
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

72103
10.1038/s41598-024-72103-w
Article
Short-term multi-energy consumption forecasting for integrated energy system based on interactive multi-scale convolutional module
Liu Fang csuliufang@csu.edu.cn

12
Huang Yucong 1
Wang Yalin 12
Xia E 1
Qureshi Hassaan 3
1 https://ror.org/00f1zfq44 grid.216417.7 0000 0001 0379 7164 School of Automation, Central South University, Changsha, 410083 Hunan China
2 National Engineering Research Centre of Advanced Energy Storage Materials, Changsha, 410083 Hunan China
3 grid.412117.0 0000 0001 2234 2376 School of Electrical Engineering and Computer Science, National University of Science and Technology, H-12, Islamabad, Pakistan
13 9 2024
13 9 2024
2024
14 2138220 6 2024
3 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Accurate consumption forecasting is of great importance to grasp the energy consumption habits of consumers and promote the stable and efficient operation of integrated energy system (IES). To this end, this paper proposes an interactive multi-scale convolutional module-based short-term multi-energy consumption forecasting method for IES. Firstly, based on multi-scale feature fusion and multi-energy interactive learning, a novel interactive multi-scale convolutional module is proposed to extract and share the coupling information between energy consumption from different scales without increasing network parameters. Then, a short-term multi-energy consumption forecasting method is proposed, where different forecasting network structures are selected in different seasons to make full use of seasonal and coupling characteristics of the energy consumption, thus enhancing prediction performance. Furthermore, a Laplace distribution-based loss function weight optimization method is proposed to dynamically balance the loss magnitude and training speed of joint forecast tasks more robustly. Finally, the effectiveness and superiority of the proposed method are verified by comparative simulation experiments.

Keywords

Integrated energy system
Multi-scale feature fusion
Multi-energy interactive learning
Seasonal and coupling characteristics
Consumption forecasting
Subject terms

Electrical and electronic engineering
Energy infrastructure
http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China 62373373 Liu Fang Natural Science Foundation of Hunan Province of China2024JJ3033 Liu Fang issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

As a new energy supply mode fusing multiple energy carrier types, such as electricity, cooling and heating, the integrated energy system (IES) has become an efficient way to settle the energy shortage issue1,2. Through conversion and storage devices, different energy carrier types transform and complement each other, greatly improving the energy utilization rate in IES3,4. Accurate short-term energy consumption forecasting can enable energy providers to anticipate consumer demand in advance, foster the economic and low-carbon operation of IES, and improve the response speed. However, the frequent and complex interactions among multi-energy sources make consumption forecasting in IES much more difficult and challenging than that in traditional single energy system.

Traditional short-term consumption forecasting methods for single energy system usually forecast different types of energy consumption independently5. In recent years, the artificial intelligence-based methods have always been the major research hotspot, including the classical shallow machine learning methods such as gradient boosting regression (GBR)6, extreme learning machine (ELM)7 as well as artificial neural networks (ANN)8 and the emerging deep learning methods9–11. Owing to the deeper feature extraction ability and stronger long-term dependency capture capability, the latter has gradually occupied the dominant position in energy consumption forecasting task. Literature12 uses the long short-term memory (LSTM) neural network combined with the stationary wavelet transform (SWT) technique to forecast the energy consumption of individual households. Literature13 proposes a hybrid electric consumption forecasting method based on genetic algorithm (GA) and bidirectional gated recurrent unit (BiGRU) neural network. However, the above forecast models based on recurrent neural network (RNN) often face the problem of gradient disappearance. The proposal of temporal convolutional network (TCN) proves that networks with convolutional architecture can also achieve excellent results in energy consumption forecasting14,15. In16, several TCN-based models are adopted to conduct energy consumption forecasting task and all outperform LSTM. By combining the TCN and light gradient boosting machine (LightGBM), literature17 proposes a novel short-term consumption forecasting model for industrial consumers. In18, convolutional neural network (CNN) is used for electric consumption forecasting after being fine tuned by enhanced grey wolf optimizer (EGWO). Nevertheless, there is still room for improvement for the existing convolutional architecture-based models in sufficient feature extraction and utilization.

Different from traditional single energy system, multi-energy consumption in IES is usually forecasted jointly due to the strong coupling characteristics among them. In19, a LSTM-based model is used to extract the high dimensional potential feature in consumption data, and GBR is adopted to build a featrue fusion layer to grasp the coupling characteristics of electric, cooling and heating consumption. Literature20 integrates CNN, GRU, multi-task learning and ensemble learning to obtain better prediction results for IES. A multi-energy consumption forecasting method considering the multi-energy coupling of variation characteristic curves is proposed in21, which combines multi-task learning, LSTM and the least square support vector regression (LSSVR) method. Although the current research can reach high joint prediction accuracy of multi-energy consumption through the augmentation strategy like ensemble learning or multi-task learning, there still exist some deficiencies. Many existing models are not competent at comprehensively digging the coupling features and relationships between strongly correlated energy types from multiple scales, and the information sharing layer in some models will reduce the computational efficiency. What’s more, the above-mentioned research ignores the fact that the multi-energy consumption coupling relationship varies with seasons, leading to the established forecasting model not being precise enough.

The above discussion focuses on model structure, while in practical operation, the training processes of joint forecasting tasks are carried out at the same time. And how to reasonably determine the weights of each task’s loss functions is crucial to the training effectiveness as well as forecasting performance of the model, which is also an issue that cannot be ignored. Literature22 proposes the uncertainty weight method, which uses the homoscedastic uncertainty to dynamically weight each task’s losses, avoiding the time-consuming process of manually weight adjusting and it has been widely applied in many IES consumption forecast-related papers20,23. However, the original uncertainty weight method is based on Gaussian likelihood, and the derived loss function is squared with the absolute error, making the training process of the model susceptible to the influence of data outliers. Secondly, the regularization term in this method may cause negative loss value. In addition, it only considers the magnitude balance of each task’s losses, while neglecting the training speed balance.

To solve the issues stated above, this paper proposes an interactive multi-scale convolutional module-based short-term (IMSCS) multi-energy consumption forecasting method, and the innovations could be outlined as follows: Based on multi-scale feature fusion (MSF) and multi-energy interactive learning (MEIL), a novel interactive multi-scale convolutional (IMSC) module is proposed, which can extract and share the coupling information between multi-energy consumption from different scales without increasing network parameters.

A short-term multi-energy consumption forecasting method is proposed to accurately grasp the energy consumption behavior of IES consumers in four seasons, where different forecasting network structures are tailored and selected for each season according to their multi-energy coupling situations.

A Laplace distribution-based loss function weight optimization method is proposed to foster the training process of IMSC module and improve the performance of joint forecast. This method can simultaneously balance the loss magnitude and training speed of each task more robustly, while avoiding the occurrence of negative loss value.

The remainder of this paper is arranged as follows: In “Structure introduction and energy consumption analysis of IES”, the structure introduction and energy consumption analysis of IES are carried out. In “IMSCS multi-energy consumption forecasting method”, the proposed IMSCS multi-energy consumption forecasting method is explained in detail. Case studies and conclusion are given in “Case studies” and “Conclusion”, respectively.

Structure introduction and energy consumption analysis of IES

The structure of IES

Fig. 1 The overall structure of IES.

Figure 1 shows the overall structure of IES. The energy of IES derives from power and gas grids and is consumed in the form of electricity, cooling and heating. It can be seen that the electrical energy coming from power grid is converted into cooling and heating in addition to meeting the demands of various electric consumption. At the same time, the gas energy coming from gas grid is converted into electricity, cooling and heating, respectively. What’s more, heating can also be converted into cooling. The energy conversion mentioned above is achieved by devices including electric refrigerator, gas turbine, absorption chiller, heat exchanger, etc. Except for the energy conversion devices, IES also contains energy storage devices to store excess energy24.Fig. 2 The real consumption curves of electricity, cooling and heating throughout the year.

Energy consumption characteristics analysis of IES

In this paper, the energy consumption data obtained from the Campus Metabolism system, an interactive web tool created by Arizona State University, is taken as an example to illustrate the proposed method25. Totally three years of electric, cooling and heating consumption data in Tempe campus from 2017 to 2019 are collected to conduct our study. Through preliminary analysis of the dataset, two prominent energy consumption characteristics of IES are concluded as follows. Seasonal characteristics. Figure 2 displays the real consumption curves of electricity, cooling and heating throughout the year. It is stipulated that spring begins in March and ends in May, summer begins in June and ends in August, autumn begins in September and ends in November, and winter begins in December and ends in February. On the one hand, the power levels of the multi-energy consumption exhibit obvious seasonal characteristics. The average power level of heating consumption reaches the highest in winter and the lowest in summer, which is exactly contrary to that of electric and cooling consumption. In spring, the curves of electric and cooling consumption are roughly rising, while the curve of heating consumption is declining, and the same complementary trend can also be seen in autumn. On the other hand, the fluctuations of three consumption curves exhibit obvious seasonal characteristics. The fluctuations of electric and cooling consumption curves in winter are smaller than those in other three seasons, but the heating consumption curve fluctuates severely in winter and tends to be stable in summer. Therefore, seasonal characteristics should be a major consideration in consumption forecasting.

Coupling characteristics. Unlike traditional single energy system, there are strong coupling characteristics among different energy consumption in IES, which can be inferred from many aspects. In terms of IES operation mechanism, electrical energy, cold energy as well as heat energy do not just flow separately, but interact and transform from each other through various energy conversion devices, fundamentally determining the strong correlation between them. From the aspect of historical consumption curves, it can be observed from Fig. 2 that when the electric and cooling consumption curves show an upward trend, the heating consumption curve usually appears downward trend, and vice versa. This implies the similarity and complementarity of the multi-energy consumption and further indicates that they are related to each other. In order to further explore the coupling characteristics in IES, Fig. 3 plots the scatter distribution of electric, cooling and heating consumption, and two conclusions can be drawn from it: 1) The correlation between energy consumption is liner or nonlinear rather than just simple linear. 2) There is a positive correlation between electric and cooling consumption, while heating consumption is negatively correlated with electric and cooling consumption, respectively. So, how to deeply explore the linear and nonlinear correlation among multi-energy consumption and make full use of their coupling characteristics are also vital for consumption forecasting of IES.

Energy consumption correlation analysis of IES

This section focuses on quantitative analysis of the correlation among multi-energy consumption in IES so as to better capture the law of energy consumption coupling characteristics changing with seasons. Spearman correlation coefficient (SCC) is a distribution free rank correlation coefficient, which can be used for analyzing the degree of correlation between two monotonously linear or nonlinear variables26. The SCC method has low requirements for calculation and is less affected by the outliers, so, it is suitable for quantifying the correlation among multi-energy consumption with linear and nonlinear relationship. SCC is calculated as follows:1 ρs=1-6∑i=1ndi2n3-n

where di=rg(xi)-rg(yi). rg(xi) and rg(yi) denote the ranks of two sequences xi and yi, respectively. n is the amount of sample. The closer the absolute value of ρs is to 1, the stronger the correlation between x and y is.Fig. 3 The scatter distribution of electric, cooling and heating consumption.

Fig. 4 SCC heat map of multi-energy consumption in four seasons.

Figure 4 displays the SCC heat map of multi-energy consumption in four seasons based on the data in 2017 and 2018. On the whole, it can be found that the SCC correlation varied with season, and the SCC between electric and heating consumption is always the minimum in every season. Specifically, the SCC correlation coefficients between electric and cooling consumption as well as cooling and heating consumption are both relatively high in spring, with values of 0.73 and 0.81, respectively. In summer, the SCC between heating and cooling consumption is only 0.11, while the one between heating and electric consumption is even smaller to almost 0, implying that the heating consumption has little correlation with the other two energy types, which is consistent with common sense in daily life. The SCC of the three energy types all exceeds 0.7 in autumn, indicating that they relate each other strongly in this season, and their mutual information can help to promote higher consumption forecasting accuracy of each other. In winter, only the SCC between heating and cooling consumption is greater than 0.7, implying the strong correlation between them.

IMSCS multi-energy consumption forecasting method

Interactive multi-scale convolutional module

As mention in “Structure introduction and energy consumption analysis of IES”, the coupling characteristic is one of the most prominent energy consumption characteristics of IES. How to grasp the coupling relationship among multi-energy consumption and use it to obtain more accurate forecasting results are what this section focuses on. Figure 5 displays the structure of the proposed IMSC module. Here, the interaction between electric and cooling consumption is taken as an example to illustrate the operation mechanism of the IMSC module, and their input features are represented by Fe and Fc, respectively.Fig. 5 The structure of IMSC module.

After being input into IMSC module, the two feature sequences undergo MEIL for coupling information sharing, which contains two steps. Firstly, Fe and Fc are projected to Fe1 and Fc1 by two distinct convolutional modules ψe and ψc, respectively. The convolutional module in IMSC mainly consists of two 1D convolutional layers, which first extend the input feature dimension from C to h∗C and then map it back from h∗C to C, ensuring the high-level feature representation of time series is captured and the feature dimension unchanged. At the same time, the replication padding operation is used to keep time dimension invariance. In terms of activation functions, Tanh activation function and LeakyRelu activation function, an improved version of Relu, are selected to introduce nonlinear transformation into the neural network. And the Dropout layer is applied to avoid overfitting issue. After performing exponential operation, Fe1 and Fc1 interact with each other by Hadamard product. The above process can be summarized as Eq. (2) and Eq. (3), where ⊙ stands for Hadamard product.2 Fe1s=Fe1⊙exp(ψc(Fc))

3 Fc1s=Fc1⊙exp(ψe(Fe))

Secondly, as shown in Eq. (4) and Eq. (5), the obtained features Fe1s and Fc1s are projected to Fe2 and Fc2 by the second convolutional modules of their own and complete the next interaction by adding or subtracting each other.4 Fe2s=Fe2±ϕc(Fc1s)

5 Fc2s=Fc2±ϕe(Fe1s)

The MEIL realizes the multi-scale coupling information interaction and sharing between two energy types only through simple addition or subtraction and Hadamard product operations, without adding network parameters, so as to ensure the computational efficiency.

After that, two features Fe2s and Fc2s are processed by the third convolutional modules ηe and ηc, respectively. Then, the multi-scale features of two energy types are extracted by conducting addition and self-attention mechanism of the MSF module, which can filter out redundant information coming from shallow to deep layers and output features that the current task prefers to concentrate on. The computational process of self-attention mechanism for Fmix is based on the following formulas:6 Q=FmixWq,K=FmixWk,V=FmixWv

7 α=softmax(QKTDk)

8 Fatten=αV

where Q, K and V represent query space, key space and value space, respectively, while Wq, Wk, and Wv are corresponding trainable weight matrices. Dk is the dimension of each line in Q, and softmax() denotes the Softmax normalized exponential function.

Finally, the output Fe′ and Fc′ of the proposed IMSC module are obtained by adding the output features of self-attention and the original input features through residual connection, containing rich self and mutual information.

Short-term multi-energy consumption forecasting method

The proposed IMSC module can grasp the coupling relationship among multi-energy consumption from the multi-scale, having taken full use of coupling characteristics. However, as analyzed in “Structure introduction and energy consumption analysis of IES”, the degree of correlation between energy consumption varies seasonally. For two energy types that have little correlation, few homogeneous features can be learned by the IMSC module, sometimes even causing counterproductive consequences if they are forecasted jointly.

Therefore, to comprehensively consider the coupling and seasonal characteristics of energy consumption, a short-term multi-energy consumption forecasting method based on SCC correlation coefficient and IMSC module is proposed. In this method, for those two energy types with SCC exceeding the set threshold, the proposed IMSC module is used to mine and share the coupling information between them to achieve joint forecast, while for the energy type with SCC lower than the set threshold with the other two energy types, the MSF is used as core forecasting module to conduct seperate forecast. Figure 6 shows four possible network structures of the proposed IMSCS consumption forecasting method, corresponding to situations where the number of SCC exceeding the threshold is 0, 1, 2 and 3, and only one kind of structure is selected for the consumption forecasting of certain season according to its SCC results.Fig. 6 Four possible network structures for consumption forecasting.

Laplace distribution-based loss function weight optimization

To balance the loss magnitude and training speed of joint forecast tasks using IMSC module more robustly, a novel loss function weight optimization method based on Laplace distribution, uncertainty weight method and dynamic weight average method27 is proposed in this section.

Let f(x) be the forecast model output with weights W on input x. The likelihood between f(x) and the observed value y is defined by the following Laplace distribution:9 p(y|fW(x))=Lp(y|fW(x),λ)=12λexp(-|y-fW(x)|λ)

where λ>0 represents the noise scalar, corresponding to the homoscedastic uncertainty of the current task.

According to the maximum likelihood estimate, the parameters in the Laplace distribution is determined by maximizing the log likelihood of the model with respect to W and λ:10 logp(y|fW(x))∝-|y-fW(x)|λ-log2λ

Now we take the case where IMSC module is adopted to predict the consumption of all three energy types jointly as an example. Assume that the three outputs y1, y2 and y3 follow the Laplace distribution:11 p(y1,y2,y3|fW(x))=p(y1|fW(x))·p(y2|fW(x))·p(y3|fW(x))=Lp(y1|fW(x),λ1)·Lp(y2|fW(x),λ2)·Lp(y3|fW(x),λ3)

Then, the loss function of the whole model is equivalent to minimizing the negative log likelihood as follows:12 L(W,λ1,λ2,λ3)=-logp(y1,y2,y3|fW(x))∝1λ1|y1-fW(x)|+1λ2|y2-fW(x)|+1λ3|y3-fW(x)|+log23λ1λ2λ3=1λ1L1(W)+1λ2L2(W)+1λ3L3(W)+log23λ1λ2λ3

where L1(W)=|y1-fW(x)| is the loss of the first task and λ1 denotes the corresponding homoscedastic uncertainty, learning and determining the relative weight of L1(W), similarly for L2(W), L3(W).

As seen from Eq. (12), the loss function of each task derived from Laplace likelihood has the linear relationship with absolute error, which makes the model more robust to outliers in the dataset. More generally, Eq. (13) is obtained when Eq. (12) is extended to K tasks:13 L(W,λ1,…,λK)=∑k=1K(1λkLk(W)+log2λk)

The effect of log2λk is to act as a regularization term to avoid noise λk increasing too much, but when λk<0.5, it may cause negative loss value. We then modify log2λk slightly and get the following formula:14 L(W,λ1,…,λK)=∑k=1K(1λkLk(W)+ln(1+2λk))

In addition, another weight ωkt is introduced into Eq. (14) to further balance the training speed of each task. The final loss function L is obtained as follows:15 ωkt=Kexp(rkt-1/T)∑i=1Kexp(rit-1/T)

16 rkt-1=Lkt-1(W)Lkt-2(W)

17 L=∑k=1K(ωktλkLk(W)+ln(1+2λk))

where Lkt(W) is the average loss of task k in the t-th epoch and T is an adjustable parameter.

By learning and calculating the task-dependent homoscedastic uncertainty and the average loss variation, the proposed Laplace distribution-based loss function weight optimization method can simultaneously balance the loss magnitude and training speed of each task. At the same time, the 1-norm loss function with linear relationship with absolute error can better mitigate the influence of the abnormal values on the estimated results.Fig. 7 The flowchart of IMSCS multi-energy consumption forecasting method.

Table 1 Dataset description.

Content	Description	
Time-scale	2017/01/01-2019/12/31	
Resolution	1 h	
Examples	26,280 rows	
Attributes	Electric consumption (kW), cooling consumption (Tons),

Heating consumption (mmBtu)

	

Table 2 Selection results of the network structure.

Seasons	Network description	Structure diagram	
Spring	The electric and cooling consumption forecasting tasks as well as heating and cooling consumption forecasting tasks use IMSC module for information sharing	Figure 6c	
Summer	Only electric and cooling consumption forecasting tasks use IMSC module for information sharing	Figure 6b	
Autumn	Three consumption forecasting tasks all use IMSC module for information sharing	Figure 6d	
Winter	Only cooling and heating consumption forecasting tasks use IMSC module for information sharing	Figure 6b	

Fig. 8 The values of SCC between current and historical consumption in four seasons.

Table 3 Hyperparameter ranges of the proposed model.

Hyperparameter	Kernel size	Feature dimension expansion factor	Learning rate	
Range	[3, 4, 5, 7]	[1, 5, 10]	[0.001, 0.01, 0.1]	

Modeling process and evaluation index

The flowchart of the proposed IMSCS multi-energy consumption forecasting method is shown in Fig. 7, mainly involving the following four steps:

Step 1: Data processing and dataset division. First, eliminate the outliers and fill in the missing data. Then, divide the original dataset into four subsets according to the season division in “Structure introduction and energy consumption analysis of IES”. Finally, divide each subset into training, validation and test set and standardize the data that has been cleaned.

Step 2: Model selection and input determination. Calculate the SCC among energy consumption of four subsets and select the forecasting model structure for each season. At the same time, calculate the SCC between current and historical consumption power to determine the length of input lag.

Step 3: Model training and configuration determination. In this step, learning rate dynamic adjustment and training early stopping techniques are introduced to assist model training when validation loss is no longer improved. And the optimal hyperparameters are got by trial and error.

Step 4: Consumption forecasting and performance evaluation. Input the test set into the trained model to obtain the consumption forecasting results and evaluate the performance of the model by the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE):18 MAE=1n∑i=1n|yi′-yi|

19 RMSE=1n∑i=1n(yi′-yi)2

20 MAPE=1n∑i=1n|yi′-yi|yi×100%

where n denotes the number of samples, yi and yi′ are the actual and forecasting values, respectively.

Case studies

All the experiments in this section are carried out on the Pytorch deep learning library on Pycharm platform under Windows 10 operating system with Intel (R) Core (TM) i7-9700 CPU 3.00GHz.

Dataset description and data processing

In this paper, the multi-energy consumption data is obtained from the Tempe campus of Arizona State University, whose details are shown in Table 1. The meteorological data of the corresponding region is from the National Renewable Energy Laboratory28. For the unity of units, Eq. (21) is used to convert the units of cooling and heating consumption into kW:21 1kW=0.284Tons=0.0034mmBtu

In order to obtain high-quality data, the quartile method and the linear interpolation method are adopted respectively to eliminate outliers and fill in missing values. Then, the cleaned data is standardized by the following formula:22 x′=x-μσ

where x and x′ denote the values before and after standardization, μ and σ are the mean and standard deviation of the training set samples, respectively.

Input determination and model selection

After data processing, the original dataset is divided into four subsets corresponding to four seasons, and each subset is further divided into training set, validation set and test set based on the ratio of 8:1:1. The numbers of days in each subset are both 276 days in spring and summer subsets, 273 days in autumn subset and 270 days in winter subset. To prevent data leakage, the input determination and model selection are only based on the data in 2017 and 2018.

The input variables of consumption forecasting model contain the historical multi-energy consumption and the meteorological information, including temperature, humidity, precipitable water, wind speed, dew point, and air pressure. And the ouput of the model is the predicted multi-energy consumption value for the next hour. However, how to determine the reasonable length of input lag to achieve higher forecasting accuracy while ensuring computational efficiency is also the issue that needs to be considered. In our study, the SCC values between the current consumption power and those with different lags of each kind of energy consumption in different seasons are firstly calculated. Then, the lag of the consumption whose SCC is first lower than the set threshold, which is 0.6 in input lag determination, is selected as the input lag of the forecasting model in this season. Figure 8 shows the values of SCC between current and historical consumption in four seasons, and the input lags of each season are finally set as 5 in spring, 4 in summer, 8 in autumn and 4 in winter.

As for the forecasting model selection, the SCC threshold is set as 0.7. From Fig. 4 in “Structure introduction and energy consumption analysis of IES”, it can be known that the SCC correlation coefficients between electric and cooling consumption as well as cooling and heating consumption are greater 0.7 in spring, while the SCC correlation coefficients of the three energy types all exceed 0.7 in autumn. In summer, only the SCC between electric and cooling consumption is greater than 0.7. And in winter, only the SCC between cooling and heating consumption exceeds the threshold. So, the selection results of the forecasting network structure for each season are shown in Table 2. Table 4 Forecasting results of multi-energy consumption in spring.

Energy types	Method	MAE/kW	RMSE/kW	MAPE/%	
Electricity	Case 1	471.4709	639.8967	2.26	
Case 2	433.2422	605.5378	2.06	
Case 3	400.3233	568.7635	1.90	
Case 4	414.8212	570.2221	1.97	
Case 5	394.4999	568.5049	1.87	
Cooling	Case 1	678.4995	866.2640	3.15	
Case 2	599.3738	778.7821	2.76	
Case 3	555.2711	711.4448	2.56	
Case 4	521.7585	689.5363	2.40	
Case 5	520.5940	681.8899	2.41	
Heating	Case 1	61.0158	77.5505	3.17	
Case 2	56.6302	71.9137	2.96	
Case 3	53.1820	69.3159	2.75	
Case 4	54.1673	70.5773	2.80	
Case 5	51.2693	67.4819	2.66	
The best values are given in bold.

Fig. 9 Forecasting results of multi-energy consumption in spring.

Table 5 Forecasting results of multi-energy consumption in summer.

Energy types	Method	MAE/kW	RMSE/kW	MAPE/%	
Electricity	Case 1	622.3792	850.4317	2.37	
Case 2	591.1546	789.9039	2.22	
Case 3	552.9095	768.5283	2.08	
Case 4	565.1968	771.2881	2.13	
Case 5	550.6065	766.2816	2.07	
Cooling	Case 1	1347.7302	2101.3607	2.50	
Case 2	1154.9375	1531.9469	2.24	
Case 3	996.5950	1308.3576	1.97	
Case 4	1001.8290	1325.9787	1.99	
Case 5	982.3446	1293.6344	1.95	
Heating	Case 1	23.3728	32.6075	1.53	
Case 2	23.2017	32.2000	1.52	
Case 3	23.2017	32.2000	1.52	
Case 4	23.2504	32.4811	1.52	
Case 5	23.2017	32.2000	1.52	
The best values are given in bold.

Table 6 Forecasting results of multi-energy consumption in autumn.

Energy types	Method	MAE/kW	RMSE/kW	MAPE/%	
Electricity	Case 1	509.9674	701.8867	2.57	
Case 2	437.8095	606.0393	2.19	
Case 3	379.3419	551.0911	1.88	
Case 4	401.5385	559.3743	2.00	
Case 5	368.6501	537.7498	1.82	
Cooling	Case 1	863.0870	1104.7976	6.02	
Case 2	750.0402	998.5206	5.07	
Case 3	540.6322	727.3369	3.33	
Case 4	621.4112	858.6875	3.97	
Case 5	494.8306	686.3253	2.98	
Heating	Case 1	81.7648	127.4912	3.47	
Case 2	70.0593	94.3404	3.13	
Case 3	64.4182	87.2616	2.88	
Case 4	65.8510	88.8053	2.98	
Case 5	63.9376	86.6746	2.84	
The best values are given in bold.

Table 7 Forecasting results of multi-energy consumption in winter.

Energy types	Method	MAE/kW	RMSE/kW	MAPE/%	
Electricity	Case 1	362.5645	459.8130	2.18	
Case 2	258.9646	362.8377	1.54	
Case 3	258.9646	362.8377	1.54	
Case 4	327.9549	438.7482	1.98	
Case 5	258.9646	362.8377	1.54	
Cooling	Case 1	340.8732	445.5276	3.14	
Case 2	343.7012	453.8811	3.20	
Case 3	292.1221	393.0635	2.75	
Case 4	316.9280	420.9438	3.01	
Case 5	296.2579	396.3922	2.81	
Heating	Case 1	83.7813	106.9499	2.68	
Case 2	80.1134	103.1566	2.61	
Case 3	75.7621	98.2745	2.48	
Case 4	76.5029	99.1241	2.50	
Case 5	74.8269	97.7077	2.44	
The best values are given in bold.

Fig. 10 Forecasting results of multi-energy consumption in summer.

Fig. 11 Forecasting results of multi-energy consumption in autumn.

Fig. 12 Forecasting results of multi-energy consumption in winter.

Fig. 13 Average accuracy improvement on different models: (a) electricity; (b) cooling; (c) heating.

Performance of the proposed consumption forecasting method

To demonstrate the effectiveness of the proposed multi-energy consumption forecasting method, the following five cases are set up in this section:

Case 1: The multi-energy consumption is forecasted separately using the network with three sequentially connected convolutional modules.

Case 2: The multi-energy consumption is forecasted separately using the network with MSF module.

Case 3: The multi-energy consumption is forecasted using the network structure selected in Table 2, but the weights of loss functions for joint forecast tasks are all set to 1.

Case 4: The multi-energy consumption is forecasted using the network structure selected in Table 2, but the weights of loss functions for joint forecast tasks are determined by the Gaussian distribution-based loss function weight optimization method.

Case 5: The multi-energy consumption is forecasted using the proposed IMSCS method.

For models in all cases, the convolutional module uses the structure shown in Fig. 5, while the optimizer is Adam. The maximum training epoch, the batch size, and the dropout rate are set to 100, 100 and 0.2, respectively. Especially, the loss function is set to MSE in case 4 and the MAE loss function is used in the other cases. The remaining hyperparameters are explored within the specified range in Table 3, similar to29.

The short-term multi-energy consumption forecasting results of each case on the test set are presented in Tables 4, 5, 6 and 7. Since the heating consumption forecasting task in summer uses the MSF-based model, the results of case 3 as well as case 5 are consistent with case 2. And the same situation also occurs on electric consumption forecasting task in winter. The following findings can be drawn from Tables 4, 5, 6 and 7. Except for the cooling consumption forecasting results in winter, all the evaluation indexes of case 2 are better than case 1, which indicates that the MSF module can effectively fuse the concrete and abstract features from shallow and deep layers, making up for the shortcoming of traditional convolutional architecture networks in multi-scale feature extraction.

The MAE, RMSE and MAPE of the electric, cooling and heating consumption joint forecasting results in case 3, case 4 and case 5 are all lower than those of case 1 and case 2, proving the superiority of the proposed IMSC module in mining and sharing multi-scale coupling features between strongly correlated energy types. Particularly, forecasting the multi-energy consumption jointly in autumn can reach significant improvement compared with forecasting separately, because the correlation between three energy types is very high in this season, and the sharing of their coupling information can dramatically help to boost the forecasting accuracy. It also shows that it is essential to consider the energy consumption coupling changes of different seasons, as what the method proposed in this paper does.

The accuracy of case 5 is higher than those of case 3 and case 4 in the overwhelming majority of situations, indicating that using proposed Laplace distribution-based loss function weight optimization method to dynamically adjust loss weights of each prediction task can better balance the training process of their own, thereby further promoting the forecasting performance. Although case 4 also adopts the loss function weight optimization method, the modeling approach based on Gaussian likelihood will cause significant fluctuations in loss when there is a large deviation between the predicted value and the true one, making it difficult to determine the optimal loss weight. As a result, the forecast performance of case 4 is even inferior to that of case 3. Therefore, the Laplace likelihood with higher robustness is utilized in this paper.

At the same time, to compare different models more intuitively, the forecasting curves in one week of each case are also shown in Figs. 9, 10, 11 and 12. It is seen that the consumption forecasting curves of case 1 fit the curves of ground truth worst, often exhibiting significant deviations during peak and valley periods, particularly in tasks like the cooling consumption forecast in Fig. 10, the cooling as well as the heating consumption forecast in Fig. 11 and the heating consumption forecast in Fig. 12. Following case 1, there are also some obvious deviations between the consumption curves of case 2 and those of ground truth in some tasks, such as the heating consumption forecast in Fig. 9 and the cooling consumption forecast in Fig. 10. Compared with case 1 and case 2, the forecast curves of case 4 fit the real ones better, but they are still inferior to those of case 3 and case 5. To sum up, the consumption forecasting curves of case 5 are generally the closest to the curves of ground truth, which is consistent with the findings from Tables 4, 5, 6 and 7.

Moreover, to facilitate the model comparison, Fig. 13 displays the average accuracy improvement of the proposed model on each consumption forecasting tasks. Compared with case 1, the proposed model gets the largest improvement in terms of MAE, RMSE and MAPE, which are 20.02%, 15.71% and 22.17% for electricity; 28.98%, 32.31% and 31.46% for cooling; and 14.68%, 17.57% and 12.83% for heating, followed by case 2, case 4 and case 3. From the perspective of energy type, the proposed model obtains the maximum accuracy improvement on cooling consumption forecasting task. This is because the cooling consumption often has similar or complementary trend to the electric and heating consumption. Adopting the proposed method can enable the cooling consumption forecasting network to learn these similar and complementary features, so as to foster its own forecast process. What’s more, the heating consumption only has strong correlation with others in autumn, and its consumption curve in summer is very rigid, so, the average accuracy improvement on heating consumption forecasting task ranks the last.

Comparison of different forecasting methods

In this section, the proposed IMSCS method is compared with two machine learning methods GBR and ANN, and two commonly used RNN-based deep learning methods LSTM and BiLSTM to further evaluate its performance. For GBR, the loss function is least squres. For ANN and two RNN-based algorithms, the optimizer is Adam and the loss function is MAE, while the maximum training epoch, the batch size, and the dropout rate are set to 100, 100 and 0.2, respectively. The tuning ranges of the remaining hyperparameters are shown in Table 8.Fig. 14 Average MAPE of different methods.

Table 8 Hyperparameter ranges of different models.

Model	Hyperparameter	Range	
GBR	Learning rate	[0.001, 0.01, 0.1]	
ANN	Hidden size	[50, 100, 150]	
Learning rate	[0.001, 0.01, 0.1]	
LSTM, BiLSTM	Hidden size	[32, 64, 128]	
Learning rate	[0.001, 0.01, 0.1]	

Table 9 MAPE results of different methods.

Energy types	Method	MAPE/%	
Spring	Summer	Autumn	Winter	
Electricity	GBR	2.12	2.31	2.41	1.92	
ANN	2.24	2.28	2.22	1.95	
LSTM	2.15	2.15	2.24	1.55	
BiLSTM	2.00	2.16	2.02	1.44	
IMSCS	1.87	2.07	1.82	1.54	
Cooling	GBR	2.60	2.26	6.98	3.60	
ANN	2.81	2.15	4.20	3.67	
LSTM	2.43	2.10	3.35	2.97	
BiLSTM	2.44	2.06	3.93	3.10	
IMSCS	2.41	1.95	2.98	2.81	
Heating	GBR	2.79	1.55	3.34	2.76	
ANN	2.98	1.69	3.15	2.52	
LSTM	2.75	1.55	2.96	2.49	
BiLSTM	2.72	1.52	3.24	2.47	
IMSCS	2.66	1.52	2.84	2.44	
The best values are given in bold.

The MAPE results of every model in test set are calculated and shown in Table 9. As can be seen, IMSCS gets the highest accuracy in eleven out of twelve forecasting tasks, verifying the superiority and effectiveness of the proposed IMSCS method in extracting and sharing coupling information between multi-energy consumption and boosting the precision of IES consumption forecasting. At the same time, IMSCS achieves the greatest forecast improvement in autumn, the season with the strongest energy consumption fluctuation, proving the importance of considering the coupling and seasonal characteristics of multi-energy consumption in forecast model.

Furthermore, the average MAPE of different methods are shown in Fig. 14. For two machine learning methods, the average MAPE of GBR and ANN are 2.89% and 2.66%, respectively. As for two RNN-based deep learning models, LSTM and BiLSTM obtains the average accuracy improvement of 10.15% and 8.65% compared with ANN, illustrating the advantage of deep neural networks in processing multivariable nonlinear time series data. Among all of the forecast models, the proposed IMSCS method has the lowest average MAPE, which are 7.82%, 6.28%, 15.79% and 22.49% smaller than BiLSTM, LSTM, ANN and GBR, respectively.

Conclusion

This paper proposes a novel short-term multi-energy consumption forecasting method for IES called IMSCS, comprehensively considering the seasonal and coupling characteristics of multi-energy consumption to achieve higher prediction accuracy. To fully utilize the coupling characteristics, a brand new IMSC module is proposed, which can extract and share the coupling information between energy consumption from different scales without increasing network parameters. To make full use of the seasonal characteristics and dig the inner quarterly coupling information between strongly correlated energy types, the IMSCS method is proposed, where different forecasting network structures are selected quarterly based on the seasonal SCC calculation results. To foster the training process of joint forecast, a Laplace distribution-based loss function weight optimization method is proposed considering the magnitude balance, training speed balance and the positive value of the loss function simultaneously. Case studies verify the effectiveness and superiority of the proposed IMSCS method compared with the convolutional architecture models and commonly used machine learning models as well as RNN-based deep learning models. In the future, the special historical data characteristics and user behavior habits of winter electric consumption will become the focus of research to obtain better forecast results. In addition, how to use consumption forecasting to help economic and low-carbon dispatching of IES is also a practical research direction.

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 62373373, in part by the Natural Science Foundation of Hunan Province of China under Grant 2024JJ3033, and in part by the Fundamental Research Funds for the Central Universities of Central South University, China under Project 2024ZZTS0796.

Author contributions

F.L. and Y.H. contributed to conceptualization, methodology, sofware, and writing-original draf preparation. Y.W. and E.X. contributed to writing, reviewing, and editing. H.Q. contributed to experimental results sorting. All authors reviewed the manuscript.

Data availibility

The datasets used during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Ma, T. et al. Users energy consumption behavior analysis for integrated energy system based on spark platform. In 2018 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2), 1–6 (2018).
2. Byun J Hong I Kang B Park S A smart energy distribution and management system for renewable energy distribution and context-aware services based on user patterns and load forecasting IEEE Trans. Consum. Electron. 2011 57 436 444 10.1109/TCE.2011.5955177
Byun, J., Hong, I., Kang, B. & Park, S. A smart energy distribution and management system for renewable energy distribution and context-aware services based on user patterns and load forecasting. IEEE Trans. Consum. Electron. 57, 436–444 (2011).10.1109/TCE.2011.5955177
3. Wang Y Hu J Liu N Energy management in integrated energy system using energy-carbon integrated pricing method IEEE Trans. Sustain. Energy 2023 14 1992 2005 10.1109/TSTE.2023.3295573
Wang, Y., Hu, J. & Liu, N. Energy management in integrated energy system using energy-carbon integrated pricing method. IEEE Trans. Sustain. Energy 14, 1992–2005 (2023).10.1109/TSTE.2023.3295573
4. Zhong J Optimal operation of energy hub: An integrated model combined distributionally robust optimization method with stackelberg game IEEE Trans. Sustain. Energy 2023 14 1835 1848 10.1109/TSTE.2023.3252519
Zhong, J. et al. Optimal operation of energy hub: An integrated model combined distributionally robust optimization method with stackelberg game. IEEE Trans. Sustain. Energy 14, 1835–1848 (2023).10.1109/TSTE.2023.3252519
5. Wang C A transformer-based method of multienergy load forecasting in integrated energy system IEEE Trans. Smart Grid 2022 13 2703 2714 10.1109/TSG.2022.3166600
Wang, C. et al. A transformer-based method of multienergy load forecasting in integrated energy system. IEEE Trans. Smart Grid 13, 2703–2714 (2022).10.1109/TSG.2022.3166600
6. González-Briones, A., Hernández, G., Pinto, T., Vale, Z. & Corchado, J. M. A review of the main machine learning methods for predicting residential energy consumption. In 2019 16th International Conference on the European Energy Market (EEM), 1–6 (2019).
7. Duan, J. et al. Electricity consumption forecasting using extreme learning machine with the generalized maximum correntropy. In 2021 IEEE 5th Conference on Energy Internet and Energy System Integration (EI2), 3251–3255 (2021).
8. Zahedi, R., Aslani, A., Gitifar, A., Farahani, O. N. & Yousefi, H. Application of artificial neural network in predicting building’s energy consumption. In 2023 8th International Conference on Technology and Energy Management (ICTEM), 1–5 (2023).
9. Lin, Q., Kuang, H. & Xilin, Z. Design and implementation of big data forecasting system based on intelligent transportation. IEEE Trans. Consumer Electron. 1–1 (2023).
10. Jayashankara M Shah P Sharma A Chanak P Singh SK A novel approach for short-term energy forecasting in smart buildings IEEE Sens. J. 2023 23 5307 5314 10.1109/JSEN.2023.3237876
Jayashankara, M., Shah, P., Sharma, A., Chanak, P. & Singh, S. K. A novel approach for short-term energy forecasting in smart buildings. IEEE Sens. J. 23, 5307–5314 (2023).10.1109/JSEN.2023.3237876
11. Fang L He B A deep learning framework using multi-feature fusion recurrent neural networks for energy consumption forecasting Appl. Energy 2023 348 121563 10.1016/j.apenergy.2023.121563
Fang, L. & He, B. A deep learning framework using multi-feature fusion recurrent neural networks for energy consumption forecasting. Appl. Energy 348, 121563 (2023).10.1016/j.apenergy.2023.121563
12. Yan K Li W Ji Z Qi M Du Y A hybrid lstm neural network for energy consumption forecasting of individual households IEEE Access 2019 7 157633 157642 10.1109/ACCESS.2019.2949065
Yan, K., Li, W., Ji, Z., Qi, M. & Du, Y. A hybrid lstm neural network for energy consumption forecasting of individual households. IEEE Access 7, 157633–157642 (2019).10.1109/ACCESS.2019.2949065
13. Inteha, A., Nahid-Al-Masood, Hussain, F. & Khan, I. A. A data driven approach for day ahead short term load forecasting. IEEE Access 10, 84227–84243 (2022).
14. Shaojie Bai, J. Z. K. & Koltun, V. An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. ArXiv, 2018 (2018).
15. Liu, M. et al. SCINet: Time series modeling and forecasting with sample convolution and interaction. Adv. Neural Inf. Process. Syst. (2022).
16. Zuo, C. & Hu, W. Short-term load forecasting for community battery systems based on temporal convolutional networks. In 2021 IEEE 2nd International Conference on Information Technology, Big Data and Artificial Intelligence (ICIBA), vol. 2, 11–16 (2021).
17. Wang Y Short-term load forecasting for industrial customers based on tcn-lightgbm IEEE Trans. Power Syst. 2021 36 1984 1997
Wang, Y. et al. Short-term load forecasting for industrial customers based on tcn-lightgbm. IEEE Trans. Power Syst. 36, 1984–1997 (2021).
18. Jalali SMJ Ahmadian S Khosravi A A novel evolutionary-based deep convolutional neural network model for intelligent load forecasting IEEE Trans. Industr. Inf. 2021 17 8243 8253 10.1109/TII.2021.3065718
Jalali, S. M. J., Ahmadian, S. & Khosravi, A. A novel evolutionary-based deep convolutional neural network model for intelligent load forecasting. IEEE Trans. Industr. Inf. 17, 8243–8253 (2021).10.1109/TII.2021.3065718
19. Wang, S., Wang, S., Chen, H. & Gu, Q. Multi-energy load forecasting for regional integrated energy systems considering temporal dynamic and coupling characteristics. Energy 195 (2020).
20. Wang, X., Wang, S. & Zhao, Q. A multi-energy load prediction model based on deep multi-task learning and ensemble approach for regional integrated energy systems. Int. J. Electr. Power Energy Syst. 126 (2021).
21. Wang S Multienergy load forecasting for regional integrated energy systems considering multienergy coupling of variation characteristic curves Front. Energy Res. 2021 9 1
Wang, S. et al. Multienergy load forecasting for regional integrated energy systems considering multienergy coupling of variation characteristic curves. Front. Energy Res. 9, 1 (2021).
22. Kendall, A., Gal, Y. & Cipolla, R. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. In 2018 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 7482–91 (2018).
23. Niu D Yu M Sun L Gao T Wang K Short-term multi-energy load forecasting for integrated energy systems based on cnn-bigru optimized by attention mechanism Appl. Energy 2022 313 118801 10.1016/j.apenergy.2022.118801
Niu, D., Yu, M., Sun, L., Gao, T. & Wang, K. Short-term multi-energy load forecasting for integrated energy systems based on cnn-bigru optimized by attention mechanism. Appl. Energy 313, 118801 (2022).10.1016/j.apenergy.2022.118801
24. Guo Y Bilstm multitask learning-based combined load forecasting considering the loads coupling relationship for multienergy system IEEE Trans. Smart Grid 2022 13 3481 3492 10.1109/TSG.2022.3173964
Guo, Y. et al. Bilstm multitask learning-based combined load forecasting considering the loads coupling relationship for multienergy system. IEEE Trans. Smart Grid 13, 3481–3492 (2022).10.1109/TSG.2022.3173964
25. “AUS Campus Metabolism,” December 3, 2022. [Online]. Available: http://cm.asu.edu/.
26. Spearman CS The proof and measurement of association between two things Am. J. Psychol. 1904 15 72 101 10.2307/1412159
Spearman, C. S. The proof and measurement of association between two things. Am. J. Psychol. 15, 72–101 (1904).10.2307/1412159
27. Liu, S., Johns, E. & Davison, A. J. End-to-end multi-task learning with attention. ArXiv, 2018 (2018).
28. “NSRDB Data Viewer,” December 3, 2022. [Online]. Available: https://maps.nrel.gov/nsrdb-viewer/.
29. Chen, Y., Xiao, J.-W., Wang, Y.-W. & Li, Y. Regional wind-photovoltaic combined power generation forecasting based on a novel multi-task learning framework and tpa-lstm. Energy Convers. Manag. 297 (2023).
