A distributed power distribution network probabilistic power flow calculation method, system, device and medium considering space-time correlation

Abstract

This invention relates to the field of intelligent dispatching technology for distribution networks, and discloses a method, system, device, and medium for calculating probabilistic power flow in distributed generation distribution networks considering spatiotemporal correlation. The method includes: acquiring historical data and constructing a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed generation sources and loads in the distribution network; generating an initial sample matrix of the output of the distributed generation sources and loads through sampling, and performing correlation correction; and using each set of samples in the correlation sample set as a deterministic scenario, substituting it into the power flow equation of the distribution network for solution, to obtain the probability distribution of node voltage and branch power flow, as well as the probability index of exceeding limits. This invention can accurately identify the spatiotemporal correlation and non-normal distribution characteristics of distributed generation output and loads. Through power flow solution and statistical analysis based on real samples, it can accurately output the probability distribution of node voltage and branch power flow, as well as the probability index of exceeding limits, providing a reliable decision-making basis for distribution network operation and dispatching.

Description

Technical Field

[0001] This invention relates to the field of intelligent dispatching technology for distribution networks, and in particular to a method, system, device, and medium for calculating probabilistic power flow in distributed generation distribution networks that considers spatiotemporal correlation. Background Technology

[0002] The large-scale integration of clean distributed generation (DG) sources such as solar and wind power into distribution networks is a core trend in energy transition. However, DG output is intermittent and uncertain, and there is significant spatiotemporal coupling between DG sources and between DG and loads, exacerbating the complexity of distribution network operation. Traditional deterministic power flow methods are insufficient to accurately reflect operational risks, making probabilistic power flow crucial for grid safety dispatch. The increasing demand for high-proportion DG integration in current distribution networks necessitates probabilistic power flow solutions that can accurately capture spatiotemporal correlations to support grid planning and operational decisions.

[0003] Existing probabilistic power flow calculation techniques for distribution networks often simplify the relationship between distributed generation (DG) output and loads by assuming independence, failing to consider the spatiotemporal correlations between DGs at different locations and between DGs and loads, or using only simple linear models to characterize the correlations. This fails to accurately match the nonlinear correlation characteristics in actual operation. This problem causes the generated samples to deviate from the real operating scenario, resulting in significant deviations in the probability distribution calculations of key indicators such as node voltage and branch power flow. This directly affects the accuracy of distribution network risk assessment and makes it difficult to meet the refined operation and management requirements of scenarios with high proportions of DG access. Summary of the Invention

[0004] In view of the aforementioned existing problems, this invention is proposed. Therefore, this invention provides a probabilistic power flow calculation method for distributed generation distribution networks that considers spatiotemporal correlations to solve the above problems.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a probabilistic power flow calculation method for distributed generation distribution networks that considers spatiotemporal correlation, comprising: acquiring historical data of the distribution network and constructing a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed generation sources and loads in the distribution network; Based on the joint probability distribution model, an initial sample matrix of the distributed power output and load is generated by sampling the sample data. The initial sample matrix is ​​corrected for correlation to generate a correlation sample set that conforms to the joint probability distribution model; Each set of samples in the correlation sample set is taken as a deterministic scenario and substituted into the power flow equation of the distribution network to solve for the output sample set of branch power flow and node voltage. Statistical analysis is performed on the output sample set to obtain the probability distribution of node voltage and branch power flow, as well as the probability index of exceeding limits.

[0006] As a preferred embodiment of the probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation described in this invention, the method includes: constructing a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed generation sources and loads in the distribution network, comprising: Historical data on the output and load of each distributed power source are obtained separately, and the marginal probability distribution of the historical data is determined. Based on the historical data, the output of the multiple distributed power sources and the correlation structure between loads are described by the Copula function, and the parameters of the Copula function are estimated. The joint probability distribution model is constructed by combining each of the marginal probability distributions with the Copula function. The beneficial effect of this preferred scheme is that by preserving the fluctuation characteristics of each variable itself, it accurately describes the nonlinear relationship between them, making the constructed joint distribution model closer to the actual operation law of the distribution network, and providing a probabilistic basis for subsequent sampling with high fidelity.

[0007] As a preferred embodiment of the probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation described in this invention, the initial sample matrix for generating the output and load of the distributed generation includes: By using the Latin hypercube sampling method, the cumulative probability interval of each variable is divided into N smaller intervals, and a probability value is randomly selected from each interval to generate a probability sample. Based on the probability samples, they are converted into physical quantity samples through the inverse function of the marginal distribution. Each of the variables The samples are randomly paired to generate an initial sample matrix of N×n; The Latin hypercube sampling employs an optimization strategy, which includes minimizing the correlation coefficient or maximizing the minimum distance, to improve the spatial filling of the initial samples.

[0008] As a preferred embodiment of the distributed power distribution network probabilistic power flow calculation method considering spatiotemporal correlation described in this invention, the method includes: performing correlation correction on the initial sample matrix to generate a correlation sample set conforming to the joint probability distribution model, including: Based on the joint probability distribution model, the corresponding correlation coefficient matrix is ​​calculated and Cholesky decomposition is performed to obtain the lower triangular matrix; Based on the lower triangular matrix, the initial sample matrix is ​​linearly transformed, and the final correlation sample matrix is ​​obtained through the inverse function of the marginal distribution of each variable. The beneficial effect of this preferred scheme is that it calculates the rank correlation coefficient matrix based on Copula parameters, performs linear transformation on independent normal samples through Cholesky decomposition, and makes the rank correlation structure between samples completely consistent with the Copula model. While introducing correlation, it ensures that each variable sample strictly regresses its original marginal distribution, generating an input sample set that truly conforms to the real scenario.

[0009] As a preferred embodiment of the probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation described in this invention, the output sample set for obtaining branch power flow and node voltage includes: Each set of samples in the correlation sample matrix is ​​used as a deterministic injection power, substituted into the power flow equation, and the power flow equation is solved. Record the voltage magnitude vector of all nodes and the power flow vector of all branches for each scenario to generate an output sample set; The advantage of this preferred solution is that it solves multiple sets of related samples as multiple deterministic scenarios in sequence, thereby obtaining a sample set that can reflect the range of operational fluctuations.

[0010] As a preferred embodiment of the probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation described in this invention, the following steps are performed: Statistical analysis is conducted on the output sample set to obtain the probability distribution of node voltages and branch power flows, as well as the probability index of exceeding limits, including: The kernel density estimation method is used to fit the probability density function of the output sample set to estimate the probability density function and cumulative distribution function of node voltage and branch power flow, and the over-limit probability index of each node is calculated based on the preset safe operation threshold. The over-limit probability index includes the node voltage over-limit probability or the branch power flow overload probability, which is calculated by the proportion of over-limit samples in the statistical output sample set.

[0011] As a preferred embodiment of the probabilistic power flow calculation method for distributed generation power distribution networks considering spatiotemporal correlation described in this invention, the construction of the joint probability distribution model further includes: The marginal probability distribution is fitted to a Beta distribution, a Weibull distribution, or a normal distribution based on the statistical characteristics of historical data. The parameters of the Copula function are estimated using the maximum likelihood estimation method or the method of moments estimation.

[0012] Secondly, the present invention provides a probabilistic power flow calculation system for distributed generation distribution networks that considers spatiotemporal correlations, comprising: The joint distributed modeling module is used to acquire historical data of the distribution network and construct a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed power sources and loads in the distribution network. The sampling module is used to generate an initial sample matrix of the distributed power output and load by sampling the sample data based on the joint probability distribution model. The correlation sample generation module is used to correct the correlation of the initial sample matrix and generate a correlation sample set that conforms to the joint probability distribution model. The probabilistic power flow calculation module is used to take each set of samples in the correlation sample set as a deterministic scenario, substitute it into the power flow equation of the distribution network, and solve it to obtain the output sample set of branch power flow and node voltage. The statistical evaluation module is used to perform statistical analysis on the output sample set to obtain the probability distribution of node voltage and branch power flow and the first-level over-limit probability index.

[0013] Thirdly, the present invention provides a computer device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the probabilistic power flow calculation method for distributed power distribution networks that considers spatiotemporal correlation.

[0014] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the probabilistic power flow calculation method for a distributed power distribution network considering spatiotemporal correlation.

[0015] Compared with existing technologies, the advantages of this invention are as follows: This invention constructs a joint probability distribution model through a Copula function, without relying on the assumption of normal distribution, and can accurately identify the spatiotemporal correlation and non-normal distribution characteristics of distributed generation output and load, thus improving the authenticity of the samples; by combining Latin hypercube sampling and Cholesky decomposition correction, it improves sampling efficiency and reduces computational redundancy while ensuring the consistency of sample correlation; through power flow solution and statistical analysis based on real samples, it can accurately output the probability distribution of node voltage and branch power flow and the probability of exceeding limits, providing a reliable decision-making basis for distribution network operation and scheduling, effectively improving the distribution network's ability to accommodate distributed generation, and ensuring the safe and economical operation of the power grid. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the overall process of a probabilistic power flow calculation method for distributed generation distribution networks that considers spatiotemporal correlation, according to an embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0019] Reference Figure 1 As an embodiment of the present invention, a probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation is provided, comprising: S101, Obtain historical data of the distribution network and construct a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed power sources and loads in the distribution network; S102, based on the joint probability distribution model, generates an initial sample matrix of distributed power output and load by sampling sample data; S103, perform correlation correction on the initial sample matrix to generate a correlation sample set that conforms to the joint probability distribution model; S104. Each set of samples in the relevant sample set is taken as a deterministic scenario and substituted into the power flow equation of the distribution network to solve for the output sample set of branch power flow and node voltage. S105 performs statistical analysis on the output sample set to obtain the probability distribution of node voltage and branch power flow, as well as the probability index of exceeding limits.

[0020] In this embodiment, a distribution network topology analysis and directed graph model are first constructed. During the analysis and standardization of basic distribution network ledger data, the input data sources include distribution network equipment ledger data, such as data on lines, transformers, and switching equipment; the power grid CIM / XML model file; and node electrical parameters. The vertices of the graphical elements in the model represent distribution network nodes, bound to node ID, type, rated voltage, and voltage over-limit threshold, such as the national standard allowable deviation of ±7% for 10kV distribution networks, i.e., Vmin=0.93pu and Vmax=1.07pu. Edges correspond to the lines and transformer branches between adjacent nodes, bound to branch ID, parent node ID, child node ID, three-phase impedance parameters, and thermal stability limit values. The thermal stability limit values ​​are used for subsequent overload probability calculations.

[0021] Furthermore, topology layering and numbering optimization are performed. Taking the balancing node of the substation outgoing line as the root node, i.e., layer 0, the breadth-first search (BFS) algorithm is used to number all nodes in the network hierarchically. The parent node level is always lower than the child node level, which fully adapts to the iterative logic of the forward-backward substitution method and avoids reverse calculation errors. A node level comparison table and a parent-child node association table are generated to clarify the upstream and downstream topological relationships of the radial network.

[0022] Furthermore, the mapping and binding of random variables to topology nodes establishes a one-to-one correspondence between random variables and physical topology, resolving the disconnect between the probabilistic model and the physical nodes of the power grid. Specifically, for each DG access node, two core random variables are bound: DG active power output and DG active power output. DG's reactive power output For each load access node, two core random variables are bound: the load active power. Reactive power of load ;form 3D random variable vector ,in Total number of nodes + Total number of load nodes This process clarifies the node ID, physical meaning, and electrical constraint boundaries corresponding to each random variable, such as the upper and lower limits of DG output and the range of load power fluctuations, providing a precise node mapping foundation for subsequent joint distribution modeling, sampling, and power flow calculation.

[0023] The matrix-based storage of three-phase unbalanced topology parameters is designed for three-phase unbalanced power flow models. A standardized parameter matrix is ​​pre-constructed to improve power flow calculation efficiency. The node-branch association matrix has the dimension of "number of nodes × number of branches," with an element value of 1 indicating that the branch's parent node is that node, -1 indicating that the branch's child node is that node, and 0 indicating no association. This is used for fast indexing of current and power during the forward and backward iteration processes. The three-phase branch impedance matrix corresponds to each branch... The impedance submatrix includes the self-impedance of each phase and the mutual impedance between phases, fully adapting to the voltage and current calculations in three-phase unbalanced scenarios; the safety limit matrix pre-stores the voltage over-limit thresholds of all nodes and the power flow overload thresholds of all branches, providing a unified benchmark for the subsequent over-limit probability calculation of S105.

[0024] In a preferred embodiment, constructing a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed power sources and loads in a distribution network includes: Historical data on the output and load of each distributed power source are obtained separately, and the marginal probability distribution of the historical data is determined. Based on historical data, the Copula function is used to describe the output of multiple distributed power sources and the correlation structure between loads, and the parameters of the Copula function are estimated. By combining each marginal probability distribution with the Copula function, a joint probability distribution model is constructed.

[0025] Specifically, this step is used to construct a probabilistic model that accurately reflects the complex dependencies between multiple random variables, such as photovoltaic power output, wind power output, and load power at different locations. Traditional methods often assume that variables are independent or describe them only using linear correlation coefficients, failing to capture nonlinear and asymmetric tail correlations. Copula theory, through Sklar's theorem, transforms multidimensional random vectors... joint distribution Decomposed into the marginal distributions of each variable and a Copula function connecting these marginal distributions , is represented as: in, Following a uniform distribution on [0,1], by choosing an appropriate Copula function And estimate its parameters This allows us to describe the spatiotemporal relationship structure between variables while preserving their individual fluctuation characteristics.

[0026] It should be noted that this invention constructs a joint probability distribution model using the Copula function, which can accurately identify the spatiotemporal correlation and non-normal distribution characteristics of distributed generation output and load without relying on the normal distribution assumption, thus improving the authenticity of the samples. By combining Latin hypercube sampling and Cholesky decomposition correction, the sampling efficiency is improved and computational redundancy is reduced while ensuring the consistency of sample correlation. Through power flow solution and statistical analysis based on real samples, the probability distribution of node voltage and branch power flow and the probability of exceeding limits can be accurately output, providing a reliable decision-making basis for distribution network operation and scheduling, effectively improving the distribution network's ability to accommodate distributed generation, and ensuring the safe and economical operation of the power grid.

[0027] Furthermore, in step S101, the Copula function is any one or a combination of Gaussian Copula, t-Copula, and Archimedes Copula. The choice of Copula function type is based on the analysis of the correlation structure of historical data. Gaussian Copula is suitable for symmetrical linear correlations; t-Copula can capture symmetrical tail correlations; Archimedes Copula can reflect asymmetric correlations of the lower or upper tail respectively, such as Clayton and Gumbel. The most suitable Copula can be selected through goodness-of-fit tests, such as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC).

[0028] Gaussian Copula is represented as: in, It is the inverse cumulative distribution function of the standard univariate normal distribution. It has a mean of zero and a correlation coefficient matrix of... The joint cumulative distribution function of the multivariate standard normal distribution, and its density function. Represented as: in, Represents the standard normalized vector. This represents the linear correlation coefficient matrix.

[0029] In one alternative implementation, tCopula is represented as: in, It has degrees of freedom. of one dollar t The inverse cumulative distribution function of the distribution, It has degrees of freedom. The correlation coefficient matrix is diversity t The joint cumulative distribution function of the distribution.

[0030] In another alternative implementation, the Archimedes Copula, exemplified by Clayton Copula, is represented as follows: in, As a relevant parameter, this Copula is more sensitive to changes in the lower tail and is suitable for describing the strong correlation of variables at low output or low load.

[0031] Based on the different actual correlation characteristics between wind power and photovoltaic power output data, the most suitable correlation model, Copula, should be flexibly selected. For example, when multiple photovoltaic power plants experience a simultaneous sharp drop in output due to the passage of the same cloud layer, their correlation is asymmetrical. In this case, choosing an Archimedes Copula such as Clayton can accurately reflect this risk of simultaneous drop.

[0032] In a preferred embodiment, constructing the joint probability distribution model further includes: Marginal probability distributions are fitted to Beta, Weibull, or normal distributions based on the statistical characteristics of historical data. The parameters of the Copula function are estimated using either the maximum likelihood estimation method or the method of moments estimation.

[0033] Specifically, step S101 includes: Step 1: Obtain historical data on the output and load of each distributed power source to determine its marginal probability distribution; For the random variables For example, the active power output of a photovoltaic power station, based on its Historical observation data Determine its probability distribution Assuming it follows a certain family of parametric distributions, the distribution parameters are estimated through samples. .

[0034] Marginal probability distributions, based on the statistical characteristics of historical data, are fitted to a Beta distribution, a Weibull distribution, or a normal distribution.

[0035] Taking photovoltaic output-Beta distribution as an example: Normalize output force The fit is a Beta distribution. This represents the actual active power output of the i-th photovoltaic power station. Let represent the rated active power output of the i-th photovoltaic power station, and its probability density function (PDF) is expressed as: in, Let represent the Beta probability density function of the i-th normalized photovoltaic output, describing the probability distribution characteristics of the photovoltaic output in the interval [0,1]; shape parameter It can be obtained through the method of moments, expressed as: in, and These are the sample mean and variance, respectively. The two shape parameters representing the Beta distribution are both positive real numbers, which together determine the shape of the Beta distribution curve.

[0036] Taking the wind speed / wind power-Weibull distribution as an example: wind speed The fit is a Weibull distribution, and its PDF representation is as follows: Among them, scale parameter and shape parameters It can be solved by maximum likelihood estimation (MLE), that is, maximizing the log-likelihood function. , is represented as: Wind power output Through the wind turbine power curve Correlation with wind speed is obtained directly using a nonparametric kernel density estimation method.

[0037] In one alternative implementation, when determining the marginal probability distribution, for variables that are not easily parameterized, such as complex loads, their probability density function is directly estimated, expressed as: in, It refers to kernel functions, such as Gaussian kernels. , For bandwidth, the cumulative distribution function (CDF) is given. Through the Obtained by numerical integration.

[0038] Step 2: Based on historical data, estimate the Copula function parameters that describe the output of multiple distributed power sources and the correlation structure between loads; the Copula function parameters are estimated using the maximum likelihood estimation method or the method of moments estimation.

[0039] Estimate the parameters of the Copula function. Let the selected Copula function be... ,in These are parameters to be estimated. Based on historical observation data. Convert it into a uniformly distributed sample : in, Let represent the marginal cumulative distribution function of the i-th random variable.

[0040] The log-likelihood function of Copula is constructed using the maximum likelihood estimation (MLE) method. , is represented as: in, It is the density function of Copula, and the parameter estimates are obtained by solving the following optimization problem: in, This represents the core parameters to be estimated for the Copula function.

[0041] In an alternative implementation, two-stage maximum likelihood estimation (IFM) can also be used, by first estimating the parameters of each marginal distribution. Then based on the transformed uniform samples Estimating Copula parameters .

[0042] In another alternative implementation, the method of moments is used, which solves the problem by utilizing the principle that the theoretical moments of the Copula function are equal to the sample moments. For example, for the bivariate case, Kendall's method is commonly used. Or Spearman' Estimate the parameters for Archimedes Copula. With Kendall There are often explicit functional relationships. For example, ClaytonCopula: Therefore, we can first calculate the Kendall's score of the sample. coefficient Then, the parameter estimates are obtained through the inverse function. .

[0043] Step 3: Combine each marginal probability distribution with the Copula function to construct a joint probability distribution model.

[0044] Specifically, a joint probability distribution model is constructed based on Sklar's theorem, which determines the marginal distributions of the variables in step one. Compared with the Copula function estimated in step two Combined, forming the final The joint probability distribution model is expressed as: The joint probability density function of this model is: in, It is the first The marginal probability density function of each variable, the model fully describes the randomness of all DG output and load and the relationships between them. The spatiotemporal correlation structure is characterized.

[0045] In a preferred embodiment, generating an initial sample matrix of distributed power output and load includes: By using the Latin hypercube sampling method, the cumulative probability interval of each variable is divided into N smaller intervals, and a probability value is randomly selected from each interval to generate a probability sample. Based on probability samples, they are transformed into physical quantity samples through the inverse function of marginal distribution. Each of the variables The samples are randomly paired to generate an initial sample matrix of N×n; Latin hypercube sampling employs optimization strategies, including minimizing the correlation coefficient or maximizing the minimum distance, to improve the spatial filling of the initial samples.

[0046] Specifically, to perform Monte Carlo simulations, a large number of samples of input random variables need to be generated. Latin hypercube sampling (LHS) is a stratified sampling technique that covers the entire probability distribution space of variables better with fewer samples than simple random sampling.

[0047] For each random variable There are a total of , let the sampling size be . The cumulative probability distribution range of the variable [0,1] is divided into equal parts. Non-overlapping intervals: , ,…, A probability value is drawn independently and randomly within each interval. ,in Indicates the sample number.

[0048] The inverse function of the marginal cumulative distribution function of each variable Convert probability samples into physical quantity samples : Will Each of the variables Each sample is randomly paired to form Initial sample matrix of dimension At this point, the samples of each variable corresponding to each column have the correct marginal distribution, but the statistical independence between the variables corresponding to each column is imposed and has not yet reflected the correlation modeled in step S101.

[0049] Furthermore, the Latin hypercube sampling employs an optimization strategy, assuming the initial random pairing generates a sample matrix of... By iteratively swapping elements in any two rows, thus preserving the marginal distribution of each column, all variables are made equal to... linear correlation coefficient between samples Minimizing the sum of the absolute values ​​of is expressed as: In the method of maximizing minimum distance, in probability space In, define sample points and The Euclidean distance between them is the optimization objective, which is to maximize the minimum distance between all sample points, expressed as: It should be noted that the optimization strategy is used to improve the spatial filling of the initial LHS samples. The method of minimizing the correlation coefficient makes the empirical correlation coefficient between columns of the initial independent sample matrix as close to zero as possible by iteratively exchanging the positions of sample pairs. The method of maximizing the minimum distance makes the distribution of all sample points in the probability space as uniform as possible through optimization.

[0050] Latin hypercube sampling (LHS) is more efficient than pure random sampling, covering a wider range of possibilities more quickly. However, the initial LHS samples may be randomly paired between variables. Introduced optimization strategies, such as minimizing correlation coefficients and maximizing minimum distances, are equivalent to intelligently permuting the initial samples. The goal is to make these sample points more evenly and representatively distributed in the multidimensional probability space, while minimizing spurious associations introduced by the sampling process itself.

[0051] In a preferred embodiment, the initial sample matrix is ​​corrected for correlation to generate a correlation sample set that conforms to the joint probability distribution model, including: Based on the joint probability distribution model, the corresponding correlation coefficient matrix is ​​calculated and Cholesky decomposition is performed to obtain the lower triangular matrix; The initial sample matrix is ​​linearly transformed using the lower triangular matrix, and the final correlation sample matrix is ​​obtained by using the inverse function of the marginal distribution of each variable.

[0052] It should be noted that this step is used to modify the independent samples generated by LHS into samples with the correlation structure described by the Copula function.

[0053] Specifically, based on the Copula function parameters estimated in step S101 Calculate its corresponding 2D symmetric positive definite rank correlation coefficient matrix and the matrix Perform Cholesky decomposition to obtain the lower triangular matrix. ,satisfy .

[0054] The initial sample matrix Each column corresponds to a sample value for each variable, which is then transformed into a standard normal distribution using its empirical distribution function. From the samples, we obtain the matrix. It can be accessed through To achieve, among which, It is the standard normal distribution function. Let represent the empirical cumulative distribution function of the i-th random variable, which is a nonparametric cumulative distribution function obtained through frequency statistics based on actual historical samples. Let represent the k-th standard normal sample after the Cholesky decomposition linear transformation of the i-th random variable.

[0055] For matrix Perform a linear transformation: Transformed matrix The samples in each column thus have a relationship formed by... The defined correlation, and each column still approximately follows a standard normal distribution.

[0056] Will Each column follows the standard normal distribution function. Convert back to a uniform distribution in [0,1]: The matrix obtained at this time Each column is a uniformly distributed sample on [0,1], and the columns have target Copula correlations.

[0057] Furthermore, the correlation coefficient matrix is ​​either the Kendall rank correlation coefficient matrix or the Spearman rank correlation coefficient matrix calculated based on the Copula function and its parameters.

[0058] Based on the estimated Copula parameters Calculate its corresponding Rank correlation coefficient matrix For Gaussian Copula and tCopula, their linear dependence matrix... It can be used directly as a parameter or derived from it. For Archimedes Copula, Kendall's algorithm needs to be calculated. matrix For ClaytonCopula, there is Then through approximation relationships Alternatively, Spearman's method can be obtained directly through numerical integration of the Copula function. matrix .

[0059] For matrix (or Perform Cholesky decomposition: LHS generates an independent standard normal sample matrix. The matrix has a mean of 0 and a variance of 1 in each column, and the columns are independent. The matrix is ​​then transformed as follows: After transformation, The covariance matrix is It has become relevant to the target.

[0060] Furthermore, after step S103 and before step S104, the method further includes: performing an inverse probability integral transformation on the samples after correlation correction, so that the samples of each variable strictly follow their own marginal probability distribution.

[0061] A uniformly distributed sample matrix with correlation is obtained through Cholesky decomposition and normal transformation. Then, apply the inverse marginal distribution function of the corresponding variable to each element: To obtain the final physical quantity sample matrix Each column of this matrix follows And all columns together obey the Copula function. The joint distribution described.

[0062] In a preferred embodiment, obtaining the output sample set of branch power flow and node voltage includes: Each set of samples in the correlation sample matrix is ​​used as the deterministic injection power, substituted into the power flow equation, and the power flow equation is solved. Record the voltage magnitude vector of all nodes and the power flow vector of all branches for each scenario to generate an output sample set.

[0063] Specifically, the N sets of correlation samples generated in step S103 are... As N distinct operating scenarios, deterministic power flow calculations are performed sequentially.

[0064] For each scenario Solve the following system of nonlinear equations: in, For nodes The net injected active and reactive power, including DG output and load; For node voltage magnitude and phase angle; Elements of the node admittance matrix; This represents the voltage phase angle difference between node i and node j.

[0065] For radial distribution networks, the forward-backward substitution method is used to efficiently solve the power flow equations of the distribution network, and the results are obtained for each scenario. The node voltage magnitude vector and branch power flow vector The forward-backward substitution method is particularly suitable for radial distribution networks. Its calculation process is stable and efficient, and it does not require the formation of a Jacobian matrix. It includes back-substitution to calculate the injected current at the nodes, forward-substitution to update the node voltage, and iteration until convergence.

[0066] Specifically, let there be a total of There are 12 nodes, where node 1 is the ballast node. All node voltages are initialized to their rated values, such as... .

[0067] Back-substitution (reverse) process: Starting from the end node, calculate the current of each branch layer by layer towards the root node. For each node... The injected current is: in, Net injected power, For node-to-ground parallel admittance, This indicates taking the conjugate. For branches... That is, connecting the parent node and child nodes The current in a branch is equal to the sum of all currents flowing downstream from that child node: in, branch road l The current, Let be the current at child node c. Let be the current of the downstream node m of child node c.

[0068] Forward process: Starting from the root node, the node voltage is updated layer by layer towards the terminal node, represented as: in, branch road The impedance; repeat the iteration until convergence, for example, satisfying... , The iterative convergence accuracy of power flow calculation is represented by a very small positive real number, such as 10. -3 Or 10 -6 pu.

[0069] In this step, the power flow equations for the distribution network are a three-phase unbalanced power flow model applicable to radial distribution networks. For a three-phase system, i.e., phases A, B, and C, all scalar quantities are extended to three-dimensional phasors. Node admittance matrix. Become A block matrix, where each block is a The submatrix represents the three-phase coupling relationship between nodes, including self-impedance and mutual impedance. The power flow equations are extended as follows: in, , represents the three-phase voltage phasor of the i-th node. Let A, B, and C be the phase voltages at node i, respectively. The current and voltage calculations in the forward-backward substitution method also need to be performed in three-dimensional phasor space, taking into account interphase coupling.

[0070] It should be noted that this invention takes into account the possibility of three-phase imbalance in actual distribution networks. In this case, the power flow model needs to establish independent equations for each phase, and the node admittance matrix, voltage, and power are all three-phase quantities. The forward-backward substitution method also needs to be extended to a three-phase version to more accurately assess the imbalance distribution of voltage and power flow in each phase.

[0071] In low-voltage distribution networks, due to the random connection of single-phase loads, the three-phase current and voltage are often unbalanced. Traditional simplified models may mask this imbalance and underestimate the risk of overvoltage or overload in a particular phase. By using a three-phase unbalanced model for power flow calculation, the voltage and power flow of each phase (A, B, and C) are calculated separately. The resulting probability assessment truly reflects the actual operation of the distribution network, thus guiding operators to take targeted three-phase load adjustments or reactive power compensation measures.

[0072] In a preferred embodiment, statistical analysis is performed on the output sample set to obtain the probability distribution of node voltage and branch power flow, as well as the probability index of exceeding limits, including: The kernel density estimation method is used to fit the probability density function of the output sample set to estimate the probability density function and cumulative distribution function of node voltage and branch power flow, and the over-limit probability index of each node is calculated based on the preset safe operation threshold. The probability of exceeding limits includes the probability of node voltage exceeding limits or the probability of branch power flow overload, which is calculated by the proportion of samples exceeding limits in the statistical output sample set.

[0073] Specifically, the output sample set obtained from power flow calculations for N scenarios. Perform statistical analysis. For any given amount of attention... For example, the voltage at a certain node Or the power of a certain branch Its sample set It can be used to estimate its probability density function (PDF) and cumulative distribution function (CDF), which can be expressed using the kernel density estimation (KDE) method, as follows: in, It's a kernel function. For bandwidth.

[0074] For the set safety limits Such as the lower voltage limit Or branch thermal stability limit Its probability of exceeding the limit It can be approximated as: in, This is an indicator function that takes the value 1 when the condition is true and 0 otherwise. These represent the minimum and maximum safety limits, respectively; the probability of exceeding limits includes the probability of node voltage exceeding limits and / or the probability of branch power flow overload.

[0075] For node voltage It is below the lower limit The probability is: Node voltage Above the upper limit The probability is: in, It is an indicator function for branches. The apparent power flow Its overload probability is: It should be noted that probabilistic power flow calculations generate massive amounts of data, condensing complex probability distribution curves into simple and clear risk warning figures that can be directly compared with thresholds in safe operation procedures, providing quantitative basis for scheduling decisions.

[0076] In this embodiment, the distributed power source includes a photovoltaic power generation system and a wind power generation system, and the load includes at least one of residential load, commercial load and industrial load.

[0077] wind speed The distribution is as follows: Wind power output With wind speed Through the wind turbine power curve .

[0078] It should be noted that residential, commercial, and industrial loads have different daily curve shapes and fluctuation characteristics, and should be treated differently when constructing their marginal distribution or time series models. Their Copula-related parameters may also be different.

[0079] Distributed power sources, such as photovoltaic and wind power, which exhibit high volatility, and various loads that constitute the main source of uncertainty, are examples of this approach. This demonstrates that the method in this embodiment is not intended to solve all power flow problems, but is specifically designed to address the new challenges posed by the current high proportion of renewable energy integrated into the distribution network. This distinguishes it from methods that handle traditional deterministic power flows or those containing only a small amount of distributed generation (DG); it also guides potential users of the technology.

[0080] It should be noted that this invention constructs a joint probability distribution model using the Copula function, without relying on the assumption of a normal distribution. This accurately identifies the spatiotemporal correlation and non-normal distribution characteristics of distributed generation output and load, improving the authenticity of the samples. By combining Latin hypercube sampling and Cholesky decomposition correction, the sampling efficiency is improved and computational redundancy is reduced while ensuring the consistency of sample correlation. Through power flow solution and statistical analysis based on real samples, the probability distribution of node voltage and branch power flow, as well as the probability of exceeding limits, can be accurately output, providing a reliable decision-making basis for distribution network operation and scheduling. This effectively enhances the distribution network's ability to accommodate distributed generation and ensures the safe and economical operation of the power grid.

[0081] The above is an illustrative scheme of a probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation, according to this embodiment. It should be noted that the technical solution of this probabilistic power flow calculation system for distributed generation distribution networks considering spatiotemporal correlation belongs to the same concept as the technical solution of the aforementioned probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation. Details not described in detail in the technical solution of the probabilistic power flow calculation system for distributed generation distribution networks considering spatiotemporal correlation in this embodiment can be found in the description of the technical solution of the aforementioned probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation.

[0082] This embodiment provides a probabilistic power flow calculation system for distributed generation distribution networks that considers spatiotemporal correlations, including: The joint distributed modeling module is used to acquire historical data of the distribution network and construct a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed power sources and loads in the distribution network. The sampling module is used to generate an initial sample matrix of distributed power output and load by sampling sample data based on the joint probability distribution model. The correlation sample generation module is used to correct the correlation of the initial sample matrix and generate a correlation sample set that conforms to the joint probability distribution model. The probabilistic power flow calculation module is used to treat each set of samples in the relevant sample set as a deterministic scenario, substitute it into the power flow equation of the distribution network, and solve it to obtain the output sample set of branch power flow and node voltage. The statistical evaluation module is used to perform statistical analysis on the output sample set to obtain the probability distribution of node voltage and branch power flow and the first-level over-limit probability index.

[0083] This embodiment also provides a computer device suitable for probabilistic power flow calculations in distributed generation distribution networks that consider spatiotemporal correlations, including: The system includes a memory and a processor. The memory stores computer-executable instructions, and the processor executes these instructions to implement a probabilistic power flow calculation method for distributed power distribution networks that considers spatiotemporal correlations, as proposed in the above embodiments.

[0084] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements a probabilistic power flow calculation method for distributed power distribution networks that considers spatiotemporal correlation, as proposed in the above embodiments.

[0085] The storage medium proposed in this embodiment and the method for calculating the probabilistic power flow of a distributed power distribution network considering spatiotemporal correlation proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0086] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0087] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating probabilistic power flow in a distributed generation distribution network considering spatiotemporal correlation, characterized in that, include: Historical data of the distribution network are obtained to construct a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed power sources and loads in the distribution network. Based on the joint probability distribution model, an initial sample matrix of the distributed power output and load is generated by sampling the sample data. The initial sample matrix is ​​corrected for correlation to generate a correlation sample set that conforms to the joint probability distribution model; Each set of samples in the correlation sample set is taken as a deterministic scenario and substituted into the power flow equation of the distribution network to solve for the output sample set of branch power flow and node voltage. Statistical analysis is performed on the output sample set to obtain the probability distribution of node voltage and branch power flow, as well as the probability index of exceeding limits.

2. The method for calculating probabilistic power flow in a distributed generation distribution network considering spatiotemporal correlation as described in claim 1, characterized in that, The joint probability distribution model for the spatiotemporal correlation of multiple distributed generation outputs and loads in a distribution network includes: Historical data on the output and load of each distributed power source are obtained separately, and the marginal probability distribution of the historical data is determined. Based on the historical data, the output of the multiple distributed power sources and the correlation structure between loads are described by the Copula function, and the parameters of the Copula function are estimated. The joint probability distribution model is constructed by combining each of the marginal probability distributions with the Copula function.

3. The method for calculating probabilistic power flow in a distributed generation distribution network considering spatiotemporal correlation as described in claim 1, characterized in that, Generating the initial sample matrix of the distributed power output and load includes: By using the Latin hypercube sampling method, the cumulative probability interval of each variable is divided into N smaller intervals, and a probability value is randomly selected from each interval to generate a probability sample. Based on the probability samples, they are converted into physical quantity samples through the inverse function of the marginal distribution. Each of the variables The samples are randomly paired to generate an initial sample matrix of N×n; The Latin hypercube sampling employs an optimization strategy, which includes minimizing the correlation coefficient or maximizing the minimum distance, to improve the spatial filling of the initial samples.

4. The method for calculating probabilistic power flow in a distributed generation distribution network considering spatiotemporal correlation as described in claim 3, characterized in that, The initial sample matrix is ​​modified for correlation to generate a correlation sample set that conforms to the joint probability distribution model, including: Based on the joint probability distribution model, the corresponding correlation coefficient matrix is ​​calculated and Cholesky decomposition is performed to obtain the lower triangular matrix; The initial sample matrix is ​​linearly transformed based on the lower triangular matrix, and the final correlation sample matrix is ​​obtained through the inverse function of the marginal distribution of each variable.

5. The method for calculating probabilistic power flow in a distributed generation distribution network considering spatiotemporal correlation as described in claim 4, characterized in that, The output sample set for obtaining branch power flow and node voltage includes: Each set of samples in the correlation sample matrix is ​​used as a deterministic injection power, substituted into the power flow equation, and the power flow equation is solved. Record the voltage magnitude vector of all nodes and the power flow vector of all branches for each scenario to generate an output sample set.

6. The method for calculating probabilistic power flow in a distributed generation distribution network considering spatiotemporal correlation as described in claim 5, characterized in that, Statistical analysis is performed on the output sample set to obtain the probability distribution of node voltage and branch power flow, as well as the probability index of exceeding limits, including: The kernel density estimation method is used to fit the probability density function of the output sample set to estimate the probability density function and cumulative distribution function of node voltage and branch power flow, and the over-limit probability index of each node is calculated based on the preset safe operation threshold. The over-limit probability index includes the node voltage over-limit probability or the branch power flow overload probability, which is calculated by the proportion of over-limit samples in the statistical output sample set.

7. The method for calculating probabilistic power flow in a distributed generation distribution network considering spatiotemporal correlation as described in claim 2, characterized in that, Constructing a joint probability distribution model also includes: The marginal probability distribution is fitted to a Beta distribution, a Weibull distribution, or a normal distribution based on the statistical characteristics of historical data. The parameters of the Copula function are estimated using the maximum likelihood estimation method or the method of moments estimation.

8. A probabilistic power flow calculation system for distributed generation distribution networks considering spatiotemporal correlation, employing the probabilistic power flow calculation method for distributed generation distribution networks considering spatiotemporal correlation as described in any one of claims 1 to 7, characterized in that, include: The joint distributed modeling module is used to acquire historical data of the distribution network and construct a joint probability distribution model of the spatiotemporal correlation between the output of multiple distributed power sources and loads in the distribution network. The sampling module is used to generate an initial sample matrix of the distributed power output and load by sampling the sample data based on the joint probability distribution model. The correlation sample generation module is used to correct the correlation of the initial sample matrix and generate a correlation sample set that conforms to the joint probability distribution model. The probabilistic power flow calculation module is used to take each set of samples in the correlation sample set as a deterministic scenario, substitute it into the power flow equation of the distribution network, and solve it to obtain the output sample set of branch power flow and node voltage. The statistical evaluation module is used to perform statistical analysis on the output sample set to obtain the probability distribution of node voltage and branch power flow and the first-level over-limit probability index.

9. A computer device, characterized in that, include: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the probabilistic power flow calculation method for distributed power distribution networks considering spatiotemporal correlation as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores computer-executable instructions, which, when executed by a processor, implement the steps of the probabilistic power flow calculation method for distributed power distribution networks considering spatiotemporal correlation as described in any one of claims 1 to 7.

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