Allocation Model of Carbon Emission Permits for the Electric Power Industry with a Combination Subjective and Objective Weighting Approach

: The electric power industry plays a vital role in carbon emissions reduction efforts. The initial allocation of carbon emission permits to the electric power industry is the key to ensuring the effective operation of the carbon trading market. In this study, the multiple correlated factors that affect the carbon emission permit allocation system were extracted. Then, based on the experts’ knowledge and experience, the subjective weight of each index was determined using an improved analytic hierarchy process. Subsequently, the indices were mapped using an improved entropy weight method, and the objective weight of each index was adaptively determined. Finally, the comprehensive weight of each index was determined by optimizing the combination of its subjective and objective weights, and an allocation model of carbon emission permits for the electric power industry was established. A case study of a province by comparative simulation was performed. The simulation results showed that compared with conventional allocation schemes that consider single factors, the theoretical estimates obtained using the proposed model more objectively reflected the actual situation of carbon emissions reduction permits and responsibilities in the region.


Introduction
The increasing prominence of climate change and energy issues presents serious challenges to ecosystems; accordingly, achieving low-carbon development has become a common goal in various industries [1]. The Kyoto Protocol, signed in 1997, aims to reduce carbon emissions through the international carbon trading market [2]. Carbon trading markets have since been established in various regions including Europe and the United States. The practical experiences of various countries demonstrate that carbon emissions trading, particularly carbon emission permits quota transactions, plays a crucial role in meeting carbon emission reduction goals [3].
The electric power industry, as one of the most important energy sectors, plays an important role in reducing emissions [4]. The initial allocation of carbon emission permits for the electric power industry is the critical foundation for ensuring the effective operation of the carbon trading market, which is a multi-objective, multi-level, multi-stakeholder complex project.

Multiple Related Factors
The Coase theorem [13] notes that an unclear definition of property permits is the main cause of negative external problems. The primary task of controlling excessive carbon emissions is clarifying the enterprises' permits to use environmental resources. Different regions vary relatively substantially with respect to economic level, endemic resources, energy structure, and emission reduction technologies. Affected by factors such as regional environmental capacity and developmental needs, the power generation capacities of many provinces and cities are unable to meet the local power demand. Therefore, transregional power transmission plays a vital role in ensuring the regional power supply [14]. Under these circumstances, it is unfair for the costs of power generation carbon emissions and carbon emission reductions to be completely carried by the energysupplying regions. Analyzing the multiple correlated factors that affect electric power industry carbon emissions is critical to formulating a reasonable and fair initial carbon emission rights allocation scheme [15].
Here, the factor decomposition method was used to decompose the electric power industry carbon emissions and analyze the multiple correlated factors that affect the emissions, as shown in Equation (1). Table 1 shows the definition of each symbol in Equation (1).
( * * * * * ) ( * * * * * )  Total number of regions As no significant short-term change in the coal quality of China is expected to occur, Fi can be assumed to be a constant. Additionally, three other influential factors should be considered when calculating the carbon emission permits for the i th region: transmission loss ratio, historical carbon emissions, and power generation. The importance of historical carbon emissions is evident. Considering the power generation is the result of the neglect of the absolute difference in the proportion index. Failure to limit carbon emissions constraints in high-power generation regions will result in a lack of enthusiasm from power generation industries to reduce emissions. The reason for considering transmission loss is that carbon emissions occur in power production during power transmission and distribution. Based on the relationships between each influential factor and carbon emission reduction responsibilities, the indices were categorized into two types, namely, performance and cost indices, as shown in Table 2.

Index
Relationship Index Type i G A higher economic level of a region indicates that more emissions reduction responsibility should be given to that region and smaller carbon emission permits should be allocated to that region.
Cost i C A higher power consumption per unit GDP of a region should result in smaller carbon emission permits allocated to that region. Cost i M A higher power generation/power consumption ratio of a region indicates that the region exports more power. Thus, the region must reduce its the responsibilities with a high power generation/power consumption ratio and increase its carbon emission permits.
Performance i S To actively guide clean energy power generation, reducing the carbon emission permits for a region with a high proportion of thermal power generation is necessary. Cost Figure 1 shows the key factors affecting the regional carbon emission allocation for the electric power industry. The combination of subjective and objective weighting methods provides an optimal solution to the problem of weighting multiple correlated factors. The subjective weighting method makes full use of the knowledge and experience of decision makers, but is influenced by subjective preference and relies too much on the opinions of decision makers. The objective weighting method relies on actual sample data to make judgments, which can better reflect the data information carried by each indicator; however, the method only considers the distribution of the data that cannot reflect the importance of each indicator in reality. Both methods have the problem of information loss, whereas the combination weighting method can minimize the loss of information and make the weighting result as scientific and as reasonable as possible.

Subjective Weight
Analytic hierarchy process (AHP), a classical subjective weighting method with the goal of making people's thinking orderly and hierarchical, makes use of less quantitative information to mathematicize the decision-making thinking process using an in-depth analysis of the essence, influencing factors, and their internal relations of decision-making problems. Given the interference by human factors, the traditional AHP is easy to fall into the local optimum in the actual decisionmaking process, and the consistency of the judgment matrix needs to be checked [16]. This paper optimizes the judgment matrix to prevent it from being unable to pass the consistency test and fall into the local optimum.
The decision makers are experts that should cover all relevant fields including government, energy, power, environmental protection, etc. They work in authoritative institutes in the field and have many years of relevant work experience. For experts from the same field, take only their average or weighted average to participate in the synthesis. To ensure the effectiveness of the review, appropriate specifications should be established so that experts use the same criteria for the measurements. Additionally, the experts should be asked to give detailed reasons for the evaluation results. In order to ensure that the evidence is independent of each other, conditions and facilities for independent review by experts will be provided. Experts will independently review in accordance with the law, and no unit or individual may illegally interfere. The number of experts is generally an odd number.
According to the decision makers' knowledge and experience, the multi-correlated influencing factors in Table 2 are sorted in descending order of importance to establish a decision matrix. To illustrate the universality of the method, n indices are assumed.
where , i j x is the j th index of the i th region. A total of m regions with n indices exist.
According to the experts' opinions, the importance of the j th indicator (marked as  j ) and the (j + 1) th indicator (marked as  Table 3.
, which shows that Therefore, any element in the judgment matrix satisfies , , , *     s r rt st , and the judgment matrix is consistent. Then, the subjective weight value of the j th indicator can be calculated.

Objective Weight
The multiple correlated factors differ relatively significantly in both dimension and numerical value. Extracting features from the real number series of these indices is very difficult. However, investigating the effective feature parameters of indices is generally easier by using a certain method to uniformly map them to a certain feature space to construct a new identification parameter system. The information entropy method is considered a simple but very effective spatial mapping method that can reflect the spatial structure of original data and show more visual, conspicuous feature relationships between the factors.
The concept of entropy first appeared in thermodynamics and was used to measure the uniformity of energy distribution in a system. More uniformly distributed energy results in greater entropy [17]. In information theory, the function of information is to eliminate uncertainty in the understanding of a matter. Entropy was introduced into information theory to measure the uncertainty of the system state [18]. Assuming that a system has n states and the probability for the system to be in each state is ( 1,2, )   j p j s , the information entropy of the system is When the system is in the equal-probability state (i.e., 1  j p s ), the entropy has the maximum value ( ln  d s), which is referred to as its extremum property.
Information entropy is objectively determined by a system's internal attributes. From a statistical perspective, greater entropy results in a more disorderly system; smaller entropy results in more abundant and effective information being provided for formulating a scheme. Therefore, among all of the indices, those with small entropy should have a high weight [19]. Based on this approach, an improved entropy weight method was employed to determine the weight of each correlated influential factor.

Normalize the Indicator
Normalize the indicator using the dispersion method, and when an index is a performance index, , m i n , , max, min, When an index is a cost index, max, , , max, min,

Calculation of the Information Entropy Output by Each Index
The information entropy j d of the j th index is where , , ,

Calculation of the Attribute Weight Vector of Each Index
The weight of the j th index calculated using the conventional entropy weight method is Relevant research demonstrates that when entropy is within a certain range, a small difference in entropy may cause a several-fold change in the entropy weight, which is inconsistent with the information carried by the entropy. To prevent this issue from occurring, an improved entropy weighting method is employed to calculate the weight of the j th index:

Comprehensive Weight
The correct evaluation of weights should consider the subjective judgment of the evaluator and the objective information transmitted by the indicators. Here, the linear weighted combination method is used to calculate the comprehensive weights of the indicators.
(1 ) The value of  is based on the final decision-maker's preference for subjective judgment and objective results. If subjective judgment is preferred, then 0.5 <  < 1. If objective results are preferred, then 0 <  < 0.5; otherwise,  = 0.5.
The weight of the carbon emission permits in the i th region is determined by the comprehensive weight of each indicator.
Assuming that Q is the total amount of carbon emission permits that can be used for the allocation, then the carbon emission permits that can be allocated in the i th region are as shown.

Case Study
In this section, the proposed carbon emission permits allocation scheme is illustrated using an example. Table 4 shows the value of each index for five regions of a certain province in 2018.  These indicators in descending order of importance are as follows: According to the experts' opinions or experiences, the importance of the two adjacent indicators is compared. Table 5 shows the comparative value of importance for adjacent indicators.  Table 6. Thus, the proportion of each component of carbon emission permits in each region can be calculated according to the subjective and objective weights, as shown in Figure 2.    Region 1 has the highest historical carbon emissions, an indicator that is considered to be the most important by experts and that should be allocated with the largest number of carbon emission permits when considering the historical carbon emission scale. However, given its relatively high economic development level, region 1 should carry a relatively higher level of the carbon emission reduction responsibility. The subjective weight allocation ratio was the largest, and the objective weight allocation ratio was also larger; therefore, ultimately, the number of carbon emission permits allocated to the region was the largest, accounting for 31.77% of all such permits.
Region 2 generates a relatively large amount of power, but had the lowest carbon emission intensity. Additionally, the region has a relatively small proportion of thermal power generation and generates most of its power using clean energy. The region has a relatively high economic development level and should thus carry a higher level of the carbon emissions reduction responsibility. However, to actively guide clean energy power generation, it is necessary to increase the region's carbon emission permits. Through comprehensive consideration, region 2 was ultimately allocated a medium level of carbon emission permits, accounting for 19.86% of the total carbon emission permits.
Region 3 has the highest ratio of power generation to power consumption (20) and exports most of its generated power to other regions; consequently, its carbon emission reduction responsibility should be lowered. Moreover, region 3 has a relatively large historical carbon emission scale; therefore, it should be allocated a relatively large number of carbon emission permits. Although the region had the largest transmission loss, according to the experts' experience, the proportion of carbon emissions corresponding to transmission loss was very small. Therefore, the final carbon emission permits in region 3 are not strongly affected by transmission loss. Given the largest objective weight allocation proportion, the proportion of the final carbon emission permits of region 3 was the second largest (23.53%).
Region 4 has the highest standard coal consumption for thermal power generation (366 g/kWh). To guide and accelerate the elimination of power generation systems with low-efficiency and highconsumption, reducing the carbon emission permits allocated to this region is necessary. Additionally, most of the power consumed in region 4 relies on long-term exports from other regions. Therefore, region 4 should carry a relatively higher level of carbon emission reduction responsibility. Thus, region 4 was allocated the fewest carbon emission permits, accounting for 11.44% of all such permits.
Region 5 has a relatively low economic development level and exports a certain amount of power to other regions. However, region 5 has the lowest historical carbon emissions. To support the region's economic development, the allocation amount should be increased appropriately. As the objective weight occupies a certain proportion of the allocation, through comprehensive consideration, region 5 was allocated a relatively small number of carbon emission permits, corresponding to a comprehensive weight of 13.4%. Figure 3 also indicates that the proposed subjective and objective allocation method of the carbon emission permits allocation scheme comprehensively considers the multi-correlated influencing factors, and the final allocation result falls within the interval of considering the distribution result of a single factor, which is scientific and reasonable. This final allocation result was also a more acceptable solution for the allocation.
The proposed carbon emission permits allocation scheme based on the subjective and objective weighting method reasonably apportions permits based on an in-depth analysis of the carbon emission process in the electric power industry. Thus, this scheme considers the fundamental function of power in economic development, the environmental costs of energy bases, the contribution of the power supply to society, and the uneven distribution of resources among regions. Such an approach allows the transfer of reasonable carbon emission permits from regions rich in clean power-generating resources to regions deficient in these resources, thereby ensuring each region's permits to fairly use clean power-generating resources. Additionally, the proposed scheme can help actively guide the transition of the regional power source structure to clean energy power generation and facilitate the implementation of national policies for the electric power industry. For regions that largely rely on power imports, their external carbon emission reduction responsibilities are internalized, which can help mobilize their enthusiasm for supporting power supply regions. For relatively less-developed regions, the proposed scheme can help reduce their power generation costs and carbon emissions reduction pressure, facilitating the sustainable and healthy development of their energy structures and economies.
In summary, the proposed carbon emission permits allocation scheme for the electric power industry based on the subjective and objective weighting method can organically combine the objective information transmitted by the index sample data with the knowledge and experience of decision makers and fully embody the scientificness and fairness of the allocation scheme.

Conclusions
The carbon emission permits allocation scheme of the power industry based on the subjective and objective weighting method proposed in this paper cannot only overcome the disadvantage of inconsistency between the entropy value and the transmitted information in the traditional entropy weighting method. However, the scheme also prevents the problem that the judgment matrix in the AHP cannot pass the consistency test, leading to the decision-making problem. By optimizing the combination of subjective and objective weights, the combined weighting method not only highlights the inherent differences in the attributes of the sample data, but also pays enough attention to the indicators that experts believe need to be focused on, and obtains the comprehensive quantitative value of multi-correlated indicators, thus avoiding one-sided evaluation results that are too subjective or too objective. Compared with the traditional method of considering a single factor, the method proposed in this paper, considering the influence of multi-correlated factors, the theoretical calculation results are consistent with the actual emissions reduction responsibility.
The established model considers the fundamental function of power in economic development and the environmental costs of energy bases. Through the reasonable allocation of carbon emission permits, this model achieves the following: reasonable reallocation of carbon emission reduction responsibilities between regions; improvements in the developed regions' enthusiasm for supporting energy bases in reducing carbon emissions; assisting with increasing the proportion of clean energy in power generation; and promotion of energy restructuring and coordinated regional economic development. For regions that largely rely on imported power, external carbon emission responsibilities are internalized to stimulate enthusiasm for energy conservation and carbon emissions reduction. For relatively less-developed regions, the proposed method can help reduce carbon emissions reduction pressure and facilitate sustainable and healthy economic development. Such a model can also be used as a theoretical basis for regional carbon emission permits allocation in the electric power industry to facilitate joint regional carbon emissions reduction efforts and the realization of national carbon emissions reduction goals.
Author Contributions: X.X.P. and H.L. conceived of the presented idea. X.X.P. developed the theory and performed the computations. J.J.H. verified the analytical methods. Y.S. and H.F.H. was encouraged to investigate a specific aspect and supervised the findings of this work. All of the authors discussed the results and contributed to the final manuscript. All authors have read and agreed to the published version of the manuscript.
Funding: This work was supported by a major program of the National Natural Science Foundation of China, entitled "Stabilization mechanism and analytical method for stochastic-deterministic coupled electric power systems," under Grant No. 51190103.

Conflicts of Interest:
The authors have no conflicts of interest.