Power distribution network fault prediction method and system
By constructing a time series prediction model for seasonal terms, trend terms, residual terms and holiday terms, the problem of prediction inaccurate caused by ignoring the impact of meteorological and holidays in the prior art is solved, and more accurate failure prediction and the effect of reducing failure rate is achieved.
Patent Information
- Application Number
- CN202411825018.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-12
- Publication Date
- 2025-03-18
- Estimated Expiration
- 2044-12-12
AI Technical Summary
The existing distribution network prediction methods ignore the impact of weather and holidays on the failure rate when collecting data, resulting in inaccurate prediction results.
By collecting power failure data and preprocessing it, a time series prediction model including seasonal terms, trend terms, residual terms and holiday terms is constructed, prediction results are generated, and threshold analysis and historical data are compared to formulate response measures.
Improve the accuracy of distribution network fault prediction, and more accurately predict the time and location of failures, thereby reducing failure rates and economic losses.
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Figure CN119644039A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of distribution network fault prediction, and in particular to a distribution network fault prediction method and system. Background Art
[0002] The distribution network is composed of overhead lines, cables, towers, distribution transformers, disconnectors, reactive power compensators and some ancillary facilities. It plays an important role in distributing electric energy in the power grid. With the rapid development of smart grids, the large number of uncertain access to distributed power sources has made the fault information of the distribution network more and more complex, and the accurate and rapid analysis of faults has become more and more difficult. In order to ensure the highly intelligent operation of the distribution network, it is necessary to monitor the feeder operation data in real time, timely warn of abnormal situations, and quickly locate and handle faults, and predict faults based on existing data. Therefore, it is necessary to use distribution network fault prediction methods.
[0003] Most of the existing distribution network prediction methods ignore the impact of weather and holidays on the occurrence rate of distribution network failures when collecting data, resulting in inaccurate prediction results. For example, on holidays in sunny weather, the load of the distribution network in mobile stalls and pedestrian streets increases due to the increase in tourists, which increases the failure rate. On holidays in stormy weather, the load of the distribution network in indoor supermarkets and cinemas increases due to the increase in tourists, which increases the failure rate. Summary of the invention
[0004] In view of the above-mentioned problems, the present invention is proposed.
[0005] Therefore, the technical problem solved by the present invention is that the existing distribution network prediction methods mostly ignore the impact of weather and holidays on the distribution network failure rate when collecting data, thereby making the prediction results inaccurate.
[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:
[0007] In a first aspect, an embodiment of the present invention provides a distribution network fault prediction method, comprising:
[0008] Collect power fault data and pre-process them to obtain a fault data set;
[0009] Based on the fault data set, a time series prediction model is constructed and fitted;
[0010] Based on the fitted time series forecasting model, create a data frame with a specified forecast time range;
[0011] Based on the fitted time series prediction model and the data frame, generate prediction results and perform threshold analysis;
[0012] Compare forecast results with historical data and develop countermeasures.
[0013] As a preferred solution for distribution network fault prediction method, the following is proposed:
[0014] The prediction results are compared with historical data and the response measures are formulated including:
[0015] The prediction results are compared with the historical data stored in the big data to obtain the measures that need to be implemented to deal with the results.
[0016] As a preferred solution for distribution network fault prediction method, the following is proposed:
[0017] The construction and fitting of a time series prediction model based on the fault data set includes:
[0018] Build a time series forecasting model including seasonal terms, trend terms, residual terms, and holiday terms.
[0019] As a preferred solution for distribution network fault prediction method, the following is proposed:
[0020] The constructing and fitting a time series prediction model based on the fault data set also includes:
[0021] In time series forecasting, for all time t, there are two forms, namely, additive form and multiplicative form, where the additive form is expressed as:
[0022] y t =S t +T t +R t
[0023] Among them, S t is the seasonal term, T t is the trend term, R t For the remaining items.
[0024] As a preferred solution for distribution network fault prediction method, the following is proposed:
[0025] The constructing and fitting a time series prediction model based on the fault data set also includes:
[0026] The multiplication form is:
[0027] y t =S t ×T t ×R t
[0028] Taking the logarithm of the multiplication, the additive and multiplicative forms are equivalent:
[0029] Iny t=InS t +InT t +InR t
[0030] The expression of adding the holiday term ε(t) is:
[0031] y(t)=g(t)+s(t)+h(t)+ε(t)
[0032] Among them, g(t) is the trend term, which indicates the trend of the time series in the non-periodic range; s(t) is the seasonal term, which is in weeks or years; h(t) is the holiday term, which indicates whether there are holidays within the time range; ε(t) is the error term / residual term;
[0033] The g(t) trend term is a function of the logistic regression function and piecewise linear function. The logistic regression function is expressed as:
[0034] f(x)=C / (1+e- k(x-m) )
[0035] Among them, C is the maximum asymptotic value of the curve, k represents the growth rate of the curve, m represents the midpoint of the curve, the special form of the logistic regression function is the sigmoid function, and the derivative form of the sigmoid function is:
[0036] y′=y(1-y).
[0037] As a preferred solution for distribution network fault prediction method, the following is proposed:
[0038] The constructing and fitting a time series prediction model based on the fault data set also includes:
[0039] Introducing the holiday impact range parameter κ i , there are L holidays, the formula is:
[0040]
[0041] Z(t)=(1 {t∈Di} ,···,1 {t∈DL} )
[0042] κ=(κ1,···,κ1) T
[0043] Among them, κ~Normal(0,v 2 ), when the value is larger, it means that the holiday has a greater impact on the model; when the value is smaller, it means that the holiday has a smaller impact on the model.
[0044] As a preferred solution for distribution network fault prediction method, the following is proposed:
[0045] The generating of prediction results based on the fitted time series prediction model and the data frame and performing threshold analysis include:
[0046] By setting a data frame of the prediction time range in the prediction model, the predicted value and its confidence interval are obtained; the confidence interval of the predicted value is compared with the actual value, and an alarm is issued when the predicted value exceeds the threshold or the actual value exceeds the confidence interval.
[0047] In a second aspect, an embodiment of the present invention provides a distribution network fault prediction system, including:
[0048] The data preparation and preprocessing module is used to collect and preprocess the power fault data to obtain the fault data set;
[0049] Model building and fitting module, used to build and fit the time series prediction model based on the fault data set;
[0050] The future data frame creation module is used to create a data frame of a specified prediction time range based on the fitted time series prediction model;
[0051] A prediction and analysis module, used to generate prediction results and perform threshold analysis based on the fitted time series prediction model and the data frame;
[0052] The overall coordination and response module is used to compare the forecast results with historical data and formulate response measures.
[0053] In a third aspect, an embodiment of the present invention provides a computing device, including:
[0054] Memory and processor;
[0055] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the one or more programs are executed by the one or more processors, the one or more processors implement the distribution network fault prediction method as described in any embodiment of the present invention.
[0056] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium storing computer-executable instructions, which implement the distribution network fault prediction method when executed by a processor.
[0057] The beneficial effects of the present invention are as follows: the present invention uses a time series prediction algorithm to analyze and process the internal data of power grid enterprises in the collected data source platform and the relevant information on the external environment, i.e., big data, crawled by crawlers, and comprehensively considers the meteorological conditions and holidays in the time period and area to be predicted during the analysis and processing, that is, the accuracy of the prediction is improved by enriching and expanding the existing content and fields, thereby facilitating the foresighted maintenance and prevention of the distribution network according to the prediction results, thereby reducing the failure rate of the distribution network, and at the same time reducing the economic and other losses caused by the failure of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS
[0058] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.
[0059] Figure 1 It is an overall flow chart of the distribution network fault prediction method of the present invention;
[0060] Figure 2 It is a schematic diagram of the internal structure of the trend item of the distribution network fault prediction method described in the present invention. DETAILED DESCRIPTION
[0061] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.
[0062] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.
[0063] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.
[0064] Example 1
[0065] Reference Figure 1, which is the first embodiment of the present invention, and provides a distribution network fault prediction method, comprising:
[0066] S1: Collect power fault data and preprocess them to obtain a fault data set;
[0067] S2: Based on the fault data set, a time series prediction model is constructed and fitted;
[0068] S3: Create a data frame with a specified forecast time range based on the fitted time series forecasting model;
[0069] S4: Based on the fitted time series prediction model and the data frame, generate prediction results and perform threshold analysis;
[0070] S5: Compare the forecast results with historical data and formulate countermeasures.
[0071] It should be noted that, through steps S1-S5, in the process of power fault data collection, preprocessing, modeling, prediction, analysis and formulation of countermeasures, fault prediction and risk management are systematically implemented, thereby improving the stability and reliability of power grid operation.
[0072] Example 2
[0073] Reference Figure 1 and Figure 2 , which is an embodiment of the present invention, provides a distribution network fault prediction method based on the previous embodiment, including:
[0074] In the embodiment of the present application, the power fault data is collected and preprocessed in the above step S1 to obtain a fault data set including:
[0075] Data collection: collect and pre-process the internal data of power grid enterprises in the data source platform;
[0076] Data extraction: Extract, deduplicate and preprocess the external environment information data uploaded to the big data platform;
[0077] Data preprocessing includes analysis of factors affecting distribution network failures, data mining extraction, and sample screening.
[0078] Specifically, data extraction is completed through a keyword extraction algorithm, wherein the formula of the extraction algorithm is TF-IDF=TF*IDF, wherein TF is term frequency, which refers to the number of times a certain term appears in an article / the total number of terms in the article, and IDF is inverse document frequency.
[0079] The extraction logic of TF-IDF=TF*IDF is: first, perform word segmentation, part-of-speech screening, deduplication and stop word removal on the text of the keywords to be extracted to obtain candidate keywords; secondly, calculate the TF-IDF values of all candidate keywords and take the keywords with the largest TF-IDF values among all candidate keywords as the final keywords of the document.
[0080] In another possible implementation, data extraction can also be completed by the following method:
[0081] Machine learning algorithms: Use supervised learning or unsupervised learning algorithms to identify and extract relevant keywords. For example, you can train a classification model to determine whether a word is a keyword.
[0082] Natural language processing (NLP) technology: Use NLP toolkits (such as spaCy, NLTK, etc.) to perform entity recognition, named entity extraction, etc. to extract keywords with specific meanings.
[0083] Text summarization technology: Use text summarization algorithms to automatically generate text summaries and extract important keywords from them.
[0084] Topic models: such as Latent Dirichlet Allocation (LDA), can identify topics in text and extract keywords for each topic.
[0085] Statistical methods: In addition to TF-IDF, other statistical indicators can be used to evaluate the importance of keywords, such as variants of term frequency-inverse document frequency, information gain, chi-square test, etc.
[0086] Deep learning models: Use pre-trained language models (such as BERT, RoBERTa, etc.) to extract keywords. These models can capture more complex semantic relationships.
[0087] In the embodiment of the present application, in the above step S2, based on the fault data set, constructing a time series prediction model and performing fitting includes:
[0088] Construct a model object for Prophet time series forecasting. The model includes seasonal terms, trend terms, residual terms, and holiday terms. Use the fit method to fit the preprocessed fault data set to the model.
[0089] Among them, the Prophet time series forecast includes two forms for all time t, namely the additive form and the multiplicative form, where the additive form is expressed as:
[0090] y t =S t +T t +Rt
[0091] Among them, S t is the seasonal term, T t is the trend term, R t For the remaining items.
[0092] The multiplication form is:
[0093] y t =S t ×T t ×R t
[0094] Taking the logarithm of the multiplication, the additive and multiplicative forms are equivalent:
[0095] Iny t =InS t +InT t +InR t
[0096] That is, when predicting the model, the logarithm of y is taken first, and then the time series is decomposed.
[0097] In the model building stage, the Prophet time series forecast also includes the holiday term ε(t). The expression of adding the holiday term ε(t) is:
[0098] y(t)=g(t)+s(t)+h(t)+ε(t)
[0099] g(t) is the trend term, which indicates the non-periodic trend of the time series; s(t) is the seasonal term, which is in weeks or years; h(t) is the holiday term, which indicates whether there are holidays within the time range; ε(t) is the error term / residual term.
[0100] like Figure 2 As shown, the g(t) trend term is a function of the logistic regression function and piecewise linear function, and the logistic regression function is expressed as:
[0101] f(x)=C / (1+e -k(x-m ))
[0102] Among them, C is the maximum asymptotic value of the curve, k represents the growth rate of the curve, m represents the midpoint of the curve, the special form of the logistic regression function is the sigmoid function, and the derivative form of the sigmoid function is:
[0103] y′=y(1-y).
[0104] In the model building stage, the Prophet time series forecast needs to set the change point position, and the setting method of the change point position includes manual and automatic selection. When setting the change point, it is necessary to see whether some boundary conditions are reasonable. S change points are placed, and the position of the change point is at timestamp s j , 1≤j≤S At these time stamps, the change in growth rate needs to be given; suppose there is such a vector δ∈R s : where δ j Indicates that at timestamp s j If the initial growth rate is replaced by k, then the growth rate at timestamp t is k+∑ j∶td>sj δj, through an indicator function is a(t)∈{0,1} s ,that is So the growth rate at timestamp t is k+a T δ, once the variable k is determined, another parameter m is adjusted accordingly. When the growth rate k is adjusted, the offset m corresponding to each change point should also be adjusted accordingly to connect the last time point of each segment. Therefore, through mathematical calculation, we can get: Substitute into the above logistic regression model:
[0105]
[0106] Where: a(t)=(a1(t),···,a s (t)) T ,δ=(δ1,···,δ s ) T ,γ=(γ1,···,γ s ) T .
[0107] The form of the piecewise linear function is:
[0108] g(t)=(k+a(t)δ)·t+(m+a(t) T γ)
[0109] k is the growth rate, δ is the change in the growth rate, m is the offset parameter, and γ is the offset parameter. The biggest difference between the piecewise linear function and the logistic regression function is the different settings of γ. In the piecewise linear function, γ=(γ1,···,γ s ) T ,γ j =-s j δ j .
[0110] In the model construction stage, the seasonal term model uses Fourier series to simulate the periodicity of the time series: P = 365.25 means a yearly period, P = 7 means a weekly period, the holiday term means that for the i-th holiday, Di means the period before and after the holiday, and a parameter κ is required i To express the impact range of holidays, that is, there are L holidays, the formula is:
[0111]
[0112] Z(t)=(1 {t∈Di} ,···,1 {t∈DL} )
[0113] κ=(κ1,···,κ1) T
[0114] Among them, κ~Normal(0,v 2 ) and the normal distribution is affected by v = holidays_prior_scale, the default value is 10, when the value is larger, it means that the holiday has a greater impact on the model; when the value is smaller, it means that the holiday has a smaller impact on the model;
[0115] The Fourier series has the form: N is the number of periods you want to use in the model.
[0116] For example, for a sequence with a yearly period (P=365.25), N=10; for a sequence with a weekly period (P=7), N=3;
[0117] When N=10,
[0118] When N=3,
[0119] Therefore, the seasonal term of the time series is: s(t) = X(t)β, and the initialization of β is β~Normal(0,σ 2 ), the larger the σ value, the more obvious the seasonal effect; the smaller the value, the less obvious the seasonal effect.
[0120] In the embodiment of the present application, in the above step S3, based on the fitted time series prediction model, creating a data frame for a specified prediction time range includes:
[0121] Use the make_future_data frame method to create a data frame containing future forecast dates, specifying the time range for the forecast.
[0122] For example, if it is necessary to predict the fault data for the next 365 days, periods=365 can be set, and the frequency can be specified (eg freq='D' means daily).
[0123] It should be noted that this step ensures that the forecast time range is accurate and provides a clear time frame for subsequent forecasts. By setting an appropriate time interval, the precision and practicality of the forecast can be improved.
[0124] In the embodiment of the present application, the above step S4 generates a prediction result based on the fitted time series prediction model and the data frame, and performs a threshold analysis, including:
[0125] By setting a data frame of the prediction time range in the prediction model, the predicted value and its confidence interval are obtained; the confidence interval of the predicted value is compared with the actual value, and an alarm is issued when the predicted value exceeds the threshold or the actual value exceeds the confidence interval.
[0126] In another possible implementation, a predict method is used to generate a prediction result, including a predicted value, a confidence interval, etc.
[0127] Use the plot method to visualize the prediction results, including actual values, predicted values, and confidence intervals.
[0128] Set a threshold (such as a failure rate exceeding a certain value) and trigger an alarm when the prediction result reaches or exceeds the threshold.
[0129] It should be noted that the visual prediction results provided by this step help to intuitively understand future trends and uncertainties; threshold analysis can timely discover potential failure risks and take measures in advance.
[0130] In the embodiment of the present application, the prediction result is compared with the historical data in the above step S5, and the response measures are formulated including:
[0131] The prediction results are compared with the historical data stored in the big data to obtain the measures that need to be implemented to deal with the results.
[0132] Specifically, the forecast results are compared with historical data to analyze the accuracy and deviation of the forecast.
[0133] Based on the comparison results, the performance of the prediction model is evaluated and the model is tuned if necessary.
[0134] Develop specific response measures, such as increasing maintenance frequency, adjusting operating parameters, etc.
[0135] It should be noted that this step verifies the accuracy of the prediction and improves the reliability of decision-making by comparing historical data; formulating targeted response measures can effectively prevent failures and improve the stability and safety of system operation.
[0136] Example 3
[0137] The above is a schematic scheme of the distribution network fault prediction method of this embodiment. It should be noted that the technical scheme of the distribution network fault prediction system and the technical scheme of the above distribution network fault prediction method belong to the same concept, and the details of the technical scheme of the distribution network fault prediction system in this embodiment that are not described in detail can all be referred to the description of the technical scheme of the above distribution network fault prediction method.
[0138] This embodiment also provides a system based on the distribution network fault prediction method, including:
[0139] The data preparation and preprocessing module is used to collect and preprocess the power fault data to obtain the fault data set;
[0140] Model building and fitting module, used to build and fit the time series prediction model based on the fault data set;
[0141] The future data frame creation module is used to create a data frame of a specified prediction time range based on the fitted time series prediction model;
[0142] A prediction and analysis module, used to generate prediction results and perform threshold analysis based on the fitted time series prediction model and the data frame;
[0143] The overall coordination and response module is used to compare the forecast results with historical data and formulate response measures.
[0144] This embodiment further provides a computing device, which is applicable to the case of the distribution network fault prediction method, including:
[0145] Memory and processor; the memory is used to store computer executable instructions, and the processor is used to execute computer executable instructions to implement the distribution network fault prediction method proposed in the above embodiment.
[0146] This embodiment further provides a storage medium on which a computer program is stored. When the program is executed by a processor, the distribution network fault prediction method proposed in the above embodiment is implemented.
[0147] The storage medium proposed in this embodiment and the distribution network fault prediction method proposed in the above embodiment belong to the same inventive concept. The technical details not fully described in this embodiment can be referred to the above embodiment, and this embodiment has the same beneficial effects as the above embodiment.
[0148] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.
Claims
1. A distribution network fault prediction method, characterized in that: include: Collect power fault data and pre-process them to obtain a fault data set; Based on the fault data set, a time series prediction model is constructed and fitted; Based on the fitted time series forecasting model, create a data frame with a specified forecast time range; Based on the fitted time series prediction model and the data frame, generate prediction results and perform threshold analysis; Compare forecast results with historical data and develop countermeasures.
2. The distribution network fault prediction method according to claim 1, characterized in that: The prediction results are compared with historical data and the response measures are formulated including: The prediction results are compared with the historical data stored in the big data to obtain the measures that need to be implemented to deal with the results.
3. The distribution network fault prediction method according to claim 2, characterized in that: The construction and fitting of a time series prediction model based on the fault data set includes: Build a time series forecasting model including seasonal terms, trend terms, residual terms, and holiday terms.
4. The distribution network fault prediction method according to claim 3, characterized in that: The constructing and fitting a time series prediction model based on the fault data set also includes: In time series forecasting, for all time t, there are two forms, namely, additive form and multiplicative form, where the additive form is expressed as: y t =S t +T t +R t Among them, S t is the seasonal term, T t is the trend term, R t For the remaining items.
5. The distribution network fault prediction method according to claim 4, characterized in that: The constructing and fitting a time series prediction model based on the fault data set also includes: The multiplication form is: and t =S t ×T t ×R t Taking the logarithm of the multiplication, the additive and multiplicative forms are equivalent: Iny t =InS t +InT t +InR t The expression of adding the holiday term ε(t) is: y(t)=g(t)+s(t)+h(t)+ε(t) Among them, g(t) is the trend term, which indicates the trend of the time series in the non-periodic range; s(t) is the seasonal term, which is in weeks or years; h(t) is the holiday term, which indicates whether there are holidays within the time range; ε(t) is the error term / residual term; The g(t) trend term is a function of the logistic regression function and piecewise linear function. The logistic regression function is expressed as: f(x)=C / (1+e -k(x-m) ) Among them, C is the maximum asymptotic value of the curve, k represents the growth rate of the curve, m represents the midpoint of the curve, the special form of the logistic regression function is the sigmoid function, and the derivative form of the sigmoid function is: y′=y(1-y).
6. The distribution network fault prediction method according to claim 5, characterized in that: The constructing and fitting a time series prediction model based on the fault data set also includes: Introducing the holiday impact range parameter κ i , there are L holidays, the formula is: Z(t)=(1 {t∈Di} ,···,1 {t∈DL} ) k=(k1,···,k1) T Among them, κ~Normal(0,v 2 ), when the value is larger, it means that the holiday has a greater impact on the model; when the value is smaller, it means that the holiday has a smaller impact on the model.
7. The method for predicting distribution network faults according to claim 6, characterized in that: The generating of prediction results based on the fitted time series prediction model and the data frame and performing threshold analysis include: By setting a data frame of the prediction time range in the prediction model, the predicted value and its confidence interval are obtained; the confidence interval of the predicted value is compared with the actual value, and an alarm is issued when the predicted value exceeds the threshold or the actual value exceeds the confidence interval.
8. A system using the distribution network fault prediction method according to any one of claims 1 to 7, characterized in that: include: The data preparation and preprocessing module is used to collect and preprocess the power fault data to obtain the fault data set; Model building and fitting module, used to build and fit the time series prediction model based on the fault data set; The future data frame creation module is used to create a data frame of a specified prediction time range based on the fitted time series prediction model; A prediction and analysis module, used to generate prediction results and perform threshold analysis based on the fitted time series prediction model and the data frame; The overall coordination and response module is used to compare the forecast results with historical data and formulate response measures.
9. A computing device comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, the steps of the distribution network fault prediction method described in any one of claims 1 to 7 are implemented.
10. A computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the steps of the distribution network fault prediction method according to any one of claims 1 to 7.
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