Feature selection and prediction method and device for comprehensive load of generic court, and medium

By dynamically adjusting feature selection and adopting the multi-head attention mechanism model, the problem of insufficient accuracy of comprehensive load prediction in the pan-Taiwan area is solved, and accurate prediction and adaptive feature selection of comprehensive load in the pan-Taiwan area is achieved.

CN119906003APending Publication Date: 2025-04-29STATE GRID SHANXI ELECTRIC POWER COMPANY CHANGZHIELECTRIC POWER SUPPLY
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Patent Information

Application Number
CN202411965135.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-30
Publication Date
2025-04-29

AI Technical Summary

Technical Problem

The prior art is difficult to effectively predict the comprehensive load of the pan-Taiwan area, especially when the composition and space-time changes between the Taiwan area are large, resulting in insufficient prediction accuracy.

Method used

By collecting and processing data in advance, training prediction networks, establishing historical high-quality feature experience reference tables, and dynamically adjusting feature selection in intraday scheduling, a three-stage sequence feature selection method and a multi-head attention mechanism model are used for comprehensive load prediction.

Benefits of technology

Accurate prediction of the comprehensive load in the pan-Taiwan area is achieved, adapting to the changes in internal and external factors of the source load in the table area, and automatically and quickly conducting comprehensive load prediction and optimal feature selection of the table area.

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Abstract

The invention relates to a feature selection and prediction method and device for a comprehensive load of a generic court, and a medium, and belongs to the technical field of new energy and energy conservation. Comprising the following steps: early-stage data processing, judging whether feature selection needs to be carried out again or not, implementing three-stage sequential feature selection on partitions subjected to feature selection again, implementing training and use of a new prediction model in a transition period, implementing accurate model training of a mutual attention mechanism, and replacing a temporary model after training. The method is suitable for a dynamic partition management mode of a power distribution system, the prediction model and the characteristic variables can be adaptively changed according to the time change of internal factors of the source load of the transformer area and external factors such as weather, and the comprehensive load prediction and the optimal characteristic selection of the transformer area can be automatically and quickly realized.
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Description

Technical Field

[0001] The invention relates to a feature selection and prediction method, equipment and medium for comprehensive load in a pan-station area, and belongs to the technical field of new energy and energy conservation. Background Art

[0002] In the new distribution system, with the continuous influx of distributed source and load resources such as distributed renewable power generation, electric vehicles (charging piles, charging stations), etc. Under the influence of these distributed uncertain sources and loads, the trend of implementing new technical solutions for the new distribution system that combine main and micro coordination, distribution network hierarchical and partitioned aggregation regulation, and self-discipline control of resources within the partition is becoming more and more obvious. The "partition" mentioned here can be the inherent substation of the distribution network, or it can be a "pan-substation" including multiple physical substations and even feeders divided according to the balance of multiple distributed resources and loads in the region. These "generalized substations" can achieve supply and demand balance or stable supply and demand difference through self-regulation of source storage and load within the block within a certain duration. It can be seen that this "substation" under the new control mode of the distribution network is no longer limited to the traditional substation and may change with time. Below, there is no distinction between traditional substations and pan-substations, and they are uniformly referred to as substations.

[0003] At present, there is not much work on the prediction of the comprehensive load in the substation (the algebraic sum of the load in the area and the power generation in the area). First, the existing research results are all designed for fixed substations. They first predict the load and the photovoltaic power generation in the area respectively, and then make the algebraic sum of the two predicted values, that is, obtain them through indirect methods; second, the current prediction objects are mostly "fixed partitions + customized characteristic variables for each area", and even use the same characteristic variables for different partitions. This obviously cannot better adapt to the new distribution network, which requires timely re-division for regulation and control, and hopes that the load forecast of each partition can be as accurate as possible. That is, previous studies have ignored the composition of the substation and the spatiotemporal changes between substations, so there is a lack of special designs that can support the load forecasting of "time-varying substations" in feature selection and prediction models.

[0004] At present, in the new distribution system, there are still mostly "fixed partitions + customized characteristic variables for each partition", and even the same characteristic variables are used for load forecasting in different partitions. In fact, even for a fixed power substation, the main features used for forecasting should be different in different time periods. These previous methods are obviously not well adapted to the needs of the new distribution network "need to re-partition and regulate in a timely manner, and cannot achieve the most accurate load forecast for each partition". Summary of the invention

[0005] Technical purpose: In order to overcome the deficiencies in the prior art, the present invention provides a method, device and medium for feature selection and prediction of the comprehensive load in a pan-tai area, and a device and medium.

[0006] A method, device and medium for feature selection and prediction of comprehensive load in a pan-tai area, comprising the following steps:

[0007] Step A: Collect and process data, train and use the prediction network in advance, complete the preliminary selection of the candidate feature set and feature vector for each power substation in advance, and obtain historical data containing feature vectors as historical substation data; train the prediction network in advance, and complete the prediction tasks of the prediction before power dispatching; sort out and summarize the feature vectors and prediction models of each substation in the past, and establish a historical high-quality feature experience reference table for each substation;

[0008] Step B: In the intraday scheduling, every fixed time interval T, determine each partition A areai Is it necessary to re-select features? Implement step C for the partitions that need to re-select features; otherwise, continue to use the original prediction model and multivariate features for comprehensive load forecasting;

[0009] Step C: Perform three-stage sequential feature selection on the partitions for re-feature selection;

[0010] Step D: Implement the training and use of the new prediction model during the transition period (the training is completed within 1-2 fixed time intervals T), and then use this prediction model as a temporary model during the temporary transition period. The temporary model stops running at the start time of the model trained in step E. During this stage, in other computing resources, the model training based on the mutual attention mechanism is started at the same time.

[0011] Step E: Implement accurate model training of the mutual attention mechanism. After training, replace the temporary model and implement the comprehensive load forecasting application.

[0012] Furthermore, the feature set to be selected in step A is obtained from the historical load data, meteorological and geographical data, and time and cycle data of the region, and direct features and indirect features are extracted from each type of data as required as the features to be selected.

[0013] Further, the step A comprises:

[0014] Step A1: Construct a candidate set of historical power / load data features; read the cleaned power / load historical data of the substation area, and generate power / load feature variables. The original features are mainly the load value L(ti) at time i before the predicted time t, i=1,2,3,..... and the previous power of distributed power sources such as wind and solar; the indirect features of load are mainly the median value, mean, maximum value, etc. of the historical load at the same time every day within 7 days. Both the original features and the indirect features can be obtained by processing the original data;

[0015] Step A2: Construct a candidate set of meteorological and geographical and cultural data features; read free or purchased related numerical weather forecasts and local meteorological and cultural data. Meteorological variables include temperature, humidity, ground pressure, wind speed at different heights, irradiance, maximum temperature, average temperature and minimum temperature, etc. Geographical and cultural variables include PM2.5, evaporation, perceived temperature, rainfall and population, etc.;

[0016] Step A3: The selected set of time and periodic data feature pairs; the load data of the substation area has a certain periodicity. In order to retain the periodic characteristics of the time characteristics, the sin(t) and cos(t) functions are used here to encode the time characteristics at the same time, so as to capture the characteristics of its periodic trend, such as month, week, hour, and minute. One-hot encoding is used for holidays, and the 3 days before and after special holidays (Spring Festival, May Day, National Day, etc., which are consecutive holidays of no less than 5 days) are also marked;

[0017] Step A4: using a three-stage sequential feature selection method or other feature selection methods to perform feature selection and prediction model training;

[0018] Step A5: Summarize historical experience and establish a reference table of historical high-quality characteristic experience for each area;

[0019] Step A6: Use the current comprehensive load forecasting model to implement the forecasting task and provide the forecasting results to the dispatching link.

[0020] Furthermore, the step B comprises:

[0021] Step B1: Use DTW distance to calculate and determine the prediction trend;

[0022] Step B11: Assume that there are two comprehensive load time series P pre =a1,a2,...,a i , P tru =b1,b2,...,b j

[0023] Where a i and b j They are the time series of comprehensive load forecast value P pre and the actual value time series P tru Power data at the corresponding moment;

[0024] Step B12: Calculate the distance between each pair of points in the two time series and construct a distance matrix H(P pre ,P tru )

[0025]

[0026] Its element D(a i ,b j ) is calculated as follows:

[0027]

[0028] In the formula, d(a i ,b j ) represents the Euclidean distance between two time series;

[0029] Step B13: Calculate the DTW distance DTW(P pre ,P tru );

[0030] First, through dynamic programming, find a path from the upper left corner to the lower right corner of the matrix. The grid points passed by this path represent the aligned points in the two sequences, and the total distance of the path is the smallest. Calculate the cumulative distance along the best path found, and the final value obtained is the DTW distance between the two sequences.

[0031] Step B14: If DTW(P pre ,P tru )>ε1, it is considered that the trend value is out of bounds, and it is necessary to reselect features and update the prediction model;

[0032] Step B2: Weedie deviation is used to measure the persistent deviation between the predicted value and the actual value, which takes into account the variance structure and distribution of the model;

[0033] The calculation formula for measuring weedie deviation is as follows:

[0034]

[0035] Where n is the number of duration time intervals considered;

[0036] y i is the true value;

[0037] is the predicted value;

[0038] p is a small positive integer that can be selected based on actual conditions. For example, when it is 2, the Weedie deviation is equivalent to the average Gamma deviation.

[0039] when It is considered that the persistent deviation is out of bounds and it is necessary to reselect features and update the prediction model;

[0040] If step B1 or step B2 determines that it is necessary to reselect features and update the prediction model, then go to step C; otherwise, return and wait for the next execution of step B.

[0041] Further, the step C comprises:

[0042] Step C1: In the historical high-quality feature experience reference table of each area, and through other external factors (such as season, weather conditions, etc.), a combined query is performed to determine whether there are historical high-quality features in the same geographical area and under the same external factors;

[0043] Step C11: If there is a historical high-quality feature group under the same internal and external factors, determine whether it is completely consistent with the feature group used in step A. If it is completely consistent, execute C111; if it is not completely consistent, execute C112;

[0044] Step C111: jump to step C2;

[0045] Step C112: extract and retain the historical high-quality feature groups, which are subsequently compared with the results of step C235, and the best of the two proceed to step D and step E; this step can also guide the construction of sample sets or directly call the corresponding load forecasting model in subsequent steps;

[0046] Step C12: If there is no historical high-quality feature group under the same internal and external factors, jump to step C2;

[0047] Step C2: Implementing a three-stage sequential feature selection method

[0048] Step C21: Implement the first stage feature selection: Use the Spearman coefficient method to screen the historical load data characteristics of the problem area. The historical load characteristics include: the historical load of the area from 1 time point to 14 time points before the predicted time point, the historical load of the area from 89 time points to 102 time points, and the historical load of the area from 191 time points to 193 time points. There are 31 historical load characteristics of the area in total.

[0049] Step C22: Implement the second stage feature selection: For the historical load characteristics, meteorological and geographical humanities data characteristics, and time and cycle data characteristics of the problem area after step C21, use an integrated feature selection method, such as inputting the initial screening feature set into the constructed LightGBM model to obtain the importance score of each feature;

[0050] Step C23: Implement the third stage feature selection: by constructing a labeled virtual sample set, taking the label of D as the loop variable, looping from i=1 with a step of 1, and retaining the R obtained from the test set in each loop 2 Value, based on n R 2 The value changes, and the corresponding importance score label is retained, which is equivalent to retaining the corresponding feature variable;

[0051] Step C231: sort the n features obtained in step C22 in descending order of importance scores, with the feature with the highest importance score being labeled 1 and the feature with the lowest importance score being labeled n;

[0052] Step C232: construct an input feature set and a label set, the input feature set is the features numbered 1 to i mentioned in step C231, where 1≤i≤n; the label set is the load value of the substation, and in addition, the input feature set and the label set are divided into a training set, a validation set, and a test set according to the ratio of 70%, 10%, and 20%;

[0053] Step C233: Send the dataset constructed in step C232 to the LightGBM model for training and prediction, and retain the R of the test set. 2 value;

[0054] Step C234: let i=i+1, and execute steps C232 and C233 again until i=n;

[0055] Step C235: According to n R 2 Value, when the input feature set adds one more feature, if the test set R 2 The value is compared with the previous R 2 If the value becomes larger, the feature is retained; the set of all retained features is named the saved feature set, and R 2 The features with the highest value and those before it are retained are considered the best feature set for model input.

[0056] Step C236: Extract the historical high-quality feature group retained in step C112 and compare it with the best feature value in step C235, select the best one and proceed to step D; if the result of step C235 is better, update the historical high-quality feature experience table of each substation.

[0057] Further, the step D comprises:

[0058] Step D1: Create sample data sets of encoders such as distributed wind power and distributed photovoltaic for the subsequent comprehensive training of the encoder structure network based on the multi-head attention mechanism;

[0059] Step D11: Original input feature set: historical wind power and historical photovoltaic power, which correspond one-to-one to the time points of historical loads in the best feature set of C236 at the time points;

[0060] Step D12: Position encoding: Position encoding is performed based on sine function and cosine function to generate a position vector;

[0061] Step D13: concatenate the historical feature vector formed in step D11 and use them together as the input of the multi-head attention encoder X = [X1, X2, ...X n ];

[0062] Step D2: Build two feature extraction models based on multi-head attention encoders;

[0063] Step D21: The wind power and photovoltaic power generated in step D13 are used as inputs of two encoders respectively. The multi-head attention mechanism can extract more effective information and reduce the feature dimension when processing the model input information;

[0064] Step D22: Save the output information of the fully connected layer, recorded as extracted information, where the extracted information contains features f1 to fn, which have a total of ndims, which is equal to the output dimension out_dim of the fully connected layer;

[0065] Step D23: The output layer consists of a fully connected layer, and the loss function is set to the mean square error loss function;

[0066] Step D3: Use the data set formed in step D1 to train and extract attention from the model constructed in step D2;

[0067] Step D4: Calculate the Spearman correlation coefficient of the features f1 to fn in the extracted information with the corresponding source-load sequence of the substation area and take the absolute value, retain the features greater than 0.7, and record them as retained features. This operation not only retains the strongly correlated features, but also prevents feature redundancy;

[0068] Step D5: construct the input feature set and label set required for the comprehensive load forecast of the substation area. In addition to the two sets of retained features, the input feature set also includes the features of the best feature set selected in step C236 (including the historical load features of the substation area, date features and meteorological features); the label set consists of comprehensive load data;

[0069] Step D6: Construct a TCN-LSTM model for predicting the comprehensive load of the substation area; the model consists of an input layer, two TCN layers, a Dropout layer, an LSTM layer, and an output layer; wherein the output layer consists of a fully connected layer, and the loss function is set to a mean square error function;

[0070] Step D7: Apply the trained model to make predictions during the transition period; during the application of the model, the input features are the best feature set features in step C236 and the two sets of retained features obtained in step D4.

[0071] Further, the step E comprises:

[0072] Step E1: Create sample datasets of encoders for distributed wind power, distributed photovoltaics, and electric loads for comprehensive training of the subsequent multi-head mutual attention mechanism encoder structure network;

[0073] Step E11: Original input feature set: historical wind power, historical photovoltaic power and historical load power. These data correspond to the time points of the historical load in the best feature set in step C236. The historical load data uses the historical load in the best feature set.

[0074] Step E12: Position encoding: Position encoding is performed based on sine function and cosine function to generate a position vector.

[0075] Step E13: concatenate the historical feature vector formed in step E11 and use them together as the input of the multi-head attention encoder X = [X1, X2, ...X n ];

[0076] Step E2: Construct three feature extraction models based on multi-head mutual attention encoders;

[0077] Step E21: The wind power, photovoltaic power and historical load power generated in step E13 are used as inputs of the three encoders respectively. When the multi-head attention mechanism processes the model input information, it can extract more effective time domain information and reduce the feature dimension;

[0078] Step E22: Save the output information of the fully connected layer, recorded as extracted information, where the extracted information contains features f1 to fn, which have a total of ndims, which is equal to the output dimension out_dim of the fully connected layer;

[0079] Step E23: The output layer consists of a fully connected layer, and the loss function is set to the mean square error function;

[0080] Step E3: Use the data set formed in step E1 to train and extract attention from the model constructed in step E2;

[0081] Step E4: Calculate the Spearman correlation coefficients of the features f1 to fn in the extracted information with the corresponding source-load sequences of the substations and take the absolute values. The features with a value greater than 0.7 are retained and recorded as retained features. This operation not only retains the strongly correlated features, but also prevents feature redundancy.

[0082] Step E5: construct the input feature set and label set required for the comprehensive load forecast of the substation area. In addition to the three sets of retained features, the input feature set also includes a part of the best feature set selected in step C236 (after removing the historical load features of the substation area, the remaining date features and meteorological features, hereinafter referred to as the remaining features of the best feature set); the label set consists of comprehensive load data;

[0083] Step E6: Construct a TCN-LSTM model for predicting the comprehensive load of the substation area; the model consists of an input layer, two TCN layers, a Dropout layer, an LSTM layer, and an output layer, wherein the output layer consists of a fully connected layer, and the loss function is set to a mean square error function;

[0084] Step E7: Apply the trained model to make predictions during the transition period. During the application of the model, the input features are the remaining features of the best feature set in step C236 and the three groups of retained features obtained in step E4.

[0085] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it is based on the feature selection and prediction method, device, and medium for the comprehensive load of the pan-station area.

[0086] A computer-readable storage medium stores a computer program, which, when executed by a processor, is based on the feature selection and prediction method, device and medium for the comprehensive load of a pan-station area.

[0087] Compared with the prior art, the technical effects of the present invention are as follows:

[0088] 1. The present invention is suitable for the dynamic zoning management mode of the distribution system. It can adaptively change the prediction model and characteristic variables according to the time changes of internal factors of the source and load of the substation and external factors such as weather, and can automatically and quickly realize the comprehensive load prediction and optimal feature selection of the substation.

[0089] 2. The present invention can directly and accurately predict the comprehensive load of various types of power substations (including dynamic / static pan-substations and traditional fixed power substations), can better support the day-ahead scheduling of "multiple power substations" in different time periods to be merged into one "partition" in scheduling, and can automatically focus on the characteristic information of the prediction network input.

[0090] 3. The present invention provides a method for transition and self-update of the prediction model. The accurate prediction model can no longer extract the feature information of the external features at the same time, but fully considers the gradual influence of time on these features.

[0091] 4. The present invention proposes a three-stage sequential feature selection method. Through sequential implementation, a feature variable set that is strongly correlated with the regional load can be better selected. Because of its small computing power requirement, the speed is fast, which can change the current common practice of "ignoring the time-varying effects of features in different time periods in feature set selection" and the long-term solidification of feature variables. Through this method, even if the physical geographical boundaries of the substation change, the optimal feature set for the new substation can be quickly obtained. Because the historical comprehensive load and source load of the new substation are easy to obtain, the multi-source strongly correlated feature set of the "new substation" can be quickly obtained through step C in the implementation plan of the present invention.

[0092] 5. The present invention takes into account multi-source data such as historical load data, meteorological and geographical data, time and periodic data, and direct and indirect characteristics at the same time. It is suitable for comprehensive load prediction of substations containing distributed power sources (which can be wind, solar, wind + solar) and electric vehicles, and can directly output the comprehensive load prediction value of the substation. Because it is no longer obtained by indirect algebraic superposition, cumulative errors are avoided.

[0093] 6. The present invention provides a method for transition and self-update of the prediction model, so that before the accurate model is trained, a better model can be used to replace it, thereby reducing the prediction error in the period between the new and old comprehensive load models.

[0094] 7. The accurate prediction model of the present invention is no longer able to extract the feature information of the external features at the same time, but fully considers the gradual influence of time on these features.

[0095] 8. The present invention makes a more comprehensive decision on whether changes are needed based on the trend of the prediction curve and the accumulation of prediction errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 It is a schematic diagram of the process of the present invention;

[0097] Figure 2 It is a diagram of the connection relationship of some processes in the present invention;

[0098] Figure 3 Schematic diagram of the process of step C in the present invention;

[0099] Figure 4 Schematic diagram of the process of step D in the present invention;

[0100] Figure 5 Schematic diagram of the structure of the multi-head attention encoder in the present invention;

[0101] Figure 6 Schematic diagram of the process of step E in the present invention. DETAILED DESCRIPTION

[0102] The following is combined with Figure 1 To Attachment Figure 6 The principles and features of the present invention are described, and the examples given are only used to explain the present invention, rather than to limit the scope of the present invention.

[0103] A method, device and medium for feature selection and prediction of comprehensive load in a pan-tai area, comprising the following steps:

[0104] Step A: Collect and process data, train and use the prediction network in advance, complete the preliminary selection of the candidate feature set and feature vector for each power substation in advance, and obtain historical data containing feature vectors as historical substation data; train the prediction network in advance, and complete the prediction tasks supporting the prediction (including but not limited to the time-ahead prediction for serving the day-ahead dispatch and serving the rolling dispatch within the day) before power dispatch, and establish a historical high-quality feature experience reference table for each substation;

[0105] The candidate feature set in step A is obtained from the historical load data, meteorological and geographical data, time and cycle data of the region. For each type of data, direct features and indirect features are extracted as needed as the candidate features. The direct features are original variables, and the indirect features are generated features extracted through indirect analysis and conversion processing in the time-frequency domain.

[0106] Step A1: Construct a candidate set of historical power / load data features; read the cleaned power source / load historical data of the substation, and generate power / load feature variables. The original features are mainly the load value L(ti) at time i before the predicted time t, i = 1, 2, 3, ..., and the previous power of distributed power sources such as wind and solar; the indirect load features are mainly the median, mean, and maximum values ​​of the historical load at the same time every day within 7 days. Both the original features and the indirect features can be obtained by processing the original data; for the convenience of describing the processing idea, it is assumed without loss of generality that the time interval of the historical data is 15 minutes, that is, 96 data per day.

[0107] Step A2: Construct a candidate set of meteorological and geographical and cultural data features; read free or purchased related numerical weather forecasts and local meteorological and cultural data. Meteorological variables include temperature, humidity, ground pressure, wind speed at different heights, irradiance, maximum temperature, average temperature and minimum temperature, etc. Geographical and cultural variables include PM2.5, evaporation, perceived temperature, rainfall and population, etc.;

[0108] Step A3: The selected set of time and periodic data feature pairs; bus or substation load data has a certain periodicity. In order to retain the periodic characteristics of time features, sin(t) and cos(t) functions are used here to encode time features at the same time, so as to capture the characteristics of its periodic trend, such as month, week, hour, minute. One-hot encoding is used for holidays, and the 3 days before and after special holidays (Spring Festival, May Day, National Day, etc., which are consecutive holidays of no less than 5 days) are also marked;

[0109] Step A4: using a three-stage sequential feature selection method or other feature selection methods to perform feature selection and prediction model training;

[0110] Step A5: Summarize historical experience and establish a historical high-quality feature experience reference table for each area (including the historical high-quality features listed in the table but not limited to these high-quality features, which can be adjusted according to actual conditions); see Table 1,

[0111] Table 1 Reference table of historical high-quality characteristics of each area

[0112]

[0113]

[0114] Step A6: Use the current comprehensive load forecasting model to implement the forecasting task and provide the forecasting results to the dispatching link.

[0115] Step B: In the intraday scheduling, at a fixed time interval T of 15 minutes, determine whether it is necessary to re-select features for each partition, and implement step C for the partitions that need to re-select features; otherwise, continue to use the original prediction model and multivariate features for comprehensive load forecasting;

[0116] Step B1: Use DTW distance to calculate and determine the prediction trend;

[0117] Through step B1, we need to identify each partition A areai Forecast deviation, calculate trend value and continuous deviation value. If the trend value exceeds the limit or the deviation exceeds the set value for multiple time intervals, it is determined that feature selection needs to be re-performed. Implement step C for the partitions that need to be re-selected; otherwise, continue to use the original forecast model and multivariate features for comprehensive load forecasting.

[0118] Step B11: Assume that there are two comprehensive load time series P pre =a1,a2,...,a i , P tru =b1,b2,...,bj

[0119] Where a i and b j They are the time series of comprehensive load forecast value P pre and the actual value time series P tru Power data at the corresponding moment;

[0120] Step B12: Calculate the distance between each pair of points in the two time series and construct a distance matrix H(P pre ,P tru )

[0121]

[0122] Its element D(a i ,b j ) is calculated as follows:

[0123]

[0124] In the formula, d(a i ,b j ) represents the Euclidean distance between two time series;

[0125] Step B13: Calculate the DTW distance DTW(P pre ,P tru );

[0126] First, through dynamic programming, find a path from the upper left corner to the lower right corner of the matrix. The grid points passed by this path represent the aligned points in the two sequences, and the total distance of the path is the smallest. Calculate the cumulative distance along the best path found, and the final value obtained is the DTW distance between the two sequences.

[0127] Step B14: If DTW(P pre ,P tru )>ε1, it is considered that the trend value is out of bounds, and it is necessary to reselect features and update the prediction model;

[0128] Step B2: Weedie deviation is used to measure the persistent deviation between the predicted value and the actual value, which takes into account the variance structure and distribution of the model;

[0129] The calculation formula for measuring weedie deviation is as follows:

[0130]

[0131] Where n is the number of duration time intervals considered;

[0132] y i is the true value;

[0133] is the predicted value;

[0134] p is a small positive integer that can be selected based on actual conditions. For example, when it is 2, the Weedie deviation is equivalent to the average Gamma deviation.

[0135] when It is considered that the persistent deviation is out of bounds and it is necessary to reselect features and update the prediction model;

[0136] If step B1 or step B2 determines that it is necessary to reselect features and update the prediction model, then go to step C; otherwise, return and wait for the next execution of step B.

[0137] Step C: Implement three-stage sequential feature selection on the partition for re-feature selection (i.e., problem partition); by implementing the three-stage sequential feature selection method, rapidity can be ensured while better retaining key feature information and having good versatility for multi-source data.

[0138] Step C1: In the historical high-quality feature experience reference table of each area, and through other external factors (such as season, weather conditions, etc.), a combined query is performed to determine whether there are historical high-quality features in the same geographical area and under the same external factors;

[0139] Step C11: If there is a historical high-quality feature group under the same internal and external factors, determine whether it is completely consistent with the feature group used in step A. If it is completely consistent, execute C111; if it is not completely consistent, execute C112;

[0140] Step C111: jump to step C2;

[0141] Step C112: extract and retain the historical high-quality feature groups, which are subsequently compared with the results of step C235, and the best of the two proceed to step D and step E; this step can also guide the construction of sample sets or directly call the corresponding load forecasting model in subsequent steps;

[0142] Step C12: If there is no historical high-quality feature group under the same internal and external factors, jump to step C2;

[0143] Step C2: Implementing a three-stage sequential feature selection method

[0144] Step C21: Implement the first stage feature selection: Use the Spearman coefficient method to screen the historical load data characteristics of the problem area. The historical load characteristics include the historical load of the area from 1 time point to 14 time points before the predicted time point; the historical load of the area from 89 time points to 102 time points; the historical load of the area from 191 time points to 193 time points; there are 31 historical load characteristics in total;

[0145] Step C22: Implement the second stage feature selection: For the historical load characteristics, meteorological and geographical humanities data characteristics, and time and cycle data characteristics of the problem area after step C21, use an integrated feature selection method, such as inputting the initial screening feature set into the constructed LightGBM model to obtain the importance score of each feature;

[0146] Step C23: Implement the third stage feature selection: by constructing a labeled virtual sample set, taking the label of D as the loop variable, looping from i=1 with a step of 1, and retaining the R obtained from the test set in each loop 2 Value, based on n R 2 The value changes, and the corresponding importance score label is retained, which is equivalent to retaining the corresponding feature variable;

[0147] Step C231: sort the n features obtained in step C22 in descending order of importance scores, with the feature with the highest importance score being labeled 1 and the feature with the lowest importance score being labeled n;

[0148] Step C232: construct an input feature set and a label set, the input feature set is the features numbered 1 to i mentioned in step C231, where 1≤i≤n; the label set is the load value of the substation, and in addition, the input feature set and the label set are divided into a training set, a validation set, and a test set according to the ratio of 70%, 10%, and 20%;

[0149] Step C233: Send the dataset constructed in step C232 to the LightGBM model for training and prediction, and retain the R of the test set. 2 value;

[0150] Step C234: let i=i+1, and execute steps C232 and C233 again until i=n;

[0151] Step C235: According to n R 2 Value, when the input feature set adds one more feature, if the test set R 2 The value is compared with the previous R 2 If the value becomes larger, the feature is retained; the set of all retained features is named the saved feature set, and R 2 The features with the highest value and those before it are retained are considered the best feature set for model input.

[0152] Step C236: Extract the historical high-quality feature group retained in step C112 and compare it with the best feature value in step C235, select the best one and proceed to step D; if the result of step C235 is better, update the historical high-quality feature experience table of each substation.

[0153] The implementation method of step C is shown in Figure 3 , Figure 3 Only one algorithm that can be used in each stage is given, but the actual application is not limited to this algorithm.

[0154] Step D: Implement the training and use of the new prediction model (MHAE-TCN-LSTM joint prediction model) during the transition period. The training is completed within 1-2 fixed time intervals T. Then, during the temporary transition period, this prediction model is used as a temporary model. During this stage, in other computing resources, model training based on the mutual attention mechanism is started at the same time; the running stop time is the starting time of the model trained in step E.

[0155] Step D1: Create sample data sets of encoders such as distributed wind power and distributed photovoltaic for the subsequent comprehensive training of the encoder structure network based on the multi-head attention mechanism;

[0156] Step D11: Original input feature set: historical wind power and historical photovoltaic power, which correspond one-to-one to the time points of historical loads in the best feature set of C236 at the time points;

[0157] Step D12: Position encoding: Position encoding is performed based on sine function and cosine function to generate a position vector;

[0158] Step D13: concatenate the historical feature vector formed in step D11 and use them together as the input of the multi-head attention encoder X = [X1, X2, ...X n ];

[0159] Step D2: Build two feature extraction models based on multi-head attention encoders;

[0160] Step D21: The wind power and photovoltaic power generated in step D13 are used as inputs of two encoders respectively. The multi-head attention mechanism can extract more effective information and reduce the feature dimension when processing the model input information;

[0161] Step D22: Save the output information of the fully connected layer, recorded as extracted information, where the extracted information contains features f1 to fn, which have a total of ndims, which is equal to the output dimension out_dim of the fully connected layer;

[0162] The calculation is based on the following:

[0163] (1) Calculate the attention distribution and information weighting, as shown in formula (D-1) respectively.

[0164] α i =softmax(a(Q,K i))(D-1)

[0165] Where: α i Indicates the degree of attention paid to the i-th information when querying Q in the upper and lower data;

[0166] a(Q,K i ) represents the attention scoring function. The method proposed in this paper uses the additive attention model for scoring.

[0167] Calculate the information weight, as shown in formula (D-2)

[0168]

[0169] Where: X is the input of the encoder;

[0170] att(Q,X) is the final sequence weighted by the attention score, that is, the sequence after encoding the input information X according to the multi-head attention score.

[0171] (2) The feedforward neural network composed of the relu activation function receives the output feature vector A of the previous sublayer, which can be expressed as formula (D-3).

[0172] FNN=w1(relu(w2A+b2))+b1(D-3)

[0173] Where: w1 and w2 represent weights;

[0174] b1 and b2 represent bias;

[0175] FNN represents the calculation result after the feedforward neural network.

[0176] Step D23: The output layer consists of a fully connected layer, and the loss function is set to the mean square error function;

[0177] The final extracted information is obtained after a fully connected layer transforms the dimension of the output information of the previous layer. The number of feature types contained in the extracted information is equal to the output dimension set by the fully connected layer.

[0178] It is worth noting that the multi-head attention sublayer and the feedforward neural network sublayer both use residual connections and layer normalization to solve the gradient vanishing problem. The actual output of each sublayer can be expressed as formula (D-4).

[0179] y=layernorm(x+sublayer(x)) (D-4)

[0180] Where: y represents the output of each sub-layer;

[0181] x represents the input of each sub-layer;

[0182] sublayer indicates the current sublayer;

[0183] layernorm means layer normalization.

[0184] Step D3: Use the data set formed in step D1 to train and extract attention from the model constructed in step D2;

[0185] Step D4: Calculate the Spearman correlation coefficient of the features f1 to fn in the extracted information with the corresponding source-load sequence of the substation (i.e., the substation power sequence and the substation load sequence) and take the absolute value, retain the features greater than 0.7, and record them as retained features. This operation not only retains the strongly correlated features, but also prevents feature redundancy;

[0186] Step D5: construct the input feature set and label set required for the comprehensive load forecast of the substation area. In addition to the two sets of retained features, the input feature set also includes the features of the best feature set selected in step C236 (including historical substation load features, date features, and meteorological features); the label set consists of comprehensive load data;

[0187] Step D6: Construct a TCN-LSTM model for predicting the comprehensive load of the substation area; the model consists of an input layer, two TCN layers, a Dropout layer, an LSTM layer, and an output layer; wherein the output layer consists of a fully connected layer, and the loss function is set to a mean square error function;

[0188] Step D7: Apply the trained model to make predictions during the transition period; during the application of the model, the input features are the best feature set features in step C236 and the two sets of retained features obtained in step D4.

[0189] Figure 4 Schematic diagram of the process of step D in the present invention.

[0190] Step E: Implement the model training of the mutual attention mechanism. After training, replace the temporary model and implement the comprehensive load forecasting application. This step is similar to step D, but slightly different. The model structure is shown in Figure 6 The technical idea is to realize the attention of external factors such as historical power generation of distributed resources, historical load of the substation, and meteorology in the time domain. In other words, through the mutual attention mechanism, the input features extracted and injected into the TCN-LSTM sub-model may not be at the same time. This can play a good role in the case where some external factors such as meteorology data do not come from the substation and the distributed sources and loads in the substation may be correlated.

[0191] Step E1: Create sample datasets of encoders for distributed wind power, distributed photovoltaics, and electric loads for comprehensive training of the subsequent multi-head mutual attention mechanism encoder structure network;

[0192] Step E11: Original input feature set: historical wind power, historical photovoltaic power and historical load power. These data correspond to the time points of the historical load in the best feature set in step C236. The historical load data uses the historical load in the best feature set.

[0193] Step E12: Position encoding: Position encoding is performed based on sine function and cosine function to generate a position vector.

[0194] Step E13: concatenate the historical feature vector formed in step E11 and use them together as the input of the multi-head attention encoder X = [X1, X2, ...X n ];;

[0195] Step E2: Construct three feature extraction models based on multi-head mutual attention encoders;

[0196] Step E21: The wind power, photovoltaic power and historical load power generated in step E13 are used as inputs of the three encoders respectively. When the multi-head attention mechanism processes the model input information, it can extract more effective time domain information and reduce the feature dimension;

[0197] Step E22: Save the output information of the fully connected layer, recorded as extracted information, where the extracted information contains features f1 to fn, which have a total of ndims, which is equal to the output dimension out_dim of the fully connected layer;

[0198] Step E23: The output layer consists of a fully connected layer, and the loss function is set to the mean square error function;

[0199] Step E3: Use the data set formed in step E1 to train and extract attention from the model constructed in step E2;

[0200] Step E4: Calculate the Spearman correlation coefficient of the features f1 to fn in the extracted information with the corresponding source-load sequence of the substation (i.e., the substation power sequence and the substation load sequence) and take the absolute value, and retain the features greater than 0.7, which are recorded as retained features. This operation not only retains the strongly correlated features, but also prevents feature redundancy;

[0201] Step E5: construct the input feature set and label set required for the comprehensive load forecast of the substation area. In addition to the three sets of retained features, the input feature set also includes a part of the best feature set selected in step C236 (after removing the historical load features of the substation area, the remaining date features and meteorological features, hereinafter referred to as the remaining features of the best feature set); the label set consists of comprehensive load data;

[0202] Step E6: Construct a TCN-LSTM model for predicting the comprehensive load of the substation area; the model consists of an input layer, two TCN layers, a Dropout layer, an LSTM layer, and an output layer, wherein the output layer consists of a fully connected layer, and the loss function is set to a mean square error function;

[0203] Step E7: Apply the trained model to make predictions during the transition period. During the application of the model, the input features are the remaining features of the best feature set in step C236 and the three groups of retained features obtained in step E4.

[0204] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it is based on the feature selection and prediction method, device, and medium for the comprehensive load of the pan-station area.

[0205] A computer-readable storage medium stores a computer program, which, when executed by a processor, is based on the feature selection and prediction method, device and medium for the comprehensive load of a pan-station area.

[0206] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method, device and medium for feature selection and prediction of comprehensive load in a pan-tai area, characterized in that: The steps include: Step A: Collect and process data, train and use the prediction network in advance, complete the preliminary selection of the candidate feature set and feature vector for each power substation in advance, and obtain historical data containing feature vectors as historical substation data; train the prediction network in advance, and complete the prediction tasks of the prediction before power dispatching; sort out the feature vectors and prediction models of each substation in the past, and establish a historical high-quality feature experience reference table for each substation; Step B: In the intraday scheduling, every fixed time interval T, determine each partition A areai Is it necessary to re-select features? Implement step C for the partitions that need to re-select features; otherwise, continue to use the original prediction model and multivariate features for comprehensive load forecasting; Step C: Perform three-stage sequential feature selection on the partitions for re-feature selection; Step D: Implement the training and use of the new prediction model in the transition period. The training is completed within 1-2 fixed time intervals T. Then, during the temporary transition period, this prediction model is used as a temporary model. The operation stop time of the temporary model is the start time of the model trained in step E. During this stage, in other computing resources, the model training based on the mutual attention mechanism is started at the same time. Step E: Implement accurate model training of the mutual attention mechanism. After training, replace the temporary model and implement the comprehensive load forecasting application.

2. The feature selection and prediction method, device and medium for the pan-taiwan comprehensive load according to claim 1, characterized in that: The candidate feature set in step A is obtained from the historical load data, meteorological and geographical data, and time and cycle data of the region. For each type of data, direct features and indirect features are extracted as required as the candidate features.

3. The feature selection and prediction method, device and medium for the pan-taiwan comprehensive load according to claim 1, characterized in that: The step A comprises: Step A1: Construct a candidate set of historical power / load data features; read the cleaned power / load historical data of the substation area, and generate power / load feature variables. The original features are mainly the load value L(ti) at time i before the predicted time t, i = 1, 2, 3, ..... and the previous power of distributed power sources such as wind and solar; the indirect features of load are mainly the median value, mean value, and maximum value of the historical load at the same time every day within 7 days. Both the original features and the indirect features can be obtained by processing the original data; Step A2: Construct a candidate set of meteorological and geographical and cultural data features; read free or purchased related numerical weather forecasts and local meteorological and cultural data. Meteorological variables include temperature, humidity, ground pressure, wind speed at different heights, irradiance, maximum temperature, average temperature and minimum temperature. Geographical and cultural variables include PM2.5, evaporation, perceived temperature, rainfall and population. Step A3: A set of pairs of time and periodic data features to be selected; bus or substation load data has a certain periodicity. In order to retain the periodic characteristics of the time feature, the sin(t) and cos(t) functions are used here to encode the time feature at the same time, so as to grasp the characteristics of its periodic trend. One-hot encoding is used for holidays, and the three days before and after special holidays are also marked; Step A4: using a three-stage sequential feature selection method or other feature selection methods to perform feature selection and prediction model training; Step A5: Summarize historical experience and establish a reference table of historical high-quality characteristic experience for each area; Step A6: Use the current comprehensive load forecasting model to implement the forecasting task and provide the forecasting results to the dispatching link.

4. The feature selection and prediction method, device and medium for the pan-taiwan comprehensive load according to claim 1, characterized in that: The step B comprises: Step B1: Use DTW distance to calculate and determine the prediction trend; Step B11: Assume that there are two comprehensive load time series P pre =a1,a2,...,a i , P tru =b1,b2,...,b j Where a i and b j They are the time series of comprehensive load forecast value P pre and the actual value time series P tru Power data at the corresponding moment; Step B12: Calculate the distance between each pair of points in the two time series and construct a distance matrix H(P pre ,P tru ) Its element D(a i ,b j ) is calculated as follows: In the formula, d(a i ,b j ) represents the Euclidean distance between two time series; Step B13: Calculate the DTW distance DTW(P pre ,P tru ); First, through dynamic programming, find a path from the upper left corner to the lower right corner of the matrix. The grid points passed by this path represent the aligned points in the two sequences, and the total distance of the path is the smallest. Calculate the cumulative distance along the best path found, and the final value obtained is the DTW distance between the two sequences. Step B14: If DTW(P pre ,P tru )>ε1, it is considered that the trend value is out of bounds, and it is necessary to reselect features and update the prediction model; Step B2: Weedie deviation is used to measure the persistent deviation between the estimated value and the actual value, taking into account the variance structure and distribution of the model; The calculation formula for measuring weedie deviation is as follows: Where n is the number of duration time intervals considered; y i is the true value; is the predicted value; p is a small positive integer that can be selected based on actual conditions. For example, when it is 2, the Weedie deviation is equivalent to the average Gamma deviation. when It is considered that the persistent deviation is out of bounds and it is necessary to reselect features and update the prediction model; If step B1 or step B2 determines that it is necessary to reselect features and update the prediction model, then go to step C; otherwise, return and wait for the next execution of step B.

5. The method, device and medium for feature selection and prediction of the comprehensive load of the pan-tai area according to claim 1 are characterized in that: The step C comprises: Step C1: In the historical high-quality feature experience reference table of each area, and through other external factor fields, a combined query is performed to determine whether there are historical high-quality features in the same geographical area and under the same external factors; Step C11: If there is a historical high-quality feature group under the same internal and external factors, determine whether it is completely consistent with the feature group used in step A. If it is completely consistent, execute C111; if it is not completely consistent, execute C112; Step C111: jump to step C2; Step C112: extract and retain the historical high-quality feature groups, which are subsequently compared with the results of step C235, and the best of the two proceed to step D and step E; this step can also guide the construction of sample sets or directly call the corresponding load forecasting model in subsequent steps; Step C12: If there is no historical high-quality feature group under the same internal and external factors, jump to step C2; Step C2: Implementing a three-stage sequential feature selection method Step C21: Implement the first stage feature selection: Use the Spearman coefficient method to screen the historical load data characteristics of the problem area. The historical load characteristics include: the historical load of the area from 1 time point to 14 time points before the predicted time point, the historical load of the area from 89 time points to 102 time points, and the historical load of the area from 191 time points to 193 time points. There are 31 historical load characteristics of the area in total. Step C22: Implement the second stage feature selection: For the historical load characteristics, meteorological and geographical humanities data characteristics, and time and cycle data characteristics of the problem area after step C21, use an integrated feature selection method, such as inputting the initial screening feature set into the constructed LightGBM model to obtain the importance score of each feature; Step C23: Implement the third stage feature selection: by constructing a labeled virtual sample set, taking the label of D as the loop variable, looping from i=1 with a step of 1, and retaining the R obtained from the test set in each loop 2 Value, based on n R 2 The value changes, and the corresponding importance score label is retained, which is equivalent to retaining the corresponding feature variable; Step C231: sort the n features obtained in step C22 in descending order according to their importance scores, with the feature with the highest importance score being labeled 1 and the feature with the lowest importance score being labeled n; Step C232: construct an input feature set and a label set, the input feature set is the features numbered 1 to i mentioned in step C231, where 1≤i≤n; the label set is the load value of the substation, and in addition, the input feature set and the label set are divided into a training set, a validation set, and a test set according to the ratio of 70%, 10%, and 20%; Step C233: Send the dataset constructed in step C232 to the LightGBM model for training and prediction, and retain the R of the test set. 2 value; Step C234: let i=i+1, and execute steps C232 and C233 again until i=n; Step C235: According to n R 2 Value, when the input feature set adds one more feature, if the test set R 2 Compared with the previous R 2 If the value becomes larger, the feature is retained; the set of all retained features is named the saved feature set, and R 2 The features with the highest value and those retained before it are considered the best feature set for model input. Step C236: Extract the historical high-quality feature group retained in step C112 and compare it with the best feature value in step C235, select the best one and proceed to step D; if the result of step C235 is better, update the historical high-quality feature experience table of each substation.

6. The method, device and medium for feature selection and prediction of the comprehensive load of the pan-taiwan region according to claim 1, characterized in that: The step D comprises: Step D1: Create sample data sets of encoders such as distributed wind power and distributed photovoltaic for the subsequent comprehensive training of the encoder structure network based on the multi-head attention mechanism; Step D11: Original input feature set: historical wind power and historical photovoltaic power, which correspond one-to-one to the time points of historical loads in the best feature set of C236 at the time points; Step D12: Position encoding: Position encoding is performed based on sine function and cosine function to generate a position vector; Step D13: concatenate the historical feature vector formed in step D11 and use them together as the input of the multi-head attention encoder X = [X1, X2, ...X n ]; Step D2: Build two feature extraction models based on multi-head attention encoders; Step D21: The wind power and photovoltaic power generated in step D13 are used as inputs of two encoders respectively. The multi-head attention mechanism can extract more effective information and reduce the feature dimension when processing the model input information; Step D22: Save the output information of the fully connected layer, recorded as extracted information, where the extracted information contains features f1 to fn, which have a total of ndims, which is equal to the output dimension out_dim of the fully connected layer; Step D23: The output layer consists of a fully connected layer, and the loss function is set to the mean square error function; Step D3: Use the data set formed in step D1 to train and extract attention from the model constructed in step D2; Step D4: Calculate the Spearman correlation coefficient of the features f1 to fn in the extracted information with the corresponding source-load sequence of the substation area and take the absolute value, retain the features greater than 0.7, and record them as retained features. This operation not only retains the strongly correlated features, but also prevents feature redundancy; Step D5: construct the input feature set and label set required for the comprehensive load forecasting of the substation area. In addition to the two sets of retained features, the input feature set also includes features including the best feature set selected in step C236; the label set consists of comprehensive load data; Step D6: Construct a TCN-LSTM model for predicting the comprehensiveness of the substation area; the model consists of an input layer, two TCN layers, a Dropout layer, an LSTM layer, and an output layer; wherein the output layer consists of a fully connected layer, and the loss function is set to a mean square error function; Step D7: Apply the trained model to make predictions during the transition period; during the application of the model, the input features are the best feature set features in step C236 and the two sets of retained features obtained in step D4.

7. The method, device and medium for feature selection and prediction of comprehensive load in the pan-taiwan region according to claim 1, characterized in that: The step E comprises: Step E1: Create sample datasets of encoders for distributed wind power, distributed photovoltaics, and electric loads for comprehensive training of the subsequent multi-head mutual attention mechanism encoder structure network; Step E11: Original input feature set: historical wind power, historical photovoltaic power and historical load power. These data correspond to the time points of the historical load in the best feature set in step C236. The historical load data uses the historical load in the best feature set. Step E12: Position encoding: Position encoding is performed based on sine function and cosine function to generate a position vector. Step E13: concatenate the historical feature vector formed in step E11 and use them together as the input of the multi-head attention encoder X = [X1, X2, ...X n ]; Step E2: Construct three feature extraction models based on multi-head mutual attention encoders; Step E21: The wind power, photovoltaic power and historical load power generated in step E13 are used as inputs of the three encoders respectively. When the multi-head attention mechanism processes the model input information, it can extract more effective time domain information and reduce the feature dimension; Step E22: Save the output information of the fully connected layer, recorded as extracted information, where the extracted information contains features f1 to fn, which have a total of ndims, which is equal to the output dimension out_dim of the fully connected layer; Step E23: The output layer consists of a fully connected layer, and the loss function is set to the mean square error function; Step E3: Use the data set formed in step E1 to train and extract attention from the model constructed in step E2; Step E4: Calculate the Spearman correlation coefficients of the features f1 to fn in the extracted information with the corresponding source-load sequences of the substations and take the absolute values. The features with a value greater than 0.7 are retained and recorded as retained features. This operation not only retains the strongly correlated features, but also prevents feature redundancy. Step E5: construct the input feature set and label set required for the comprehensive load forecasting of the substation area. In addition to the three sets of retained features, the input feature set also includes features including a part of the best feature set selected in step C236; the label set consists of comprehensive load data; Step E6: Construct a TCN-LSTM model for predicting the comprehensive load of the substation area; the model consists of an input layer, two TCN layers, a Dropout layer, an LSTM layer, and an output layer, wherein the output layer consists of a fully connected layer, and the loss function is set to a mean square error function; Step E7: Apply the trained model to make predictions during the transition period. During the application of the model, the input features are the remaining features of the best feature set in step C236 and the three groups of retained features obtained in step E4.

8. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, it is based on the feature selection and prediction method, device and medium for the pan-station area comprehensive load according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it is based on the feature selection and prediction method, device and medium for the pan-taiwan comprehensive load according to any one of claims 1 to 7.