Distribution network abnormal data prediction method and system based on data analysis

By clustering and predicting the distribution network data, combining BP neural network and locust optimization algorithm, the problem of predicting abnormal data in distribution network is solved, the stability and reliability of the power system are improved, and the risk of power outage is reduced.

CN119322774AActive Publication Date: 2025-01-17WUZHONG POWER SUPPLY COMPANY STATE GRID NINGXIA ELECTRIC POWER
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Patent Information

Application Number
CN202411444515.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Priority Date
2024-10-11
Filing Date
2024-10-16
Publication Date
2025-01-17
Estimated Expiration
2044-10-16

AI Technical Summary

Technical Problem

The prior art is difficult to effectively predict and prevent abnormal data from distribution networks, resulting in reduced stability and reliability of the power system, increasing maintenance costs, and even large-scale power outages.

Method used

By collecting distribution network data of multiple historical time points of multiple types, clustering and classification, the average value of non-failed and faulty abnormal time periods is calculated, and combined with the BP neural network prediction model and locust optimization algorithm, from two Predict and analyze historical and future distribution network data from an angle to reduce data contingency and improve analysis accuracy.

Benefits of technology

Accurate prediction and analysis of abnormal data of distribution networks is realized, the stability and reliability of the power system are improved, maintenance costs are reduced, and the occurrence of power outages is reduced.

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Abstract

The invention discloses a distribution network abnormal data prediction method and system based on data analysis, and relates to the field of abnormal data prediction analysis, and the method comprises the steps: carrying out the average value calculation of an initial non-fault type abnormal time period matrix and an initial fault type abnormal time period matrix, and improving the accuracy of subsequent analysis; the historical distribution network data matrix is predicted from two aspects, one aspect is to predict the distribution network data in future time according to the change trend of the distribution network data at a plurality of historical time points along with time; secondly, by searching the periodicity of the abnormal data in the distribution network and comparing the periodicity with the existing abnormal data of the distribution network with the known periodicity, the most similar existing abnormal data of the distribution network is used as the data of the distribution network at the future time point; two analysis results are obtained from the two angles, and finally the two analysis results are comprehensively compared and analyzed, so that the final analysis result is more comprehensive and accurate.
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Description

Technical Field

[0001] The present invention belongs to the field of abnormal data prediction and analysis, and in particular, relates to a distribution network abnormal data prediction method and system based on data analysis. Background Art

[0002] Chinese patent CN117472898B discloses a distribution network abnormal data error correction method and system based on fusion, which collects distribution network data and determines whether there is abnormal data therein; if there is second power abnormal data, the position of the abnormal data is obtained, and the power data sequence is divided into a normal power data subsequence and an abnormal power data subsequence; the normal power data subsequence is input into a preset LSTM neural network for training to obtain a first target LSTM model; at least one normal power data associated with a certain abnormal power data is input into the first target LSTM model to obtain predicted power data, and the predicted power data replaces the abnormal power data.

[0003] Abnormal distribution network data may reduce the stability and reliability of the power system, affect the power quality, increase maintenance costs, and may even cause large-scale power outages; therefore, if the abnormal distribution network data cannot be predicted, measures cannot be taken in advance to prevent the occurrence of the above situations, thereby causing economic losses to enterprises and even affecting people’s daily lives. Summary of the invention

[0004] In view of the problems in the related art, the present invention proposes a distribution network abnormal data prediction method and system based on data analysis to overcome the above-mentioned technical problems existing in the existing related art.

[0005] In order to solve the above technical problems, the present invention is achieved through the following technical solutions:

[0006] The present invention is a distribution network abnormal data prediction method based on data analysis, comprising the following steps:

[0007] S1. Collect distribution network data of various types and multiple historical time points to obtain a distribution network data matrix set;

[0008] S2. Perform clustering operation on the distribution network data matrix set to obtain a distribution network data classification matrix; then classify the distribution network data classification matrix to obtain an initial non-fault type abnormal time period matrix and an initial fault type abnormal time period matrix; calculate the average value of the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix to obtain an average matrix of the non-fault type abnormal time period set and an average matrix of the fault type abnormal time period set;

[0009] S3, collecting distribution network data of multiple types and multiple historical time points to be predicted again to obtain a historical distribution network data matrix; predicting and classifying and analyzing the distribution network data at future times according to the historical distribution network data matrix to obtain a first analysis result;

[0010] S4. Classify the distribution network abnormality data in the historical distribution network data matrix to obtain a historical non-fault abnormal time period matrix and a historical fault abnormal time period matrix;

[0011] S5. Perform a prediction analysis on the historical non-fault type abnormal time period matrix and the historical fault type abnormal time period matrix according to the average matrix of the non-fault type abnormal time period set and the average matrix of the fault type abnormal time period set to obtain a second analysis result;

[0012] S6. Compare the first analysis result and the second analysis result to obtain a final non-fault type abnormal time period matrix and a final fault type abnormal time period matrix;

[0013] Different distribution network data have different changing trends over time and need to be analyzed separately. Therefore, collecting distribution network data of various types and multiple historical time points provides data support for the subsequent analysis of the time point distribution of abnormal data in the distribution network data; clustering the distribution network data matrix set, the distribution network data with similar data are aggregated, which facilitates the subsequent calculation of the average value of the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix; by calculating the average value of the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix, the sporadic nature of the data is reduced, thereby improving the accuracy of subsequent analysis; by collecting and predicting distribution network data of various types and multiple historical time points, a data basis is provided for subsequent prediction operations; this scheme predicts the historical distribution network data matrix from two perspectives. One is to predict the distribution network data in the future based on the changing trend of the distribution network data of multiple historical time points over time, and to perform the prediction on the predicted future distribution network data. The first step is to classify and analyze the abnormal data in the distribution network data at the future time point; because electricity consumption and production are affected by daily life patterns, industrial production cycles, seasonal changes and other factors; for example, household and commercial electricity consumption will have different patterns on weekdays and weekends, daytime and nighttime, while industrial electricity consumption may have more obvious periodicity, such as changes by shift or production cycle; in addition, seasonal changes will also affect electricity demand, such as the increase in power load caused by the increase in air conditioning use in summer, so the distribution network data is usually periodic; thus, the second is to find the periodicity of abnormal data in the distribution network, compare the distribution network data collected at multiple historical time points with the existing distribution network abnormal data with known cycles, and use the most similar existing distribution network abnormal data as the distribution network data at the future time point, and then classify and analyze the distribution network data at the future time point; obtain two analysis results from these two perspectives, and finally compare and analyze the two analysis results comprehensively, so that the final analysis result is more comprehensive and accurate.

[0014] Preferably, the S1 comprises the following steps:

[0015] S11, set a plurality of distribution network data types and corresponding data statistical cycles to obtain a distribution network data type set a={a 1 ,a 2 ,...,a i ,...,a a′} and data statistical period set b′={b 1 ′,b 2 ′,...,b i ′,...,b a ″},a i represents the type of the i-th type of network configuration data set, a′ represents the total number of network configuration types set; b i' represents the data statistics period set for the i-th type of distribution network data;

[0016] Set the same number of historical time points for the data statistical period corresponding to each distribution network data type to obtain the historical time point matrix as follows,

[0017]

[0018] in, Indicates the jth historical time point set for the data statistics period corresponding to the i-th type of distribution network data. Indicates the total number of historical time points set for the data statistics period corresponding to each type of distribution network data;

[0019] According to the historical time point matrix And the collection distribution network data type set a = {a 1 ,a 2 ,...,a i ,...,a a′}, and obtain a distribution network data matrix set;

[0020] S12: Set the corresponding abnormal data threshold for each type of distribution network data to obtain the abnormal data threshold set. represents the abnormal data threshold set for the i-th type of network configuration data;

[0021] The distribution network data types include electrical parameters such as voltage, current, active power, reactive power, frequency, and circuit breaker and isolation status information. The change cycles of these different types of distribution network data are different. Therefore, a targeted data statistical cycle is set for each type of distribution network data. This makes the collected distribution network data of each type more complete and reflects its periodicity. Secondly, the abnormal data thresholds of different types of distribution network data are also different. Therefore, the corresponding abnormal data thresholds are set for different types of distribution network data, which improves the accuracy of subsequent analysis.

[0022] Preferably, S2 comprises the following steps:

[0023] S21, performing a clustering operation on each distribution network data matrix in the distribution network data matrix set to obtain a distribution network data classification matrix c; as follows,

[0024]

[0025] Among them, c ij represents the j-th classification of the distribution network data matrix corresponding to the i-th distribution network data type; cijkk′ Indicates c ij The distribution network data at the k′th historical time point in the kth data statistical period; Indicates c ij The total number of data statistical cycles corresponding to the distribution network data;

[0026] S22. Setting the threshold value set for the number of consecutive time points represents the continuous time point number threshold corresponding to the i-th type of network configuration data; and the abnormal data threshold set When the time point data of the distribution network abnormal data in each cycle of each classified distribution network data matrix corresponding to each distribution network data type in the distribution network data classification matrix c is less than the corresponding continuous time point number threshold, the time period corresponding to the distribution network abnormal data is used as the non-fault type abnormal time period; otherwise, the time period corresponding to the distribution network abnormal data is used as the fault type abnormal time period; the initial non-fault type abnormal time period matrix d is obtained. 1 and the initial fault type abnormal time period matrix d 2 ;as follows,

[0027]

[0028] Among them, d 1ij and d 2ij They represent the non-fault abnormal time period matrix and fault abnormal time period matrix of the jth classification corresponding to the i-th distribution network data type respectively; they are as follows,

[0029]

[0030] in, Respectively represent d 1ij The starting time point and the ending time point of the k′th non-fault abnormal time period in the kth data statistical period; Respectively represent d 2ij The starting time point and the ending time point of the k′th fault type abnormal time period in the kth data statistical period; d 1 ' ij d 2 ' ij Respectively represent d 1ij The total number of non-fault abnormal time periods in each data statistical period and d 2ij The total number of fault-type abnormal time periods in each data statistical period;

[0031] S23, respectively calculating the initial non-fault type abnormal time period matrix d 1 and the initial fault type abnormal time period matrix d2 The average value of the start and end time points of each non-fault abnormal time period in each classification and the average value of the start and end time points of each fault abnormal time period are obtained to obtain the average matrix d of the non-fault abnormal time period set 3 And the average matrix d of the fault type abnormal time period set 4 ; They are as follows,

[0032]

[0033] Among them, d 3ij d 4ij They represent the non-fault type abnormal average time period set and the fault type abnormal average time period set of the jth classification corresponding to the i-th distribution network data type; they are as follows,

[0034]

[0035] in, Respectively represent d 3ij The average value of the starting time point and the ending time point of the k′th non-fault type abnormal average time period in ; Respectively represent d 4ij The average value of the starting time point and the ending time point of the k′th fault type abnormal average time period in the calculation formula are as follows:

[0036]

[0037] Since there are many possibilities for the occurrence of abnormal data, such as sudden centralized power consumption or failure of each electrical component; for the former, it is temporary, so the abnormal data caused by it is short-lived, and when the centralized power consumption ends, the abnormal data will return to normal; while for the latter, it is permanent and irreversible, requiring manual repair; therefore, it lasts longer; based on the above, in this scheme, the abnormal data appearing in the distribution network data is divided into non-fault-type abnormal time periods, that is, the time periods where the abnormal data that can be automatically recovered is located, and fault-type abnormal time periods, that is, the time periods where the abnormal data that cannot be recovered is located.

[0038] Preferably, the S21 comprises the following steps:

[0039] S211. Building locust populations represents the i-th locust in the locust population, represents the size of the locust population; sets the maximum number of iterations of the locust population to e 1 , the current number of iterations is e 2 , the dimension of the search space is

[0040] S212, randomly selecting a number of distribution network data sets from the distribution network data matrix set as initial classification center data for multiple times to obtain an initial classification center data matrix set; using the initial classification center data matrix set as an initial position matrix set of the locust population e′ k′ represents the initial position matrix of the i-th locust in the locust population; as follows,

[0041]

[0042] Among them, e′ k′ij Represents e′ k′ The initial classification center data set of the jth classification corresponding to the i-th distribution network data type, e′ k′ijk Represents e′ k′ij The initial classification center data at the k-th historical time point;

[0043] S213, calculating the distribution network data matrix set b according to the initial position matrix set 2 = {b 21 ,b 22 ,...,b 2i ,...,b 2a′ The sum of the Euclidean distances between each distribution network dataset and the corresponding classification center dataset in} is used to obtain the Euclidean distance data matrix as follows,

[0044]

[0045] in, Represents e′ k′ij Each distribution network data in the corresponding category is sent to e′ k′ij The sum of the Euclidean distances between ;

[0046] According to the Euclidean distance data matrix Set the fitness function of the locust population as follows,

[0047]

[0048] S214, start iteration, before iteration, the current iteration number e 2 Set to 1; the fitness function of the locust population is used in the first round of iteration Calculate the initial position matrix set The fitness value of the initial position matrix of each locust in the first fitness value set is obtained to obtain a first fitness value set; the maximum fitness value and the initial position of the corresponding locust are selected from the first fitness value set as the first global optimal fitness value and the first global optimal position respectively; the initial position matrix set is adjusted according to the first global optimal fitness value and the first global optimal position. The initial position matrix of each locust is updated, and after the update is completed, the current number of iterations e 2 Add 1 and enter the next iteration;

[0049] Except for the first round of iteration, the fitness function of the locust population is used in each other round of iteration. Calculate the fitness value of the position matrix of each locust obtained in the previous round of iteration to obtain a second fitness value set; select the maximum fitness value and the initial position of the corresponding locust from the second fitness value set as the second global optimal fitness and the second global optimal position respectively; update the position matrix of each locust obtained in the previous round of iteration according to the second global optimal fitness and the second global optimal position; after the update is completed, update the current iteration number e 2 Add 1 and enter the next iteration;

[0050] S215, when e 2 ≥e 1 When , the iteration is stopped to obtain the final global optimal position; the final global optimal position is used as the final classification center data matrix; the distribution network data matrix set b is quantized according to the final classification center data matrix 2 = {b 21 ,b 22 ,...,b 2i ,...,b 2a′} to classify and obtain the distribution network data classification matrix c;

[0051] The locust optimization algorithm has the advantages of balancing global search and local search, having strong global search capabilities, and being able to find better solutions in complex search spaces. Therefore, in this scheme, the locust optimization algorithm is used to perform multiple iterations to optimize each classification center data in the distribution network data matrix set, and the overall discrete degree of the distribution network data matrix set is used as its fitness function. As the iteration proceeds, the overall discrete degree of the distribution network data matrix set will become lower and lower, that is, the classification center data found will be more accurate.

[0052] Preferably, S3 comprises the following steps:

[0053] S31. Setting a set of time points to be predicted and future time points f 1i 、f 2iThey represent the i-th time point to be predicted and the future time point respectively, and f 1 ′、f 2 ′ respectively represent the total number of the set time points to be predicted and the future time points;

[0054] According to the network configuration data type set a={a 1 ,a 2 ,...,a i ,...,a a′} and the set of time points to be predicted Collect distribution network data of various distribution network data types to obtain historical distribution network data matrix as follows,

[0055]

[0056] in, The network configuration data representing the i-th network configuration data type corresponding to the j-th time point to be predicted;

[0057] S32, construct an initial BP neural network prediction model and set the training data ratio and the test data ratio; according to the training data ratio and the test data ratio, the historical distribution network data matrix Perform data division to obtain a historical distribution network training data matrix, a historical distribution network test data matrix, and a historical distribution network to-be-predicted data matrix;

[0058] The historical distribution network training data matrix and the historical distribution network test data matrix are respectively used to train and test the initial BP neural network prediction model; after the training and testing are completed, the final BP neural network prediction model is obtained;

[0059] S33, cooperate with the future time point set The final BP neural network prediction model is used to perform prediction operations on the historical distribution network to be predicted data matrix to obtain the future distribution network data matrix as follows,

[0060]

[0061] in, Represents the predicted network data of the i-th network data type corresponding to the j-th future time point;

[0062] S34, the future distribution network data matrix The distribution network data and abnormal data threshold set at each future time point in Compare with the corresponding abnormal data threshold in to obtain the future distribution network abnormal time period matrix;

[0063] S35, cooperate with the threshold value set of the number of consecutive time points Classify each future distribution network abnormal time period in the future distribution network abnormal time period matrix to obtain the first non-fault abnormal time period matrix to be analyzed and the first fault type abnormal time period matrix h to be analyzed; respectively,

[0064]

[0065] in, Represent the future distribution network data matrix respectively The starting time point and the ending time point of the jth non-fault abnormal time period corresponding to the i-th distribution network data type; Represent the future distribution network data matrix respectively The starting time point and the ending time point of the jth fault type abnormal time period corresponding to the i-th distribution network data type; h i ′ respectively represent the future distribution network data matrix The total number of non-fault abnormal time periods and fault abnormal time periods corresponding to the i-th type of distribution network data type;

[0066] By constructing the final BP neural network prediction model, a prediction model is provided for the subsequent prediction operation of the historical distribution network data matrix to be predicted.

[0067] Preferably, in S32, the historical distribution network training data matrix and the historical distribution network test data matrix are respectively used to train and test the initial BP neural network prediction model; after the training and testing are completed, obtaining the final BP neural network prediction model includes the following steps:

[0068] S321, setting a training error threshold; inputting the historical distribution network training data matrix into the initial BP neural network prediction model for training; during the training process, when the training error is less than the training error threshold, stopping the training operation to obtain a trained BP neural network prediction model; otherwise, continuing the training until the training error is less than the training error threshold;

[0069] S322, set a test accuracy threshold; input the historical distribution network test data matrix into the trained BP neural network prediction model for testing, and obtain the test accuracy after the test is completed; when the test accuracy is greater than or equal to the test accuracy threshold, use the trained BP neural network prediction model as the final BP neural network prediction model; otherwise, return to S321 to continue training the trained BP neural network prediction model until the test accuracy is greater than or equal to the test accuracy threshold;

[0070] By using the historical distribution network training data matrix and the historical distribution network test data matrix to train and test the initial BP neural network prediction model, the final BP neural network prediction model has good prediction ability for each type of distribution network time series data.

[0071] Preferably, S4 comprises the following steps:

[0072] S41, the historical distribution network data matrix The distribution network data and abnormal data threshold set at each time point to be predicted Compare with the corresponding abnormal data threshold in to obtain the historical distribution network abnormal time period matrix;

[0073] S42, cooperate with the threshold set of the number of consecutive time points Each historical distribution network abnormal time period in the historical distribution network abnormal time period matrix is ​​classified to obtain the historical non-fault abnormal time period matrix g and the historical fault abnormal time period matrix g′; they are as follows:

[0074]

[0075] in, Represents the historical distribution network data matrix The starting time point and the ending time point of the jth non-fault abnormal time period corresponding to the i-th distribution network data type; Represents the historical distribution network data matrix The starting time point and the ending time point of the jth fault type abnormal time period corresponding to the i-th distribution network data type; g i ′ represents the historical distribution network data matrix The total number of non-fault abnormal time periods and fault abnormal time periods corresponding to the i-th type of distribution network data type;

[0076] The collected distribution network data at multiple historical time points are compared with the existing distribution network abnormality data with known cycles, and the most similar existing distribution network abnormality data is used as the distribution network data at a future time point, and the distribution network data at the future time point is classified and analyzed.

[0077] Preferably, S5 comprises the following steps:

[0078] S51, calculating the historical non-fault type abnormal time period matrix g and the non-fault type abnormal time period set average matrix d 3 The Euclidean distance between each non-fault-type abnormal time period set of the corresponding row in and the historical fault-type abnormal time period matrix g′ and the average matrix d of the fault-type abnormal time period set 4The Euclidean distance between each fault type abnormal time period set of the corresponding row in the first Euclidean distance matrix l is obtained. 1 and the second Euclidean distance matrix l 2 ; They are as follows,

[0079]

[0080] Among them, l 1ij , l 2ij Respectively represent the data of the i-th row in the historical non-fault abnormal time period matrix g and d 3ij The Euclidean distance between the data in the i-th row of the historical fault type abnormal time period matrix g′ and d 4ij The Euclidean distance between

[0081] S52, select the first Euclidean distance matrix l 1 and the second Euclidean distance matrix l 2 The smallest Euclidean distance in each row, and the corresponding non-fault abnormal time period set and fault abnormal time period set are respectively used as the data of the historical non-fault abnormal time period set of the corresponding row in the historical non-fault abnormal time period matrix g at the future time and the data of the historical fault abnormal time period set of the corresponding row in the historical fault abnormal time period matrix g′ at the future time, to obtain the second non-fault abnormal time period matrix to be analyzed and the second fault type abnormal time period matrix to be analyzed They are as follows:

[0082]

[0083]

[0084] in, as well as Respectively represent the second non-fault abnormal time period matrix to be analyzed and the second fault type abnormal time period matrix to be analyzed The starting time point and the ending time point of the jth non-fault abnormal time period and the fault abnormal time period corresponding to the i-th distribution network data type;

[0085] The distribution network data collected at multiple historical time points are compared with the average matrix of non-fault type abnormal time periods and the average matrix of fault type abnormal time periods. Since the average matrix of non-fault type abnormal time periods and the average matrix of fault type abnormal time periods are periodic abnormal time periods, the most similar existing distribution network abnormal data can directly reflect the distribution network abnormal data in the future.

[0086] Preferably, the S6 comprises the following steps:

[0087] S61: Calculate the first non-fault abnormal time period matrix to be analyzed And the second non-fault abnormal time period matrix to be analyzed The union of the fault-type abnormal time periods at the corresponding positions in is used to obtain the final non-fault-type abnormal time period matrix;

[0088] S62: Calculate the first to-be-analyzed fault type abnormal time period matrix h and the second to-be-analyzed fault type abnormal time period matrix h. The union of the fault type abnormal time periods at the corresponding positions in , and the final fault type abnormal time period matrix is ​​obtained;

[0089] By obtaining the first non-fault type abnormal time period matrix to be analyzed and the second non-fault type abnormal time period matrix to be analyzed and the first fault type abnormal time period matrix to be analyzed and the second fault type abnormal time period matrix to be analyzed, and finally performing a union operation on the first non-fault type abnormal time period matrix to be analyzed and the second non-fault type abnormal time period matrix to be analyzed and the first fault type abnormal time period matrix to be analyzed and the second fault type abnormal time period matrix to be analyzed, the final analysis result is more comprehensive and accurate.

[0090] A distribution network abnormal data prediction system based on data analysis includes a first distribution network data acquisition module, a clustering module, a first distribution network abnormal data classification module, an abnormal data time point mean value acquisition module, a second distribution network data acquisition module, a first prediction analysis module, a second distribution network abnormal data classification module, a second prediction analysis module and a comparative analysis module.

[0091] The present invention has the following beneficial effects:

[0092] 1. In the present invention, by calculating the average value of the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix, the sporadic nature of the data is reduced, thereby improving the accuracy of subsequent analysis; the historical distribution network data matrix is ​​predicted from two perspectives, one is to predict the distribution network data in the future time according to the changing trend of the distribution network data of multiple historical time points over time; the second is to find the periodicity of the abnormal data in the distribution network, and compare it with the existing distribution network abnormal data with a known period, and use the most similar existing distribution network abnormal data as the distribution network data at the future time point; two analysis results are obtained from these two perspectives, and finally the two analysis results are comprehensively compared and analyzed, so that the final analysis result is more comprehensive and accurate.

[0093] 2. In the present invention, the locust optimization algorithm is used to perform multiple iterations to optimize each classification center data in the distribution network data matrix set, and the overall discrete degree of the distribution network data matrix set is used as its fitness function, so that as the iteration proceeds, the classification center data found is more accurate.

[0094] 3. In the present invention, the initial BP neural network prediction model is trained and tested by using the historical distribution network training data matrix and the historical distribution network test data matrix respectively, so that the final BP neural network prediction model obtained has good prediction ability for each type of distribution network time series data.

[0095] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] In order to more clearly illustrate the technical solutions of the embodiments of the invention, the drawings required for describing the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, they can also obtain drawings based on these drawings without paying creative work.

[0097] Figure 1 The present invention is a schematic diagram of a flow chart of a distribution network abnormal data prediction system based on data analysis for predicting distribution network abnormal data. DETAILED DESCRIPTION

[0098] The following will be combined with the drawings in the embodiments of the invention to clearly and completely describe the technical solutions in the embodiments of the invention. Obviously, the described embodiments are only part of the embodiments of the invention, not all of the embodiments. Based on the embodiments in the invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the invention.

[0099] In the description of the present invention, it is necessary to understand that the terms "opening", "upper", "lower", "top", "middle", "inside" and the like indicating orientation or positional relationship are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the components or elements referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the invention.

[0100] Embodiment 1

[0101] This embodiment is a distribution network abnormal data prediction method based on data analysis, comprising the following steps:

[0102] S1. Collect distribution network data of various types and multiple historical time points to obtain a distribution network data matrix set;

[0103] The S1 comprises the following steps:

[0104] S11, set a plurality of distribution network data types and corresponding data statistical cycles to obtain a distribution network data type set a={a 1 ,a 2,...,a i ,...,a a′} and data statistical period set b′={b 1 ′,b 2 ′,...,b i ′,...,b a ″},a i represents the type of the i-th type of network configuration data set, a′ represents the total number of network configuration types set; b i ' represents the data statistics period set for the i-th type of distribution network data;

[0105] Set the same number of historical time points for the data statistical period corresponding to each distribution network data type to obtain the historical time point matrix as follows,

[0106]

[0107] in, represents the jth historical time point set for the data statistical period corresponding to the i-th type of distribution network data, and a~ represents the total number of historical time points set for the data statistical period corresponding to each type of distribution network data;

[0108] According to the historical time point matrix And the collection distribution network data type set a = {a 1 ,a 2 ,...,a i ,...,a a′}, and obtain a distribution network data matrix set;

[0109] S12: Set the corresponding abnormal data threshold for each type of distribution network data to obtain the abnormal data threshold set. represents the abnormal data threshold set for the i-th type of network configuration data;

[0110] S2. Perform clustering operation on the distribution network data matrix set to obtain a distribution network data classification matrix; then classify the distribution network data classification matrix to obtain an initial non-fault type abnormal time period matrix and an initial fault type abnormal time period matrix; calculate the average value of the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix to obtain an average matrix of the non-fault type abnormal time period set and an average matrix of the fault type abnormal time period set;

[0111] The S2 comprises the following steps:

[0112] S21, performing a clustering operation on each distribution network data matrix in the distribution network data matrix set to obtain a distribution network data classification matrix c; as follows,

[0113]

[0114] Among them, c ij represents the j-th classification of the distribution network data matrix corresponding to the i-th distribution network data type; c ijkk′ Indicates c ij The distribution network data at the k′th historical time point in the kth data statistical period; Indicates c ij The total number of data statistical cycles corresponding to the distribution network data;

[0115] The S21 comprises the following steps:

[0116] S211. Building locust populations represents the i-th locust in the locust population, represents the size of the locust population; sets the maximum number of iterations of the locust population to e 1 , the current number of iterations is e 2 , the dimension of the search space is

[0117] S212, randomly selecting a number of distribution network data sets from the distribution network data matrix set as initial classification center data for multiple times to obtain an initial classification center data matrix set; using the initial classification center data matrix set as an initial position matrix set of the locust population e′ k′ represents the initial position matrix of the i-th locust in the locust population; as follows,

[0118]

[0119] Among them, e′ k′ij Represents e′ k′ The initial classification center data set of the jth classification corresponding to the i-th distribution network data type, e′ k′ijk Represents e′ k′ij The initial classification center data at the k-th historical time point;

[0120] S213, calculating the distribution network data matrix set b according to the initial position matrix set 2 = {b 21 ,b 22 ,...,b 2i ,...,b 2a′ The sum of the Euclidean distances between each distribution network dataset and the corresponding classification center dataset in} is used to obtain the Euclidean distance data matrix as follows,

[0121]

[0122] in, Represents e′ k′ij Each distribution network data in the corresponding category is sent to e′ k′ij The sum of the Euclidean distances between ;

[0123] According to the Euclidean distance data matrix Set the fitness function of the locust population as follows,

[0124]

[0125] S214, start iteration, before iteration, the current iteration number e 2 Set to 1; the fitness function of the locust population is used in the first round of iteration Calculate the initial position matrix set The fitness value of the initial position matrix of each locust in the first fitness value set is obtained to obtain a first fitness value set; the maximum fitness value and the initial position of the corresponding locust are selected from the first fitness value set as the first global optimal fitness value and the first global optimal position respectively; the initial position matrix set is adjusted according to the first global optimal fitness value and the first global optimal position. The initial position matrix of each locust is updated, and after the update is completed, the current number of iterations e 2 Add 1 and enter the next iteration;

[0126] Except for the first round of iteration, the fitness function of the locust population is used in each other round of iteration. Calculate the fitness value of the position matrix of each locust obtained in the previous round of iteration to obtain a second fitness value set; select the maximum fitness value and the initial position of the corresponding locust from the second fitness value set as the second global optimal fitness and the second global optimal position respectively; update the position matrix of each locust obtained in the previous round of iteration according to the second global optimal fitness and the second global optimal position; after the update is completed, update the current iteration number e 2 Add 1 and enter the next iteration;

[0127] S215, when e 2 ≥e 1 When , the iteration is stopped to obtain the final global optimal position; the final global optimal position is used as the final classification center data matrix; the distribution network data matrix set b is quantized according to the final classification center data matrix 2 = {b 21 ,b 22,...,b 2i ,...,b 2a′} to classify and obtain the distribution network data classification matrix c;

[0128] S22. Setting the threshold value set for the number of consecutive time points represents the continuous time point number threshold corresponding to the i-th type of network configuration data; and the abnormal data threshold set When the time point data of the distribution network abnormal data in each cycle of each classified distribution network data matrix corresponding to each distribution network data type in the distribution network data classification matrix c is less than the corresponding continuous time point number threshold, the time period corresponding to the distribution network abnormal data is used as the non-fault type abnormal time period; otherwise, the time period corresponding to the distribution network abnormal data is used as the fault type abnormal time period; the initial non-fault type abnormal time period matrix d is obtained. 1 and the initial fault type abnormal time period matrix d 2 ;as follows,

[0129]

[0130] Among them, d 1ij and d 2ij They represent the non-fault abnormal time period matrix and fault abnormal time period matrix of the jth classification corresponding to the i-th distribution network data type respectively; they are as follows,

[0131]

[0132] in, Respectively represent d 1ij The starting time point and the ending time point of the k′th non-fault abnormal time period in the kth data statistical period; Respectively represent d 2ij The starting time point and the ending time point of the k′th fault type abnormal time period in the kth data statistical period; d 1 ' ij d 2 ' ij Respectively represent d 1ij The total number of non-fault abnormal time periods in each data statistical period and d 2ij The total number of fault-type abnormal time periods in each data statistical period;

[0133] S23, respectively calculating the initial non-fault type abnormal time period matrix d 1 and the initial fault type abnormal time period matrix d 2The average value of the start and end time points of each non-fault abnormal time period in each classification and the average value of the start and end time points of each fault abnormal time period are obtained to obtain the average matrix d of the non-fault abnormal time period set 3 And the average matrix d of the fault type abnormal time period set 4 ; They are as follows,

[0134]

[0135] Among them, d 3ij d 4ij They represent the non-fault type abnormal average time period set and the fault type abnormal average time period set of the jth classification corresponding to the i-th distribution network data type; they are as follows,

[0136]

[0137] in, Respectively represent d 3ij The average value of the starting time point and the ending time point of the k′th non-fault type abnormal average time period in ; Respectively represent d 4ij The average value of the starting time point and the ending time point of the k′th fault type abnormal average time period in the calculation formula are as follows:

[0138]

[0139] S3, collecting distribution network data of multiple types and multiple historical time points to be predicted again to obtain a historical distribution network data matrix; predicting and classifying and analyzing the distribution network data at future times according to the historical distribution network data matrix to obtain a first analysis result;

[0140] The S3 comprises the following steps:

[0141] S31. Setting a set of time points to be predicted and future time points f 1i 、f 2i They represent the i-th time point to be predicted and the future time point respectively, and f 1 ′、f 2 ′ respectively represent the total number of the set time points to be predicted and the future time points;

[0142] According to the network configuration data type set a={a 1 ,a 2 ,...,a i ,...,a a′} and the set of time points to be predicted Collect distribution network data of various distribution network data types to obtain historical distribution network data matrix as follows,

[0143]

[0144] in, The network configuration data representing the i-th network configuration data type corresponding to the j-th time point to be predicted;

[0145] S32, construct an initial BP neural network prediction model and set the training data ratio and the test data ratio; according to the training data ratio and the test data ratio, the historical distribution network data matrix Perform data division to obtain a historical distribution network training data matrix, a historical distribution network test data matrix, and a historical distribution network to-be-predicted data matrix;

[0146] The historical distribution network training data matrix and the historical distribution network test data matrix are respectively used to train and test the initial BP neural network prediction model; after the training and testing are completed, the final BP neural network prediction model is obtained;

[0147] In S32, the historical distribution network training data matrix and the historical distribution network test data matrix are respectively used to train and test the initial BP neural network prediction model; after the training and testing are completed, the final BP neural network prediction model is obtained, including the following steps:

[0148] S321, setting a training error threshold; inputting the historical distribution network training data matrix into the initial BP neural network prediction model for training; during the training process, when the training error is less than the training error threshold, stopping the training operation to obtain a trained BP neural network prediction model; otherwise, continuing the training until the training error is less than the training error threshold;

[0149] S322, set a test accuracy threshold; input the historical distribution network test data matrix into the trained BP neural network prediction model for testing, and obtain the test accuracy after the test is completed; when the test accuracy is greater than or equal to the test accuracy threshold, use the trained BP neural network prediction model as the final BP neural network prediction model; otherwise, return to S321 to continue training the trained BP neural network prediction model until the test accuracy is greater than or equal to the test accuracy threshold;

[0150] S33, cooperate with the future time point set The final BP neural network prediction model is used to perform prediction operations on the historical distribution network to be predicted data matrix to obtain the future distribution network data matrix as follows,

[0151]

[0152] in, Represents the predicted network data of the i-th network data type corresponding to the j-th future time point;

[0153] S34, the future distribution network data matrix The distribution network data and abnormal data threshold set at each future time point in Compare with the corresponding abnormal data threshold in to obtain the future distribution network abnormal time period matrix;

[0154] S35, cooperate with the threshold value set of the number of consecutive time points Classify each future distribution network abnormal time period in the future distribution network abnormal time period matrix to obtain the first non-fault abnormal time period matrix to be analyzed and the first fault type abnormal time period matrix h to be analyzed; respectively,

[0155]

[0156] in, Represent the future distribution network data matrix respectively The starting time point and the ending time point of the jth non-fault abnormal time period corresponding to the i-th distribution network data type; Represent the future distribution network data matrix respectively The starting time point and the ending time point of the jth fault type abnormal time period corresponding to the i-th distribution network data type; h i ′ respectively represent the future distribution network data matrix The total number of non-fault abnormal time periods and fault abnormal time periods corresponding to the i-th type of distribution network data type;

[0157] S4. Classify the distribution network abnormality data in the historical distribution network data matrix to obtain a historical non-fault abnormal time period matrix and a historical fault abnormal time period matrix;

[0158] The S4 comprises the following steps:

[0159] S41, the historical distribution network data matrix The distribution network data and abnormal data threshold set at each time point to be predicted Compare with the corresponding abnormal data threshold in to obtain the historical distribution network abnormal time period matrix;

[0160] S42, cooperate with the threshold set of the number of consecutive time points Each historical distribution network abnormal time period in the historical distribution network abnormal time period matrix is ​​classified to obtain the historical non-fault abnormal time period matrix g and the historical fault abnormal time period matrix g′; they are as follows:

[0161]

[0162] in, Represents the historical distribution network data matrix The starting time point and the ending time point of the jth non-fault abnormal time period corresponding to the i-th distribution network data type; Represents the historical distribution network data matrix The starting time point and the ending time point of the jth fault type abnormal time period corresponding to the i-th distribution network data type; g i ′ represents the historical distribution network data matrix The total number of non-fault abnormal time periods and fault abnormal time periods corresponding to the i-th type of distribution network data type;

[0163] S5. Perform a prediction analysis on the historical non-fault type abnormal time period matrix and the historical fault type abnormal time period matrix according to the average matrix of the non-fault type abnormal time period set and the average matrix of the fault type abnormal time period set to obtain a second analysis result;

[0164] The S5 comprises the following steps:

[0165] S51, calculating the historical non-fault type abnormal time period matrix g and the non-fault type abnormal time period set average matrix d 3 The Euclidean distance between each non-fault-type abnormal time period set of the corresponding row in and the historical fault-type abnormal time period matrix g′ and the average matrix d of the fault-type abnormal time period set 4 The Euclidean distance between each fault type abnormal time period set of the corresponding row in is obtained to obtain the first Euclidean distance matrix and the second Euclidean distance matrix;

[0166] S52, selecting the smallest Euclidean distance in each row of the first Euclidean distance matrix and the second Euclidean distance matrix, and using the corresponding non-fault type abnormal time period set and the fault type abnormal time period set as the data of the historical non-fault type abnormal time period set of the corresponding row in the historical non-fault type abnormal time period matrix at the future time and the data of the historical fault type abnormal time period set of the corresponding row in the historical fault type abnormal time period matrix at the future time, respectively, to obtain a second non-fault type abnormal time period matrix to be analyzed and a second fault type abnormal time period matrix to be analyzed;

[0167] S6. Compare the first analysis result and the second analysis result to obtain a final non-fault type abnormal time period matrix and a final fault type abnormal time period matrix;

[0168] The S6 comprises the following steps:

[0169] S61, calculating the union of the fault-type abnormal time periods at corresponding positions in the first non-fault-type abnormal time period matrix to be analyzed and the second non-fault-type abnormal time period matrix to be analyzed, to obtain a final non-fault-type abnormal time period matrix;

[0170] S62: Calculate the union of the fault type abnormal time periods at corresponding positions in the first fault type abnormal time period matrix to be analyzed and the second fault type abnormal time period matrix to be analyzed to obtain a final fault type abnormal time period matrix.

[0171] Embodiment 2

[0172] The present embodiment discloses a distribution network abnormal data prediction system based on data analysis, the system can implement the method of the above embodiment, including a first distribution network data acquisition module, a clustering module, a first distribution network abnormal data classification module, an abnormal data time point mean value acquisition module, a second distribution network data acquisition module, a first prediction analysis module, a second distribution network abnormal data classification module, a second prediction analysis module and a comparative analysis module;

[0173] The first distribution network data collection module is used to collect distribution network data of multiple types and multiple historical time points to obtain a distribution network data matrix set;

[0174] The clustering module is used to perform clustering operations on the distribution network data matrix set to obtain a distribution network data classification matrix;

[0175] The first distribution network abnormal data classification module is used to classify the distribution network data classification matrix to obtain an initial non-fault type abnormal time period matrix and an initial fault type abnormal time period matrix;

[0176] The abnormal data time point mean value acquisition module is used to calculate the average value of the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix to obtain the non-fault type abnormal time period set average matrix and the fault type abnormal time period set average matrix;

[0177] The second distribution network data collection module is used to collect distribution network data of multiple types and multiple historical time points to be predicted again to obtain a historical distribution network data matrix;

[0178] The first prediction and analysis module is used to predict and classify the distribution network data at a future time according to the historical distribution network data matrix to obtain a first analysis result;

[0179] The second distribution network abnormal data classification module is used to classify the distribution network abnormal data in the historical distribution network data matrix to obtain a historical non-fault type abnormal time period matrix and a historical fault type abnormal time period matrix;

[0180] The second prediction and analysis module is used to perform prediction and analysis on the historical non-fault type abnormal time period matrix and the historical fault type abnormal time period matrix according to the average matrix of the non-fault type abnormal time period set and the average matrix of the fault type abnormal time period set to obtain a second analysis result;

[0181] The comparison and analysis module is used to compare the first analysis result and the second analysis result to obtain a final non-fault type abnormal time period matrix and a final fault type abnormal time period matrix.

[0182] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0183] The preferred embodiments of the invention disclosed above are only used to help explain the invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the invention, so that those skilled in the art can understand and use the invention well.

Claims

1. A distribution network abnormal data prediction method based on data analysis, characterized in that: The following steps are involved: S1. Collect distribution network data of various types and multiple historical time points to obtain a distribution network data matrix set; S2. Perform clustering operation on the distribution network data matrix set to obtain a distribution network data classification matrix; then classify the distribution network data classification matrix to obtain an initial non-fault type abnormal time period matrix and an initial fault type abnormal time period matrix; calculate the average value of the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix to obtain an average matrix of the non-fault type abnormal time period set and an average matrix of the fault type abnormal time period set; S3, collecting distribution network data of multiple types and multiple historical time points to be predicted again to obtain a historical distribution network data matrix; According to the historical distribution network data matrix, the distribution network data at a future moment is predicted and classified and analyzed to obtain a first analysis result; S4, classifying the distribution network abnormality data in the historical distribution network data matrix to obtain a historical non-fault type abnormal time period matrix and a historical fault type abnormal time period matrix; S5. Perform a prediction analysis on the historical non-fault type abnormal time period matrix and the historical fault type abnormal time period matrix according to the average matrix of the non-fault type abnormal time period set and the average matrix of the fault type abnormal time period set to obtain a second analysis result; S6. Compare the first analysis result and the second analysis result to obtain a final non-fault type abnormal time period matrix and a final fault type abnormal time period matrix.

2. A distribution network abnormal data prediction method based on data analysis according to claim 1, characterized in that: The S1 comprises the following steps: S11. Set a plurality of distribution network data types and corresponding data statistical periods to obtain a distribution network data type set and a data statistical period set; set the same number of historical time points for the data statistical period corresponding to each distribution network data type to obtain a historical time point matrix; obtain a distribution network data matrix set according to the historical time point matrix and the distribution network data of a plurality of data statistical periods with abnormal distribution network data corresponding to each distribution network data type in the distribution network data type set; S12. Set a corresponding abnormal data threshold for each type of distribution network data to obtain an abnormal data threshold set.

3. A distribution network abnormal data prediction method based on data analysis according to claim 2, characterized in that: The S2 comprises the following steps: S21, performing a clustering operation on each distribution network data matrix in the distribution network data matrix set to obtain a distribution network data classification matrix; S22, setting a threshold set for the number of continuous time points; in conjunction with the threshold set for the number of continuous time points and the threshold set for abnormal data, when the time point data of the distribution network abnormal data in each cycle of each classified distribution network data matrix corresponding to each distribution network data type in the distribution network data classification matrix is ​​less than the corresponding threshold for the number of continuous time points, the time period corresponding to the distribution network abnormal data is used as a non-fault abnormal time period; otherwise, the time period corresponding to the distribution network abnormal data is used as a fault abnormal time period; an initial non-fault abnormal time period matrix and an initial fault abnormal time period matrix are obtained; S23. Calculate the average values ​​of the start time point and the end time point of each non-fault type abnormal time period in each category in the initial non-fault type abnormal time period matrix and the initial fault type abnormal time period matrix, as well as the average values ​​of the start time point and the end time point of each fault type abnormal time period, respectively, to obtain the average matrix of the non-fault type abnormal time period set and the average matrix of the fault type abnormal time period set.

4. A distribution network abnormal data prediction method based on data analysis according to claim 3, characterized in that: The S21 comprises the following steps: S211, constructing a locust population; setting the maximum number of iterations of the locust population to e1 and the current number of iterations to e2; S212, randomly selecting a number of distribution network data sets from the distribution network data matrix set as initial classification center data for multiple times to obtain an initial classification center data matrix set; using the initial classification center data matrix set as an initial position matrix set of the locust population; S213, calculating the sum of the Euclidean distances between each distribution network data set in the distribution network data matrix set and the corresponding classification center data set according to the initial position matrix set, to obtain a Euclidean distance data matrix; and setting the fitness function of the locust population according to the Euclidean distance data matrix; S214, start iteration; in each round of iteration, use the fitness function of the locust population to calculate the fitness value of the position matrix of each locust obtained in the previous round of iteration and update the position matrix of each locust obtained in the previous round of iteration; S215. When e2≥e1, stop iteration and obtain the final global optimal position; use the final global optimal position as the final classification center data matrix; classify the distribution network data matrix set according to the final classification center data matrix to obtain the distribution network data classification matrix.

5. A distribution network abnormal data prediction method based on data analysis according to claim 4, characterized in that: The S3 comprises the following steps: S31, setting a set of time points to be predicted and a set of future time points; collecting distribution network data of multiple distribution network data types according to the distribution network data type set and the set of time points to be predicted, and obtaining a historical distribution network data matrix; S32, constructing an initial BP neural network prediction model; performing data partitioning on the historical distribution network data matrix to obtain a historical distribution network training data matrix, a historical distribution network test data matrix, and a historical distribution network to-be-predicted data matrix; respectively using the historical distribution network training data matrix and the historical distribution network test data matrix to train and test the initial BP neural network prediction model; after the training and testing are completed, the final BP neural network prediction model is obtained; S33, in conjunction with the future time point set, using the final BP neural network prediction model to perform a prediction operation on the historical distribution network to-be-predicted data matrix to obtain a future distribution network data matrix; S34, comparing the distribution network data at each future time point in the future distribution network data matrix with the abnormal data threshold value corresponding to the abnormal data threshold value set to obtain a future distribution network abnormal time period matrix; S35. Classify each future distribution network abnormal time period in the future distribution network abnormal time period matrix in cooperation with the continuous time point number threshold set to obtain a first non-fault abnormal time period matrix to be analyzed and a first fault abnormal time period matrix to be analyzed.

6. A distribution network abnormal data prediction method based on data analysis according to claim 5, characterized in that: The S4 comprises the following steps: S41, comparing the distribution network data of each time point to be predicted in the historical distribution network data matrix with the abnormal data threshold corresponding to the abnormal data threshold set, to obtain a historical distribution network abnormal time period matrix; S42. Classify each historical distribution network abnormal time period in the historical distribution network abnormal time period matrix in cooperation with the continuous time point number threshold set to obtain a historical non-fault abnormal time period matrix and a historical fault abnormal time period matrix.

7. A distribution network abnormal data prediction method based on data analysis according to claim 6, characterized in that: The S5 comprises the following steps: S51, calculating the Euclidean distance between each non-fault type abnormal time period set in the corresponding row of the historical non-fault type abnormal time period matrix and the average matrix of the non-fault type abnormal time period set, and the Euclidean distance between each fault type abnormal time period set in the corresponding row of the historical fault type abnormal time period matrix and the average matrix of the fault type abnormal time period set, to obtain a first Euclidean distance matrix and a second Euclidean distance matrix; S52. Select the smallest Euclidean distance in each row of the first Euclidean distance matrix and the second Euclidean distance matrix, and use the corresponding non-fault type abnormal time period set and fault type abnormal time period set as the data of the historical non-fault type abnormal time period set of the corresponding row in the historical non-fault type abnormal time period matrix at the future time and the data of the historical fault type abnormal time period set of the corresponding row in the historical fault type abnormal time period matrix at the future time, respectively, to obtain the second non-fault type abnormal time period matrix to be analyzed and the second fault type abnormal time period matrix to be analyzed.

8. A distribution network abnormal data prediction method based on data analysis according to claim 7, characterized in that: The S6 comprises the following steps: S61, calculating the union of the fault-type abnormal time periods at corresponding positions in the first non-fault-type abnormal time period matrix to be analyzed and the second non-fault-type abnormal time period matrix to be analyzed, to obtain a final non-fault-type abnormal time period matrix; S62: Calculate the union of the fault type abnormal time periods at corresponding positions in the first fault type abnormal time period matrix to be analyzed and the second fault type abnormal time period matrix to be analyzed to obtain a final fault type abnormal time period matrix.

9. A system for implementing the distribution network abnormal data prediction method based on data analysis as described in any one of claims 1 to 8.

Citation Information

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