**2. Current Situation and Influencing Factors Selection of Electric Power Substitution in China**

#### *2.1. Current Situation of Electric Power Substitution*

The rapid growth of China's economy is accompanied by excessive energy consumption. In order to narrow the gap of energy utility between China and developed countries, the concept of energy conservation should be penetrated through energy exploitation, transportation and utilization. Proper use of energy and improving energy efficiency are the main goals of energy development in the future. Electric power substitution projects have great development potential in the future.

Electric power substitution uses electric power to replace coal-fired heating. Through the large-scale centralized conversion of power, electric power substitution can improve the efficiency of fuel use and reduce pollutant emissions to optimize the terminal energy structure and promote environmental protection. Electric power substitutions include coal substitution by electricity, oil substitution by electricity, and electrification of agricultural production, etc. Different substitution methods for each field are shown in the Table 1 below.



Despite various methods to promote electric power substitution, scientific and reasonable policies are necessary in promoting the substitution work. Since 2015, the Chinese government has promulgated 226 supporting policies to encourage electric power substitution, guiding the society to choose electric energy actively, and gradually eliminate the high pollution and low efficiency of energy use. Government support is not only subjective to propaganda and guidance, but also to strengthen the construction of electric power to improve the competitiveness of electricity continuously in power market. The relevant electricity alternative development policies are shown in the Table 2 below.

As can be seen from Table 2, a good policy environment has been provided to develop energy substitutions. The government issued guidance on electric power substitution promotion, using the substitution work as a national strategy. Then, supporting policies came to support the pilot work of clean energy heating in winter in northern areas, to promote the prevention and control of air pollution in Beijing-Tianjin-Hebei Region and the surrounding areas. Electric power substitution has been regarded as an important part of the national "13th Five-Year Plan" in the electricity industry and modern comprehensive transportation system.


**Table 2.** Policies supporting electric power substitution work.

With the creation of new policies, the scale of electric power substitution has been expanding. Implementation plans of electric power substitution have come out as well. Presently, China's electric power substitution projects are mainly carried out in the field of substituting coal and oil. Electric heating and electric vehicles—as the main alternative methods—have achieved remarkable results. In 2017, 101,807 electric power substitution projects were implemented nationwide, with 128.6 billion kWh of electricity in all substituting fields. Among them, 8.8 billion kWh comes from residential heating, 77.4 billion kWh from industrial (agricultural) production and manufacturing, 12.8 billion kWh from transportation, 23.9 billion kWh from electric power supply and consumption, and 5.8 billion kWh from household electrification and other fields, which is equivalent to a reduction of 64.4 million tons of coal-fired burning. The emission reduction is about 110 million tons of carbon dioxide, 5.2 million tons of sulfur dioxide and nitrogen oxides.

#### *2.2. Analysis on Influencing Factors of Electric Power Substitution Potential*

With the development of global energy internet, electric power substitution is facing new opportunities. The substitution work is affected by energy consumption, GDP, energy prices, investment in renewable power assets and average concentration of P.M. 2.5 and other factors.

#### (1). Electricity consumption

Electricity consumption is an important index used to measure the level of national electrification. Electrification represents the proportion of electric power, and reflects the changes of social energy consumption structure. The increase of electricity consumption directly leads to the improvement of social electrification. Meanwhile, the improvement of electrification shows an increase in social energy-use technology, which can effectively reduce the cost of electric power substitution projects and reach further promotion of electric power substitution.

#### (2). GDP per capita

GDP is an important indicator reflecting the economic development in China, which is an important factor affecting the demand of electricity. The economy of a region will have impacts on electricity and other energies' consumption. Research on power and energy has been made, and scholars have regarded GDP per capita as the decisive factor affecting electricity demand, which means that China's electricity demand and GDP growth are endogenous with a significant and stable relationship. In addition, the rise in GDP can promote residents' living standards. As people are becoming richer, they may pay more attention to the energy structure. Thus, the promotion of electric power substitution can be further improved. Therefore, GDP per capita is chosen as an indicator to show the impact of economic development on power substitution in China.

(3). Annual investment increment in electric power industry

The relationship between the investment in electric power industry and social electricity consumption is positive. Investing in electric power assets shows the attention society attaches to the development of the electric power industry. The investment in the electric power industry includes investment in power grid construction and investment in generators. Both will bring an increase in electricity consumption, which can indirectly improve the replacing effects of electricity to other energy resources. Two indicators—the annual investment increment in electric power industry and in power grid construction—are chosen in the following analysis.

(4). Electric power installed capacity

The electric power installed capacity is proportional to the total generating capacity, which helps promote electric power substitution work. In addition, renewable power generation has lower operating costs and less pollution emissions. Substituting fossil resources with renewable power will further improve the social benefits and achieve pollution reduction from power supply side. Therefore, as an important indicator, electric power installed capacity of renewable energy is considered in forecasting the market potential of electric power substitution projects.

(5). Renewable power generation

Renewable energy utilization is significant to energy structure adjustment under low-carbon mechanism. Using clean energies to generate will effectively reduce the proportion of coal-fired thermal power, thereby reducing the environmental burden. Besides, integrating more renewable power into the substitution work will help with the power curtailment problem, and large-scale utilization of renewable energy achieves substitutions for traditional fuels from the generation side. Thus, the implementation scope of electric power substitutions will be further expanded, and the environmental benefits will be significantly improved.

(6). Carbon emissions

The rising carbon emissions has forced the government and all sectors of society to pay more attention to the energy consumption structure. According to China's "National Independent Contribution" in 2030—compared with the situation in 2005—carbon dioxide emissions should achieve the peak value, carbon dioxide emissions per unit GDP will decrease by 60% to 65% and the proportion of non-fossil energy in primary energy consumption should reach about 20%. Facing the double pressures of international emission reduction commitments and domestic resources and environment, promoting clean energy usage is an important means to achieve carbon emission reduction. Constrained by carbon emission targets, enterprises' awareness of environmental protection will raise. With the development of clean technology, the electric power substitution work shall be promoted in large scale [22].

#### **3. Methodology**

#### *3.1. Pearson Test*

Pearson correlation coefficient is a method used to measure the degree of correlation between two variables. The correlation value is between 1 and −1, where 1 means that variables are completely positive, 0 means irrelevant, and −1 means completely negative. The correlation value between (*X*,*Y*) is calculated as follows.

$$\begin{array}{rcl}P\_{\mathbf{x},\mathbf{y}} &=& \frac{\text{cov}(\mathbf{X},\mathbf{Y})}{\sigma\_{\mathbf{X}}\sigma\_{\mathbf{Y}}} = \frac{E((\mathbf{X}-\mu\mathbf{X})(\mathbf{Y}-\mu\mathbf{y}))}{\sigma\_{\mathbf{X}}\sigma\_{\mathbf{Y}}}\\ &=& \frac{E(\mathbf{X}\mathbf{Y}) - E(\mathbf{X})E(\mathbf{Y})}{\sqrt{E(\mathbf{X}^2) - E^2(\mathbf{X})}\sqrt{E(\mathbf{Y}^2) - E^2(\mathbf{Y})}}\end{array} \tag{1}$$

The numerical value of *Px*,*<sup>y</sup>* reflects the linear correlation degree of *Y* and *X*, which is between [−1, 1]. The conclusion is as follows.


#### *3.2. Cuckoo Search Optimization*

Enlighted by the brood parasitism behaviors of cuckoo birds, the Cuckoo Search optimization (CSO) algorithm, which is a natural heuristic algorithm developed by Yang in 2009 [40]. The cuckoo bird lays eggs in the nest of the host-bird's nest and removes the eggs of the host. Occasionally, some cuckoo eggs look similar to host eggs and get the opportunity to be raised. In other cases, these eggs may be found by the host birds, who will throw them away or leave the nests to find other places to build new nests. Each egg in a nest represents a solution, and a cuckoo egg stands for a new solution. CSO uses new and potentially better solutions to replace not-so-good solutions in the nests.

The CSO method operates as follows. The cuckoo lays only one egg at a time and randomly places the egg in a nest. The nest with the highest quality egg (the solution to the problem) will remain to the next turn. The number of the nests which can be laid eggs in is fixed, and the probability that the host bird can select the cuckoo eggs is *pa* ∈ [0, 1].

Under this situation, the host bird can choose to throw the cuckoo eggs or find a new nest to replace the old one. If not detected, the cuckoo eggs will be successfully hatched up and find new hatching sites through Lévy flight. Considering the Lévy flight behavior of the cuckoo birds' nest-seeking feature, assume that there are *N* cuckoo eggs in the *D*-dimensional search space. The location of the number *i* egg under the *k*th iteration is *xk i* , and the new solution *xk*+<sup>1</sup> *<sup>i</sup>* can be expressed as follows.

$$\mathbf{x}\_{i}^{k+1} = \mathbf{x}\_{i}^{k} + \delta\_{i} \tag{2}$$

$$
\delta\_i = \alpha \times s\_i \oplus (\mathbf{x}\_i^k - \mathbf{x}^{\text{best}}),
\tag{3}
$$

where, α > 0 is the step size, which relates to the scale of the problem. δ*<sup>i</sup>* is the changing amount of position that needs to be taken, and ⊕ is the entry wise multiplications.

The random step is produced by the symmetric Lévy distribution.

$$s\_i = \frac{u}{|v|^{1/\beta'}}\tag{4}$$

where, *u*(*u*1, *u*2, ··· , *ud*), *v*(*v*1, *v*2, ··· , *vd*) are vectors in the *D*-dimensional space. β = 3/2. The sub-vectors of *u* and *v* obey normal distribution.

$$u \sim N(0, \sigma\_u^2), v \sim N(0, \sigma\_v^2) \tag{5}$$

$$
\sigma\_u \sim \left(\frac{\Gamma(1+\beta)\cdot\sin(\pi\cdot\beta/2)}{\Gamma((1+\beta)/2)\cdot\beta\cdot2^{(\beta-1)/2}}\right)^{1/\beta}, \sigma\_v = 1. \tag{6}
$$

Lévy flight includes a random directional linear motion sequence with no characteristic scale, and the step size of each sequence satisfies the heavy-tailed distribution. The relatively short straight-line move with a larger frequency will be intermittently replaced by the longer-step move with less frequency. Lévy flight ensures the comprehensiveness of searching, so that the search efficiency of CSO is higher than that of the standard Gauss random processes.

#### *3.3. Extreme Learning Machine*

ELM, proposed by Professor Huang in 2004, is a fast and efficient single-layer feedforward neural network algorithm. ELM is essentially a linear-in-the-parameter model, so its learning process is easy to converge to the global minimum. Due to the random input weights and hidden layer thresholds, the number of hidden layer nodes significantly influence the performance of the model. For a Single-hidden Layer Feedforward Neural network (SLFN), ELM uses the number of hidden layers to train—which greatly reduces the training time and computational complexity. The main idea of the ELM model is to randomly set the network weights and then obtain the inverse output matrix of the hidden layer. Compared with other learning models, the ELM model operates extremely fast and maintains a better accuracy and has therefore been widely used in many fields. In the ELM training process, the number of neurons in the hidden layer is the only need. Therefore, the output weight matrix of the hidden layer can be calculated without adjusting the connection weight between the input layer neurons and the hidden layer neurons and the deviation of the hidden layer neurons.

The network-training model of extreme learning machine adopts the former single hidden layer structure. Assuming there are *N* sets of initial training set (*xi*,*tt*), the input layer includes *xi* = [*xi*1, *xi*2, ... *xin*] <sup>T</sup> <sup>∈</sup> *Rn*, and the target output layer is *ti* = [*t*1*i*, *<sup>t</sup>*2*i*, ... *tmi*] <sup>T</sup> <sup>∈</sup> *Rm*. The hidden layer contains *L* nodes. The activation function *g*(*x*) is expressed as follows.

$$\sum\_{i=1}^{L} \beta\_i g\_i(\mathbf{x}\_i) = \sum\_{i=1}^{L} \beta\_i g(w\_i \mathbf{x}\_j + b\_i) = y\_j \qquad j = 1, 2, \dots, N \tag{7}$$

where, *yj* represents the output vectors of ELM. β*<sup>i</sup>* represents the weight vectors connecting the hidden layer and the output layer. *wi* represents the weight vectors that connects the hidden layer and the input layer. *bi* and *g*(*wi*·*xj* + *bi*) are threshold value and the output value of the hidden node *i*.

*Processes* **2019**, *7*, 584

The objective of an ELM is to search for a suitable set of β, ω, and *b* to approximate all training sample pairs with zero error.

$$\sum\_{j=1}^{N} \|t\_j - y\_j\| = \sum\_{j=1}^{N} \|t\_j - \sum\_{i=1}^{L} \beta\_i \lg(w\_i x\_j + b\_i)\| = 0. \tag{8}$$

Formula (7) can be expressed as:

$$H\beta = T\tag{9}$$

$$H = \begin{bmatrix} g(w\_1x\_1b\_1)g(w\_2x\_1b\_2)\cdots g(w\_lx\_1b\_L) \\ g(w\_1x\_2b\_1)g(w\_2x\_2b\_2)\cdots g(w\_lx\_2b\_L) \\ \vdots \\ g(w\_1x\_Nb\_1)g(w\_2x\_Nb\_2)\cdots g(w\_lx\_Nb\_L) \end{bmatrix}\_{N\times L} \tag{10}$$

$$\boldsymbol{\beta} = [\beta\_1, \beta\_2, \dots, \beta\_L]\_{L \times 1'}^{-1} \text{ and } T = [t\_1, t\_2, \dots, t\_L]\_{L \times 1'}^{-1} \tag{11}$$

where *H* is the output matrix of the hidden layer; β is the weights vector connecting the hidden layer nodes with the output layer neurons; and *T* represents the target output.

When the activation function is infinite differentiable, ELM analytically calculates the hidden-output weights by searching for a minimal norm least square solution of the following linear equation.

$$\|H\hat{\beta} - T\| = \min\_{\beta} \|H\beta - T\|\,\,\,\,\,\tag{12}$$

*H*β = *T* , (13)

$$
\beta = H^T T,\tag{14}
$$

where *H*<sup>T</sup> denotes the Moore-Penrose generalized inverse of the hidden-layer output matrix *H*.
