Multifeature Short-Term Power Load Forecasting Based on GCN-LSTM

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Introduction
As the country vigorously promotes the energy revolution and implements the China "double carbon" goal, a new-type power system bearing carbon peaking and carbon neutrality and implementing the new development concept comes into being, and accurate power load prediction can greatly improve the power utilization rate and reduce carbon emissions [1]. However, the new-type power system under the background of the user side can use demand that is increasingly diverse, so we need through the meter and the factors infuencing diversity system load forecasting accuracy, thus power prediction based on the rational allocation of a variety of forms, improve energy utilization efciency and economical system operation, and through the demand response plan to realize power balance between supply and demand, improve the operation reliability of the new-type power system [2,3].
At present, short-term load forecasting methods for power systems mainly include time series analysis, statistical analysis, and machine learning analysis. Among them, time series analysis means fnding the load variation rule from the series to make an efective prediction, but it lacks consideration of external factors and thus has a large load prediction deviation, which mainly includes the exponential smoothing model method [4], Kalman flter method [5], Fourier expansion method model [6], etc. Te statistical method refers to load prediction based on statistical theory and further considers the infuences of holidays, time series infection points, and other factors based on time series analysis to improve the accuracy of load prediction. However, there are also problems such as complex modeling, including vector autoregression models [7], multiple linear regression models [8], and uncertainty analysis theory [9]. Te third is the machine learning analysis method, which mainly includes grey projection and random forest algorithms [10], deep belief network prediction [11], multicore support vector machine algorithm [12], long short-term memory model [13], etc. Machine learning analysis methods can efectively learn the temporal and nonlinear relationships of data but cannot efectively identify the feature information among discontinuous data.
Te traditional short-term load forecasting method cannot account for too many factors and has high requirements in the form of data input, so the model is relatively complex. Due to the inherent characteristics of the new-type power system, such as diversifed forms of energy use and substitutable ways of energy use, the power load is comprehensively afected by diversifed infuencing factors such as user behavior, region, and climate, so that the short-term load forecasting under the background of the new-type power system faces three new challenges: (1) More diversifed infuencing factors should be considered comprehensively to ensure the prediction accuracy and reliability of the short-term load of the new-type power system; (2) quantify more nonquantifable factors, such as regional topological relations and meteorological information, and integrate them into the prediction model to fully tap the potential of massive information contained in power big data; and (3) further optimize the prediction algorithm and simplify the complexity of the model on the premise of retaining massive information to improve the training efciency of the prediction model.
To solve the above problems, this paper proposes a shortterm load forecasting method based on GCN-LSTM, in which GCN extracts the spatial features of non-Euclidean structure graph data and the LSTM network extracts the temporal features of the data. Te model uses historical load data, regional, meteorological, and date factors as input to construct continuous feature maps according to time-sliding Windows. GCN extracts the potential relationships in the feature map to form a feature vector, then constructs the feature vector using time series as input data and applies the LSTM network for short-term load forecasting. Finally, the GCN-LSTM model is compared with LSTM, CNN-LSTM, and TCN-LSTM models in load forecasting accuracy and characteristic dimensions, and the rationality and efectiveness of the proposed method are verifed.

Load Influencing Factors and Quantitative Model
In the context of a new-type power system with multienergy integration, power load prediction is not only afected by historical load data but also by meteorological factors, date factors, regional factors, etc., which requires us to do three tasks. First is the preprocessing of historical load data to remove defective and missing values; second is correlation analysis, removing weak correlation factors; and third is to establish a quantitative model to quantify the factors that cannot be directly applied to the model.

Historical Load Data.
Historical load data is an important factor in load forecasting. However, due to the unreliable equipment in power grid production and the error-prone data recorded manually, there are a lot of abnormal and incomplete data in power load data. Due to the large amount of data, the incompleteness and inaccuracy of the data can easily be amplifed, thus afecting subsequent data mining and analysis. In this paper, regression imputation is adopted to clean the data. Regression flling equation is established through the complete dataset, and random items are added to the flling value during the flling process, and then the missing data is flled by the predicted value of the regression equation. Te random regression flling method can make the best use of the information of the data itself and solve the collinearity problem of the predictor variables.
Te estimated value of the missing value in the load data y i can be expressed as follows: where y is the missing variable, x j (j � 1, 2, ..., n) is a complete variable that has a linear regression relationship with y and ε i is a random item whose flling value increases during the flling process, so as to reduce the defects of prediction error and distorted customer service sample distribution. Ten the min-max standardized transformation is used for the data.
where x * is the normalized value; x max and x min are the maximum and minimum values in the sample data, respectively.

Meteorological Factors.
Due to the strong randomness of power load afected by meteorological factors, correlation analysis must be carried out between power load and meteorological factors, and input variables of the load forecasting model should be selected reasonably [14]. In this paper, the Spearman rank correlation coefcient is used to test the correlation between power load and meteorology, and the infuencing factors of multivariate load prediction are selected according to the rank correlation value. Spearman rank correlation coefcient converts the original data with sample size n into rank data. Te original data x i and y i of infuencing factors X and Y are arranged in order from largest to smallest, x i ′ and y i ′ are the original data and the positions of the arranged data x i and y i , and x i ′ and y i ′ are the rank order of variables x i and y i . Te Spearman rank diference d i and Spearman rank correlation coefcient ρ s are as follows: Te open data of electricity consumption in a park in southern China in 2022 was used as the research object; the sampling rate was 60 min/time, and the corresponding meteorological information, including temperature and pressure, was collected. Spearman rank correlation coefcient was used to test the correlation between load and meteorological factors, and the results are shown in Figure 1.
Temperature has the strongest correlation with power load, with a correlation coefcient of 0.6. Precipitation, dew point temperature, and humidity are strongly correlated, among which the correlation coefcients are 0.5, 0.5, and − 0.4. However, other variables are weak, which are basically consistent with the objective law of user energy use. In this paper, meteorological factors with |ρ s | > 0.30 are selected as input features to train the model. Te main infuencing factors include temperature, dewpoint temperature, humidity, and precipitation.

Date Factors.
Te date factor is also an important part of new-type power systems short-term load forecasting. Te power load in China is mainly industrial, which on holidays is signifcantly reduced compared with that on workdays. Tis paper applies the 0-1 variable to quantify the information on workdays and holidays in date factors, which is shown in Table 1.

Regional Factors.
Users in diferent regions present diferent power consumption patterns, so the regional topology is also considered as a load infuencing factor. Terefore, the adjacency matrix A is used to quantify the topology structure [15] and describe the connection relationship between nodes and edges. If there is a connection between two nodes, the corresponding element is 1, otherwise it is 0.
In summary, the infuencing factors of load forecasting are divided into four categories: historical load data, regional factors, meteorological factors, and date factors, as shown in Figure 2.
Meteorological factors include temperature, dew point temperature, humidity, and precipitation. Date factors include workdays and holidays. Regional factor includes topology structure, as shown in Table 2.

Model Establishment
GCN is a convolutional neural network with non-Euclidean structure as the research object, which was proposed by Bruna et al. in 2013 [16]. Tere are many such structures in power systems, social networks, and other aspects. GCN provides a new idea for the processing of non-Euclidean data and has been widely used in network analysis, air quality prediction, trafc fow prediction, etc. [17].
For graph G, input signal X, and output signal Y, the processing method f adopted by GCN is as follows [18]: where X n t is the model input load characteristic matrix, historical data, meteorological factor, date factor, and regional factor are the four attribute characteristics represented by X, and t is the length of the historical time series Y is the output of the model; and A is the adjacency matrix. Te matrix element represents the connection relationship between nodes, 0 represents no connection between two nodes, and 1 represents a connection.
Te forward propagation formula of graph convolution is where I is the identity matrix, A � A + I; D is a diagonal matrix; H l and W l are output and parameter values of layer 1, respectively; and σ(·) denotes the activation function. A multilayer graph convolutional network is shown in Figure 3. Te graph data in the input layer is signal X. Te characteristics of each node in the graph data are converted from X to Z through several layers of GCN, but the connection relation A between nodes does not change.

LSTM Model. LSTM was proposed by Hochreiter et al.
in 1997 to solve the long-term dependence problem in recurrent neural network (RNN) [19]. LSTM adopts the forget gate, input gate, and output gate to solve the "gradient disappearance" in model training and can learn long-and short-term dependence information of time series. Te basic unit of LSTM is shown in Figure 4.

GCN-LSTM Model.
Te short-term load prediction of the new-type power system is to predict the load power size of the next time t through the historical time data of each region with a time of h and the spatial relationship of each region A.
where h is the length of the historical power generation curve; X all t is the set of various renewable energy generation curves at time t; X l t+1 is the predicted power of an electrical load at time t + 1; k is the length of time you need to predict. Obviously, when k � 1, the model is a one-step prediction, and when k > 1, the model is a multistep prediction.
Te power load of each node can be expressed as follows: International Transactions on Electrical Energy Systems where X t is the power load size in diferent regions at time t; A is the spatial infuence relationship between diferent regions; and F is the GCN-LSTM model. Te model is composed of GCN and LSTM, as shown in Figure 5.
In this paper, the historical time series data of length h is input into the model, and the two-layer GCN structure is used to analyze the topological structure of diferent regions and extract spatial features. Ten, data with spatial characteristics are input into the LSTM to learn the temporal features. Finally, the predicted data are obtained through a dense layer. Te specifc training process of the GCN-LSTM model is shown in Figure 6.

Evaluation Index.
In order to evaluate the performance of the prediction, four indexes, the mean absolute percentage error y MAPE , forecasting accuracy y FA , and R-square y R 2 are set according to the evaluation load prediction index of State Grid Co., LTD [20].

Date factors
Holidays Topology structure

Regional factors
where n is the total prediction times; X act (i) and X pred (i) are the true and predicted values of the load at time i, respectively; and X act is the average value of the true load value.

Case Studies.
Te historical electrical load data of the Mingzhu industrial park in southern China is selected from the public data on electricity consumption during 2020-2022. Te time step is 1 hour, and there are 26,280 data vectors in total, among which the load data curve is shown in Figure 7, and the topological relationship is shown in Figure 8.

Forget gate
Input gate Output gate σ σ σ

International Transactions on Electrical Energy Systems
Te hardware platform is confgured as GN8, a Tencent Cloud GPU computing server with 6 cores, 56 GB, and 5 Mbps, which is programmed in Python language and implemented by calling the PyTorch library for the model.

Cross-Validation Analysis.
In order to verify the overall efectiveness of the GCN-LSTM model, cross-validation analysis is essential. In this paper, the K-fold crossvalidation method is adopted to divide the data into n pieces, one of which is used as the test set and the other n − 1 pieces as the training set. Te accuracy of the model is calculated repeatedly to evaluate the average accuracy of the model, so as to avoid the problem of dividing the training set and the test set and interfering with the model results. Set the value of k to change from 0 to 15 with a step of 5. Te test was repeated 20 times in each case, and the statistical results were obtained as shown in Table 3.
It can be seen from Table 3 that the error of the training set generally increases after grouping compared with the case where k � 0 is not grouped. In addition, the error of the training set decreases with the increase in k value. Tis is because when k � 0 or the value is large, there are more samples involved in training the model, and applying this model to predict the training set has less error. As for the  error of the test set, the error of the test set gradually decreases with the increase in k value. Compared with the case of k � 0 and the case of k value 15, although the error of the training set with k value 15 is larger than that of the ungrouped case, the error of the test set is smaller than that of the ungrouped case, which indicates that increasing the k value is conducive to improving the generalization ability of the model. As shown in Figure 9, the single training time of the GCN-LSTM model under diferent k values. It can be seen from the fgure that although increasing the k value is conducive to improving model generalization ability, it also leads to an increase in training time. Tis paper sets the model k value at 10 by weighing the prediction accuracy and training time.
On the basis of cross-verifcation k � 10, several other optimal parameters need to be set. Whereas the core of GCN is 3, the core of LSTM is 1, and other relevant parameter settings of GCN-LSTM in this paper are shown in Table 4.

Comparative Analysis.
In order to comprehensively evaluate the GCN-LSTM model in terms of load forecasting accuracy, characteristic dimensions, training time, and prediction duration, three existing methods, LSTM [21], CNN-LSTM [22], and TCN-LSTM [23], are selected for comparison.
First, the four models are trained separately, and their feature dimension and training time are summarized and sorted out, and the results are shown in Table 5.
As shown in Table 5, the feature dimension of LSTM only contains historical load information, that is, the load value at the hour of every day, and the feature dimension is 1.
In addition to historical load information, the data processed by CNN-LSTM and TCN-LSTM models also contain date features and meteorological features. Among them, the date factor is subdivided into two characteristics: working day and holiday, while the meteorological factor includes four characteristics: temperature, dew point temperature, humidity, and precipitation. Te feature dimension of both models is 7. In addition to the historical load information, date features, and meteorological features, the GCN-LSTM needs to deal with the spatial infuence relationship between diferent regions, whose characteristic dimension is 8.
In terms of training time, because the LSTM model is relatively simple and has a low feature dimension, the training time is the shortest, which only takes 32 s. Te training time of the other three hybrid models increases to varying degrees due to their relatively complex models and high feature dimensions. Te GCN-LSTM model has the highest feature dimension due to the input image data, but the training time is 57 s, which is only 25 s longer than that of the LSTM model. CNN-LSTM and TCN-LSTM models are input in the form of massive data, and the input dimension is large. Compared with the LSTM model, the training time of CNN-LSTM and TCN-LSTM increases by 97 s and 109 s, respectively.
Ten load prediction is performed on the trained model. Te proposed GCN-LSTM model and LSTM model are used to predict the load of the new-type power system in the next 24 hours, and the importance of the joint neural network is verifed. Te results are shown in Figure 10.
In the predicted 24-hour load, the electrical load fuctuates greatly from 9 to 13 hours. Te traditional LSTM prediction method is conservative in the face of severe load fuctuation and cannot describe the load change well. Te prediction curve of the model proposed in this paper has a high degree of ftting to the real curve, which can better describe the load change trend even in periods of severe fuctuation, and the prediction efect is better.
Te three combined models in this paper are applied to predict the load of the new-type power system in the next 24 hours, and the necessity of the combined GCN neural network is verifed. Te results are shown in Figure 11.
As shown in Figure 11, the prediction methods using neural network association can all well represent load fuctuations, but the performance is diferent in aspects such as prediction accuracy and characteristic dimension. Furthermore, the four models were comprehensively evaluated in terms of forecasting accuracy, feature dimension, training time, and so on.    Table 6 shows that the traditional forecasting method LSTM only studies one characteristic, which is a MAPE of 6.02%; the forecasting accuracy is only 93.98%, and the model ftting efect is not good. R 2 is only 0.50. On the basis of this model, when TCN, CNN, or GCN are mixed with it, three evaluation indexes are improved to varying degrees, whereas the performance efects of the three models are still diferent in the specifc analysis. In addition to temporal features, TCN and CNN models can also integrate meteorological factors and date factors, and the prediction accuracy is improved by 2.28% and 1.18%, respectively, compared with LSTM. Although the model ft has improved, R 2 still fails to meet the expectations. Te proposed model GCN-LSTM can further efectively learn spatial features, with the highest prediction accuracy of 98.27% and the best model ftting with R 2 of 0.81.
Te four models are comprehensively evaluated in terms of MAPE, forecasting accuracy, model ft, feature dimension, and training time, and the superiority of the proposed GCN-LSTM load prediction model is verifed. Te high accuracy also refects the efectiveness and versatility of the model.

Conclusions
In view of the China "double carbon" target under the newtype power system construction and the user side can use demand increasingly diverse challenges, a GCN-LSTM short-term load forecasting method for new-type power systems, considering multiple factors is proposed. Te case demonstrated the advantages of the proposed method from three perspectives: characteristic dimension, training time, and prediction accuracy as follows: (1) Te GCN-LSTM network hybrid model can be applied to short-term load forecasting of large-scale and high-dimensional complex power systems. Compared with the traditional short-term load forecasting method, the input is transformed from   (2) Te GCN-LSTM network hybrid model has a large amount of data processing, and the training time is not greatly afected due to the efcient processing ability of GCN on image data. Although the training time is less than that of the LSTM model, it is better than the CNN-LSTM and TCN-LSTM models. (3) Te GCN model has a unique advantage in feature extraction, providing a large number of efective data inputs for the LSTM network model, while still showing a good prediction trend for the heavy load fuctuation. Terefore, the load accuracy of the GCN-LSTM network hybrid model has improved compared with other comparison models.

Data Availability
Te original data of power load forecasting used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that there are no conficts of interest.