CN110611334A - A method for output correlation of multiple wind farms based on Copula-garch model - Google Patents

Abstract

The invention relates to the field of wind power generation, in particular to a method for modeling the output correlation of multiple wind farms by using a Copula-garch function. The method includes: collecting active power output distribution data of the wind farms; checking the arch effect of the wind farms, and then The Garch(P,Q) model is established to fit the marginal distribution function of the wind farm, and then according to the SKlar theorem, the combined output distribution of multiple wind farms is divided into the form of multiplying the marginal distribution function and the Copula function; Corresponding four indicators; determine the weight of each indicator in each function, calculate the attribute measure value according to the weight value, and determine the grading standard corresponding to each copula function according to the attribute measure value, and select the copula corresponding to the optimal level The function is the optimal copula function of the wind farm. Convert the uncertainty research of wind power output into deterministic research, and solve the problem that the selection of the optimal correlation function does not conform to the actual situation.

Description

A method for output correlation of multiple wind farms based on Copula-garch model

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 farms by using a Copula-garch function.

Background technique

In the context of large-scale wind power being connected to the grid, multiple wind farms are often connected to the grid at the same time, which leads to a strong correlation between wind farms with similar geographical locations. Ignoring this correlation can lead to a large discrepancy between wind power analysis and actual operation, which in turn has a series of undesirable consequences.

In the application of multi-wind farm output correlation, the methods that can be used to describe the correlation mainly include: Pearson correlation coefficient, Spearman correlation coefficient, Kendall correlation coefficient, matrix transformation method and Copula function method. Among these methods, Pearson correlation coefficient and matrix transformation are suitable for variables with linear and normal distribution; the other methods can be applied to variables with any distribution. The currently applied method only considers the uncertainty of wind power output, but does not consider the volatility of wind power, and when selecting the optimal correlation function, only the correlation coefficient is considered, and the function is not verified with the actual sample.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a multi-wind farm output correlation method based on the Copula-garch model, and the currently applied method only considers the uncertainty of the wind power output, but does not consider the fluctuation of the wind power, so that the The problem of choosing the optimal correlation function does not match the actual situation.

The present invention is realized in this way,

A method for output correlation of multiple wind farms based on the Copula-garch model, the method includes:

1) Collect the active power output distribution data of the wind farm;

2) The arch effect test is carried out on the wind farm, and then the Garch(P,Q) model is established to fit the marginal distribution function of the wind farm. Then, according to the SKlar theorem, the combined output distribution of multiple wind farms is divided into the marginal distribution function and the Copula function. The form of multiplication; find out the four indicators corresponding to the five types of Copula functions;

3) Determine the weight of each index in each function, calculate the attribute measurement value according to the weight value, and determine the classification standard corresponding to each copula function according to the attribute measurement value, and select the copula function corresponding to the optimal grade as the wind farm The optimal copula function for .

Further, the method includes: Garch(P,Q) model:

Among them: ε _t represents the variable residual, α ₀ > 0, α _i ≥ 0, i > 0, the marginal distribution is a combination of all greater than 0, P is the non-negative integer lag conditional variance, Q is the non-negative integer square conditional 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: the Euclidean distance d _Gu , the maximum distance d _z , the difference d _τ between the Kendall correlation coefficients and the difference d _ρ between the Spearman correlation coefficients.

Further, an attribute space of four indicators is established to generate a standard grading matrix:

a _ij =X _i.min +j·(X _i.max -X _i.min )/5, wherein X _i.min is the minimum value of the matrix element, and X _i.max is the maximum value of the matrix element;

x _i (i=1, 2, 3, 4) is the evaluation standard: P is the attribute space of the index x _i , P _j , j=1, 2,..., 5 is the level of pros and cons, P ₁ P is the best, and P is the worst; a _ij is the j _- th grading standard of the index i on the attribute space P; the index x _i has the attribute of P _m , denoted as "x _i ∝P _m ", and its attribute degree is denoted by λ _xi (P _j ) to represent, is the attribute measurement value, the calculation formula of the attribute measurement value of the model is:

where ω _i is the weight of the evaluation standard x _i , which is determined by the entropy method;

According to the confidence criterion, the pros and cons of the Copula model m are obtained:

In the formula, the confidence level is δ∈(0.5～1), and the Copula function of level P ₁ with the highest rating is used as the optimal joint distribution model of the desired wind farm output.

Compared with the prior art, the present invention has the following beneficial effects:

The invention transforms the uncertainty research of wind power output into deterministic research, describes the fluctuation of wind power with the garch model, establishes the edge distribution of the wind farm respectively, and then obtains the Copula function according to the joint output distribution of the wind farm, By comparing the correlation coefficient and verifying the degree of fit with the actual sample, the optimal Copula function is selected, and the Copula-garch model is finally established.

Description of drawings

FIG. 1 is a statistical diagram of the output frequency of a wind farm 1 according to an embodiment of the present invention;

FIG. 2 is a statistical diagram of the output frequency of the wind farm 2 according to an embodiment of the present invention;

3 is a statistical diagram of the combined output frequency of two wind farms according to an embodiment of the present invention;

FIG. 4 is a Clayton-Copula density function provided by an embodiment of the present invention;

5 is a Clayton-Copula distribution function diagram provided by an embodiment of the present invention;

6 is a binary t-Copula density function provided by an embodiment of the present invention;

7 is a diagram of a binary t-Copula distribution function provided by an embodiment of the present invention;

FIG. 8 is an empirical Copula distribution function diagram provided by an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

A method for output correlation of multiple wind farms based on the Copula-garch model, the method includes:

1) Collect the active power output distribution data of the wind farm;

2) The arch effect test is carried out on the wind farm, and then the Garch(P,Q) model is established to fit the marginal distribution function of the wind farm. Then, according to the SKlar theorem, the combined output distribution of multiple wind farms is divided into the marginal distribution function and the Copula function. The form of multiplication; find out the four indicators corresponding to the five types of Copula functions;

3) Determine the weight of each index in each function, calculate the attribute measurement value according to the weight value, and determine the classification standard corresponding to each copula function according to the attribute measurement value, and select the copula function corresponding to the optimal grade as the wind farm The optimal copula function for .

The active output sequence of multiple wind farms is a heteroscedastic sequence, and the Garch model can effectively fit long-term heteroscedastic variables. Therefore, it is more suitable for the establishment of the marginal distribution of wind farms.

Using the Garch(P,Q) model to fit the marginal distribution of wind farms can well describe the changes of variables.

Garch(P,Q) model:

Among them: ε _t represents the variable residual, α ₀ > 0, α _i ≥ 0, i > 0, the marginal distribution is a combination of all greater than 0, P is the non-negative integer lag conditional variance, Q is the non-negative integer square conditional variance.

Copula function exists as a function connecting joint distribution function and marginal distribution function, so it is also called connecting function.

For Sklar's theorem: Let the joint distribution function of random variables X ₁ , X ₂ ,...,X _n be H, and the marginal distribution function be F ₁ (X ₁ ),F ₂ (X ₂ ),...,F _n (X _n ), then there is a Copula function C such that H(x ₁ ,x ₂ ,...,x _n )=C[F ₁ (x ₁ ),F ₂ (x ₂ ),.... ..,F _n (x _n )]

If the marginal distribution function F is a continuous function, the joint distribution function C is uniquely determined. It can be seen from this theorem that the joint output distribution of multiple wind farms can be divided into the form of multiplying the marginal distribution function and the Copula function. Therefore, the variables are not required to have the same marginal distribution. Any marginal distribution can be connected to a joint distribution through the Copula function, and the information of the random sequence is in the marginal distribution function, so in the process of converting through the Copula function, almost no Data distortion occurs.

The five types of Copula functions include: Normal-Copula function, t-Copula function, Gumbel-Copula function, Clayton-Copula function and Frank-Copula function.

When using the Copula function, it includes the following steps: determine the marginal distribution function of the variable, calculate and obtain the parameters of the Copula function according to the skalr theorem, and then select the appropriate Copula function according to the appropriate evaluation index, and establish the distribution. Finally, according to the obtained correlation function.

The indicators that are mainly considered when analyzing and selecting the most suitable Copula function include fit indicators: the Euclidean distance d _Gu (the distance sum of the sample empirical distribution function value and the Copula joint distribution function value) and the maximum distance d _z (the sample empirical distribution function value). The smaller the difference between the value and the maximum value of the Copula joint distribution function), the closer the model is to the empirical distribution; and the correlation index: the difference between the Kendall correlation coefficient d _τ and the Spearman correlation coefficient difference d _ρ , the smaller the two values, the better The closer the empirical data model is to the selected model.

Definition: Take the sample (x _i , y _i ) from the two-digit overall sample (X, Y), denote F(x) and G(y) as the empirical distribution function of X and Y, and u and v as the transformation of X and Y After the uniform distribution, the empirical distribution of the sample can be defined as:

In the formula: I[G(y _i )≤v] is an indicative function, when F(x _i )≤u, I[F(x _i )≤u]=1; when F(x _i )>u , I[F(x _i )≤u]=0, set C( _{u i} ,vi ) as the value of Copula joint distribution function, then its Euclidean distance is defined as:

The maximum distance is defined as:

According to the above analysis, it can be concluded that the optimal Copula function can be classified as a decision-making problem, which can be carried out by using the entropy weight optimization theory. First, the attribute space of four indicators is established, and a standard hierarchical matrix is generated:

a _ij =X _i.min +j·(X _i.max -X _i.min )/5, wherein X _i.min is the minimum value of the matrix element, and X _i.max is the maximum value of the matrix element;

x _i (i=1, 2, 3, 4) is the evaluation standard: P is the attribute space of the index x _i , P _j , j=1, 2,..., 5 is the level of pros and cons, P ₁ P is the best, and P is the worst; a _ij is the j _- th grading standard of the index i on the attribute space P; the index x _i has the attribute of P _m , denoted as "x _i ∝P _m ", and its attribute degree is denoted by λ _xi (P _j ) to represent, is the attribute measurement value, the calculation formula of the attribute measurement value of the model is:

where ω _i is the weight of the evaluation standard x _i , which is determined by the entropy method;

According to the confidence criterion, the pros and cons of the Copula model m are obtained:

In the formula, the confidence level is δ∈(0.5～1), and the Copula function of level P ₁ with the highest rating is used as the optimal joint distribution model of the desired wind farm output.

The above entropy value method is specifically:

1) n targets to be evaluated, m evaluation indicators, and b _ij is the value of the j-th indicator of the i-th target. Normalization of indicators: Homogenization of heterogeneous indicators. Since the measurement units of various indicators are not uniform, before using them to calculate comprehensive indicators, they must be standardized, that is, the absolute value of the indicators is converted into relative value, and let x _ij =|x _ij |, so as to solve the problem of homogenization of various inhomogeneous index values. Moreover, since the values of positive indicators and negative indicators have different meanings (the higher the positive indicator value is, the better, and the lower the negative indicator value is, the better), therefore, different algorithms are used to standardize the data for high and low indicators. The specific method is as follows:

Positive indicators:

Negative indicators:

Then b' _ij is the value of the j-th index of the i-th target (i=1,2,...,n; j=1,2,...,m)

2) Calculate the proportion of the i-th target under the j-th indicator to this indicator:

3) Calculate the entropy value of the jth index:

Here, two wind farms 1 and 2 in Fuxin City, Liaoning Province, which are geographically close to each other, are taken as examples. The real data of active power output in 2018 is taken as a simulation example. The data sampling interval is 15 minutes, and the time is one year. First, determine the marginal distribution function of wind power output.

The calculation method of the results in this embodiment is the kernel density estimation method, and the output frequency statistics of the two wind farms are used, as shown in Figure 1 and 2, and the joint output distribution diagram, as shown in Figure 3. It can be seen that the output of the two wind farms is extremely low on the upper tail, and the lower tail protrudes significantly, so the two wind farms have asymmetric distribution of the tail, that is, when the output of the two wind farms is small at the same time, it accounts for a large proportion.

Due to the strong randomness and uncertainty of the output of wind farms, and the normality test of the two wind farms is carried out, the results show that they do not obey the normal distribution and cannot be simulated by common distributions such as t distribution and normal distribution. The output probability distribution of the wind farm. Therefore, the more versatile Copula function is used for correlation modeling. The marginal distribution of wind power output is simulated by the non-parametric estimation method, namely the kernel density estimation method, as shown in Figure 4 and Figure 5, respectively.

Selection of the optimal Copula function

According to the characteristics of five Copula functions, three functions, t-Copula function, Clayton-Copula function and Normal-Copula function, which describe asymmetric distribution and include tail distribution characteristics are selected for correlation evaluation. With the help of the entropy weight optimization theory, the optimal function is selected to complete the modeling of the correlation of the wind farm. The index parameter values are shown in Table 1.

Table 1 Evaluation index parameter values

The attribute test matrix is obtained as:

Then calculate the four entropy weights of the four models respectively, and then evaluate the attribute measurement values: λ(P ₁ )=0.6154, λ(P ₂ )=0.3832 (which is the attribute measurement value of Clayton-Copula), and take the confidence δ= 0.65 to get the m value corresponding to each function. If m=2, the corresponding rating is P ₂ . The corresponding ratings obtained by each function are shown in Table 2.

Table 2 Summary of rating results of various types of Copula models

According to the data in the chart, the Clayton-Copula function is the closest to the final result. The maximum likelihood estimation method is used to verify the results, and the Euclidean squared distance of the Clayton-Copula function is the smallest. Therefore, the Clayton-Copula function is selected to describe the correlation between wind farm 1 and wind farm 2.

Bringing the edge distributions of the kernel density estimates of the two wind farms into the Clayton-Copula function and the binary t-Copula function can obtain the density function and distribution function diagrams modeled by the two functions

The t-Copula and Clayton-Copula functions are analyzed and compared with the empirical Copula functions respectively. The calculation and analysis results are shown in Figures 4, 5, 6, 7, and 8. The Clayton-Copula functions are closer to the empirical Copula functions. And according to the Clayton-Copula function characteristics: asymmetric distribution, lower tail correlation, upper tail asymptotically independent, just in line with the characteristics of data distribution. Therefore, the Clayton-Copula function is the best correlation function of the two wind farms, thus, a Copula-garch correlation model based on the Clayton-Copula function is established.

In this embodiment, for multiple wind farms with similar geographical locations, the kernel density estimation method is used to establish an edge distribution solution, and an output correlation function between multiple wind farms is established. Among various Copula functions, the Kendall correlation coefficient, Spearman correlation coefficient, Euclidean distance and maximum distance are used to analyze and compare them. Combined with the entropy weight optimization theory, the Clayton-Copula function is determined to be the difference between wind farm 1 and wind farm 2. The optimal correlation function is used to establish the optimal Copula-garch correlation model. It can be seen from the function that the joint distribution has a strong lower tail correlation. In the application of wind power analysis, ignoring this correlation may lead to a series of situations that are inconsistent with the actual operation and increase the risk of safe and stable operation of the power grid.

The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

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: epsilon_tRepresenting the residual of the variable, alpha₀＞0，α_iAnd 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 d_GuMaximum distance d_zThe difference d between the Kendall correlation coefficients_τDifference d between the correlation coefficient and Spearman_ρ。

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:

a_ij＝X_i.min+j·(X_i.max-X_i.min) /5 wherein X_i.minIs the minimum value of the matrix elements, X_i.maxIs the maximum value of the matrix elements;

x_i(i ═ 1,2,3,4) as evaluation criteria: p is an index x_iProperty space of P_jJ 1,2, 5 is a quality grade, P₁Grade optimum, P₅Worst-grade; a is_ijThe j-th grading standard of the index i on the attribute space P; index x_iHaving P_mAttribute, let' x_i∝P_m", the degree of attribute is represented by λ_xi(P_j) 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 omega_iTo evaluate the standard x_iThe 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.