CN113723717B - Method, device, equipment and readable storage medium for predicting short-term load before system day - Google Patents
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Abstract
The invention relates to a method, a device, equipment and a readable storage medium for predicting the short-term load of a system in the day, wherein the method comprises the following steps: collecting historical data and preprocessing the historical data; constructing a training sample set by utilizing the preprocessed historical data; training a pre-established XGboost multi-target regression model by using a training sample set to obtain a trained XGboost multi-target regression model; generating predicted sample features; and inputting the characteristics of the predicted samples into the trained XGboost multi-target regression model to obtain the predicted short-term load. According to the technical scheme, the efficiency of model training, deployment and prediction is improved, and the accuracy of short-term load prediction is improved.
Description
Technical Field
The invention belongs to the technical field of energy monitoring equipment, and particularly relates to a method, a device, equipment and a readable storage medium for predicting the short-term load of a system in the day ahead.
Background
The production, transmission, distribution and use of electric energy are carried out simultaneously, because the electric energy cannot be stored in large quantity, the supply and demand of the electric energy must be kept balanced in real time, and the power dispatching needs to make the start and stop of a unit and the maintenance plan of electric equipment in advance according to the future load demand, so the accurate load prediction has important significance for the dispatching operation of a power grid, and the load prediction level directly influences the economic benefit and the social benefit of an electric power system.
The short-term load prediction before the system day generally refers to the prediction of load demands at 96 moments in 15 minutes every day in advance, and belongs to the typical supervised regression problem in the field of machine learning. In the traditional load prediction, problem modeling is usually decomposed into a regression problem of a single target moment by moment, the moment to be predicted is considered to have a correlation with the load value and meteorological factors at the same moment in a historical day, and 96 regression models are trained by utilizing historical data to predict the load values at 96 moments in the future. The method usually ignores the continuous characteristic of the load curve in a long time range, and is easy to cause the under-fitting of the model. Meanwhile, 96 models need to be trained, feature engineering and sample engineering need to be performed on each model, time consumption is often large, and training of complex models by using a large amount of data is not facilitated.
Disclosure of Invention
In view of the above, the present invention provides a method, an apparatus, a device and a readable storage medium for predicting a short-term load in a system day ahead, so as to solve the problems in the prior art that a model is under-fitted and training 96 models takes a lot of time, which is not favorable for training a complex model using a large amount of data.
According to a first aspect of embodiments of the present application, there is provided a method for predicting a short-term load before a system day, the method including:
acquiring historical data and preprocessing the historical data;
constructing a training sample set by utilizing the preprocessed historical data;
training a pre-established XGboost multi-target regression model by using the training sample set to obtain a trained XGboost multi-target regression model;
generating predicted sample features;
and inputting the predicted sample characteristics into the trained XGboost multi-target regression model to obtain the predicted short-term load.
Further, the historical data includes: historical short-term load values, historical meteorological values and historical load variations;
the meteorological indexes in the historical meteorological values comprise: temperature, humidity, rainfall, wind, and cloud cover.
Further, the preprocessing the historical data includes:
filling missing values in the historical data by using an interpolation method, and performing normalization processing on the historical data after the missing values are filled to obtain the preprocessed historical data.
Further, the constructing a training sample set by using the preprocessed historical data includes:
and dividing the time of the preprocessed historical data into 96 time points, and constructing a training sample set by using the preprocessed historical data of the 96 time points.
Further, the training of the pre-established XGBoost multi-objective regression model by using the training sample set to obtain the trained XGBoost multi-objective regression model includes:
dividing the training sample set into a training set and a verification set;
and training the pre-established XGboost multi-target regression model by using the training set until the error between the obtained predicted historical load value and the actual historical load value is smaller than a first threshold value when the pre-established XGboost multi-target regression model is verified by using the verification set, finishing the training and obtaining the trained XGboost multi-target regression model.
Further, the predicting the sample feature includes:
load values of k-M time points before the time to be predictedAnd the meteorological values of k-M time points before the time to be predictedLoad variation of k-M time points before the time to be predictedA month feature, a date type feature, an hour feature where the start time to be predicted is located, and a minute feature of the start time to be predicted;
wherein k is a time point to be predicted; m is a tunable hyperparameter, and M is a positive integer value; load variation of k-M time points before time to be predictedAnd so on.
Further, the step of inputting the prediction sample characteristics into the trained XGBoost multi-objective regression model to obtain the predicted short-term load includes:
determining an objective function of the trained XGboost multi-objective regression model according to the following formula:
in the above formula, the first and second carbon atoms are,n is the total number of predicted sample features,m is the total number of time points to be predicted;for the feature vector of the ith prediction sample feature,the actual load value of the k time point to be predicted of the ith prediction sample characteristic,the predicted load value of the kth predicted sample characteristic at the time point to be predicted at the t-1 th iteration is obtained,to predict the load value at the kth point in time to be predicted, a new model is added in the t-th iteration,the complexity of the new model added for the t-th iteration when predicting the load value of the kth time point to be predicted,is a loss function;
inputting the predicted sample characteristics as independent variables into the objective function of the trained XGboost multi-objective regression modelAnd when the load is less than or equal to the second threshold or the iteration round number t is equal to a third threshold, outputting the predicted loads of all the time points, wherein the predicted loads of all the time points are predicted short-term loads.
According to a second aspect of the embodiments of the present application, there is provided a system day-ahead short-term load prediction apparatus, the apparatus including:
the preprocessing module is used for acquiring historical data and preprocessing the historical data;
the construction module is used for constructing a training sample set by utilizing the preprocessed historical data;
the training module is used for training a pre-established XGboost multi-target regression model by using the training sample set to obtain a trained XGboost multi-target regression model;
a generation module for generating predicted sample features;
and the prediction module is used for inputting the characteristics of the prediction samples into the trained XGboost multi-target regression model to obtain the predicted short-term load.
According to a third aspect of embodiments of the present application, there is provided a system day-ahead short-term load prediction apparatus, including:
a memory having an executable program stored thereon;
a processor for executing the executable program in the memory to implement the steps of the system day-ahead short-term load prediction method described above.
According to a fourth aspect of the embodiments of the present application, there is provided a readable storage medium, on which an executable program is stored, the executable program, when executed by a processor, implementing the steps of the method for predicting the short-term load before day of the system as described above.
By adopting the technical scheme, the invention can achieve the following beneficial effects: by acquiring historical data, preprocessing the historical data, constructing a training sample set by using the preprocessed historical data, training a pre-established XGboost multi-target regression model by using the training sample set to obtain the trained XGboost multi-target regression model, generating a prediction sample characteristic, and inputting the prediction sample characteristic into the trained XGboost multi-target regression model to obtain a predicted short-term load, the efficiency of model training, deployment and prediction is improved, and the accuracy of short-term load prediction is also improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow diagram illustrating a method of system day-ahead short-term load prediction, according to an exemplary embodiment;
fig. 2 is a block diagram illustrating a system day-ahead short-term load prediction apparatus according to an exemplary embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the examples given herein without any inventive step, are within the scope of the present invention.
Fig. 1 is a flow chart illustrating a method for predicting a short-term load before a system day according to an exemplary embodiment, which may be used in a terminal, but not limited to, as shown in fig. 1, including the steps of:
step 101: collecting historical data and preprocessing the historical data;
step 102: constructing a training sample set by utilizing the preprocessed historical data;
step 103: training a pre-established XGboost multi-target regression model by using a training sample set to obtain a trained XGboost multi-target regression model;
step 104: generating predicted sample features;
step 105: and inputting the characteristics of the predicted samples into the trained XGboost multi-target regression model to obtain the predicted short-term load.
The embodiment of the invention provides a system day-ahead short-term load forecasting method, which is different from the traditional method, the day-ahead short-term load forecasting problem is defined as a multi-target learning task, and the forecasting of load values at 96 moments in the future is realized by constructing a multi-target regression model. Specifically, historical data are collected and preprocessed, a training sample set is constructed by the preprocessed historical data, a pre-established XGboost multi-target regression model is trained by the training sample set to obtain the trained XGboost multi-target regression model, and training and prediction of the multi-target regression model are achieved; by generating the prediction sample characteristics and inputting the prediction sample characteristics into the trained XGboost multi-target regression model, the predicted short-term load is obtained, the model training, deploying and predicting efficiency is improved, and the short-term load predicting accuracy is improved.
Further, the historical data includes: historical short-term load values, historical meteorological values and historical load variations;
weather indicators in the historical weather values include: temperature, humidity, rainfall, wind, and cloud cover.
Further, the step 101 of preprocessing the history data includes:
and filling missing values in the historical data by using an interpolation method, and performing normalization processing on the historical data after the missing values are filled to obtain preprocessed historical data.
It should be noted that the manners of "filling up missing values in history data by using interpolation" and "performing normalization processing on history data after filling up missing values" related to the embodiments of the present invention are well known to those skilled in the art, and therefore, the specific implementation manner thereof is not described too much.
Further, step 102 includes:
and dividing the time of the preprocessed historical data into 96 time points, and constructing a training sample set by using the preprocessed historical data of the 96 time points.
It will be appreciated that the time of day is divided into 96 time points, each of which is 15 minutes apart. Compared with the traditional method, the sample construction method can obtain the sample amount which is nearly 96 times, can effectively support the full update of the model parameters on the large-scale characteristic space, and avoids model under-fitting.
It should be noted that for the multi-objective regression task, each label in the sample is modeled by using the same model and features, so that compared with the conventional method, the complexity of model training is greatly reduced, and the method is beneficial to training the model by using a large number of data sets.
Further, step 103 includes:
dividing a training sample set into a training set and a verification set;
and training the pre-established XGboost multi-target regression model by using the training set until the error between the obtained predicted historical load value and the actual historical load value is smaller than a first threshold value when the pre-established XGboost multi-target regression model is verified by using the verification set, finishing the training and obtaining the trained XGboost multi-target regression model.
Further, predicting the sample features includes:
load values of k-M time points before the time to be predictedAnd the meteorological values of k-M time points before the time to be predictedLoad variation of k-M time points before the time to be predictedA month feature, a date type feature, an hour feature where the start time to be predicted is located, and a minute feature of the start time to be predicted;
wherein k is a time point to be predicted; m is a tunable hyperparameter, and M is a positive integer value; load variation of k-M time points before time to be predictedAnd so on.
Specifically, the month feature refers to 12 months of the year, the date feature refers to each day in each month, and the date type feature refers to monday through sunday.
For example, as can be seen from the above description, if a day is divided into 96 time points, and each time point is separated by 15 minutes, then the time point for predicting the sample feature is also divided into 96 time points, and 0 am is the first time point. Assuming that the load value at 1 am in the next morning needs to be predicted, k is 5. Assuming that M is 4, k-M =5-4=1, k-M +1=5-4+1=2, k-M +2=5-4+2=3, and k-M +3=5-4+3= 4.
It should be noted that the dmlc native XGBoost multi-objective regression model cannot support training and prediction of the multi-objective regression model, and as shown below, the XGBoost model of a single objective regression task defines a loss function as follows:
in the above formula, the first and second carbon atoms are,n is the total number of samples;for the ith sample, label,the feature vector of the i-th sample,the predicted value of the model for the ith sample in the t-1 th iteration,the new model is added for the t-th iteration,the complexity of the model to be added for the t-th iteration,is a loss function.
In the technical solution provided in the embodiment of the present invention, the XGBoost multi-objective regression model loss function is modified to support the multi-objective regression model, and then, step 105 includes:
determining an objective function of the trained XGboost multi-objective regression model according to the following formula:
in the above formula, the first and second carbon atoms are,n is the total number of predicted sample features,m is the total number of time points to be predicted;for the feature vector of the ith prediction sample feature,the actual load value of the k time point to be predicted of the ith prediction sample characteristic,the predicted load value of the kth predicted sample characteristic at the time point to be predicted at the t-1 th iteration is obtained,to predict the load value at the kth point in time to be predicted, a new model is added in the t-th iteration,the complexity of the new model added for the t-th iteration when predicting the load value of the kth time point to be predicted,is a loss function;
inputting the predicted sample characteristics as independent variables into the target function of the trained XGboost multi-target regression modelAnd when the load is less than or equal to the second threshold or the iteration round number t is equal to the third threshold, outputting the predicted load of all the time points, wherein the predicted load of all the time points is the predicted short-term load.
It is understood that the method provided by the embodiment of the present invention may embody the power load as a continuous time sequence, and the load value at the time point to be predicted is not only related to the historical time point, but also has a great correlation with the load value at the nearest available point.
Experiments prove that after the system short-term load prediction method provided by the embodiment of the invention is stably operated for a period of time, the statistical average RMPSE precision can reach 97.29%, and the precision is obviously improved compared with the precision of 94.43% in the earlier-stage deployment traditional method. In the aspect of operation efficiency, the new method framework separates a model training flow from a prediction flow, the training flow is a timing scheduling task, the prediction flow is a calling task, and compared with a traditional method which couples the training flow and the prediction flow together, the prediction efficiency is greatly improved, and the time consumption is improved to 400ms from the previous time consumption of nearly 30 s.
The embodiment of the invention provides a system day-ahead short-term load forecasting method, which is different from the traditional method, the day-ahead short-term load forecasting problem is defined as a multi-target learning task, and the forecasting of load values at 96 moments in the future is realized by constructing a multi-target regression model. Specifically, historical data are collected and preprocessed, a training sample set is constructed by the preprocessed historical data, a pre-established XGboost multi-target regression model is trained by the training sample set to obtain the trained XGboost multi-target regression model, and training and prediction of the multi-target regression model are achieved; by generating the prediction sample characteristics and inputting the prediction sample characteristics into the trained XGboost multi-target regression model, the predicted short-term load is obtained, the model training, deployment and prediction efficiency is improved, and the short-term load prediction accuracy is improved.
An embodiment of the present invention further provides a system short-term load forecasting apparatus before day, as shown in fig. 2, the apparatus includes:
the preprocessing module is used for acquiring historical data and preprocessing the historical data;
the construction module is used for constructing a training sample set by utilizing the preprocessed historical data;
the training module is used for training a pre-established XGboost multi-target regression model by utilizing a training sample set to obtain the trained XGboost multi-target regression model;
a generation module for generating predicted sample features;
and the prediction module is used for inputting the characteristics of the prediction samples into the trained XGboost multi-target regression model to obtain the predicted short-term load.
Further, the historical data includes: historical short-term load values, historical meteorological values and historical load variations;
weather indicators in the historical weather values include: temperature, humidity, rainfall, wind, and cloud cover.
Further, the preprocessing module is specifically configured to:
and filling missing values in the historical data by using an interpolation method, and performing normalization processing on the historical data after the missing values are filled to obtain preprocessed historical data.
Further, the building block is specifically configured to:
and setting the time point length of the preprocessed historical data to be 96, and constructing a training sample set by using the preprocessed historical data of the 96 time points.
Further, the training module is specifically configured to:
dividing a training sample set into a training set and a verification set;
and training the pre-established XGboost multi-target regression model by using the training set until the error between the obtained predicted historical load value and the actual historical load value is smaller than a first threshold value when the pre-established XGboost multi-target regression model is verified by using the verification set, finishing the training and obtaining the trained XGboost multi-target regression model.
Further, predicting the sample features includes:
load values of k-M time points before the time to be predictedAnd the meteorological values of k-M time points before the time to be predictedLoad variation of k-M time points before the time to be predictedA month feature, a date type feature, an hour feature where the start time to be predicted is located, and a minute feature of the start time to be predicted;
where k is the time to be predictedPoint; m is a tunable hyperparameter, and M is a positive integer value; load variation of k-M time points before time to be predictedAnd so on.
Further, the prediction module is specifically configured to:
determining an objective function of the trained XGboost multi-objective regression model according to the following formula:
in the above formula, the first and second carbon atoms are,n is the total number of predicted sample features,m is the total number of time points to be predicted;for the feature vector of the ith prediction sample feature,the actual load value of the k time point to be predicted of the ith prediction sample characteristic,the predicted load value of the kth predicted sample characteristic at the time point to be predicted at the t-1 th iteration is obtained,to predict the load value at the kth point in time to be predicted, a new model is added in the t-th iteration,for predicting the k-th time to be predictedThe complexity of a new model increased by the t-th iteration at the moment of the load value of the point,is a loss function;
inputting the predicted sample characteristics as independent variables into the target function of the trained XGboost multi-target regression modelAnd when the load is less than or equal to the second threshold or the iteration round number t is equal to the third threshold, outputting the predicted load of all the time points, wherein the predicted load of all the time points is the predicted short-term load.
The embodiment of the invention provides a system day-ahead short-term load forecasting method, which is different from the traditional method, the day-ahead short-term load forecasting problem is defined as a multi-target learning task, and the forecasting of load values at 96 moments in the future is realized by constructing a multi-target regression model. Specifically, historical data are collected through a preprocessing module and preprocessed, a construction module constructs a training sample set by using the preprocessed historical data, the training module trains a pre-established XGboost multi-target regression model by using the training sample set to obtain the trained XGboost multi-target regression model, and training and prediction of the multi-target regression model are achieved; the prediction sample characteristics are generated through the generation module, and the prediction sample characteristics are input into the trained XGboost multi-objective regression model through the prediction module to obtain the predicted short-term load, so that the model training, deploying and predicting efficiency is improved, the short-term load predicting accuracy is improved, and compared with the traditional method.
It is to be understood that the apparatus embodiments provided above correspond to the method embodiments described above, and corresponding specific contents may be referred to each other, which are not described herein again.
The embodiment of the invention also provides a system day-ahead short-term load prediction device, which comprises:
a memory having an executable program stored thereon;
and the processor is used for executing the executable program in the memory to realize the steps of the system day-ahead short-term load prediction method provided by the embodiment.
The embodiment of the invention also provides a readable storage medium, on which an executable program is stored, and the executable program realizes the steps of the system short-term load prediction method in the day before when being executed by a processor.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (9)
1. A method for predicting a short-term load of a power system in the day ahead, the method comprising:
acquiring historical data and preprocessing the historical data;
constructing a training sample set by utilizing the preprocessed historical data;
training a pre-established XGboost multi-target regression model by using the training sample set to obtain a trained XGboost multi-target regression model;
generating predicted sample features;
inputting the predicted sample characteristics into the trained XGboost multi-target regression model to obtain a predicted short-term load;
inputting the predicted sample characteristics into the trained XGboost multi-objective regression model to obtain a predicted short-term load, wherein the predicted short-term load comprises the following steps:
determining an objective function of the trained XGboost multi-objective regression model according to the following formula:
in the above formula, the first and second carbon atoms are,n is the total number of predicted sample features,m is the total number of time points to be predicted;for the feature vector of the ith prediction sample feature,for the actual load value of the power grid at the kth time point to be predicted of the ith prediction sample characteristic,predicting a load value of the power grid at a kth time point to be predicted of the ith prediction sample characteristic during the t-1 th iteration,to predict the grid load value at the kth point of time to be predicted, a new model is added in the t-th iteration,the complexity of a new model which is added in the t-th iteration when the grid load value of the kth time point to be predicted is predicted,is a loss function;
inputting the predicted sample characteristics as independent variables into the objective function of the trained XGboost multi-objective regression modelLess than or equal to a second threshold or number of iterations t, etcAnd outputting the predicted loads of all the time points at the third threshold, wherein the predicted loads of all the time points are predicted short-term loads.
2. The method of claim 1, wherein the historical data comprises: historical short-term power grid load values, historical meteorological values and historical load variation;
the meteorological indexes in the historical meteorological values comprise: temperature, humidity, rainfall, wind, and cloud cover.
3. The method of claim 1, wherein the pre-processing the historical data comprises:
and utilizing an interpolation method to fill missing values in the historical data, and carrying out normalization processing on the historical data after the missing values are filled to obtain the preprocessed historical data.
4. The method of claim 1, wherein constructing a training sample set using the preprocessed historical data comprises:
and dividing the time of the preprocessed historical data into 96 time points, and constructing a training sample set by using the preprocessed historical data of the 96 time points.
5. The method as claimed in claim 1, wherein the training of the pre-established XGBoost multi-objective regression model by using the training sample set to obtain the trained XGBoost multi-objective regression model comprises:
dividing the training sample set into a training set and a verification set;
and training the pre-established XGboost multi-target regression model by using the training set until the error between the obtained predicted historical power grid load value and the actual historical power grid load value is smaller than a first threshold value when the pre-established XGboost multi-target regression model is verified by using the verification set, finishing training and obtaining the trained XGboost multi-target regression model.
6. The method of claim 1, wherein predicting the sample features comprises:
the power grid load value of k-M time points before the time to be predictedAnd the meteorological values of k-M time points before the time to be predictedLoad variation of k-M time points before the time to be predictedA month feature, a date type feature, an hour feature where the start time to be predicted is located, and a minute feature of the start time to be predicted;
7. An apparatus for predicting a short-term load before a day in a power system, the apparatus comprising:
the preprocessing module is used for acquiring historical data and preprocessing the historical data;
the construction module is used for constructing a training sample set by utilizing the preprocessed historical data;
the training module is used for training a pre-established XGboost multi-target regression model by using the training sample set to obtain a trained XGboost multi-target regression model;
a generation module for generating predicted sample features;
the prediction module is used for inputting the characteristics of the prediction samples into the trained XGboost multi-target regression model to obtain predicted short-term load;
the prediction module is specifically configured to:
determining an objective function of the trained XGboost multi-objective regression model according to the following formula:
in the above formula, the first and second carbon atoms are,n is the total number of predicted sample features,m is the total number of time points to be predicted;for the feature vector of the ith prediction sample feature,for the actual load value of the power grid at the kth time point to be predicted of the ith prediction sample characteristic,predicting a load value of the power grid at a kth time point to be predicted of the ith prediction sample characteristic during the t-1 th iteration,to predict the grid load value at the kth point of time to be predicted, a new model is added in the t-th iteration,for predicting the grid load of the kth time point to be predictedThe complexity of the new model added in the t-th iteration at load,is a loss function;
inputting the predicted sample characteristics as independent variables into the target function of the trained XGboost multi-target regression modelAnd when the load is less than or equal to the second threshold or the iteration round number t is equal to the third threshold, outputting the predicted load of all the time points, wherein the predicted load of all the time points is the predicted short-term load.
8. A power system day-ahead short-term load prediction apparatus, comprising:
a memory having an executable program stored thereon;
a processor for executing the executable program in the memory to implement the steps of the method of any one of claims 1-6.
9. A readable storage medium having stored thereon an executable program, wherein the executable program, when executed by a processor, performs the steps of the method of any one of claims 1-6.
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