Power distribution network typical scene construction method and system considering source-load correlation

Abstract

The invention provides a power distribution network typical scene construction method and system considering source-load correlation, and relates to the technical field of power distribution network operation scene generation, and the method comprises the steps: building a photovoltaic output probability density model and a load level probability density model of each time period through a non-parameter estimation method, according to the photovoltaic output probability density model and the load level probability density model of the corresponding time period, establishing a time sequence joint probability distribution model of the photovoltaic output and the load level of each time period by using a Copula function method; and sampling the time sequence joint probability distribution model of each time period to generate a large number of time sequence scene samples considering photovoltaic output and load level uncertainty and correlation, and performing scene reduction to obtain a power distribution network typical scene considering source-load uncertainty and correlation. The operation scene of the power distribution network is accurately simulated, and an accurate data basis is provided for follow-up planning operation or optimization scheduling of the power distribution network.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network operation scenario generation, and particularly to a method and system for constructing a typical scenario of a distribution network considering the correlation between sources and loads. Background Art

[0002] The output of distributed new energy is significantly affected by weather conditions and has strong randomness and volatility. After large-scale distributed new energy is connected to the distribution network, it not only brings great uncertainties to the system operation, but also makes the operation scenarios of the distribution network increasingly complex and diverse, posing great challenges to power grid regulation. In order to effectively address these challenges, generating distribution network operation scenarios that can reflect complex and diverse operating states has become the key, which can provide basic research data for subsequent distribution network planning operation or optimal dispatching problems. However, the existing traditional power grid operation scenario generation mostly relies on static scenarios or simplified models, ignoring the dynamic correlation between sources (photovoltaic output) and loads (load levels). The planning operation or optimal dispatching results obtained based on such operating scenarios are often inaccurate or even deviate from reality.

[0003] Therefore, it is very important to better simulate the distribution network operation scenario and accurately match the source-load uncertainty characteristics in the distribution network. On the other hand, the output of new energy such as photovoltaic in the distribution network and the load level show a certain correlation during some periods of a day. Ignoring the influence of this factor may also lead to inaccurate results of distribution network optimal dispatching. Therefore, the correlation between source-load output in different periods needs to be further considered during the process of simulating the distribution network operation scenario.

[0004] Based on this, the present invention is proposed. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and system for constructing a typical scenario of a distribution network considering the correlation between sources and loads, so as to accurately simulate the distribution network operation scenario and provide an accurate data basis for subsequent distribution network planning operation or optimal dispatching.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] In a first aspect, the present invention provides a method for constructing a typical scenario of a distribution network considering the correlation between sources and loads, including: establishing a probability density model of photovoltaic output and a probability density model of load level for each period through non-parametric estimation method; establishing a time-series joint probability distribution model of photovoltaic output and load level for each period according to the probability density model of photovoltaic output and the probability density model of load level in the corresponding period and using the Copula function method; sampling the time-series joint probability distribution model of each period to generate a large number of time-series scenario samples considering the uncertainty and correlation of photovoltaic output and load level, and obtaining a typical scenario of the distribution network considering source-load uncertainty and correlation after scenario reduction.

[0008] In the first aspect, the present invention provides a preferred solution, wherein the probability density models of photovoltaic power output and load level for each period are established by non-parametric estimation method. Specifically, the Gaussian mixture model is used in the non-parametric estimation method to establish the probability density models of photovoltaic power output and load level for each period, which specifically includes: inputting the historical data set containing photovoltaic power output and load level; establishing the probability density models of photovoltaic power output and load level by using the Gaussian mixture model according to the historical data set; respectively determining the number of Gaussian components constituting the probability density models of photovoltaic power output and load level; and solving the probability density models of photovoltaic power output and load level with the known number of Gaussian components.

[0009] In the first aspect, the present invention provides a preferred solution, wherein the step of respectively determining the number of Gaussian components constituting the probability density models of photovoltaic power output and load level specifically includes: calculating the fitting accuracy characterization index of the Gaussian mixture model with different numbers of Gaussian components for the probability density models of photovoltaic power output and load level, and selecting the number of Gaussian components included in the Gaussian mixture model with the smallest fitting accuracy characterization index as the optimal number of Gaussian components; and the fitting accuracy characterization index adopts the AIC index.

[0010] In the first aspect, the present invention provides a preferred solution, wherein the step of solving the probability density models of photovoltaic power output and load level with the known number of Gaussian components is specifically solved by the expectation-maximization algorithm.

[0011] In the first aspect, the present invention provides a preferred solution, wherein the step of establishing the time series joint probability distribution model of photovoltaic power output and load level for each period according to the probability density models of photovoltaic power output and load level for the corresponding period by using the Copula function method specifically includes: determining the marginal distribution functions of photovoltaic power output and load level for each period according to the probability density models of photovoltaic power output and load level for the corresponding period; determining the optimal Copula function for each period; and using the optimal Copula function for the corresponding period to fit the marginal distribution functions of photovoltaic power output and load level for each period to obtain the time series joint probability distribution model of photovoltaic power output and load level for each period.

[0012] The present invention provides a preferred solution in the first aspect. The determination of the optimal Copula function adopted for each time period specifically includes: for each time period, obtaining Copula functions including the following types: Normal-Copula function, t-Copula function, Frank-Copula function, Clayton-Copula function, and Gumbel-Copula function; using the minimum square Euclidean distance between the empirical Copula function and various Copula functions as a criterion for goodness-of-fit discrimination, and taking the Copula function corresponding to the minimum square Euclidean distance as the optimal Copula function for describing the correlation between photovoltaic output and load level in this time period.

[0013] The present invention provides a preferred solution in the first aspect. Sampling the time series joint probability distribution model for each time period to generate a large number of time series scenario samples considering the uncertainties and correlations of photovoltaic output and load level, and obtaining typical scenarios of the distribution network considering source-load uncertainties and correlations after scenario reduction. Among them, the scenario reduction uses the K-means clustering algorithm to cluster a large number of time series scenario samples to extract a part of the time series scenario samples for constructing typical scenarios of the distribution network.

[0014] The present invention provides a preferred solution in the first aspect. Using the K-means clustering algorithm for scenario clustering, wherein the optimal number of clusters of the K-means clustering algorithm is determined based on the elbow method of the SSE index.

[0015] The present invention provides a preferred solution in the first aspect. Sampling the time series joint probability distribution model for each time period to generate a large number of time series scenario samples considering the uncertainties and correlations of photovoltaic output and load level, specifically including: using the Monte Carlo method to sample the time series joint probability distribution model for each time period to obtain N time series marginal distribution sample groups of photovoltaic output and load level in the t-th time period; calculating the inverse function of the photovoltaic output marginal distribution function and the inverse function of the load level marginal distribution function in the t-th time period; substituting each sample in the time series marginal distribution sample group into the corresponding inverse function to obtain a large number of the time series scenario samples considering the uncertainties and correlations of photovoltaic output and load level.

[0016] In a second aspect, the present invention provides a system for constructing a typical scenario of a distribution network considering source-load correlation, including: a probability density model construction module for establishing a probability density model of photovoltaic output and a probability density model of load level for each time period by using non-parametric estimation method; a time-series joint probability distribution model construction module for establishing a time-series joint probability distribution model of photovoltaic output and load level for each time period according to the probability density model of photovoltaic output and the probability density model of load level for the corresponding time period and by using the Copula function method; a typical scenario construction module for the distribution network for sampling the time-series joint probability distribution model for each time period to generate a large number of time-series scenario samples considering the uncertainties and correlations of photovoltaic output and load level, and obtaining a typical scenario of the distribution network considering source-load uncertainties and correlations after scenario reduction.

[0017] Compared with the prior art, the present invention has the following beneficial technical effects:

[0018] The method and system for constructing a typical scenario of a distribution network considering source-load correlation according to the present invention can generate scenarios that can better reflect the uncertainties and correlations of photovoltaic output and load level in each time period in the historical data used, accurately simulate the operation scenarios of the distribution network, provide an accurate data basis for distribution network planning operation or optimal dispatching, improve the accuracy of distribution network planning operation or optimal dispatching results, and ultimately contribute to improving the reliability of the operation of the distribution network system. In addition, the proposed method can alleviate the problem of insufficient historical data of source-load output to better conduct research on distribution network planning and operation problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0020] Figure 1 It is a flowchart of the method for constructing a typical scenario of a distribution network considering source-load correlation provided by a specific embodiment of the present invention;

[0021] Figure 2 It is a module diagram of the system for constructing a typical scenario of a distribution network considering source-load correlation provided by a specific embodiment of the present invention;

[0022] Figure 3 It is a flowchart of the method for constructing a typical scenario of a distribution network considering source-load correlation provided by another specific embodiment of the present invention;

[0023] Figure 4The graph of the historical PV output data in a certain place in a year in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0024] Figure 5 The graph of the historical load level data in a certain place in a year in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0025] Figure 6 The probability density curve graph of the PV output at 12 o'clock in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0026] Figure 7 The fitting situation graph of the marginal distribution function of the PV output fitted by the kernel density estimation method for the PV output at 12 o'clock in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0027] Figure 8 The fitting situation graph of the marginal distribution function of the PV output fitted by GMM for the PV output at 12 o'clock in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0028] Figure 9 The PV output scenario graph generated by sampling using the Monte Carlo method in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0029] Figure 10 The load level scenario graph generated by sampling using the Monte Carlo method in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0030] Figure 11 The graph of the change of the SSE index under different numbers of clusters in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0031] Figure 12 The generated source-load typical operation scenario graph (scenario one) in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0032] Figure 13 The generated source-load typical operation scenario graph (scenario two) in the practical application case of the method for constructing a typical distribution network scenario considering source-load correlation provided by a specific embodiment of the present invention;

[0033] Figure 14 The source-load typical operation scenario diagram (Scenario 3) generated in the practical application case of the method for constructing a typical scenario of a distribution network considering source-load correlation provided by a specific embodiment of the present invention;

[0034] Figure 15 The source-load typical operation scenario diagram (Scenario 4) generated in the practical application case of the method for constructing a typical scenario of a distribution network considering source-load correlation provided by a specific embodiment of the present invention. Specific embodiments

[0035] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0036] Embodiment 1

[0037] Please refer to Figure 1 , in a preferred embodiment, a method for constructing a typical scenario of a distribution network considering source-load correlation is mainly implemented through the following steps:

[0038] S1. Establish a probability density model of photovoltaic output and a probability density model of load level for each time period by non-parametric estimation method.

[0039] Currently, most of the probability density modeling methods for random variables use parametric estimation methods. The parametric estimation method assumes that the random variable follows a specific probability distribution model (such as Gaussian distribution, Beta distribution, Weibull distribution, etc.), and then estimates the specific parameters in its expression to obtain the probability distribution model of the random variable. However, in the power system, due to the strong influence of weather conditions on photovoltaic output, it has strong volatility and randomness, and as the load types in the distribution network become more diverse, the uncertainty of the overall load level is also increasing. Therefore, there is a great deal of uncertainty in random variables such as photovoltaic output and load level. In this case, if the parametric estimation method is used for probability density modeling, there will be a problem of insufficient accuracy.

[0040] Therefore, considering the uncertainties of random variables such as photovoltaic output and load level in the power system, in this embodiment, the non-parametric estimation method is adopted, without making fixed assumptions about the probability distribution of random variables such as photovoltaic output and load level in advance. In the specific implementation process of this embodiment, the Gaussian mixture model is specifically selected to perform probability density modeling on the photovoltaic output and load level at different times of the day in the source-load output historical dataset, which can realize mining the characteristics of actual historical data, obtaining model parameters and then obtaining the model expression, and can fit random variables that follow any probability distribution, so as to better reflect the uncertainties of actual random variables such as photovoltaic output and load level.

[0041] S2. According to the photovoltaic output probability density model and load level probability density model corresponding to each time period and using the Copula function method, establish the time series joint probability distribution model of the photovoltaic output and load level for each time period (also known as: the source-load output time series joint probability distribution model).

[0042] Considering that the photovoltaic output and load level in the same area of the distribution network often have strong correlations in multiple time periods of a day, in order to improve the reliability of the distribution network operation, after completing the above probability density modeling, the correlation between the photovoltaic output and load level in different time periods will be further analyzed.

[0043] S3. Sample the time series joint probability distribution model for each time period to generate a large number of time series scenario samples considering the uncertainties and correlations of photovoltaic output and load level, and obtain the typical scenarios of the distribution network considering source-load uncertainties and correlations after scenario reduction.

[0044] Please refer to Figure 2 , correspondingly, this embodiment provides a distribution network typical scenario construction system considering source-load correlation, which is mainly composed of the following modules and is used to execute the above method of this embodiment:

[0045] Probability density model construction module 1, used to establish the photovoltaic output probability density model and load level probability density model for each time period by the non-parametric estimation method;

[0046] Time series joint probability distribution model construction module 2, used to establish the time series joint probability distribution model of the photovoltaic output and load level for each time period according to the photovoltaic output probability density model and load level probability density model corresponding to each time period and using the Copula function method;

[0047] Distribution network typical scenario construction module 3, used to sample the time series joint probability distribution model for each time period to generate a large number of time series scenario samples considering the uncertainties and correlations of photovoltaic output and load level, and obtain the typical scenarios of the distribution network considering source-load uncertainties and correlations after scenario reduction.

[0048] Embodiment 1: Method and System for Constructing Typical Scenarios of Distribution Networks Considering Source-Load Correlation. The non-parametric estimation method is used to perform probability density modeling on the photovoltaic output and load level within different time periods of a day in the historical source-load output dataset, so as to mine the characteristics of actual historical data, which can reflect the uncertainties of random variables such as actual photovoltaic output and load level. Furthermore, the correlation between photovoltaic output and load level at different time periods is analyzed and sampled to generate a large number of time-series scenario samples considering the uncertainties and correlations of photovoltaic output and load level. The finally constructed scenarios can better reflect the uncertainties and correlations of photovoltaic output and load level in each time period of the historical data used, accurately simulate the operation scenarios of the distribution network, provide an accurate data basis for distribution network planning operation or optimal dispatching, improve the accuracy of distribution network planning operation or optimal dispatching results, and ultimately contribute to improving the reliability of the operation of the distribution network system.

[0049] Embodiment 2

[0050] Please refer to Figure 3 , on the basis of the above embodiments, a more preferable and more detailed embodiment is provided, which is specifically as follows:

[0051] S1. Establish a probability density model of photovoltaic output and a probability density model of load level for each time period through the non-parametric estimation method.

[0052] More specifically, the Gaussian Mixture Model (GMM) adopted in this embodiment is a non-parametric model that can effectively describe the mixed density distribution, and has many advantages such as good fitting characteristics and easy processing. Essentially, GMM describes the probability distribution characteristics of random variables through the linear weighted combination of multiple Gaussian components ( ). Compared with single probability distribution models such as normal distribution and Beta distribution, GMM can accurately describe the probability density distribution of random variables with irregular distribution characteristics by selecting an appropriate number of Gaussian components and adjusting the parameters (mean, variance) and weight coefficients of each corresponding sub-Gaussian component. Specifically, it includes the following sub-steps:

[0053] S11. Input the historical dataset containing photovoltaic output and load level (also known as: source-load output historical dataset). In a preferred embodiment, the historical dataset uses the photovoltaic output and load level conditions of a certain place in Northeast China throughout the year in 2018. One day is divided into 24 time periods, and the source-load historical output data of each time period within this year are used to fit the probability distribution model of source-load output in the corresponding time period.

[0054] S12. Establish a probability density model of photovoltaic output and a probability density model of load level according to the historical dataset and using the Gaussian Mixture Model (GMM).

[0055] More specifically, the photovoltaic output probability density model and the load level probability density model are both established through the following process: For the random variables (photovoltaic output, load level) , the formula for estimating its probability density function (PDF) using GMM can be expressed as follows, that is, obtaining the probability density model of the random variable (photovoltaic output or load level):

[0056] (1)

[0057] (2)

[0058] In the formula, it is assumed that there are a total of N samples, is the number of Gaussian components selected; , and are the weight, mean, and variance of the y-th Gaussian function (Gaussian component) respectively; is the y-th Gaussian component of the model, which can be expressed as:

[0059] (3)

[0060] In the formula, T represents the transpose symbol in linear algebra.

[0061] S13. Determine the number of Gaussian components that make up the photovoltaic output probability density model and the load level probability density model respectively.

[0062] More specifically, the solution of the probability density model of the random variable (photovoltaic output or load level) established using GMM involves two key issues. The first issue is how to determine the optimal number of Gaussian components Y that make up the model. Increasing the number of Gaussian components in GMM can improve the fitting accuracy of the model to the probability distribution of the random variable, but at the same time it also increases the computational complexity of the model. Reducing the number of Gaussian components in the model improves the computational efficiency of the model but also causes a loss in the fitting accuracy of the probability model.

[0063] Further, in a more preferred embodiment, in S12, the number of Gaussian components that make up the photovoltaic output probability density model and the load level probability density model is determined respectively, which is specifically implemented through the following steps: Calculate the fitting accuracy characterization indexes of Gaussian mixture models with different numbers of Gaussian components for the photovoltaic output probability density model and the load level probability density model, and select the number of Gaussian components included in the Gaussian mixture model with the smallest fitting accuracy characterization index as the optimal number of Gaussian components; The fitting accuracy characterization index uses the AIC index. More specifically, this preferred solution is to reasonably select the number of Gaussian components in the GMM. In this embodiment, the Alike (Akaike information criterion, AIC) information criterion is introduced to evaluate the fitting accuracy of GMMs with different numbers of Gaussian components for the PDF of random variables, and the number of Gaussian components included in the GMM with the smallest AIC index (the smaller the AIC index, the higher the fitting accuracy for the random variable) is selected as the optimal number of Gaussian components. The specific calculation formula of the AIC index is as follows:

[0064] (4)

[0065] In the formula, and respectively represent the number of parameters to be estimated (parameters to be solved) of the GMM and the likelihood function.

[0066] S14. Solve the photovoltaic output probability density model and the load level probability density model with the known number of Gaussian components. Specifically, the maximum expectation algorithm is used for solving.

[0067] The second problem is the parameter estimation of the model. Specifically, since the GMM contains hidden variables (due to the lack of information on which distribution the sample belongs to), it is impossible to directly determine the model parameters by taking derivatives and estimating the maximum likelihood function. Therefore, in this embodiment, the Expectation Maximization (EM) algorithm is preferably used to solve the parameters of the GMM. The EM algorithm is an iterative algorithm that can be used for maximum likelihood estimation or maximum a posteriori probability estimation of probability models containing hidden variables. Each iteration of the EM algorithm includes two steps of calculation, namely the E step and the M step, where the E step is used to calculate the expectation (the probability that the sample comes from the y-th Gaussian component ), and the M step is used to calculate the maximum value. The following describes the specific process of using this algorithm to solve the GMM:

[0068] 1) Determine the number of Gaussian components Y in the GMM.

[0069] 2) Initialize the relevant parameters, and give the mean, variance, and weight of each Gaussian component.

[0070] 3) Step E. Since it is impossible to determine which Gaussian component each sample comes from in GMM, the main content of Step E is to calculate the probability that the sample data comes from each Gaussian component based on the current parameter values. Let the probability that the sample comes from the y-th Gaussian component be , and its calculation formula can be expressed as:

[0071] (5)

[0072] In the formula, the superscript i represents the parameter values of each Gaussian component in the i-th iteration process, that is, , and are the weight, mean, and variance of the y-th Gaussian component in the i-th iteration process, respectively.

[0073] 4) Step M. The main content of Step M is to iteratively update the parameter values and of each Gaussian component in the (i + 1)-th iteration process based on the maximum likelihood method in parameter estimation on the assumption that the result obtained in Equation (5) is true:

[0074] (6)

[0075] (7)

[0076] (8)

[0077] In the formula, is the result of summing each probability over the samples, which can be expressed as:

[0078] (9)

[0079] 5) Repeat Step 3) and Step 4) until the parameters converge or reach the preset maximum number of iterations.

[0080] According to the above method, the probability distribution of the PV and load output in each time period can be established based on the actual historical data for subsequent analysis. The entire above-mentioned Step S1 is the process of the source-load output probability density modeling method, which considers the source-load uncertainty (volatility and randomness).

[0081] S2. Based on the PV output probability density model and the load level probability density model for the corresponding time periods and using the Copula function method, establish the time series joint probability distribution model of the PV output and the load level for each time period.

[0082] In a preferred embodiment, considering that there is often a strong correlation between the photovoltaic output and the load level within the same area of the distribution network during multiple periods of a day, in order to improve the reliability of the distribution network operation, after completing the above probability density modeling, the correlation between the photovoltaic output and the load level at different times is further analyzed. In other words, there is a certain correlation in the historical source-load output data at each time period, so the source-load correlation at different times also needs to be considered during the scenario generation process. Further, in a preferred embodiment, the Kendall rank correlation coefficient index and the Spearman rank correlation coefficient index can be selected to describe the correlation between the photovoltaic output and the load level at different times, so as to analyze the correlation between the photovoltaic output and the load level at different times, and to illustrate and verify the necessity of considering the source-load correlation in the process of constructing typical scenarios of the distribution network. Since the rank of a variable will not be changed by any strictly monotonic increasing transformation of the variable, the Kendall rank correlation coefficient and the Spearman rank correlation coefficient have no strict requirements on the distribution type of the original data, data selection and correlation form, and can be used to describe the correlation between non-normal distributed random variables such as photovoltaic and load. Compared with the Pearson correlation coefficient, it has stronger generality and robustness. The correlation between the photovoltaic output and the load level at different times is shown in Table 1.

[0083] Table 1: Correlation between photovoltaic output and load level at different times

[0084]

[0085] Since the photovoltaic output is weak during the night period and the correlation between the two is not obvious, the correlation situation during the 8-17 period with strong photovoltaic output is mainly given. It can be seen from the data in Table 1 that there is a certain correlation between the photovoltaic output and the load level from 8 to 17 when the photovoltaic output is strong. Especially in the morning period, as factories start work, the photovoltaic output and the load level increase synchronously, showing a strong correlation. Therefore, it is necessary to establish a joint probability distribution model considering the correlation of the outputs of the two to ensure that the constructed source-load typical scenarios can more accurately fit the actual data situation, and then improve the accuracy of the subsequent analysis results of the distributed photovoltaic carrying capacity of the distribution network.

[0086] Further, to deal with the correlation between random variables, the Copula function method is preferably used. The Copula function method has great advantages in dealing with the non-linear and asymmetric correlation of random variables. It can replace a multi-dimensional distribution with a Copula function and the cumulative probability distribution functions of each variable.

[0087] Further, to establish a time-series joint probability distribution model of the photovoltaic output and the load level at different times, it is mainly realized through the following sub-steps:

[0088] S21. Determine the marginal distribution functions of PV output and load level for each time period according to the PV output probability density model and the load level probability density model corresponding to the time period. To determine the marginal distribution functions of PV output and load level at different time periods, based on the basic knowledge of probability theory, the marginal distribution functions of PV output and load level and and can be obtained by integrating the probability density functions of the two at this time period and The probability density functions of PV output and load level and are modeled by GMM for the probability density distribution functions of the two, and the specific process is implemented through the above step S1.

[0089] S22. Determine the optimal Copula function for each time period. For each time period, obtain the following 5 types of Copula functions: Normal-Copula function, t-Copula function, Frank-Copula function, Clayton-Copula function, and Gumbel-Copula function. Specifically, Copula functions can be mainly divided into two categories: elliptical distribution family functions and Archimedean distribution family functions. Among them, the elliptical distribution family functions mainly include the Normal-Copula function and the t-Copula function; the Archimedean distribution family functions mainly include the Frank-Copula function, the Clayton-Copula function, and the Gumbel-Copula function. The tail characteristics of the Normal-Copula function are asymptotically independent and asymptotic, the tail characteristics of the t-Copula function are asymptotic, the tail characteristics of the Frank-Copula function are asymptotically independent and asymptotic, the tail characteristics of the Clayton-Copula function are highly sensitive to the lower tail and asymmetric, and the tail characteristics of the Gumbel-Copula function are highly sensitive to the upper tail and asymmetric. Therefore, different Copula functions have different tail characteristics and can describe different correlation relationships between random variables. Therefore, selecting an appropriate Copula function at different time periods can better describe the correlation relationship between PV output and load level.

[0090] S23. Use the optimal Copula function corresponding to the time period to fit the marginal distribution functions of PV output and load level for each time period, and obtain the time series joint probability distribution model of PV output and load level for each time period.

[0091] The Copula function method is based on Sklar's theorem, that is, for the joint cumulative distribution function of an n-dimensional variable (To simplify the explanation of the principle of the Copula method, the joint cumulative distribution function here is the joint probability distribution function without considering the time variable), and denote the marginal distribution functions (also known as: marginal cumulative distribution functions) of each variable as , there exists an n-dimensional Copula function C such that:

[0092] (10)

[0093] This embodiment mainly considers the correlation between photovoltaic output and load level at different time periods. Therefore, according to Equation (10), a time-series joint probability distribution model of photovoltaic output and load level at different time periods (also known as: source-load output time-series joint probability distribution model) can be constructed:

[0094] (11)

[0095] In the formula, are the data of photovoltaic output and load level at time t respectively; and represent the marginal distribution functions of photovoltaic output and load level at time t respectively; represents the Copula function used to describe the correlation between the two at time t.

[0096] To avoid redundancy, in the subsequent description, the time variable t will be omitted when there is no confusion.

[0097] In a preferred embodiment, the minimum square Euclidean distance between the empirical Copula function and various Copula functions is used as a criterion for goodness-of-fit discrimination, and the Copula function corresponding to the minimum square Euclidean distance is used as the optimal Copula function for describing the correlation between photovoltaic output and load level at this time period.

[0098] Specifically, since different Copula functions can depict different correlation characteristics between random variables, to better describe the correlation between source-load output at different time periods, this embodiment uses the square Euclidean distance between the empirical Copula function and various Copula functions as a discrimination criterion, and selects the Copula function with the smallest value of this index (the smaller the index, the better the goodness-of-fit of the selected Copula function) as the optimal Copula function for describing the correlation between photovoltaic output and load level (also known as: source-load output correlation) at the current time period.

[0099] Let ( ) be a sample of the two-dimensional variable , , are the random variables and For the empirical distribution function, the empirical Copula function can be expressed as:

[0100] (12)

[0101] In the formula, is a demonstration function. When it holds, takes 1, otherwise takes 0. The empirical Copula function refers to the function fitted according to the actually adopted source-load data, and it does not need to assume the form of the expression in advance.

[0102] Taking the Normal-Copula function as an example, its squared Euclidean distance from the empirical Copula function is specifically expressed by the following calculation formula:

[0103] (13)

[0104] In the formula, ( ).

[0105] Based on this index, the goodness-of-fit discrimination of different Copula functions can be carried out, so as to determine the optimal Copula function describing the correlation between photovoltaic output and load level at different time periods.

[0106] S3. Sample the time-series joint probability distribution model of each time period to generate a large number of time-series scenario samples considering the uncertainty and correlation of photovoltaic output and load level, and obtain the typical scenarios of the distribution network considering source-load uncertainty and correlation after scenario reduction. In other words, after selecting the optimal Copula function for each time period to establish the time-series joint probability distribution model of photovoltaic output and load level, further sample the time-series sample group of the marginal distributions of photovoltaic output and compliance level in the time-series joint probability distribution model fitted by the optimal Copula function of each time period, and finally obtain the time-series photovoltaic output and load data samples considering correlation through the inverse function of the marginal distribution functions of photovoltaic and load. In a preferred embodiment, the Monte Carlo method is used for sampling. It is specifically implemented through the following sub-steps:

[0107] S31. Use the Monte Carlo method to sample the time - series joint probability distribution model for each time period to obtain N time - series marginal distribution sample groups of photovoltaic power output and load level in the t - th time period. After selecting the optimal Copula function for each time period with the minimum squared Euclidean distance as the criterion, for the time - series source - load output joint probability distribution models established above, sample through the Monte Carlo method to obtain N marginal cumulative distribution sample groups of the joint probability distribution of photovoltaic power output and load level in the t - th time period and ( )。

[0108] S32. Calculate the inverse function of the marginal distribution function of the photovoltaic power output in the t - th time period and the inverse function of the marginal distribution function of the load level in the t - th time period 。

[0109] S33. Substitute each sample in the time - series marginal distribution sample group into the corresponding inverse function to obtain a large number of time - series samples considering the correlation between photovoltaic power output and load level (also known as: source - load time - series samples). That is, obtain a large number of time - series scenario samples considering the uncertainty and correlation between photovoltaic power output and load level

[0110] S34. Perform scenario clustering on a large number of time - series scenario samples to extract a part of the time - series scenario samples for constructing typical scenarios of the distribution network

[0111] After generating a large number of scenario samples considering source - load correlation according to the above steps, it is necessary to further perform scenario reduction to improve the subsequent solution efficiency. In a preferred embodiment, the K - means clustering algorithm is used to cluster and reduce the large number of source - load scenarios generated in step S33, and the optimal number of clusters K value of the K - means clustering algorithm is determined according to the elbow method based on the sum of squared error (SSE) index

[0112] The K - means clustering algorithm is a clustering method based on iteration and data sample type division. The basic idea of this algorithm is to generate an initial clustering center according to the data itself in advance and then continuously iterate and update until convergence to improve the clustering accuracy. The application of this algorithm to the implementation process of the present invention is as follows: First, divide the large number of obtained time - series scenario sample data into K groups, randomly select the clustering center of each group, and then calculate the distance between the remaining samples in this class and the clustering center. Allocate each scenario to the initial clustering center closest to itself according to the principle of the smallest distance. According to the data classification results, continuously iterate the scenario clustering center and calculate the sum of squared error (SSE) index of each class. When this index reaches the clustering stop condition, the clustering process ends

[0113] SSE index The smaller it is, the better the clustering effect. Its specific calculation formula can be expressed as:

[0114] (14)

[0115] In the formula, and are the clustering centers and data samples of the cluster respectively; represents the Euclidean distance between vectors; K is the number of clusters (i.e., the K groups mentioned above).

[0116] To be able to restore the overall data sample features with fewer scenarios, the elbow method based on the SSE index is selected to determine the optimal number of clusters of the K-means clustering algorithm. The specific method principle is as follows: When the value of K is less than the optimal number of clusters, as the value of K increases, the sample division will be more refined, and the aggregation degree of each cluster will also increase significantly, and the decline of the SSE index is obvious; while when the value reaches the optimal number of clusters, and then increasing the value of, the return of the obtained aggregation degree will quickly become smaller, the decline of the SSE index will suddenly decrease, and as the value continues to increase, it will gradually become flat. In other words, the change trend graph of the SSE index with the increase of the number of clusters shows an elbow shape, that is, the decline at the front end is significant, and the decline becomes flat after reaching the elbow inflection point, and the value corresponding to the elbow inflection point is the optimal number of clusters of the data.

[0117] The implementation steps of the elbow method are described as follows:

[0118] 1) Determine the upper limit of the number of clusters .

[0119] 2) For use formula (14) to calculate the SSE index corresponding to each value respectively, and draw the change curve graph of the SSE index with the increase of the K value.

[0120] 3) Select the K value corresponding to the inflection point in the change curve graph of the SSE index with the increase of the K value as the optimal number of clusters of the data.

[0121] Next, a specific implementation application scenario case will be given in combination with a method and system for constructing a typical scenario of a distribution network considering source-load correlation provided by the above preferred implementation manner of the present invention:

[0122] Taking Figure 4 and Figure 5The actual photovoltaic output and load level of a certain place in Northeast my country throughout the year (with a sampling interval of 1 hour) are used as data samples to construct a typical source-load scenario to verify the effectiveness of the proposed scenario generation method.

[0123] Figure 6 , Figure 7 and Figure 8 The results of fitting the probability distribution of photovoltaic output at 12 o'clock when the sunlight is strong using the Gaussian mixture model and the kernel density estimation method (general method) are given. It can be seen from the three figures that the probability density curve fitted by the kernel density estimation method, which is currently widely used, cannot reflect the changes in the photovoltaic output frequency histogram and performs poorly in local adaptability. In contrast, the use of the Gaussian mixture model to fit the probability density curve of photovoltaic output can more accurately reflect the multi-peak characteristics of the actual photovoltaic output, and can process local details more finely, thus achieving better fitting accuracy. In addition, from Figure 7 and Figure 8 It can be found that compared with the kernel density estimation method, the photovoltaic output marginal distribution function calculated by GMM is also more in line with the actual empirical distribution function, which further demonstrates the accuracy of the proposed method.

[0124] After completing the probability density modeling of source-load output in each period, the optimal Copula function for each time is further selected based on the minimum square Euclidean distance as the criterion. Taking the period from 8:00 to 17:00 when the photovoltaic output is strong as an example, the square Euclidean distance between different Copula functions such as Gaussian-Copula, t-Copula, Frank-Copula, Clayton-Copula, Gumbel-Copula and the empirical Copula function is shown in Table 2 below.

[0125] Table 2: Squared Euclidean distance between different Copula functions and empirical Copula functions in different time periods

[0126]

[0127] According to the results in Table 2, the optimal Copula function for each period can be determined to establish a time series joint probability distribution model that considers the source-load output correlation in different periods.

[0128] Figure 9 and Figure 10 2000 typical distribution network scenarios considering source-load correlation are generated by Monte Carlo sampling. Figure 11The variation of the SSE index under different numbers of clusters is given, and based on this, the optimal number of clusters for the source-load typical scenarios is determined to be 4.

[0129] Four typical scenarios of the distribution network considering source-load uncertainty and correlation are obtained through scenario reduction by the K-means clustering algorithm, as shown in Figure 12 , Figure 13 , Figure 14 and Figure 15 . The occurrence probabilities of each scenario are shown in Table 3.

[0130] Table 3: Occurrence probabilities of each scenario

[0131]

[0132] From Figure 12 , Figure 13 , Figure 14 and Figure 15 , it can be seen that for the source-load typical scenarios generated by the proposed method, the variation trends of the source-load output in multiple time periods of a day are consistent or opposite, with a certain degree of correlation. In addition, the differences between the generated scenarios are obvious, with typical seasonal characteristics. Among them, the photovoltaic output level in Scenario 2 is relatively high, with obvious summer characteristics; the photovoltaic output levels in Scenario 1 and Scenario 4 are slightly weak, with transitional season characteristics; the overall photovoltaic output level in Scenario 3 is relatively low, showing typical winter characteristics.

[0133] Based on the above preferred implementation manner and combined with the above specific implementation application scenario cases, the method for constructing typical scenarios of the distribution network considering source-load correlation of the present invention can comprehensively consider the influence of source-load uncertainty and correlation on the distribution network planning and operation problems. The generated source-load typical scenarios can better reflect the uncertainty and correlation of the photovoltaic output and load levels in each time period in the historical data used, and can be used as the scenario input for the distribution network optimization problem, which is beneficial to improving the reliability of the optimization results.

[0134] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above method embodiments. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0135] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as falling within the scope described in this specification. Moreover, the above embodiments only express several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. For those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A method for constructing a typical distribution network scenario considering source-load correlation, characterized in that: include: The photovoltaic output probability density model and load level probability density model for each period are established by non-parametric estimation method; According to the probability density model of photovoltaic output and the probability density model of load level in the corresponding period, the time series joint probability distribution model of photovoltaic output and load level in each period is established by using the Copula function method; The time series joint probability distribution model of each time period is sampled to generate a large number of time series scenario samples that consider the uncertainty and correlation between photovoltaic output and load level. After scenario reduction, a typical distribution network scenario that considers source-load uncertainty and correlation is obtained.

2. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 1 is characterized in that: The photovoltaic output probability density model and the load level probability density model of each time period are established by the non-parametric estimation method, wherein the non-parametric estimation method specifically adopts a Gaussian mixture model to establish the photovoltaic output probability density model and the load level probability density model of each time period, specifically including: Input is a historical dataset containing PV output and load levels; Based on the historical data set and using the Gaussian mixture model, a photovoltaic output probability density model and a load level probability density model are established; Determine the number of Gaussian components constituting the photovoltaic output probability density model and the load level probability density model respectively; Solve the photovoltaic output probability density model and load level probability density model with a known number of Gaussian components.

3. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 2, characterized in that: The method of respectively determining the number of Gaussian components constituting the photovoltaic output probability density model and the load level probability density model specifically includes: calculating the fitting accuracy characterization index of Gaussian mixture models with different numbers of Gaussian components to the photovoltaic output probability density model and the load level probability density model, and selecting the number of Gaussian components contained in the Gaussian mixture model with the smallest fitting accuracy characterization index as the optimal number of Gaussian components; the fitting accuracy characterization index adopts the AIC index.

4. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 3 is characterized in that: The photovoltaic output probability density model and the load level probability density model with a known number of Gaussian components are solved by using a maximum expectation value algorithm.

5. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 1, characterized in that: The method of establishing a time series joint probability distribution model of photovoltaic output and load level in each time period based on the photovoltaic output probability density model and load level probability density model in the corresponding time period and using the Copula function method specifically includes: Determine the photovoltaic output marginal distribution function and the load level marginal distribution function of each time period according to the photovoltaic output probability density model and the load level probability density model of the corresponding time period; Determine the optimal Copula function used in each time period; The optimal Copula function of the corresponding time period is used to fit the marginal distribution function of photovoltaic output and the marginal distribution function of load level in each time period, and the time series joint probability distribution model of photovoltaic output and load level in each time period is obtained.

6. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 5, characterized in that: The method of determining the optimal Copula function to be used in each time period specifically includes: for each time period, obtaining the following types of Copula functions: Normal-Copula function, t-Copula function, Frank-Copula function, Clayton-Copula function and Gumbel-Copula function; using the minimum square Euclidean distance between the empirical Copula function and various types of Copula functions as a criterion for goodness of fit judgment, and using the Copula function corresponding to the minimum square Euclidean distance as the optimal Copula function for describing the correlation between photovoltaic output and load level in the time period.

7. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 1, characterized in that: The time series joint probability distribution model of each time period is sampled to generate a large number of time series scenario samples that consider the uncertainty and correlation between photovoltaic output and load level, and after scene reduction, a typical distribution network scenario that considers source-load uncertainty and correlation is obtained, wherein the scene reduction uses a K-means clustering algorithm to perform scene clustering on a large number of time series scenario samples to extract a part of the time series scenario samples for constructing a typical distribution network scenario.

8. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 7, characterized in that: The K-means clustering algorithm is used to perform scene clustering, wherein the optimal number of clusters of the K-means clustering algorithm is determined based on the elbow method of the SSE indicator.

9. The method for constructing a typical distribution network scenario considering source-load correlation according to claim 5, characterized in that: The sampling of the time series joint probability distribution model of each time period generates a large number of time series scenario samples that consider the uncertainty and correlation between photovoltaic output and load level, specifically including: The Monte Carlo method is used to sample the time series joint probability distribution model of each period to obtain N time series marginal distribution sample groups of photovoltaic output and load level in the tth period; Calculate the inverse function of the marginal distribution function of photovoltaic output and the inverse function of the marginal distribution function of load level in the tth period; Substitute each sample in the time series marginal distribution sample group into the corresponding inverse function to obtain a large number of time series scenario samples that consider the uncertainty and correlation between photovoltaic output and load level.

10. A distribution network typical scenario construction system considering source-load correlation, used to execute the distribution network typical scenario construction method considering source-load correlation as described in any one of claims 1 to 9, characterized in that: include: The probability density model building module is used to establish the probability density model of photovoltaic output and the probability density model of load level in each time period through non-parametric estimation method; The time series joint probability distribution model construction module is used to establish the time series joint probability distribution model of photovoltaic output and load level in each time period based on the photovoltaic output probability density model and load level probability density model of the corresponding time period and using the Copula function method; The typical scenario construction module of the distribution network is used to sample the time series joint probability distribution model of each time period to generate a large number of time series scenario samples that consider the uncertainty and correlation of photovoltaic output and load level, and obtain the typical distribution network scenario that considers source-load uncertainty and correlation after scenario reduction.

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