CN107918920B - Output correlation analysis method for multiple photovoltaic power stations - Google Patents

Abstract

The invention discloses a power output correlation score of a multi-photovoltaic power stationThe analysis method includes the steps of constructing a simplified K-level pair copula function model by utilizing collected photovoltaic output historical data of a photovoltaic power station, sampling by utilizing the simplified K-level pair copula function model, and generating a model sample point set P ═ P₁,P₂,…，P_i,…，P_n]And obtaining the output correlation among the multi-photovoltaic power stations through the linear correlation coefficient of the model sample point set P. The method considers the relevance among a plurality of power stations, simultaneously, the simplified model can greatly increase the calculation speed, the model is utilized to generate the photovoltaic output samples, the pairwise relevance analysis among the plurality of photovoltaic power stations is realized under the condition of accurate and less samples, and the analysis accuracy is improved.

Description

Output correlation analysis method for multiple photovoltaic power stations

Technical Field

The invention relates to a new energy of an electric power system, in particular to output correlation analysis of a multi-photovoltaic power station, and belongs to the field of data analysis.

Background

In recent years, large-scale photovoltaic is connected into a transmission network and a distribution network of a power system so as to relieve the problem of environmental pollution and reduce network loss. Compared with traditional schedulable power generation, photovoltaic power generation has obviously different characteristics. Firstly, due to the influence of meteorological factors, the photovoltaic power is intermittent and random; secondly, when the number of the photovoltaic power stations is increased, the correlation of the output among the photovoltaic power stations becomes more complex, so that the output of the multi-photovoltaic power station needs to be modeled and subjected to correlation analysis to better predict the operation capacity of the power system under the condition of photovoltaic access.

Modeling is carried out aiming at photovoltaic output and relevance analysis is carried out, and the existing methods comprise three methods: one is to assume that the photovoltaic output follows Beta probability distribution, the other is to obtain a probability model of the photovoltaic output through hourly diffuse radiation, and the third is to adopt multivariate nuclear density estimation method. The probability models of the former two methods only consider the randomness of photovoltaic output, but do not consider the correlation between the photovoltaic outputs, and are not suitable for analyzing and planning the power system. The third method has higher calculation accuracy and calculation efficiency only under a two-dimensional model, and the calculation burden is increased sharply when the number of the photovoltaic power stations is increased.

The Copula function is used for modeling the output of a plurality of photovoltaic power stations and analyzing the relevance, so that the method is an effective method. Different Copula functions can describe the relevance of two different random variables, and the pair Copula model is the extension of Copula theory, can make up different Copula functions, and then carry out accurate modeling to photovoltaic output to carry out correlation analysis.

Disclosure of Invention

The invention aims to overcome the defects that the output modeling of a multi-photovoltaic power station is inaccurate and relevance is not considered in the conventional method, provides a multi-photovoltaic power station output modeling method, and performs output relevance analysis on the basis of the method so as to better evaluate the influence of a photovoltaic access power system.

The technical solution to solve the above technical problems of the present invention is as follows:

a method for analyzing the output correlation of a multi-photovoltaic power station comprises the following specific steps:

1) collecting photovoltaic output historical data from n photovoltaic power stations, wherein m photovoltaic output historical samples collected in the ith photovoltaic power station are as follows: s_i＝[s_i1,s_i2,…,s_im]The historical samples collected by the n power stations are as follows: s₁,S₂,…,S_n；

2) Constructing a simplified K (K is 3 or 4) level pair copula function model by utilizing the photovoltaic output historical data;

3) sampling by using the simplified pair copula function model to generate a model sample point set P ═ P₁,P₂,…,P_n],P_i＝[p_i1,p_i2,…,p_iq]Q is the number of photovoltaic output model samples of the ith photovoltaic power station generated by utilizing a pair copula function model;

4) calculating the linear correlation coefficient of the model sample point set P according to the following formula to obtain the output correlation and coefficient between the multi-photovoltaic power stations

The larger the value, the stronger the linear correlation between the representative photovoltaic power station i and the representative photovoltaic power station j:

wherein, P_i、P_jIs any two sample points in the set P of model sample points,

are respectively P_iAnd P_jThe standard deviation of (a) is determined,

are respectively P_iAnd P_jE is desired.

Constructing a simplified K (K is 3 or 4) level pair copula function model in the step 2, and specifically comprising the following steps:

2A. for historical samples S₁,S₂,…,S_nBy using a nuclear density estimation method to obtainTo edge probability distribution function F₁,F₂,…,F_n；

2B. Using the following equation, the historical sample S₁,S₂,…,S_nTransformed into transformed samples u₁,u₂,…,u_n：

u_i＝F_i(S_i),i＝1,2,...,n

Wherein u is_i＝[u_i1,u_i2,…,u_im],i＝1,…,n；

2C. Using transform samples u₁,u₂,…,u_nRespectively applying normal copula function, Frank copula function, Clayton copula function, t copula function, Guassian copula function and Gumbel copula function to the first layer L₁Fitting each node of the copula sequence to obtain a first layer L₁copula sequence { C_1,2,C_1,3,…,C_1,nIn which C is_1,iIs a first layer L₁The copula function, i is 1,2, … n, for each node, performing euclidean distance test by using the above various copula functions, and if the euclidean distance is the minimum, the copula function is the optimal copula function of the node, then the respective optimal copula function combination of all nodes in the first layer is the optimal copula sequence;

2D. transform sample u₁And u_1+i(i ═ 1, …, n-1) into the following formula:

u produced from the first layer_2|1,u_3|1,…,u_n|1The method of 2C is repeated as a new transformed sample, resulting in a second layer L₂copula sequence { C_2,3|1,C_2,4|1,…,C_2,n|1}；

2E. similarly, transform samples u obtained from layer j-1_j|1,…,j-1And u_{j+i|1,…,j-1}(i ═ 1, …, n-1) into the following formula:

u produced from the j-1 th layer_j|1,…,j-1,u_{j+1|1,…,j-1},…,u_n|1,…,j-1The method of 2C is repeated as a new transformed sample to obtain the j-th layer L_jcopula sequence { C_{j,j+1|1,…,j-1},C_{j,j+2|1,…,j-1},C_{j,n|1,…,j-1}}；

2F. method with 2E until the K-th layer L is produced_Kcopula sequence { C_{K,K+1,3|1,…,K-1},C_{K,K+2|1,…,K-1},C_{K,n|1,…,K-1}}；

2G, from the K +1 th layer to the n-1 th layer, simplifying the two layers into a multivariable normal copula function based on L in 2F_Kcopula sequence, using the following formula to generate transform samples u_K+1|1,…,K,u_K+2|1,…,K,…,u_n|1,…,K：

Fitting the multivariate normal copula function by using the samples and the copula fit of the self-carried function copula of the matlab software to obtain

Sampling by using a K-layer pair copula function model in the step 3 to generate photovoltaic output model sample points, which specifically comprises the following steps:

3A. Generation of K obeys [0,1 ]]Uniformly distributed samples U_j|1,…,j-1(j ═ 1, …, K), yielding n-K samples X that obey a standard normal distribution_K+i|1,…,K(i-1, …, n-K) using the multivariate normal copula function

And sample X_K+i|1,…,K(i-1, …, n-K), using the following formula to produce n-K samples U_K+i|1,…,K(i＝1,…,n-K)：

Using two samples U generated in 3A_j|1,…,j-1(j ═ 1, …, K) and U_K+i|1,…,K(i ═ 1, …, n-K), using the pair copula function model constructed in step 2, each new transformed sample U was generated using the following equation:

3C. utilization type

And obtaining a photovoltaic output sample point set P generated by the pair copula model.

Compared with the prior art, the invention has the beneficial effects that:

conventionally, when a multi-photovoltaic power station carries out power correlation analysis, a large amount of original sampling data needs to be utilized, so that the calculation speed is low, the correlation relation is not deeply excavated, a photovoltaic power station output modeling method is used for collecting sample points, the sample data amount can be reduced on the basis of keeping original sample characteristics, but the relevance among the multiple power stations cannot be considered in the photovoltaic power station output modeling by the traditional method, so that the modeling is not accurate enough. The photovoltaic output of the photovoltaic power station is modeled by the simplified pair copula, the relevance among a plurality of power stations is considered by the model, meanwhile, the calculation speed can be greatly increased by the simplified model, the photovoltaic output sample is generated by the model, pairwise relevance analysis among the plurality of photovoltaic power stations is realized under the condition of accurate and small amount of samples, and the analysis accuracy is improved.

Drawings

FIG. 1 is a flow chart of a method for analyzing the output correlation of a multi-photovoltaic power plant

FIG. 2 is a schematic diagram of the K-class pair copula structure in step 2

FIG. 3 is a flow chart of constructing a simplified K (K ═ 3 or 4) class pair copula function model in step 2

Detailed Description

In order to make the invention more comprehensible, preferred embodiments are described in detail below with reference to the accompanying drawings. Fig. 1 is a flowchart of a method for analyzing the output correlation of a multi-photovoltaic power station, which includes the following steps 1 to 4.

Step 1,

Collecting photovoltaic output historical data from n photovoltaic power stations, wherein m photovoltaic output historical samples collected in the ith photovoltaic power station are as follows: s_i＝[s_i1,s_i2,…,s_im]The historical samples collected by the n power stations are as follows: s₁,S₂,…,S_n；

Step 2, constructing a simplified K (K is 3 or 4) level pair copula function model by using the photovoltaic output historical data, wherein fig. 2 is a K level pair copula structure schematic diagram without considering the layer of an edge distribution function, the figure has K +1 level pair copula and 1 st to K level layers are the searched optimal pair copula sequence models, and the higher level data are weaker in relevance, so that the K +1 to n-1 levels can be completely simplified into one layer, namely the K +1 level, and can be approximately represented by a multivariable normal copula function, and the calculation speed can be accelerated. FIG. 3 is a complete flow chart of step 2, comprising the following steps 2A to 2G:

2A. for historical samples S₁,S₂,…,S_nThe method adopts a kernel density estimation method, and concretely adopts a function ksDensity carried by Matlab software to obtain an edge probability distribution function F₁,F₂,…,F_n；

2B. Using the following equation, the historical sample S₁,S₂,…,S_nTransformed into transformed samples u₁,u₂,…,u_n，

u_i＝F_i(S_i),i＝1,2,...,n

Wherein u is_i＝[u_i1,u_i2,…,u_im],i＝1,…,n；

2C. Using transform samples u₁,u₂,…,u_nRespectively applying normal copula function, Frank copula function, Clayton copula function, t copula function, Guassian copula function and Gumbel copula function to the first layer L₁coFitting each node of the pula sequence to obtain a copula function sequence: { C_1,2,C_1,3,…,C_1,nIn which C is_1,iI-1, 2, … n is the first layer L₁And fitting the several copula functions to perform Euclidean distance test on various copula function combination forms by using the following formula, wherein the minimum Euclidean distance is the copula function with the optimal node, and the copula function combination with the optimal nodes in the first layer is the optimal copula sequence:

wherein, I is an indication function, if the condition in the parentheses is satisfied, the indication function is 1, and if the condition is not satisfied, the indication function is 0, and C represents the copula functions;

2D. transform sample u₁And u_1+i(i-1, …, n-1) into the formula to yield u of the first layer_2|1,u_3|1,…,u_n|1：

U produced from the first layer_2|1,u_3|1,…,u_n|1The method of 2C is repeated as a new transformed sample, resulting in a second layer L₂copula sequence { C_2,3|1,C_2,4|1,…,C_2,n|1}；

2E. similarly, transform samples u obtained from layer j-1_j|1,…,j-1And u_{j+i|1,…,j-1}(i ═ 1, …, n-1) into the following formula:

u produced from the j-1 th layer_j|1,…,j-1,u_{j+1|1,…,j-1},…,u_n|1,…,j-1The method of 2C is repeated as a new transformed sample to obtain the j-th layer L_jcopula sequence { C_{j,j+1|1,…,j-1},C_{j,j+2|1,…,j-1},C_{j,n|1,…,j-1}}；

2F. method with 2E until the K-th layer L is produced_Kcopula sequence { C_{K,K+1,3|1,…,K-1},C_{K,K+2|1,…,K-1},C_{K,n|1,…,K-1}}；

2G, from the K +1 th layer to the n-1 th layer, can be simplified into a multivariable normal copula function based on L in 2F_Kcopula sequence, using the following formula to generate transform samples u_K+1|1,…,K,u_K+2|1,…,K,…,u_n|1,…,KFitting the multivariate normal copula function by using the samples and the copula fit function carried by the matlab software to obtain

Step 3, sampling by using the simplified pair copula function model to generate photovoltaic output model sample points, and the specific steps are as follows:

3A. Generation of K obeys [0,1 ]]Uniformly distributed samples U_j|1,…,j-1(j ═ 1, …, K), yielding n-K samples X that obey a standard normal distribution_K+i|1,…,K(i-1, …, n-K) using the multivariate normal copula function

And sample X_K+i|1,…,K(i-1, …, n-K), using the following formula to produce n-K samples U_K+i|1,…,K(i＝1,…,n-K)：

Using two samples U generated in 3A_j|1,…,j-1(j ═ 1, …, K) and U_K+i|1,…,K(i ═ 1, …, n-K), using the pair copula function model constructed in step 2, each new transformed sample U was generated using the following equation:

3C. utilization type

And obtaining a photovoltaic output sample point set P generated by the pair copula model.

Step 4, calculating the linear correlation coefficient of the model sample point set P according to the following formula to obtain the output correlation and coefficient between the multi-photovoltaic power stations

The larger the value, the stronger the linear correlation between the representative photovoltaic power station i and the representative photovoltaic power station j:

wherein, P_i、P_jIs any two sample points in the set P of model sample points,

are respectively P_iAnd P_jThe standard deviation of (a) is determined,

are respectively P_iAnd P_jE is desired.

The method adopts the simplified pair copula to model the output of the photovoltaic power station, the model considers the relevance among a plurality of power stations, simultaneously the simplified model can greatly increase the calculation speed, the output sample is generated by utilizing the model, the pairwise relevance analysis among the photovoltaic power stations is realized under the condition of accurate and less samples, and the analysis accuracy is improved.

Claims (2)

1. A method for analyzing output correlation of a multi-photovoltaic power station is characterized by comprising the following steps:

1) collecting photovoltaic output historical data from n photovoltaic power stations as historical sample S₁，S₂，...，S_nAnd the historical sample of m photovoltaic outputs collected by the ith photovoltaic power station is as follows: s_i＝[s_i1，s_i2，...，s_im]；

2) Utilize above-mentioned photovoltaic output historical data, construct and simplify K level pair copula function model, K is 3 or 4, specifically:

2A. for historical samples S₁，S₂，...，S_nObtaining an edge probability distribution function F by adopting a kernel density estimation method₁，F₂，...，F_n；

2B. sampling the history S₁，S₂，...，S_nTransformed into transformed samples u₁，u₂，...，u_nThe formula is as follows:

u_i＝F_i(S_i)，i＝1，2，...，n

wherein u is_i＝[u_i1，u_i2，...，u_im]，i＝1，...，n；

2C. Using transform samples u₁，u₂，...，u_nRespectively applying normal copula function, Frank copula function, Clayton copula function, t copula function, Guassian copula function and Gumbel copula function to the first layer L₁Fitting each node of the copula sequence to obtain a first layer L₁copula sequence { C_1，2，C_1，3，...，C_1，nIn which C is_1，iIs a first layer L₁The copula functions, i is 1,2,.. n, and for each node, performing Euclidean distance test by using the various copula functions, wherein the minimum Euclidean distance is the copula function with the optimal node, and the copula function combination with the optimal nodes of the first layer is the optimal copula sequence;

2D. transform sample u₁And u_1+i1, n-1 is substituted into the following formula:

u produced from the first layer_2|1，u_3|1，...，u_m|1Repeating the step 2C as a new transformed sample to obtain a second layer L₂copula sequence { C_2，3|1，C_2，4|1，...，C_2，n|1}；

2E. similarly, transform samples u obtained from layer j-1_{j|1，...，j-1}And u_{j+i|1，...，j-1}1, n-1 is substituted into the following formula:

u produced from the j-1 th layer_{j|1，...，j-1}，u_{j+1|1，...，j-1}，...，u_{n|1，...，j-1}Repeating the step 2C as a new transform sample to obtain a j layer L_jcopula sequence { C_{j，j+1|1，...，j-1}，C_{j，j+2|1，...，j-1}，C_{j，m|1，...，j-1}}；

2F. method with 2E until the K-th layer L is produced_Kcopula sequence { C_{K，K+1，3|1，...，K-1}，C_{K，K+2|1，...，K-1}，C_{K，n|1，...，K-1}}；

2G, from the K +1 th layer to the n-1 th layer, simplifying the two layers into a multivariable normal copula function based on the L in the step 2F_Kcopula sequence, using the following formula to generate transform samples u_{K+1|1，...，K}，u_{K+2|1，...，K}，...，u_{n|1，...，K}：

Fitting the multivariate normal copula function by using the samples and the copula fit of the self-carried function of matlab software to obtain

3) Sampling by using the simplified K-level pair copula function model to generate a model sample point set P ═ P₁，P₂，...，P_i，...，P_n]，P_i＝[p_i1，p_i2，...，p_iq]Q is the number of photovoltaic output model samples of the ith photovoltaic power station generated by utilizing the simplified K-level pair copula function model;

4) calculating the linear correlation coefficient of the model sample point set P according to the following formula to obtain the output correlation and coefficient between the multi-photovoltaic power stations

The larger the value, the stronger the linear correlation between the representative photovoltaic power station i and the representative photovoltaic power station j:

wherein, P_i、P_jIs any two sample points in the set P of model sample points,

are respectively P_iAnd P_jThe standard deviation of (a) is determined,

are respectively P_iAnd P_jE is desired.

2. The method of claim 1 wherein the sampling with the K-layer pair copula function model to generate photovoltaic output model sample points comprises the steps of:

3A. Generation of K obeys [0,1 ]]Uniformly distributed samples U_{j|1，...，j-1}J 1.. K, yielding n-K samples X that follow a standard normal distribution_{K+i|1，...，K}，i＝1,., n-K, using the multivariate normal copula function

And sample X_{K+i|1，...，K}n-K, using the formula to produce n-K samples U_{K+i|1，...，K}，i＝1，...，n-K：

Using two samples U generated in step 3A_{j|1，...，j-1}J 1, K and U_{K+i|1，...，K}Using the simplified K-level pair copula function model constructed in step 2, each new transform sample U is generated using the following equation:

3C. utilization type

And obtaining a photovoltaic output sample point set P generated by the pair copula model.

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