Rural power distribution network time sequence voltage distribution evaluation method and system based on probability modeling

Abstract

The invention relates to a power system risk assessment technology, in particular to a rural power distribution network time sequence voltage distribution assessment method and system based on probability modeling, and the method comprises the steps: carrying out the GMM modeling of the historical data of distributed photovoltaic and load power, constructing the correlation between distributed photovoltaic output GMM and load power GMM through a Gaussian Copula function, and obtaining a joint distribution model; adopting MCS sampling to generate distributed photovoltaic and load power samples as power injection of the rural power distribution network; a Newton-Raphson method is used to complete rural power distribution network time sequence probabilistic load flow calculation; gMM modeling is carried out on the power flow voltage, and a comprehensive evaluation index based on analytic integration is used for evaluating voltage distribution characteristics. The method can effectively solve the time sequence limitation problem of rural power distribution network static probabilistic load flow calculation under high-proportion distributed photovoltaic and novel load access, depicts voltage time sequence distribution characteristics, dynamically evaluates the voltage out-of-limit risk, and provides decision support for operation optimization of the rural power distribution network.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system risk assessment, and in particular relates to a method and system for assessing the temporal voltage distribution of a rural power distribution network based on probability modeling. Background Art

[0002] With the large-scale integration of distributed photovoltaics and the diversified development of new loads arising from rural industrial transformation, rural distribution networks face the challenge of uncertainty on both the source and load sides. The intermittent nature of distributed photovoltaic output, the random fluctuations of new loads, and the spatiotemporal coupling of the two lead to frequent voltage fluctuations in rural distribution networks and a significant increase in the risk of bidirectional overshooting. Traditional probabilistic power flow analysis methods are mostly based on static scenarios or single probability distribution assumptions, making it difficult to accurately characterize the correlation and complex distribution characteristics of source and load power, nor to reflect the continuous fluctuation characteristics of voltage. At the same time, traditional static probabilistic power flow calculations based on Monte Carlo simulations are inefficient and cannot meet the needs of real-time risk warnings. In addition, existing risk quantification indicators are mostly based on a single voltage overshoot probability or expected value, which cannot effectively reflect the severity of the impact on the system.

[0003] Therefore, a new method needs to be proposed to perform efficient time-series probabilistic power flow calculation based on accurate modeling of the correlation and complex distribution characteristics of source and load power, so as to capture the time-series distribution characteristics of voltage, and then realize the refined dynamic assessment of voltage over-limit risk through a comprehensive evaluation index system. Summary of the Invention

[0004] The present invention provides a method and system for evaluating the time-series voltage distribution of a rural distribution network based on probability modeling, which is used to solve the defects of the existing probabilistic power flow analysis in the distribution network voltage time-series distribution evaluation caused by ignoring the source-load time-series correlation and the single risk quantification indicator, and realize the refinement and time-series evaluation of the voltage distribution of the rural distribution network.

[0005] The present invention provides a method for evaluating the time-series voltage distribution of a rural distribution network based on probability modeling, comprising the following steps: GMM modeling is performed on historical data of distributed photovoltaic output and load power to quantify the uncertainty of source and load power at each node in the rural distribution network; The correlation between the distributed photovoltaic output and the load power GMM modeled by the Gaussian Copula function is constructed to obtain a joint distribution model that characterizes the correlation and complex distribution characteristics; The joint distribution model is sampled as the power injection of each node at each moment in the rural distribution network, and the Newton-Raphson method is used to calculate the time series probabilistic power flow. The GMM model is used to calculate the voltage flow results of each node at each moment after the time series probability power flow calculation is completed, and the voltage time series distribution characteristics are evaluated using a comprehensive evaluation index based on analytical integration.

[0006] According to the method for evaluating the time-series voltage distribution of a rural distribution network based on probability modeling provided by the present invention, the method for performing GMM modeling on the historical data of distributed photovoltaic output and load power is as follows: Assume that the rural power distribution network consists of nodes and lines. A node is a specific location for connecting, distributing or controlling electric energy. The node is the location where the line in the distribution network is connected to the load or distributed photovoltaic. nodes; process the distributed photovoltaic output and load power historical data of the rural distribution network, and , At the moment , The data are divided into the same data set to obtain the distributed photovoltaic output data set and load power datasets ; Fit the data set to the GMM model, and its probability density function is: (1) Where, For the K The weights of the Gaussian components satisfy formula (2), is a univariate Gaussian distribution, satisfying formula (3), is the mean, is the variance; (2) (3) Determining the optimal number of components using the Bayesian Information Criterion , use the expectation maximization algorithm to solve the parameters and .

[0007] According to the method for evaluating the time-series voltage distribution of a rural distribution network based on probability modeling provided by the present invention, the correlation between the distributed photovoltaic output and the load power GMM constructed by the Gaussian Copula function is implemented as follows: The GMM model of distributed photovoltaic output and load power at each node at each time is used as the marginal distribution of the joint distribution model. The data is mapped to the standard normal space through probability integral transformation. The covariance matrix is ​​used to characterize the correlation. The marginal distribution and the correlation are integrated into the joint distribution through the Gaussian Copula function. For rural distribution network system nodes , At the same time, the probability density function of the GMM model is the weighted sum of multiple Gaussian distributions, and its cumulative distribution function is calculated by integration: (4) Where, is the cumulative distribution function of the standard normal distribution; The original distribution of distributed photovoltaic output and load power historical data is converted into a uniform distribution by using probability integral transformation. , and its corresponding uniform variable is: (5) By inverse normal transformation, uniform variables are transformed Converted to standard normal variable ,at this time Obey the standard normal distribution , and its calculation formula is: (6) Where, is the inverse cumulative distribution function of the standard normal distribution; Each node Combined into vector , obeys the multidimensional normal distribution ,in is the correlation coefficient matrix.

[0008] According to the method for evaluating the time-series voltage distribution of a rural distribution network based on probability modeling provided by the present invention, the method for obtaining the joint distribution model that characterizes the correlation and complex distribution characteristics is as follows: The Gaussian Copula function is used to characterize the correlation of the GMM of each node, and the covariance matrix of the Gaussian Copula function is calculated: (7) (8) In the covariance matrix, For variables and The covariance of Standardization, conversion to correlation coefficient , and its calculation formula is: (9) Where, For variables The variance of For variables variance; Convert the covariance matrix to a correlation matrix: (10) The GMM marginal distribution and the Gaussian Copula function are integrated into a joint distribution. The joint distribution formula is the product of the GMM marginal distribution and the Gaussian Copula function, as shown in formula (11): (11) Among them, Gaussian Copula function for: (12).

[0009] According to the method for evaluating the time-series voltage distribution of a rural distribution network based on probability modeling provided by the present invention, the method for sampling the joint distribution model as the power injection of each node at each moment in the rural distribution network and using the Newton-Raphson method to perform time-series probability power flow calculation is implemented as follows: S1. Generate sampling samples of the joint distribution model through Cholesky decomposition as the power injection of each node at each time in the rural distribution network; The distribution network system has N nodes, each corresponding to a random variable. The standard normal distribution required for joint distribution modeling is N-dimensional, which has the same dimension as the number of nodes. S groups of initial samples are generated from the N-dimensional standard normal distribution: (13) Perform Cholesky decomposition on the correlation coefficient matrix R of the joint distribution to obtain the decomposition matrix L. The calculation formula is shown in formula (14), and then the sample , the formula is shown in formula (15): (14) (15) For each node With sample , the sample Converted to a uniformly distributed variable, the calculation formula is: (16) Solve the inverse cumulative distribution function of the GMM model: (17) The joint distribution of distributed photovoltaic output and load power in the rural distribution network system is calculated to obtain the distributed photovoltaic output sample. and load power samples , ; As the power injection of each node at each moment; rural distribution network system node , At the moment , The power injection is ; S2. Based on the power injection samples obtained in S1, use the Newton-Raphson method to perform time-series probabilistic power flow calculations to obtain time-series power flow voltage results. The nodes of the rural distribution network are divided into three categories: balancing nodes, PQ nodes and PV nodes. Node 1 is set as a balancing node, and its voltage amplitude is and phase angle Fixed; the remaining nodes are set as PQ nodes, and their active power and reactive power is a known value, the voltage amplitude and phase angle is the value to be evaluated; At the moment Establish the power flow equation, node Injected active power and reactive power They are: (18) (19) Where, is the total number of nodes in the rural distribution network, and Node admittance The real and imaginary parts of For each node, the power imbalance is defined as: (20) (twenty one) Where, and Active power and reactive power injected into the node, and is the node active power and reactive power during the iterative calculation process, which is calculated from the voltage estimation value during the iterative calculation process; The partial derivatives of the power imbalance with respect to the voltage amplitude and phase angle are organized into a matrix form to obtain the Jacobian matrix : (twenty two) In the In the iterations, the correction 、 Calculated by the following formula: (twenty three) Update the node voltage using the correction value: (twenty four) (25) Continue iterating until the following convergence conditions are met: (26) Where, is the preset convergence threshold; For each group of joint distribution samples at each moment, the power flow equations of formula (18) to formula (26) are calculated to complete the time series probability power flow calculation, and finally the time series power flow voltage result is obtained. , ; .

[0010] According to the method for evaluating the time series voltage distribution of a rural distribution network based on probability modeling provided by the present invention, the GMM modeling of the power flow voltage results of each node at each time obtained after the time series probability power flow calculation is completed, and the implementation method of evaluating the voltage time series distribution characteristics using a comprehensive evaluation index based on analytical integration is as follows: System nodes At the moment The power flow voltage results For GMM modeling, its probability density function is: (27) Based on the probability density function of the node voltage, the node voltage is calculated using the analytical integration method. At the moment The voltage over-limit probability is obtained and the voltage over-limit risk value is obtained: (28) Where, is the voltage over-limit risk value, For nodes At the moment The GMM voltage probability density function, and are the upper and lower limits of the node voltage operating range respectively; In the rural distribution network system, the utility preference index function is used to define the node voltage excess severity function, and the calculation formula is as follows: (29) (30) Where, It is a risk factor, the larger its value is, the more sensitive it is to risk; is the voltage excursion index, is the system reference voltage Combining the voltage over-limit risk value and the voltage over-limit severity function, a comprehensive evaluation index for voltage over-limit risk is proposed. , the calculation formula is as follows: (31) Where, For nodes At the moment The voltage over-limit comprehensive risk index; By calculating the comprehensive voltage over-limit risk index, the time periods with large fluctuations in the time-series voltage distribution of each node and the severity of their over-limit risks are identified, and the source-load characteristics and operation optimization of the rural distribution network are analyzed.

[0011] The present invention also provides a rural distribution network time sequence voltage distribution evaluation system based on probability modeling, which is applied to the rural distribution network time sequence voltage distribution evaluation method based on probability modeling. The system includes a GMM module, a joint distribution module, a power flow calculation module and an index evaluation module; The GMM module is used to perform GMM modeling on the historical data of distributed photovoltaic output and load power, and quantify the uncertainty of source and load power at each node in the rural distribution network; The joint distribution module is used to construct the correlation between distributed photovoltaic output and load power GMM through Gaussian Copula function, and obtain a joint distribution model that characterizes the correlation and complex distribution characteristics; The power flow calculation module is used to sample the joint distribution model as the power injection of each node at each time in the rural distribution network, and use the Newton-Raphson method to perform time series probability power flow calculation; The index evaluation module is used to perform GMM modeling on the power flow voltage results of each node at each moment after the time series probability power flow calculation is completed, and use the comprehensive evaluation index based on analytical integration to evaluate the voltage time series distribution characteristics.

[0012] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method for evaluating the temporal voltage distribution of a rural distribution network based on probability modeling.

[0013] The present invention also provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the method for evaluating the temporal voltage distribution of a rural distribution network based on probability modeling.

[0014] The present invention also provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the method for evaluating the temporal voltage distribution of a rural distribution network based on probability modeling.

[0015] Compared with the prior art, the present invention has the following beneficial effects: Based on the GMM model and Gaussian Copula function, a joint distribution model of distributed photovoltaic output and load power was constructed, which can accurately characterize the complex distribution characteristics and correlation of source and load.

[0016] Sampling the source-load joint distribution model at each moment as power injection and performing time-series probabilistic power flow calculation can effectively reflect the time-series variation trend of voltage and characterize the time-series distribution characteristics of node voltage.

[0017] A GMM model of the power flow voltage results is constructed, and a comprehensive evaluation index based on analytical integration is proposed to evaluate the voltage time series distribution characteristics. Considering the dual factors of voltage over-limit probability and voltage over-limit severity, the high-risk time periods and their over-limit risk severity in the time series voltage distribution of each node are accurately identified. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0019] Figure 1 This is a flow chart of a method for evaluating time-series voltage distribution in a rural distribution network based on probability modeling provided by an embodiment of the present invention; Figure 2 This is a structural diagram of an IEEE 33-node power distribution system with a high proportion of distributed photovoltaic penetration provided by an embodiment of the present invention; Figure 3 1 is a probability density function diagram of a GMM model of a node 10 of an IEEE 33-node power distribution system at each moment provided by an embodiment of the present invention; Figure 4 This is a sample correlation matrix diagram of the distributed photovoltaic joint distribution model at the 10th hour provided by an embodiment of the present invention; Figure 5 This is a line graph of 50 groups of sample data sampled from the load joint distribution model at the 10th hour provided by an embodiment of the present invention; Figure 6 24-hour time-series voltage distribution diagram from node 2 to node 33 provided by an embodiment of the present invention; Figure 7 This is a 24-hour voltage over-limit comprehensive risk index diagram provided by an embodiment of the present invention; Figure 8 It is a structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0020] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0021] This embodiment of the rural distribution network time-series voltage distribution assessment method based on probabilistic modeling quantifies the uncertainty of source-load power at each node in the rural distribution network by performing GMM modeling on historical data of distributed photovoltaic and load power. The correlation between the distributed photovoltaic output GMM and the load power GMM is constructed using a Gaussian Copula function to obtain a joint distribution model. MCS sampling is used on the joint distribution probability density function to generate distributed photovoltaic and load power samples, which are used as power injection for the rural distribution network. The joint distribution samples at each moment are input into the power flow calculation at each moment, and the Newton-Raphson method is used to complete the rural distribution network time-series probabilistic power flow calculation. GMM modeling is performed on the power flow voltage results at each node at each moment, and a comprehensive evaluation index based on analytical integration is used to dynamically evaluate the voltage distribution characteristics. This embodiment can effectively address the time-series constraint problem of static probabilistic power flow calculation in rural distribution networks under the background of high-proportion distributed photovoltaic and new load access, characterize the voltage time-series distribution characteristics, dynamically evaluate the voltage over-limit risk, and provide decision support for the operation optimization of rural distribution networks.

[0022] like Figure 1 As shown, this embodiment provides a method for evaluating the time-series voltage distribution of a rural distribution network based on probability modeling, comprising the following steps: Step 1. Perform GMM modeling on the historical data of distributed photovoltaic output and load power.

[0023] Rural power distribution network is mainly composed of nodes and lines. Nodes are specific locations used to connect, distribute or control electric energy. The nodes mentioned in this invention are the locations where lines in the power distribution network are connected to loads or distributed photovoltaics. Nodes. Process the distributed photovoltaic output and load power history data of the rural distribution network and ( ) at the moment ( ) data into the same data set to obtain the distributed photovoltaic output data set and load power datasets ; Fit the data set to the GMM model, and its probability density function is: (1) Where, is the weight of the kth Gaussian component, satisfying formula (2), is a univariate Gaussian distribution, satisfying formula (1), is the mean, is the variance; (2) (3) Determine the optimal number of components using the Bayesian Information Criterion (BIC) , using the expectation maximization (EM) algorithm to solve for the parameters and .

[0024] Step 2. Use the Gaussian Copula function to construct the correlation between the distributed photovoltaic output and load power GMM modeled in step 1, and obtain a joint distribution model that characterizes the correlation and complex distribution characteristics.

[0025] First, the GMM model of distributed photovoltaic output and load power at each node at each time in step 1 is used as the marginal distribution of the joint distribution model. Then, the data is mapped to the standard normal space through probability integral transformation, and the covariance matrix is ​​used to characterize the correlation. Finally, the marginal distribution and the correlation are integrated into a joint distribution through the Gaussian Copula function.

[0026] For rural distribution network system nodes ( ) At the same time, the probability density function of the GMM model is the weighted sum of multiple Gaussian distributions, and its cumulative distribution function is calculated by integration: (4) Where, is the cumulative distribution function of the standard normal distribution; The original distribution of distributed photovoltaic output and load power historical data is converted into a uniform distribution by using probability integral transformation. , and its corresponding uniform variable is: (5) By inverse normal transformation, uniform variables are transformed Converted to standard normal variable ,at this time Obey the standard normal distribution , and its calculation formula is: (6) Where, is the inverse cumulative distribution function of the standard normal distribution; Each node Combined into vector , obeys the multidimensional normal distribution ,in is the correlation coefficient matrix; The Gaussian Copula function is used to characterize the correlation of the GMM of each node, and the covariance matrix of the Gaussian Copula function is calculated: (7) (8) In the covariance matrix, For variables and The covariance of Standardization, conversion to correlation coefficient , and its calculation formula is: (9) Where, For variables The variance of For variables variance; This converts the covariance matrix into a correlation coefficient matrix: (10) The GMM marginal distribution and the Gaussian Copula function are integrated into a joint distribution. The joint distribution formula is the product of the GMM marginal distribution and the Gaussian Copula function, as shown in formula (11): (11) Among them, Gaussian Copula function for: (12) Step 3. Sampling the joint distribution model constructed in step 2 as the power injection of each node at each time in the rural distribution network, and using the Newton-Raphson method to calculate the time series probability power flow, the specific method is as follows: Step 3.1. Generate a sample of the joint distribution model constructed in step 2 through Cholesky decomposition as the power injection of each node at each time in the rural distribution network; The distribution network system has N nodes. Since each node corresponds to a random variable, the standard normal distribution required for joint distribution modeling is N-dimensional, which is the same as the number of nodes. S groups of initial samples are generated from the N-dimensional standard normal distribution: (13) Perform Cholesky decomposition on the correlation coefficient matrix R of the joint distribution to obtain the decomposition matrix L. The calculation formula is shown in formula (14), and then the sample , the formula is shown in formula (15): (14) (15) For each node With sample , the sample Converted to a uniformly distributed variable, the calculation formula is: (16) Solve the inverse cumulative distribution function of the GMM model: (17) Perform step 3.1 calculation on the joint distribution of distributed photovoltaic output and load power in the rural distribution network system to obtain the distributed photovoltaic output sample and load power samples ( ; ) as the power injection of each node at each moment. Therefore, the rural distribution network system node ( ) at the moment ( ) is injected into .

[0027] Step 3.2. Based on the power injection samples obtained in step 3.1, use the Newton-Raphson method to perform a time-series probabilistic power flow calculation to obtain a time-series power flow voltage result. The nodes of the rural distribution network are divided into three categories: balancing nodes, PQ nodes and PV nodes. Node 1 is set as a balancing node, and its voltage amplitude is and phase angle Fixed; the remaining nodes are set as PQ nodes, and their active power and reactive power is a known value, the voltage amplitude and phase angle To be evaluated.

[0028] At the moment Establish the power flow equation, node Injected active power and reactive power They are: (18) (19) Where, is the total number of nodes in the rural distribution network, and Node admittance The real and imaginary parts of For each node, the power imbalance is defined as: (20) (twenty one) Where, and Active power and reactive power injected into the node, and is the node active power and reactive power during the iterative calculation process, which is calculated from the voltage estimation value during the iterative calculation process; The partial derivatives of the power imbalance with respect to the voltage amplitude and phase angle are organized into a matrix form to obtain the Jacobian matrix : (twenty two) In the In the iterations, the correction 、 Calculated by the following formula: (twenty three) Update the node voltage using the correction value: (twenty four) (25) Continue iterating until the following convergence conditions are met: (26) Where, is the preset convergence threshold; For each group of joint distribution samples at each moment, the power flow equations of formula (18) to formula (26) are calculated, that is, the time series probability power flow calculation is completed, and the time series power flow voltage result is finally obtained. , ; .

[0029] Furthermore, in step 4, the power flow voltage results of each node at each time obtained after the time series probability power flow calculation in step 3.2 are used for GMM modeling, and the voltage time series distribution characteristics are evaluated using a comprehensive evaluation index based on analytical integration. The specific method is as follows: System nodes At the moment The power flow voltage results For GMM modeling, its probability density function is: (27) Based on the probability density function of the node voltage, the node voltage is calculated using the analytical integration method. At the moment The voltage exceeding limit probability is calculated to obtain the voltage exceeding limit risk value: (28) Where, is the voltage over-limit risk value, For nodes At the moment The GMM voltage probability density function, and are the upper and lower limits of the node voltage operating range respectively.

[0030] In rural distribution network systems, various devices are installed at various nodes, and their risk tolerance for voltage over-limit varies. In order to sensitively reflect the severity of voltage over-limit at different nodes at different times, a utility preference index function is used to define the node voltage over-limit severity function. The calculation formula is as follows: (29) (30) Where, It is a risk factor, the larger its value is, the more sensitive it is to risk; is the voltage excursion index, is the system reference voltage.

[0031] Finally, combining the voltage over-limit risk value and the voltage over-limit severity function, a comprehensive evaluation index for voltage over-limit risk is proposed. , the calculation formula is as follows: (31) Where, For nodes At the moment The voltage over-limit comprehensive risk index.

[0032] By calculating the comprehensive voltage over-limit risk index, the time periods with large fluctuations in the time-series voltage distribution of each node and the severity of their over-limit risks can be quickly identified, providing decision support for source-load characteristic analysis and operation optimization of rural distribution networks.

[0033] This specific embodiment uses the historical data of distributed photovoltaic output and load power of a rural distribution network in a certain area for modeling, and uses the IEEE33 node distribution system as a simulation example to perform time series probabilistic power flow calculation and time series voltage distribution evaluation. , timing analysis step size hours, total duration Hour.

[0034] Figure 2The following diagram shows the structure of the IEEE 33-node distribution system for high-proportion distributed photovoltaic penetration used in this specific embodiment. The system has a total power of 10 MVA, a system base voltage of 12.66 kV, a total active load of 4 MW, and a total reactive power of 2.3 MVAR. Node 1 is the reference balancing node, and the remaining 32 nodes are divided into three types of regional nodes: agricultural, industrial, and residential. The corresponding load power factors are 0.8, 0.85, and 0.95, respectively, to reflect the actual load status of the rural distribution network. The photovoltaic penetration rate is 80%, and the access capacities of PV1 to PV5 are 0.5, 0.8, 0.8, 0.5, and 0.5 MW, respectively.

[0035] According to the Bayesian information criterion, the optimal number of Gaussian components K = 3 is selected to establish the GMM model of distributed photovoltaic and load, and GMM modeling is performed on the distributed photovoltaic and load power of the three types of regional nodes. Figure 3 It is the probability density function diagram of the GMM model of node 10 in the IEEE 33-node distribution system at each time.

[0036] To avoid the sample distortion problem caused by independent random sampling of the distributed photovoltaic and load GMM models at each node, this paper constructs the correlation of the source-load GMM model through the Gaussian Copula function, obtains the source-load power joint distribution model and performs sampling. The samples will be used as the node power injection data for the time-series probabilistic power flow calculation of the IEEE33-node distribution system. Figure 4 This is the correlation matrix diagram of the sampling samples of the joint distribution model of distributed photovoltaics in the 10th hour. Figure 5 It is a line chart of 50 groups of sample data sampled from the load joint distribution model in the 10th hour. Figure 4 and Figure 5 It can be seen that the sampling samples of the joint distribution model of distributed photovoltaics and loads have different degrees of correlation, indicating that the Copula function can effectively construct the correlation between GMM models, and the obtained joint distribution model can accurately characterize the correlation between the complex distribution characteristics of source and load.

[0037] The source-load joint distribution model at each moment is sampled as power injection, and the time series probability flow calculation is performed to obtain the time series flow voltage result. Figure 6 This is the 24-hour time-series voltage distribution diagram from node 2 to node 33, which clearly reflects the time-series change trend of the voltage at each node.

[0038] A GMM model of power flow voltage results is constructed, considering the dual factors of voltage over-limit probability and voltage over-severity, and a comprehensive evaluation index is proposed to evaluate the voltage time series distribution characteristics, and the voltage over-limit comprehensive risk index is calculated. Figure 7 The 24-hour voltage over-limit comprehensive risk index diagram accurately identifies the high-risk time periods in the time-series voltage distribution and their over-limit risk severity.

[0039] The following describes a rural distribution network time series voltage distribution evaluation system based on probability modeling provided by the present invention, which includes a GMM module, a joint distribution module, a power flow calculation module and an index evaluation module; The GMM module is used to perform GMM modeling on the historical data of distributed photovoltaic output and load power, and quantify the uncertainty of source and load power at each node in the rural distribution network; The joint distribution module is used to construct the correlation between distributed photovoltaic output and load power GMM through Gaussian Copula function, and obtain a joint distribution model that characterizes the correlation and complex distribution characteristics; The power flow calculation module is used to sample the joint distribution model as the power injection of each node at each time in the rural distribution network, and use the Newton-Raphson method to perform time series probability power flow calculation; The index evaluation module is used to perform GMM modeling on the power flow voltage results of each node at each moment after the time series probability power flow calculation is completed, and use the comprehensive evaluation index based on analytical integration to evaluate the voltage time series distribution characteristics.

[0040] Figure 8 An example of a physical structure diagram of an electronic device is shown below. Figure 8 As shown, the electronic device may include: a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may invoke logic instructions in the memory to execute a method for evaluating the temporal voltage distribution of a rural distribution network based on probabilistic modeling.

[0041] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0042] On the other hand, the present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute a rural distribution network time-series voltage distribution evaluation method based on probability modeling.

[0043] In another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which is implemented when executed by a processor to perform a rural distribution network time-series voltage distribution evaluation method based on probability modeling.

[0044] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0045] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for evaluating the temporal voltage distribution of a rural distribution network based on probability modeling, characterized in that: The following steps are involved: GMM modeling is performed on historical data of distributed photovoltaic output and load power to quantify the uncertainty of source and load power at each node in the rural distribution network; The correlation between the distributed photovoltaic output and the load power GMM modeled by the Gaussian Copula function is constructed to obtain a joint distribution model that characterizes the correlation and complex distribution characteristics; The joint distribution model is sampled as the power injection of each node at each moment in the rural distribution network, and the Newton-Raphson method is used to calculate the time series probabilistic power flow. The GMM model is used to calculate the voltage flow results of each node at each moment after the time series probability power flow calculation is completed, and the voltage time series distribution characteristics are evaluated using a comprehensive evaluation index based on analytical integration.

2. The method for evaluating the time series voltage distribution of a rural distribution network based on probability modeling according to claim 1 is characterized in that: The method of performing GMM modeling on the historical data of distributed photovoltaic output and load power is as follows: Assume that the rural power distribution network consists of nodes and lines. A node is a specific location for connecting, distributing or controlling electric energy. The node is the location where the line in the distribution network is connected to the load or distributed photovoltaic. nodes; process the distributed photovoltaic output and load power historical data of the rural distribution network, and , At the moment , The data are divided into the same data set to obtain the distributed photovoltaic output data set and load power datasets ; Fit the data set to the GMM model, and its probability density function is: （1） Where, For the K The weights of the Gaussian components satisfy formula (2), is a univariate Gaussian distribution, satisfying formula (3), is the mean, is the variance; （2） （3） Determining the optimal number of components using the Bayesian Information Criterion , use the expectation maximization algorithm to solve the parameters and .

3. The method for evaluating time-series voltage distribution in rural distribution networks based on probability modeling according to claim 1, characterized in that: The implementation method of the correlation between the distributed photovoltaic output and the load power GMM constructed by the Gaussian Copula function is as follows: The GMM model of distributed photovoltaic output and load power at each node at each time is used as the marginal distribution of the joint distribution model. The data is mapped to the standard normal space through probability integral transformation. The covariance matrix is ​​used to characterize the correlation. The marginal distribution and the correlation are integrated into the joint distribution through the Gaussian Copula function. For rural distribution network system nodes , At the same time, the probability density function of the GMM model is the weighted sum of multiple Gaussian distributions, and its cumulative distribution function is calculated by integration: （4） Where, is the cumulative distribution function of the standard normal distribution; The original distribution of distributed photovoltaic output and load power historical data is converted into a uniform distribution by using probability integral transformation. , and its corresponding uniform variable is: （5） By inverse normal transformation, uniform variables are transformed Converted to standard normal variable ,at this time Obey the standard normal distribution , and its calculation formula is: （6） Where, is the inverse cumulative distribution function of the standard normal distribution; Each node Combined into vector , obeys the multidimensional normal distribution ,in is the correlation coefficient matrix.

4. The method for evaluating the time series voltage distribution of a rural distribution network based on probability modeling according to claim 3 is characterized in that: The method of obtaining the joint distribution model that characterizes the correlation and complex distribution characteristics is as follows: The Gaussian Copula function is used to characterize the correlation of the GMM of each node, and the covariance matrix of the Gaussian Copula function is calculated: （7） （8） In the covariance matrix, For variables and The covariance of Standardization, conversion to correlation coefficient , and its calculation formula is: （9） Where, For variables The variance of For variables variance; Convert the covariance matrix to a correlation matrix: （10） The GMM marginal distribution and the Gaussian Copula function are integrated into a joint distribution. The joint distribution formula is the product of the GMM marginal distribution and the Gaussian Copula function, as shown in formula (11): （11） Among them, Gaussian Copula function for: （12）。 5. The method for evaluating the time series voltage distribution of a rural distribution network based on probability modeling according to claim 1 is characterized in that: The method of sampling the joint distribution model as the power injection of each node at each time in the rural distribution network and using the Newton-Raphson method to calculate the time series probability power flow is as follows: S1. Generate sampling samples of the joint distribution model through Cholesky decomposition as the power injection of each node at each time in the rural distribution network; The distribution network system has N nodes, each corresponding to a random variable. The standard normal distribution required for joint distribution modeling is N-dimensional, which has the same dimension as the number of nodes. S groups of initial samples are generated from the N-dimensional standard normal distribution: （13） Perform Cholesky decomposition on the correlation coefficient matrix R of the joint distribution to obtain the decomposition matrix L. The calculation formula is shown in formula (14), and then the sample , the formula is shown in formula (15): （14） （15） For each node With sample , the sample Converted to a uniformly distributed variable, the calculation formula is: （16） Solve the inverse cumulative distribution function of the GMM model: （17） The joint distribution of distributed photovoltaic output and load power in the rural distribution network system is calculated to obtain the distributed photovoltaic output sample. and load power samples , ; As the power injection of each node at each moment; rural distribution network system node , At the moment , The power injection is ; S2. Based on the power injection samples obtained in S1, use the Newton-Raphson method to perform time-series probabilistic power flow calculations to obtain time-series power flow voltage results. The nodes of the rural distribution network are divided into three categories: balancing nodes, PQ nodes and PV nodes. Node 1 is set as a balancing node, and its voltage amplitude is and phase angle Fixed; the remaining nodes are set as PQ nodes, and their active power and reactive power is a known value, the voltage amplitude and phase angle is the value to be evaluated; At the moment Establish the power flow equation, node Injected active power and reactive power They are: （18） （19） Where, is the total number of nodes in the rural distribution network, and Node admittance The real and imaginary parts of For each node, the power imbalance is defined as: （20） （21） Where, and Active power and reactive power injected into the node, and is the node active power and reactive power during the iterative calculation process, which is calculated from the voltage estimation value during the iterative calculation process; The partial derivatives of the power imbalance with respect to the voltage amplitude and phase angle are organized into a matrix form to obtain the Jacobian matrix : （22） In the In the iterations, the correction 、 Calculated by the following formula: （23） Update the node voltage using the correction value: （24） （25） Continue iterating until the following convergence conditions are met: （26） Where, is the preset convergence threshold; For each group of joint distribution samples at each moment, the power flow equations of formula (18) to formula (26) are calculated to complete the time series probability power flow calculation, and finally the time series power flow voltage result is obtained. , ; .

6. The method for evaluating the time series voltage distribution of a rural distribution network based on probability modeling according to claim 1 is characterized in that: The implementation method of performing GMM modeling on the power flow voltage results of each node at each time obtained after the time series probability power flow calculation is completed, and using the comprehensive evaluation index based on analytical integration to evaluate the voltage time series distribution characteristics is as follows: System nodes At the moment The power flow voltage results Perform GMM modeling, and its probability density function is: （27） Based on the probability density function of the node voltage, the node voltage is calculated using the analytical integration method. At the moment The voltage over-limit probability is obtained and the voltage over-limit risk value is obtained: （28） Where, is the voltage over-limit risk value, For nodes At the moment The GMM voltage probability density function, and are the upper and lower limits of the node voltage operating range respectively; In the rural distribution network system, the utility preference index function is used to define the node voltage excess severity function, and the calculation formula is as follows: （29） （30） Where, It is a risk factor, the larger its value is, the more sensitive it is to risk; is the voltage excursion index, is the system reference voltage Combining the voltage over-limit risk value and the voltage over-limit severity function, a comprehensive evaluation index for voltage over-limit risk is proposed. , the calculation formula is as follows: （31） Where, For nodes At the moment The voltage over-limit comprehensive risk index; By calculating the comprehensive voltage over-limit risk index, the time periods with large fluctuations in the time-series voltage distribution of each node and the severity of their over-limit risks are identified, and the source-load characteristics and operation optimization of the rural distribution network are analyzed.

7. A rural distribution network time series voltage distribution evaluation system based on probability modeling, characterized by: Applied to the rural distribution network time series voltage distribution evaluation method based on probability modeling as described in any one of claims 1 to 5, the system includes a GMM module, a joint distribution module, a power flow calculation module and an index evaluation module; The GMM module is used to perform GMM modeling on the historical data of distributed photovoltaic output and load power, and quantify the uncertainty of source and load power at each node in the rural distribution network; The joint distribution module is used to construct the correlation between distributed photovoltaic output and load power GMM through Gaussian Copula function, and obtain a joint distribution model that characterizes the correlation and complex distribution characteristics; The power flow calculation module is used to sample the joint distribution model as the power injection of each node at each time in the rural distribution network, and use the Newton-Raphson method to perform time series probability power flow calculation; The index evaluation module is used to perform GMM modeling on the power flow voltage results of each node at each moment after the time series probability power flow calculation is completed, and use the comprehensive evaluation index based on analytical integration to evaluate the voltage time series distribution characteristics.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method for evaluating the time sequence voltage distribution of a rural distribution network based on probability modeling according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the method for evaluating the temporal voltage distribution of a rural distribution network based on probability modeling as claimed in any one of claims 1 to 6 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the method for evaluating the temporal voltage distribution of a rural distribution network based on probability modeling according to any one of claims 1 to 6 are implemented.

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