CN110611334A - Copula-garch model-based multi-wind-farm output correlation method - Google Patents
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Abstract
The invention relates to the field of wind power generation, in particular to a method for modeling the output correlation of multiple wind power plants by using Copula-garch functions, which comprises the following steps: acquiring active power output distribution data of a wind power plant; performing arch effect inspection on the wind power plant, further establishing a Garch (P, Q) model to fit an edge distribution function of the wind power plant, and splitting the joint output distribution of the multiple wind power plants into a form of multiplying the edge distribution function and a Copula function according to SKlar theorem; four indexes respectively corresponding to the five classes of Copula functions are solved; determining the weight of each index in each function, calculating according to the weight to obtain an attribute metric value, determining the classification standard corresponding to each copula function according to the attribute metric value, and selecting the copula function corresponding to the optimal grade as the optimal copula function of the wind power plant. The uncertainty research of wind power output is converted into certainty research, and the problem that the optimal correlation function is selected and is not in accordance with the reality is solved.
Description
Technical Field
The invention relates to the field of wind power generation, in particular to a method for modeling the output correlation of multiple wind power plants by using Copula-garch functions.
Background
Under the background that large-scale wind power is connected into a power grid, the condition that multiple wind power plants are connected to the power grid at the same time often occurs, and therefore strong correlation exists between the wind power plants in similar geographic positions. Neglecting this correlation results in a large difference between wind power analysis and actual operation, which in turn produces a series of adverse consequences.
In the application of the multi-wind farm output correlation, the methods which can be used for describing the correlation are mainly as follows: pearson correlation coefficients, Spearman correlation coefficients, Kendall correlation coefficients, matrix transformation methods, and Copula function methods. In the methods, Pearson correlation coefficients and matrix transformation are suitable for linear and normal distribution of variables; the remaining ones can be applied to arbitrarily distributed variables. The currently applied method only considers the uncertainty of the wind power output and does not consider the volatility of the wind power, and only considers the correlation coefficient when selecting the optimal correlation function and does not verify the fitting degree of the function and an actual sample.
Disclosure of Invention
The invention aims to solve the technical problem of providing a Copula-garch model-based multi-wind power plant output correlation method, and solves the problem that the currently applied method only considers the uncertainty of wind power output and does not consider the fluctuation of wind power, so that the optimal correlation function is selected and is not in accordance with the reality.
The present invention is achieved in such a way that,
a Copula-garch model-based multi-wind farm output correlation method comprises the following steps:
1) acquiring active power output distribution data of a wind power plant;
2) performing arch effect inspection on the wind power plant, further establishing a Garch (P, Q) model to fit an edge distribution function of the wind power plant, and splitting the joint output distribution of the multiple wind power plants into a form of multiplying the edge distribution function and a Copula function according to SKlar theorem; four indexes respectively corresponding to the five classes of Copula functions are solved;
3) determining the weight of each index in each function, calculating according to the weight to obtain an attribute metric value, determining the classification standard corresponding to each copula function according to the attribute metric value, and selecting the copula function corresponding to the optimal grade as the optimal copula function of the wind power plant.
Further, the method comprises: garch (P, Q) model:
wherein: epsilontRepresenting the residual of the variable, alpha0＞0，αiAnd more than or equal to 0, i is more than 0, the edge distribution is a combination of which the edge distribution is more than 0, P is a non-negative integer hysteresis condition variance, and Q is a non-negative integer square condition variance.
Further, the five types of Copula functions include: Normal-Copula function, t-Copula function, Gumbel-Copula function, Clayton-Copula function, and Frank-Copula function.
Further, the four indicators include: euclidean distance dGuMaximum distance dzThe difference d between the Kendall correlation coefficientsτDifference d between the correlation coefficient and Spearmanρ。
Further, establishing attribute spaces of four indexes, and generating a standard hierarchical matrix:
aij＝Xi.min+j·(Xi.max-Xi.min) /5 wherein Xi.minIs the minimum value of the matrix elements, Xi.maxIs the maximum value of the matrix elements;
xi(i ═ 1,2,3,4) as evaluation criteria: p is an index xiProperty space of PjJ 1,2, 5 is a quality grade, P1Grade optimum, P5Worst-grade; a isijAs index i inThe jth ranking criterion on sexual space P; index xiHaving PmAttribute, let' xi∝Pm", the degree of attribute is represented by λxi(Pj) And expressing as an attribute metric value, the calculation formula of the attribute metric value of the model is as follows:
in the formula of omegaiTo evaluate the standard xiThe weight of (2) is determined by an entropy method;
according to the confidence criterion, solving the quality grade m of the Copula model:
confidence delta epsilon (0.5-1) in the formula, and highest-grade P1And the Copula function of the stage is used as an optimal combined distribution model of the output of the wind power plant.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, on the basis of converting the uncertainty research of wind power output into the certainty research, the fluctuation of wind power is described by using a garch model, the edge distribution of a wind power plant is respectively established, a Copula function is further solved according to the combined output distribution of the wind power plant, the optimal Copula function is selected by correlation coefficient comparison and the fitting degree verification with an actual sample, and finally a Copula-garch model is established.
Drawings
Fig. 1 is a statistical graph of output frequency of a wind farm 1 according to an embodiment of the present invention;
fig. 2 is a statistical graph of output frequency of the wind farm 2 according to the embodiment of the present invention;
FIG. 3 is a statistical graph of joint output frequency of two wind power plants according to an embodiment of the present invention;
FIG. 4 is a Clayton-Copula density function provided by an embodiment of the present invention;
FIG. 5 is a diagram of a Clayton-Copula distribution function provided by an embodiment of the present invention;
FIG. 6 is a binary t-Copula density function provided by an embodiment of the present invention;
FIG. 7 is a diagram of a binary t-Copula distribution function according to an embodiment of the present invention;
fig. 8 is a diagram of an empirical Copula distribution function provided in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following 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.
A Copula-garch model-based multi-wind farm output correlation method comprises the following steps:
1) acquiring active power output distribution data of a wind power plant;
2) performing arch effect inspection on the wind power plant, further establishing a Garch (P, Q) model to fit an edge distribution function of the wind power plant, and splitting the joint output distribution of the multiple wind power plants into a form of multiplying the edge distribution function and a Copula function according to SKlar theorem; four indexes respectively corresponding to the five classes of Copula functions are solved;
3) determining the weight of each index in each function, calculating according to the weight to obtain an attribute metric value, determining the classification standard corresponding to each copula function according to the attribute metric value, and selecting the copula function corresponding to the optimal grade as the optimal copula function of the wind power plant.
Active power output sequences of multiple wind power plants belong to heteroscedastic sequences, and a Garch model can effectively fit long-term heteroscedastic variables, so that the method is more suitable for edge distribution establishment of the wind power plants.
The change of the variable can be well described by fitting a Garch (P, Q) model to the edge distribution of the wind power plant.
Garch (P, Q) model:
wherein: epsilontRepresenting the residual of the variable, alpha0＞0，αiAnd more than or equal to 0, i is more than 0, the edge distribution is a combination of which the edge distribution is more than 0, P is a non-negative integer hysteresis condition variance, and Q is a non-negative integer square condition variance.
The Copula function exists as a function connecting a joint distribution function and an edge distribution function, and is also called a connection function.
For the Sklar theorem: setting a random variable X1,X2,……,XnHas a joint distribution function of H and an edge distribution function of F1(X1),F2(X2),……,Fn(Xn) Then there is a Copula function C, such that H (x)1,x2,......,xn)＝C[F1(x1),F2(x2),......,Fn(xn)]
If the edge distribution function F is a continuous function, the joint distribution function C is uniquely determined. From this theorem, it can be seen that the multi-wind farm joint contribution distribution can be split into the form of multiplication of the edge distribution function and the Copula function. Therefore, the variables are not required to have the same edge distribution, any edge distribution can be connected into a combined distribution through the Copula function, and the information of the random sequence is in the edge distribution function, so that the data distortion hardly occurs in the process of conversion through the Copula function.
The five classes of Copula functions include: Normal-Copula function, t-Copula function, Gumbel-Copula function, Clayton-Copula function, and Frank-Copula function.
The method comprises the following steps of determining an edge distribution function of a variable, calculating and obtaining parameters of the Copula function according to the skalr theorem, selecting a proper Copula function according to a proper evaluation index, establishing distribution and finally obtaining a correlation function.
The main considerations in the analysis of the selection of the most suitable Copula function include the fitness indicators: euclidean distance dGu(sum of distances between sample empirical distribution function value and Copula joint distribution function value) and maximum distance dz(sample empirical distribution function)The maximum of the value and Copula joint distribution function value) the smaller the difference, the closer the model is to the empirical distribution; and a correlation index: difference d between kendall correlation coefficientsτDifference d between the correlation coefficient and SpearmanρThe smaller these two values are, the closer the empirical data model is to the selected model.
Defining: taking a sample (X) from a two-bit population (X, Y)i，yi) Note that f (x) and g (y) are X, Y empirical distribution functions, and u and v are X, Y transformed uniform distributions, so that the empirical distribution of the sample can be defined as:
in the formula: i [ G (y)i)≤v]For an illustrative function, when F (x)i) When u is less than or equal to u, I [ F (x)i)≤u]1 is ═ 1; when F (x)i) When > u, I [ F (x)i)≤u]0, C (u)i,vi) For Copula's joint distribution function value, its euclidean distance is defined as:
the maximum distance is defined as:
according to the analysis, the optimal Copula function can be classified as a decision problem, the decision problem can be carried out by adopting an entropy weight optimal selection theory, firstly, an attribute space of four indexes is established, and a standard grading matrix is generated:
aij＝Xi.min+j·(Xi.max-Xi.min) /5 wherein Xi.minIs the minimum value of the matrix elements, Xi.maxIs the maximum value of the matrix elements;
xi(i＝12,3,4) are evaluation criteria: p is an index xiProperty space of PjJ 1,2, 5 is a quality grade, P1Grade optimum, P5Worst-grade; a isijThe j-th grading standard of the index i on the attribute space P; index xiHaving PmAttribute, let' xi∝Pm", the degree of attribute is represented by λxi(Pj) And expressing as an attribute metric value, the calculation formula of the attribute metric value of the model is as follows:
in the formula of omegaiTo evaluate the standard xiThe weight of (2) is determined by an entropy method;
according to the confidence criterion, solving the quality grade m of the Copula model:
confidence delta epsilon (0.5-1) in the formula, and highest-grade P1And the Copula function of the stage is used as an optimal combined distribution model of the output of the wind power plant.
The entropy method is specifically as follows:
1) n targets to be evaluated, m evaluation indexes, bijIs the value of the jth index of the ith target. Normalization processing of indexes: heterogeneous indexes are homogeneous, and because the measurement units of all indexes are not uniform, before the indexes are used for calculating the comprehensive indexes, the indexes are standardized, namely the absolute values of the indexes are converted into relative values, and x is madeij＝|xijTherefore, the homogenization problem of various heterogeneous index values is solved. Moreover, since the positive index and the negative index have different meanings (the higher the positive index value is, the better the negative index value is), the data normalization processing is performed on the high and low indexes by using different algorithms. The specific method comprises the following steps:
the forward direction index is as follows:
negative direction index:
then bijThe value of the j index (i 1,2, …, n; j 1,2, …, m) of the ith target
2) Calculating the proportion of the ith target in the j index:
3) calculating the entropy value of the j index:
here, 2 wind farms 1 and 2 in close geographical positions of funxin city, liaoning province are taken as an example. And taking the real data of the active power output in 2018 all the year as a simulation example. The data sampling interval time is 15min, and one year is taken as time. Firstly, determining an edge distribution function of wind power output.
The calculation method of the result of the embodiment is a kernel density estimation method, and is implemented by using output frequency statistical graphs of two wind power plants, such as fig. 1 and fig. 2, and a combined output distribution graph, such as fig. 3. It can be seen that the two wind power plants have low power output and obvious protruding lower tails, so that the two wind power plants have tail asymmetrical distribution, namely, the two wind power plants occupy a large proportion when the power output is small at the same time.
Because the output of the wind power plants has strong randomness and uncertainty, and the two wind power plants are subjected to normality test, the result shows that the output probability distribution of the wind power plants is not obeyed to normal distribution, and the output probability distribution of the wind power plants cannot be simulated by common distributions such as t distribution and normal distribution. Therefore, a Copula function with stronger universality is adopted for correlation modeling. The edge distribution of the wind power output is simulated by using a nonparametric estimation method, namely a nuclear density estimation method, which is shown in fig. 4 and 5 respectively.
Selection of optimal Copula function
According to 5 Copula function characteristics, three functions of a t-Copula function, a Clayton-Copula function and a Normal-Copula function, which describe asymmetric distribution and contain tail distribution characteristics, are selected for correlation evaluation. And (3) selecting an optimal function by means of an entropy weight preference theory to complete the modeling of the correlation of the wind power plant, wherein index parameter values are shown in table 1.
TABLE 1 evaluation index parameter values
Solving an attribute test matrix as follows:
then four entropy weights of the four models are respectively calculated, and then an attribute measurement value is evaluated: lambda (P)1)＝0.6154，λ(P2) 0.3832 (attribute measurement value of Clayton-Copula), obtaining m value corresponding to each function by taking confidence degree delta as 0.65, and if m is 2, the corresponding rating is P2And (4) stages. The corresponding ratings obtained for each function are shown in table 2.
TABLE 2 summary of various Copula model rating results
According to the data in the chart, the Clayton-Copula function is selected to be closest to the finally obtained result. And verifying the result by adopting a maximum likelihood estimation method to obtain the minimum Euclidean distance of the Clayton-Copula function, so that the Clayton-Copula function is selected to describe the correlation between the wind farm 1 and the wind farm 2.
The kernel density estimated edge distribution of the two wind power plants is substituted into a Clayton-Copula function and a binary t-Copula function to obtain a density function and distribution function graph modeled by the two functions
The t-Copula and the Clayton-Copula functions are analyzed and compared with the empirical Copula function respectively, and the calculation and analysis results show that the Clayton-Copula functions are closer to the empirical Copula function as shown in FIGS. 4, 5, 6, 7 and 8. And according to the Clayton-Copula function characteristics: asymmetric distribution, lower tail correlation and upper tail gradual independence just meet the characteristics of data distribution. Therefore, the Clayton-Copula function is the optimal correlation function of the two wind power plants, and a Copula-garch correlation model based on the Clayton-Copula function is established.
In the embodiment, for multiple wind farms with similar geographic positions, the edge distribution solution is established by using a kernel density estimation method, and an output correlation function between the multiple wind farms is established. In various Copula functions, Kendall correlation coefficients, Spearman correlation coefficients, Euclidean distances and maximum distances are analyzed and compared, and the Clayton-Copula function is determined to be the optimal correlation function of the wind power plant 1 and the wind power plant 2 by combining an entropy weight optimization theory, so that the optimal Copula-garch correlation model is established. And it can be seen from the function that the combined distribution has strong lower tail correlation, in the wind power analysis application, neglecting the correlation may cause a series of conditions inconsistent with the actual operation, and increase the risk of the safe and stable operation of the power grid.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A Copula-garch model-based multi-wind farm output correlation method is characterized by comprising the following steps:
1) acquiring active power output distribution data of a wind power plant;
2) performing arch effect inspection on the wind power plant, further establishing a Garch (P, Q) model to fit an edge distribution function of the wind power plant, and splitting the joint output distribution of the multiple wind power plants into a form of multiplying the edge distribution function and a Copula function according to SKlar theorem; four indexes respectively corresponding to the five classes of Copula functions are solved;
3) determining the weight of each index in each function, calculating according to the weight to obtain an attribute metric value, determining the classification standard corresponding to each copula function according to the attribute metric value, and selecting the copula function corresponding to the optimal grade as the optimal copula function of the wind power plant.
2. A method according to claim 1, characterized in that the method comprises: garch (P, Q) model:
wherein: epsilontRepresenting the residual of the variable, alpha0＞0，αiAnd more than or equal to 0, i is more than 0, the edge distribution is a combination of which the edge distribution is more than 0, P is a non-negative integer hysteresis condition variance, and Q is a non-negative integer square condition variance.
3. The method of claim 1, wherein the five classes of Copula functions comprise: Normal-Copula function, t-Copula function, Gumbel-Copula function, Clayton-Copula function, and Frank-Copula function.
4. The method of claim 1, wherein the four metrics comprise: euclidean distance dGuMaximum distance dzThe difference d between the Kendall correlation coefficientsτDifference d between the correlation coefficient and Spearmanρ。
5. The method according to claim 1 or 4, characterized in that an attribute space of four indices is established, generating a standard hierarchical matrix:
aij＝Xi.min+j·(Xi.max-Xi.min) /5 wherein Xi.minIs the minimum value of the matrix elements, Xi.maxIs the maximum value of the matrix elements;
xi(i ═ 1,2,3,4) as evaluation criteria: p is an index xiProperty space of PjJ 1,2, 5 is a quality grade, P1Grade optimum, P5Worst-grade; a isijThe j-th grading standard of the index i on the attribute space P; index xiHaving PmAttribute, let' xi∝Pm", the degree of attribute is represented by λxi(Pj) And expressing as an attribute metric value, the calculation formula of the attribute metric value of the model is as follows:
in the formula of omegaiTo evaluate the standard xiThe weight of (2) is determined by an entropy method;
according to the confidence criterion, solving the quality grade m of the Copula model:
confidence delta epsilon (0.5-1) in the formula, and highest-grade P1And the Copula function of the stage is used as an optimal combined distribution model of the output of the wind power plant.
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| CN112711864A (en) * | 2021-01-18 | 2021-04-27 | 国网浙江省电力有限公司电力科学研究院 | Distribution network cable quality index correlation model construction and data expansion method |
| CN112711864B (en) * | 2021-01-18 | 2024-06-07 | 国网浙江省电力有限公司电力科学研究院 | Distribution network cable quality index correlation model construction and data expansion method |
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