CN112288164A - Wind power combined prediction method considering spatial correlation and correcting numerical weather forecast - Google Patents

Wind power combined prediction method considering spatial correlation and correcting numerical weather forecast Download PDF

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CN112288164A
CN112288164A CN202011184024.9A CN202011184024A CN112288164A CN 112288164 A CN112288164 A CN 112288164A CN 202011184024 A CN202011184024 A CN 202011184024A CN 112288164 A CN112288164 A CN 112288164A
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向月
胡帅
刘俊勇
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Abstract

The invention discloses a wind power combined prediction method considering spatial correlation and correcting numerical weather forecast, aiming at the defects of the traditional GP based on a single kernel function, a plurality of kernel functions are combined to obtain an optimal kernel function scheme, and a prediction model is established on the basis of the GP based on the combined kernel function. Considering that the data complexity of the multidimensional meteorological factors is high, screening key factors through an automatic correlation judgment algorithm, and establishing an NWP wind speed deviation correction model. And simultaneously, analyzing the wind speed time sequences of the target wind power plant and the adjacent wind power plants by using a spatial correlation method, obtaining the time difference corresponding to the strongest correlation by using a Pearson correlation coefficient method, and establishing a spatial correlation model. And based on the combined weighted prediction model of the models, the combined model weight coefficient is obtained by a Lagrange method. Therefore, the numerical weather forecast deviation correction method and the space correlation method are effectively combined through the combined weighted prediction model, and the prediction accuracy of the wind power is improved.

Description

Wind power combined prediction method considering spatial correlation and correcting numerical weather forecast
Technical Field
The invention relates to the technical field of wind power prediction, in particular to a wind power combined prediction method considering spatial correlation and correcting numerical weather forecast.
Background
The increasing exhaustion of fossil energy and the environmental pollution caused by the exhaustion become serious, and the development of renewable energy is urgent. Wind energy, as a green, pollution-free renewable energy source, has been increasing in permeability in the power grid in recent years. According to the data provided by the global wind energy council, the global installed capacity of wind power reaches 591GW (ground wire), wherein 184GW is used in China, and the installed wind power is ranked the first globally. However, the randomness and intermittence of wind power output cause great difficulty in accurate prediction of the wind power output, and certain challenges are brought to safe and stable operation of a power grid and reduction of the air curtailment quantity. Therefore, accurate wind power prediction is increasingly gaining importance.
Wind power prediction methods can be broadly classified into statistical methods, physical methods, and spatial correlation methods. The commonly used statistical prediction methods include time series analysis methods and artificial intelligence methods, the former methods include differential Autoregressive Integrated Moving Average (ARIMA), Autoregressive Moving Average (ARMA), Autoregressive model (AR), etc., and these methods have better prediction effect on linear data. The latter includes artificial neural networks, support vector machines, support vector regression, etc., which better take into account non-linear factors. The statistical method has the advantages of simple modeling and quick calculation. However, the statistical model has a limited application due to the large requirement of the training set data volume. If the historical data of a newly-built wind power plant is insufficient, the difficulty of training a wind power prediction model is increased. In general, statistical methods are suitable for short-term prediction.
The adverse effects of historical data loss can be overcome by physical methods, commonly based on Numerical Weather Prediction (NWP) data in combination with "wind speed-power curves". The NWP takes meteorological data and surface information as initial conditions, key information of a physical model is obtained by solving fluid mechanics and thermodynamic equations, and the prediction time scale can be increased to a certain extent. However, thermodynamics are not stable, sometimes influenced by weather, and will affect the accuracy of NWP. And the slowly updated numerical weather forecast also causes certain errors to the wind power prediction.
Spatial Correlation (SC) refers to predicting a target wind farm using information of neighboring wind farms, and the method has an important value for improving prediction accuracy when wind resource data of the target wind farm is insufficient. When only single wind power plant data is used, the problems of data shortage or untimely information acquisition and the like may exist, so that the prediction efficiency is reduced, and the shortage can be made up by using a spatial correlation method. The method takes into account factors such as the geographical position and the terrain of the wind power plant, and can solve the problem of low prediction accuracy caused by sudden change of wind speed to a certain extent.
In order to improve the limitation of a single statistical or physical model in wind power prediction, some researches combine multiple methods, such as a statistical method and a physical method, to establish a combined prediction model so as to improve the accuracy of wind power prediction and the applicability of the model. However, the neural network, which is a statistical method widely applied at present, has the disadvantages of low convergence rate and easy overfitting. Gaussian Processes (GPs) are an effective non-linear, non-parametric probabilistic prediction method, and compared with other statistical models, GPs contains fewer parameters, which can simplify the calculation process. In addition, the GP has the capability of self-adaptively acquiring the hyper-parameters, and the modeling process is flexible. However, because the wind speed changes drastically, the GP of the conventional single kernel function has limited capability of predicting the wind power, and the inventor finds that combining multiple kernels can make the prediction result more accurate. Meanwhile, the existing research does not consider the factors such as the time sequence, the spatial property and the inaccuracy of numerical weather forecast of the wind power prediction at the same time.
Disclosure of Invention
In view of the above problems in the prior art, the present invention provides a wind power combination prediction method with higher accuracy, which takes spatial correlation and corrects a numerical weather forecast into account.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a wind power combined prediction method considering spatial correlation and correcting numerical weather forecast comprises the following steps:
s100, reading historical data of a wind power plant a and data of various meteorological factors in a numerical weather forecast, wherein the meteorological factors at least comprise wind speed, wind direction, temperature, air pressure and relative humidity;
s200, screening out meteorological factors with strong correlation with wind power from the meteorological factors through an automatic correlation judgment algorithm, establishing a prediction model based on a Gaussian process by taking data of the meteorological factors as input variables, and obtaining a wind power prediction value P1；
S300, establishing a wind speed correction model according to corresponding known wind speed data, taking the wind speed data corrected by the wind speed correction model as the input of a prediction model based on the Gaussian process, and then performing wind power prediction to obtain a wind power prediction value P2；
S400, aiming at m wind power plants b adjacent to the wind power plant amPerforming spatial correlation analysis, and respectively calculating each wind power plant bmPearson correlation coefficient of wind power plant a and corresponding delay time delta tmAnd thus through the wind farm bmThe wind speed of the wind power plant a at the moment t is predicted according to the historical wind speed, a multi-dimensional prediction model is established by combining other meteorological factor data except the wind speed of the wind power plant a at the moment t, and a wind power prediction value P of the wind power plant a at the moment t is obtained2+m；
S500, based on P2、P2+mEstablishing a combined model, solving the weight coefficient of each prediction model in the combined model by using a Pearson correlation coefficient and a Lagrange multiplier method, and establishing a combined weighted wind power prediction model;
s600, predicting the wind power of the wind power plant a by using the combined weighted wind power prediction model, and outputting a wind power prediction value P of the wind power plant a.
Further, the wind power combination prediction method considering the spatial correlation and correcting the numerical weather forecast further includes:
step S700, respectively calculating the base P1、P2、P2+mStandard of model of PAnd three error evaluation indexes of the root mean square error NRMSE, the average absolute percentage error MAPE and the normalized average absolute error NMAE are subjected to comparative analysis, and the wind power predicted value with the minimum error precision is used as the final wind power predicted value of the wind power plant a to be output.
Specifically, the prediction model establishing process based on the gaussian process in step S200 is as follows:
establishing a gaussian expression, and outputting a function g (x) ═ to-be-predicted function f (x) + gaussian white noise e (x), wherein the output function g (x) ═ to-be-predicted function f (x) + gaussian white noise e (x) is expressed as: g (X) N (m (X), K (X, X) + σn 2I) Where m (x) is a mean function, σnIs the unit variance of white Gaussian noise, I is an n-dimensional unit matrix, and K (X, X) is a covariance matrix containing an element Kij＝k(xi,xj)，i,j＝1,2,…,n；
Forming a training set d ═ { X, y } of the Gaussian regression prediction process according to historical data of the wind farm a, wherein the input set X ═ X ═ y }i∈RDI 1, …, n, forming an input vector x with D dimension by data of various meteorological factors, and an output set yiI is 1,2, …, n is formed by corresponding wind power observation values, and the prediction parameters in the Gaussian expression are determined through the training set;
output y and predicted value f according to training set*Joint prior distribution of (c):
Figure BDA0002750964280000041
determining a mean of results for the Gaussian process based prediction model
Figure BDA0002750964280000042
Sum variance Σ*：
Figure BDA0002750964280000043
Figure BDA0002750964280000044
In the formula, x*Representing a new input value, k*Is k (X, X)*)＝k(x*,X)T＝[k(x1,x*),…,k(xn,x*)]For simplification of (2), X and X are indicatediN x 1 order covariance matrix between, k (x)*,x*) As a new input value x*Its own covariance.
Specifically, the covariance matrix K (X, X) selects one of the following functions as a kernel function:
1) squared exponential covariance function:
Figure BDA0002750964280000045
2) rational quadratic covariance function:
Figure BDA0002750964280000046
3) matern covariance function, v 3/2:
Figure BDA0002750964280000047
4) matern covariance function, v 5/2:
Figure BDA0002750964280000051
in the formula, σfIs the signal covariance and l is the length scale parameter.
Specifically, the learning of the hyper-parameters in the gaussian process is completed by a maximum likelihood estimation algorithm:
Figure BDA0002750964280000052
in the formula, f*The output power value in the wind power prediction is taken as K, and K is a kernel function of a Gaussian process;
determining the length scale parameter matched with each meteorological factor parameter value in the Gaussian process through an automatic correlation judgment algorithm, thereby judging the meteorological factor with strong correlation with wind power:
Figure BDA0002750964280000053
in this equation, D is the dimension of the input vector x, the number of types of meteorological factors, b is a deviation, and all superparameters are included in the vector θ ═ θ (θ)0,L,b)TWherein L represents L ═ L1,……,lDParameter in { C }, hyperparameter { l }1,……,lDIs used to implement auto-correlation decisions, with liThe length is shortened, and the function is corresponding to the input variable xiThe more sensitive, the stronger the correlation of the input variables.
More specifically, in step S300, a wind speed correction model expression is constructed according to wind speed prediction data in a numerical weather forecast and actual wind speed data corresponding to historical data of a wind farm a, and meteorological factor data having the largest influence on wind speed in all meteorological factors of the numerical weather forecast is screened out through an automatic correlation determination algorithm and used as input of the wind speed correction model expression, the wind speed prediction data is also used as input, and an air outlet speed correction model is established by using the actual wind speed data as output.
More specifically, in step S400, according to the wind farm a and the adjacent wind farm bmObtaining the wind speed sequences of the wind power field a and the adjacent wind power fields, and using the Pearson correlation coefficient etavThe correlation size between different wind power plant wind speed sequences is quantitatively analyzed:
Figure BDA0002750964280000054
in the formula, N is the number of wind speed correlation analysis samples, va、vbiRespectively wind farm a and adjacent wind farm bm(i-1, …, m), thereby obtaining a wind speed observed valueObtaining a wind farm a and an adjacent wind farm bmCorresponding delay time deltat therebetweenmAnd therefore, the wind speed of the wind power plant a is predicted by using the wind speed data of the adjacent wind power plants.
In step S400, a pearson correlation coefficient η is selectedvThe delay time corresponding to the maximum point of (a) is taken as the time difference between the two wind farms.
More specifically, in step S500, weighting is performed according to the contribution degree of different prediction models to the predicted value, and an expression of a combined weighting model is established:
Figure BDA0002750964280000061
in the formula, the predicted power of the n wind power prediction models is PnThe corresponding weight coefficient is betan；
The error of wind power in each wind power prediction model is epsilonnCorresponding variance is ζnThe variance of the combined weighting model is:
Figure BDA0002750964280000062
in the formula, Cov (. beta.)iεi,βjεj) Predicting the covariance of model errors for each wind power; the weight distribution is performed by taking the minimum prediction variance sum as an objective function, and the following formula is satisfied:
Figure BDA0002750964280000063
and solving the minimum value of the prediction error variance through a Lagrange method, thus solving each weight coefficient in the combined weighted model and determining the combined weighted wind power prediction model.
In the process of solving each weight coefficient, introducing a Lagrange multiplier:
Figure BDA0002750964280000064
respectively to betaiAnd lambda to obtain partial derivative, making its partial derivative be zero, obtaining weight coefficient beta1、β2、…、βn。
Compared with the prior art, the invention has the following beneficial effects:
(1) according to the method, the data complexity of the multidimensional meteorological factors is considered to be high, an automatic correlation determination (ARD) algorithm is used, key factors are selected from the multidimensional data, and an NWP wind speed correction model is established. The corrected wind speed replaces the NWP wind speed, and the wind speed precision and the generalization performance of the forecasting model are effectively improved.
(2) According to the method, the wind speed time sequences of the target wind power plant and the adjacent wind power plants are analyzed by using a spatial correlation method, the adjacent wind power plants are introduced to predict the target wind power plants, the influence of the terrain and the geographic position of the wind power plants on the power is reflected, and the defect of insufficient prediction accuracy caused by insufficient data of the target wind power plants is overcome.
(3) Aiming at the defects of the traditional GP based on a single kernel function, the invention combines various kernel functions to obtain the optimal kernel function scheme, and establishes a novel combined weighted wind power prediction model on the basis of the Gaussian process based on the combined kernel function. And according to the seasonal variation of the wind speed, under the condition of establishing different seasons, the weighted value of the model is determined by adopting a Lagrange multiplier method, so that the error of the combined model is reduced, and the prediction precision of the wind power is effectively improved.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention.
FIG. 2 is a schematic flow chart of an NWP wind speed correction model according to an embodiment of the invention.
FIG. 3 is a schematic diagram of a spatial translation method according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of predicted power and error in different seasons according to an embodiment of the present invention, where fig. 4a is spring, fig. 4b is summer, fig. 4c is autumn, and fig. 4d is winter.
Detailed Description
The present invention is further illustrated by the following figures and examples, which include, but are not limited to, the following examples.
Examples
As shown in fig. 1 to 4, the wind power combination prediction method considering spatial correlation and modified numerical weather forecast includes the following steps:
s100, reading historical data of a wind power plant a and data of various meteorological factors in a numerical weather forecast, wherein the meteorological factors at least comprise wind speed, wind direction, temperature, air pressure and relative humidity;
s200, screening out meteorological factors with strong correlation with wind power from the meteorological factors through an automatic correlation judgment algorithm, establishing a prediction model based on a Gaussian process by taking data of the meteorological factors as input variables, and obtaining a wind power prediction value P1；
S300, establishing a wind speed correction model according to corresponding known wind speed data, taking the wind speed data corrected by the wind speed correction model as the input of a prediction model based on the Gaussian process, and then performing wind power prediction to obtain a wind power prediction value P2；
S400, aiming at m wind power plants b adjacent to the wind power plant amPerforming spatial correlation analysis, and respectively calculating each wind power plant bmPearson correlation coefficient of wind power plant a and corresponding delay time delta tmAnd thus through the wind farm bmThe wind speed of the wind power plant a at the moment t is predicted according to the historical wind speed, a multi-dimensional prediction model is established by combining other meteorological factor data except the wind speed of the wind power plant a at the moment t, and a wind power prediction value P of the wind power plant a at the moment t is obtained2+m；
S500, based on P2、P2+mEstablishing a combined model, solving the weight coefficient of each prediction model in the combined model by using a Pearson correlation coefficient and a Lagrange multiplier method, and establishing a combined weighted wind power prediction model;
s600, predicting the wind power of the wind power plant a by using the combined weighted wind power prediction model, and outputting a wind power prediction value P of the wind power plant a.
Further, the wind power combination prediction method considering the spatial correlation and correcting the numerical weather forecast further includes:
step S700, respectively calculating the base P1、P2、P2+mAnd the standard root mean square error NRMSE, the average absolute percentage error MAPE and the normalized average absolute error NMAE of the model P are compared and analyzed, and the wind power predicted value with the minimum error precision is used as the final wind power predicted value of the wind power plant a to be output.
Specifically, the prediction model establishing process based on the gaussian process:
the Gaussian process is a parameter-free machine learning algorithm established on the basis of Bayesian theory, can adaptively obtain the optimal hyper-parameters, the prediction result and the confidence interval thereof, and has the advantages of high training speed and suitability for processing complex data such as high dimension, nonlinearity and the like.
Is provided with an input set X ═ Xi∈RDI 1, …, n, and y { y } is the output seti1,2, …, n, taking a combination d of an input set and an output set { X, y } as a training set of the gaussian regression prediction process, and assuming that f (X) follows a gaussian distribution, the expression is:
f(x)～N(m(x),k(x,x'))…………(1)
in the formula, m (x) represents a mean function, k (x, x') represents a covariance function, and each is defined as:
m(x)＝E[f(x)]…………(2)
k(x,x')＝E[(f(x)-m(x))(f(x')-m(x'))]]…………(3)
let d be the training set and consist of n observations, d { (x)i,yi) I ═ 1, …, n }, where x denotes the input vector in D dimensions and y denotes the output value, and since there are n inputs x, the D × n matrix can be used to represent the entire input data. In the Gaussian process, the target output typically contains white Gaussian noise e (x), which is assumed to be zero mean, unit variance, formulaThe following were used:
e(x)～N(0,σn 2)…………(4)
after adding the noisy sequence of the Gaussian white noise, the expression is as follows:
g(x)＝f(x)+e(x)…………(5)
so g (x) also obeys a gaussian distribution, which can be expressed as:
g(x)～N(m(x),K(X,X)+σn 2I)…………(6)
in the formula, I is an n-dimensional unit matrix, K (X, X) is a covariance matrix containing an element Kij＝k(xi,xj) I, j ═ 1,2, …, n, also referred to as kernel functions.
In this example, the following four kernel functions are selected:
1) squared exponential covariance function:
Figure BDA0002750964280000101
2) rational quadratic covariance function:
Figure BDA0002750964280000102
3) matern covariance function, v 3/2:
Figure BDA0002750964280000103
4) matern covariance function, v 5/2:
Figure BDA0002750964280000104
in the formula, σfThe signal covariance is taken as the signal covariance, l is a length scale parameter, and reasonably selecting the kernel function is the key for ensuring the prediction precision. The optimal kernel function scheme may be selected by:
the combination of the four kernel functions is selected as：k(x,x′)＝k1(x,x′)+k2(x,x′)；
The prediction error indicators for different kernel functions and combinations thereof are shown in table 1 below:
TABLE 1 prediction error index for different kernel functions and combinations thereof
Kernel function and combination RMSE(MW) MAPE MAE(MW)
SE 6.069902 0.395229 5.653775
RQ 6.156618 0.39465 5.647139
Mat(v＝3/2) 6.77634 0.405166 6.091823
Mat(v＝5/2) 6.812558 0.405619 6.11798
SE+RQ 5.730346 0.327676 5.01388
SE+Mat(v＝3/2) 4.24602 0.25317 4.807119
SE+Mat(v＝5/2) 5.586123 0.330217 4.914534
RQ+Mat(v＝3/2) 6.291651 0.337668 5.354872
RQ+Mat(v＝5/2) 6.196443 0.341961 5.305759
Mat(v＝3/2)+Mat(v＝5/2) 5.899431 0.337354 5.108981
As can be seen from table 1, the prediction errors of the combined kernel functions are all smaller than the prediction error of the single kernel function, and the prediction error is the smallest when the SE kernel function is combined with Mat (v-3/2). In the following prediction, a gaussian process model based on the combined kernel function is used for wind power prediction.
Output y and predicted value f of training set*The joint prior distribution of (a) is a gaussian process, as follows:
Figure BDA0002750964280000111
in the formula, x*Representing a new input value, k*Is k (X, X)*)＝k(x*,X)T＝[k(x1,x*),…,k(xn,x*)]For simplification of (2), X and X are indicatediN x 1 order covariance matrix between, k (x)*,x*) As a new input value x*Its own covariance. According to the joint Gaussian distribution principle, the mean value of the prediction result based on the Gaussian process is provided
Figure BDA0002750964280000116
Sum variance Σ*Respectively as follows:
Figure BDA0002750964280000112
Figure BDA0002750964280000113
the learning of the hyper-parameters of the Gaussian process is completed by a maximum likelihood estimation algorithm:
Figure BDA0002750964280000114
in the formula, f*And K is the output power value in the wind power prediction, and is the kernel function of the Gaussian process. The maximum likelihood function allows the determination of the values of parameters in a gaussian process, extended by incorporating a separate length scale parameter for each input variable, and the relative importance of different inputs to be inferred from the observed data, called auto-correlationAnd (3) judging algorithm:
Figure BDA0002750964280000115
in this equation, D is the dimension of the input vector x, the number of types of meteorological factors, b is a deviation, and all superparameters are included in the vector θ ═ θ (θ)0,L,b)TWherein L represents L ═ L1,……,lDParameter in { C }, hyperparameter { l }1,……,lDIs used to implement auto-correlation decisions, with liThe length is shortened, and the function is corresponding to the input variable xiThe more sensitive, the stronger the correlation of the input variables.
Specifically, the establishing process of the NWP wind speed correction model comprises the following steps:
according to the wind speed prediction data in the numerical weather forecast and the actual wind speed data corresponding to the historical data of the wind farm a, a wind speed correction model expression is constructed, the meteorological factor data which has the largest influence on the wind speed in all meteorological factors of the numerical weather forecast are screened out through an automatic correlation judgment algorithm and used as the input of the wind speed correction model expression, the wind speed prediction data is also used as the input, the actual wind speed data is used as the output, and an air outlet speed correction model is established. The corrected NWP wind speed is closer to the actual wind speed, the accuracy of wind speed prediction is improved, and the accuracy of wind power prediction is further improved. For example, the wind power prediction value P is obtained by using the corrected wind speed data as the input of a prediction model based on the Gaussian process2。
Specifically, the establishing process of the multidimensional prediction model based on the spatial correlation method comprises the following steps:
a certain spatial correlation exists between the wind speeds of the target wind power plant and the surrounding area, and the wind speed of the target wind power plant is predicted by selecting the proper historical wind speed of the adjacent wind power plant, so that the accuracy of wind power prediction can be effectively improved. And when the target wind power plant lacks a part of historical data, the target wind power plant can be predicted by utilizing the data of the adjacent wind power plant. Meanwhile, considering that some wind power plants are located in areas with complex terrain, the influence of wind speed mutation caused by the complex terrain on prediction is difficult to reflect only by means of self data, and the problem can be well solved by using a spatial correlation method for prediction. The selected target wind farm and the adjacent wind farm are not always on the same straight line, and the target wind farm and the adjacent wind farm can be processed by adopting a space translation method, and a schematic diagram of the target wind farm and the adjacent wind farm is shown in fig. 3.
Drawing a straight line through the target wind power plants to enable the straight line to be located between the selected peripheral wind power plants, drawing the vertical line of the straight line through each adjacent wind power plant, and obtaining the corresponding intersection point. When the distance between the adjacent wind farm and its corresponding intersection point is short, the data at the intersection point may be identical to the data of the adjacent wind farm.
When performing spatial correlation analysis between wind farms, a large amount of historical data of neighboring wind farms and a target wind farm is required. The time difference between different wind farm wind speed sequences needs to be accurately calculated. In the research, the Pearson correlation coefficient is used for quantitatively analyzing the correlation magnitude between different wind power plant wind speed sequences, and the formula is as follows:
Figure BDA0002750964280000121
in the formula, N is the number of wind speed correlation analysis samples, va、vbiRespectively wind farm a and adjacent wind farm bm(i-1, …, m). The closer the correlation coefficient is to 1, the stronger the positive correlation. Under the condition of different time differences, the wind speed sequences of the target wind power plant and the adjacent wind power plants and the corresponding Pearson correlation coefficients are obtained, and the larger the correlation coefficient is, the higher the similarity of the wind speed sequences of the two wind power plants is represented. Therefore, the delay time corresponding to the maximum value point of the correlation coefficient is selected as the time difference between the two wind power plants, and the target wind power plant is predicted by using the data of the adjacent wind power plants. For example, wind farm a and wind farm b are calculated separately1And wind farm b2The Pearson spatial correlation coefficient and the corresponding delay time Deltat thereof, and the point with the maximum correlation coefficient is selected as the optimal delay time. Respectively through wind farms b1、b2Historical wind speed ofPredicting wind speed v of wind farm at moment a3、v4(ii) a Adding other factors such as wind direction, temperature, air pressure, humidity and the like of the wind power plant at the moment a and t, establishing a multi-dimensional prediction model, and obtaining wind power P3 and P of the wind power plant at the moment a and t4。
Specifically, the building process of the combined weighted wind power prediction model is as follows:
weighting according to the contribution degree of different prediction models to the predicted value, and assuming that n stroke power prediction models exist, the predicted powers are respectively P1、P2、…、PnThe corresponding weight coefficient is beta1、β2、…、βnThe expression of the combined weighting model is:
Figure BDA0002750964280000131
the error of wind power in each wind power prediction model is epsilon1、ε2、…、εnCorresponding variance is ζ1、ζ2、…、ζnThe variance of the combined weighting model is:
Figure BDA0002750964280000132
in the formula, Cov (. beta.)iεi,βjεj) The model error is predicted for each wind power corresponding to the covariance of each other.
The combined weighting model takes the minimized forecasting variance sum as an objective function when carrying out weight value distribution, and the following formula is satisfied:
Figure BDA0002750964280000141
and solving the minimum value of the prediction error variance through a Lagrange method, thus solving each weight coefficient in the combined weighted model and determining the combined weighted wind power prediction model.
In the process of solving each weight coefficient, introducing a Lagrange multiplier:
Figure BDA0002750964280000142
respectively to betaiAnd lambda to obtain partial derivative, making its partial derivative be zero, obtaining weight coefficient beta1、β2、…、βn。
In different seasons, the prediction results of different prediction methods are shown in fig. 4, where fig. 4a shows the predicted power and error in spring, fig. 4b shows the predicted power and error in summer, fig. 4c shows the predicted power and error in autumn, and fig. 4d shows the predicted power and error in winter. Wind farm b1、b2Is a wind farm adjacent to wind farm a.
Under different season scenes of spring, summer, autumn and winter, compared with the situation before wind speed correction, the predicted power value after wind speed correction is closer to the actual value, and the prediction precision is improved. The accuracy of the wind power predicted value under each scene obtained based on the spatial correlation model is superior to the NWP wind power predicted value before wind speed correction. It can be seen from the figure that the wind power in each season is not in a relatively stable state, and has relatively large fluctuation, wherein the wind speed in spring is the largest, and the wind power value thereof is also the largest, so that the absolute error value of the wind power is also the largest, and then in winter and autumn, the wind speed in summer is smaller, and the error value is also correspondingly smaller than that in other seasons.
The combined weighted model is used for wind power prediction, the predicted value is closer to the actual value, the prediction accuracy is higher than that of other methods, the prediction error of each season is obviously reduced, and the provided combined weighted wind power prediction model is reasonable. The prediction error evaluation indexes of the above models are shown in table 2.
As can be seen from the prediction error evaluation index table in Table 2, the prediction accuracy obtained by the combined weighted prediction model is obviously higher than that of a single model, for example, the three indexes of NRMSE, MAPE and NMAE are respectively reduced by 0.33078-1.5919 MW, 0.0287-0.12918 and 0.17644-2.69465 MW in spring, 0.01102-0.15111 MW in summer, 0.0494-0.21913 and 0.01448-0.28154 MW in autumn, 0.31536-0.76779 MW, 0.03481-0.2738 and 0.35463-1.14045 MW in autumn, and 0.46431-1.53667 MW, 0.07372-0.16959 and 1.15365-2.72491 MW in winter.
TABLE 2 wind power prediction error evaluation indexes of different models
Figure BDA0002750964280000151
Defining a calculation formula of the prediction accuracy improvement of the combined weighting model as
Figure BDA0002750964280000152
In the formula, epsilonNWPRepresenting the predicted NRMSE error value, ε, after correction based on NWP errormixThe NRMSE error values representing the combined weighted prediction model show an improvement in prediction accuracy over the NWP-based prediction model of 37.49% in spring, 10.88% in summer, 31.88% in fall, 35.67% in winter, and an average improvement of 28.98% in each season. The applicability of the combined weighted prediction model is obviously superior to that of a single prediction model, and the prediction accuracy of the wind power can be effectively improved while the prediction time scale is increased.
The above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, but all changes that can be made by applying the principles of the present invention and performing non-inventive work on the basis of the principles shall fall within the scope of the present invention.

Claims (10)

1. A wind power combined prediction method considering spatial correlation and correcting numerical weather forecast is characterized by comprising the following steps:
s100, reading historical data of a wind power plant a and data of various meteorological factors in a numerical weather forecast, wherein the meteorological factors at least comprise wind speed, wind direction, temperature, air pressure and relative humidity;
s200, screening out meteorological factors with strong correlation with wind power from the meteorological factors through an automatic correlation judgment algorithm, establishing a prediction model based on a Gaussian process by taking data of the meteorological factors as input variables, and obtaining a wind power prediction value P1；
S300, establishing a wind speed correction model according to corresponding known wind speed data, taking the wind speed data corrected by the wind speed correction model as the input of a prediction model based on the Gaussian process, and then performing wind power prediction to obtain a wind power prediction value P2；
S400, aiming at m wind power plants b adjacent to the wind power plant amPerforming spatial correlation analysis, and respectively calculating each wind power plant bmPearson correlation coefficient of wind power plant a and corresponding delay time delta tmAnd thus through the wind farm bmThe wind speed of the wind power plant a at the moment t is predicted according to the historical wind speed, a multi-dimensional prediction model is established by combining other meteorological factor data except the wind speed of the wind power plant a at the moment t, and a wind power prediction value P of the wind power plant a at the moment t is obtained2+m；
S500, based on P2、P2+mEstablishing a combined model, solving the weight coefficient of each prediction model in the combined model by using a Pearson correlation coefficient and a Lagrange multiplier method, and establishing a combined weighted wind power prediction model;
s600, predicting the wind power of the wind power plant a by using the combined weighted wind power prediction model, and outputting a wind power prediction value P of the wind power plant a.
2. The combined wind power prediction method taking into account spatial correlation and modified numerical weather forecast of claim 1, further comprising:
step S700, respectively calculating the base P1、P2、P2+mAnd the three error evaluation indexes of the standard root mean square error NRMSE, the average absolute percentage error MAPE and the normalized average absolute error NMAE of the model P are compared and analyzed, and the wind power predicted value with the minimum error precision is used as the final wind power forecast of the wind power plant aAnd outputting a measured value.
3. The combined wind power prediction method considering spatial correlation and modified numerical weather forecast according to claim 2, wherein the prediction model establishing process based on the gaussian process in step S200 is as follows:
establishing a gaussian expression, and outputting a function g (x) ═ to-be-predicted function f (x) + gaussian white noise e (x), wherein the output function g (x) ═ to-be-predicted function f (x) + gaussian white noise e (x) is expressed as: g (X) N (m (X), K (X, X) + σn 2I) Where m (x) is a mean function, σnIs the unit variance of white Gaussian noise, I is an n-dimensional unit matrix, and K (X, X) is a covariance matrix containing an element Kij＝k(xi,xj)，i,j＝1,2,...,n；
Forming a training set d ═ { X, y } of the Gaussian regression prediction process according to historical data of the wind farm a, wherein the input set X ═ X ═ y }i∈RDI 1.. n, an input vector x of D dimension is formed by data of various meteorological factors, and an output set y ═ y ·iForming an i | (1, 2.·, n) | by a corresponding wind power observation value, and determining a prediction parameter in the Gaussian expression through the training set;
output y and predicted value f according to training set*Joint prior distribution of (c):
Figure FDA0002750964270000021
determining a mean of results for the Gaussian process based prediction model
Figure FDA0002750964270000022
Sum variance Σ*：
Figure FDA0002750964270000023
Figure FDA0002750964270000024
In the formula, x*Representing a new input value, k*Is k (X, X)*)＝k(x*,X)T＝[k(x1,x*),...,k(xn,x*)]For simplification of (2), X and X are indicatediN x 1 order covariance matrix between, k (x)*,x*) The covariance of the new input value x itself.
4. The combined wind power prediction method taking into account spatial correlation and modified numerical weather forecast according to claim 3, characterized in that the covariance matrix K (X, X) selects as a kernel function one of the following functions:
1) squared exponential covariance function:
Figure FDA0002750964270000025
2) rational quadratic covariance function:
Figure FDA0002750964270000031
3) matern covariance function, v 3/2:
Figure FDA0002750964270000032
4) matern covariance function, v 5/2:
Figure FDA0002750964270000033
in the formula, σfIs the signal covariance and l is the length scale parameter.
5. The combined wind power prediction method considering spatial correlation and modified numerical weather forecast of claim 4, wherein the learning of hyper-parameters in Gaussian process is estimated by maximum likelihoodThe calculation method comprises the following steps:
Figure FDA0002750964270000034
in the formula, f*The output power value in the wind power prediction is taken as K, and K is a kernel function of a Gaussian process;
determining the length scale parameter matched with each meteorological factor parameter value in the Gaussian process through an automatic correlation judgment algorithm, thereby judging the meteorological factor with strong correlation with wind power:
Figure FDA0002750964270000035
in this equation, D is the dimension of the input vector x, the number of types of meteorological factors, b is a deviation, and all superparameters are included in the vector θ ═ θ (θ)0,L,b)TWherein L represents L ═ L1,......,lDParameter in { C }, hyperparameter { l }1,......,lDIs used to implement auto-correlation decisions, with liThe length is shortened, and the function is corresponding to the input variable xiThe more sensitive, the stronger the correlation of the input variables.
6. The wind power combined prediction method considering spatial correlation and correcting numerical weather forecast according to any one of claims 1 to 5, wherein in step S300, a wind speed correction model expression is constructed according to wind speed prediction data in the numerical weather forecast and corresponding actual wind speed data in historical data of a wind farm, and a wind speed correction model is constructed by screening out meteorological factor data having the largest influence on wind speed from all meteorological factors in the numerical weather forecast through an automatic correlation determination algorithm as input of the wind speed correction model expression, taking the wind speed prediction data as input, and taking the actual wind speed data as output.
7. The combined wind power prediction method taking into account spatial correlation and modified numerical weather forecast of claim 6In step S400, according to the wind farm a and the adjacent wind farm bmObtaining the wind speed sequences of the wind power field a and the adjacent wind power fields, and using the Pearson correlation coefficient etavThe correlation size between different wind power plant wind speed sequences is quantitatively analyzed:
Figure FDA0002750964270000041
in the formula, N is the number of wind speed correlation analysis samples, va、vbiRespectively wind farm a and adjacent wind farm bm(i ═ 1.. said., m) to obtain wind speed observations of wind farm a and adjacent wind farm bmCorresponding delay time deltat therebetweenmAnd therefore, the wind speed of the wind power plant a is predicted by using the wind speed data of the adjacent wind power plants.
8. The combined wind power prediction method considering spatial correlation and modified numerical weather forecast of claim 7, wherein in step S400, the Pearson correlation coefficient η is selectedvThe delay time corresponding to the maximum point of (a) is taken as the time difference between the two wind farms.
9. The combined wind power prediction method considering spatial correlation and modified numerical weather forecast according to claim 8, wherein in step S500, weighting is performed according to the contribution degree of different prediction models to the predicted value, and an expression of the combined weighting model is established:
Figure FDA0002750964270000042
in the formula, the predicted power of the n wind power prediction models is PnThe corresponding weight coefficient is betan；
The error of wind power in each wind power prediction model is epsilonnCorresponding variance is ζnThe variance of the combined weighting model is:
Figure FDA0002750964270000043
in the formula, Cov (. beta.)iεi,βjεj) Predicting the covariance of model errors for each wind power;
the weight distribution is performed by taking the minimum prediction variance sum as an objective function, and the following formula is satisfied:
Figure FDA0002750964270000051
and solving the minimum value of the prediction error variance through a Lagrange method, thus solving each weight coefficient in the combined weighted model and determining the combined weighted wind power prediction model.
10. The method of claim 9, wherein a lagrangian multiplier is introduced in the process of calculating each weight coefficient:
Figure FDA0002750964270000052
respectively to betaiAnd lambda to obtain partial derivative, making its partial derivative be zero, obtaining weight coefficient beta1、β2、…、βn。
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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113297791A (en) * 2021-05-18 2021-08-24 四川大川云能科技有限公司 Wind power combined prediction method based on improved DBN
CN113516320A (en) * 2021-09-14 2021-10-19 国能日新科技股份有限公司 Wind speed correction and predicted wind speed optimization method and device based on multi-objective genetic algorithm
US20210341646A1 (en) * 2020-12-23 2021-11-04 Beijing Baidu Netcom Science And Technology Co., Ltd. Weather parameter prediction model training method, weather parameter prediction method, electronic device and storage medium
CN113609758A (en) * 2021-07-19 2021-11-05 电子科技大学 Power prediction method for newly-built wind power plant
CN113847214A (en) * 2021-09-15 2021-12-28 国电投河南新能源有限公司 Icing detection method for large wind generating set
CN114971005A (en) * 2022-05-20 2022-08-30 厦门大学 Bay water temperature combination prediction method based on LSTM and differential regression model dynamic weighting
CN116187540A (en) * 2023-01-03 2023-05-30 国网江西省电力有限公司电力科学研究院 Wind power station ultra-short-term power prediction method based on space-time deviation correction
CN116992222A (en) * 2023-09-27 2023-11-03 长江三峡集团实业发展(北京)有限公司 Method, device, equipment and medium for migration learning of wind element correction model

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2015070480A1 (en) * 2013-11-14 2015-05-21 国家电网公司 Method for managing energy of battery energy storage power station based on wind power prediction
CN106971032A (en) * 2017-03-16 2017-07-21 天津大学 Wind speed forecasting method based on nonparametric probability and numerical weather forecast
CN108898251A (en) * 2018-06-29 2018-11-27 上海电力学院 Consider the marine wind electric field power forecasting method of meteorological similitude and power swing
CN110737975A (en) * 2019-10-08 2020-01-31 国家电网有限公司 Wind power plant wind speed and power prediction and abnormality correction method based on empirical mode decomposition and autoregressive model

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2015070480A1 (en) * 2013-11-14 2015-05-21 国家电网公司 Method for managing energy of battery energy storage power station based on wind power prediction
CN106971032A (en) * 2017-03-16 2017-07-21 天津大学 Wind speed forecasting method based on nonparametric probability and numerical weather forecast
CN108898251A (en) * 2018-06-29 2018-11-27 上海电力学院 Consider the marine wind electric field power forecasting method of meteorological similitude and power swing
CN110737975A (en) * 2019-10-08 2020-01-31 国家电网有限公司 Wind power plant wind speed and power prediction and abnormality correction method based on empirical mode decomposition and autoregressive model

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
NIYA CHEN等: "Short-Term Wind Power Forecasting Using Gaussian Processes" *

Cited By (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20210341646A1 (en) * 2020-12-23 2021-11-04 Beijing Baidu Netcom Science And Technology Co., Ltd. Weather parameter prediction model training method, weather parameter prediction method, electronic device and storage medium
CN113297791A (en) * 2021-05-18 2021-08-24 四川大川云能科技有限公司 Wind power combined prediction method based on improved DBN
CN113297791B (en) * 2021-05-18 2024-02-06 四川大川云能科技有限公司 Wind power combination prediction method based on improved DBN
CN113609758A (en) * 2021-07-19 2021-11-05 电子科技大学 Power prediction method for newly-built wind power plant
CN113609758B (en) * 2021-07-19 2023-06-02 电子科技大学 Power prediction method for newly-built wind power plant
CN113516320A (en) * 2021-09-14 2021-10-19 国能日新科技股份有限公司 Wind speed correction and predicted wind speed optimization method and device based on multi-objective genetic algorithm
CN113847214B (en) * 2021-09-15 2023-12-29 国电投河南新能源有限公司 Icing detection method for large wind generating set
CN113847214A (en) * 2021-09-15 2021-12-28 国电投河南新能源有限公司 Icing detection method for large wind generating set
CN114971005A (en) * 2022-05-20 2022-08-30 厦门大学 Bay water temperature combination prediction method based on LSTM and differential regression model dynamic weighting
CN114971005B (en) * 2022-05-20 2024-06-07 厦门大学 Bay water temperature combination prediction method based on LSTM and differential regression model dynamic weighting
CN116187540A (en) * 2023-01-03 2023-05-30 国网江西省电力有限公司电力科学研究院 Wind power station ultra-short-term power prediction method based on space-time deviation correction
CN116187540B (en) * 2023-01-03 2023-09-12 国网江西省电力有限公司电力科学研究院 Wind power station ultra-short-term power prediction method based on space-time deviation correction
CN116992222B (en) * 2023-09-27 2024-01-26 长江三峡集团实业发展(北京)有限公司 Method, device, equipment and medium for migration learning of wind element correction model
CN116992222A (en) * 2023-09-27 2023-11-03 长江三峡集团实业发展(北京)有限公司 Method, device, equipment and medium for migration learning of wind element correction model

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