CN112952843B - Distributed photovoltaic probability power flow calculation method for power distribution network based on Copula theory - Google Patents
Distributed photovoltaic probability power flow calculation method for power distribution network based on Copula theory Download PDFInfo
- Publication number
- CN112952843B CN112952843B CN202110338862.5A CN202110338862A CN112952843B CN 112952843 B CN112952843 B CN 112952843B CN 202110338862 A CN202110338862 A CN 202110338862A CN 112952843 B CN112952843 B CN 112952843B
- Authority
- CN
- China
- Prior art keywords
- function
- power
- distributed photovoltaic
- copula
- variable
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
Landscapes
- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Photovoltaic Devices (AREA)
Abstract
The application provides a distributed photovoltaic probability power flow calculation method of a power distribution network based on a Copula theory, which comprises the following steps: constructing an accumulated distribution function and an inverse function of each distributed photovoltaic output power, selecting a Copula function, and generating a random number matrix; sampling the generated random number matrix by using a Latin hypercube sampling method to obtain a Latin hypercube sampled sample matrix, and establishing the sample matrix of the distributed photovoltaic power generation variable according to the inverse function of the accumulated distribution function of the distributed photovoltaic power generation variable; and taking the established sample matrix of the distributed photovoltaic power generation power variable as an input quantity to carry into a node injection power equation f and a branch power flow equation g for cyclic calculation to obtain calculated values of the system node voltage X and the branch power flow Z, and calculating digital characteristics and probability distribution of the output random variable node voltage X and the branch power flow Z by using a statistical method. The method can effectively improve the calculation accuracy and has shorter solving time.
Description
Technical Field
The application relates to the technical field of power flow design of power systems, in particular to a distributed photovoltaic probability power flow calculation method of a power distribution network based on Copula theory.
Background
In order to solve the problems of energy shortage, ecological environment deterioration and the like, the development concept of intensive, intelligent, low-carbon and green novel urban construction is provided in China, the innovation of the traditional urban system and the technological innovation are emphasized, and the development mode of new energy and low-carbon economy is changed. In this context, as a green power generation technology, the level of penetration in the distribution network is gradually increasing, and distributed power generation systems based on renewable energy sources have attracted more and more attention, becoming a viable option in sustainable development environments. However, the output power of the distributed photovoltaic is closely related to meteorological conditions such as solar radiation and temperature, and the output power among the distributed photovoltaic power stations with relatively close geographic positions has relatively strong space-time correlation, so that the research of the probability power flow calculation problem considering the distributed photovoltaic correlation has important significance for accurately and comprehensively evaluating the power flow operation characteristics of the power system.
Disclosure of Invention
In view of the above, the application aims to provide a distributed photovoltaic probability power flow calculation method of a power distribution network based on Copula theory, which can effectively improve calculation accuracy and has shorter solving time.
The application is realized by adopting the following scheme: a distributed photovoltaic probability load flow calculation method of a power distribution network based on a Copula theory specifically comprises the following steps:
constructing an accumulated distribution function and an inverse function of each distributed photovoltaic output power, selecting a Copula function, and generating a random number matrix;
sampling the generated random number matrix by using a Latin hypercube sampling method to obtain a Latin hypercube sampled sample matrix, and establishing the sample matrix of the distributed photovoltaic power generation variable according to the inverse function of the accumulated distribution function of the distributed photovoltaic power generation variable;
and taking the established sample matrix of the distributed photovoltaic power generation power variable as an input quantity to carry into a node injection power equation f and a branch power flow equation g for cyclic calculation to obtain calculated values of the system node voltage X and the branch power flow Z, and calculating digital characteristics and probability distribution of the output random variable node voltage X and the branch power flow Z by using a statistical method.
Further, the step of constructing the cumulative distribution function and the inverse function of each distributed photovoltaic output power, selecting a Copula function, and generating a random number matrix specifically includes the following steps:
constructing an accumulated distribution function and an inverse function of each distributed photovoltaic output power according to historical data of the distributed photovoltaic power generation output power;
constructing an empirical Copula function of the output power of the distributed photovoltaic power generation; the least square Euclidean distance is used as a goodness-of-fit index, the square Euclidean distance between each theoretical Copula function and the empirical Copula function is calculated, and the Copula function corresponding to the minimum value is selected as the theoretical Copula function to describe the output correlation between the distributed photovoltaics;
and generating a random number matrix meeting the correlation by using the selected theoretical Copula function according to the correlation coefficient matrix of the distributed photovoltaic power generation power variable.
Further, the building of the cumulative distribution function and the inverse function of each distributed photovoltaic output power is specifically as follows:
empirical cumulative distribution function u=f of distributed photovoltaic output power random variable w e (w) and its inverse function w=f e -1 The calculation steps of (u) are as follows:
s201: n discrete data w for a random variable w 1×n ＝[w 1 ,…,w n ]Sequencing from small to large to obtain w 1×n '＝[w 1 ',…,w n ']；
S202: the empirical cumulative distribution function u=f of the random variable w is calculated as follows e (w) and its inverse function w=f e -1 (u)。
Wherein round is a fractional part rounding function, w j ' is the actual measurement data of the jth random variable after being sequenced from small to large, and n is the number of actual measurement discrete data of the random variable.
Further, the empirical Copula function is as follows:
wherein I is an indicating function, i=0 when the condition in brackets is not satisfied, whereas i=1; w (W) n×M ＝[w 1,j ,...,w M,j ]J=1,..n is an n x M-dimensional matrix of observation samples,is a sequence statistic and is 1.ltoreq.i 1 ,...,i M ≤n；i M Indicating the ith of the ordered random variable measured data from small to large M Bit, w M,j The jth measured discrete data representing the mth random variable, M being the number of random variables.
The square Euclidean distance between each theoretical Copula function and the empirical Copula function is as follows:
wherein C is the theoretical Copula function selected for use, C e Is an empirical Copula function;
according to the above formula, the square Euclidean distance d between each theoretical Copula function and the empirical Copula function is calculated n (C,C e ) And selecting a theoretical Copula function corresponding to the least square Euclidean distance to describe the relevance of the distributed photovoltaic output.
Further, the generating the random number matrix satisfying the correlation by using the selected theoretical Copula function according to the correlation coefficient matrix of the distributed photovoltaic power generation power variable specifically includes:
assume that the distributed photovoltaic power generation power variable has M random variables, which are w respectively 1 ,w 2 ,...,w M The cumulative distribution function is u=f e (w) the inverse of the cumulative distribution function is w=f e -1 (u) the correlation coefficient matrix is ρ x The number of random numbers is N, and a selected theoretical Copula function is utilized to generate a matrix meeting the correlation coefficient as rho x Random number matrix U of (2) N×M The method comprises the following steps:
wherein u is i,j Represents line ij columns of elements.
Further, the empirical Copula function of the output power of the distributed photovoltaic power generation is constructed; the least square Euclidean distance is used as a goodness-of-fit index, the square Euclidean distance between each theoretical Copula function and the empirical Copula function is calculated, and the Copula function corresponding to the minimum value is selected as the theoretical Copula function to describe the output correlation between the distributed photovoltaics, wherein the output correlation is specifically as follows:
random number matrix U generated by Latin hypercube sampling pair N×M U of the first column of (2) 1 Sampling, wherein the Latin hypercube sampling number is set to K times, K<N and N are the number of random numbers, and are 0,1]The interval is equally divided into K subintervalsFor the t th subinterval->In U 1 Finding one sample u h,1 Satisfy subinterval->And record sample u h,1 In U 1 Position c in (a) t After sampling all subintervals, the resulting position vector is c= [ C = 1 ,...,c k ]Based on the position vector C, the random number matrix U N×M Corresponding samples are selected from the second column to the M column, and a sample matrix UL after Latin hypercube sampling is established K×M ：
According to Latin hypercube sampled sample matrix UL K×M ，Representing the M-th random variable position vector as c k Is a sample of the data; and combining the inverse of the cumulative distribution function of the distributed photovoltaic power variablesFunction w=f e -1 (u) generating a sample matrix W of distributed photovoltaic power generation power variables K×M ：
The method comprises the steps of taking a sample matrix of an established distributed photovoltaic power generation power variable as an input quantity to carry into a node injection power equation f and a branch power flow equation g for cyclic calculation to obtain calculated values of a system node voltage X and a branch power flow Z, and calculating and outputting digital characteristics and probability distribution of the random variable node voltage X and the branch power flow Z by using a statistical method, wherein the digital characteristics and probability distribution are specifically as follows:
sample matrix W of the established distributed photovoltaic power generation power variable K×M Taking the input quantity of the deterministic power flow calculation model as the input quantity of the node injection power equation f and the branch power flow equation g for cyclic calculation to obtain calculated values of the node voltage X and the branch power flow Z of the system;
extracting distributed photovoltaic power generation power variable sample matrix W by calculation in each cycle K×M Is used as a power flow calculation input quantity;
and calculating the digital characteristics and probability distribution of the node voltage X and the branch power flow Z of the output random variable by adopting a statistical method.
The application also provides a distributed photovoltaic probability power flow calculation system of the power distribution network based on the Copula theory, which comprises a memory, a processor and computer program instructions which are stored on the memory and can be run by the processor, wherein the computer program instructions can realize the method steps when the processor runs the computer program instructions.
The application also provides a computer readable storage medium having stored thereon computer program instructions executable by a processor, which when executed by the processor are capable of carrying out the method steps as described above.
Compared with the prior art, the application has the following beneficial effects: the application fully considers the correlation problem among DG generated power, describes the correlation of distributed photovoltaic output by selecting a reasonable Copula function, combines the Copula theory with a Latin hypercube sampling method, and provides a probability power flow calculation method capable of flexibly processing the correlation of the random variable of the distributed photovoltaic input, which can effectively improve the calculation accuracy and has shorter solving time.
Drawings
FIG. 1 is a schematic diagram of a method according to an embodiment of the present application.
Fig. 2 is a schematic diagram of a specific example topology of an embodiment of the present application.
FIG. 3 is a graph showing the voltage variance distribution of each node of the system calculated by the Monte Carlo method according to the embodiment of the present application.
FIG. 4 is a graph showing the variance distribution of the power flow of each node of the system calculated by the Monte Carlo method according to the embodiment of the present application.
Detailed Description
The application will be further described with reference to the accompanying drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
As shown in fig. 1, the embodiment provides a distributed photovoltaic probability power flow calculation method for a power distribution network based on Copula theory, which specifically includes the following steps:
constructing an accumulated distribution function and an inverse function of each distributed photovoltaic output power, selecting a Copula function, and generating a random number matrix;
sampling the generated random number matrix by using a Latin hypercube sampling method to obtain a Latin hypercube sampled sample matrix, and establishing the sample matrix of the distributed photovoltaic power generation variable according to the inverse function of the accumulated distribution function of the distributed photovoltaic power generation variable;
and taking the established sample matrix of the distributed photovoltaic power generation power variable as an input quantity to carry into a node injection power equation f and a branch power flow equation g for cyclic calculation to obtain calculated values of the system node voltage X and the branch power flow Z, and calculating digital characteristics and probability distribution of the output random variable node voltage X and the branch power flow Z by using a statistical method.
Further, the step of constructing the cumulative distribution function and the inverse function of each distributed photovoltaic output power, selecting a Copula function, and generating a random number matrix specifically includes the following steps:
constructing an accumulated distribution function and an inverse function of each distributed photovoltaic output power according to historical data of the distributed photovoltaic power generation output power;
constructing an empirical Copula function of the output power of the distributed photovoltaic power generation; the least square Euclidean distance is used as a goodness-of-fit index, the square Euclidean distance between each theoretical Copula function and the empirical Copula function is calculated, and the Copula function corresponding to the minimum value is selected as the theoretical Copula function to describe the output correlation between the distributed photovoltaics;
and generating a random number matrix meeting the correlation by using the selected theoretical Copula function according to the correlation coefficient matrix of the distributed photovoltaic power generation power variable.
In this embodiment, the building of the cumulative distribution function and the inverse function of each distributed photovoltaic output power is specifically:
empirical cumulative distribution function u=f of distributed photovoltaic output power random variable w e (w) and its inverse function w=f e -1 The calculation steps of (u) are as follows:
s201: n discrete numbers for a random variable wAccording to w 1×n ＝[w 1 ,…,w n ]Sequencing from small to large to obtain w 1×n '＝[w 1 ',…,w n ']；
S202: the empirical cumulative distribution function u=f of the random variable w is calculated as follows e (w) and its inverse function w=f e -1 (u)。
Wherein round is a fractional part rounding function, w j ' is the actual measurement data of the jth random variable after being sequenced from small to large, and n is the number of actual measurement discrete data of the random variable.
In this embodiment, the empirical Copula function is as follows:
wherein I is an indicating function, i=0 when the condition in brackets is not satisfied, whereas i=1; w (W) n×M ＝[w 1,j ,...,w M,j ]J=1,..n is an n x M-dimensional matrix of observation samples,is a sequence statistic and is 1.ltoreq.i 1 ,...,i M ≤n；i M Indicating the ith of the ordered random variable measured data from small to large M Bit, w M,j The jth measured discrete data representing the mth random variable, M being the number of random variables.
The square Euclidean distance between each theoretical Copula function and the empirical Copula function is as follows:
wherein C is the theoretical Copula function selected for use, C e Is an empirical Copula function;
according to the above formula, the square Euclidean distance d between each theoretical Copula function and the empirical Copula function is calculated n (C,C e ) And selecting a theoretical Copula function corresponding to the least square Euclidean distance to describe the relevance of the distributed photovoltaic output.
In this embodiment, the square euclidean distance between each theoretical Copula function and the empirical Copula function is as follows:
wherein C is a theoretical Copula function selected, and mainly comprises a normal Copula function, a tCopula function, a Gumbelcopula function, a ClaytonCoula function and a FrankCoula function. C (C) e Is an empirical Copula function;
according to the above formula, the square Euclidean distance d between each theoretical Copula function and the empirical Copula function is calculated n (C,C e ) And selecting a theoretical Copula function corresponding to the least square Euclidean distance to describe the relevance of the distributed photovoltaic output.
In this embodiment, the generating, according to the correlation coefficient matrix of the distributed photovoltaic power generation power variable, the random number matrix satisfying the correlation by using the selected theoretical Copula function specifically includes:
assume that the distributed photovoltaic power generation power variable has M random variables, which are w respectively 1 ,w 2 ,...,w M The cumulative distribution function is u=f e (w) the inverse of the cumulative distribution function is w=f e -1 (u) the correlation coefficient matrix is ρ x The number of random numbers is N, and a selected theoretical Copula function is utilized to generate a matrix meeting the correlation coefficient as rho x Random number matrix U of (2) N×M The method comprises the following steps:
wherein u is i,j Representing the ith row and jth column elements.
In this embodiment, the empirical Copula function of the output power of the distributed photovoltaic power generation is constructed; the least square Euclidean distance is used as a goodness-of-fit index, the square Euclidean distance between each theoretical Copula function and the empirical Copula function is calculated, and the Copula function corresponding to the minimum value is selected as the theoretical Copula function to describe the output correlation between the distributed photovoltaics, wherein the output correlation is specifically as follows:
random number matrix U generated by Latin hypercube sampling pair N×M U of the first column of (2) 1 Sampling, wherein the Latin hypercube sampling number is set to K times, K<N and N are the number of random numbers, and are 0,1]The interval is equally divided into K subintervalsFor the t th subinterval->In U 1 Finding one sample u h,1 Satisfy subinterval->And record sample u h,1 In U 1 Position c in (a) t After sampling all subintervals, the resulting position vector is c= [ C = 1 ,...,c k ]Based on the position vector C, the random number matrix U N×M Corresponding samples are selected from the second column to the M column, and a sample matrix UL after Latin hypercube sampling is established K×M ：
According to Latin hypercube sampled sample matrix UL K×M ，Representing the M-th random variable position vector as c k Is a sample of the data; and combining the inverse function w=f of the cumulative distribution function of the distributed photovoltaic power variables e -1 (u) generating a sample matrix W of distributed photovoltaic power generation power variables K×M ：
The method comprises the steps of taking a sample matrix of an established distributed photovoltaic power generation power variable as an input quantity to carry into a node injection power equation f and a branch power flow equation g for cyclic calculation to obtain calculated values of a system node voltage X and a branch power flow Z, and calculating and outputting digital characteristics and probability distribution of the random variable node voltage X and the branch power flow Z by using a statistical method, wherein the digital characteristics and probability distribution are specifically as follows:
sample matrix W of the established distributed photovoltaic power generation power variable K×M Taking the input quantity of the deterministic power flow calculation model as the input quantity of the node injection power equation f and the branch power flow equation g for cyclic calculation to obtain calculated values of the node voltage X and the branch power flow Z of the system;
extracting distributed photovoltaic power generation power variable sample matrix W by calculation in each cycle K×M Is used as a power flow calculation input quantity;
and calculating the digital characteristics and probability distribution of the node voltage X and the branch power flow Z of the output random variable by adopting a statistical method.
The embodiment also provides a distributed photovoltaic probability power flow calculation system of a power distribution network based on Copula theory, which comprises a memory, a processor and computer program instructions stored on the memory and capable of being executed by the processor, wherein the computer program instructions can realize the method steps as described above when the processor executes the computer program instructions.
The present embodiment also provides a computer readable storage medium having stored thereon computer program instructions executable by a processor, which when executed by the processor are capable of carrying out the method steps as described above.
Specific examples of the present embodiment are as follows:
a standard IEEE33 node power distribution system is used for carrying out simulation operation on probability power flow, the power reference of the system is 100MW, the reference voltage is 12.66kV, and the total load of the power distribution network is 3715kW+j2300kVar. A specific network structure is shown in fig. 2. And respectively accessing the distributed photovoltaic power stations at the nodes 17 and 21.
And taking the 3-ten-thousand Monte Carlo probability load flow calculation result as an accurate result to compare and judge the accuracy of the proposed method. The table below gives the comparison of 2 probabilistic load flow calculations.
According to comparison of data results, the error of the calculation results of the two methods is smaller, and the probability power flow calculation method of the embodiment is verified to have higher accuracy, and meanwhile, the calculation time of the method and the Monte Carlo method is respectively 2.3s and 9.6s, so that the method has obvious advantages in calculation speed.
In order to further explain the effectiveness and accuracy of the method in consideration of distributed photovoltaic correlation probability power flow calculation, fig. 3 and fig. 4 respectively show voltage variances and power flow variance distribution diagrams of all nodes of a system calculated by the method and a monte carlo method. The probability flow variance distribution curves are basically coincident, so that the method can accurately calculate the correlation among the photovoltaic output and calculate the probability flow in the power system, and the influence of the distributed photovoltaic access on the running state of the power system can be estimated more accurately.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present application, and is not intended to limit the application in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present application still fall within the protection scope of the technical solution of the present application.
Claims (5)
1. A distributed photovoltaic probability power flow calculation method of a power distribution network based on a Copula theory is characterized by comprising the following steps:
constructing an accumulated distribution function and an inverse function of each distributed photovoltaic output power, selecting a Copula function, and generating a random number matrix;
sampling the generated random number matrix by using a Latin hypercube sampling method to obtain a Latin hypercube sampled sample matrix, and establishing the sample matrix of the distributed photovoltaic power generation variable according to the inverse function of the accumulated distribution function of the distributed photovoltaic power generation variable;
taking the established sample matrix of the distributed photovoltaic power generation power variable as an input quantity to carry into a node injection power equation f and a branch power flow equation g for cyclic calculation to obtain calculated values of a system node voltage X and a branch power flow Z, and calculating digital characteristics and probability distribution of the output random variable node voltage X and the branch power flow Z by using a statistical method;
the method for constructing the cumulative distribution function and the inverse function of the output power of each distributed photovoltaic, selecting a Copula function and generating a random number matrix specifically comprises the following steps:
constructing an accumulated distribution function and an inverse function of each distributed photovoltaic output power according to historical data of the distributed photovoltaic power generation output power;
constructing an empirical Copula function of the output power of the distributed photovoltaic power generation; the least square Euclidean distance is used as a goodness-of-fit index, the square Euclidean distance between each theoretical Copula function and the empirical Copula function is calculated, and the Copula function corresponding to the minimum value is selected as the theoretical Copula function to describe the output correlation between the distributed photovoltaics;
generating a random number matrix meeting the correlation by using a selected theoretical Copula function according to a correlation coefficient matrix of the distributed photovoltaic power generation power variable;
the building of the cumulative distribution function and the inverse function of the output power of each distributed photovoltaic is specifically as follows:
empirical cumulative distribution function u=f of distributed photovoltaic output power random variable w e (w) and its inverse function w=f e -1 The calculation steps of (u) are as follows:
s201: n discrete data w for a random variable w 1×n ＝[w 1 ,…,w n ]Sequencing from small to large to obtain w 1×n '＝[w 1 ',…,w n ']；
S202: the empirical cumulative distribution function u=f of the random variable w is calculated as follows e (w) and its inverse function w=f e -1 (u)；
Wherein round is a fractional part rounding function, w j ' is the actual measurement data of the jth random variable after being sequenced from small to large, and n is the number of the actual measurement discrete data of the random variable;
the empirical Copula function is as follows:
wherein I is an indicating function, i=0 when the condition in brackets is not satisfied, whereas i=1; w (W) n×M ＝[w 1,j ,...,w M,j ]J=1,..n is an n x M-dimensional matrix of observation samples,is a sequence statistic and is 1.ltoreq.i 1 ,...,i M ≤n；i M Indicating the ith of the ordered random variable measured data from small to large M Bit, w M,j The jth actually measured discrete data of the Mth random variable is represented, and M is the number of the random variables;
the square Euclidean distance between each theoretical Copula function and the empirical Copula function is as follows:
wherein C is the theoretical Copula function selected for use, C e Is an empirical Copula function;
according to the above formula, the square Euclidean distance d between each theoretical Copula function and the empirical Copula function is calculated n (C,C e ) Selecting a theoretical Copula function corresponding to the least square Euclidean distance to describe the relevance of the distributed photovoltaic output;
the generation of the random number matrix meeting the correlation by using the selected theoretical Copula function according to the correlation coefficient matrix of the distributed photovoltaic power generation power variable is specifically as follows:
assume that the distributed photovoltaic power generation power variable has M random variables, which are w respectively 1 ,w 2 ,...,w M The cumulative distribution function is u=f e (w) the inverse of the cumulative distribution function is w=f e -1 (u) the correlation coefficient matrix is ρ x The number of random numbers is N, and a selected theoretical Copula function is utilized to generate a matrix meeting the correlation coefficient as rho x Random number matrix U of (2) N×M The method comprises the following steps:
wherein u is i,j Representing the ith row and jth column elements.
2. The method for calculating the distributed photovoltaic probability power flow of the power distribution network based on the Copula theory according to claim 1, wherein an empirical Copula function of the output power of the distributed photovoltaic power generation is constructed; the least square Euclidean distance is used as a goodness-of-fit index, the square Euclidean distance between each theoretical Copula function and the empirical Copula function is calculated, and the Copula function corresponding to the minimum value is selected as the theoretical Copula function to describe the output correlation between the distributed photovoltaics, wherein the output correlation is specifically as follows:
random number matrix U generated by Latin hypercube sampling pair N×M U of the first column of (2) 1 Sampling, wherein the Latin hypercube sampling number is set to K times, K<N and N are the number of random numbers, and are 0,1]The interval is equally divided into K subintervalsFor the t th subinterval->In U 1 Finding one sample u h,1 Satisfy subinterval->And record sample u h,1 In U 1 Position c in (a) t After sampling all subintervals, the resulting position vector is c= [ C = 1 ,...,c k ]Based on the position vector C, the random number matrix U N×M Corresponding samples are selected from the second column to the M column, and a sample matrix UL after Latin hypercube sampling is established K×M ：
According to Latin hypercube sampled sample matrix UL K×M ，u cK,M Representing the M-th random variable position vector as c k Is a sample of the data; and combining the inverse function w=f of the cumulative distribution function of the distributed photovoltaic power variables e -1 (u) generating a sample matrix W of distributed photovoltaic power generation power variables K×M ：
3. The distributed photovoltaic probability power flow calculation method of a power distribution network based on Copula theory according to claim 1, wherein the method is characterized in that the sample matrix of the built distributed photovoltaic power generation power variable is taken as input quantity to carry into node injection power equation f and branch power flow equation g for cyclic calculation to obtain calculated values of system node voltage X and branch power flow Z, and the numerical characteristics and probability distribution of the output random variable node voltage X and the branch power flow Z are calculated by using a statistical method specifically as follows:
sample matrix W of the established distributed photovoltaic power generation power variable K×M Taking the input quantity of the deterministic power flow calculation model as the input quantity of the node injection power equation f and the branch power flow equation g for cyclic calculation to obtain calculated values of the node voltage X and the branch power flow Z of the system;
extracting distributed photovoltaic power generation power variable sample matrix W by calculation in each cycle K×M Is used as a power flow calculation input quantity;
and calculating the digital characteristics and probability distribution of the node voltage X and the branch power flow Z of the output random variable by adopting a statistical method.
4. A distributed photovoltaic probability load flow calculation system for a power distribution network based on Copula theory, comprising a memory, a processor and computer program instructions stored on the memory and executable by the processor, the computer program instructions when executed by the processor being capable of implementing the method according to any one of claims 1 to 3.
5. A computer readable storage medium, having stored thereon computer program instructions executable by a processor, which when executed by the processor, are capable of implementing the method of any of claims 1-3.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110338862.5A CN112952843B (en) | 2021-03-30 | 2021-03-30 | Distributed photovoltaic probability power flow calculation method for power distribution network based on Copula theory |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110338862.5A CN112952843B (en) | 2021-03-30 | 2021-03-30 | Distributed photovoltaic probability power flow calculation method for power distribution network based on Copula theory |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112952843A CN112952843A (en) | 2021-06-11 |
| CN112952843B true CN112952843B (en) | 2023-09-19 |
Family
ID=76227478
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110338862.5A Active CN112952843B (en) | 2021-03-30 | 2021-03-30 | Distributed photovoltaic probability power flow calculation method for power distribution network based on Copula theory |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112952843B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103151803A (en) * | 2013-03-14 | 2013-06-12 | 吉林省电力有限公司电力科学研究院 | Method for optimizing wind power system-contained unit and backup configuration |
| CN105790258A (en) * | 2016-03-15 | 2016-07-20 | 国电南瑞科技股份有限公司 | Latin hypercube sampling method probabilistic power flow calculation method based on normal Copula function |
| WO2017157058A1 (en) * | 2016-03-15 | 2017-09-21 | 国电南瑞科技股份有限公司 | Probabilistic load flow calculation method considering admitting ability of power grid |
| CN108649605A (en) * | 2018-05-22 | 2018-10-12 | 国网内蒙古东部电力有限公司通辽供电公司 | A kind of grid-connected allowed capacity planing methods of DER based on the double-deck scene interval trend |
| CN111162537A (en) * | 2020-01-16 | 2020-05-15 | 广东工业大学 | Latin hypercube sampling method probability load flow calculation method based on combined Copula function |
-
2021
- 2021-03-30 CN CN202110338862.5A patent/CN112952843B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103151803A (en) * | 2013-03-14 | 2013-06-12 | 吉林省电力有限公司电力科学研究院 | Method for optimizing wind power system-contained unit and backup configuration |
| CN105790258A (en) * | 2016-03-15 | 2016-07-20 | 国电南瑞科技股份有限公司 | Latin hypercube sampling method probabilistic power flow calculation method based on normal Copula function |
| WO2017157058A1 (en) * | 2016-03-15 | 2017-09-21 | 国电南瑞科技股份有限公司 | Probabilistic load flow calculation method considering admitting ability of power grid |
| CN108649605A (en) * | 2018-05-22 | 2018-10-12 | 国网内蒙古东部电力有限公司通辽供电公司 | A kind of grid-connected allowed capacity planing methods of DER based on the double-deck scene interval trend |
| CN111162537A (en) * | 2020-01-16 | 2020-05-15 | 广东工业大学 | Latin hypercube sampling method probability load flow calculation method based on combined Copula function |
Non-Patent Citations (1)
| Title |
|---|
| 基于非参数估计和最优Copula的电力系统概率潮流算法;李权;王鑫;郎永波;王昕;;电气自动化(第03期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112952843A (en) | 2021-06-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Mi et al. | Short‐term power load forecasting method based on improved exponential smoothing grey model | |
| CN104485665B (en) | Meter and the dynamic probability trend computational methods of forecasting wind speed error temporal correlation | |
| Sheng et al. | Probabilistic power flow calculation using non-intrusive low-rank approximation method | |
| Yang et al. | Probabilistic short-term wind power forecast using componential sparse Bayesian learning | |
| CN109802394B (en) | Probability load flow calculation method considering distributed power supply and electric vehicle access | |
| Fan et al. | Uncertainty evaluation algorithm in power system dynamic analysis with correlated renewable energy sources | |
| CN110619389A (en) | Load prediction method and system of combined cooling heating and power system based on LSTM-RNN | |
| CN107480825B (en) | Photovoltaic power station optimization planning method considering capacity credibility | |
| CN103106314B (en) | The sequential modelling method of probabilistic of solar photovoltaic power output power | |
| CN107834547B (en) | Power transmission network planning method considering wind power plant output power correlation characteristic | |
| CN109558968B (en) | Wind farm output correlation analysis method and device | |
| CN106786608B (en) | A kind of uncertain harmonic flow calculation method suitable for distributed generation resource access | |
| CN111797132B (en) | Multi-renewable energy power station power scene generation method considering space-time correlation | |
| CN105634018A (en) | Random response surface method and interior point method based wind-power-plant-contained random optimal power flow solving method | |
| CN105449667A (en) | Prediction method for reliability of power generation system and power transmission system | |
| Huang et al. | Adaptive static equivalences for active distribution networks with massive renewable energy integration: a distributed deep reinforcement learning approach | |
| CN109447512B (en) | Large power grid reliability assessment method based on uniform design | |
| CN107221933A (en) | A kind of probability load flow calculation method | |
| CN112952843B (en) | Distributed photovoltaic probability power flow calculation method for power distribution network based on Copula theory | |
| Lu et al. | Wind farm layout design optimization through multi-scenario decomposition with complementarity constraints | |
| CN107276093A (en) | The Probabilistic Load computational methods cut down based on scene | |
| CN115173421A (en) | Probability optimal power flow calculation method based on progressive Latin hypercube sampling | |
| CN115619447A (en) | Monthly electricity sales combined prediction method, equipment and medium | |
| CN113705885B (en) | VMD, XGBoost and TCN fused power distribution network voltage prediction method and system | |
| Li et al. | Application of time series model in relative humidity prediction |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |