Power distribution network topology identification method considering feeder flexible interconnection

Abstract

The invention provides a power distribution network topology identification method considering feeder flexible interconnection, and the method comprises the steps: constructing a two-stage topology identification frame, and taking a historical data identification stage as a first stage; a real-time identification stage is regarded as a second stage; after topology recognition operation is executed by adopting an improved expectation maximization algorithm, determining a topology category, adding the topology category into an original record, and generating historical mark data; in the second stage, all the historical marked data obtained in the first stage are adopted for machine learning training to generate a plurality of topological classifiers, the trained classifiers are used for marking real-time measurement, credibility analysis is carried out, and credible marked data are obtained; and according to a result of credibility analysis, sending credible labeled data to a historical labeled database to update machine learning training of a classifier, and re-identifying unreliable data by adopting a Bayesian recursion model. According to the method, the observability of the flexible medium-voltage power distribution network topology is improved.

Description

Technical Field

[0001] The present invention belongs to the field of power distribution, and in particular relates to a distribution network topology identification method considering flexible interconnection of feeders. Background Art

[0002] After the SOP (smart soft switch) is connected, the voltage support and other characteristics provided by the SOP may hinder the transmission of power outage information when fault isolation occurs, reducing the observability of the distribution network topology. The application of the improved expectation maximization algorithm based on digital drive to the topology identification of the distribution network containing SOP provides a feasible technical approach to solve this problem. In the prior art in this regard, a document proposes a method for identifying the topology of the distribution network based on a real-time measurement device. The method uses the expected value and variance of power consumption, approximates the measured value as a random variable of the normal distribution through the maximum likelihood principle, and quickly calculates the confidence level of identifying the correct topology. It is necessary to assume that the measurement error is small, which is difficult to meet in practical applications. In order to be applicable to single-phase, two-phase and three-phase lines, a document proposes a method for automatically determining the topology structure, line parameters and phase connection between customers and lines in the low-voltage system using smart meter measurement data. The method performs granularity and sensitivity analysis and takes into account the quality of smart meter data, but requires sufficient quantity and quality of smart meter data, which is difficult to collect in practice. Other literature proposes a topology identification algorithm based on a small number of line current sensor measurements and available node power injection pseudo-measurements, using multiple measurement snapshots to improve the accuracy of TI and its robustness to pseudo-measurement errors. However, it requires precise current measurements and pseudo-measurements, and measurement errors may exist in practical applications.

[0003] Existing data-driven topology recognition technologies require sufficient smart meter data quality and coverage. In practical applications, due to economic and management constraints, the available data is limited and of average quality. Factors such as noise and measurement errors will also affect the accuracy of the algorithm. In addition, the distribution network structure is relatively simple and the factors considered are limited, making it unsuitable for scenarios such as flexible distribution networks.

[0004] As the end of the power grid, the distribution network has a low coverage rate of automation devices and weak topological observability, which affects the safety and reliability of the power grid. With the access of a high proportion of distributed energy, the management of the distribution network has become more complicated. In addition, the existence of SOP will interfere with the identification of distribution network topology changes, especially after fault isolation, the voltage support provided by SOP may hinder the transmission of power outage information. Therefore, improving the ability of SOP to identify the topological structure of the distribution network and solving the problem of unclear topological structure when its state changes are crucial for the stable operation of the new distribution network. In the data-driven distribution network topology identification research, in order to accurately identify the topological structure of the distribution network, it is usually necessary to assist with automated measurement devices or collect measurement data of known topological categories. However, due to economic and management factors, the number of automated devices is limited, and it is usually difficult to know the number of topological categories in advance in practical applications. At present, the application scenarios of topological identification are mostly based on structures such as radial, ring and island configurations, and most of them do not consider the impact of SOP in flexible interconnected distribution networks. Summary of the invention

[0005] To solve the above technical problems, the present invention provides a distribution network topology identification method considering flexible interconnection of feeders, and proposes an improved expectation maximization topology identification method based on the basic characteristics of a medium-voltage distribution network containing SOPs. The method performs topological category identification on historical batch data of node pairs containing SOPs to obtain historical labeled data, and according to a machine learning method, uses the historical labeled data to train a feasible classifier, predicts the real-time topology, performs credibility analysis and re-identification, thereby improving the observability of the flexible medium-voltage distribution network topology.

[0006] In order to achieve the above object, the present invention adopts the following technical solution: A distribution network topology identification method considering feeder flexible interconnection includes the following steps: Step 1: Build a two-stage topology recognition framework, treating the historical data recognition stage as the first stage, where a record represents the node measurement value at a certain point in time. , vector Including voltage amplitude and phase angle, vector Including active and reactive injection; where i is the i-th record and j is the j-th topology category; the real-time identification stage is regarded as the second stage; Step 2: After performing the topology recognition operation using the improved expectation maximization algorithm, determine the topology category , add it to the original record to generate historical tag data ; Step 3: In the second stage, all the historical labeled data obtained in the first stage are used for machine learning training to generate multiple topological classifiers, and the trained classifiers are used to label the real-time measurements and perform credibility analysis to obtain credible labeled data; Step 4: Based on the results of the credibility analysis, the credible labeled data is sent to the historical label database to update the machine learning training of the classifier, and the unreliable data is re-identified using the Bayesian recursive model.

[0007] Beneficial effects: The present invention proposes an improved expectation maximization algorithm that can handle an unknown number of topological categories without pre-specifying the number of categories. This is an important improvement to the traditional EM (expectation maximization) algorithm. The segmentation strategy adopted by the improved algorithm effectively processes mixed topological data by merging and segmenting topological categories in the iterative process. The algorithm designs an optimized iterative calculation process, reduces the consumption of computing resources, and improves the efficiency of processing large-scale data sets. The algorithm trains the classifier through historical data and uses it for the prediction of real-time data. At the same time, the training model is updated through real-time data, realizing the effective combination of historical and real-time data.

[0008] The method of the present invention has low requirements on the quality and accuracy of measurement data, is applicable to data commonly collected in the current distribution network, can process an unknown number of topological categories, and effectively process mixed topological data. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 This is a schematic diagram of a distributed flexible distribution network; Figure 2 It is a principle framework diagram of a distribution network topology identification method considering feeder flexible interconnection of the present invention; Figure 3 Flowchart for improving the expectation-maximization algorithm; Figure 4a , Figure 4b , Figure 4c is the topology recognition result; where Figure 4a The topology recognition results of SOP in the (15,16)(12,22) node pair scenario (5 topology types and their proportions). Figure 4b The topology recognition results of SOP in the (15,16)(21,8) node pair scenario (5 topology types and their proportions). Figure 4c The topology recognition results of SOP in the (15,16)(12.22) node pair scenario (3 topology types and their proportions); Figure 5a , Figure 5b The log-probability plots before and after correction of the test samples. DETAILED DESCRIPTION

[0010] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0011] Consider Figure 1 The distributed energy flexible distribution network shown in the figure, each feeder in the system is composed of distributed generation components, SOP components, and power load components.

[0012] like Figure 2 As shown, a distribution network topology identification method considering feeder flexible interconnection of the present invention comprises the following steps: Step 1: Build a two-stage topology recognition framework, treating the historical data recognition stage as the first stage, where a record represents the node measurement value at a certain point in time. , vector Including voltage amplitude and phase angle, vector Including active and reactive injection; where i is the i-th record and j is the j-th topology category; the real-time identification stage is regarded as the second stage.

[0013] Step 2: After performing the topology recognition operation using the improved expectation maximization algorithm, determine the topology category , add it to the original record to generate labeled data .

[0014] Step 3: In the second stage, all the historical labeled data obtained in the first stage are used for machine learning training to generate multiple topological classifiers, and the trained classifiers are used to label the real-time measurements and perform credibility analysis to obtain credible labeled data.

[0015] Step 4: Based on the results of the credibility analysis, the credible labeled data is sent to the historical label database to update the machine learning training of the classifier, and the unreliable data is re-identified using the Bayesian recursive model.

[0016] Specifically, the step 2 includes: The improved expectation maximization algorithm is a variant of the EM algorithm, which is used to deal with the problem of unknown number of topological categories in historical data. The unsupervised classification of historical data can be regarded as a parameter estimation problem for unknown mixtures of topological categories. The historical data recognition model integrates topological estimation and category selection in one algorithm. The parameters of the improved expectation maximization algorithm include: (1) Parameter estimation: The parameters are expressed as: ; in, are the parameters in the historical topology identification problem, is the total number of topological categories, For the sample The proportion of records in topological categories, For the A topology parameter vector of topology classes, representing the line state with unknown connectivity. The dimension of is the number of rows of unknown states, the elements are binary, and the corresponding lines are 1 when connected, otherwise they are 0.

[0017] (2) Judgment index: If after EM iterations, two or more topological classes are found to have the same topological parameter vector ( ), then its topological category proportion Add and remove duplicate topological categories.

[0018] If all topological categories account for If both are not 0 and there are no repeated topological parameters, a topological category is selected for splitting. for: ; in, is the i-th record, is the number of records, is the topological parameter vector of the jth topological category, For the parameters Internal given In the case The probability of is the conditional distribution of the jth topology of the i-th record in the sample.

[0019] The category with the smallest judgment index is selected for splitting, because it means that the data points within this category have the lowest fit with the current model and may contain multiple different topological structures.

[0020] (3) Probability density: For a given topology class , probability density function It can be expressed as an error The Gaussian distribution has a mean of 0 and a covariance matrix of Determined by the standard deviation of the measurement error. The probability density calculation of the distribution network system containing SOP is based on the power flow equation, which is: ; ; ; ; in, They are two nodes connected to the SOP switch. is the active power balance equation, is the reactive power balance equation, is the active / reactive power generated at the node, is the active / reactive power of the load, is the active / reactive power of the converter in the SOP.

[0021] , They represent the active power and reactive power injected into the grid at node i: ; ; in, , are the conductance and susceptance on the jth line, , is the voltage amplitude and phase angle of the ith node, is the total number of lines. is an element in the PDN association matrix L, Indicates that the j-th line leaves, enters, or separates from the ith node. , is the element in the PDN association matrix u, where , They represent the starting and ending node numbers of the j-th row respectively.

[0022] According to the power flow equation and node voltage measurements Calculate the actual power value Then perform Taylor expansion and use the first-order Taylor expansion to approximate the power measurement error , which represents the measured value The actual power value Based on the Gaussian distribution assumption of the error, in a given topology In the case of The probability density function of .

[0023] like Figure 3 As shown, the improved expectation maximization algorithm includes the following steps: Step 2.1: Initialize, initialize the number of topological categories, assuming that there is Topological categories, starting with two different topological structures; parameter initialization, initializing each topological category parameter including topological connection status and category proportion .generally, Initialized to equal values, if any categories, then the initial proportion of each category is .

[0024] Step 2.2: EM iteration, perform standard EM algorithm iteration.

[0025] Step 2.3: Topological category merging, determine whether there are parameters of two or more topological categories If they are the same, they will be merged into one category and the proportion of that category will be increased. And set the proportion of the other category to 0.

[0026] Step 2.4: Topological category splitting, if no category can be merged, select a judgment index The smallest topological category is split, and new topological categories that may exist in the data are added.

[0027] Split the selected topological category into two new categories and increase the number of topological categories. If the algorithm decides to split the category in the kth iteration , then in the E and M steps of the k+1th iteration, except Other topological categories besides , , ..., , , ..., ) will be fixed and will not be updated. , its topological parameters will be updated in the new iteration, including adjusting the connection status, voltage amplitude, phase angle and other parameters of the line.

[0028] Step E is to adjust the parameters according to the current The estimated Elements in the matrix . Conditional distribution It can also be viewed as the posterior probability that the i-th record belongs to the j-th topological category.

[0029] ; Step M Update Parameters Estimated value: ; ; Optimization Problem The variables in and Closely related to power flow calculation. The model in is a nonlinear integer programming problem and also a non-convex problem.

[0030] Step 2.5: Repeat steps 2.2 to 2.3 until the maximum number of iterations is reached and the number of topological categories is finally determined. , the proportion of each category , and the topological connection status of each category , get the historical marking data.

[0031] Step 2.6: Train classifiers based on historical data, using the labeled data generated by the improved expectation maximization algorithm, and train multiple topology classifiers through machine learning methods. These classifiers will serve as tools in the real-time topology recognition phase, with node measurement values ​​as input and corresponding topology categories as output.

[0032] Step 2.7: Topology recognition of real-time data, use the trained classifier to predict the topology category of the real-time measurement data. When the diversity and richness of the training data are sufficient, the classifier can efficiently predict the topology category of the real-time data.

[0033] Step 2.8: Perform credibility analysis on the prediction results of the classifier by calculating the logarithmic probability that each record belongs to its predicted topological category. The logarithmic probability formula is: ; in, Represents a given topological class Next, record The probability density function of . is the residual vector based on the measurement error, ( is the total number of nodes). is related to the topological category The related covariance matrix, exp represents the exponential function, and the superscript T represents the transpose of the matrix. and The same can also be expressed as ,in[ ] is a measurement record, [ ] is the corresponding real value. In use and When the error is obtained, it can be calculated based on the probability density function of the specified error distribution. However, in practice, it is difficult to accurately obtain is not easy. Here, we will use a probability density calculation method that relies only on node measurements. Assuming the measurement error and Obey Gaussian distribution ~ and , then the real value and Satisfies the following expression: ; ; Using a first-order Taylor expansion: ; ; From the above formula, we can see that ,in .but Can be replaced by , which only contains measured values.

[0034] Covariance matrix The standard deviation in It can be determined based on the relative error% of the measurement. For a given average value The measured value of It can cover more than 99.7% of the Gaussian curve area. , The calculation expression is: ; The log probability is compared with a set threshold to determine the confidence of the prediction result.

[0035] Step 2.9: Perform error correction. For prediction results that are judged to be unreliable, use the Bayesian recursive model to re-identify. The iterative formula of the Bayesian recursive model is: ; in, It is in In the iterations, given the error vector When , the record belongs to the topological category The posterior probability of . is the total number of possible topological categories.

[0036] The model considers all possible topological classes and updates the probability of each topological class based on the current measurement error and the posterior probability of the previous iteration.

[0037] Step 2.10: Dynamically update and maintain, add the topological labels of the real-time measurement data that have passed the credibility analysis and error correction to the historical tag database to regularly update the training of the classifier, thereby improving the accuracy of the classifier.

[0038] Step 2.11: Repeat steps 2.1 to 2.7 until all input real-time data can be reliably identified.

[0039] The present invention proposes a data-driven method for improving the expectation maximization algorithm for identifying the topological structure of the distribution network for a flexible interconnected distribution network containing SOP. Topological identification is performed based on a 33-node system, which contains 32 branches, of which 2 branches are SOP node pairs and 8 branches have unknown connection status. Topological identification is performed on three scenarios of SOP in node pairs (15,16)(12,22), (15,16)(21,8), and (15,16)(12,22). The simulation results of topological identification (topological types and proportions) are as follows: Figure 4a , Figure 4b , Figure 4c As shown in the figure, it can be seen that the topology recognition method based on the improved expectation maximization algorithm has a good recognition effect, and can also improve the topology identifiability of the SOP distribution network, which has good practical application value; among them, Figure 4a The topology recognition results of SOP in the (15,16)(12,22) node pair scenario (5 topology types and their proportions). Figure 4b The topology recognition results of SOP in the (15,16)(21,8) node pair scenario (5 topology types and their proportions). Figure 4c The topology recognition results of SOP in the (15,16)(12.22) node pair scenario (3 topology types and their proportions).

[0040] Figure 5a , gives the real-time recognition based on the classifier, and identifies the topological category containing a SOP node pair through a linear vector machine. The logarithmic probability of each record can be seen. Since the topological category of records 66-86 does not exist in the historical data, its logarithmic probability is much smaller than other records. The threshold of the logarithmic probability is obtained based on a large amount of data of correct topology and incorrect topology, which is used to determine whether to assign an unreliable topology to the data record. According to the deviation of the data, the threshold is set to -50, and records 66 to 96 are regarded as unreliable records, such as Figure 5a As shown. It is put into the classification learner for retraining, and then retested with the trained classifier. After error correction, the new logarithmic probability is within the normal range, as shown in Figure 5b As shown in the figure, the recognition accuracy is improved from 96.2% to 98.9%.

Claims

1. A distribution network topology identification method considering flexible interconnection of feeders, characterized in that: The steps include: Step 1: Build a two-stage topology recognition framework, treating the historical data recognition stage as the first stage, where a record represents the node measurement value at a certain point in time. , vector Including voltage amplitude and phase angle, vector Including active and reactive injection; where i is the i-th record and j is the j-th topology category; the real-time identification stage is regarded as the second stage; Step 2: After performing the topology recognition operation using the improved expectation maximization algorithm, determine the topology category , add it to the original record to generate historical tag data ; Step 3: In the second stage, all the historical labeled data obtained in the first stage are used for machine learning training to generate multiple topological classifiers, and the trained classifiers are used to label the real-time measurements and perform credibility analysis to obtain credible labeled data; Step 4: Based on the results of the credibility analysis, the credible labeled data is sent to the historical label database to update the machine learning training of the classifier, and the unreliable data is re-identified using the Bayesian recursive model.

2. A distribution network topology identification method considering feeder flexible interconnection according to claim 1, characterized in that: The step 2 comprises: The improved expectation-maximization algorithm is a variant of the expectation-maximization algorithm, which is used to deal with the problem of unknown number of topological categories in historical data; the unsupervised classification of historical data is regarded as a parameter estimation problem of unknown mixture of topological categories; the historical data recognition model integrates topological estimation and category selection in one algorithm; the parameters of the improved expectation-maximization algorithm include: (1) Parameter estimation: The parameters are expressed as: ； in, are the parameters in the historical topology identification problem, is the total number of topological categories, For the sample The proportion of records in topological categories, For the A topology parameter vector of topology categories, representing the line status with unknown connectivity; The dimension is the number of rows of unknown states, the elements are binary, and the corresponding lines are 1 when connected, otherwise they are 0; (2) Judgment index: If after EM iterations, it is found that there are two or more topological classes with the same topological parameter vector, that is, , then its topological category proportion Add and remove duplicate topological categories; If all topological categories account for If both are not 0 and there are no repeated topological parameters, a topological category is selected for splitting; Judgment Index for: ； in, is the i-th record, is the number of records, is the topological parameter vector of the jth topological category, For the parameters Internal given In the case The probability of is the conditional distribution of the jth topology of the i-th record in the sample; Select the category with the smallest judgment index for splitting; (3) Probability density: For a given topology class , probability density function Expressed as error The Gaussian distribution has a mean of 0 and a covariance matrix of Determined by the standard deviation of the measurement error; the probability density calculation of the SOP distribution network system is based on the power flow equation, which is: ； ； ； ； in, They are two nodes connected to the SOP switch. is the active power balance equation, is the reactive power balance equation, is the active / reactive power generated at the node, is the active / reactive power of the load, is the active / reactive power of the converter in the SOP; , They represent the active power and reactive power injected into the grid at node i: ； ； in, , are the conductance and susceptance on the jth line, , is the voltage amplitude and phase angle of the ith node, is the total number of lines; is an element in the PDN association matrix L, It indicates that the j-th line leaves, enters or separates from the i-th node; , is the element in the PDN association matrix u, where , Respectively represent the "start" and "end" node numbers of the j-th row; According to the power flow equation and node voltage measurements Calculate the actual power value ; Then perform Taylor expansion and use the first-order Taylor expansion to approximate the power measurement error , which represents the measured value The actual power value The difference between the two; Based on the Gaussian distribution assumption of the error, in a given topology In the case of The probability density function of .

3. A distribution network topology identification method considering feeder flexible interconnection according to claim 2, characterized in that: The improved expectation maximization algorithm includes the following steps: Step 2.1: Initialize, initialize the number of topological categories, assuming that there is Topological categories, starting with two different topological structures; parameter initialization, initializing each topological category parameter including topological connection status and category proportion , Initialized to equal values, if any categories, then the initial proportion of each category is ; Step 2.2: Expectation-maximization iteration, perform standard expectation-maximization algorithm iteration; Step 2.3: Topological category merging, determine whether there are parameters of two or more topological categories Same; if the same, they will be merged into one category and the proportion of this category will be increased And set the proportion of the other category to 0; Step 2.4: Topological category splitting, if no category can be merged, select a judgment index The smallest topological category is split to increase the new topological categories that may exist in the data; Step 2.5: Repeat steps 2.2 to 2.3 until the maximum number of iterations is reached and the number of topological categories is finally determined. , the proportion of each category , and the topological connection status of each category , get the historical marking data; Step 2.6: Train the classifier based on historical data, and use the labeled data generated by the improved expectation-maximization algorithm to train multiple topological classifiers through machine learning methods; Step 2.7: Topology recognition of real-time data, using the trained classifier to predict the topology category of the real-time measurement data; Step 2.8: Perform credibility analysis on the prediction results of the classifier by calculating the logarithmic probability that each record belongs to its predicted topological category; Step 2.9: Perform error correction. For prediction results that are judged to be unreliable, use the Bayesian recursive model to re-identify; Step 2.10: Dynamically update and maintain, add the topological labels of the real-time measurement data that have passed the credibility analysis and error correction to the historical tag database to regularly update the training of the classifier, thereby improving the accuracy of the classifier; Step 2.11: Repeat steps 2.1 to 2.7 until all input real-time data can be reliably identified.

4. A distribution network topology identification method considering feeder flexible interconnection according to claim 3, characterized in that: The step 2.4 includes: splitting the selected topological category into two new categories, increasing the number of topological categories; if the algorithm Determine the split category in the round iteration , then in the E and M steps of the k+1th iteration, except The topology parameters of other topology categories except for , , ..., , , ..., ; For the split categories , its topological parameters will be updated in the new iteration, including adjusting the connection status, voltage amplitude, and phase angle of the line.

5. A distribution network topology identification method considering feeder flexible interconnection according to claim 3, characterized in that: In step 2.6, the topology classifier is used as a tool in the real-time topology identification stage, with the input being the node measurement value and the output being the corresponding topology category.

6. A distribution network topology identification method considering feeder flexible interconnection according to claim 3, characterized in that: In step 2.8, the logarithmic probability formula is: ； in, Represents a given topological class Next, record The probability density function of is the residual vector based on the measurement error, , is the total number of nodes; is related to the topological category The relevant covariance matrix, exp represents the exponential function, and the superscript T represents the transpose of the matrix; and Same, or expressed as ,in[ ] is a measurement record, [ ] is the corresponding real value; In use and When the error is obtained, it is calculated according to the probability density function of the specified error distribution; The log probability is compared with a set threshold to determine the confidence of the prediction result.

7. A distribution network topology identification method considering feeder flexible interconnection according to claim 3, characterized in that: In step 2.9, the iteration formula of the Bayesian recursive model is: ； in, It is in In the iterations, given the error vector When , the record belongs to the topological category The posterior probability of is the total number of possible topological categories; the Bayesian recursive model considers all possible topological categories and updates the probability of each topological category based on the current measurement error and the posterior probability of the previous iteration.

Images