecole des Mines de Paris, 2006.] in experience error statistics method compare.The interval division of prediction distribution distortion rate evaluation index, interval probability and interval interior theoretical drop point number are as shown in table 2.

Table 2 interval division, probability and drop point number

Table 3 has provided the prediction distribution distortion rate index comparative 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 than experience error statistics method, further illustrates the rationality of the inventive method to the error forecast of distribution.

Table 3 prediction distribution distortion rate (%) relatively

5.3 scene prediction analysis on its rationality

Utilize the SVM predicated error that prediction obtains to test set to set up DCC-MGARCH (1,1) model, prediction obtains the dynamic conditional correlation matrix as shown in Figure 6.Related coefficient has just to be had negatively, and fluctuation range is [0.77～1].This correlation matrix has comprised the correlation information between three all periods of wind field output power predicated errors.Marginal probability density in conjunction with correlation matrix and single wind field by the period output power predicts the outcome, and forms the joint probability density function of windy electric field output power.Because the joint probability density dimension is higher, for the convenience of showing and applying, adopt the multiple random variable sample technique to form the multidimensional scene.

Certain joint probability density is predicted the outcome as the scene set (capacity is 50 scenes) of inputting formation as shown in Figure 7.Wherein, black zone circle thick line is the Power Output for Wind Power Field actual value.The spacetime correlation relation that the scene that forms has comprised Power Output for Wind Power Field, as can be seen from the figure the scene that forms can comprise most actual values.In order further to verify the effectiveness of spacetime correlation characteristic and the reliability of scene that the inventive method forms, the present invention adopts energy mark (Es) index to compare comprising with the two class scene set that do not comprise the spacetime correlation characteristic.The Es index is to estimate a kind of common counter of scene reliability, be worth more more reasonable [the GNEITING T of bright the formed scene of novel, STANBERRY LI, GRIMIT EP, et al.Assessing probabilistic forecasts of multivariate quantities, the probabilistic type prediction and evaluation of with an application to ensemble predictions of surface winds(polytomy variable also is applied in the combined prediction of surface wind) .Test2008,17:211-235.].The Es index is:

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

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

Should be noted, form while not comprising the scene set of associate feature matrix, only need the diagonal matrix E of the correlation matrix unit of being set to.The two class scene collection Es index comparative results that are 2000 to size are as shown in table 4.Wherein, E is corresponding for not comprising the Es index result of experience error statistics method of spacetime correlation characteristic, and R corresponding be the Es index result of the inventive method of comprising associate feature.As seen from the table, all be less than the scene collection Es value of experience error statistics method prediction by the scene collection Es value of text method prediction, illustrate and consider that the formed scene set of spacetime correlation characteristic is more realistic.

The Es index of table 4 scene relatively

Although above-mentioned, by reference to the accompanying drawings the specific embodiment of the present invention is described; but be 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 modifications that creative work can make or distortion still in protection scope of the present invention.

Claims (8)

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

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

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

Step (3): comprehensive single wind field output power marginal probability density predicts the outcome and correlation matrix obtains the joint probability density function of windy output power, and forms the multidimensional scene that comprises the spacetime correlation characteristic by the 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), the support vector machine regressive prediction model is expressed as:

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

In formula: y _outputfor stochastic variable to be predicted; x _inputfor input vector; x _ifor the input vector in training sample; I is used for identifying sample, i=1, and 2 ..., M; K () is kernel function, adopts the gaussian kernel function form; M is the 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, it is characterized in that, sparse Bayesian learning model in described step (1) is Power Output for Wind Power Field to be carried out on the basis of One-Point-Value prediction at SVM, set up the SBL model, carry out the marginal probability density function prediction of error, and then obtain the distributed intelligence of following period predicated error; The predicated error of each period is expressed as:

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

In formula, e _t+k/tpredicated error for the t+k period;

for SVM wind power One-Point-Value predicts the outcome; p _t+kfor the wind power true measurement, t carries out constantly for prediction; Hop count when k is prediction.

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,

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

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

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;

variance for Power Output for Wind Power Field;

with

mean respectively SBL error prediction expectation value and variance;

it is SVM wind power single-point predicted value.

5. 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 (2), windy output power predicated error characteristic carried out to statistical study:

At first, when different to same Power Output for Wind Power Field, intersegmental predicated error sequence is carried out cross correlation function CCF calculating, intersegmental correlationship during analyses and prediction; Carry out cross correlation function CCF computational analysis to deriving from without the output power predicated error of the different prediction periods of wind energy turbine set.

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

Utilize cross correlation function CCF to analyze in twos the computing formula of correlationship between wind power predicated error sequence to be:

${\mathrm{\&rho;}}_{i,j}=\frac{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,i}-{\mathrm{\&mu;}}_i)\&CenterDot;(e_{n,j}-{\mathrm{\&mu;}}_j)}{\sqrt{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,i}-{\mathrm{\&mu;}}_i)}\&CenterDot;\sqrt{{\mathrm{\&Sigma;}}_{n-1}^N(e_{n,j}-{\mathrm{\&mu;}}_j)}}---\left(4\right)$

In formula: subscript i, j is in order to identify prediction period; The n scope is 1～N, in order to identify sample; ρ _i,jmean the related coefficient between i period and j period wind power predicated error, its span is [1,1]; μ _iand μ _jrepresent respectively the wind power predicated error serial mean of i period and j period; e _n,in the sample that means error sequence i, e _n,jn the sample that means error sequence j.

7. 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 correlation-Multivariate autoregressive conditional different Variance model: its dynamic correlation structure is set as:

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

$Q_t=[1-\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_p-\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_q]\stackrel{\&OverBar;}{Q}+\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_p{\mathrm{\&epsiv;}}_{t-p}{\mathrm{\&epsiv;}}_{t-p}^T+\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_q{Q}_{t-p}---\left(5\right)$

ε _t＝D _t ^-1r _t

In formula: r _tfor K * 1 dimensional vector, the predicated error average that its element is each each period of wind energy turbine set; ε _tfor K * 1 dimensional vector standardized residual; R _tfor the dynamic conditional correlation matrix, its symmetrical matrix that is K * K dimension, diagonal entry is 1, and the off-diagonal element absolute value is less than 1;

unconditional variance matrix for K * K dimension standardized residual; α _pand β _qfor the setting coefficient of DCC model, wherein, p and q are the hysteresis exponent number, 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, the condition standard deviation that its element is stochastic variable, this stochastic variable is obeyed monobasic broad sense ARCH process, and monobasic broad sense ARCH process GARCH (M, N) is:

$h_{\mathrm{it}}={\mathrm{\&omega;}}_i^{*}+\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{im}}^{*}{\mathrm{\&epsiv;}}_{\mathrm{it}-m}^2+\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{in}}^{*}{h}_{\mathrm{it}-n}---\left(6\right)$

In formula: h _itthe different variance of condition that means i stochastic variable;

for model parameter, wherein, m and n are the hysteresis exponent number, and scope is respectively: 1～M and 1～N.

8. 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 concrete steps of described step (3) are: windy interior output power multivariate normal distribution of a plurality of periods

mean, its probability density function is:

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

In formula:

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

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

C=ARA (8)

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

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

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

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