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Article

Prediction of Whole Social Electricity Consumption in Jiangsu Province Based on Metabolic FGM (1, 1) Model

1
College of Information Management, Nanjing Agricultural University, Nanjing 210031, China
2
School of Information Management, Nanjing University, Nanjing 210023, China
*
Author to whom correspondence should be addressed.
Submission received: 11 April 2022 / Revised: 17 May 2022 / Accepted: 21 May 2022 / Published: 24 May 2022

Abstract

:
The achievement of the carbon peaking and carbon neutrality targets requires the adjustment of the energy structure, in which the dual-carbon progress of the power industry will directly affect the realization process of the goal. In such terms, an accurate demand forecast is imperative for the government and enterprises’ decision makers to develop an optimal strategy for electric energy planning work in advance. According to the data of the whole social electricity consumption in Jiangsu Province of China from 2015 to 2019, this paper uses the improved particle swarm optimization algorithm to calculate the fractional-order r of the FGM (1, 1) model and establishes a metabolic FGM (1, 1) model to predict the whole social electricity consumption in Jiangsu Province of China from 2020 to 2023. The results show that in the next few years the whole social electricity consumption in Jiangsu Province will show a growth trend, but the growth rate will slow down generally. It can be seen that the prediction accuracy of the metabolic FGM (1, 1) model is higher than that of the GM (1, 1) and FGM (1, 1) models. In addition, the paper analyzes the reasons for the changes in the whole society electricity consumption in Jiangsu Province of China and provides support for government decision making.

1. Introduction

On 22 September 2020, President Xi Jinping of China delivered an important statement at the general debate of the 75th session of the UN General Assembly, stressing that “China will adopt more effective policies to achieve the peak of CO2 emissions before 2030 and strive to achieve carbon neutrality before 2060”. In December 2020, The Central Economic Work Conference of China listed the “carbon peak and carbon neutralization” as one of the key tasks in 2021. At the same time, many countries are making strategic adjustments. Germany is currently implementing the “Energiewende” plan to transition to a non-nuclear and low-carbon energy system [1,2]; Japan has decided to fundamentally adjust its energy supply structure, relying more on energy structure diversification and renewable energy, thereby improving energy efficiency and reducing carbon emissions [3,4]; and the UK proposes the British energy security strategy, which puts offshore wind and nuclear power at the core of its policy, aiming to achieve 95% of electricity from low-carbon energy sources by 2030 [5,6]. Similarly, the change in energy structure is the key for China to achieve “two-carbon” goals on the premise of maintaining economic growth and the share of the manufacturing industry. In 2020, the CO2 emissions from China’s energy consumption accounted for about 8% of the total emissions, of which the power industry accounted for about 42.5%. Therefore, the carbon peak and carbon neutrality of the electric energy industry is very important. Forecasting electricity consumption is significant for making power planning scientific and ensuring sustainable economic development. Jiangsu province is one of the provinces with the highest level of comprehensive development in China and is also an important area that scholars pay attention to in terms of economic development, energy consumption, and environmental protection. The economic and social development of Jiangsu province needs the support of electric energy, so it is very necessary to predict the power consumption of the whole society. The prediction results can provide decision supports for the government and enterprises.
At present, the prediction methods of electricity consumption mainly consist of traditional econometric models and artificial intelligence (AI) models [7,8]. Traditional econometric prediction models include the least squares regression model (LSR) [9], autoregressive integrated moving average model (ARIMA) [10], vector autoregressive model (VAR) [11], etc. These methods take into account the time-series characteristics of power consumption and can effectively predict short-term power consumption. However, they have high requirements for sample size [12]. The AI methods mainly include support vector machine (SVM) [13], artificial neural networks (ANN) [14,15,16], and so on. These methods do not need to consider the distribution characteristics of data and can characterize the nonlinear relationship of the model. However, the characteristics of sequence are not considered when using an artificial intelligence method to predict power consumption [17]. Furthermore, the classical methods cannot deal with prediction problems where historical data need to be represented by linguistic values. On this basis, Zadeh [18] first proposed fuzzy set theory to handle language-valued problems. There are many methods for fuzzy modeling of time series, such as the Takagi–Sugeno rules [19], fuzzy neural network [20], fuzzy gray system [21], and so on. Fuzzy models of time series have been used to predict the stock index, enrollment in universities [22,23,24], and outpatient appointments [25]. Lee et al. used fuzzy time series (FTS) for electricity consumption prediction and combined this method with an artificial neural network, adaptive neuro-fuzzy inference system, and least squares support vector machines for comparison. Through the data tests of seven countries, it was found that the FTS model has the best accuracy among the studies in most countries [26].
Gray systems have been proposed by Deng [27] as an effective model for systems with partially known internal characteristics, which are used to deal with incomplete information. Gray systems largely involve the use of gray sets and gray numbers, just as fuzzy theory uses fuzzy sets and fuzzy numbers. Gray sets use the concept of gray numbers and regard the characteristic function values of a set as gray numbers. Gray numbers are numbers that only know the range of values but not the exact value. The algorithm for gray numbers is very similar to interval values [28]. If the eigenfunction values are restricted to be in the range [0, 1], the gray sets can be regarded as an extension of the type-1 fuzzy set [29,30]. A common assumption is that gray sets are equivalent to interval-valued fuzzy sets, but deeper studies show that an interval-valued fuzzy set should be assumed to be equal to gray numbers only if the gray numbers are assumed to contain only continuous data. However, the generalized gray numbers can contain both continuous data and discrete data, which makes them different from interval-valued fuzzy sets. Therefore, it can be said that a gray number is a generalization of an interval-valued fuzzy set [31,32].
The gray prediction method is used to establish a model through a small amount of incomplete information to predict the future development trend, among which the GM (1, 1) model is the most common. Scholars have deeply studied the GM (1, 1) model based on the background value, initialization condition, parameter estimation method, model properties, and other aspects [33,34,35,36,37]. Aiming at the problem of the poor accuracy of the GM (1, 1) model, Wu et al. proposed the FGM (1, 1) model, which reduced the error by selecting an appropriate fractional order [38,39,40,41,42]. Guo et al. [43] used the quarterly compound fractional gray model to predict the air quality in 22 cities in China. Pei and Liu [44] made a predictive analysis of the business environment of economies along the Belt and Road using the fractional-order gray model. Khan and Osinska [45] compared the prediction accuracy of FGM (1, 1) with traditional models, such as standard GM (1, 1) and ARIMA (1, 1, 1), by predicting energy consumption at the aggregate and disaggregated levels of the BRICS countries, confirming that both the FGM (1, 1) and ARIMA (1, 1, 1) models are effective in the prediction of energy consumption. Zhao and Wu [46] used the FGM (1, 1) model to predict the number of lightly polluted days in the Jing-Jin-Ji region of China and suggested the Jing-Jin-Ji region should adjust measures to fulfill a significant improvement in air quality. Tong et al. [47] made a prediction of the Tianjin municipal solid waste disposal volume by using the FGM (1, 1) model and found that in the next three years the amounts of garbage removal and harmless treatment will both show increasing trends. Yang and Xue [48] discussed an example of a per capita power generation forecast using an improved fractional gray model with error feedback. Meng and Wu [49] established a fractional-order cumulative gray forecast model to forecast the per capita water consumption in 31 districts in China from 2019 to 2024. Fang et al. [50] used a gray system model with fractional order accumulation to improve the prediction performance for the maintenance cost of a weapon system. Zhao et al. [51] used an FGM (1, 1) model to forecast the added value of high-tech industries in Hebei Province. Xiong and Wu [52] used the FGM (1, 1) model to forecast China’s express business volume. Through the comparison of the commonly used models of the gray system, Cheng et al. [53] found that the combination model of a fractional-order GM (1, 1) and the Markov model has the highest prediction accuracy and used it to predict the carbon emission intensity of China’s transportation industry. However, the FGM (1, 1) model does not consider the impact of future disturbance factors on the system.
The existing studies mainly focus on the optimization and application scope of the traditional gray forecasting model and the modeling method of the fractional GM (1, 1) model. For the selection method of the optimal fractional order in the FGM (1, 1) model and how to reduce the influence of new information, few scholars have conducted research at present. To remedy these deficiencies, this paper proposes an FGM (1, 1) model based on the principle of metabolism and verifies the model using the whole society power consumption data of Jiangsu province from 2015 to 2019. Among them, the fractional order is obtained by using the improved particle swarm optimization algorithm. In the modeling process, the model constantly adds the latest information, removes old information, and dynamically generates the prediction series so as to improve the prediction accuracy. The prediction results show that the whole social electricity consumption of Jiangsu province will still show an upward trend from 2020 to 2023.

2. Modeling Process of Metabolic FGM (1, 1) Model and Particle Swarm Optimization Algorithm

2.1. Modeling Process of FGM (1, 1) Model

The modeling process of the FGM (1, 1) model is as follows.
(1) According to the original non-negative data, the original non-negative sequence is given.
X 0 = x 0 1 , x 0 2 , , x 0 n 1 , x 0 n
(2) Through the accumulative formula x r = Σ i = 1 k C k i + r 1 k i x 0 i , the r-order accumulation sequence is as follows, where C k i + r 1 k i = k i + r 1 k i + r 2 r + 1 r k i ! , C r 1 0 = 1 , C k k + 1 = 0 , the parameter k means the time, and r means the order of cumulative generation.
X r = x r 1 , x r 2 , , x r n 1 , x r n
(3) The whitening differential equation is as follows, where “a” and “b” are called the development gray number and endogenous control gray number, respectively. “Whitening” means to increase the whiteness of the system and make the information more transparent. The whitening process is a process from discrete to continuous. During this period, information may be equal, and false information may also be added. This is part of the reason why the gray model is called “gray”.
d x r t d t + a x r t = b
The solution of the above equation is exponential, as follows.
x r t + 1 = x 0 1 b a e a t + b a
The parameters are obtained using the least square method.
a ^ b ^ = B T B 1 B T Y
where B = 0.5 x r 1 + x r 2 1 0.5 x r 2 + x r 3 1 0.5 x r n 1 + x r n 1 , Y = x r 2 x r 1 x r 3 x r 2 x r n x r n 1 .
(4) Through substituting a ^ and b ^ , the time response function is as follows.
x ^ r k + 1 = x 0 1 b ^ a ^ e X ^ k + b ^ a ^
where x ^ r k + 1 is the value of time k + 1 .
(5) By using the r-order inverse accumulated generating operator in X ^ r = x ^ r 1 , x ^ r 2 , , x ^ r n 1 , x ^ r n , the reduction sequence is as follows.
α r X ^ r = α 1 x ^ r 1 r 1 , α 1 x ^ r 1 r 2 , , α 1 x ^ r 1 r n
where α 1 x ^ r 1 r k = x ^ 1 1 r k x ^ r 1 r k 1 .
Therefore, the prediction sequence is as follows.
X ^ 0 = x ^ 0 1 , x ^ 0 2 , , x ^ 0 n 1 , x ^ 0 n
(6) Model testing. The average absolute percentage error (MAPE) is obtained by comparing the actual value with the predicted value to evaluate the accuracy. The expression of MAPE is as follows.
M A P E = 100 % × 1 n × k = 1 n x 0 k x ^ 0 k x 0 k

2.2. Particle Swarm Optimization Algorithm

In the existing research on energy forecasting, scholars mostly use heuristic algorithms to solve the model, such as the genetic algorithm (GA) [54,55,56], ant colony algorithm (ACA) [57,58,59], simulated annealing algorithm (SA) [60], gray wolf algorithm [61,62,63], and particle swarm optimization algorithm (PSO) [64,65], etc. GA has a strong global optimal solution search ability, but it has defects, such as a poor local search ability and “prematurity”, which cannot guarantee algorithm convergence. SA is beneficial to avoid falling into a local optimal solution, but the search efficiency is poor. The gray wolf algorithm has the characteristics of strong convergence performance, few parameters, and easy implementation. However, in some problems, it has the shortcomings of low solution accuracy, slow convergence speed, and an easy-to-fall-into local optimum. ACA requires a long search time and is prone to stagnation. Compared with other heuristic algorithms, the PSO algorithm can converge to the global optimal solution with a larger probability, and it is an efficient parallel search algorithm. Therefore, this paper uses the PSO algorithm for calculation. At the same time, we dynamically adjust the parameter w in the calculation process so as to ensure that each particle can search more finely in a large range so that the algorithm has a high probability to converge to the global optimal solution.
The particle swarm optimization algorithm (PSO) was first proposed by American electrical engineer Eberhart and social psychologist Kennedy [66,67] based on the foraging behavior of a flock of birds that is widely used in various calculations [68,69,70,71]. In the foraging model of a flock of birds, each individual can be regarded as a particle, and the flock of birds can be regarded as a particle swarm. Particles iterate by tracking local and global optimality to achieve optimal decisions. The essence of particle swarm optimization is a random search algorithm that can converge to the global optimal solution with a high probability [72,73].
Suppose there are N particles to form a population in a D -dimensional target search space, where the i particle ( i = 1, 2, …, N ) represents a vector of D-dimensions. It is denoted by
X i = x i 1 , x i 2 , , x i D , i = 1 , 2 , , N
In another words, the position of each particle is a potential solution, and X i can be substituted into the objective function to calculate its adaptive value.
The “flight” velocity of the i particle is also a D -dimensional vector, denoted as:
V i = v i 1 , v i 2 , , v i D , i = 1 , 2 , , N
The optimal position of the i particle and the entire particle group searched so far are an individual extreme value
P B e s t = p i 1 , p i 2 , , p i D , i = 1 , 2 , , N
and global extreme value
G B e s t = g i 1 , g i 2 , , g i D , i = 1 , 2 , , N
respectively.
When the two optimal values are not found, the particle swarm optimization algorithm uses the following formulas to update the particle velocity and position.
v i j t + 1 = w v i j t + c 1 r 1 t p i j t x i j t + c 2 r 2 t g i j t x i j t
x i j t + 1 = x i j t + v i j t + 1
where w is non-negative and is called the inertia factor. The learning factors c 1 and c 2 are non-negative constants, also known as acceleration constants.   r 1 t and r 2 t are uniform random numbers in the range [0, 1]. v i j t is the speed of the particle, v i j t v m a x , v m a x , v m a x is a constant set by the user to limit the speed of the particle. The right side of Formula (14) is composed of three parts: the first part is the “inertia” or “momentum” part, which represents the previous velocity of the particle and is used to ensure the global convergence performance of the algorithm; the second part is the “cognition” part, which reflects the particle’s memory or recall of its own historical experience, indicating that the particle tends to approach the best position in its history; and the third part is the “social” part, which reflects the group’s historical experience of cooperation and knowledge sharing among particles, and represents the tendency of particles to approach the optimal position in the history of the group or neighborhood. The latter two parts enable the algorithm to have local convergence ability.

2.3. Algorithm Design

According to the characteristics of the particle swarm optimization algorithm, a dynamic adjustment of w in the search process balances the abilities of global search and local search. Let c 1 = c 2 = 2, N = 50, the maximum number of iterations is t m a x = 100, set the stop criterion to eps = 10−6. To avoid particles “oscillating” near the global optimal solution, let [74]
w = w m a x w m a x w m i n × t t m a x
where t m a x , t , w m i n , and w m a x represent the maximum number of evolutions, the current iteration number, the minimum inertia weight, and the maximum inertia weight. w varies within the range of 0.1–0.9. The flow chart of the improved particle swarm optimization algorithm is shown in Figure 1.

2.4. Modeling Process of Metabolic FGM (1, 1) Model

In previous studies, in order to solve the problem that the prediction error of the GM (1, 1) model increases with the extension of time, scholars mostly used the metabolic method to improve the GM (1, 1) model [75,76,77] and rarely used this method to optimize the FGM (1, 1) model. This paper presents a new FGM (1, 1) model based on metabolism. On one hand, the model has the advantages of the FGM (1, 1) models; on the other hand, the random perturbations are taken into account over time to improve the accuracy of the model. The steps of the metabolic FGM (1, 1) model are as follows.
Step1: The FGM (1, 1) model is established to predict x ^ 0 n + 1 using the original sequences X 0 = x 0 1 , x 0 2 , , x 0 n 1 , x 0 n ;
Step2: Add x ^ 0 n + 1 to the end of the original sequence Χ 0 and remove the data x 0 1 whose importance is reduced due to the passage of time. Therefore, the dimension of the original sequence remains unchanged, and the original sequence becomes x 0 2 , x 0 3 , , x 0 n 1 , x 0 n , x ^ 0 n + 1 . Then, continue to build the FGM (1, 1) model until the prediction goal is completed. This model makes full use of the new information and makes the prediction more accurate.

3. Case Study

An FGM (1, 1) model was constructed based on the data of the whole social electricity consumption in Jiangsu province from 2015 to 2019 (Unit: 100 million kW∙h, data from website of China’s National Bureau of Statistics), where the original sequence was X 0 = 5114.70 ,   5458.95 ,   5807.89 ,   6128.27 ,   6264.36 . As can be seen from Χ 0 , the whole social electricity consumption in Jiangsu province showed an upward trend from 2015 to 2019, and the annual growth rates were 6.73%, 6.39%, 5.52%, and 2.22%, respectively. The upward trend was gradually stabilizing, indicating that the energy conservation and emission reduction policies proposed by the Jiangsu provincial government have played a role in restraining the growth of the whole social electricity consumption. Therefore, the FGM (1, 1) model was established to predict the whole social electricity consumption in Jiangsu Province (the model is named model 1). The calculation process of the FGM (1, 1) model is as follows.
The initial sequence of the whole social electricity consumption in Jiangsu province is X 0 = 5114.70 ,   5458.95 ,   5807.89 ,   6128.27 ,   6264.36 . The iterative process of the particle swarm optimization algorithm is shown in Figure 2. The results show that the fractional-order r finally converges to 0.065.
The 0.065 order cumulative sequence is as follows.
X 0.065 = x 0.065 1 ,   x 0.065 2 , x 0.065 3 ,   x 0.065 4 , x 0.065 5 = 5114.7 ,   5818.41 ,   6341.51 ,   6817.52 ,   7087.8
a ^ and b ^ can be calculated by the formula a ^ b ^ = B T B 1 B T Y = 0.2672 2168.83 , where B = 5466.55 1 6079.96 1 6579.52 6952.66 1 1 , Y = 703.7055 523.1038 476.0134 270.2761 .
Then, the times series function is as follows.
x ^ 0.065 k + 1 = 5114.7 2168.83 0.2672 e 0.2672 k + 2168.83 0.2672
Therefore,
X ^ 0.065 = x ^ 0.065 1 , x ^ 0.065 2 , x ^ 0.065 3 , x ^ 0.065 4 , x ^ 0.065 5 , x ^ 0.065 6 = 5114.7 ,   5818.421 ,   6357.107 ,   6769.463 ,   7085.115 ,   7326.741 X ^ 1 = x ^ 0.065 0.935 1 , x ^ 0.065 0.935 2 , , x ^ 0.065 0.935 6 = 5114.7 ,   10600.67 ,   16424.15 ,   22503.35 ,   28767.67 ,   35162.01
The predicted values are as follows.
X ^ 0 = x ^ 0 1 , x ^ 0 2 , , x ^ 0 5 , x ^ 0 6 = 5114.7 ,   5485.97 ,   5823.49 ,   6079.2 ,   6264.33 ,   6394.34
When r = 1, the prediction results of the GM (1, 1) model can be obtained. The MAPE values of the GM (1, 1) model and FGM (1, 1) model are given in Table 1.
It can be seen in Table 1 that the MAPE values of the GM (1, 1) model and the FGM (1, 1) model (r = 0.065) are 0.7% and 0.21%, respectively, which indicates that the simulation results of these two models are relatively accurate. Comparing the two results, it can be found that the MAPE value of the FGM (1, 1) model is smaller than the GM (1, 1) model’s, which indicates that the prediction results of the FGM (1, 1) model are more accurate. At the same time, from Table 2, by comparing the MAPE values of the FGM (1, 1) model, predicted based on the electricity consumption data of other provinces, it can be found that the MAPE values of these cases are less than 1%, which shows that the FGM (1, 1) model is effective in electricity consumption prediction [78].
In order to reduce the impact of future disturbance factors on the system, the paper proposed to build a metabolism-based FGM (1, 1) model and use the improved PSO algorithm to calculate the fractional order of the model. First, the 2020 data predicted by the FGM (1, 1) model were added to the initial sequence, and the 2015 data were removed. Then, the new initial sequence was X 0 = 5458.95 ,   5807.89 ,   6128.27 ,   6264.36 , 6394.34 . The prediction values of 2021–2023 are 6429.05(model 2), 6492.04 (model 3), and 6499.04 (model 4), respectively, by the metabolic FGM (1, 1) model. The prediction results of the metabolic FGM (1, 1) model are shown in Table 3.
It can be seen in Table 3 that the MAPE values of model 1–model 4 are 0.21%, 0.15%, 0.14%, and 0.12%, respectively, which shows that the prediction results of the metabolic FGM (1, 1) model are more accurate than the FGM (1, 1) model. Figure 3, Figure 4 and Figure 5 shows the iterative process from model 2 to model 4, respectively.
As can be seen in Table 4, compared with other models such as statistical methods and machine learning models, the MAPE of the metabolic FGM (1, 1) model is the smallest [79,80,81]. It was found that the metabolic FGM (1, 1) model is an effective method and a powerful tool for predicting the whole society electricity consumption with small samples.

4. Results and Discussion

As can be seen in Table 3, the whole social electricity consumption in Jiangsu province during 2020–2023 still shows an increasing trend year by year, and the annual growth rates are 2.08%, 0.54%, 0.98%, and 0.11%, respectively. It can be seen that the overall growth rate is slowing down, and the main reasons are as follows.
(1) The impact of policy. In order to achieve the goal of “dual carbon” proposed by China, Jiangsu province has written “carbon peaking and carbon neutrality goals” into the “14th Five-Year Plan” and formulated a specific action plan. For example, Nanjing city has launched the construction of a low-carbon pioneer city and formulated an action plan to take the lead in reaching the peak of carbon emissions, and Suzhou city has integrated the “dual carbon” goal into the urban governance.
(2) The adjustment of industrial structure. Jiangsu province has been vigorously promoting industrial transformation and upgrading, high-energy-consuming industries have been controlled, and emerging industries have developed rapidly. In 2019, the growth rate of power consumption in high-energy-consuming industries in Jiangsu Province was lower than that of the whole society. The electricity consumption of the science and technology service industry and internet industry in Jiangsu province increased by 8.8% and 13.6%, respectively, indicating that the pace of economic restructuring and industrial upgrading has accelerated, and new growth points have been further explored.
(3) Comprehensively promoting green power consumption. Jiangsu province is exploring the synergistic interaction between green electricity consumption and production to guide power users to optimize power consumption.

5. Conclusions

The realization of carbon peaking and carbon neutrality requires an adjustment of the energy structure, and the reform progress of the power industry will directly affect the process of achieving the goals. To help government and enterprise decision makers conduct power and energy planning work in advance, this paper proposes the metabolic FGM (1, 1) model based on the improved PSO algorithm and uses the GM (1, 1) model, FGM (1, 1) model, and metabolic FGM (1, 1) model to predict the whole social electricity consumption in Jiangsu province from 2020 to 2023. The results show that the metabolic FGM (1, 1) model has the least prediction error. The prediction results show that under the background of the “dual carbon” policy, the whole society electricity consumption of Jiangsu province will maintain an increasing trend from 2020 to 2023, but the overall growth rate shows a downward trend.
However, when the sample length is too long, the prediction error of the metabolic FGM (1, 1) model will increase. Therefore, the metabolic FGM (1, 1) model is more suitable for short-term predictions. In addition, other heuristic algorithms can be used in the future to find the optimal parameters for the model.

Author Contributions

Conceptualization, M.C.; date curation, M.C.; methodology, S.Z. and L.W.; resources, L.W.; software, S.Z.; supervision, L.W.; visualization, D.Z.; writing—original draft, S.Z.; writing—review and editing, D.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the China Postdoctoral Science Foundation (grant number 2017M611785) and the Jiangsu Planned Projects for Postdoctoral Research Funds (grant number 1601091C).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Acknowledgments

The authors also gratefully acknowledge anonymous reviewers for their helpful comments and suggestions, which improved the paper.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Flow chart of improved particle swarm optimization algorithm.
Figure 1. Flow chart of improved particle swarm optimization algorithm.
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Figure 2. Fractional-order convergence process of model 1.
Figure 2. Fractional-order convergence process of model 1.
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Figure 3. Fractional-order convergence process of model 2.
Figure 3. Fractional-order convergence process of model 2.
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Figure 4. Fractional-order convergence process of model 3.
Figure 4. Fractional-order convergence process of model 3.
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Figure 5. Fractional-order convergence process of model 4.
Figure 5. Fractional-order convergence process of model 4.
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Table 1. The MAPE values of GM (1, 1) model and FGM (1, 1) model.
Table 1. The MAPE values of GM (1, 1) model and FGM (1, 1) model.
YearActual Value
(100 Million kW∙h)
GM (1, 1)
(100 Million kW∙h)
FGM (1, 1) (r = 0.065)
(100 Million kW∙h)
20155114.705114.705114.70
20165458.955531.115485.97
20175807.895783.075823.49
20186128.276046.516079.20
20196264.366321.966264.33
MAPE 0.7%0.21%
Table 2. The fitting values and MAPE values of other provinces’ power (100 million kW∙h).
Table 2. The fitting values and MAPE values of other provinces’ power (100 million kW∙h).
YearBeijing
(Actual Value)
Beijing
(Fitted Value)
Tianjin
(Actual Value)
Tianjin
(Fitted Value)
Hebei
(Actual Value)
Hebei
(Fitted Value)
2015952.72952.72800.6800.63175.683175.68
20161020.271016.85807.93797.063264.523260.24
20171066.891079.12805.59822.083441.743452.72
20181142.381128.55855.14850.643665.663657.37
20191166.41171.16878.43878.043856.063855.98
r 0.9 0.1 0.1
MAPE 0.62% 0.79% 0.14%
Table 3. Results of metabolic FGM (1, 1) model (100 million kW∙h).
Table 3. Results of metabolic FGM (1, 1) model (100 million kW∙h).
YearActual valueModel 1Model 2Model 3Model 4
20155114.75114.7
20165458.955485.975485.95
20175807.895823.495807.95807.89
20186128.276079.26114.366128.286128.27
20196264.366264.336288.046276.076264.35
2020 6394.346383.746371.426384.36
2021 6429.056439.936448.37
2022 6492.046482.8
2023 6499.04
r 0.0650.82070.94680.9417
MAPE 0.21%0.15%0.14%0.12%
Table 4. Comparison with similar studies in the literature.
Table 4. Comparison with similar studies in the literature.
ModelARIMAESANNSFOGM (1, 1)MGM (1, n)GM (1, 1)FGM (1, 1)Metabolic FGM (1, 1)
MAPE3.21%2.86%11.00%1.77%0.82%0.70%0.21%0.12%
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Zhang, S.; Wu, L.; Cheng, M.; Zhang, D. Prediction of Whole Social Electricity Consumption in Jiangsu Province Based on Metabolic FGM (1, 1) Model. Mathematics 2022, 10, 1791. https://0-doi-org.brum.beds.ac.uk/10.3390/math10111791

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Zhang S, Wu L, Cheng M, Zhang D. Prediction of Whole Social Electricity Consumption in Jiangsu Province Based on Metabolic FGM (1, 1) Model. Mathematics. 2022; 10(11):1791. https://0-doi-org.brum.beds.ac.uk/10.3390/math10111791

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Zhang, Siyu, Liusan Wu, Ming Cheng, and Dongqing Zhang. 2022. "Prediction of Whole Social Electricity Consumption in Jiangsu Province Based on Metabolic FGM (1, 1) Model" Mathematics 10, no. 11: 1791. https://0-doi-org.brum.beds.ac.uk/10.3390/math10111791

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