Energy is vital for the sustainable development of China. Accurate forecasts of annual energy demand are essential to schedule energy supply and provide valuable suggestions for developing related industries. In the existing literature on energy use prediction, the artificial intelligence-based (AI-based) model has received considerable attention. However, few econometric and statistical evidences exist that can prove the reliability of the current AI-based model, an area that still needs to be addressed. In this study, a new energy demand forecasting framework is presented at first. On the basis of historical annual data of electricity usage over the period of 1985–2015, the coefficients of linear and quadratic forms of the AI-based model are optimized by combining an adaptive genetic algorithm and a cointegration analysis shown as an example. Prediction results of the proposed model indicate that the annual growth rate of electricity demand in China will slow down. However, China will continue to demand about 13 trillion kilowatt hours in 2030 because of population growth, economic growth, and urbanization. In addition, the model has greater accuracy and reliability compared with other single optimization methods.
Energy, which is a vital input for the economic and social development of any economy, has gained special attention. Combined with globalization and industrialization, global energy demand has been increasing continually for decades and is expected to rise approximately 30% from 2015 to 2035 in accordance with the worldwide economic growth [
Given the importance of accurate energy forecasts, extant studies using different estimation methods have been undertaken since the 1970s. In general, these early studies can be classified into two major categories: econometric [
This study aims to present a more scientific AI-based energy demand forecasting framework that ensures the reliability of predicted results. The electricity demand of China is forecasted as an example to show the process of implementing this framework. In addition, the predicted results are beneficial for policy makers to perform appropriate measures to bridge the electricity gap and arrange the supply of electricity demand.
The rest of the paper is organized as follows. Section
Energy estimation modeling has attracted wide spread interest among current practitioners and academicians. The commonly used econometric techniques include cointegration analysis, autoregressive integrated moving average (ARIMA) model, partial least square regression (PLSR), and vector error correction model. The ML method mainly refers to the AI model, support vector regression (SVR) method, and Grey forecasting method. Their details are described in the following sections.
Cointegration analysis can establish a long-run relationship among variables, and the forecasting results are reliably shown through tests ranging from unit root to cointegration analysis [
Any optimization technique requires information on future scenarios and a search for the best solutions against a test criterion. In this case, ML techniques are superior and are frequently used to solve these two problems. The ML models include several tools, such as the AI, SVR, and Grey forecasting methods. To motivate our research, we focused particularly on the AI-based model.
The concept of SVR is developed from the computation of a linear regression function in a high-dimensional feature space where the input data are mapped via a nonlinear function, which can be found in Vapnik [
Energy Grey forecasting model adopts the essential part of Grey system theory. In energy demand forecasting [
AI-based prediction method predicts energy use according to its correlated variables, such as population growth, economic growth, and economic structure [
The current AI-based prediction method is generally composed of four main steps: data collection, data preprocessing, model training, and model testing. With the superiority in time series processing, the AI-based model displays a good performance in predicting future energy demands. However, a spurious regression problem occurs in a wide range of time series analysis in econometrics owing to its nonstationarity. The current AI-based model cannot avoid this problem. If the selected variables do not satisfy the basic requirements of constructing a cointegration relationship over the sample period, the AI-based forecasting models cannot be employed to make energy demand projections because the nexus between energy demand and its factors will change in the medium and long term. Therefore, the mechanism for predicting energy demand should be reformulated.
In the precedent AI-based models, the commonly employed independent variables were around population, GDP, urbanization, industrialization, energy price, and energy mix. Three forms of the estimation models, including linear, quadratic, and exponential forms, were then adopted for data training [
The “fittest” weights are finally searched through different AI tools, such as GA, ACO, and hybrid algorithms, based on the fitness function employed to monitor the forecasting accuracy, which aims to minimize the sum of squared error between the actual and estimated values shown as follows:
After obtaining the optimal weights, the model was applied to forecast the future energy demand under different scenarios. Compared with the traditional econometric energy demand forecasting model, the proposed AI-based model frequently demonstrates higher prediction accuracy. However, according to economic theory, these periodical characteristics of economic variables will not change in the medium and long term when an economy remains in a consistent state. Consequently, their historical relationship between energy demand and factors in the sampling period should be entirely stable. When this relationship was satisfied, it could be used for forecasting energy demand. However, the current AI-based energy demand forecasting model does not determine this historical relationship through econometric and statistical analysis. This condition can be recognized as a “black-box” without knowing the internal relationship between energy demand and its affecting factors [
As indicated in the abovementioned conventional AI-based model, the AI tool is directly applied to obtain the optimal weights for the model after preprocessing the original data. Then, the model is employed to forecast future energy demand. However, the prediction results are not reliable when the variables cannot build a stable and long-run relationship or when the parameters will change over time. Therefore, the model stability tests should be performed before proceeding to obtain the fittest weights through the AI tools. The cointegration analysis is widely employed as a key econometric method to forecast mid- and long-run energy demand because it can establish a long-run relationship among variables [
The frameworks for the conventional and new AI-based energy demand forecasting model.
According to cointegration theory, the existence of a long-run equilibrium relationship among economic variables is based on the stationary linear combination of a time series. The cointegration relationship over the sampling period can be tested when the economic variables are integrated at
After verifying the existence of a long-run relationship among variables, the next step is to test the prediction accuracy performance of the model and determine whether the estimated parameters will change with time. Parameter inconsistency may result in poor consequences on inferences and lead to wrong conclusions. For the Johansen–Juselius cointegration test technique, the stability test for the vector autoregressive model should be conducted through the unit root analysis. Meanwhile, for the ARDL bound approach, the cumulative (CUSUM) and cumulative sum of squares (CUSUMSQ) are suitable for the stability test because their statistics are updated recursively and plotted against the break points.
In this section, electricity demand forecasting in China is shown as an example based on our new framework. First, we list the electric energy demand-affecting factors and the proxy variables based on existing electricity demand prediction literature. Second, given that the AI-based model does not require many explanatory variables, we employ the cointegration analysis to select the variables that can be contributed toward building a long-run relationship. Third, we employ the adaptive genetic algorithm (AGA), which is superior to conventional AI algorithms, to optimize the model. Based on the above estimation, three scenarios for economic growth, namely, low (Scenario A), business as usual (Scenario B), and high (Scenario A), are set. Finally, the electricity demand projections for the three scenarios are conducted.
Electricity demand can be viewed as a causal function of several affecting factors, such as population, GDP, electricity prices, economic structure, urbanization, and life styles [
To forecast the electricity demand, we use 31 years of observed data from 1985 to 2015. Electricity consumption in each year is measured in trillion (1012) kilowatt hours (KWH), and population is measured as 100 million (108) persons. GDP data are measured in trillion Yuan (1012) RMB and adjusted to the constant price in 1985. Economic structure is denoted by the ratio of output in the tertiary industry to GDP (%). The share of the urban population to the total population is used to substitute the urbanization rate (%). To represent the price for electricity, we use the price index for fuel and power to denote the electricity price. The price index for the base year (1985) is assumed to be 1.00, and the price index for other years is adjusted to the constant price index of 1985. The definition of the variables is shown in Table
Definition and description for the variables.
Variables | Definition | Max | Min | Mean | Std. dev. |
---|---|---|---|---|---|
|
ln form of total electricity energy consume (1012 KWH) | 1.7393 | −0.8873 | 0.4418 | 0.8381 |
|
ln form of total population (108) | 2.6208 | 2.3594 | 2.5208 | 0.0769 |
|
ln form of gross domestic product (trillion Yuan RMB 1012) | 2.6540 | −0.0944 | 1.2919 | 0.8578 |
|
ln form of the ratio of tertiary sector to GDP (%) | 3.9160 | 3.3810 | 3.6459 | 0.1506 |
|
ln form of the urban population to the total (%) | 4.0271 | 3.1659 | 3.5881 | 0.2809 |
|
ln form of price index for the electricity demand | 2.6623 | 0.0000 | 1.6674 | 0.0825 |
The trends of electricity demand and its factors (1985–2015).
As mentioned in Section
The flowchart of adaptive genetic algorithm.
After data collection and preprocess, the first step is to perform the unit root test to determine whether the time series satisfies the basic conditions for constructing the cointegration relationship. Considering that ADF and PP tests are distorted in small sample sizes, the Ng and Perron [
Results based on Ng-Perron unit root test.
Variables | Level | The first difference | The second difference | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
MZa | MZt | MSB | MPT | MZa | MZt | MSB | MPT | MZa | MZt | MSB | MPT | |
|
|
−1.71 | 0.23 | 4.02 |
|
−2.90 | 0.15 | 1.93 |
|
−0.93 | 0.44 | 10.62 |
|
1.19 | 1.74 | 1.46 | 145.21 |
|
−3.10 | 0.15 | 1.45 | −1.94 | −0.97 | 0.50 | 12.46 |
|
|
−2.45 | 0.18 | 2.39 |
|
−2.17 | 0.22 | 2.70 |
|
−2.50 | 0.19 | 2.08 |
|
|
0.41 | 0.55 | 24.74 |
|
−2.56 | 0.18 | 2.03 |
|
−2.40 | 0.20 | 2.17 |
|
−4.68 | −1.30 | 0.28 | 5.66 |
|
−1.81 | 0.27 | 3.74 |
|
−2.61 | 0.18 | 1.85 |
|
−2.23 | −0.88 | 0.39 | 9.69 |
|
−2.38 | 0.18 | 2.52 |
|
−3.30 | 0.15 | 1.16 |
|
−2.17 | −0.97 | 0.44 | 37.97 | −7.99 | −1.79 | 0.23 | 11.90 | −5.41 | −1.62 | 0.30 | 16.77 |
|
−3.16 | −1.07 | 0..34 | 24.85 | −0.41 | −0.25 | 0.61 | 85.70 | −9.73 | −2.21 | 0.23 | 9.36 |
|
|
−4.25 | 0.12 | 2.70 | −10.23 | −2.19 | 0.21 | 9.20 | −13.39 | −2.58 | 0.19 | 6.85 |
|
|
−2.87 | 0.17 | 5.57 | −13.87 | −2.58 | 0.19 | 6.87 | −11.60 | −2.39 | 0.21 | 7.96 |
|
−13.31 | −2.57 | 0.19 | 6.91 | −6.75 | −1.82 | 0.27 | 13.50 | −13.89 | −2.62 | 0.19 | 6.64 |
|
−0.48 | −0.20 | 0.41 | 42.25 | −14.15 | −2.60 | 0.18 | 6.83 |
|
−3.34 | 0.15 | 4.08 |
|
||||||||||||
Critical values (intercept) | Critical values (intercept and trend) | |||||||||||
|
||||||||||||
1% level | −13.80 | −2.58 | 0.17 | 1.78 | −23.80 | −3.42 | 0.14 | 4.03 | ||||
5% level | −8.10 | −1.98 | 0.23 | 3.17 | −17.30 | 2.91 | 0.17 | 5.48 | ||||
10% level | −5.70 | −1.62 | 0.27 | 4.45 | −14.20 | −2.62 | 0.18 | 6.67 |
The first six rows in Table
Next, we conducted the test to determine the presence of a long-run relationship using the ARDL bounds testing approach. The ordinary least squares (OLS) procedure is first employed for the next equation, which is expressed as
To obtain the optimal lag length for the equation, the ARDL bounds approach should estimate
The null hypothesis in the equation is
Null should be rejected when the calculated
Results of bounds testing approach based on SBC.
Electricity demand function |
|
Lag order | Cointegration | |
---|---|---|---|---|
|
2.5629 | 1 | Inconclusive | |
|
|
2 | Yes | |
|
2.5507 | 2 | Inconclusive | |
|
1.8554 | 2 | No | |
|
2.5478 | 2 | Inconclusive | |
|
|
2 | Yes | |
|
||||
Critical values | ||||
|
||||
|
| |||
|
||||
1% level | 4.134 | 5.761 | 4.280 | 5.840 |
5% level | 2.910 | 4.193 | 3.058 | 4.223 |
10% level | 2.407 | 3.517 | 2.525 | 3.560 |
As shown in Table
CUSUM and CUSUMSQ are applied to show the stability of the model, as shown in Figure
Plot of CUSUM (a) and CUSUMSQ (b).
In the figure, the plots of CUSUM and CUSUMSQ are located within the critical bounds at the 5% significance level, which suggests that the model is stable. Accordingly, the cointegration relationship between electric energy demand and its factors is reliable.
After the long-run equilibrium relationship among the variables is verified, AGA is employed to optimize the coefficients of (
To estimate the coefficients for the linear and quadratic forms, the observed data from 1985 to 2015 are used. The linear form for the optimal model is written as follows (for simplicity, we do not present the results in exponential form):
In addition, the quadratic form for the optimal model is expressed as
To evaluate the performance of the prediction model, the model must be compared with other forecasting optimal models (GA, ACO, GM, and OLS) using MAE, MSE, MAPE, and RMSE. The corresponding definitions of MAE, MSE, MAPE, and RMSE are shown as follows:
Prediction accuracy test for the optimal model.
Method | Criteria | MAE | MSE | MAPE (%) | RMSE |
---|---|---|---|---|---|
AGA (linear) | 0.3122 | 0.1023 | 2.01 | 0.3198 | |
AGA (quadric) | 0.2704 | 0.0932 | 1.73 | 0.3052 | |
GA (linear) Canyurt and Öztürk [ |
0.4212 | 0.1652 | 2.95 | 0.4064 | |
GA (quadric) | 0.3408 | 0.1206 | 2.44 | 0.3473 | |
ACO (Toksari [ |
0.5874 | 0.3165 | 4.15 | 0.5626 | |
GM (Hsu and Chen [ |
0.6731 | 0.4239 | 5.83 | 0.6511 | |
OLS | 0.8019 | 0.4832 | 8.68 | 0.6951 |
The original and prediction time series of electric energy consumption.
The abovementioned framework is applied to forecast electricity demand from 2016 to 2030 based on three scenarios. The trends of the affecting factors are described as follows:
Hypothesis of variables for the three different scenarios (unit: %).
Period | Growth rate of GDP | Growth rate of population | Growth rate of economic structure | Growth rate of urbanization | ||
---|---|---|---|---|---|---|
Scenario A | Scenario B | Scenario C | ||||
2016–2020 | 7.0 | 6.5 | 6.0 | 0.60 | 2.0 | 1.5 |
2021–2025 | 6.5 | 6.0 | 5.5 | 0.70 | 2.2 | 0.8 |
2026–2030 | 6.0 | 5.5 | 5.0 | 0.75 | 2.5 | 0.4 |
The electricity demand of China can be forecasted after the assumptions of the factors are established. In Figures
Electricity demand in Scenario A.
Electricity demand in Scenario B.
Electricity demand in Scenario C.
The electricity demand of China will continue growing in the medium and long term regardless of the adjustments in economic structure. Under the high-growth scenario (Scenarios A), the electricity demand will still increase rapidly because of the economic growth, urbanization process, and population growth of China. However, the annual growth rate of electricity demand will decrease to 5.8% during the 2016–2030 period in Scenario A owing to the decline in annual growth rate of economic growth and the adjustment in economic structure. This value is much lower compared with that in the period of 2000–2015. In 2020, 2025, and 2030, the electricity demand of China will be 8.2585, 11.139, and 13.821 trillion KWH according to the quadratic form of this model (Figure
In this study, we develop a new framework to predict energy demand based on the conventional AI models and cointegration theory. To develop energy forecasts, we emphasize the use of appropriate data and econometric techniques rather than several computer packages for demand estimation techniques provided by previous studies. In this new framework, the energy demand-affecting factors, which are used as the independent variables in the prediction model, are determined based on theoretical analysis and selected by statistical and econometric analysis or tests. Finally, the future electricity demands of China from 2016 to 2030 are predicted as an example for the new model by using the modified AI-based model. Compared with several previous AI-based literatures, we prove that the present forecasting model demonstrates exceptional performance in forecasting electric energy demand.
The prediction results of electricity demand indicate that population growth, economic growth, and urbanization are the leading forces contributing to the increase of electricity demand, whereas economic structure adjustment is responsible for the decline of electricity consumption. Several specific results are listed below: an electricity demand growth is observed in China in the following years (i.e., 2016–2030). However, the future annual growth rate is lower compared with the last decades. Based on our analysis, electricity demand will still continue to increase at an annual average rate of about 5.5% and will be about 13 trillion KWH in 2030. This value corresponds to nearly two times compared with the 2015 level. The forecasts would be valuable for policy makers in China in planning future energy policies.
The authors declare that they have no conflicts of interest.