Power distribution network probabilistic load flow calculation method and system based on input-output joint distribution

Abstract

The application discloses a power distribution network probabilistic load flow calculation method and system based on input-output joint distribution, the method carries out probability modeling on random input variables in the power distribution network, and obtains a GMM joint probability distribution; based on mean vectors of each Gaussian component in the GMM joint probability distribution, the power distribution network nonlinear load flow model is segmented linearized, and a segmented linearized load flow model is obtained; based on the GMM joint probability distribution and the segmented linearized load flow model, a GMM model of the power distribution network load flow calculation input-output vector joint probability distribution is obtained; and an analytic result of the probabilistic load flow calculation is obtained. According to the application, the accurate probability density function of state quantities such as node voltage and branch load flow can be directly obtained through the edge distribution without a large number of sample simulations, and efficient and high-precision analytic calculation of the probability evaluation of the power distribution network operation state is realized.

Description

Technical Field

[0001] This invention belongs to the field of power system distribution network operation analysis technology, and relates to a method and system for calculating the probabilistic power flow of distribution networks based on the joint distribution of input and output. Background Technology

[0002] With the advancement of the "dual carbon" goals, the penetration rate of electric vehicles and distributed renewable energy in the power distribution network continues to increase. However, the high proportion of electric vehicle charging load and the random access of distributed renewable energy pose significant challenges to the safe and stable operation of the power distribution network. The spatiotemporal uncertainty of user charging behavior and the intermittent and random nature of renewable energy output may lead to a surge in local power grid load, exacerbating risks such as line overload and voltage exceeding limits.

[0003] The spatiotemporal distribution of electric vehicle charging load is influenced by multiple factors, including user travel habits, charging methods (fast charging / slow charging), and grid control strategies, exhibiting high randomness and coupling. The output of renewable energy sources is also highly uncertain due to meteorological factors. Against this backdrop, the nonlinear characteristics of the distribution network become more prominent, further increasing the difficulty of quantifying the uncertainty of power flow in the distribution network.

[0004] Existing methods for quantifying power flow uncertainty in distribution networks often employ surrogate models such as Gaussian process regression (GPR) and polynomial chaos expansion (PCE) to approximate nonlinear power flow models. These methods perform well in small-sample, non-high-dimensional problems. However, most of these methods are single-output models. If multiple output variables are involved in the power flow calculation, a large number of surrogate models need to be established, which significantly increases modeling and simulation time. Furthermore, existing uncertainty quantification methods still rely on Monte Carlo simulations, which can only obtain analytical solutions when the input random variables are independent, making it difficult to meet the efficiency requirements of online operation evaluation of practical distribution networks. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for calculating probabilistic power flow in distribution networks based on joint input-output distribution.

[0006] The present invention adopts the following technical solution.

[0007] A method for calculating probabilistic power flow in a distribution network based on joint input-output distribution, the method comprising: Step 1: Based on historical data, perform probabilistic modeling of random input variables in the distribution network to obtain the GMM joint probability distribution of the random input variable vector; Step 2: Based on the mean vector of each Gaussian component in the joint probability distribution of the GMM, the nonlinear power flow model of the distribution network is piecewise linearized to obtain the piecewise linearized power flow model. Step 3: Based on the joint probability distribution of the GMM and the piecewise linearized power flow model, obtain the GMM model of the joint probability distribution of the input and output vectors for power flow calculation in the distribution network; Step 4: Based on the GMM model of the joint probability distribution of the input and output vectors, solve for the analytical results of the probability power flow calculation.

[0008] Preferably, step 1 specifically includes: Step 1.1: Denote the vector composed of random input variables in the power distribution network as the random input variable vector. x ,collection x of n Historical samples X 1, X 2, ..., X n ; Step 1.2: Based on historical samples, establish a random input variable vector using the kernel density estimation method of the Gaussian kernel function. x Joint probability density function: (1) Where: N( ) is the Gaussian kernel function; H t It is the first t Historical samples X t The bandwidth matrix; the number of Gaussian components in the joint probability density function. K b = n Weighting coefficient 1 / n mean vector for X t covariance matrix For the first t Historical samples X t bandwidth matrix H t ; Step 1.3: Use the density-preserving hierarchical expectation-maximization algorithm to reduce the Gaussian component number of the joint probability density function, and obtain the joint probability distribution of the GMM of the random input variable vector. .

[0009] Preferably, the distribution network has a high proportion of electric vehicles and new energy sources connected to it; the random input variables include charging load, new energy output, and node load.

[0010] Preferably, the density-preserving hierarchical expectation-maximization algorithm described in step 1.3 reduces the Gaussian component number to the following optimization problem: The probability distributions satisfy the joint probability density function virtual sample set X ,beg The parameters make The log-likelihood function has the largest expected value, as shown below: (2) In the formula: For the first k The weights of each Gaussian component; For the first k The mean vector of Gaussian components; For the first k The covariance matrix of Gaussian components; K for Gaussian component number; As expected.

[0011] Preferably, the optimization problem is solved iteratively using the EM algorithm, and the iterative process includes E-steps and M-steps; The E-step calculation of variational coefficients As shown below: (3) (4) (5) The M-step is based on variational coefficients. Update the weights of the Gaussian components Mean vector Covariance matrix As shown below: (6) (7) (8) In the formula: As an intermediate variable, The index corresponding to the minimum value of the intermediate variable; These are variational coefficients. t =1、…、 K b , k = 1、…、 K , express The Middle t Gaussian component pairs The Middlek The degree of attribution of each Gaussian component K b , K These represent the joint probability density function and the number of Gaussian components in the joint probability distribution of the GMM, respectively; the symbol tr represents the trace of the matrix. M It is a constant.

[0012] Preferably, in step 2, based on the random input variable vector x Joint probability distribution of GMM The mean vector of each Gaussian component in the distribution network nonlinear power flow model Piecewise linearization is performed to obtain the piecewise linearized power flow model, as follows: (10) In the formula: for x = Jacobian matrix for power flow calculation using the Newton-Raphson method; for The Middle k The mean vector of Gaussian components; Γ( ) represents a nonlinear function; y This represents the output variable vector.

[0013] Preferably, in step 3, based on the joint probability distribution of the GMM and the piecewise linearized power flow model, a GMM model of the joint probability distribution of the input and output vectors for power flow calculation in the distribution network is obtained, as follows: (17)

[0014]

[0015] in, z For random input variable vectors x and output variable vector y The input and output vectors formed; K The number of Gaussian components in the joint probability distribution of GMM; oh k For the event The probability of occurrence, the event Indicates input random variables x Joint probability distribution of GMM The mean vector is The covariance matrix is The k One Gaussian component; To The lower triangular matrix obtained by performing Cholesky decomposition. u It is a vector of variables that follows a standard Gaussian distribution; Γ( ) represents a nonlinear function; m y,k =Γ( m x,k ), S xy,k = S x,k TT k , S yx,k = T k S x,k , S y,k = T k S x,k TT k , m y,k , S xy,k , S yx,k , S y,k For the k-th Gaussian component, y mean vector x and y cross-covariance matrix, y and x cross-covariance matrix, y The covariance matrix.

[0016] Preferably, in step 4, the probability density function of the output variable is obtained from the GMM model of the joint probability distribution of the input and output vectors, and used as the analytical result of the probability power flow calculation: (18) In the formula: It is the first l One output variable; m l,k = m y,k ( l ), S ll,k = S y,k ( l , l ), m l,k , S ll,kFor the k-th Gaussian component, the th l The mean of the nth output variable, the nth l The variance of each output variable, m y,k ( l )for m y,k The l One element, S y,k ( l , l )for S xy,k The l Line 1 l Column elements, m y,k , S xy,k For the k-th Gaussian component, y mean vector x and y The cross-covariance matrix.

[0017] A distribution network probabilistic power flow calculation system based on joint input-output distribution, the system comprising: The probability modeling module is used to perform probability modeling on random input variables in the distribution network based on historical input data of the distribution network, and to obtain the joint probability distribution of the random input variable vectors by GMM. The piecewise linearization module is used to perform piecewise linearization on the nonlinear power flow model of the distribution network based on the mean vector of each Gaussian component in the joint probability distribution of the GMM, so as to obtain a piecewise linearized power flow model. The GMM model construction module is used to obtain a GMM model of the joint probability distribution of the input and output vectors of the power flow calculation in the distribution network based on the joint probability distribution of the GMM and the piecewise linearized power flow model. The analytical result solving module is used to solve the analytical results of probability power flow calculation based on the GMM model of the joint probability distribution of the input and output vectors.

[0018] A terminal includes a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of the method.

[0019] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method.

[0020] Compared with the prior art, the beneficial effects of the present invention include at least the following: This invention linearizes nonlinear power flow segments and combines them with the joint probability distribution of the GMM (Gross Flow Model) of random input variables to obtain a GMM model of the joint probability distribution of the input and output vectors for power flow calculation in distribution networks. This model can accurately characterize the complex statistical features of various random variables, adapt to multi-output evaluation scenarios, and directly solve for the analytical results of probabilistic power flow without relying on Monte Carlo simulation, while improving computational accuracy and efficiency.

[0021] This invention eliminates the need for extensive sample simulations, enabling the direct and precise determination of the probability density functions of state variables such as node voltage and branch power flow through edge distribution. This achieves efficient and high-precision analytical calculations for probabilistic assessment of the operating state of the distribution network.

[0022] This invention employs the EM algorithm to iteratively solve optimization problems. In the E-step calculation of variational coefficients, by introducing intermediate variables and their exponential functions, numerical overflow is avoided when calculating variational coefficients. For a large initial number of Gaussian components, the variational coefficients can be calculated efficiently.

[0023] This invention will randomly input variable vectors x and power flow output variable vector y Constructing into input-output joint variables z Furthermore, a GMM model with joint input and output probability distribution is established, unifying the complete probability information and mapping relationship information between multiple input variables and multiple output variables into a single analytical model. This avoids the need to establish separate surrogate models for multiple output variables, thereby improving computational efficiency while ensuring computational accuracy. Attached Figure Description

[0024] Figure 1 This is a flowchart of a probabilistic power flow calculation method for distribution networks based on the joint distribution of input and output, according to the present invention.

[0025] Figure 2 This is a wiring diagram of a 33-node system in an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0027] Embodiment 1 of the present invention provides a method for calculating probabilistic power flow in a distribution network based on joint input-output distribution, such as... Figure 1 As shown, it includes: Step 1: Based on historical data, perform probabilistic modeling of random input variables in the distribution network to obtain the GMM joint probability distribution of the random input variable vector; More preferably, probabilistic modeling is performed on the random variables in the distribution network with a high proportion of electric vehicles and new energy sources, establishing a joint probability distribution of the random input variables based on a Gaussian mixture model (GMM), specifically including: Step 1.1: Denote the vector composed of random input variables such as charging load, renewable energy output, and nodal load in the distribution network with a high proportion of electric vehicles and renewable energy as follows: x ,collection x of n Historical samples X 1, X 2, ..., X n .

[0028] Step 1.2: Establish the joint probability density function of the random vectors using the kernel density estimation (KDE) method based on the Gaussian kernel function, as shown below: (1) Where: N( ) is the Gaussian kernel function; H t It is the first t Sample X t The bandwidth matrix. The probability distribution estimated by KDE is considered to have... n The basis GMM of each component, therefore K b = n For the first t Each component, weighting coefficient 1 / n mean vector for X t covariance matrix for H t .

[0029] Step 1.3: The density-preserving hierarchical expectation maximization (DPHEM) algorithm is used to reduce the Gaussian component number of the basis GMM. This algorithm transforms the reduction of the Gaussian component number into the following optimization problem: satisfying the basis model for the probability distribution virtual sample set X ,beg The parameters simplify the model. The log-likelihood function has the largest expected value, as shown below: (2) In the formula: To simplify GMM x The joint probability density function; For the first k The weights of each Gaussian component; For the first k The mean vector of Gaussian components; For the first k The covariance matrix of Gaussian components; K To simplify the Gaussian component number of GMM; virtual sample set X Depend on m It consists of virtual samples, and there is no need to actually generate the samples during the actual solution process; As expected.

[0030] The optimization problem (2) is solved iteratively using the EM algorithm. The main steps of its iterative process are divided into E-step and M-step. The E-step is shown below: (3) (4) (5) The M-step is shown below: (6) (7) (8) In the formula: It is an introduced intermediate variable. The index corresponding to the minimum value of the intermediate variable; ( t = 1、…、 K b , k = 1、…、 K ) are variational coefficients; the symbol tr represents the trace of the matrix; M It is a constant, usually set to 10. K b .

[0031] Step 2: Based on the mean vector of each Gaussian component in the joint probability distribution of the GMM, the nonlinear power flow model of the distribution network is piecewise linearized to obtain the piecewise linearized power flow model. More preferably, based on the random input variable GMM model obtained in step 1, the nonlinear power flow model of the distribution network is piecewise linearized to obtain a piecewise linearized power flow model, specifically including: The nonlinear power flow model is denoted as: (9) In the formula: Γ( ) represents a nonlinear power flow model. x This represents a vector of random input variables, specifically the uncertain output and load of distributed power sources. y This represents the output variable vector, which is the desired output electrical quantity of the power distribution system, including node voltage, branch current, branch power, or branch power loss.

[0032] For GMM-based x The joint probability distribution is The k Each component , nonlinear function Γ( )exist Linearization, i.e.: (10) In the formula: for x = The Jacobian matrix for power flow calculation using the Newton-Raphson method. For the output electrical quantities to be determined, this can be treated as an output variable vector. y Find its value with respect to the random input variable. x Jacobian matrix T Thus, a piecewise linearized model is obtained.

[0033] Step 3: Based on the joint probability distribution of the GMM and the piecewise linearized power flow model, obtain the GMM model of the joint probability distribution of the input and output vectors for power flow calculation in the distribution network; More preferably, based on the piecewise linearized power flow model in step 2 and the joint probability distribution of the input variables GMM in step 1, a GMM model for the joint probability distribution of the "input-output" of power flow calculation in the distribution network is obtained, specifically including: According to the law of total probability, input random variables x joint probability distribution It can be equivalently expressed as equation (11): (11) in: (12) In the formula: It is an event, representing the parameter as and The k Gaussian components It is an event The probability of an event occurring. When it occurs, according to the properties of the multidimensional Gaussian distribution,x It can be represented as: (13) in, From the Cholesky decomposition, u It is a vector of variables that follows a standard Gaussian distribution.

[0034] input vector x and output vector y The input-output vector formed is denoted as z According to the first k A linear power flow model (10), event Below z It can be represented as: (14) In the formula: I Let be the identity matrix. Substituting equation (13) into equation (14) yields: (15) Based on the above formula and the properties of the multidimensional Gaussian distribution, given an event... Down z The joint probability density function can be derived as follows: (16) In the formula: m y,k =Γ( m x,k ), S xy,k = S x,k TT k , S yx,k = T k S x,k , S y,k = T k S x,k TT k Considering the probabilities of different events oh 1, ... oh K , z The joint probability density function is finally derived as follows: (17) In the formula, joint variables z In yThe output electrical quantity vector to be determined may include node voltage, branch current, branch power, and branch power loss.

[0035] Step 4: Based on the GMM model of the joint probability distribution of the input and output vectors, solve for the analytical results of the probability power flow calculation.

[0036] More preferably, based on the "input-output" joint probability distribution GMM model obtained in step 3, the analytical results of the probability power flow calculation are directly solved, specifically including: According to equation (17), the probability density function of any output variable can be obtained, that is, the marginal distribution of the "input-output" joint probability density function. Based on the properties of the GMM model, the marginal distribution of the probability density function of the input-output joint variable can be obtained. l Taking one output variable as an example, its probability density function can be expressed as: (18) In the formula: It is the first l The output variable can be any one of node voltage, branch current, branch power, or branch power loss. m l,k = m y,k ( l ), S ll,k = S y,k ( l , l ), ( l )and( l , l ) represent the element indices of vectors and matrices, respectively.

[0037] The proposed probabilistic power flow calculation method for distribution networks based on joint input-output distribution was tested using the IEEE 33-bus distribution system as follows: The wiring diagram of the test system is as follows Figure 2 As shown, the system connects four photovoltaic (PV) generator sets, one wind turbine set, and one electric vehicle (EV) charging station. Each PV generator set has a capacity of 0.8 MW, each wind turbine set has a capacity of 1.2 MW, and each charging station contains 20 charging piles of 42 kW each. The load demand at each node follows a Gaussian distribution, and the relevant data were collected from the actual system. Using the Monte Carlo simulation results as the baseline, a probabilistic power flow calculation method based on PCE and GPR surrogate models was selected as the comparison method.

[0038] The steps of probabilistic power flow calculation for distribution networks based on the joint probability distribution of "input-output" in power flow calculation according to this invention are as follows: Input historical data of random input variables such as charging load and new energy output in the power distribution network; A random vector is formed by collecting samples according to step 1.1; Establish the joint probability density function of the random vectors based on the KDE method based on the Gaussian kernel function in step 1.2; The number of Gaussian components of the base GMM is reduced according to the DPHEM algorithm in step 1.3; Establish a piecewise linearized power flow model of the distribution network based on equations (9) and (10) in step 2; Based on equations (11)-(17) in step 3, the GMM model for the joint probability distribution of the input-output in power flow calculation of the distribution network is obtained; The probability density function of the output variable to be determined can be directly solved according to equation (18) in step 4.

[0039] The results are shown in Tables 1 and 2.

[0040] Table 1 Comparison of relative errors of mean and standard deviation for different probability power flow calculation methods

[0041] Table 2 Comparison of time consumption for different probability power flow calculation methods

[0042] As shown in Table 1, in most cases, the GMM method of this invention yields more accurate results than the PCE and GPR methods. Regarding standard deviation, the error of the results obtained by the GMM method is significantly smaller than that of the PCE and GPR methods, with maximum errors of 8.91% and 29.76%, respectively. The GMM method only shows slightly larger errors than the PCE and GPR methods when estimating the mean of line current and total active power loss, but the estimation error is still less than 1%. As shown in Table 2, the calculation time of the GMM method of this invention is significantly reduced to only 0.705s, which is 430 times, 665 times, and 3171 times faster than PCE, GPR, and MCS, respectively.

[0043] Embodiment 2 of the present invention provides a distribution network probabilistic power flow calculation system based on joint input-output distribution, the system comprising: The probability modeling module is used to perform probability modeling on random input variables in the distribution network based on historical input data of the distribution network, and to obtain the joint probability distribution of the random input variable vectors by GMM. The piecewise linearization module is used to perform piecewise linearization on the nonlinear power flow model of the distribution network based on the mean vector of each Gaussian component in the joint probability distribution of the GMM, so as to obtain a piecewise linearized power flow model. The GMM model construction module is used to obtain a GMM model of the joint probability distribution of the input and output vectors of the power flow calculation in the distribution network based on the joint probability distribution of the GMM and the piecewise linearized power flow model. The analytical result solving module is used to solve the analytical results of probability power flow calculation based on the GMM model of the joint probability distribution of the input and output vectors.

[0044] Embodiment 3 of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of the method.

[0045] Embodiment 4 of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0046] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0047] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0048] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0049] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0050] Finally, 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 the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for calculating probabilistic power flow in a distribution network based on joint input-output distribution, characterized in that, The method includes: Step 1: Based on historical data, perform probabilistic modeling of random input variables in the distribution network to obtain the GMM joint probability distribution of the random input variable vector; Step 2: Based on the mean vector of each Gaussian component in the joint probability distribution of the GMM, the nonlinear power flow model of the distribution network is piecewise linearized to obtain the piecewise linearized power flow model. Step 3: Based on the joint probability distribution of the GMM and the piecewise linearized power flow model, obtain the GMM model of the joint probability distribution of the input and output vectors for power flow calculation in the distribution network; Step 4: Based on the GMM model of the joint probability distribution of the input and output vectors, solve for the analytical results of the probability power flow calculation.

2. The distribution network probabilistic power flow calculation method based on joint input-output distribution according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Denote the vector composed of random input variables in the power distribution network as the random input variable vector. x ,collection x of n Historical samples X 1, X 2, ..., X n ; Step 1.2: Based on historical samples, establish a random input variable vector using the kernel density estimation method of the Gaussian kernel function. x Joint probability density function: （1） Where: N( ) is the Gaussian kernel function; H t It is the first t Historical samples X t The bandwidth matrix; the number of Gaussian components in the joint probability density function. K b = n Weighting coefficients 1 / n mean vector for X t covariance matrix For the first t Historical samples X t bandwidth matrix H t ; Step 1.3: Use the density-preserving hierarchical expectation-maximization algorithm to reduce the Gaussian component number of the joint probability density function, and obtain the joint probability distribution of the GMM of the random input variable vector. .

3. The distribution network probabilistic power flow calculation method based on joint input-output distribution according to claim 2, characterized in that: The distribution network has a high proportion of electric vehicles and new energy sources connected to it; the random input variables include charging load, new energy output and node load.

4. The distribution network probabilistic power flow calculation method based on joint input-output distribution according to claim 2, characterized in that: Step 1.3 describes a density-preserving hierarchical expectation-maximization algorithm that reduces the Gaussian component number to the following optimization problem: The probability distributions satisfy the joint probability density function virtual sample set X ,beg The parameters make The log-likelihood function has the largest expected value, as shown below: （2） In the formula: For the first k The weights of each Gaussian component; For the first k The mean vector of Gaussian components; For the first k The covariance matrix of Gaussian components; K for Gaussian component number; As expected.

5. The distribution network probabilistic power flow calculation method based on joint input-output distribution according to claim 4, characterized in that: The optimization problem is solved iteratively using the EM algorithm, which includes E-steps and M-steps. The E-step calculation of variational coefficients As shown below: （3） （4） （5） The M-step is based on variational coefficients. Update the weights of the Gaussian components Mean vector Covariance matrix As shown below: （6） （7） （8） In the formula: As an intermediate variable, The index corresponding to the minimum value of the intermediate variable; These are variational coefficients. t = 1、…、 K b , k = 1、…、 K , express Middle t Gaussian component pairs Middle k The degree of attribution of each Gaussian component K b , K These represent the joint probability density function and the number of Gaussian components in the joint probability distribution of the GMM, respectively; the symbol tr represents the trace of the matrix. M It is a constant.

6. The distribution network probabilistic power flow calculation method based on joint input-output distribution according to claim 1, characterized in that: In step 2, based on the random input variable vector x Joint probability distribution of GMM The mean vector of each Gaussian component in the distribution network nonlinear power flow model Piecewise linearization is performed to obtain the piecewise linearized power flow model, as follows: （10） In the formula: for x = Jacobian matrix for power flow calculation using the Newton-Raphson method; for Middle k The mean vector of Gaussian components; Γ( ) represents a nonlinear function; y This represents the output variable vector.

7. The distribution network probabilistic power flow calculation method based on joint input-output distribution according to claim 6, characterized in that: In step 3, based on the joint probability distribution of the GMM and the piecewise linearized power flow model, the GMM model of the joint probability distribution of the input and output vectors for power flow calculation in the distribution network is obtained, as follows: （17） in, z For random input variable vectors x and output variable vector y The input and output vectors formed; K The number of Gaussian components in the joint probability distribution of GMM; ω k For the event The probability of occurrence, the event Indicates input random variables x Joint probability distribution of GMM The mean vector is The covariance matrix is The k One Gaussian component; To The lower triangular matrix obtained by performing Cholesky decomposition. u It is a vector of variables that follows a standard Gaussian distribution; Γ( ) represents a nonlinear function; μ y,k =Γ( μ x,k ), Σ xy,k = Σ x,k TT k , Σ yx,k = T k Σ x,k , Σ y,k = T k Σ x,k TT k , μ y,k , Σ xy,k , Σ yx,k , Σ y,k For the k-th Gaussian component, y mean vector x and y cross-covariance matrix, y and x cross-covariance matrix, y The covariance matrix.

8. The distribution network probabilistic power flow calculation method based on joint input-output distribution according to claim 7, characterized in that: In step 4, the probability density function of the output variable is obtained from the GMM model of the joint probability distribution of the input and output vectors, and is used as the analytical result of the probability power flow calculation: （18） In the formula: It is the first l One output variable; μ l,k = μ y,k ( l ), Σ ll,k = Σ y,k ( l , l ), μ l,k , Σ ll,k For the k-th Gaussian component, the th l The mean of the nth output variable, the nth l The variance of each output variable, μ y,k ( l )for μ y,k The l One element, Σ y,k ( l , l )for Σ xy,k The l Line number l Column elements, μ y,k , Σ xy,k For the k-th Gaussian component, y mean vector x and y The cross-covariance matrix.

9. A distribution network probabilistic power flow calculation system based on joint input-output distribution, comprising the method described in any one of claims 1-8, characterized in that, The system includes: The probability modeling module is used to perform probability modeling on random input variables in the distribution network based on historical input data of the distribution network, and to obtain the joint probability distribution of the random input variable vectors by GMM. The piecewise linearization module is used to perform piecewise linearization on the nonlinear power flow model of the distribution network based on the mean vector of each Gaussian component in the joint probability distribution of the GMM, so as to obtain a piecewise linearized power flow model. The GMM model construction module is used to obtain a GMM model of the joint probability distribution of the input and output vectors of the power flow calculation in the distribution network based on the joint probability distribution of the GMM and the piecewise linearized power flow model. The analytical result solving module is used to solve the analytical results of probability power flow calculation based on the GMM model of the joint probability distribution of the input and output vectors.

10. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-8.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-8.

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