A comprehensive energy system multi-element load prediction method based on a graph attention mechanism and a generative adversarial network

By combining the graph attention mechanism and the generative adversarial network prediction framework GAN-GAT-TCN, the problem of difficulty in ensuring the accuracy and robustness of the spatial and temporal characteristics of multi-dimensional load data in integrated energy systems is solved, and the accuracy and adaptability of multi-dimensional load forecasting are improved.

CN119940619BActive Publication Date: 2025-10-24KUNMING UNIV OF SCI & TECH
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Patent Information

Application Number
CN202510009959.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-01-03
Publication Date
2025-10-24
Estimated Expiration
2045-01-03

AI Technical Summary

Technical Problem

In integrated energy systems, the spatial and temporal characteristics of multivariate load data make it difficult to ensure the accuracy and robustness of multivariate load forecasting.

Method used

The prediction framework GAN-GAT-TCN based on graph attention mechanism and generative adversarial network is adopted. Graph attention convolutional network (GAT) and temporal convolutional network (TCN) are combined to realize adversarial learning through generative adversarial neural network (GAN) to extract spatial and temporal features of multivariate loads.

Benefits of technology

It significantly improves the accuracy and robustness of multi-element load forecasting, improves the forecasting precision and adaptability, and can better handle multi-element load forecasting problems in integrated energy systems.

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Abstract

The present application relates to a kind of based on the integrated energy system multivariate load prediction method of graph attention mechanism and generative adversarial network, belong to integrated energy system multivariate load prediction technical field.The method proposes a new prediction framework based on GAN-GAT-TCN, for the strong interaction and strong coupling characteristics of integrated energy system multivariate load prediction, using cross-correlation coefficient to carry out correlation analysis on the preprocessed electric, heat, cold load data and its influencing factors, obtain adjacency matrix, using GAN to predict electric, heat, cold load, wherein GAT as generator, can extract the space dimension information between electric, heat, cold load data and its influencing factors, TCN as judge, can extract the time dimension information inside electric, heat, cold load data, to obtain the final prediction result in the way of mutual confrontation, improve the accuracy and robustness of multivariate load prediction, provide direction for integrated energy system multivariate load prediction technology.
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Description

TECHNICAL FIELD

[0001] The present application relates to a kind of based on graph attention mechanism and the comprehensive energy system multivariate load prediction method of generative adversarial network, belong to comprehensive energy system multivariate load prediction technical field. BACKGROUND

[0002] With energy structure transformation, constructing multi-energy complementary comprehensive energy system becomes a powerful measure to reduce system carbon emissions and improve energy efficiency. Comprehensive energy system integrates multiple energy sources and integrates energy storage technology to achieve efficient energy planning and scheduling to meet the multi-load demand of users such as cold, heat and electricity. However, the coupling of multiple energy sources and the access of new energy systems bring randomness and uncertainty to the load of comprehensive energy system, so the accuracy of load forecasting is the basic condition for the optimal scheduling of comprehensive energy system, and therefore higher requirements are put forward for accurate multi-load forecasting.

[0003] Scholars have done a lot of work on load forecasting. Traditional load forecasting refers to the prediction of a single type of load, and mathematical statistics and machine learning methods are often used. Yan TY uses time decomposition technology to apply linear regression method to achieve accurate prediction of power load. Yang GH proposes a Holt-Winters exponential smoothing prediction method to improve load forecasting accuracy. Wu J developed a new support vector regression prediction method. Although statistical methods take into account the characteristics of time data, their effectiveness may be affected when facing nonlinear or non-stationary data due to the limitations of assumptions. While machine learning can effectively solve the limitations of statistical methods in nonlinear mining, it cannot automatically learn the defects in sequence data and needs to manually select input features, which may damage the time integrity of data.

[0004] In recent years, with the improvement of computer performance and the diversification of data types, deep learning has become the mainstream research method. It can extract high-dimensional abstract information from massive data through multiple layers of nonlinear mapping without constructing an accurate mathematical model, and has strong generalization ability and nonlinear mapping ability. Memarzadeh G established a short-term load forecasting model based on long short-term (LSTM) network by analyzing the dynamic characteristics and internal rules of the load. Kong W proposed a prediction framework based on LSTM recurrent neural network, which overcomes the high volatility and uncertainty of the load. However, single model often has limitations. In order to improve the prediction accuracy, many scholars try to use combined models to complement each other to improve the prediction effect. Rafi SH proposed an integrated prediction method based on convolutional neural network and long short-term memory network to improve the accuracy of load forecasting. Hu W proposed a short-term load forecasting model based on optimized VMD-mRMR-LSTM, which effectively solves the shortcomings of traditional methods in considering the correlation and comprehensiveness of feature values of time series data. Yang X L constructed a LSTM neural network prediction model that integrates self-attention mechanism, deeply mines the characteristics of load sequence, and significantly improves the accuracy of load forecasting.

[0005] The above documents focus on single load forecasting, while multi-element load forecasting in integrated energy systems is more complex and needs to consider external factors and internal multi-energy flow transmission and mutual coupling. Therefore, Li C proposed a multi-element load forecasting method that combines neural networks and transfer learning, uses the Pearson correlation coefficient to select the main influencing factors, uses convolutional neural networks and gated recurrent units to establish a prediction model, and dynamically adjusts the structure by introducing the maximum mean difference strategy to adapt to complex environments. The example results show that this method significantly improves the prediction accuracy and model robustness. Liu H quantitatively analyzes the coupling relationship between multiple energy loads in integrated energy systems through a combination model of multivariate phase space reconstruction and support vector regression, and realizes accurate prediction. Wang C proposes a multi-task learning model based on ResNet-LSTM network and attention mechanism to deeply mine the coupling relationship between multiple loads and improve prediction accuracy. By introducing the attention mechanism, the shared features are selected differently for different sub-tasks, thereby realizing joint prediction of multiple loads. The above documents all mine the coupling relationship between multiple loads in integrated energy systems on the time scale, without considering the coupling relationship between multiple loads in space. Combining the time characteristics and spatial characteristics of multiple loads can improve the prediction accuracy. SUMMARY

[0006] The application aims to provide a comprehensive energy system multi-element load prediction method based on a graph attention mechanism and a generative adversarial network, aiming to solve the technical problem that it is difficult to guarantee the accuracy and robustness of multi-element load prediction under the spatial and temporal characteristics of multi-element load data.

[0007] To achieve the above purpose, the technical solution adopted by the application is: a comprehensive energy system multi-element load prediction method based on a graph attention mechanism and a generative adversarial network, which, in view of the strong interaction and strong coupling characteristics of comprehensive energy system multi-element load data, uses multi-energy interaction and coupling characteristics and time sequence characteristics to establish a new prediction framework GAN-GAT-TCN, which combines a graph attention convolutional network (GAT) for learning spatial feature representation and a time sequence convolutional network (TCN) for learning time feature representation, and uses a generative adversarial neural network (GAN) to make the two networks GAT and TCN learn in an adversarial manner to generate data closer to the true value. The application fully considers the spatial and temporal characteristics of multi-element load data, significantly improves the accuracy and robustness of multi-element load prediction, and has high prediction accuracy and good adaptability when dealing with comprehensive energy system multi-element load prediction problems. The specific steps are:

[0008] Step 1: data preprocessing of comprehensive energy system cold, heat and power operation data, including data cleaning and data standardization, filling in missing data in original comprehensive energy load data, eliminating abnormal data, and normalizing;

[0009] Step 2: using the maximum mutual information coefficient (MIC) algorithm to analyze the correlation between the comprehensive energy system cold, heat and power load and the comprehensive energy system load influencing factor variables, calculating the correlation between the data, and obtaining the MIC value;

[0010] Step 3: selecting the comprehensive energy system influencing factor variables with high correlation as the factor screening set, and using the MIC value and the comprehensive energy system cold, heat and power load to form an adjacency matrix;

[0011] Step 4: combining the comprehensive energy system cold, heat and power load data and the comprehensive energy system factor screening set, and dividing them into training set, validation set and test set according to the proportion;

[0012] Step 5: inputting the divided data into the GAN model, where GAT is the generator and TCN is the judge, training and learning the electric, heat and cold load on the training set, verifying the accuracy and reliability of the training model on the validation set, and finally outputting the prediction results of the electric, heat and cold load on the test set;

[0013] Step 6: calculating the error between the model prediction value and the actual value using evaluation indexes.

[0014] The Step2 is specifically:

[0015] Select solar radiation, wind speed, dry bulb temperature, dew point temperature, humidity, holiday data as the influencing factors of electric load, cooling load and heating load data;

[0016] The integrated energy system influencing factor data and integrated energy system cooling and heating and power operation data are grid divided;

[0017] The divided data is used as input to use the maximum mutual information coefficient MIC algorithm for correlation analysis, and the mutual information values of the two groups of variables are obtained;

[0018] The mutual information values are used to measure the correlation between the integrated energy system influencing factor data and the integrated energy system cooling and heating and power operation data.

[0019] The Step3 is specifically:

[0020] The variables of the integrated energy system load and the integrated energy system influencing load are selected as the nodes of the constructed graph;

[0021] The maximum mutual information coefficient value is used to represent the correlation degree between two nodes;

[0022] The first k variables are selected according to the MIC value from large to small to establish the adjacency relationship, and the adjacency matrix of the node value of the maximum mutual information coefficient is formed.

[0023] The Step5 is specifically:

[0024] GAT is used as the generator, and TCN is used as the discriminator, while the spatiotemporal characteristics of the integrated energy system multivariate data are mined;

[0025] In the prediction process, the data set is input into the generator with GAT as the model, the spatial information of the data is extracted, and the generator prediction result is input into the discriminator and the true value for identification;

[0026] The true probability of the data is analyzed, the time convolution model used by the discriminator is used to extract the time information of the data, and in the case of false identification, the generator is returned for training, and in the case of true identification, the prediction result is output.

[0027] The Step6 is specifically:

[0028] Root mean square error RMSE, mean absolute error MAE and Nash efficiency coefficient NSE are used as evaluation indexes to analyze the model, and the calculation formula is as follows:

[0029]

[0030] In the formula, is the integrated energy system cooling and heating and power load prediction value; yi is the actual value of cooling, heating and electricity load of the integrated energy system; It is the sample mean of cooling, heating and electricity load data of the integrated energy system.

[0031] The beneficial effects of the present invention are:

[0032] For spatial dimension information, the MIC algorithm is used to construct an adjacency matrix to connect the cooling, heating and electricity loads of the integrated energy system and the variables of related influencing factors of the integrated energy system. The graph attention network is used to learn the spatial relationship between multiple loads and their influencing factors. By introducing the attention mechanism, shared features are differentiated for different subtasks, considering the external factors of the integrated energy system and the transmission and mutual coupling between internal multiple energy flows, thereby realizing the joint prediction of multiple loads.

[0033] For temporal information, a temporal convolutional network is used for extraction. This network is primarily based on causal dilated convolutions and can extract temporal features from time series with a relatively small number of convolutional layers. This paper introduces a Generative Adversarial Network (GAN) to achieve adversarial learning between the GAT and TCN for spatiotemporal prediction. The integration of spatiotemporal information improves the model's prediction accuracy, significantly improving the fitting of actual values ​​and bringing the fitted line closer to the ideal state. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of the multi-element load forecasting method for an integrated energy system of the present invention. DETAILED DESCRIPTION

[0035] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Example 1: Figure 1 As shown in the figure, a multi-element load forecasting method for an integrated energy system based on a graph attention mechanism and a generative adversarial network is presented, which specifically includes the following steps:

[0037] Step 1: Preprocess the cooling, heating, and power operation data of the integrated energy system, including data cleaning and data standardization, fill in missing data in the original integrated energy load data, remove abnormal data, and perform normalization.

[0038] Specifically, linear interpolation is used to fill in missing values. For the yth missing data, the method of filling in the missing data using linear interpolation is as follows:

[0039]

[0040] In the formula: m < y < m + 1, m is the relative position of the missing data, and l is the time interval of the missing data; T(y) is the filled comprehensive energy system load data; T(m + 1) is the comprehensive energy system load data with time sequence m + 1; and T(m) is the comprehensive energy system load data with time sequence m.

[0041] Specifically, the data standardization is a normalization process, and the comprehensive energy system load data is normalized to eliminate the influence of the dimension, and the formula is:

[0042]

[0043] In the formula, x is the original value of the data; is the normalized x; mean(X train ) represents the average value of the training set X train ; and std(X train ) represents the standard deviation of the training set X train .

[0044] Step 2: The MIC algorithm is used to analyze the correlation between the comprehensive energy system cold-heat-electricity load and the comprehensive energy system load influencing factor variables, calculate the correlation between the data, and obtain the MIC value;

[0045] Step 2.1: The data is divided into grids;

[0046] Step 2.2: The mutual information value is calculated under different grid resolutions, and the calculation steps are as follows:

[0047] Step 2.2.1: The comprehensive energy system load variable X is a discrete sequence about the time sequence, and the value is X1, X2, …, X n at the time step interval, and the information entropy h(X) is used to measure the uncertainty of the comprehensive energy system load variable X, and the information entropy h(X) is as follows:

[0048]

[0049] P(X1), P(X2), …, P(X n ) are the probability distributions of the comprehensive energy system load variable X.

[0050] Step 2.2.2: Let the joint probability of the comprehensive energy system load variable X and the comprehensive energy system influencing factor variable Y be P(X, Y), that is, the probability of the association of the two variables, and the joint entropy is used to describe the association degree between the comprehensive energy system load variable X and the comprehensive energy system influencing factor variable Y, the greater the joint entropy, the lower the association degree between X and Y, and the higher the uncertainty, and the joint entropy is as follows:

[0051]

[0052] Step2.2.3: For discrete comprehensive energy system load variable X and comprehensive energy system influencing factor variable Y, conditional entropy is used to describe the uncertainty of one random variable when the other random variable is fixed, and the conditional entropy is as follows:

[0053]

[0054] In the formula: H(Y|X) is the unknown information of the remaining comprehensive energy system influencing factor variable Y when the comprehensive energy system load variable X is known.

[0055] The joint entropy and conditional entropy have the following relationship:

[0056] H(X,Y) = H(X) + H(Y|X) = H(Y) + H(X|Y)

[0057] The mutual information between the comprehensive energy system load variable X and the comprehensive energy system influencing factor variable Y can measure the amount of information reduced due to the knowledge of one random variable from another random variable, which is expressed by the following formula:

[0058]

[0059] Step2.3: Standardize the mutual information value, and the standardization formula is as follows:

[0060]

[0061] In the formula: I(X;Y) st is the standardized mutual information value, |X| and |Y| are the grid numbers occupied by the comprehensive energy system load variable X and the comprehensive energy system influencing factor variable Y, respectively.

[0062] Step2.4: The largest element selected from the feature matrix is MIC.

[0063] Step3: Select the comprehensive energy system influencing factor variable with high correlation as the factor screening set, and use the MIC value and the comprehensive energy system cold-heat-electricity load to construct an adjacency matrix;

[0064] Specifically, an adjacency matrix is constructed, the comprehensive energy system influencing factor variable with high correlation is selected as the factor screening set, the MIC is used to determine the connection relationship between variables, and the size of the mutual information value between nodes determines the construction of the edge between nodes. First, select the load and the variable influencing the load as the nodes V;E var of the graph G var (V,E varThe correlation between two nodes is represented; the k variables with larger MIC values are selected to establish adjacency relationship, and the adjacency matrix G is constructed var As follows:

[0065]

[0066] In the formula: The mutual information value between the comprehensive energy system load variable X and the comprehensive energy system influencing factor variable Y.

[0067] Step4: The comprehensive energy system cold heat and electricity load data and the comprehensive energy system factor screening set are combined, and are divided into training set, validation set and test set according to the proportion;

[0068] Specifically, the comprehensive energy system cold heat and electricity load data and the comprehensive energy system factor screening set can be divided into training set, validation set and test set according to the proportion of 7:2:1;

[0069] Step5: The divided data is input into the GAN model, wherein GAT is used as the generator and TCN is used as the judge; the electricity, heat and cold load is trained and learned on the training set, the accuracy and reliability of the trained model is verified on the validation set, and finally the prediction result of the electricity, heat and cold load is output on the test set;

[0070] Step5.1: The same discriminator loss function J D The difference between different networks lies in the generator loss function J G The discriminator loss function J D :

[0071]

[0072] In the formula, G is the definition function of the generator; z is the input of the generator, including the comprehensive energy system load data, the comprehensive energy system influencing factor variable and its MIC value; β G is the parameter of the generator; D is the definition function of the discriminator; x is the input of the discriminator, including the comprehensive energy system cold heat and electricity load data trained by the generator; β D is the parameter of the generator; x-P data represents the statistical distribution P of the real sample data X of the comprehensive energy system cold heat and electricity load data , that is, x belongs to the real sample data; D(x) represents the input function of the discriminator; G(z) represents the input function of the generator.

[0073] Step5.2: The generator continuously inputs data, and the discriminator continuously detects data, and the two ends are repeatedly opposed. The sum of the generator and discriminator loss functions is 0, that is:

[0074] J G= -J D

[0075] Generator function value J G The smaller, the better. According to the above formula: function value J G The smaller, the better. According to the above formula: function value J D The larger, the better. The value function of zero-sum game is:

[0076] V F (β D ,β G ) = -J D (β D ,β G )

[0077] Then the optimal solution of the generator is:

[0078] β G* = argminmaxV F (β D ,β G )

[0079] The optimization objective function of the generated GAN network is obtained:

[0080]

[0081] In the formula, z-P z (z) indicates that z conforms to the encoded statistical distribution P z .

[0082] Step5.3: The integrated energy system load data, integrated energy system influencing factor variables and MIC values are input into the generative adversarial neural network to obtain generated data G(z).

[0083] Step5.4: The integrated energy system cold-heat-electricity load real data x and the generated data G(z) are input into the discriminator model for identification, and the real probability of the data is analyzed. First, 50% of the data is taken as real data, and the other 50% of the data is taken as pseudo data. The purpose is to make the output data close to the real data, and obtain the output D(x) close to 1 and the output D(G(z)) close to 0.

[0084] Step5.5: Update the generator model parameters through the objective function to optimize the generator model.

[0085] Step5.6: Update the discriminator model parameters through the objective function to optimize the discriminator model.

[0086] Step5.7: Repeat Step5.4-Step5.6 until the discriminator outputs D(x) and D(G(z)) converge to 0.5, then the training is completed.

[0087] Step6: Calculate the error between the predicted value and the actual value of the evaluation index model;

[0088] The root mean square error RMSE, the mean absolute error MAE and the Nash efficiency coefficient NSE are used as evaluation indexes to calculate the error between the predicted value and the actual value of the model, and the formula is as follows:

[0089]

[0090] In the formula, is the predicted value of the cold, heat and electricity load of the integrated energy system; y i is the actual value of the cold, heat and electricity load of the integrated energy system; is the sample mean of the cold, heat and electricity load data of the integrated energy system. The RMSE directly represents the prediction accuracy of the model, the MAE considers the allowable error in actual application, and the NSE is the controllable degree of the model prediction output to the input variable.

[0091] The specific embodiments of the application are described in detail above with reference to the drawings, but the application is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the application.

Claims

1. A method for integrated energy system multi-element load forecasting based on graph attention mechanism and generative adversarial network, characterized in that, The method comprises the following steps: Step 1: data preprocessing of cold, heat and electricity operation data of the integrated energy system, including data cleaning and data standardization, filling in missing data in the original integrated energy load data, eliminating abnormal data, and normalizing the data; Step 2: using the MIC algorithm to analyze the correlation between the integrated energy system cold, heat and electricity load and the integrated energy system load influencing factor variables, calculating the correlation between the data, and obtaining the MIC value; Step 3: selecting the integrated energy system influencing factor variables with high correlation as the factor screening set, and using the MIC value and the integrated energy system cold, heat and electricity load to form an adjacency matrix; Step 4: combining the integrated energy system cold, heat and electricity load data and the integrated energy system factor screening set, and dividing them into training set, validation set and test set according to the proportion; Step 5: inputting the divided data into the GAN model, wherein GAT is used as the generator and TCN is used as the discriminator, training and learning the electricity, heat and cold load on the training set, verifying the accuracy and reliability of the training model on the validation set, and finally outputting the prediction results of the electricity, heat and cold load on the test set; Step 6: calculating the error between the model prediction value and the actual value by using the evaluation index; The Step 5 is specifically: Step 5.1: Same discriminator loss function J for GAN D The difference between the different networks is the generator loss function J G The discriminator loss function J D : In the formula, G is the definition function of the generator, z is the input of the generator, which contains the comprehensive energy system load data, comprehensive energy system influencing factor variables and their MIC values; β G is the parameter of the generator; D is the definition function of the discriminator; x is the input of the discriminator, which contains the comprehensive energy system cold, heat and electricity load data trained by the generator; β D is the parameter of the generator; P represents the statistical distribution of the real sample data X of the comprehensive energy system cold, heat and electricity load data , that is, x belongs to the real sample data; D(x) represents the input function of the discriminator; G(z) represents the input function of the generator; Step 5.2: the generator continuously inputs data, and the discriminator continuously detects data. The two ends repeatedly confront each other, and the sum of the loss functions of the generator and the discriminator is 0, that is: J G = -J D Generator function value J G The smaller the better, according to the formula: function value J G The smaller the better, according to the formula: function value J D The larger the better, the value function of zero-sum game is: V F (β D ,β G )=-J D (β D ,β G ) Then the optimal solution of the generator is: β G* = argminmaxV F (β D ,β G ) The optimization objective function of the generated GAN network is: wherein represents a statistical distribution P of z that conforms to the encoding z ; Step 5.3: inputting the integrated energy system load data, the integrated energy system influencing factor variables and their MIC values into the generative adversarial neural network to obtain the generated data G(z); Step 5.4: inputting the integrated energy system cold, heat and electricity load real data x and the generated data G(z) into the discriminator model for identification, analyzing the real probability of the data, taking 50% of the data as real data and the other 50% of the data as pseudo data, so that the output data is close to the real data, and the output D(x) is close to 1 and the output D(G(z)) is close to 0; Step 5.5: updating the generator model parameters through the objective function to optimize the generator model; Step 5.6: updating the discriminator model parameters through the objective function to optimize the discriminator model; Step 5.7: repeating steps Step 5.4-Step 5.6 until the discriminator outputs D(x) and D(G(z)) converge to 0.5, and then the training is completed.

2. The integrated energy system multi-element load forecasting method based on graph attention mechanism and generative adversarial network according to claim 1, characterized in that, The Step 2 is specifically: Selecting solar radiation, wind speed, dry-bulb temperature, dew point temperature, humidity and holiday data as the influencing factors of the electricity load, cold load and heat load data; Grid division is performed on the integrated energy system influencing factor data and the integrated energy system cold, heat and electricity operation data; The divided data is used as input to perform correlation analysis by using the maximum mutual information coefficient MIC algorithm to obtain the mutual information value of the two groups of variables; The mutual information value is used to measure the correlation between the integrated energy system influencing factor data and the integrated energy system cold, heat and electricity operation data.

3. The method of claim 1, wherein, The Step3 is specifically: The variables of the comprehensive energy system load and the comprehensive energy system influence load are selected as nodes of the constructed graph; The correlation between two nodes is represented by the maximum mutual information coefficient value; The first k variables are selected according to the MIC value from large to small to establish an adjacency relationship, and an adjacency matrix with the maximum mutual information coefficient as the node value is formed.

4. The integrated energy system multi-element load forecasting method based on graph attention mechanism and generative adversarial network according to claim 1, characterized in that, The Step5 is specifically: GAT is used as the generator, and TCN is used as the discriminator, while the spatial and temporal characteristics of the comprehensive energy system multi-element data are mined; In the prediction process, the data set is input into the generator with GAT as the model, the spatial information of the data is extracted, and the generator prediction result is input into the discriminator and the true value for identification; The true probability of the data is analyzed, the time information of the data is extracted by using the time convolution model used by the discriminator, the generator is returned for training in the case of false identification, and the prediction result is output in the case of true identification.

5. The integrated energy system multi-element load forecasting method based on graph attention mechanism and generative adversarial network according to claim 1, characterized in that, The Step6 is specifically: The root mean square error RMSE, the mean absolute error MAE and the Nash efficiency coefficient NSE are used as evaluation indexes to analyze the model, and the calculation formula is as follows: In the formula, is the cold, heat and electricity load prediction value of the integrated energy system; y i is the true value of the cold, heat and electricity load of the integrated energy system; is the mean value of the cold, heat and electricity load data samples of the integrated energy system.

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