A power grid multipoint linearization probabilistic power flow calculation method and system

Abstract

The application discloses a kind of power grid multipoint linearization probabilistic power flow calculation method and system, it is related to power system technical field, its technical points are: the present application is based on kernel density estimation function and constructs the source load probability distribution model of the probability distribution of source data and load data of electric power network, based on uniform design sampling or Copula function to the source load probability distribution model is discrete sampling, so that the source, load data sampled has correlation, avoid to ignore the correlation of source, load data and produce power flow calculation error, in the face due to new energy mass access leads to source data fluctuation range too big and load data daily substantial change, it can improve power flow calculation efficiency while giving consideration to calculation accuracy, avoid the situation that single point linearization power flow calculation cannot adapt to node injection power too deviate from benchmark operating point, therefore the calculation method mentioned in the present application improves the calculation accuracy and calculation efficiency of probabilistic power flow, can be better applied in new energy power grid scene.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and more specifically, to a method and system for calculating multi-point linearized probabilistic power flow in a power grid. Background Technology

[0002] Probabilistic power flow (PPF) is adaptable to scenarios with high-proportion renewable energy integration leading to strong uncertainties in power systems. It is an effective tool for uncertainty analysis in power systems, comprehensively considering the high degree of uncertainty in system operation and obtaining the probability distribution of corresponding state variables. For wind turbine and photovoltaic power output with large fluctuation ranges, most current research still uses two-parameter Weibull and Beta distributions to fit their output probability distributions. The advantage of this approach is its simplicity and ease of implementation. For load distribution, a normal distribution model is often used. In existing technologies, traditional probabilistic power flow calculation methods based on Monte Carlo sampling have very high accuracy, but due to the large amount of power flow calculation, the calculation efficiency is low, making it difficult to meet the requirements of rapid calculation and unable to be directly applied to real-time monitoring. In addition, the core idea of ​​commonly used single-point fast probabilistic power flow calculation methods is to linearize the power flow equation at the reference operating point, which can effectively reduce the amount of calculation and improve efficiency. However, when the input variables fluctuate greatly around the reference value, the linearized power flow calculation will deviate from the reference point, resulting in significant errors. Therefore, conventional linearization methods cannot cope with strong fluctuations in the system. When wind and solar turbines or loads are geographically close, the correlation of input variables will also be introduced. Ignoring the correlation will lead to a large deviation in the calculation results. Summary of the Invention

[0003] To address the issues of computational efficiency and accuracy deviations in existing probabilistic power flow calculations, this invention aims to provide a multi-point linearized probabilistic power flow calculation method and system for power grids. This invention constructs a source-load probability distribution model describing the probability distribution of source and load data in the power grid based on a kernel density estimation function. It then performs discrete sampling on the source-load probability distribution model using uniform design sampling or a Copula function, ensuring the sampled source and load data are correlated and avoiding power flow calculation errors caused by ignoring this correlation. Regarding improving computational efficiency, this invention proposes a multi-point linearized power flow calculation method suitable for situations with large fluctuations in node injected power. Facing the increasing fluctuation range of source data due to the large-scale integration of new energy sources and significant intraday variations in load data, this method improves power flow calculation efficiency while maintaining computational accuracy. It avoids the limitations of single-point linearized power flow calculations that cannot adapt to situations where node injected power deviates significantly from the baseline operating point. Therefore, the calculation method mentioned in this invention improves both the accuracy and efficiency of probabilistic power flow calculations and can be better applied to new energy power grid scenarios.

[0004] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0005] A first aspect of this application provides a method for calculating multi-point linearized probabilistic power flow in a power grid, the method comprising:

[0006] Acquire source data, node network parameters, and load data of the power grid, where the source data is the unit output data and the load data is the power load data;

[0007] The source-charge probability distribution model of the source data and charge data is constructed using the kernel density estimation function;

[0008] Discrete sampling is performed on the source-load probability distribution model based on uniform design sampling to obtain the first sample data. Alternatively, a Copula function is constructed between the source data and the load data, and the Copula function is used to sample the source-load probability distribution model to obtain the second sample data with correlation, wherein the first sample data and the second sample data are used as input data.

[0009] A preset node injection power fluctuation threshold is set. When the node injection power fluctuation area is greater than the node injection power fluctuation threshold, the node injection power fluctuation area is divided into equally spaced segments. The reference power value of each segment is determined, and the power flow calculation is performed based on the reference power value to obtain the sensitivity matrix corresponding to each segment.

[0010] Multi-point linear power flow calculations are performed based on node network parameters, input data, and sensitivity matrices to obtain output data including node state data and branch power flow data. Probabilistic feature analysis is then performed on the output data to obtain its probability distribution.

[0011] In one implementation, the unit output data is historical unit output data or predicted unit output data, the power load data is historical power load data or predicted power load data, and the node network data includes basic power network parameters and baseline operating point data.

[0012] In one implementation, a source-charge probability distribution model for the source data and charge data is constructed using a kernel density estimation function, specifically including:

[0013] The optimal window width for kernel density estimation is calculated based on the source data or load data. When the source data is the output data of wind turbine generators and the distribution of power load data is similar to a Gaussian distribution, a source-load probability distribution model for the source data and load data is constructed using a Gaussian kernel function and the optimal window width; or...

[0014] When the load data follows a unimodal symmetric normal distribution, a source-load probability distribution model of the source data and the load data is constructed using the normal distribution function; or,

[0015] When the source data is the output data of photovoltaic units, the source and load probability distribution models of the source data and load data are constructed using the beta distribution function.

[0016] In one implementation, a Copula function is constructed between the source data and the load data. This Copula function is then used to sample relevant second sample data from the source-load probability distribution model. Specifically:

[0017] The correlation coefficients between nodes in the power grid are calculated based on the node network parameters of the power grid, and a correlation coefficient matrix of the power grid is constructed based on the correlation coefficients of multiple nodes.

[0018] A preset correlation coefficient threshold is set. When the correlation coefficient is greater than the threshold, a Copula function with correlation is determined based on the source data and load data of the node and the correlation coefficient.

[0019] Substituting the sample data and correlation coefficient matrix that follow a [0,1] distribution in the source-load probability distribution model into the inverse function of the correlated Copula function, we obtain a multidimensional random variable that follows a [0,1] distribution and is correlated, where the sample data consists of source data and load data;

[0020] By processing the correlated multidimensional random variables that follow a [0,1] distribution using the inverse function of the cumulative distribution function, we obtain a second sample of correlated data.

[0021] In one implementation, discrete sampling is performed on the source load probability distribution model based on uniform design sampling to obtain the first sample data, specifically as follows:

[0022] If any random variable is independent of the other random variables, then for any random variable, the first sample data of the random variable is transformed by equal probability based on the sample data that follows the [0,1] distribution and the cumulative distribution function in the source load probability distribution model.

[0023] In one implementation, the sample data in the source load probability distribution model that follows a [0,1] distribution are obtained through the following steps:

[0024] Suppose we need to generate sample data of n random variables following a distribution [0,1], where N is the total number of samples and α is an arbitrary positive integer. Generate a positive integer vector H. 1×n =[h1,h2,…,h n ], where h1=1, h i ∈(1,α) and none of the elements in the vector are equal;

[0025] From multivariate distribution Select n independent samples to form vector B 1×n=[b1,b2,…,b n ];

[0026] Matrix E is generated by simple random sampling. n×N =[e1,e2,…,e j ,…,e n ] T (e j =[e j1 ,e j2 ,…,e jN ]), where the random variable e follows a uniform distribution on [-0.5, 0.5], and T represents the transpose of the matrix;

[0027] In constructing the source load probability distribution model, sample data U follows a [0,1] distribution. n×N =[u1,u2,…,u i ,…,u n ] T (u i =[u i1 ,u i2 ,…,u iN element u in ]) ij for: Where i = 1, 2, ..., n, j = 1, 2, ..., N.

[0028] In one implementation, a preset node injection power fluctuation threshold is defined. When the node injection power fluctuation region exceeds the node injection power fluctuation threshold, the node injection power fluctuation region is divided into equally spaced segments. A reference power value is determined for each segment, and power flow calculation is performed based on the reference power value to obtain the sensitivity matrix corresponding to each segment. Specifically:

[0029] The average value of the node injection power at the endpoints of each region is used as the reference power value for each region.

[0030] The power flow equations are linearized at the reference power values ​​for each region to obtain the Jacobian matrix for each region, and the sensitivity matrix is ​​obtained based on the inverse of the Jacobian matrix.

[0031] In one implementation, the step of performing multi-point linear power flow calculation based on node network parameters, input data, and sensitivity matrix to obtain output data including node state data and branch power flow data specifically involves:

[0032] When the power fluctuation of the wind turbine at node j of the power grid in the k-th segment region exceeds the node-injected power fluctuation threshold, the disturbance Δx to the state variables of node i of the power grid i for:

[0033]

[0034] In the formula, ΔS j The output disturbance of the wind turbine unit; ΔS1, ΔS2, ..., ΔS j-1 ,ΔS j+1 ,…,ΔS m For the disturbance amounts of the remaining nodes; The power output disturbance ΔS of the wind turbine j The disturbance Δx of the state variable of the i-th node of the power grid i The influence coefficient, ij, is the Jacobian matrix J. k -1 The element in the i-th row and j-th column;

[0035] The changes in node status and power flow of each branch of the power grid caused by the power fluctuation at node j are calculated based on the sensitivity matrix and the power output disturbance of the wind turbine.

[0036] Linearized power flow calculations are performed based on the power flow equations and input data to obtain the baseline node state data of each node in the power grid and the baseline power flow of each branch.

[0037] The output data, which includes node status data and branch power flow data, is obtained by merging the node status data and branch power flow data of each node in the power grid with the reference node status data and the reference power flow data of each branch.

[0038] A second aspect of this application provides a multi-point linearized probabilistic power flow calculation system for a power grid, the system comprising:

[0039] The data acquisition unit is used to acquire source data, node network parameters and load data of the power grid, where the source data is the unit output data and the load data is the power load data.

[0040] The probability distribution model building module is used to construct the source-load probability distribution model of the source data and the load data from the kernel density estimation function.

[0041] The data sampling module is used to perform discrete sampling on the source load probability distribution model based on uniform design sampling to obtain the first sample data, or to construct a Copula function between the source data and the load data, and use the Copula function to sample the source load probability distribution model to obtain the second sample data with correlation, wherein the first sample data and the second sample data are used as input data.

[0042] The sensitivity matrix calculation module is used to preset the node injection power fluctuation threshold. When the node injection power fluctuation area is greater than the node injection power fluctuation threshold, the node injection power fluctuation area is divided into equally spaced segments, the reference power value of each segment is determined, and the power flow calculation is performed based on the reference power value to obtain the sensitivity matrix corresponding to each segment.

[0043] The power flow calculation module is used to perform multi-point linear power flow calculations based on node network parameters, input data, and sensitivity matrices, and obtain output data including node state data and branch power flow data. Probabilistic feature analysis is then performed on the output data to obtain its probability distribution.

[0044] In one implementation, the probability distribution model building module is further used for:

[0045] The optimal window width for kernel density estimation is calculated based on the source data or load data. When the source data is the output data of wind turbine generators and the distribution of power load data is similar to a Gaussian distribution, a source-load probability distribution model for the source data and load data is constructed using a Gaussian kernel function and the optimal window width; or...

[0046] When the load data follows a unimodal symmetric normal distribution, a source-load probability distribution model of the source data and the load data is constructed using the normal distribution function; or,

[0047] When the source data is the output data of photovoltaic units, the source and load probability distribution models of the source data and load data are constructed using the beta distribution function.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. This invention constructs a source-load probability distribution model based on a kernel density estimation function to describe the probability distribution of power grid source and load data. It uses uniform design sampling or a Copula function to discretize the source-load probability distribution model, ensuring the sampled source and load data are correlated. This avoids power flow calculation errors caused by ignoring the correlation between source and load data. To address the issue of improving computational efficiency, this invention proposes a multi-point linearized power flow calculation method suitable for large fluctuations in node injected power. Facing the increasing fluctuation range of source data due to the large-scale integration of new energy sources and significant intraday changes in load data, this method can improve power flow calculation efficiency while maintaining computational accuracy. It avoids the inability of single-point linearized power flow calculation to adapt to situations where node injected power deviates too much from the baseline operating point. Therefore, the calculation method mentioned in this invention improves the accuracy and efficiency of probabilistic power flow calculation and can be better applied to new energy power grid scenarios.

[0050] 2. This invention describes a source-load probability model with multimodal and asymmetric probability distributions using a kernel density estimation function. Compared to commonly used Weibull or normal distributions, it has a better fitting effect and more accurately reflects the probability characteristics of strong uncertainty on both sides of the source-load distribution. The uniform design sampling method used can cover the sample space more efficiently with a smaller sampling scale than the traditional simple random sampling method, reducing the sample clustering effect caused by simple random sampling.

[0051] 3. This invention uses the Copula function to describe the correlation of input variables, taking into account the possible correlation of input random variables in the power system. Conventional analytical and simulation methods generally treat source-load side random variables as independent variables, ignoring errors that may be caused by variable correlation when performing data processing and power flow calculations. However, the Copula theory can completely describe the linear or nonlinear correlation of multidimensional input random variables, and the derived correlation metric does not change under linear transformation and strict monotonically increasing transformation. It is suitable for describing the correlation between the output of new energy units that are geographically and spatially close, as well as the correlation of load-side data of the same type, ensuring that the sampled data obtained is more consistent with the actual operating status data of the system.

[0052] In addition, this application also provides a power grid multi-point linearized probabilistic power flow calculation system, which has the same technical effects as the above-mentioned power grid multi-point linearized probabilistic power flow calculation method, and will not be described in detail here. Attached Figure Description

[0053] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0054] Figure 1 A flowchart illustrating a probabilistic power flow calculation method for multi-point linearization of a power grid, provided as an embodiment of this application;

[0055] Figure 2 A diagram of an IEEE 30-node system provided for an embodiment of this application;

[0056] Figure 3 A schematic diagram of the probability distribution model of the wind turbine output at node 6 in the IEEE 30-node system provided in this application embodiment;

[0057] Figure 4 A schematic diagram of the probability distribution model of the wind turbine output connected to node 22 in the IEEE 30-node system provided in this application embodiment;

[0058] Figure 5 A schematic diagram of wind turbine output sample data with correlation between nodes 6 and 22 provided in the embodiments of this application;

[0059] Figure 6 The node voltage magnitude probability density function curve obtained by the multi-point linearized power flow calculation method provided in the embodiments of this application;

[0060] Figure 7 This is a schematic diagram of a multi-point linearized probabilistic power flow calculation system for a power grid, provided as an embodiment of this application. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0062] It should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0063] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a multi-point linearized probabilistic power flow calculation method for power grids, provided in an embodiment of this application. This method is applied to new energy power grids, such as... Figure 1 As shown, the method includes the following steps:

[0064] S110 acquires source data, node network parameters, and load data of the power grid, where the source data is the unit output data and the load data is the power load data.

[0065] In this embodiment, the acquired power output data and power load data of the new energy generating units are used. The power output data of the new energy generating units includes the power output data of wind turbines and photovoltaic units, i.e., generators whose power generation varies greatly due to environmental factors. The power load data is the electricity load of users on the load side. The aforementioned power output data and power load data of the new energy generating units are common knowledge to those skilled in the art and will not be described in detail. As for obtaining the node network parameters of the power grid, as those skilled in the art should know, the power grid is part of the power system and consists of substations and lines of various voltages. Its main function is to transform voltage (transformation) and transmit and distribute electrical energy. It is an important infrastructure for coordinating power production, distribution, transmission and consumption. It is a system composed of transmission, transformation and distribution lines connecting various power plants, substations and power users. Therefore, the node network parameters of the power grid include the basic parameters such as voltage, power and phase of the lines under that node. This is also common knowledge to those skilled in the art, and this embodiment will only describe it briefly.

[0066] Specifically, in one embodiment, the unit output data is historical unit output data or predicted unit output data, the power load data is historical power load data or predicted power load data, and the node network data includes basic power network parameters and baseline operating point data.

[0067] S120, constructs the source-load probability distribution model of source data and load data using the kernel density estimation function;

[0068] Kernel density estimation technique is used to construct probability distribution models for both sources and loads, and a unified source-load probability distribution model is established. For power source or load input variables whose distribution conforms to unimodal symmetry, a simpler normal distribution model is used to describe their probability distribution. For some sample data that are not easy to estimate using common kernel functions (such as some photovoltaic output), a Beta distribution model can be used for fitting.

[0069] S130, Discrete sampling is performed on the source-load probability distribution model based on uniform design sampling to obtain the first sample data, or, a Copula function is constructed between the source data and the load data, and the Copula function is used to sample the source-load probability distribution model to obtain the second sample data with correlation, wherein the first sample data and the second sample data are used as input data.

[0070] In this example, to ensure the sampling samples cover the probability distribution space of the input variables and improve the efficiency of the sampling technique, Uniform Design Sampling (UDS) is used instead of traditional simple random sampling to sample data from the source-load probability model in the network. This ensures the accuracy of the calculation results and avoids excessive errors caused by data clustering effects resulting from simple random sampling. In this embodiment, for renewable energy output or load data with regional correlation, a joint cumulative distribution function (Copula function) of the correlated input variables is constructed based on Copula theory. Correlated data is then sampled from this function, making the calculation results closer to the actual system situation.

[0071] It should be understood that both the first sample data and the second sample data refer to the unit output data and the power load data.

[0072] S140: Preset node injection power fluctuation threshold. When the node injection power fluctuation area is greater than the node injection power fluctuation threshold, the node injection power fluctuation area is divided into equally spaced segments. The reference power value of each segment is determined, and the power flow calculation is performed based on the reference power value to obtain the sensitivity matrix corresponding to each segment.

[0073] In this embodiment, power sources or loads with large power fluctuation ranges are divided into multiple regions. Considering that when the penetration rate of new energy reaches a high level, the range of power injection fluctuations at nodes increases, leading to a non-negligible error in the power flow calculation results of single-point linearization at the baseline operating point. The output ranges of some wind power, photovoltaic, and other new energy units with significant fluctuations are divided to obtain the power flow sensitivity matrix corresponding to the baseline value of each region. The increment of output fluctuations on node states and branch power flow is calculated separately and superimposed on the baseline operating power flow results, thereby reducing the error introduced by single-point linearization power flow calculation.

[0074] S150 performs multi-point linear power flow calculations based on node network parameters, input data, and sensitivity matrix to obtain output data including node state data and branch power flow data. Probabilistic feature analysis is then performed on the output data to obtain its probability distribution.

[0075] In steps S140 and S150 of the above embodiments, traditional probabilistic power flow calculation is based on Monte Carlo simulation, which performs multiple independent power flow calculations on the sampled data. To ensure calculation accuracy, the amount of sampled data is enormous, leading to long calculation times and low efficiency, making it unsuitable for power systems with large node scales. To address the issue of improving calculation efficiency, this invention proposes a multi-point linearized power flow calculation method suitable for power injection fluctuations with large node power fluctuations. Facing the increasing power output fluctuations of source-measured units due to the large-scale integration of new energy sources and the significant intraday power variations in load data on the load side, this method can greatly improve calculation efficiency while maintaining accuracy, avoiding the inability of single-point linearized power flow calculations to adapt to situations where node injected power deviates too much from the baseline operating point.

[0076] In one embodiment, a source-charge probability distribution model for the source data and charge data is constructed using a kernel density estimation function, specifically including:

[0077] The optimal window width for kernel density estimation is calculated based on the source data or load data. When the source data is the output data of wind turbine generators and the distribution of power load data is similar to a Gaussian distribution, a source-load probability distribution model for the source data and load data is constructed using a Gaussian kernel function and the optimal window width; or...

[0078] When the load data follows a unimodal symmetric normal distribution, a source-load probability distribution model of the source data and the load data is constructed using the normal distribution function; or,

[0079] When the source data is the output data of photovoltaic units, the source and load probability distribution models of the source data and load data are constructed using the beta distribution function.

[0080] Specifically, the optimal window width for kernel density estimation is calculated based on the source data or charge data: In the formula, σ is the standard deviation of the kernel density estimation data, and n is the data size;

[0081] The actual output power of new energy sources (such as wind power) and the power load on the load side are relatively close to the Gaussian distribution. Therefore, the Gaussian kernel function is used for estimation. The Gaussian kernel function is as follows:

[0082] The kernel density estimation based on the Gaussian kernel function is as follows:

[0083] In the formula: h is the window width; w is the sample data of the random variable, w i Let K be the i-th sample data. Different kernel functions K(·) can be used for data with different distributions. Commonly used kernel functions include Uniform, Triangular, Epanechnikov, Quartic, Triweight, Gaussian, and Cosine.

[0084] For load data that follows a unimodal symmetric normal distribution, the expected values ​​of the active and reactive power demands of the user load are known to be μ. P and μ Q The standard deviation is σ P and σ Q Its probability distribution is described using a normal distribution model:

[0085]

[0086] For samples with extreme probability distribution characteristics (such as the output of certain photovoltaic units), the Beta distribution is used to fit their probability density function:

[0087]

[0088] In the formula, P and R M These are the actual output power and the maximum output power of the solar cell array, respectively; the expressions for parameters α and β are as follows: In the formula, μ and σ are the sample mean and standard deviation, respectively.

[0089] In one embodiment, a Copula function is constructed between the source data and the load data. This Copula function is then used to sample relevant second sample data from the source-load probability distribution model. Specifically:

[0090] The correlation coefficients between nodes in the power grid are calculated based on the node network parameters of the power grid, and a correlation coefficient matrix of the power grid is constructed based on the correlation coefficients of multiple nodes.

[0091] A preset correlation coefficient threshold is set. When the correlation coefficient is greater than the threshold, a Copula function with correlation is determined based on the source data and load data of the node and the correlation coefficient.

[0092] Substituting the sample data and correlation coefficient matrix that follow a [0,1] distribution in the source-load probability distribution model into the inverse function of the correlated Copula function, we obtain a multidimensional random variable that follows a [0,1] distribution and is correlated, where the sample data consists of source data and load data;

[0093] By processing the correlated multidimensional random variables that follow a [0,1] distribution using the inverse function of the cumulative distribution function, we obtain a second sample of correlated data.

[0094] Specifically, in this embodiment, the Pearson correlation coefficient ρ can be used. wi,wj Describes the input variable w that has a certain correlation in a real network. i With w j :

[0095] In the formula These represent the input variables w respectively. i w j The sample mean; further, a correlation coefficient matrix can be constructed among n input random variables in a power system:

[0096]

[0097] Determine the Gaussian Copula function for correlated random variables. Take a two-dimensional Gaussian Copula function as an example:

[0098] In the formula w i w j Let ρ be any correlated random variable. wi,wj The Pearson correlation coefficient is used; the form of the n-dimensional Gaussian Copula function is similar to the above formula.

[0099] Given n-dimensional sample data U that follows a [0,1] distribution n×N =[u1,u2,…,u i ,…,u n ] T (u i =[u i1 ,u i2 ,…,u iN ]) and the correlation coefficient matrix ρ are substituted into the inverse function C of the m-dimensional Gaussian Copula function. -1This yields an n-dimensional random variable V that follows a [0,1] distribution and is correlated. n×N =[v1,v2,…,v i ,…,v n ] T (v i =[v i1 ,v i2 ,…,v iN ]), that is, V n×N =C -1 (U n×N ).

[0100] Based on the inverse function of the cumulative distribution function of the input random variable Generate a sample matrix W of n-dimensional random variables with correlation. n×N =[w1,w2,…,w i ,…,w n ] T (w i =[w i1 ,w i2 ,…,w iN ]), that is, the second sample data is In the formula w i Let i be the sample of the i-th correlated random variable. It is the inverse function of its cumulative distribution function.

[0101] In one embodiment, discrete sampling is performed on the source load probability distribution model based on uniform design sampling to obtain the first sample data, specifically as follows:

[0102] If any random variable is independent of the other random variables, then for any random variable, the first sample data of the random variable is transformed by equal probability based on the sample data that follows the [0,1] distribution and the cumulative distribution function in the source load probability distribution model.

[0103] Specifically, if a random variable is independent of other variables, then for that random variable k, according to the source load probability distribution model and cumulative distribution function F mentioned in the above embodiments... k The random variable k can be generated by applying the principle of equal probability transformation, i.e., the first sample data is...

[0104] By combining the sample matrices of the first and second sample data obtained in the above embodiments, we can obtain the sample matrix of the random variable of the injected power of n nodes in the network, that is, the sample matrix W of the input data. n×N =[w1,w2,…,w i ,…,w n ] T (w i =[wi1 ,w i2 ,…,w iN ]).

[0105] As a specific embodiment, the sample data in the source load probability distribution model that follows a [0,1] distribution are obtained through the following steps:

[0106] Suppose we need to generate sample data of n random variables following a distribution [0,1], where N is the total number of samples and α is an arbitrary positive integer. Generate a positive integer vector H. 1×n =[h1,h2,…,h n ], where h1=1, h i ∈(1,α) and none of the elements in the vector are equal;

[0107] From multivariate distribution Select n independent samples to form vector B 1×n =[b1,b2,…,b n ];

[0108] Matrix E is generated by simple random sampling. n×N =[e1,e2,…,e j ,…,e n ] T (e j =[e j1 ,e j2 ,…,e jN ]), where the random variable e follows a uniform distribution on [-0.5, 0.5], and T represents the transpose of the matrix;

[0109] In constructing the source load probability distribution model, sample data U follows a [0,1] distribution. n×N =[u1,u2,…,u i ,…,u n ] T (u i =[u i1 ,u i2 ,…,u iN element u in ]) ij for: Where i = 1, 2, ..., n, j = 1, 2, ..., N.

[0110] In one embodiment, a preset node injection power fluctuation threshold is defined. When the node injection power fluctuation region exceeds the node injection power fluctuation threshold, the node injection power fluctuation region is divided into equally spaced segments. A reference power value is determined for each segment, and power flow calculation is performed based on the reference power value to obtain the sensitivity matrix corresponding to each segment. Specifically:

[0111] The average value of the node injection power at the endpoints of each region is used as the reference power value for each region.

[0112] The power flow equations are linearized at the reference power values ​​for each region to obtain the Jacobian matrix for each region, and the sensitivity matrix is ​​obtained based on the inverse of the Jacobian matrix.

[0113] In one embodiment, the step of performing multi-point linear power flow calculation based on node network parameters, input data, and sensitivity matrix to obtain output data including node state data and branch power flow data specifically involves:

[0114] When the power fluctuation of the wind turbine at node j of the power grid in the k-th segment region exceeds the node-injected power fluctuation threshold, the disturbance Δx to the state variables of node i of the power grid i for:

[0115]

[0116] In the formula, ΔS j The output disturbance of the wind turbine unit; ΔS1, ΔS2, ..., ΔS j-1 ,ΔS j+1 ,…,ΔS m For the disturbance amounts of the remaining nodes; The power output disturbance ΔS of the wind turbine j The disturbance Δx of the state variable of the i-th node of the power grid i The influence coefficient, ij, is the Jacobian matrix. The element in the i-th row and j-th column;

[0117] The changes in node status and power flow of each branch of the power grid caused by the power fluctuation at node j are calculated based on the sensitivity matrix and the power output disturbance of the wind turbine.

[0118] Linearized power flow calculations are performed based on the power flow equations and input data to obtain the baseline node state data of each node in the power grid and the baseline power flow of each branch.

[0119] The output data, which includes node status data and branch power flow data, is obtained by merging the node status data and branch power flow data of each node in the power grid with the reference node status data and the reference power flow data of each branch.

[0120] In this embodiment, the power source or load with a large power fluctuation range is divided into multiple regions. Based on the number of regions, a corresponding reference value is selected for deterministic power flow calculation to obtain the sensitivity matrix corresponding to each region. Multi-point linearized power flow calculation is performed based on the input random variable sample data and the multi-region sensitivity matrix to obtain output variable data including node voltage, amplitude, phase, and active and reactive power components of branch power flow. Probability statistics are then performed on the output data to obtain the probability distribution of the output variables. Specifically, steps 401-407 are as follows:

[0121] Step 401: Linearize the power flow equations. At the reference operating point W0, perform a Taylor expansion of the nodal power equations and branch power flow equations:

[0122]

[0123] Ignoring higher-order terms, we can derive the expression for the random perturbation of the node state variables:

[0124]

[0125] The power flow equations are now simplified to the following expression:

[0126]

[0127] In the formula, X, Z, and W represent the node state, branch power flow, and node injected power matrices, respectively; S0 is the sensitivity matrix of the reference operating point, S0 = J0. -1 And T0 = G0J0 -1 Where J0 is the Jacobian matrix of the baseline running point, and the elements of the G0 matrix can be obtained from the Jacobian matrix:

[0128]

[0129]

[0130] Step 402: Considering the differences in the fluctuation amplitude on the source and load sides, piecewise linearization is adopted for some nodes with large disturbances to reduce the impact of single-point linearization on the error of power flow calculation results. Assume that a wind turbine is connected at point i, and its output fluctuation range is 0 to S. jm Divide it into m equal segments: 0~S j1 ,S j1 ~S j2 ,…,S jm-1 ~S jm The corresponding baseline values ​​for each region are: E j1 =(0+S) j1 ) / 2,E j2 =(S j1 +S j2) / 2,…,E jm =(S jm-1 +S jm ) / 2; the baseline values ​​for the injected power at the remaining n-1 nodes are: E1, E2, ..., E i-1 E i+1 ,…,E n ;

[0131] Step 403: Let E k =[E j1 E j2 ,…,E j-1 E jk E i+1 ,…,E n Let E1, E2, ..., Em be the power injected into each node of the system when the wind power output fluctuates within region k, where k = 1, 2, ..., m. The power flow equations are then applied at the reference values ​​E1, E2, ..., Em. m Linearization yields the Jacobian matrices J1, J2, ..., J for the corresponding regions. m ;

[0132] Step 404: When the power fluctuation of the wind turbine at node j occurs in the k-th region, the disturbance Δx to the state variable of node i is calculated. i for:

[0133]

[0134] In the formula ΔS j The output disturbance of the wind turbine unit; ΔS1, ΔS2, ..., ΔS j-1 ,ΔS j+1 ,…,ΔS m For the disturbance quantities of the remaining nodes; (J) k -1 ) ij For ΔS j For Δx i The influence coefficient is J k -1 The element in the i-th row and j-th column;

[0135] Step 405: Statistically analyze all random variable sample data in the network to obtain the expected value W0 of the injected power of each node as the baseline operating point, and obtain J0 through deterministic power flow calculation. Based on the equation described in step 401 and the sample W obtained in step 307... n×N Perform linearized power flow calculations to obtain the output random variable data X. n×N With Z n×N :

[0136]

[0137] Step 406: Perform multi-point linearization processing separately for units or loads with large power fluctuation ranges. Calculate the impact of input data with different fluctuation ranges on the output data based on the regional divisions in Steps 403 and 404. Assuming that a certain data point of the wind power output at node j is within region k, then:

[0138]

[0139] In the formula (S) k ) j For the j-th column element of the sensitivity matrix corresponding to region k, (T k ) j Similarly; ΔX j With ΔZ j These represent the changes in the state of each node and the power flow of each branch of the system caused by the power fluctuation at node j.

[0140] Step 407: Combine the results obtained in Step 405 and Step 406 to obtain the multi-point linearized power flow calculation results X and Z; perform probabilistic feature analysis on the results to obtain the corresponding probability distribution, including the probability density function of node voltage amplitude and phase, active and reactive components of branch power flow, and cumulative distribution function.

[0141] To verify the feasibility and effectiveness of the probabilistic power flow calculation method provided in the embodiments of this application, a case study was conducted on an IEEE standard 30-node system. The calculation programs were all compiled using MATLAB on a computer.

[0142] Application Example 1: Using the IEEE standard 30-node system as the test system, such as... Figure 2 As shown, wind turbines with a rated output of 2.5*30MW are connected to nodes 6, 22, 27, and 28 respectively, with a wind power penetration rate of approximately 43% and a constant power factor of -0.98. The output of thermal power units at nodes 2 and 5 is reduced by 60MW and 30MW respectively. Data modeling and power flow calculations are performed using the MATLAB platform.

[0143] First, a model is constructed for the output probability distribution of the new energy generating units connected to the system. Kernel density estimation is used to fit the probability distribution of wind power output data at nodes 6 and 22, as shown below. Figure 2 and Figure 3 The results show that the modeling technology used in this invention can well describe the multi-peak and asymmetric nature of the power output fluctuations of new energy sources, and the same applies to the power output of units at nodes 27 and 28.

[0144] The correlation coefficient matrix between the input wind farm raw data of node 6 and node 22 is calculated as follows: We further construct the Copula function of the marginal distribution of the two, and use uniform design sampling technique to sample the data to obtain correlated data samples.

[0145] Figure 4 This example demonstrates the distribution of correlated power output data samples between wind turbines at nodes 6 and 22, generated using Copula theory. The sample size is 60,000, proving that the correlation processing method proposed in this invention can effectively describe the correlation between the power output of wind farms at nodes 6 and 22. This example can simultaneously consider the correlation of power output from multiple wind turbines at nodes 6, 22, 27, and 28, generating four sets of correlated wind power output data, based on the same principle as described above. In this example, the correlation between loads is temporarily disregarded, treating each load in the system as an independent random variable. If load correlation needs to be considered, the method described above applies.

[0146] The power of the wind farm at each node was further segmented, with each segment set at 5MW, resulting in 15 regions (pu, with a baseline capacity of 100MVA), namely [0,0.05], [0.05,0.10], ..., [0.70,0.75]. The sensitivity matrix of each region was calculated to facilitate subsequent multi-point linearized power flow calculations. To verify the accuracy of this calculation method for Example 1, the results of 60,000 Monte Carlo simulations (MCSM) were used as a benchmark. The multi-point linearization calculation method proposed in this invention was compared with the conventional single-point linearization method (both with a sampling scale of 60,000 simulations). The selected error indices were variance and average root mean square (ARMS). The comparison results are shown in Table 1.

[0147] Table 1 Comparison of ARMS of partial node voltage amplitude and branch power

[0148]

[0149] The comparison results shown in Table 1 demonstrate that the ARMS value of the multi-point linearization method proposed in this invention is significantly lower than that of single-point linearization, with most ARMS values ​​remaining below 0.5%. Furthermore, the accuracy improvement compared to single-point linearization is significant, as seen in U3 and P. 12-15 With P 15-23 The calculation results show an accuracy improvement of over 90%, proving that the accuracy of the method proposed in this invention is significantly improved compared to traditional methods. It can be effectively applied to probabilistic power flow calculations for power systems with a high proportion of new energy access and considering strong uncertainties on both the source and load sides.

[0150] Figure 6This is a comparison chart of the probability distribution of the voltage amplitude at node 4 in this scenario. The comparison objects are the probability density functions obtained by three different calculation methods: Monte Carlo simulation, single-point linearization, and multi-point linearization. The chart shows that the multi-point linearization calculation method proposed in this paper is closer to the true probability distribution than the single-point linearization method, and can more accurately describe the probability distribution characteristics of the output random variable.

[0151] To further verify the computational efficiency of the method proposed in this invention, we compared the computation of single-point linearization and multi-point linearization with 60,000 samples, using 60,000 Monte Carlo simulations as a benchmark. The comparison results are shown in Table 2.

[0152] Table 2. Comparison of speeds using different power flow calculation methods.

[0153] method Calculation speed / s MSCM 482.9 Single-point linearization 0.6 Multi-point linearization 2.1

[0154] As can be seen from Table 2, the time difference between the single-point linearization and multi-point linearization methods lies in the multiple power flow calculations performed during piecewise linearization. The multi-point linearization probabilistic power flow calculation method proposed in this invention, which considers correlation, is more time-consuming than the conventional single-point linearization method. However, while maintaining computational accuracy, this method significantly improves computational efficiency compared to the traditional MSCM method.

[0155] To better verify that the proposed method can adapt to scenarios with a high proportion of renewable energy access, the total wind farm access capacity at each node in the system was gradually increased under reasonable adjustments. Based on the MSCM calculation results, single-point linearization and multi-point linearization probabilistic power flow calculation methods were compared, with the network and source-load data remaining the same as described above. Then, using the voltage amplitude at node 19 and the active power transmitted through lines 12-15 as results, variance and root mean (ARMS) were used to measure the calculation accuracy of different methods. The comparison results are shown in Table 3.

[0156] Table 3 Comparison of errors in power flow calculation results under different wind turbine connection capacities

[0157]

[0158] As shown in Table 3, the uncertainty increases as the capacity of wind turbines connected to the system increases. At this point, the error introduced by the single-point linearization calculation method (such as voltage U) becomes more significant. 19 The ARMS value gradually increased from 0.345 to 0.793, while the multi-point linearization calculation method proposed in this paper controlled the maximum error to 0.335. Compared with the single-point linearization method, it has obvious advantages, can better adapt to high-proportion new energy access scenarios, and effectively improve the accuracy of probabilistic power flow calculation.

[0159] Based on the same inventive concept, this embodiment provides a multi-point linearized probabilistic power flow calculation system for power grids. Because the principles by which these systems solve problems are similar... Figure 1 The proposed method for calculating multi-point linearized probabilistic power flow in a power grid is similar to that shown; therefore, the implementation of these systems can be found in [reference needed]. Figure 1 The embodiments of the methods shown are repeated hereafter, as are the examples. Figure 7 As shown, the system includes:

[0160] The data acquisition unit 710 is used to acquire source data, node network parameters and load data of the power grid, wherein the source data is the unit output data and the load data is the power load data.

[0161] The probability distribution model construction module 720 is used to construct the source-load probability distribution model of the source data and the load data from the kernel density estimation function.

[0162] The data sampling module 730 is used to perform discrete sampling on the source load probability distribution model based on uniform design sampling to obtain first sample data, or to construct a Copula function between the source data and the load data, and use the Copula function to sample the source load probability distribution model to obtain a second sample data with correlation, wherein the first sample data and the second sample data are used as input data.

[0163] The sensitivity matrix calculation module 740 is used to preset the node injection power fluctuation threshold. When the node injection power fluctuation area is greater than the node injection power fluctuation threshold, the node injection power fluctuation area is divided into equally spaced segments to determine the reference power value of each segment. Based on the reference power value, power flow calculation is performed to obtain the sensitivity matrix corresponding to each segment.

[0164] The power flow calculation module 750 is used to perform multi-point linear power flow calculations based on node network parameters, input data, and sensitivity matrix to obtain output data including node state data and branch power flow data. Probabilistic feature analysis is performed on the output data to obtain the probability distribution of the output data.

[0165] As can be seen, the multi-point linearized probabilistic power flow calculation system for power grids provided in the above embodiments constructs a source-load probability distribution model describing the probability distribution of source and load data in the power grid based on a kernel density estimation function. It then performs discrete sampling on the source-load probability distribution model based on uniform design sampling or a Copula function, ensuring the sampled source and load data are correlated. This avoids power flow calculation errors caused by ignoring the correlation between source and load data. Regarding the issue of improving computational efficiency, this invention proposes a multi-point linearized power flow calculation method suitable for nodes with large power injection fluctuations. Facing the increasing fluctuation range of source data due to the large-scale integration of new energy sources and the significant intraday changes in load data, this method can greatly improve computational efficiency while maintaining computational accuracy. It avoids the inability of single-point linearized power flow calculation to adapt to situations where node injected power deviates too much from the baseline operating point. Therefore, the calculation method mentioned in this invention improves the computational accuracy and efficiency of probabilistic power flow and can be better applied to new energy power grid scenarios.

[0166] In one implementation, the probability distribution model building module is further used for:

[0167] The optimal window width for kernel density estimation is calculated based on the source data or load data. When the source data is the output data of wind turbine generators and the distribution of power load data is similar to a Gaussian distribution, a source-load probability distribution model for the source data and load data is constructed using a Gaussian kernel function and the optimal window width; or...

[0168] When the load data follows a unimodal symmetric normal distribution, a source-load probability distribution model of the source data and the load data is constructed using the normal distribution function; or,

[0169] When the source data is the output data of photovoltaic units, the source and load probability distribution models of the source data and load data are constructed using the beta distribution function.

[0170] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating multi-point linearized probabilistic power flow in a power grid, characterized in that, The methods include: Acquire source data, node network parameters, and load data of the power grid, where the source data is the unit output data and the load data is the power load data; The source-charge probability distribution model of the source data and charge data is constructed using the kernel density estimation function; Discrete sampling is performed on the source-load probability distribution model based on uniform design sampling to obtain the first sample data. Alternatively, a Copula function is constructed between the source data and the load data, and the Copula function is used to sample the source-load probability distribution model to obtain the second sample data with correlation, wherein the first sample data and the second sample data are used as input data. A preset node injection power fluctuation threshold is established. When the node injection power fluctuation area exceeds the node injection power fluctuation threshold, the node injection power fluctuation area is divided into equally spaced segments. A reference power value for each segment is determined, and power flow calculation is performed based on the reference power value to obtain the sensitivity matrix corresponding to each segment. The average node injection power at the endpoints of each segment is used as the reference power value for each segment. The power flow equation is linearized at the reference power value for each segment to obtain the Jacobian matrix corresponding to each segment, and the sensitivity matrix is ​​obtained based on the inverse of the Jacobian matrix. Multi-point linear power flow calculations are performed based on node network parameters, input data, and sensitivity matrices to obtain output data including node state data and branch power flow data. Probabilistic feature analysis is then performed on the output data to obtain its probability distribution. Specifically, when the power fluctuation of the wind turbine at node j in the k-th segment region exceeds the node's injected power fluctuation threshold, the disturbance Δx to the state variables of node i in the power grid is calculated. i for: In the formula, ΔS j The output disturbance of the wind turbine generator; ΔS1, ΔS2, ..., ΔS j-1 ,ΔS j+1 ,…,ΔS m For the disturbance quantities of the remaining nodes; (J) k -1 ) ij The power output disturbance ΔS of the wind turbine j The disturbance Δx of the state variable of the i-th node of the power grid i The influence coefficient, ij, is the Jacobian matrix J. k -1 The element in the i-th row and j-th column is used to calculate the changes in the node state and power flow of each branch of the power grid caused by the power fluctuation at node j, based on the sensitivity matrix and the power output disturbance of the wind turbine. Linearized power flow calculation is performed based on the power flow equation and input data to obtain the reference node state data and reference power flow of each branch of the power grid. The changes in the node state and power flow of each branch of the power grid are combined with the reference node state data and the reference power flow of each branch to obtain the output data including the node state data and the power flow of each branch.

2. The method for calculating multi-point linearized probabilistic power flow in a power grid according to claim 1, characterized in that, The unit output data is historical unit output data or predicted unit output data, the power load data is historical power load data or predicted power load data, and the node network data includes basic power network parameters and baseline operating point data.

3. The method for calculating multi-point linearized probabilistic power flow in a power grid according to claim 1, characterized in that, The source and charge probability distribution models for the source and charge data are constructed using the kernel density estimation function, specifically including: The optimal window width for kernel density estimation is calculated based on the source data or load data. When the source data is the output data of wind turbine generators and the distribution of power load data is similar to a Gaussian distribution, a source-load probability distribution model for the source data and load data is constructed using a Gaussian kernel function and the optimal window width; or... When the load data follows a unimodal symmetric normal distribution, a source-load probability distribution model of the source data and the load data is constructed using the normal distribution function; or, When the source data is the output data of photovoltaic units, the source and load probability distribution models of the source data and load data are constructed using the beta distribution function.

4. The method for calculating multi-point linearized probabilistic power flow in a power grid according to claim 1, characterized in that, A Copula function is constructed between the source data and the load data. This Copula function is then used to sample relevant second-sample data from the source-load probability distribution model. Specifically: The correlation coefficients between nodes in the power grid are calculated based on the node network parameters of the power grid, and a correlation coefficient matrix of the power grid is constructed based on the correlation coefficients of multiple nodes. A preset correlation coefficient threshold is set. When the correlation coefficient is greater than the threshold, a Copula function with correlation is determined based on the source data and load data of the node and the correlation coefficient. Substituting the sample data and correlation coefficient matrix that follow a [0,1] distribution in the source-load probability distribution model into the inverse function of the correlated Copula function, we obtain a multidimensional random variable that follows a [0,1] distribution and is correlated, where the sample data consists of source data and load data; By processing the correlated multidimensional random variables that follow a [0,1] distribution using the inverse function of the cumulative distribution function, we obtain a second sample of correlated data.

5. The method for calculating multi-point linearized probabilistic power flow in a power grid according to claim 1, characterized in that, Discrete sampling is performed on the source load probability distribution model based on uniform design sampling to obtain the first sample data, specifically: If any random variable is independent of the other random variables, then for any random variable, the first sample data of the random variable is transformed by equal probability based on the sample data that follows the [0,1] distribution and the cumulative distribution function in the source load probability distribution model.

6. A method for calculating multi-point linearized probabilistic power flow in a power grid according to claim 4 or 5, characterized in that, The sample data in the source load probability distribution model that follows a [0,1] distribution are obtained through the following steps: Suppose we need to generate sample data of n random variables following a distribution [0,1], where N is the total number of samples and α is an arbitrary positive integer. Generate a positive integer vector H. 1×n =[h1, h2,…, h n ], where h1=1, h i ∈(1, α) and all elements in the vector are distinct; From multivariate distribution Select n independent samples to form vector B 1×n =[b1, b2,…,b n ]; Matrix E is generated by simple random sampling. n×N =[e1, e2,…, e j ,…, e n ] T (e) j =[e j1 , e j2 ,…, e jN ]), where the random variable e follows a uniform distribution on [-0.5, 0.5], and T represents the transpose of the matrix; In constructing the source load probability distribution model, sample data U follows a [0,1] distribution. n×N =[u1, u2,…, u i ,…, u n ] T (u) i =[u i1 , u i2 ,…, u iN element u in ]) ij for: , where i=1 , 2 ,…, n, j=1 , 2 ,…, N.

7. A multi-point linearized probabilistic power flow calculation system for a power grid, characterized in that, The system includes: The data acquisition unit is used to acquire source data, node network parameters and load data of the power grid, where the source data is the unit output data and the load data is the power load data. The probability distribution model building module is used to construct the source-load probability distribution model of the source data and the load data from the kernel density estimation function. The data sampling module is used to perform discrete sampling on the source load probability distribution model based on uniform design sampling to obtain the first sample data, or to construct a Copula function between the source data and the load data, and use the Copula function to sample the source load probability distribution model to obtain the second sample data with correlation, wherein the first sample data and the second sample data are used as input data. The sensitivity matrix calculation module is used to preset the node injected power fluctuation threshold. When the node injected power fluctuation area is greater than the node injected power fluctuation threshold, the node injected power fluctuation area is divided into equally spaced segments to determine the reference power value of each segment. Based on the reference power value, power flow calculation is performed to obtain the sensitivity matrix corresponding to each segment. The average value of the node injected power at the endpoints of each segment is used as the reference power value of each segment. The power flow equation is linearized at the reference power value of each segment to obtain the Jacobian matrix corresponding to each segment. The sensitivity matrix is ​​obtained based on the inverse of the Jacobian matrix. The power flow calculation module performs multi-point linear power flow calculations based on node network parameters, input data, and sensitivity matrices, obtaining output data including node state data and branch power flow data. Probabilistic feature analysis is then performed on the output data to obtain its probability distribution. Specifically, when the power fluctuation of the wind turbine at node j in the k-th segment region exceeds the node's injected power fluctuation threshold, the disturbance Δx to the state variables of node i in the power grid is calculated. i for: In the formula, ΔS j The output disturbance of the wind turbine generator; ΔS1, ΔS2, ..., ΔS j-1 ,ΔS j+1 ,…,ΔS m For the disturbance quantities of the remaining nodes; (J) k -1 ) ij The power output disturbance ΔS of the wind turbine j The disturbance Δx of the state variable of the i-th node of the power grid i The influence coefficient, ij, is the Jacobian matrix J. k -1 The element in the i-th row and j-th column is used to calculate the changes in the node state and power flow of each branch of the power grid caused by the power fluctuation at node j, based on the sensitivity matrix and the power output disturbance of the wind turbine. Linearized power flow calculation is performed based on the power flow equation and input data to obtain the reference node state data and reference power flow of each branch of the power grid. The changes in the node state and power flow of each branch of the power grid are combined with the reference node state data and the reference power flow of each branch to obtain the output data including the node state data and the power flow of each branch.

8. The power grid multi-point linearized probabilistic power flow calculation system according to claim 7, characterized in that, The probability distribution model building module is also specifically used for: The optimal window width for kernel density estimation is calculated based on the source data or load data. When the source data is the output data of wind turbine generators and the distribution of power load data is similar to a Gaussian distribution, a source-load probability distribution model for the source data and load data is constructed using a Gaussian kernel function and the optimal window width; or... When the load data follows a unimodal symmetric normal distribution, a source-load probability distribution model of the source data and the load data is constructed using the normal distribution function; or, When the source data is the output data of photovoltaic units, the source and load probability distribution models of the source data and load data are constructed using the beta distribution function.

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