Regional electrical energy substitution potential prediction based on time series and improved back propagation neural network

A combined time-series-based regression forecasting and GRA-IPSO-BP structure is proposed to forecast the electricity replacement forecasts using a time series model based on the triple exponential smoothing forecasting method. The forecast results are corrected using the GRA-IPSO-BP structure. The results of the algorithm show that using a combination of time series and GRA-IPSO-BP structure can significantly improve the forecasting accuracy of electricity replacement compared to single-method forecasting.


Introduction
In September 2020, China put forward the goal of achieving carbon peaking by 2030 and carbon neutrality by 2060 [1].And clean replacement and electricity replacement are important ways to achieve this, receiving gradual attention [2][3][4].Electricity is a basic industry related to national security and people's livelihood, and the supply and security of electricity is related to national security strategy.Electricity replacement mainly includes three forms: first, the consumption side of electricity replacement, including in the city centralized heating, industrial and commercial, and other key areas of the implementation of the electricity to replace coal and in the city of the electricity replacement.
First, the consumer side of electricity replacement, including in the city centralized heating, industrial and commercial, and other key areas of the implementation of electricity instead of coal and in the city transportation, agricultural irrigation, and other areas of electricity instead of oil.The second is the production side of electricity replacement by clean electricity to replace traditional fossil energy generation.Third is the transport side electricity replacement, mainly in the west and north.The main purpose is to transport clean power from the west and north to the east and central regions to replace coal with electricity.Although China has become the largest country in electricity production and consumption and the largest country in installed wind power and photovoltaic power generation, the per capita level is significantly lower than that of developed countries.As a result, China's 13th Five-Year Plan for Electricity Development formulated the key task of "implementing electricity replacement and optimizing energy consumption structure"; in 2022, the "Guidance on Further Promoting Electricity replacement" was issued, which clearly put forward the target of "the proportion of electricity to enduse energy consumption will reach about 30% by 2025", and comprehensively promoted the green and low-carbon transformation of end-use energy.
Chen [5] constructed a potentiality of electricity replacement assessment index system from seven aspects to assess the potentiality of electricity replacement.Li and Chen [6] established an environmental load model on electricity replacement and realized the effective forecasting of terminal electricity replacement by scenarios.In [7][8], a particle swarm optimization SVM-based method was proposed to analyze the potentiality of the electricity replacement.Liu et al. [9] forecasted all end-use energy consumption and the proportion of electricity to end-use energy consumption based on a logistic model, respectively.Zheng [10] constructed a data envelopment analysis model and a grey forecasting model to analyze the potentiality of electricity replacement in rural China in the short and long term.Shan et al. [11] used a ridge regression method to analyze the relationship between end-use electricity replacement and population and energy prices in Beijing.They constructed a scalable stochastic environmental impact assessment model to decompose and quantify each factor.However, the forecasting accuracy does not fully meet the demand.
On this basis, a combined time-series-based regression forecasting and improved structure is proposed to analyze the potentiality of the electricity replacement.Using historical data from local statistical bureaus, the regional electricity replacement potentiality is forecasted and analyzed.

Quantifying the potentiality for electricity replacement
The share of electricity in end-use energy consumption is an important indicator of the structure of enduse energy consumption and the degree of electrification in a country or region.An increase in the share indicates that electricity is replacing other energy sources in the end-use energy consumption chain; a constant or decreasing share does not indicate that electricity is replacing other energy sources, even if the total electricity consumption increases.
The electricity used in year t is ( ) e A t and all the energy used is ( ) A t .It is assumed that the end-use pattern remains constant over a short period of time.The quantity of electricity replacement in year t+1 is defined as the product of the difference between the quantity of electricity used in that year as a percentage of all energy use and the quantity of electricity used in the previous year as a percentage of all energy use and all quantity of energy used in that year, i.e.: ( 1) e e e e e

A t A t A t B t A t A t A t A t
where ( 1) A t are the quantity of electricity substituted, the actual quantity of electricity used, and all quantity of energy used in year t+1, respectively.

Time-series-based on triple exponential smoothing forecasting method
The process of using time series to forecast the quantity of electricity replacement is shown in Figure 1.The relationship between the share of end-use electricity and the quantity of electricity replacement is: , " , (0) ( ) e C n ).The level ratio of the calculation series is: If all the step ratios Ȝ(k) fall in , then the end-use electricity usage share series can be forecasted as data for the time forecasting model.
After the predicted results of electricity replacement satisfies the above conditions, a quadratic cumulative series is generated by Equation ( 4). (1) (1) (1), (2), , The calculation is then performed according to the triple exponential smoothing forecasting method: (1) (2) 1 (1 ) M are the primary, secondary, and tertiary exponential smoothing values, respectively.For the selection of Į value, if Į = 0 is chosen, the forecast value of the latter period is equal to the forecast value of this period, and no new information is considered in the forecasting process; if Į = 1.0 is chosen, the forecast value of the latter period is equal to the observed value of this period, and no information from the past is believed at all.It is difficult to make a correct forecast based on these 2 extreme cases, so the value of Į should vary from 0 to 1.0.The equation for the forecasted value of the cumulative series is: ( ) where Once the forecasted values of the cumulative series are obtained, they are reduced to obtain the forecasted values of the actual electricity replacement.

Improved GRA-IPSO-BP algorithm
In the traditional gray correlation analysis method (GRA), the gray correlation degree is obtained by solving for the number of correlation coefficients between each input variable and the output variable.However, in some cases, the degree of influence of historical data on the existing situation is mixed.
The principle of the BP structure algorithm is based on the principle of minimum error, the error between the output of the network and the desired output as a criterion to continuously update the weights and thresholds.When the error satisfies the upper limit of the error target set value of the network training, the optimal solution can finally be obtained.BP structure is very powerful in computation and can imitate the intelligent processing of the human brain to find the law from the complex nonlinear input and output signals.However, in practical applications, the BP algorithm also has the following shortcomings: relying on experience to select the initial network parameters and lack of uniform standards; when there is a lot of historical data, it takes a long time to learn, which can lead to slow convergence of errors; in the process of training and learning, it is easy to fall into the problem of local minima, etc.Therefore, the improved particle swarm algorithm is used to optimize the BP structure so as to reduce the BP structure forecasting error and make the forecasting results more practical.

Historical electricity consumption
Quantitative The key indicators affecting the potentiality of the electricity replacement are selected from the input indicators affecting the potentiality of the electricity replacement using the improved GRA algorithm; the key indicators affecting the potentiality of the electricity replacement are used as independent variables, and the historical electricity replacement as dependent variables for sample training, and the BP algorithm is optimized using the IPSO algorithm.Finally, the IPSO-BP algorithm is used for forecasting, and the forecasting samples, i.e., the key indicators affecting the potentiality of the electricity replacement, are input into the forecasting model to obtain the forecasting values and carry out error calculation.Finally, the IPSO-BP algorithm is used to predict the key indicators that affect the potentiality of the electricity replacement, and the forecasted values are input into the forecasting model.The forecasting process is shown in Figure 2.

Example analysis
Table 1.Parameters of electricity and its consumption To verify the validity of the proposed combined time-series and improved BP structure forecasting method to predict the quantity of electricity replacement, the energy use and electricity use from 2003-2019 in a region of China in Table 1 were used as raw data to calculate the percentage of electricity use and to calculate the quantity of electricity replacement according to the quantitative formula of electricity replacement potentiality as a reference.Forecasts using a time-series model based on the cubic-smoothing-exponential method are shown in Figure 3 for the period 2013-2019.The relative errors were calculated separately for each year in Table 2.The smallest deviation in the relative error of the forecast values from 2013-2019 is 11.90%, while the largest deviation is 44.59%.Relying solely on the time-series model for forecasting has a large deviation in some years.If an inappropriate weighting factor is used, it can make the forecasting results unreliable.For this reason, the value of the weighting factor Į of the time series is changed, and multiple forecasts are made.For each year, a set of forecasting series is formed, with the data from 2003-2010 as the training set and the data from 2011-2012 as the validation set to train the improved BP structure.The forecasting for 2013-2019 in Table 2 was fed into the trained improved BP structure for correction.
In order to verify the superiority of the proposed method, the forecasting results of the proposed method are compared with other methods.As seen in Figure 4, the results of forecasting using only time-series are more volatile and deviate the most from the true value.Compared to time-series-based forecasting alone, the forecasting using Markov chains also fluctuates.With the combination of time-series-based and improved BP structure forecasts, the final structure corrections were closer to the true curve and less volatile.3, the fit of regression forecasting based on time series alone is 0.7031, while the fit of Markov chain forecasting is only 0.3358.The proposed algorithm reaches 0.9628.The fit is very close to 1.0000, indicating a high forecasting accuracy.The improved BP structure accomplishes a higher degree of optimization of the defects of the time series forecasting method.Therefore, the forecasting accuracy of the model is improved.

Conclusion
Firstly, the electricity replacement potentiality is quantified and characterized using electricity replacement volumes.Secondly, a combined time-series and structure forecasting model based on the cubic-smoothing-exponential method is developed to achieve short-term forecasting of electricity replacement volumes based on an analysis.The model is validated using relevant data from local statistical offices.The algorithm shows that the combined time-series-based regression forecasting and improved BP structure greatly improve the forecasting accuracy compared with individual forecasting methods, such as time-series forecasting and Markov chain forecasting.It also outperforms individual forecasting models in terms of fit, with the combined forecasting improving the fit by approximately 30%.

Figure 1 .
Figure 1.Flowchart for time-series-based regression forecasting

Figure 3 .
Figure 3.Comparison between results of time-series-based regression forecasting and actual results

Figure 4 .
Figure 4. Comparison of forecasting results of various forecasting models

Table 2 .
Results and relative errors of time-series-based regression forecasting method

Table 3 .
Fitting accuracy comparison