CN113094891A - Multi-wind-farm power modeling, PDF (Portable document Format) construction and prediction scene generation method and system - Google Patents

Multi-wind-farm power modeling, PDF (Portable document Format) construction and prediction scene generation method and system Download PDF

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CN113094891A
CN113094891A CN202110358831.6A CN202110358831A CN113094891A CN 113094891 A CN113094891 A CN 113094891A CN 202110358831 A CN202110358831 A CN 202110358831A CN 113094891 A CN113094891 A CN 113094891A
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涂青宇
苗世洪
陈霞
姚福星
殷浩然
张迪
杨炜晨
韩佶
尹斌鑫
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Huazhong University of Science and Technology
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Abstract

The invention discloses a method and a system for modeling power of multiple wind power plants, building PDF (Portable document Format), and generating a prediction scene, and belongs to the field of scene prediction of wind power. The method establishes a probability distribution model of the prediction error, and adds the probability distribution of the prediction error and the point prediction power of each wind power plant power to be used as an edge distribution model of each wind power plant power. And calculating the cumulative probability of the power data of each wind power plant as input data of the time-varying R vine Copula model. The ARIMA-GARCH-t model and the time-varying R vine Copula model are combined, so that a joint probability distribution model of the high-dimensional wind power data is established. And fitting model parameters based on the historical power data of each wind power plant, and providing a multi-wind-plant power day-ahead prediction scene generation method by combining the predicted power data of the future day of each wind power plant. The day-ahead prediction scene generation model established by the invention can better fit the time-space correlation characteristics of the power of the multiple wind power plants, and improves the accuracy and the effectiveness of the day-ahead prediction scene of the power of the multiple wind power plants.

Description

Multi-wind-farm power modeling, PDF (Portable document Format) construction and prediction scene generation method and system
Technical Field
The invention belongs to the field of scene prediction of wind power, and particularly relates to a method and a system for multi-wind power plant power modeling, PDF (Portable document Format) construction and scene prediction generation prediction.
Background
In recent years, wind power generation has been receiving attention to clean energy supply and reduce carbonization. However, at present, accurate prediction of wind power is still difficult to achieve, and under the background that wind power grid-connected capacity is rapidly increased, the problem of uncertainty of a power supply side caused by wind power prediction errors is increasingly prominent. From the viewpoint of operation of the power system, the reliability of the dispatching plan is affected, so that not only can a serious wind abandoning problem be caused, but also potential risks are brought to safe and stable operation of the power grid. Therefore, a prediction method capable of reflecting the uncertainty of the wind power is urgently needed.
In order to solve the above problems, researchers have conducted intensive research on a scene prediction method of wind power. The scene prediction is a main method for wind power probability prediction, and the basic principle is that a probability distribution model of wind power or prediction error is established through a statistical method, and then a prediction scene is generated through sampling. A plurality of scene prediction methods are proposed in the prior research, part of documents assume that prediction errors obey Beta distribution or t-location-scale distribution, and part of the research establishes a probability distribution model of the prediction errors based on a non-parameter estimation method, wherein the probability distribution model comprises a quantile regression model, an empirical cumulative probability distribution model, a nuclear density estimation model and the like.
The research aims to use long-term frequency distribution of wind power or prediction errors as probability distribution, but the current research starts to focus on the time sequence characteristic of the wind power in consideration of the autocorrelation characteristic of the wind power in a period of time, and further provides a wind power prediction scene generation method based on the time sequence characteristic. Part of documents simulate the time-varying process of wind power generation by using a Markov method; some scholars propose Auto Regression (AR) models; on the basis, the subsequent research further establishes an autoregressive-moving average (ARMA) model. The results of the above studies indicate that, taking into account the wind power time series characteristics, the irregular fluctuations and noise components in the generated prediction scene will be significantly reduced.
On the other hand, with the expansion of the wind power construction scale, a prediction scene generation method suitable for a multi-wind power plant needs to be further provided. However, when the traditional single wind farm prediction scene generation method is directly applied to a plurality of wind farms, the method has limitations, and the key problem is that the time-space correlation characteristics of the power of the plurality of wind farms need to be fully described while the advantages of the original method are kept. A better approach to this problem is to use the Copula model. The Copula model consists of two parts: the edge distribution model and the high-dimensional data are of a dependency structure, wherein the edge distribution model is an independent probability distribution model of a single-dimensional wind power sequence and can be directly applied to part of existing research results for a single wind power plant, so that good continuity is guaranteed; and the dependency structure fits the spatio-temporal correlation features between the multiple wind farm powers. Some documents model joint probability distribution of high-dimensional wind power data based on Gauss Copula models, follow-up research further provides C rattan and D rattan Copula models, and compared with the Gauss Copula models, the topological structure has higher flexibility, so that the accuracy of the models is improved.
Z.Wang and W.S.Wang, et al, in the paper "forcecast scenes of Regional farm Based on regulated Vine video Copula", adopt a static R Vine Copula model, which takes a KDE model as an edge distribution model, takes a static binary Copula model as a basic unit, generates an R Vine topological structure Based on a maximum rotation tree algorithm, establishes a static R Vine Copula model, and provides a day-ahead prediction scene generation method of multi-Wind-field power Based on the model.
However, the above method still has the following disadvantages: 1) an edge distribution model is established based on a Kernel Density Estimation (KDE) model, and the autocorrelation of the wind power in a time dimension, namely the time correlation, cannot be fitted. 2) A basic binary Copula model is adopted in the static R rattan Copula model as a part (basic unit) of the model, the dependency structure of any two wind power plants cannot be accurately fitted, and the time-varying characteristic of the power dependency of any two wind power plants is ignored, so that the spatial dependency of the power of a plurality of wind power plants cannot be accurately fitted. 3) Based on the scene generation method provided by the KDE model and the static R rattan Copula model, the time-space correlation of the generated scene is relatively larger in deviation with the time-space correlation of the actual wind power plant power.
Disclosure of Invention
Aiming at the defect that the existing model in the prior art cannot fully describe the time-space correlation characteristics of the power of multiple wind power plants and the improvement requirement, the invention provides a method and a system method for modeling the power of the multiple wind power plants, constructing PDF (Portable document Format), and generating a predicted scene, and aims to improve the accuracy of the predicted scene of the power of the multiple wind power plants in the future.
To achieve the above object, according to a first aspect of the present invention, there is provided a method for modeling a power-dependent structure of a multiple wind farm, the method comprising the steps of:
s1, respectively calculating the cumulative probability of each wind power plant power according to a wind power plant power edge probability distribution function to obtain a cumulative probability sequence of each wind power plant power;
s2, inputting the cumulative probability sequences of the power of each wind power plant to a time-varying R rattan Copula model together to obtain the time-varying R rattan Copula model of the power of the multi-wind power plant;
the time-varying R vine Copula model is constructed in the following way:
(1) establishing a pair Copula model based on a mixed time-varying binary Copula model, wherein the pair Copula model is used for representing power-dependent structural information of every two wind power plants, and the expression of the pair Copula model is as follows:
Figure BDA0002990572060000031
wherein u, v represent input data of the pair Copula model; cMixRepresenting a mixed time-varying binary Copula model; ciRepresentation selection for composition CMixThe binary Copula model of (a); omegaiIs represented by CiThe weight coefficient of (a);
Figure BDA0002990572060000032
and
Figure BDA0002990572060000033
respectively represent CMixAnd CiThe method comprises the steps that a parameter set of a model is formed, and n represents the number of binary Copula models participating in building of a mixed time-varying binary Copula model;
(2) based on the R rattan Copula model structure generation method, all mixed time-varying binary Copula models are expanded into a multi-wind-farm power-dependent structure model.
Preferably, the binary Copula model is a t Copula model, a Clayton Copula model, or a Gumbel Copula model.
Preferably, the parameters of the mixed time-varying binary Copula model are estimated by using a maximum likelihood estimation method, and the expression is as follows:
Figure BDA0002990572060000041
wherein the content of the first and second substances,
Figure BDA0002990572060000042
representing a hybrid time-varying binary Copula model CMixThe result of the parameter estimation of (2); argmax represents a function of each parameter value when the maximum is found.
Preferably, in step (2), the method for generating the R rattan structure is as follows:
step 1: taking the cumulative probability sequence of each wind power plant power as input data of a first layer tree structure in R vine, and fitting a pair Copula of any two columns of input data by using a mixed time-varying binary Copula model;
step 2: evaluating the accuracy of each pair Copula in the step 1 by using an AIC index;
and step 3: on the basis of ensuring no ring structure, determining a first layer tree structure by taking the minimum sum of AIC index values of all PairCopula models in the layer tree structure as a target, and initializing k to be 1;
and 4, step 4: in the case where the kth level "tree" structure has been generated, the input data of the (k +1) th level "tree" structure is calculated as follows:
Figure BDA0002990572060000043
wherein, Fβ(e)|γ(e)And Fα(e)|γ(e)Two columns of input data each representing a kth level "tree" structure; cα(e)，β(e)|γ(e)Representing F-base in the kth level 'tree' structureβ(e)|γ(e)And Fα(e)|γ(e)Fitting a pair Copula function; fα(e)|{γ(e)，β(e)}And Fβ(e)|{γ(e)，α(e)}Respectively representing possible input data of a (k +1) th layer 'tree' structure;
Figure BDA0002990572060000046
representing the derivation of a partial derivative;
and 5: when the kth level "tree" structure topology has been generated, enumerating all possible topologies for the (k +1) th level "tree" structure, the valid topology will satisfy the following constraints:
Figure BDA0002990572060000044
wherein e isa，ebRepresents two "edges", i.e., the pair Copula function;
Figure BDA0002990572060000045
represents the set of all "edges" in the (k +1) th level "tree" structure; # denotes the collective potential calculation;
step 6: fitting a pair Copula function by using a mixed time-varying binary Copula model for all possible topologies of the (k +1) th layer tree structure in the step 5;
and 7: determining the topology of the (k +1) th layer tree structure by taking the minimum sum of AIC index values of all pair Copula models in the (k +1) th layer tree structure as a target, wherein k is k + 1;
and 8: repeating steps 4 to 7 until the topology of all "tree" structures is generated, which together constitute the R rattan structure of the time-varying R rattan Copula model.
To achieve the above object, according to a second aspect of the present invention, there is provided a method for constructing a joint probability density function of multiple wind farm powers, the method comprising the steps of:
s1, respectively determining power edge probability distribution functions of each wind power plant based on historical power data of each wind power plant;
s2, on the basis of determining the power edge probability distribution function of each wind power plant, constructing a joint probability density function of the power of the multi-wind power plant by adopting a time-varying R vine Copula model;
the time-varying R vine Copula model is modeled by a method as described in the first aspect.
Preferably, in step S1, for each wind farm, the following operations are performed:
(1) establishing a probability density function of the power prediction error of the wind power plant based on an ARIMA-GARCH-t model;
(2) and adding the probability density function of the wind power plant power prediction error and the point prediction power of the wind power plant to obtain a sum, wherein the sum is used as the probability density function of the wind power plant power.
Has the advantages that: according to the method, the edge distribution model of each wind power plant power is established based on the ARIMA-GARCH-t model, so that the autocorrelation of the wind power in the time dimension can be reflected, namely, the time correlation can be fitted more accurately.
To achieve the above object, according to a third aspect of the present invention, there is provided a method for generating a multiple wind farm power day-ahead prediction scene, the method comprising the steps of:
the method comprises the following steps: generate an [ N ]sc×Npt×Nwf]All elements in the random matrix obey a uniform distribution U (0, 1), where NscPredicting the number of scenes for a given number of days ahead, NptIndicating the number of predicted power points, N, contained in each of the specified sceneswfRepresenting the number of wind farms;
step two: decomposing the combined probability density function of the multiple wind power plants into a form of multiplying a Pair Copula density function and an edge distribution probability density function, wherein the combined probability density function of the multiple wind power plants is generated by adopting the method in the second aspect;
step three: the following operations are performed for each scene until N is generatedscA complete day-ahead power prediction scenario;
a. assigning the values in the random matrix Rnd to the partial input data values under the structure of each level "tree" in the time-varying R rattan Copula model as follows:
Figure BDA0002990572060000061
wherein the content of the first and second substances,
Figure BDA0002990572060000062
inputting data for a part under each hierarchy 'tree' structure;
Figure BDA0002990572060000063
representing each wind farm power; i.e. iscRepresents a scene number; j is a function ofptRepresenting a data point number;
b: input data of two adjacent layers of tree structures in time-varying R vine Copula model
Figure BDA0002990572060000064
And
Figure BDA0002990572060000065
with certain data values, the pair Copula function associated with the data values is calculated according to the following formula
Figure BDA0002990572060000066
The value:
Figure BDA0002990572060000067
will be known
Figure BDA0002990572060000068
Value as a function
Figure BDA0002990572060000069
Is input with one dimension of data, will
Figure BDA00029905720600000610
Value and calculated function
Figure BDA00029905720600000611
Value substitution function
Figure BDA00029905720600000612
In and out of the function
Figure BDA00029905720600000613
Input data of another dimension, gamma denotes
Figure BDA00029905720600000614
The condition set of (1);
c: repeating the step b until the jthptThe cumulative probability value corresponding to each wind power plant power under the data point is obtained by all calculation and is recorded as
Figure BDA00029905720600000615
d: to be provided with
Figure BDA00029905720600000616
As input data, baseObtaining the jth function of the inverse function of the prediction error accumulation probability function of each wind power plantptThe expression of the sampling result of the prediction error of each wind power plant under the data points is as follows:
Figure BDA00029905720600000617
wherein the content of the first and second substances,
Figure BDA00029905720600000618
respectively represent the k-thwfWind farm at jthptThe prediction error sampling result, the accumulative probability calculation result and the inverse function of the prediction error accumulative probability function of each data point;
e: d, preprocessing the sampling result of the prediction error of each wind power plant obtained in the step d, so that the sampling result is between the minimum value and the maximum value of the prediction error in the historical data used for fitting the model;
f: adding the prediction error sampling result and the point predicted value to obtain a prediction scene value of each wind power plant power:
Figure BDA0002990572060000071
wherein the content of the first and second substances,
Figure BDA0002990572060000072
respectively represent the k-thwfWind farm at jthptPredicting scene values and point predicted values by the power of the data points;
g: j is the j th wind power plant calculated in the step fptCalculating the (j) th predicted scene value of the data pointpt+1) probability distribution of wind farm power and prediction error for each data point, jpt+1) parameter values of all pair Copula in the time-varying R rattan Copula model at the data points;
h: and repeating the steps a to g until a complete day-ahead power prediction scene is generated for all the wind power plants.
To achieve the above object, according to a fourth aspect of the present invention, there is provided a multiple wind farm power day-ahead prediction scene generation system, comprising: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is configured to read executable instructions stored in the computer-readable storage medium, and execute the method for generating the multiple wind farm power day-ahead prediction scene according to the third aspect.
Generally, by the above technical solution conceived by the present invention, the following beneficial effects can be obtained:
(1) the invention provides a modeling method for a power-dependent structure of a multi-wind-power-field, which is characterized in that a mixed time-varying binary Copula model is used as a pair Copula model, high dimensionality of the model is realized based on an R rattan structure generation method, and a time-varying R rattan Copula model with high dimensionality is established. The Copula model has a good application effect in the aspect of depicting the complex nonlinear correlation characteristics of the wind power, and by establishing the mixed time-varying binary Copula model as the pair Copula model, the defects of symmetry and relatively fixed sensitivity of the upper tail and the lower tail of the traditional binary Copula model are overcome, and the dependency structure of any two wind power plants can be more flexibly and accurately depicted. Meanwhile, parameters of the hybrid time-varying binary Copula model are calculated by introducing time-varying correlation coefficient calculation models such as DCC and pattern, and time-varying characteristics of the power spatial correlation of the multi-wind power plant can be reflected. On the basis, the model is high-dimensional based on the R rattan structure, pre-assumption on the correlation of the power of multiple wind power plants is not needed, and the differentiated high-dimensional Copula model structure topology can be flexibly fitted to the wind power plants distributed in different geographies. Therefore, the method is based on the method for establishing the dependency structure model of the power of the multiple wind power plants, and the spatial correlation characteristics of the power of the multiple wind power plants can be fitted more accurately.
(2) The invention provides a method for constructing a combined probability density function of multiple wind power plants. In the aspect of an edge distribution model, an ARIMA model and a GARCH-t model are combined, a cumulative probability function model of prediction errors is established, the model and the point prediction power of each wind power plant are added, and the edge distribution model of the power of each wind power plant is calculated. The ARIMA model and the GARCH-t model are both models based on time series characteristics, the probability distribution of subsequent data points is fitted through the size and the change trend of data in a previous period of time, the GARCH-t model further reflects the characteristic of the conditional variance of the data, and the defect that the residual flexibility of the traditional GARCH model is insufficient due to Gauss distribution fitting is overcome, so that the ARIMA-GARCH-t model is based on the ARIMA-GARCH-t model to build an edge distribution model, and the autocorrelation characteristic of the wind power in the time dimension, namely the time correlation, can be favorably described. On the other hand, as can be seen from (1), establishing a dependency structure model of a plurality of wind farm powers based on a time-varying R rattan Copula model helps to reflect "spatial correlation". Therefore, the RIMA-GARCH-t model and the time-varying R rattan Copula model are combined to establish a combined probability density function model of the power of the multi-wind power plant, the characteristics of time-space correlation can be considered, and the accuracy is higher.
(3) The invention provides a method for generating a day-ahead prediction scene of power of a multi-wind farm, which is used for generating the day-ahead prediction scene of the power of the multi-wind farm on the basis of a multi-wind farm power combined probability density function model established on the basis of a time-varying R vine Copula model. The basis of scene generation is "sampling", which is essentially the inverse of the above model. Because the edge distribution model and the Copula model of the adopted joint probability distribution model are time-varying models, the traditional sampling method of the static R rattan Copula model is not applicable any more, and a sampling and prediction scene generation method with higher applicability needs to be provided. On the other hand, the time-varying R rattan Copula model fits the time-space correlation characteristics of the multi-wind-farm power, so that the generated scene has the time dimension autocorrelation characteristics and the space dimension cross correlation characteristics which are more similar to the actually-measured wind power curve, and the accuracy and the effectiveness of the multi-wind-farm power day-ahead scene prediction are improved.
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FIG. 1 is a schematic diagram of the inventive concept provided by the present invention;
FIG. 2 is a time-varying R rattan Copula model modeling flowchart provided by the present invention;
FIG. 3 is a flow chart of ARIMA-GARCH-t model-based wind farm power edge distribution modeling provided by the invention;
FIG. 4 is a flow chart of a method for generating a multi-wind farm power day-ahead predictive scene provided by the present invention;
FIG. 5 is a multi-farm total power prediction scenario generated by the different models provided by the present invention, (a) a prediction scenario generated for the proposed model (model 1); (b) a prediction scenario generated for the independent ARIMA-GARCH-t model (model 2); (c) a prediction scenario generated for a static D vine Copula model (model 3); (d) a prediction scenario generated for the independent KDE model (model 4);
FIG. 6 is a comparison of ACF indicators for a multi-wind farm total power prediction scenario generated by different models provided by the present invention, wherein (a) the ACF indicators for the prediction scenario for the proposed model (model 1); (b) predicting ACF indicators for the scene for the independent ARIMA-GARCH-t model (model 2); (c) predicting ACF indexes of scenes for a static D rattan Copula model (model 3); (d) predicting ACF index of the scene for the independent KDE model (model 4);
FIG. 7 is a comparison of CCF indices for 2 wind farm power prediction scenarios generated by different models provided by the present invention, where (a) the CCF indices for the proposed model (model 1) prediction scenario; (b) predicting a CCF index for the scene for the independent ARIMA-GARCH-t model (model 2); (c) predicting the CCF index of the scene for a static D rattan Copula model (model 3); (d) the CCF index of the scene is predicted for the independent KDE model (model 4).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Furthermore, the technical features mentioned in the embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the inventive concept of the present invention is as follows: 1. and expressing the power of each wind power plant as a point prediction power and prediction error sum form, establishing a probability distribution model of the prediction error based on an ARIMA-GARCH-t model, and adding the probability distribution of the prediction error and the point prediction power of the power of each wind power plant to obtain an edge distribution model of the power of each wind power plant. And calculating the cumulative probability of the power data of each wind power plant as input data of the time-varying R vine Copula model. 2. A time-varying R vine Copula model is established in two steps: firstly, establishing a pair Copula model based on a mixed time-varying binary Copula model, and secondly, expanding the mixed time-varying binary Copula model into a high-dimensional model based on an R vine Copula model topological structure generation method. 3. A combined probability distribution model of high-dimensional wind power data is established by combining an ARIMA-GARCH-t model and a time-varying R rattan Copula model (abbreviated as a TRVMC model). On the basis of fitting model parameters of historical power data of each wind power plant, and combining predicted power data of points of each wind power plant in the future day, a multi-wind-plant power day-ahead prediction scene generation method is provided. The multi-wind-farm-power day-ahead prediction scene generation model established by the invention can better fit the time-space correlation characteristics of the multi-wind-farm power, and the accuracy and the effectiveness of the multi-wind-farm-power day-ahead prediction scene are improved.
The invention provides a modeling method for a power-dependent structure of multiple wind power plants, which comprises the following steps:
and S1, respectively calculating the cumulative probability of the power of each wind power plant according to the power marginal probability distribution function of the wind power plant to obtain a cumulative probability sequence of the power of each wind power plant.
And converting the original wind power data into a uniform sequence taking [0, 1] as a boundary by calculating the cumulative probability, wherein the converted sequence is used as input data of a Copula model.
And S2, inputting the cumulative probability sequences of the power of each wind power plant to a time-varying R rattan Copula model together to obtain the time-varying R rattan Copula model of the power of the multi-wind power plant.
The definition of the R vine Copula model can be expressed as follows:
(1) r rattan Copula model (marked as M-dimensional data) established aiming at M-dimensional data
Figure BDA0002990572060000101
) Is composed of M layers of mutually nested Tree structures. The M-level tree structure is respectively marked as
Figure BDA0002990572060000102
Where i is 1, 2, …, M represents a hierarchy of a "tree" structure, and so
Figure BDA0002990572060000103
(2) Each layer of 'tree' structure
Figure BDA0002990572060000104
The node (edge) set is composed of two parts, namely a node set and an edge set which are respectively marked as
Figure BDA0002990572060000105
And
Figure BDA0002990572060000106
"node" means the input data of the "tree" structure, and "edge" means the joint probability density function in the "tree" structure, which is fitted by a binary Copula function for 2-dimensional input data, is called pair Copula function.
(3) For the first level "tree" structure (i.e., i ═ 1), the "set of nodes" is computed from an edge distribution model, where the edge distribution model refers to an independent probability distribution model of the input data. For other levels of "tree" structures (i.e., i-2, …, M), the set of "edges" of the previous level of "tree" structure will correspond to the set of "nodes" in the next level of "tree" structure, i.e., M
Figure BDA0002990572060000111
The next level of "tree" structure thus has 1-dimensional less input data than the previous level of "tree" structure.
(4) The R rattan Copula model should satisfy the following constraints: any two "edges" under any "tree" structure share at most one "node".
"nodes" and "edges" are generally denoted as a combination of "condition sets" and "conditioned sets". Examples are as follows: for an "edge" e, it is assumed to be subordinate to the i-th level tree structure
Figure BDA0002990572060000112
a, b are two 'nodes' forming 'edge' e, satisfy
Figure BDA0002990572060000113
Then "edge" e can be written as e ═ α (e), β (e) | γ (e), where α (e) and β (e) are the conditioned set of "edge" e, and γ (e) is the conditioned set of "edge" e. Also, for "nodes" a, b, as defined by the PDF, it corresponds to the previous level of the "tree" structure
Figure BDA0002990572060000114
Figure BDA0002990572060000114
2 "sides" in (1) can be respectively marked as ea＝α(ea)，β(ea)|γ(ea) And eb＝α(eb)，β(eb)|γ(eb) Then, the relationship between the condition set and the conditioned set between the "nodes" a, b and the "edges" e is as follows:
γ(e)＝{α(ea)，β(ea)，γ(ea)}∩{α(eb)，β(eb)，γ(eb)}
{α(e)，β(e)}＝({α(ea)，β(ea)，γ(ea)}\γ(e))∩({α(eb)，β(eb)，γ(eb)}\γ(e))
based on the above formula, the pair Copula function corresponding to the "edge" e can be abbreviated as Cα(e)，β(e)|γ(e). "node" a, b represents the 2-dimensional input data of pair Copula, and is two conditional cumulative probability sequences, which can be abbreviated as Fα(e)|γ(e)And Fβ(e)|γ(e)。
On this basis, a joint Probability Density Function (PDF) corresponding to the M-dimensional data can be calculated as follows:
Figure BDA0002990572060000115
wherein x isiIs the ith column of input data;
Figure BDA0002990572060000116
is a collection of all input data, i.e.
Figure BDA0002990572060000117
fjntIs a collection of input data
Figure BDA0002990572060000118
The joint PDF of (1); f. ofiIs input data xiThe edge distribution model of (1);
Figure BDA0002990572060000121
represents the ith pair Copula function in the jth tree structure, Fα(e)|γ(e)And Fβ(e)|γ(e)Representing the corresponding input data.
For ease of description, the parts of the pair Copula function in parentheses are omitted from the subsequent discussion. Pair Copula is the basic unit of the R rattan Copula model, whose function is to fit a joint probability density function of two-dimensional data. And establishing a mixed time-varying binary Copula model as a pair Copula model.
As shown in fig. 2, the time-varying R vine Copula model is constructed by:
(1) establishing a pair Copula model based on a mixed time-varying binary Copula model, wherein the pair Copula model is used for representing power-dependent structural information of every two wind power plants, and the expression of the pair Copula model is as follows:
Figure BDA0002990572060000122
wherein u, v represent input data of the pair Copula model; cMixRepresenting a mixed time-varying binary Copula model; ciRepresentation selection for composition CMixThe binary Copula model of (a); omegaiIs represented by CiThe weight coefficient of (a);
Figure BDA0002990572060000123
and
Figure BDA0002990572060000124
respectively represent CMixAnd CiAnd n represents the number of the binary Copula models participating in constructing the mixed time-varying binary Copula model.
Preferably, the binary Copula model is a t Copula model, a Clayton Copula model, or a Gumbel Copula model.
The expressions are respectively as follows:
Figure BDA0002990572060000125
Figure BDA0002990572060000126
Figure BDA0002990572060000127
wherein, Ct、CCl、CGRespectively representing t Copula, Clayton Copula and Gumbel Copula models; rhot、k、
Figure BDA0002990572060000131
Representing model parameters;
Figure BDA0002990572060000132
representing the inverse of the t-distribution model.
On this basis, in order to fit the time-varying process of the correlation between the powers of the multiple wind farms, parameters of each basic binary Copula model need to be dynamically calculated, and the process is as follows:
(a) t-Copula model
For the t Copula model, the DCC (1, 1) model can be used to calculate model parameters, which are expressed as follows:
Figure BDA0002990572060000133
where ρ istRepresenting t Copula model parameters; alpha is alphaDAnd betaDIs a parameter of the DCC model;
Figure BDA0002990572060000134
is the covariance coefficient of the input data; epsilont-1Representing an array of input data at time (t-1), i.e. ∈t-1＝[ut-1，vt-1]Wherein u ist-1、vt-1Respectively (t-1) time 2-dimensional input data.
(b) Clayton Copula and Gumbel Copula models
For the Clayton Copula model and Gumbel Copula model, the parameters can be calculated using the pattern model, which is expressed as follows:
Figure BDA0002990572060000135
wherein R istA correlation coefficient representing data; omegaptt、αPttAnd betaPttIs a parameter of the pattern model; p represents the correlation coefficient R for fitting time ttThe length of the history data sequence of (2) is usually set to 10. LambdaPttThe logistic function is represented and functions to keep the computation results of the pattern model within the desired range.
In addition, the calculation result of the pattern model needs to be further converted into parameters of the Copula model, and the calculation method is as follows:
Figure BDA0002990572060000136
Figure BDA0002990572060000137
wherein the content of the first and second substances,
Figure BDA0002990572060000138
respectively representing Clayton Copula and Gumbel Copula model parameters, RtRepresenting the results of the computation of the pattern model.
In combination with the above calculation process, the parameter set of each basic binary Copula model and the mixed time-varying binary Copula model in equation (9) can be represented as:
Figure BDA0002990572060000141
Figure BDA0002990572060000142
wherein the content of the first and second substances,
Figure BDA0002990572060000143
parameter sets respectively representing t Copula, Clayton Copula, Gumbel Copula models, { αD，βD，k}、
Figure BDA0002990572060000144
Representing parameters in the corresponding model;
Figure BDA0002990572060000145
set of parameters, ω, representing a mixed time-varying binary Copula modelt、ωCl、ωGAnd weight coefficients of t Copula, Clayton Copula and Gumbel Copula models are shown.
(2) Based on the R rattan Copula model structure generation method, all mixed time-varying binary Copula models are expanded into a multi-wind-farm power-dependent structure model.
Preferably, the parameters of the mixed time-varying binary Copula model are estimated by using a maximum likelihood estimation method, and the expression is as follows:
Figure BDA0002990572060000146
wherein the content of the first and second substances,
Figure BDA0002990572060000147
representing a hybrid time-varying binary Copula model CMixThe result of the parameter estimation of (2); argmax represents a function of each parameter value when the maximum is found.
Preferably, in step (2), the method for generating the R rattan structure is as follows:
step 1: taking the cumulative probability sequence of each wind power plant power as input data of a first layer tree structure in R vine, and fitting a pair Copula of any two columns of input data by using a mixed time-varying binary Copula model;
step 2: evaluating the accuracy of each pair Copula in the step 1 by using an AIC index;
the expression is as follows:
IAIC＝2nml-2ln(Lm)
wherein, IAICRepresenting an AIC index value; n ismlRepresenting the number of parameters in the pair Copula model; l ismRepresenting the value of the maximum likelihood function.
And step 3: on the basis of ensuring no ring structure, determining a first layer tree structure by taking the minimum sum of AIC index values of all PairCopula models in the layer tree structure as a target, and initializing k to be 1;
the generation process of each layer of 'tree' structure in R vine is an optimization problem, and the optimization goal is to minimize the sum of AIC index values of all pair Copula models in the layer of 'tree' structure. In particular, for the first layer "tree" structure, it can be regarded as a shortest path problem, where the weighted value of each pair Copula model, i.e. the AIC index value, can adopt Prim algorithm for the problem.
And 4, step 4: in the case where the kth level "tree" structure has been generated, the input data of the (k +1) th level "tree" structure is calculated as follows:
Figure BDA0002990572060000151
wherein, Fβ(e)|γ(e)And Fα(e)|γ(e)Two columns of input data each representing a kth level "tree" structure; gα(e)，β(e)|γ(e)Representing F-base in the kth level 'tree' structureβ(e)|γ(e)And Fα(e)|γ(e)Fitting a pair copula function; fα(e)|{γ(e)，β(e)}And Fβ(e)|{γ(e)，α(e)}Respectively representing possible input data of a (k +1) th layer 'tree' structure;
Figure BDA0002990572060000154
representing the derivation of a partial derivative;
and 5: when the kth level "tree" structure topology has been generated, enumerating all possible topologies for the (k +1) th level "tree" structure, the valid topology will satisfy the following constraints:
Figure BDA0002990572060000152
wherein e isa，ebRepresents two "edges", i.e., the pair Copula function;
Figure BDA0002990572060000153
represents the set of all "edges" in the (k +1) th level "tree" structure; # denotes the collective potential calculation;
step 6: fitting a pair Copula function by using a mixed time-varying binary Copula model for all possible topologies of the (k +1) th layer tree structure in the step 5;
and 7: determining the topology of the (k +1) th layer tree structure by taking the minimum sum of AIC index values of all pair Copula models in the (k +1) th layer tree structure as a target, wherein k is k + 1;
and 8: repeating steps 4 to 7 until the topology of all "tree" structures is generated, which together constitute the R rattan structure of the time-varying R rattan Copula model.
The invention provides a method for constructing a joint probability density function of multiple wind power plant powers, which comprises the following steps:
s1, respectively determining power marginal probability distribution functions of the wind power plants based on historical power data of the wind power plants.
Preferably, in step S1, for each wind farm, the following operations are performed:
(1) establishing a probability density function of the power prediction error of the wind power plant based on an ARIMA-GARCH-t model;
(2) and adding the probability density function of the wind power plant power prediction error and the point prediction power of the wind power plant to obtain a sum, wherein the sum is used as the probability density function of the wind power plant power.
The power data of each wind power plant are divided into two parts, namely point prediction power data and prediction error data, wherein the point prediction refers to the existing prediction method for the expected value of the wind power. Firstly, aiming at the prediction error data of each wind power plant, establishing a probability distribution model based on an ARIMA-GARCH-t model; secondly, adding the probability distribution model of the prediction error of each wind power plant and the point prediction power, wherein the calculation result is the probability distribution model of the power of each wind power plant, and the expression is as follows:
Figure BDA0002990572060000161
wherein, Wrl、Wfc、WerrRespectively representing the actual power, the predicted power and the prediction error of the wind power plant; f. ofrlAnd ferrProbability density functions representing actual power and prediction error, respectively; the representation variables obey a certain probability distribution.
The ARIMA-GARCH-t model is a combined model, and the specific modeling process is shown in FIG. 3:
ARIMA(PAR，d，QMA) The model can be represented as follows:
Figure BDA0002990572060000162
wherein, ytRepresenting input wind powerAnd predicting an error sequence. B denotes the hysteresis operator, i.e. Bjyt＝yt-j；
Figure BDA0002990572060000164
The method is characterized by representing an n-order difference calculation process, having the function of converting input data into a stable sequence, and using an augmented Dickey-Fuller test to evaluate the stability of the sequence; mu.sAMRepresenting fixed parameters obtained by fitting; epsilontRepresents the residual; e represents an expected value operation; var denotes a variance operation, i.e.
Figure BDA0002990572060000163
Is a residual epsilontThe variance of the sequence; Φ (B), Θ (B) represent AR and MA polynomials, respectively, and the expressions are as follows:
Figure BDA0002990572060000171
wherein, PAR、QMARepresenting the order of the polynomial;
Figure BDA0002990572060000172
and
Figure BDA0002990572060000173
the fitted AR and MA coefficients are shown.
The ARIMA model can be viewed as a predictive model in which the prediction error is { εt}. Through an ARIMA model, the estimation of the probability distribution of the prediction error of the original wind power can be converted into a sequence { epsilon ] of residual errorstEstimation of probability distribution, and the function of the GARCH-t model is to fit the residual sequence εtAnd (4) probability distribution. GARCH (P)G，QAC) The t-model can be expressed as follows:
Figure BDA0002990572060000174
wherein N represents a normal distribution; representing variables subject to a certain probabilityDistributing; i ist-1Represents all history information before the time (t-1); h istRepresents a conditional variance; v. oftIs an independent same distribution variable which follows standard normal distribution, i.i.d. represents independent same distribution; mu.sGA、
Figure BDA0002990572060000175
And
Figure BDA0002990572060000176
is a fixed parameter, an ARCH coefficient and a GARCH coefficient obtained by fitting; pG、QACIndicating the order of the GARCH coefficient and ARCH coefficient.
Combining the calculation results of the ARIMA model and the GARCH-t model, the probability density function of the original wind power prediction error sequence can be obtained as follows:
Figure BDA0002990572060000177
wherein the content of the first and second substances,
Figure BDA0002990572060000178
and
Figure BDA0002990572060000179
respectively representing the calculation results of the ARIMA model and the GARCH-t model; the representation variables obey a certain probability distribution.
It should be noted that the power of each wind farm and the edge distribution of the prediction error are not the same, so the parameters of the ARIMA-GARCH-t model are also different, and the ARIMA-GARCH-t model needs to be fitted separately during modeling. In other words, for M wind farms, there are M columns of prediction error data, so M ARIMA-GARCH-t models with different parameters need to be fitted separately.
S2, on the basis of determining the power edge probability distribution function of each wind power plant, constructing a joint probability density function of the power of the wind power plants by adopting a time-varying R rattan Copula model, wherein the time-varying R rattan Copula model is modeled by the method in the first aspect.
As shown in fig. 4, the present invention provides a method for generating a multiple wind farm power day-ahead prediction scene, which comprises the following steps:
the method comprises the following steps: generate an [ N ]sc×Npt×Nwf]All elements in the random matrix obey a uniform distribution U (0, 1), where NscPredicting the number of scenes for a given number of days ahead, NptIndicating the number of predicted power points, N, contained in each of the specified sceneswfRepresenting the number of wind farms.
Step two: and decomposing the combined probability density function of the multiple wind power plants into a form of multiplying the Pair Copula density function and the edge distribution probability density function, wherein the combined probability density function of the multiple wind power plants is generated by adopting the method of the second aspect.
Step three: the following operations are performed for each scene until N is generatedscThe complete day-ahead power prediction scenario.
a. Assigning the values in the random matrix Rnd to the partial input data values under the structure of each level "tree" in the time-varying R rattan Copula model as follows:
Figure BDA0002990572060000181
wherein the content of the first and second substances,
Figure BDA0002990572060000182
inputting data for a part under each hierarchy 'tree' structure;
Figure BDA0002990572060000183
representing each wind farm power; i.e. iscRepresents a scene number; j is a function ofptRepresenting the data point number.
b: input data of two adjacent layers of tree structures in time-varying R vine Copula model
Figure BDA0002990572060000184
And
Figure BDA0002990572060000185
with certain data values, the pair Copula function associated with the data values is calculated according to the following formula
Figure BDA0002990572060000186
The value:
Figure BDA0002990572060000187
will be known
Figure BDA0002990572060000188
Value as a function
Figure BDA0002990572060000189
Is input with one dimension of data, will
Figure BDA0002990572060000191
Value and calculated function
Figure BDA0002990572060000192
Value substitution function
Figure BDA0002990572060000193
In and out of the function
Figure BDA0002990572060000194
Input data of another dimension, gamma denotes
Figure BDA0002990572060000195
The condition set of (1). Interpolation can be used for the calculation.
c: repeating the step b until the jthptThe cumulative probability value corresponding to each wind power plant power under the data point is obtained by all calculation and is recorded as
Figure BDA0002990572060000196
d: to be provided with
Figure BDA0002990572060000197
As input data, the j (th) is obtained based on the inverse function of the prediction error cumulative probability function of each wind power plantptThe expression of the sampling result of the prediction error of each wind power plant under the data points is as follows:
Figure BDA0002990572060000198
wherein the content of the first and second substances,
Figure BDA0002990572060000199
respectively represent the k-thwfWind farm at jthptThe prediction error sampling result, the accumulative probability calculation result and the inverse function of the prediction error accumulative probability function of each data point.
e: and d, preprocessing the sampling result of the prediction error of each wind power plant obtained in the step d, so that the sampling result is between the minimum value and the maximum value of the prediction error in the historical data used for fitting the model.
In order to ensure the rationality of the prediction error sampling result, the size of the sampled value needs to be limited. Assuming that the minimum and maximum values of the prediction error in the historical data used to fit the model are respectively
Figure BDA00029905720600001910
Figure BDA00029905720600001911
When the sampling result is greater than
Figure BDA00029905720600001912
At that time, set as
Figure BDA00029905720600001913
Is less than
Figure BDA00029905720600001914
At that time, set as
Figure BDA00029905720600001915
Further, the prediction error sampling result is added with the point prediction value, so that the prediction scene value of each wind power plant power can be obtained:
Figure BDA00029905720600001916
wherein the content of the first and second substances,
Figure BDA00029905720600001917
respectively represent the k-thwfWind farm at jthptAnd predicting scene values and point predicted values by the power of the data points.
f: adding the prediction error sampling result and the point predicted value to obtain a prediction scene value of each wind power plant power:
Figure BDA00029905720600001918
wherein the content of the first and second substances,
Figure BDA0002990572060000201
respectively represent the k-thwfWind farm at jthptAnd predicting scene values and point predicted values by the power of the data points.
g: j is the j th wind power plant calculated in the step fptCalculating the (j) th predicted scene value of the data pointpt+1) probability distribution of wind farm power and prediction error for each data point, jpt+1) parameter values for all pair Copula in the time-varying R rattan Copula model at the data points.
h: and repeating the steps a to g until a complete day-ahead power prediction scene is generated for all the wind power plants.
Next, the validity of the model is verified by a simulation example.
Evaluation index
For the generated multi-wind farm power prediction scene, an autocorrelation function (ACF) and a cross-correlation function (CCF) are evaluated. When the ACF and the CCF of the generated wind power prediction scene are similar to those of the actually measured wind power, the scene effectiveness is high.
For data sequence yt＝{y0，y1，y2，…，ytThe ACF index refers to the sequence ytAnd the sequence yt+k＝{y0+k，y1+k，y2+k，…，yt+kAnd (5) a correlation coefficient between the wind power plants, wherein the correlation coefficient is used for evaluating the autocorrelation of the total power prediction scene of the multiple wind power plants in the time dimension. The expression of ACF is as follows:
Figure BDA0002990572060000202
wherein, IACFRepresenting an ACF index value; e represents an expected value operation;
Figure BDA0002990572060000203
and
Figure BDA0002990572060000204
representing the sequence ytAnd yt+kAverage value of (d);
Figure BDA0002990572060000205
and
Figure BDA0002990572060000206
representing the sequence ytAnd yt+kStandard deviation of (d); k represents a delay time, and when the delay time k is 0, IACF(0)＝1。
For data sequences
Figure BDA0002990572060000207
And
Figure BDA0002990572060000208
CCF index refers to sequence
Figure BDA0002990572060000209
And sequence
Figure BDA00029905720600002010
And the correlation coefficient is used for evaluating the time-space coupling correlation between two wind power plant power prediction scenes. The expression of CCF is as follows:
Figure BDA0002990572060000211
wherein, ICCFRepresenting a CCF index value;
Figure BDA0002990572060000212
respectively representing predicted power scenes of two wind power plants;
Figure BDA0002990572060000213
and
Figure BDA0002990572060000214
representing a sequence
Figure BDA0002990572060000215
And
Figure BDA0002990572060000216
average value of (d);
Figure BDA0002990572060000217
and
Figure BDA0002990572060000218
representing a sequence
Figure BDA0002990572060000219
And
Figure BDA00029905720600002110
standard deviation of (d); k denotes a delay time, and when the delay time k is O, CCF is equivalent to a commonly used Pearson correlation coefficient.
Description of simulation data
The method is based on data development analysis of 8 northwest wind power plants, the sampling time is 3 months (90 days), and the sampling frequency is 96 points/day. Firstly, calculating parameters of an ARIMA-GARCH-t model and a TRVMC model based on point predicted power and actual measured power of each wind power plant in the previous 85 days; and secondly, taking one day of the last 5 days as an object, taking the point predicted power of each wind power plant as the point predicted power of the next day, generating 100 day-ahead predicted scenes for the power of each wind power plant, and comparing the ACF and the CCF of the generated scenes with the ACF and the CCF of the actually measured power.
Description of comparative model
In this section, 4 kinds of prediction scene generation models are selected for comparison:
model 1: the model combining ARIMA-GARCH-t and TRVMC, which is provided by the patent, is abbreviated as 'deployed' model;
model 2: independent ARIMA-GARCH-t model;
model 3: a static D vine Copula model;
model 4: independent Kernel Density Estimation (KDE) model.
In the models 2 and 4, "independent" means that correlation among power of a plurality of wind power plants is ignored, models are built for the wind power plants respectively, and a power prediction scene is generated. On the other hand, the models 2 and 4 are edge distribution models of the models 1 and 3, respectively.
On the basis of generating the power prediction scenes of all the wind power plants, the prediction scenes of the total power of the multiple wind power plants can be obtained through superposition calculation.
Simulation result
FIG. 5 shows a prediction scenario for the total power of 8 wind farms, generated with 4 models each. According to the simulation result, when a prediction scene of the total power of 8 wind power plants is generated, the fitting results of 4 models have larger difference. On the one hand, compared with the models 1 and 3, the models 2 and 4 neglect the correlation among a plurality of wind farms, so that when the power of one wind farm is larger, the power of other wind farms may be smaller, and the fluctuation range of the total power is greatly reduced after superposition calculation, thereby causing that the prediction scene cannot envelop the actually measured total power curve in some cases (see (b) in fig. 5). On the other hand, compared with the models 1 and 2, the models 3 and 4 ignore the time series characteristics of the wind power, so that when the wind power at the current moment in the generated scene is larger, the wind power at the next moment may be too small, which results in more frequent fluctuation and larger amplitude of the predicted scene generated by the models 3 and 4, and the fluctuation amplitude of the scene in some cases will greatly exceed the fluctuation amplitude of the actually-measured total power curve (see (c) in fig. 5). Compared with models 2, 3 and 4, the prediction scene generated by the model provided by the invention not only can effectively envelop the actually measured power curve, but also has the fluctuation frequency and amplitude similar to the actually measured curve, thereby effectively depicting the uncertainty condition of the wind power.
FIG. 6 shows ACF index values for 8 wind farm total power prediction scenarios generated with 4 models, respectively. According to the simulation result, the ACF value of the scene generated by the model (model 1) provided by the invention is closest to the ACF value of the actually measured total power curve, so that the wind power prediction scene generated by the model provided by the invention has the time dimension self-correlation characteristic close to the actually measured value. Theoretical analysis shows that the model 3 and the model 4 ignore the time series characteristics of the wind power, so that the predicted power of adjacent data points in the generated scene is relatively independent. For example, when the wind power of the current moment in the generated scene is large, the wind power of the next moment may be small, so that the total fluctuation range of the scene greatly exceeds the fluctuation range of the actually-measured total power curve, which weakens the autocorrelation of the generated scene, and the ACF index value is always lower than the actual value. On the other hand, compared with the model 1, the model 2 ignores the correlation among a plurality of wind power plants, so that after the power prediction scenes of the wind power plants are superposed and calculated, the fluctuation range of the model 2 for generating the total power prediction scene is greatly reduced, the autocorrelation of the generated scene is enhanced, the ACF index value is usually higher than the actual value, and one direct embodiment is that the generated scene is too smooth.
FIG. 7 shows CCF index values for a power prediction scenario generated with 4 models, respectively, for 2 of the wind farms. According to simulation results, the CCF value of a scene generated by the model (model 1) provided by the invention is closest to the CCF value of an actual measurement power curve of the wind power plant 2, so that the power prediction scenes of a plurality of wind power plants generated by the model provided by the invention have time-space correlation characteristics close to the actual measurement values. Theoretical analysis shows that the CCF value is almost always lower than the actual value, since model 2 and model 4 ignore the correlation between wind farms. Meanwhile, the CCF curves of the model 2 and the model 4 in the prediction scenes are distributed relatively dispersedly, which shows that the correlation among the 2 wind power plants in different scenes is greatly different and is not consistent with the actual situation. On the other hand, although the models 1 and 3 are based on Copula models and fit the correlation among a plurality of wind power plants, the model 1 further considers the time series characteristic of each wind power plant power and the time-varying characteristic of the correlation among the plurality of wind power plants, so that the similarity between the CCF value of the scene generated by the model 1 and the actual value is ensured. In contrast, since model 3 only takes into account the overall correlation of the wind farm, more specifically the Kendall correlation coefficient, the CCF value of the model 3 generation scenario is close to the actual value only when the delay time is 0, and is still less than the actual value.
In conclusion, the multi-wind-farm-power day-ahead prediction scene generation model established by the invention can better fit the time-space correlation characteristics of the multi-wind-farm power, and the accuracy and the effectiveness of the multi-wind-farm-power day-ahead prediction scene are improved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (8)

1. A modeling method for a multi-wind-farm power-dependent structure is characterized by comprising the following steps:
s1, respectively calculating the cumulative probability of each wind power plant power according to a wind power plant power edge probability distribution function to obtain a cumulative probability sequence of each wind power plant power;
s2, inputting the cumulative probability sequences of the power of each wind power plant to a time-varying R rattan Copula model together to obtain the time-varying R rattan Copula model of the power of the multi-wind power plant;
the time-varying R vine Copula model is constructed in the following way:
(1) establishing a pair Copula model based on a mixed time-varying binary Copula model, wherein the pair Copula model is used for representing power-dependent structural information of every two wind power plants, and the expression of the pair Copula model is as follows:
Figure FDA0002990572050000011
wherein u, v represent input data of the pair Copula model; cMixRepresenting a mixed time-varying binary Copula model; ciRepresentation selection for composition CMixThe binary Copula model of (a); omegaiIs represented by CiThe weight coefficient of (a);
Figure FDA0002990572050000012
and
Figure FDA0002990572050000013
respectively represent CMixAnd CiThe method comprises the steps that a parameter set of a model is formed, and n represents the number of binary Copula models participating in building of a mixed time-varying binary Copula model;
(2) based on the R rattan Copula model structure generation method, all mixed time-varying binary Copula models are expanded into a multi-wind-farm power-dependent structure model.
2. The method of claim 1, wherein the binary Copula model is a t Copula model, a Clayton Copula model, or a Gumbel Copula model.
3. The method of claim 1, wherein the parameters of the hybrid time-varying binary Copula model are estimated using a maximum likelihood estimation method, expressed as follows:
Figure FDA0002990572050000021
wherein the content of the first and second substances,
Figure FDA0002990572050000022
representing a hybrid time-varying binary Copula model CMixThe result of the parameter estimation of (2); argmax represents a function of each parameter value when the maximum is found.
4. The method of claim 1, wherein in step (2), the R rattan structure is generated by:
step 1: taking the cumulative probability sequence of each wind power plant power as input data of a first layer tree structure in R rattan, and fitting the pair Copula of any two columns of input data by using a mixed time-varying binary Copula model;
step 2: evaluating the accuracy of each pair Copula in the step 1 by using an AIC index;
and step 3: on the basis of ensuring no ring structure, determining a first layer tree structure by taking the minimum sum of AIC index values of all pair Copula models in the layer tree structure as a target, and initializing k to be 1;
and 4, step 4: in the case where the kth level "tree" structure has been generated, the input data of the (k +1) th level "tree" structure is calculated as follows:
Figure FDA0002990572050000023
wherein, Fβ(e)|γ(e)And Fα(e)|γ(e)Two columns of input data each representing a kth level "tree" structure; gα(e)，β(e)|y(e)Representing F-base in the kth level 'tree' structureβ(e)|γ(e)And Fα(e)|γ(e)Fitting a pair Copula function; fα(e)|{γ(e)，β(e)}And Fβ(e)|{γ(e)，α(e)}Respectively representing possible input data of a (k +1) th layer 'tree' structure;
Figure FDA0002990572050000026
representing the derivation of a partial derivative;
and 5: when the kth level "tree" structure topology has been generated, enumerating all possible topologies for the (k +1) th level "tree" structure, the valid topology will satisfy the following constraints:
Figure FDA0002990572050000024
wherein e isa，ebRepresents two "edges", i.e., the pair Copula function;
Figure FDA0002990572050000025
represents the set of all "edges" in the (k +1) th level "tree" structure; # denotes the collective potential calculation;
step 6: fitting a pair Copula function by using a mixed time-varying binary Copula model for all possible topologies of the (k +1) th layer tree structure in the step 5;
and 7: determining the topology of the (k +1) th layer tree structure by taking the minimum sum of AIC index values of all pair Copula models in the (k +1) th layer tree structure as a target, wherein k is k + 1;
and 8: repeating steps 4 to 7 until the topology of all "tree" structures is generated, which together constitute the R rattan structure of the time-varying R rattan Copula model.
5. A method for constructing a joint probability density function of power of multiple wind power plants is characterized by comprising the following steps:
s1, respectively determining power edge probability distribution functions of each wind power plant based on historical power data of each wind power plant;
s2, on the basis of determining the power edge probability distribution function of each wind power plant, constructing a joint probability density function of the power of the multi-wind power plant by adopting a time-varying R vine Copula model;
the time-varying R vine Copula model is modeled by the method of any one of claims 1 to 4.
6. The method according to claim 5, characterized in that in step S1, for each wind farm, the following operations are performed:
(1) establishing a probability density function of the power prediction error of the wind power plant based on an ARIMA-GARCH-t model;
(2) and adding the probability density function of the wind power plant power prediction error and the point prediction power of the wind power plant to obtain a sum, wherein the sum is used as the probability density function of the wind power plant power.
7. A method for generating a multi-wind-farm power day-ahead prediction scene is characterized by comprising the following steps:
the method comprises the following steps: generate an [ N ]sc×Npt×Nwf]All elements in the random matrix obey a uniform distribution U (0, 1), where NscPredicting the number of scenes for a given number of days ahead, NptIndicating the number of predicted power points, N, contained in each of the specified sceneswfRepresenting the number of wind farms;
step two: decomposing a joint probability density function of the multiple wind farm powers into a form of multiplying a Pair Copula density function by an edge distribution probability density function, the joint probability density function of the multiple wind farm powers being generated by the method of claim 5 or 6;
step three: the following operations are performed for each scene until N is generatedscA complete day-ahead power prediction scenario;
a. assigning the values in the random matrix Rnd to the partial input data values under the structure of each level "tree" in the time-varying R rattan Copula model as follows:
Figure FDA0002990572050000041
wherein the content of the first and second substances,
Figure FDA0002990572050000042
for parts under the structure of a "tree" of levelsInputting data;
Figure FDA0002990572050000043
representing each wind farm power; i.e. iscRepresents a scene number; j is a function ofptRepresenting a data point number;
b: input data of two adjacent layers of tree structures in time-varying R vine Copula model
Figure FDA0002990572050000044
And
Figure FDA0002990572050000045
with certain data values, the pair Copula function associated with the data values is calculated according to the following formula
Figure FDA0002990572050000046
The value:
Figure FDA0002990572050000047
will be known
Figure FDA0002990572050000048
Value as a function
Figure FDA0002990572050000049
Is input with one dimension of data, will
Figure FDA00029905720500000410
Value and calculated function
Figure FDA00029905720500000411
Value substitution function
Figure FDA00029905720500000412
In and out of the function
Figure FDA00029905720500000413
Input data of another dimension, gamma denotes
Figure FDA00029905720500000414
The condition set of (1);
c: repeating the step b until the jthptThe cumulative probability value corresponding to each wind power plant power under the data point is obtained by all calculation and is recorded as
Figure FDA00029905720500000415
d: to be provided with
Figure FDA00029905720500000416
As input data, the j (th) is obtained based on the inverse function of the prediction error cumulative probability function of each wind power plantptThe expression of the sampling result of the prediction error of each wind power plant under the data points is as follows:
Figure FDA0002990572050000051
wherein the content of the first and second substances,
Figure FDA0002990572050000052
respectively represent the k-thwfWind farm at jthptThe prediction error sampling result, the accumulative probability calculation result and the inverse function of the prediction error accumulative probability function of each data point;
e: d, preprocessing the sampling result of the prediction error of each wind power plant obtained in the step d, so that the sampling result is between the minimum value and the maximum value of the prediction error in the historical data used for fitting the model;
f: adding the prediction error sampling result and the point predicted value to obtain a prediction scene value of each wind power plant power:
Figure FDA0002990572050000053
wherein the content of the first and second substances,
Figure FDA0002990572050000054
respectively represent the k-thwfWind farm at jthptPredicting scene values and point predicted values by the power of the data points;
g: j is the j th wind power plant calculated in the step fptCalculating the (j) th predicted scene value of the data pointpt+1) probability distribution of wind farm power and prediction error for each data point, jpt+1) parameter values of all pair Copula in the time-varying R rattan Copula model at the data points;
h: and repeating the steps a to g until a complete day-ahead power prediction scene is generated for all the wind power plants.
8. A multiple wind farm power day-ahead predictive scene generation system, comprising: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method of generating multiple wind farm power day-ahead predictive scenes of claim 7.
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