Electric power parameter prediction method based on time sequence deep learning
By applying the power parameter prediction method based on time series deep learning in the power market, the problems of uneven resource distribution and insufficient information disclosure in the power market are solved, more accurate power parameter prediction is achieved, and the stability and efficiency of the power market are improved.
Patent Information
- Application Number
- CN202510105047.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-23
- Publication Date
- 2025-02-28
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Uneven resource distribution, market imbalance, tight and blocked power transmission, as well as imperfect market and insufficient information disclosure in the power market, resulting in increased difficulty in predicting power parameters, affecting the stability and efficiency of the power market.
The power parameter prediction method based on time series deep learning is adopted to obtain historical data and meteorological data, use random forest algorithms and neural network models to make predictions, and correct the prediction values through feature selection and statistical analysis to improve the accuracy of the prediction.
It realizes more accurate and reliable power parameter prediction, helps power market participants formulate more effective trading strategies, and optimizes the scheduling plan of the power system to ensure the safe and stable operation of the power system.
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Figure CN119539452A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of power market, and in particular to a power parameter prediction method based on time series deep learning. Background Art
[0002] With the gradual reform and development of the power market, the rules of the power market have become more and more complex, and the factors involved have become more and more extensive. In recent years, the rapid growth of renewable energy installed capacity has significantly increased its participation in the power market. Especially in provinces where renewable energy accounts for a relatively high proportion, the growth of renewable energy power generation has not only changed the operation mode of the power market, but also had a profound impact on the mechanism related to power parameters.
[0003] Renewable energy generation, especially wind and solar energy, has attracted widespread attention due to its clean and renewable characteristics. However, the power generation of these energy sources is limited by natural conditions and has strong intermittency and uncertainty. With the increase in the installed capacity of new energy, the impact of this uncertainty on the power market has become more obvious. At the same time, due to the uneven distribution of resource endowments in various regions of my country, the supply and demand of the power market has been unbalanced. The power transmission capacity in some regions is tight, and even power transmission is blocked, which further exacerbates the fluctuation of electricity prices.
[0004] On the one hand, the cost of renewable energy generation continues to decline, reducing the marginal clearing parameters of the power market and affecting the economic benefits of traditional energy (such as coal-fired power and natural gas power generation). On the other hand, due to the volatility of renewable energy generation, the power system needs more flexible adjustment resources to ensure the balance between supply and demand, which increases the complexity of the system and poses new challenges to the power parameter formulation mechanism of the power market.
[0005] In addition, the power market structure is not yet sound, information disclosure is incomplete, and market participants are unable to obtain sufficient information in a timely manner to make decisions. This leads to distortion of market power parameter signals, increases the frequency and amplitude of power parameter fluctuations, and makes it more difficult to accurately predict power parameters on the day before. This phenomenon is particularly prominent in regions with large differences in resource endowments. Summary of the invention
[0006] In view of the problems existing in the prior art, the present invention provides a method for predicting power parameters based on time series deep learning, which takes into account factors such as uneven distribution of power market resources, market imbalance, tight and blocked power transmission, as well as market imperfections and insufficient information disclosure.
[0007] To achieve the above object, the technical solution adopted by the present invention is as follows: a method for predicting power parameters based on time series deep learning, comprising the following steps: Obtaining unit duration, target time period and target market; obtaining a preset time period based on the target time period; Obtaining a historical date and time feature set according to the preset time period; Based on the unit time length and the target market, obtain the historical disclosure data set, the historical meteorological data set and the historical power parameter value set for the preset time period; Using feature selection engineering, key meteorological features are obtained according to the historical power parameter value set and the historical meteorological data set; based on the historical meteorological data set, a historical key meteorological feature data set is obtained according to the key meteorological features; Using a random forest algorithm, predicting the undisclosed data set in the target period in the target market based on the historical date and time feature set, the historical disclosed data set, the historical meteorological data set, and the historical power parameter value set; Constructing an initial neural network model, and training the initial neural network model according to the historical disclosure data set, the historical key meteorological feature data set, the historical date and time feature set, and the historical power parameter value set to obtain a power parameter prediction model; Obtaining a disclosed data set, a date and time feature set, and a key meteorological feature data set for the target period; obtaining a set of predicted power parameter values for the target period based on the disclosed data set, the undisclosed data set, the key meteorological feature data set, and the date and time feature set based on the power parameter prediction model; Obtain a unit numerical interval of the power parameter value; based on the unit numerical interval and the historical power parameter value set, respectively obtain a maximum probability numerical interval and a numerical mean using statistics, wherein the maximum probability numerical interval is a unit numerical interval with the maximum probability within the unit time length, and the numerical mean is an average value of the historical power parameter values within the unit time length and within the maximum probability numerical interval; The power parameter prediction value set is corrected according to the maximum probability numerical interval and the numerical mean to obtain a power parameter correction value set.
[0008] In some of these embodiments, the target period is 24 hours starting from midnight.
[0009] In some embodiments, the unit duration is 15 minutes.
[0010] In some embodiments, the step of obtaining the historical disclosure dataset for the preset period based on the unit duration and the target market is: Taking a preset time period as a unit, obtaining the initial disclosure data on the target market in units of a first time length; Normalizing the initial disclosure data to obtain standard disclosure data; Obtaining a standard disclosure data set according to the standard disclosure data; The historical disclosure dataset is obtained by performing missing value and outlier processing on the standard disclosure dataset.
[0011] In some embodiments, the step of acquiring the historical meteorological data set for the preset period based on the unit time length and the target market is: Taking a preset time period as a unit and a second time length as a unit, obtaining initial meteorological data of different areas in the region where the target market is located; Obtaining an initial meteorological data set according to the initial meteorological data; Processing missing values and outliers on the initial meteorological data set to obtain an intermediate meteorological data set; The intermediate meteorological data set is processed in units of the unit time length to obtain the historical meteorological data set.
[0012] In some embodiments, the shorter of the first duration and the second duration is not less than the unit duration.
[0013] In some embodiments, the first duration is the unit duration.
[0014] In some of the embodiments, the core component of the neural network initial model is LSTM, GRU or Transformer.
[0015] In some of the embodiments, when training the initial neural network model, the power parameter prediction model is obtained based on minimizing the mean square error.
[0016] In some embodiments, the formula for obtaining the power parameter correction value set by correcting the power parameter prediction value set according to the maximum probability numerical interval and the numerical mean is: ; In the formula, For the t The power parameter correction value per unit time, For the t The predicted value of power parameters per unit time, For the t Unit duration i The unit value interval is the maximum probability value interval, is the mean value within the maximum probability range, express .
[0017] Compared with the prior art, the present invention has the following beneficial effects: The present invention takes into account factors such as uneven distribution of electricity market resources, market imbalance, tight and blocked power transmission, as well as imperfect market and insufficient information disclosure, and provides more accurate and reliable target period power parameter values to adapt to the rapidly changing electricity market environment, which helps electricity market participants to better formulate trading strategies, and can also help power system operators optimize scheduling plans to ensure the safe and stable operation of the power system. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] Figure 1 This is a flow chart of the power parameter prediction method based on time series deep learning of the present invention; Figure 2 This is a graph of the initial disclosure data in the examples of the present invention; Figure 3 It is the initial meteorological data diagram in the example of the present invention; Figure 4 This is a historical meteorological data diagram after the 24-point data in the calculation example of the present invention is changed to 96-point data; Figure 5 This is a diagram of prediction results of data not disclosed in the examples of the present invention; Figure 6 A comparison chart of the predicted value of the power parameter on the first target day and the actual value of the power parameter in the calculation example of the present invention; Figure 7 A comparison chart of the predicted value of the power parameter, the corrected value of the power parameter and the actual value of the power parameter for the first target day in the calculation example of the present invention; Figure 8 It is a comparison chart of the predicted value of the power parameter, the corrected value of the power parameter and the actual value of the power parameter on the second target day in the calculation example of the present invention. DETAILED DESCRIPTION
[0019] In order to clearly illustrate the technical features of this solution, the following will be combined with the accompanying drawings and examples to describe in detail the implementation methods of this application, so that the application can fully understand how to use technical means to solve technical problems and achieve the corresponding technical effects and implement them accordingly. The embodiments of this application and the various features in the embodiments can be combined with each other without conflict, and the technical solutions formed are all within the scope of protection of this application.
[0020] In the context of uneven resource distribution, market imbalance, tight power transmission and congestion, as well as imperfect markets and insufficient information disclosure, it is particularly important to accurately predict day-ahead power parameters in regions with large amounts of renewable energy generation. This not only helps power market participants to better formulate trading strategies, but also helps power system operators optimize dispatch plans and ensure the safe and stable operation of the power system.
[0021] In the existing technology, the method of establishing linear or nonlinear regression models based on historical data and related economic indicators is mainly used, which is suitable for short-term price forecasting, but has limitations in dealing with complex nonlinear relationships and patterns. Although machine learning methods such as support vector machines (SVM), random forests (RF) and gradient boosting trees (GBT) can handle complex nonlinear relationships, they have limited processing capabilities for long time series data and fail to fully consider the intermittency and uncertainty of renewable energy generation, as well as the impact of other key factors in the power market (such as load changes, market supply and demand, etc.).
[0022] See also Figure 1 The embodiment of the present invention provides a method for predicting power parameters based on time series deep learning, comprising the following steps: Get the unit duration, target period and target market; the target period is 24 hours from midnight, which is the target day; Obtaining a preset period based on the target period; that is, the preset period is for data collection in units of days; Obtain a historical date and time feature set according to a preset time period; Based on the unit time and target market, historical disclosure data sets, historical meteorological data sets and historical power parameter value sets for a preset period are obtained; the unit time is 15 minutes, that is, the frequency of data collection is every 15 minutes, and 96 points of various data are collected every day; The steps to obtain a historical disclosure dataset for a preset period based on unit duration and target market are: The initial disclosure data in the target market is obtained by taking the preset time period as the unit and the first time period as the unit. In order to reduce the amount of data processing, the first time period is the unit time period, and the data is collected and sorted every 15 minutes in the day unit to obtain the initial disclosure data at 96 points every day. The initial disclosure data includes the load data of the entire network, the total output of new energy wind and solar power, the total power generation output, etc. Since the collected initial disclosure data are in different data dimension standards, normalization is required to ensure data consistency, that is, normalization of initial disclosure data to obtain standard disclosure data; Obtain the Standard Disclosure Dataset based on the Standard Disclosure Data; Some data are "dirty" data. Therefore, it is necessary to process missing values and outliers in the standard disclosure data set to obtain the historical disclosure data set. Interpolation is usually used to fill in missing values.
[0023] The steps to obtain the historical meteorological data set for a preset period based on unit duration and target market are as follows: Taking the preset time period as a unit, the initial meteorological data of different regions in the region where the target market is located is obtained in units of the second time length; preferably, the different regions in the region where the target market is located are different cities in the province where the target market is located, and the initial meteorological data include but are not limited to comprehensive meteorological data including wind speed, wind direction, temperature, radiation lightness, etc. at different heights; the second time length is every 1 hour, and the data is collected and sorted in units of every 1 hour of each city every day, so as to obtain various meteorological data of different cities at 24 o'clock every day; Obtaining an initial meteorological data set according to initial meteorological data; The initial meteorological data set is processed for missing values and outliers to obtain the intermediate meteorological data set; The shorter of the first and second time periods is not less than the unit time period. When the first time period is used as the unit time period, the initial meteorological data obtained in units of the second time period cannot correspond one-to-one with the data in the historical disclosure data set, and further processing is required: the intermediate meteorological data set is processed in units of the unit time period to obtain the historical meteorological data set. Specifically: first, the 24-point data is converted into 96-point data, that is, the hourly data is repeated and filled 4 times to become one point of data every 15 minutes.
[0024] Meteorological data show significant differences between cities, so it is necessary to identify the meteorological features that have the greatest impact on power parameters: adopt feature selection engineering, preferably embedded feature selection engineering, to obtain key meteorological features based on historical power parameter value sets and historical meteorological data sets; input the data from the historical power parameter value sets and historical meteorological data sets into the selected machine learning model for training, and optimize the hyperparameters through cross-validation. After the model training is completed, the feature importance scores provided by the model are used to identify the meteorological features that have the greatest impact on the prediction of power parameters, namely the key meteorological features.
[0025] Based on the historical meteorological data set, a historical key meteorological characteristic data set is obtained according to the key meteorological characteristics; The date and time feature set includes the historical date and time feature set and the date and time feature set of the target period; The steps to obtain the date and time feature set are: Get date and time data; date and time data includes date data and time data; Perform time series decomposition and feature engineering processing on date and time data to obtain date and time features. The date and time features include date features and hour features. A date and time feature set is obtained based on the date and time features. Decompose the date data, extract the year data, month data (i.e. month number (1-12)), specific date data of each month (specific date of each month (1-31)) from the date data, and calculate the week data (0-6, where 0 represents Monday) corresponding to each date through time calculation, and calculate the quarter data (1-4) according to the month; In order to solve the problem of data jumping between different values, sine and cosine functions are used to transform them and generate corresponding new features; m ϵ(1,12), monthly specific date data d ϵ(1,31), week data w ϵ(0,6) is processed as follows: ; ; ; In the formula, is the sinusoidal characteristic of the month, is the month cosine characteristic, is the sinusoidal characteristic of a specific date of each month, is the cosine characteristic of the specific date of each month, is the sinusoidal characteristic of the week, is the cosine characteristic of the week; Perform time segmentation and cyclic encoding on the moment data to obtain the corresponding hourly features; Extract hour data from timestamp h ϵ(0,23), that is, time segmentation of the moment data to reflect the fluctuation characteristics of power parameters in different hourly periods of a day; In order to solve the problem of hour data jumping between 0 and 23, the time data is processed by cyclic encoding. By using sine and cosine functions for conversion, two new features are generated, which can naturally express the continuous cycle of 24 hours a day and avoid information loss caused by sudden changes in values. The details are as follows: ; In the formula, is the hourly sinusoidal characteristic, is the hourly cosine characteristic; The random forest algorithm is used as the core prediction model. The core prediction model is trained according to the date and time feature set, the historical disclosure data set, the historical meteorological data set and the historical power parameter value set. During the training process, the cross-validation technology is used to tune the core prediction model parameters to ensure that the core prediction model can not only fit the training data well, but also has strong generalization ability. To prevent overfitting, reasonable hyperparameters such as the maximum depth and the minimum number of sample splits are set, and the number of trees in the forest is controlled. The trained core prediction model is used to predict the undisclosed data set in the target market during the target period. Construct an initial neural network model, and train the initial neural network model based on the historical disclosure data set, the historical key meteorological feature data set, the date and time feature set, and the historical power parameter value set to obtain a power parameter prediction model; The historical disclosure data set, historical key meteorological feature data set, date and time feature set and historical power parameter value set are taken as a whole to construct a training sample set. Each set of data in the training sample set includes historical disclosure data, historical key meteorological feature data, date and time feature and historical power parameter value in a preset time period. The training sample set includes a training set and a validation set. In the training sample set, the training set and the validation set are allocated at a ratio of 8:2. According to the data characteristics and prediction requirements, LSTM, GRU or Transformer are selected as the core components of the initial neural network model, and the overall structure of the initial neural network model is defined, including the input layer, hidden layer (such as LSTM layer, GRU layer or Transformer encoder layer) and output layer, to ensure that the initial neural network model can accept the above training sample set as input and output the predicted value of the power parameters in the target period; When training the initial model of the neural network, the power parameter prediction model is obtained based on the minimum mean square error; to ensure the generalization ability of the initial model of the neural network, the cross-validation technology is used, and reasonable hyperparameters such as batch size, learning rate, and number of iterations are set. The performance of the initial model of the neural network is continuously evaluated through the validation set, the mean square error (MSE) is calculated, and the parameters of the initial model of the neural network are adjusted according to the changes in MSE until the model configuration with the minimum mean square error is found. The model with the minimum mean square error is determined as the optimal model, which is the power parameter prediction model, and its weight and structure are saved; the mean square error formula is: ; In the formula, is the mean square error, is the number of samples in the validation set, is the serial number of the sample in the validation set, For the The historical power parameter values of samples, For the The predicted value of power parameters of samples; Obtain the disclosed data set and key meteorological characteristic data set of the target period; based on the power parameter prediction model, obtain the power parameter prediction value set of the target period according to the disclosed data set, the undisclosed data set, the key meteorological characteristic data set and the date and time feature set; Obtain the unit value interval of the power parameter value; divide the power parameter value into segments according to 100 yuan / MWh; Based on the unit numerical interval and the historical power parameter value set, statistics are used to obtain the maximum probability numerical interval and the numerical mean, respectively. The maximum probability numerical interval is the unit numerical interval with the maximum probability within the unit time length, and the numerical mean is the average value of the historical power parameter values within the unit time length and the maximum probability numerical interval; Obtain 96 points of historical power parameter value data collected per unit time every day in the past month, divide the power parameter values into segments according to 100 yuan / MWh, obtain the number of historical power parameter values in each unit value interval of the same unit time, and calculate the probability of each unit value interval in the same unit time; ; In the formula, For the t The historical power parameter value within the unit time is i The probability of the distribution of unit value intervals, For the t Unit time within the first i Unit value interval The number of historical power parameter values, For the t Unit time within the first i The serial number of the historical power parameter value within the unit value interval, For the t Unit time within the first i The total number of historical power parameter values within a unit value interval, is the unit duration serial number, is the unit value interval serial number, For the t The total number of historical power parameter values within a unit time period; The unit value interval corresponding to the maximum value is the maximum probability value interval ; According to the maximum probability value interval Calculate the mean of the values : In the formula, For thet The maximum probability value interval within the unit time The first Historical power parameter values, For the t The maximum probability value interval within the unit time The serial number of the historical power parameter value within, K is the t The maximum probability value interval within the unit time The total number of historical power parameter values within; The power parameter prediction value set is corrected according to the maximum probability numerical interval and the numerical mean to obtain the power parameter correction value set.
[0026] In some embodiments, the formula for obtaining the power parameter correction value set by correcting the power parameter prediction value set according to the maximum probability value interval and the value mean is: ; In the formula, For the t The power parameter correction value per unit time, For the t The predicted value of power parameters per unit time, For the t Unit duration i The unit value interval is the maximum probability value interval, is the mean value within the maximum probability range, express ; That is, when the power parameter prediction value is within the maximum probability value interval If the power parameter prediction value is within the range of 0, the power parameter correction value is obtained without processing the power parameter prediction value; otherwise, the power parameter correction value is obtained after processing the power parameter prediction value.
[0027] Case Analysis See also Figure 2 , collect the initial disclosure data of the target market, collect and organize it in units of 15 minutes per day, obtain various initial disclosure data at 96 points per day, and pre-process it to obtain the historical disclosure data set; Collect the initial meteorological data of the target market, collect and organize it in units of days and hours, and obtain 24 points of data, see Figure 3 , and convert 24-point data to 96-point data, see Figure 4 , and obtain key meteorological features through feature engineering screening, and then obtain a historical key meteorological feature data set; The existing date and time data are extended with features. Since the power parameter values in the power market are periodic and volatile, the date and time data are decomposed into time series and feature engineered to obtain a date and time feature set related to the time period, including hours, years, months, days, and corresponding trigonometric function continuous transformation features. Considering the market conditions in different provinces, some markets only have market disclosure data for the next day, while longer-term market data is insufficiently disclosed. Based on this, a random forest model is established to predict the undisclosed market information and meteorological data. Taking a certain day as an example, the undisclosed data is predicted, and the results are as follows: Figure 5 As shown; The neural network initial model is trained based on the time series deep learning method, with 100 training cycles and 20 parameter combination training in each cycle. The model with the smallest mean square error is selected as the optimal model through the validation set verification; for the prediction set data, the optimal model is first imported, and the target period characteristics consistent with the training set are input for prediction to obtain the target period power parameter prediction value. Taking the first target period, i.e. the first target day, as an example, the specific power parameter prediction value results Figure 6 As shown, the predicted results in the figure are depicted according to the predicted values of the power parameters, and the actual results are depicted according to the actual values of the power parameters; By performing statistical probability analysis on historical power parameter values, the power parameter forecast values obtained in step 5 are post-processed. Taking the first target day and the second target day as examples, the power parameter forecast value results are corrected to obtain the power parameter correction value, such as Figure 7 , 8 As shown, Figure 7 , 8 In the figure, the prediction result (prediction value) is depicted according to the prediction value of the power parameter, the correction result (correction value) is depicted according to the corrected value of the power parameter, and the real result (real value) is depicted according to the real value of the power parameter.
[0028] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions of the technical solution of the present invention by ordinary technicians in this field do not deviate from the essence and scope of the technical solution of the present invention.
Claims
1. A method for predicting power parameters based on time series deep learning, characterized in that: The following steps are involved: Get unit duration, target time period and target market; Acquire a preset time period based on the target time period; Obtaining a historical date and time feature set according to the preset time period; Based on the unit time length and the target market, obtain the historical disclosure data set, the historical meteorological data set and the historical power parameter value set for the preset time period; Using feature selection engineering, key meteorological features are obtained based on the historical power parameter value set and the historical meteorological data set; Based on the historical meteorological data set, obtaining a historical key meteorological feature data set according to the key meteorological features; Using a random forest algorithm, predicting the undisclosed data set in the target period in the target market based on the historical date and time feature set, the historical disclosed data set, the historical meteorological data set, and the historical power parameter value set; Constructing an initial neural network model, and training the initial neural network model according to the historical disclosure data set, the historical key meteorological feature data set, the historical date and time feature set, and the historical power parameter value set to obtain a power parameter prediction model; Obtaining a disclosed data set, a date and time feature set, and a key meteorological feature data set for the target period; obtaining a set of predicted power parameter values for the target period based on the disclosed data set, the undisclosed data set, the key meteorological feature data set, and the date and time feature set based on the power parameter prediction model; Get the unit value interval of the power parameter value; Based on the unit numerical interval and the historical power parameter value set, a maximum probability numerical interval and a numerical mean are obtained respectively by using statistics, wherein the maximum probability numerical interval is the unit numerical interval with the maximum probability within the unit time length, and the numerical mean is the average value of the historical power parameter values within the unit time length and within the maximum probability numerical interval; The power parameter prediction value set is corrected according to the maximum probability numerical interval and the numerical mean to obtain a power parameter correction value set.
2. The method for predicting power parameters based on time series deep learning according to claim 1, characterized in that: The target period is 24 hours starting from midnight.
3. The method for predicting power parameters based on time series deep learning according to claim 2 is characterized in that: The unit duration is 15 minutes.
4. The method for predicting power parameters based on time series deep learning according to claim 2 is characterized in that: The steps of obtaining the historical disclosure data set for the preset period based on the unit duration and the target market are: Taking a preset time period as a unit, obtaining the initial disclosure data on the target market in units of a first time length; Normalizing the initial disclosure data to obtain standard disclosure data; Obtaining a standard disclosure data set according to the standard disclosure data; The historical disclosure dataset is obtained by performing missing value and outlier processing on the standard disclosure dataset.
5. The method for predicting power parameters based on time series deep learning according to claim 4 is characterized in that: The steps of acquiring the historical meteorological data set for the preset period based on the unit time length and the target market are: Taking a preset time period as a unit and a second time length as a unit, obtaining initial meteorological data of different areas in the region where the target market is located; Obtaining an initial meteorological data set according to the initial meteorological data; Processing missing values and outliers on the initial meteorological data set to obtain an intermediate meteorological data set; The intermediate meteorological data set is processed in units of the unit time length to obtain the historical meteorological data set.
6. The method for predicting power parameters based on time series deep learning according to claim 5 is characterized in that: The shorter of the first duration and the second duration is not less than the unit duration.
7. The method for predicting power parameters based on time series deep learning according to claim 6, characterized in that: The first duration is the unit duration.
8. The method for predicting power parameters based on time series deep learning according to claim 1, characterized in that: The core components of the neural network initial model are LSTM, GRU or Transformer.
9. The method for predicting electric power parameters based on time series deep learning according to claim 8, characterized in that: When training the neural network initial model, the power parameter prediction model is obtained according to the minimum mean square error.
10. The method for predicting power parameters based on time series deep learning according to claim 1, characterized in that: The formula for obtaining the power parameter correction value set by correcting the power parameter prediction value set according to the maximum probability numerical interval and the numerical mean is: ; In the formula, For the t The power parameter correction value per unit time, For the t The predicted value of power parameters per unit time, For the t Unit duration i The unit value interval is the maximum probability value interval, is the mean value within the maximum probability range, express .
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