Smooth multi-cycle feature-based interpretable short-term load prediction method

Abstract

The invention provides an interpretable short-term load prediction method based on smooth multi-cycle characteristics. The interpretable short-term load prediction method comprises the following steps: step 1, determining a historical load time sequence, a date type and a meteorological factor of a cloud database as sample characteristics; 2, creating a group of primary functions based on time; 3, supposing that the load data comprises a plurality of periods, and needing to generate an additional primary function; 4, constructing a linear regression learning model, and selecting a hyper-parameter value on the data in the sample by using cross validation; evaluating the performance on the verification set by training the model and using a minimum error function, thereby determining the values of hyper-parameters # imgabs0 #, # imgabs1 # and # imgabs2 #; and step 5, according to the time feature vectors in the step 1 and the step 3, finishing prediction of future load by adopting the linear regression parameters after parameter optimization. According to the technical scheme, the smoothness is enhanced by representing the target estimation signal as the linear combination of the smooth basis function, and indirect support is provided for electric power supervision and electric power sustainable development.

Description

Technical Field

[0001] The invention relates to the technical field of energy storage systems, and in particular to an interpretable short-term load forecasting method based on smooth multi-period characteristics. Background Art

[0002] Electricity load forecasting plays a vital role in the formulation of energy distribution strategies and emergency management plans by utility companies. In recent years, with the large-scale access of renewable energy, load forecasting of power systems faces greater challenges, especially due to the intermittent and volatile nature of renewable energy such as wind and solar energy, which makes it difficult to predict the changes in electricity load. Traditional forecasting methods have been unable to cope with this complexity and dynamics, resulting in a decrease in forecasting accuracy. In addition, with the increasing uncertainty of climate change and user behavior, load volatility is even more difficult to capture. Therefore, how to more accurately forecast electricity load, especially how to effectively deal with the uncertainty problem in forecasting, has become a hot topic in current research. In recent years, more and more research has focused on using advanced algorithms such as machine learning and deep learning to improve the accuracy of load forecasting, and quantify uncertainty through probabilistic forecasting, interval forecasting, etc., so as to provide more reliable decision-making basis for power grid dispatching and energy management. This trend not only improves the accuracy of forecasting, but also provides innovative solutions to meet the needs of complex energy systems in the future.

[0003] Against the backdrop of widespread access to renewable energy, increased load volatility, and increasingly prominent forecasting uncertainty issues, traditional load forecasting methods rely on large amounts of data, are difficult to combine with physical models, lack explainability and transparency, require high computing resources, and are difficult to correct forecasting errors.

[0004] The Chinese patent application number is: CN201710206481.5, and the name is: A method for short-term load forecasting of power grids with adaptive local nonlinear regression deviation compensation. First, the exponential smoothing prediction method is used to predict future loads and related factor vectors based on historical load data and historical related factor vectors, and the deviation between historical load and predicted load and the deviation between historical related factor vector and predicted related factor vector are calculated. Then, linear regression is performed on the load deviation and the related factor vector deviation. The model is further subjected to an F test. If the F test fails, the support vector machine method is used for fitting; if the F test passes, the linear regression method is directly used for prediction to obtain the final short-term load forecasting result. This method uses different models to construct neural networks, and does not take into account that there is still room for further optimization at the model structure level. When considering the impact on historical electricity load, the influencing factors of dimensions such as periodic factors and meteorological factors are not fully considered, so that the relevant factors in load forecasting cannot be better captured.

[0005] The Chinese patent application number is CN201710608297.3, and the name is: Short-term and medium-term power load forecasting method based on machine learning model. This method is based on the short-term and medium-term power load forecasting method of the machine learning model. First, the data is preprocessed, that is, the abnormal data is smoothed and the missing data is filled, and the factors affecting the load change are analyzed, including historical data, time periodicity, and weather variable characteristics. In order to speed up the learning speed and improve the prediction accuracy, all input variables are normalized, and an AdaBoost algorithm with a gradient boosting regression tree as a base classifier is proposed for the final load forecast. This method takes into account factors such as time cycle and weather variables, and is suitable for situations where the demand response is the same or similar in the same period of different seasons. However, for those that are greatly affected by seasons, it is impossible to build a load forecasting model based on data from a single season, and it is impossible to accurately capture the periodic change characteristics of the load. Therefore, it is urgent to build a set of appropriate time-based basis functions to extract time characteristics (such as daily, weekly, and seasonal changes) and interactions between different cycles (such as differences in daily change patterns in a year), so as to enhance the smoothness of the load signal and better understand and analyze its characteristics. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide an interpretable short-term load forecasting method based on smooth multi-period characteristics, which enhances the smoothness by representing the target estimation signal as a linear combination of smooth basis functions, thereby providing indirect support for power regulation and sustainable development of power.

[0007] To achieve the above object, the present invention adopts the following technical solution: an interpretable short-term load forecasting method based on smooth multi-period characteristics, comprising the following steps: Step 1: Determine the historical load time series, date type, and meteorological factors of the cloud database as sample characteristics, use the K nearest neighbor interpolation method to fill in the missing values, and select and eliminate outliers; Step 2: Create a set of time-based basis functions, and design the corresponding harmonic order for the natural basis functions of the smooth periodic function according to the periodic harmonic characteristics; Step 3: Assuming that the load data has multiple periods, in order to model the interaction between different periods, it is necessary to generate additional basis functions, which are the products of basis functions associated with different periods, to extract multi-period time cross terms and further capture the interaction between different periods; Step 4: Build a linear regression learning model and use cross-validation on the in-sample data to select hyperparameter values; for a given set of hyperparameters, determine the hyperparameters by training the model and using the minimum error function to evaluate performance on the validation set. , as well as The value of represents the constant term bias of the model, represents the weight parameter of the time feature, Represents the weight parameter of past time data; Step 5: Based on the time characteristic vector, the linear regression parameters after parameter optimization are used to complete the prediction of future load.

[0008] In a preferred embodiment, the step 1 specifically includes: Step 11: Set prediction tasks, each of which uses the past M historical values To predict the future H load values, that is ; Introduce symbols , which represents the vector of M past values ​​at time t, expressed by formula (1): (1) Where T represents the maximum time step of the prediction; Step 12: Use K nearest neighbor interpolation method to fill the missing values ​​in the load data and use box plot to identify outliers; Step 13: Use the local outlier factor LOF to identify outliers, and determine whether a data point is an outlier by measuring the density difference between a data point and its neighboring points; Step 14: For the holiday factor, decompose and extract the features of "day of the year", "whether it is a weekend", and "hour of the day", and convert them into recognizable digital signals; One-hot encoding is used to expand the values ​​of discrete features to the Euclidean space. A certain value of the discrete feature corresponds to a certain point in the Euclidean space, making the distance calculation between features more reasonable.

[0009] In a preferred embodiment, the step 12 specifically includes: Step 121: Use z-score standardization to convert the data into a standard normal distribution with a mean of 0 and a variance of 1, as shown in formula (2); (2) in is the eigenvalue, is the mean of the feature, is the standard deviation of the feature; Step 122: For each sample with missing values, calculate the distance between it and other complete samples; the commonly used distance measurement method is Euclidean distance. and The distance between , and satisfy and , the distance calculation is shown in formula (3); (3) in, and It is a sample and samples In the The value of a feature, is the number of features; Step 123: After calculating the Euclidean distance, select the vector with the missing value The k complete samples with the closest Euclidean distance are used as the nearest neighbor samples, which will be used to calculate the filling value; for the missing value vector Each missing feature of , use the weighted average value of the k samples closest to the missing value on the feature to fill in the missing value; the weight is the inverse of the distance between each neighbor and the missing value, that is, the closer the distance, the greater the contribution of the sample. The corresponding formula is shown in (4); (4) in, Is a missing feature The fill value of is the nearest neighbor sample In the The value of a feature, is the nearest neighbor sample With missing samples The distance between Find the filling value of the target missing value and complete the filling of the missing values ​​in the load data.

[0010] In a preferred embodiment, the step 2 specifically includes: Step 21: Create time-based basis functions ,in Explain as The value of a time-base function at time t, is the number of time-based functions; Step 22: According to the characteristics of periodic harmonics, consider a period , which does not need to be an integer; the natural basis functions of smooth periodic functions are 2K sinusoidal Fourier terms or harmonics up to K, and the corresponding formula is shown in (5); (5) is the harmonic number, is the maximum value of a harmonic number. And the period is The period of the basis function is ; Step 23: To model different periodicities, each period is set , satisfying the conditions , and set For the The harmonics of the cycle, represents the total number of cycles; in addition, the basis functions are harmonics of all cycles The sum is expressed as , each basis function has a harmonic number.

[0011] In a preferred embodiment, the step 3 specifically includes the following steps: Step 31: Construct the cross-term function, for the number of cycles , the corresponding formula is shown in (6); (6) To calculate the cross terms between harmonics of different periods, different m and n The value of m and n is a period index that satisfies ; Cross terms Indicates harmonics and , with a coefficient of 2; for each of the cross terms or product basis functions, associate the smaller period in the product and assign a harmonic number that is the harmonic number associated with the smaller period; considering the cross terms ,in ; Combine it with the cycle Connect them and assign them harmonic numbers , is the cross-corrected harmonic number and the corresponding period is ;unless is a rational number, otherwise these cross-term basis functions are not periodic, and the cross-term basis functions are periodic; Step 32: Obtain the time-based full basis function, which corresponds to formula (7); (7) Here the basis functions are marked as , and the related harmonic number is ; The harmonics of each basis function range from to , that is, the range satisfies the interval from the minimum harmonic value to the maximum harmonic value, where are harmonics in the periodic model; and all basis functions are perpendicular to each other; Step 33: Given basis functions , creating a time-based feature vector , corresponding to formula (8); (8) Define basis functions for all real parameters , when creating features, they are evaluated only an integer number of times, where is the number of time-based functions.

[0012] In a preferred embodiment, in step 5, the linear regression parameters after parameter optimization are used to complete the future load The prediction of is shown in formula (9); (9) in, is a feature vector based only on time, The dimension is , that is, time-based features; parameters in the model is a constant offset term, which is used in the prediction Dimensional; is a time-based parameter, and its corresponding parameter matrix dimension is ; is the autoregressive parameter, and its corresponding parameter matrix dimension is .

[0013] Compared with the prior art, the present invention has the following beneficial effects: 1) Encode seasonal patterns based on time-based full basis functions and use cross terms to simulate the interaction between power loads in different periods: Creatively incorporate the interaction between power loads in different periods into the linear regression load forecasting model, and enhance the smoothness by expressing the target estimation signal as a linear combination of smooth basis functions, providing indirect support for power regulation and sustainable development of power.

[0014] 2) Advantages of the linear regression load forecasting model: It can still provide relatively accurate forecast results even when data is limited. The model is not only well interpretable, but also transparent and modifiable, making it easier for analysts to understand and adjust the model. It captures the cyclical trends in load changes by using past historical load data and a series of time-based features (such as date and hour). These time features can effectively reflect daily, weekly, seasonal and even annual fluctuations, providing reliable support for load management, dispatch optimization and energy distribution of power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 The flowchart of the explainable short-term load forecasting process model based on smooth multi-period characteristics according to the preferred embodiment of the present invention; Figure 2 This is a flow chart of the KNN algorithm of a preferred embodiment of the present invention; Figure 3 It is a schematic diagram of the local outlier factor detection principle of a preferred embodiment of the present invention; Figure 4 is the daily average power load of the preferred embodiment of the present invention (the dotted line is the training / test separation boundary within the sample); Figure 5 The power load of two different weeks on the test set of the preferred embodiment of the present invention; Figure 6 It is a hyperparameter iterative adjustment process of a preferred embodiment of the present invention; Figure 7 This is a graph of prediction results based on smoothed multi-period features using all factors according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0016] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0017] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0018] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0019] An interpretable short-term load forecasting method based on smooth multi-period characteristics, reference Figure 1-7 , including the following steps: Step 1: Determine the historical load time series, date type, meteorological factors and other factors of the cloud database as sample characteristics, use the K nearest neighbor interpolation method to fill in the missing values, and select and eliminate outliers.

[0020] Step 1.1 Select the three-year power load data, date type and meteorological factors from January 1, 2020 to December 31, 2022 as the research object, and preprocess all data (including historical load series, date type and meteorological factors). The missing values ​​are supplemented in turn by discarding, completing, and true value conversion, and the outliers are selected and eliminated. The preprocessed part of the power data (corresponding to the feature terms) is shown in Table 1.

[0021] Table 1:

[0022] In Table 1, "time" indicates a specific date and time as well as an offset time, for example: 2020-07-01 00:00:00+01:00 2020-07-01 00:00:00 indicates that this is a specific date and time; +01:00 indicates that the time is offset by +1 hour based on Coordinated Universal Time (UTC).

[0023] "End time" indicates the time after adding the offset time to the previous time. For example, 2020-07-01 00:00:00+01:00 indicates 0 o'clock. If 1 hour is added to 00:00:00, the end time is 01:00:00.

[0024] Step 1.2 uses the KNN interpolation method to fill in the missing values ​​in the load data, and uses the box plot to identify abnormal values. The filling values ​​of the input feature part are shown in Table 2.

[0025] Table 2

[0026] Step 1.3 uses the Local Outlier Factor (LOF) to identify outliers by measuring the density difference between a data point and its neighboring points to determine whether it is an outlier.

[0027] Step 1.4: For the holiday factor, decompose and extract features such as "day of the year", "whether it is a weekend", "hour of the day", etc., and convert them into recognizable digital signals.

[0028] Step 2: Create a set of appropriate time-based basis functions and design the corresponding harmonic orders for the natural basis functions of the smooth periodic functions according to the periodic harmonic characteristics.

[0029] Step 2.1 Establish time-based basis functions ,in Explain as The value of a time-base function at time t, is the number of time-based functions.

[0030] Step 2.2 According to the characteristics of periodic harmonics, consider a period , which does not need to be an integer, the natural basis functions for smooth periodic functions are the 2K sinusoidal Fourier terms or harmonics up to K.

[0031] Step 2.3 In order to model different periodicities, each period is set , satisfying the conditions , and set For the The harmonics of the cycle, represents the total number of cycles; in addition, the basis functions are harmonics of all cycles The sum is expressed as , each basis function has a harmonic number, is the maximum value of the harmonic number.

[0032] Step 3: Since the load data has multiple periods (such as daily, weekly, and annual), in order to model the interactions between different periods, additional basis functions need to be generated. These basis functions are the products of basis functions associated with different periods to extract multi-period time cross terms and further capture the interactions between different periods.

[0033] Step 3.1 Construct the cross-term function, for the number of cycles , the corresponding formula is shown in (6); (6) To calculate the cross terms between harmonics of different periods, different m and n The value of m and n is a period index that satisfies ; Cross terms Indicates harmonics and , with a coefficient of 2; for each of the cross terms or product basis functions, associate the smaller period in the product and assign a harmonic number that is the harmonic number associated with the smaller period; considering the cross terms ,in ; Combine it with the cycle Connect them and assign them harmonic numbers , is the cross-corrected harmonic number and the corresponding period is ;unless is a rational number, otherwise these cross-term basis functions are not periodic, and the cross-term basis functions are periodic.

[0034] Step 3.2 obtains the time-based full basis function, which corresponds to formula (7); (7) Here the basis functions are marked as , and the related harmonic number is ; The harmonics of each basis function range from to , that is, the range satisfies the interval from the minimum harmonic value to the maximum harmonic value, where are harmonics in a periodic model; and all basis functions are perpendicular to each other.

[0035] Step 3.3 Given the basis function , creating a time-based feature vector , corresponding to formula (8); (8) Define basis functions for all real parameters , when creating features, they are evaluated only an integer number of times, where is the number of time-based functions.

[0036] Step 4: Build a linear regression learning model and use cross-validation on the in-sample data to select appropriate hyperparameter values. For a given set of hyperparameters, the hyperparameters are determined by training the model and using the minimum error function to evaluate the performance of the point prediction objective function on the validation set. , as well as The corresponding point prediction objective function is

[0037] in, represents the constant term bias of the model, represents the weight parameter of the time feature, Represents the weight parameter of past time data, t Usually represents the time step, i represents the dimension of the prediction, is the training set, and They are t The actual value and predicted value at the moment, is a regularization term used to control the complexity of the model and avoid overfitting. It is the Frobenius norm, which is usually used for matrix norm calculation. It calculates the sum of the squares of all elements in the matrix and then takes the square root.

[0038] For the structural hyperparameters of the above network, the optimal structure is determined through cyclic greedy search, and the regularization is determined. (Controls model complexity and helps with feature selection) The value range is Regularization (Control the size of the weight to prevent overfitting) The value range is ; The range of values ​​of polynomial characteristic degree ; Use mean square error (MSE) as the loss function; cross validation fold is 10, step factor The value is , the learning rate is , initialize the weights using a uniform distribution method. Figure 6 The corresponding hyperparameter iterative adjustment process is shown.

[0039] Step 5: Based on the time feature vectors in steps 1 and 3, the linear regression parameters after parameter optimization in step 4 are used to complete the future load The prediction of in, is a feature vector based only on time, The dimension is , that is, time-based features; parameters in the model is a constant offset term, which is used in the prediction Dimensional; is a time-based parameter, and its corresponding parameter matrix dimension is ; is the autoregressive parameter, and its corresponding parameter matrix dimension is .

[0040] To visualize the seasonal changes, we first look at the daily average power load, e.g. Figure 4 We observe that the in-sample and test data are similar, with a slight increase in the energy load during the test period compared to the in-sample period. The median of the training data is 850.7 kWh, and its mean absolute deviation is 150.9. The median of the test data is 858.0 kWh, and its mean absolute deviation is 151.3. We also observe that there are two major energy demand peaks each year, one smaller in winter and one larger in summer.

[0041] Next, we look at the data at a finer scale. Figure 5 The electrical energy demand for the first week of January 2022 and the first week of August 2022, both of which are in the test data, is shown. We observe several expected phenomena, such as higher demand during the day than at night and slightly higher in summer than in winter. It can be observed that the shape of the daily demand in winter is very different from that in summer. In winter, we see a double bump with peaks in the morning and afternoon, while in summer we see a smooth daily variation with a peak in the early afternoon. In addition, even if the daily demand curves for the same season are similar, they show some variations. For example, the daily demand on Monday, January 8, 2022 is smaller and less smooth than on other days of the week.

[0042] We select the forecast horizon H =24 (a day), memory M =72 (three days), for our multi-period base, we choose P =3 cycles: daily, weekly and yearly, corresponding to the cycle , and ;Pick After completing the parameter configuration, the corresponding ablation experiments are carried out on different variants of the linear regression learning model based on multi-smoothing periodic features (the structures and training parameters of different variant models are optimized in the same way). The corresponding variant structures are as follows: • Variant Model 1: Basic linear regression model, using the historical load of the past three days to predict the power consumption of the next day, that is ; • Variant Model 2: This model uses the same multi-period features but does not use the past values ​​of the time series, i.e. ; • Variant Model 3: This model uses the past values ​​of the time series but does not use the temporal features, i.e. ; • Variant Model 4: The proposed model uses the past values ​​of the time series as well as the temporal features and considers the cross terms, i.e. .

[0043] The average absolute error (Average Absolute Error, AAE) is selected as the evaluation indicator, where: , is the test set, is the total length of the data of the corresponding set. The corresponding error evaluation results are shown in Table 3.

[0044] Table 3

[0045] Through the analysis of the results, compared with the basic linear regression model of variant 1 (the structure and training parameters are optimized in the same way), variant 4, which considers the interpretable short-term load forecasting model based on multi-smoothing periodic characteristics, can more accurately predict the load demand in the context of power market reform and smart grid construction. Figure 7 The following graph shows the forecast results of variant 4 using all factors based on smoothed multi-period features.

[0046] The present invention focuses on encoding seasonal patterns using full basis functions of time, using cross terms to simulate the interaction between power loads in different periods, and provides an interpretable short-term load forecasting method based on smooth multi-period features under the background of widespread access to renewable energy, increased load volatility and forecast uncertainty, so as to increase the forecast accuracy and interpretability under the condition of predicted load changes. First, data preprocessing is performed on historical data related to power load, including data cleaning, removal of outliers and other operations; data of different scales and ranges are unified into a specified range through normalization. Secondly, a set of appropriate time-based basis functions is created, and the corresponding harmonic order is designed for the natural basis functions of smooth periodic functions according to the periodic harmonic characteristics. Then, the load signal is represented as a linear combination of smooth basis functions (such as spline functions and polynomials) using the smooth multi-period time feature technology to enhance the smoothness; in order to model the interaction between different periods, additional basis functions need to be generated, which are the product of basis functions associated with different periods, so as to extract multi-period time cross terms and further capture the interaction between different periods. Finally, reasonable weights are assigned according to the importance of time features, and the coupled prediction of power load is realized by linear regression method.

Claims

1. An interpretable short-term load forecasting method based on smooth multi-period characteristics, characterized in that: The following steps are involved: Step 1: Determine the historical load time series, date type, and meteorological factors of the cloud database as sample characteristics, use the K nearest neighbor interpolation method to fill in the missing values, and select and eliminate outliers; Step 2: Create a set of time-based basis functions, and design the corresponding harmonic order for the natural basis functions of the smooth periodic function according to the periodic harmonic characteristics; Step 3: Assuming that the load data has multiple periods, in order to model the interaction between different periods, it is necessary to generate additional basis functions, which are the products of basis functions associated with different periods, to extract multi-period time cross terms and further capture the interaction between different periods; Step 4: Build a linear regression learning model and use cross-validation on the in-sample data to select hyperparameter values; for a given set of hyperparameters, determine the hyperparameters by training the model and using the minimum error function to evaluate performance on the validation set. , as well as The value of represents the constant term bias of the model, represents the weight parameter of the time feature, Represents the weight parameter of past time data; Step 5: Based on the time characteristic vector, the linear regression parameters after parameter optimization are used to complete the prediction of future load.

2. The interpretable short-term load forecasting method based on smooth multi-period characteristics according to claim 1 is characterized in that: The step 1 specifically includes: Step 11: Set prediction tasks, each of which uses the past M historical values To predict the future H load values, that is ; Introduce symbols , which represents the vector of M past values ​​at time t, expressed by formula (1): （1） Where T represents the maximum time step of the prediction; Step 12: Use K nearest neighbor interpolation method to fill the missing values ​​in the load data and use box plot to identify outliers; Step 13: Use the local outlier factor LOF to identify outliers, and determine whether a data point is an outlier by measuring the density difference between a data point and its neighboring points; Step 14: For the holiday factor, decompose and extract the features of "day of the year", "whether it is a weekend", and "hour of the day", and convert them into recognizable digital signals; One-hot encoding is used to expand the values ​​of discrete features to the Euclidean space. A certain value of the discrete feature corresponds to a certain point in the Euclidean space, making the distance calculation between features more reasonable.

3. The interpretable short-term load forecasting method based on smooth multi-period characteristics according to claim 2 is characterized in that: The step 12 specifically includes: Step 121: Use z-score standardization to convert the data into a standard normal distribution with a mean of 0 and a variance of 1, as shown in formula (2); （2） in is the eigenvalue, is the mean of the feature, is the standard deviation of the feature; Step 122: For each sample with missing values, calculate the distance between it and other complete samples; the commonly used distance measurement method is Euclidean distance. and The distance between , and satisfy and , the distance calculation is shown in formula (3); （3） in, and It is a sample and samples In the The value of a feature, is the number of features; Step 123: After calculating the Euclidean distance, select the vector with the missing value The k complete samples with the closest Euclidean distance are used as the nearest neighbor samples, which will be used to calculate the filling value; for the missing value vector Each missing feature of , use the weighted average value of the k samples closest to the missing value on the feature to fill in the missing value; the weight is the inverse of the distance between each neighbor and the missing value, that is, the closer the distance, the greater the contribution of the sample. The corresponding formula is shown in (4); （4） in, Is a missing feature The fill value of is the nearest neighbor sample In the The value of a feature, is the nearest neighbor sample With missing samples The distance between Find the filling value of the target missing value and complete the filling of the missing values ​​in the load data.

4. The interpretable short-term load forecasting method based on smooth multi-period characteristics according to claim 1 is characterized in that: The step 2 specifically includes: Step 21: Create time-based basis functions ,in Explain as The value of a time-base function at time t, is the number of time-based functions; Step 22: According to the characteristics of periodic harmonics, consider a period , which does not need to be an integer; the natural basis functions of smooth periodic functions are 2K sinusoidal Fourier terms or harmonics up to K, and the corresponding formula is shown in (5); （5） is the harmonic number, is the maximum value of a harmonic number. And the period is The period of the basis function is ; Step 23: To model different periodicities, each period is set , satisfying the conditions , and set For the The harmonics of the cycle, represents the total number of cycles; in addition, the basis functions are harmonics of all cycles The sum is expressed as , each basis function has a harmonic number.

5. The interpretable short-term load forecasting method based on smooth multi-period characteristics according to claim 1 is characterized in that: The step 3 specifically comprises the following steps: Step 31: Construct the cross-term function, for the number of cycles , the corresponding formula is shown in (6); （6） To calculate the cross terms between harmonics of different periods, different m and n The value of m and n is a period index that satisfies ; Cross terms Indicates harmonics and , with a coefficient of 2; for each of the cross terms or product basis functions, associate the smaller period in the product and assign a harmonic number that is the harmonic number associated with the smaller period; considering the cross terms ,in ; Combine it with the cycle Connect them and assign them harmonic numbers ; is the cross-corrected harmonic number and the corresponding period is ;unless is a rational number, otherwise these cross-term basis functions are not periodic, and the cross-term basis functions are periodic; Step 32: Obtain the time-based full basis function, which corresponds to formula (7); （7） Here the basis functions are marked as , and the related harmonic number is ; The harmonics of each basis function range from to , that is, the range satisfies the interval from the minimum harmonic value to the maximum harmonic value, where are harmonics in the periodic model; and all basis functions are perpendicular to each other; Step 33: Given basis functions , creating a time-based feature vector , corresponding to formula (8); （8） Define basis functions for all real parameters ,in, is the number of time-based functions; when creating a feature, they are evaluated only an integer number of times.

6. The interpretable short-term load forecasting method based on smooth multi-period characteristics according to claim 1 is characterized in that: In step 5, the linear regression parameters after parameter optimization are used to complete the future load The prediction of is shown in formula (9); （9） in, is a feature vector based only on time, The dimension is , that is, time-based features; parameters in the model is a constant offset term, which is used in the prediction Dimensional; is a time-based parameter, and its corresponding parameter matrix dimension is ; is the autoregressive parameter, and its corresponding parameter matrix dimension is .

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