Low ‐ Carbon Economic Bi ‐ Level Optimal Dispatching of an Integrated Power and Natural Gas Energy System Considering Carbon Trading

: The integrated power and natural gas energy system (IPGES) is of great significance to promote the coordination and complementarity of multi ‐ energy flow, and it is an important carrier to increase the proportion of wind power accommodation and achieve the goal of carbon emission reduction. In this paper, firstly, the reward and punishment ladder ‐ type carbon trading model is constructed, and the impact of the carbon trading mechanisms on the carbon emission sources in the power system is comparatively analyzed. Secondly, in order to achieve a reasonable allocation of carbon resources in IPGES, a bi ‐ level optimization model is established while taking into account the economics of dispatching and the requirements of carbon emission reduction. Among them, the outer layer is the optimal carbon price solution model considering carbon trading; in the inner layer, considering the power system constraints, natural gas system constraints, and coupling el ‐ ement operation constraints, a stochastic optimal dispatching model of IPGES based on scenario analysis is established. Scenario generation and reduction methods are used to deal with the un ‐ certainty of wind power, and the inner model is processed as a mixed integer linear programming problem. In the MATLAB environment, program the dichotomy and call the Gurobi optimization solver to complete the interactive solution of the inner and outer models. Finally, case studies that use an integrated IEEE 39 ‐ bus power system and Belgian 20 ‐ node gas system demonstrate the effectiveness and scalability of the proposed model and optimization method.


Introduction
In recent years, with the rapid development of economy and society, the ecological system is seriously endangered, and the human society is faced with an increasingly serious energy depletion crisis and environmental pollution. The energy power system has also undergone many unprecedented changes. At a global level, coal is the dominant fuel for power generation; however, its share fell 1.3 percentage points to 35.1% in 2020. The share of renewables rose to record levels in 2020 (11.7%), with the combined share of renewables and gas-fired power (35.1%) equal to coal for the first time. Natural gas is the dominant fuel used for power generation in North America, CIS, the Middle East and Africa. While in Asia, coal comprises 57% of the generation mix, a far higher share than any other region. In Europe, renewables (including biopower) are the largest source of power generation with 23.8% for the first time in 2020, overtaking nuclear on 21.6%. Generation in Europe is spread fairly evenly between renewables, nuclear, gas (19.6%) and hydro (16.9%) [1]. As the biggest developing country in the world, China shoulders an important task for CO2 emission reduction. The power industry is one of the im-portant coal-consumed and CO2 emission sources, and achieving the low-carbon operation of power industry is important for the carbon emission reduction in China [2]. By the end of November 2020, the installed capacity of coal-fired power plants accounted for about 58% of total generation capacity in China [3]. The total CO2 emission produced by coal-fired power plants (CFPPs) in China occupies 37% of the carbon emission caused by fossil fuels combustion [4]. Hence, it is necessary to develop low-carbon power generation technology to handle this challenge.
There are many low-carbon technologies for the decarbonization of the power industry in China. For example, developing renewable generation and gas-fired generation to replace coal-fired power generation. By the end of November 2020, the installed capacity of the gas-fired power plants (GFPP), wind and solar power accounted for about 4.6%, 10.8% and 11.3% in China [3], respectively. The electricity system is transitioning towards a renewable-based system, mainly due to worldwide environmental concerns, and natural gas is expected to play an important role in the future development of the electricity system [5]. This is due to the fact that GFPP are one of the least polluting conventional technologies, as well as efficient and flexible. The co-existence of these two types of power production technologies serves as a promising combination for a smooth transition to a sustainable energy system that is flexible enough to accommodate high shares of renewables [6]. As a consequence, the interactions between the electricity and natural gas systems will be strengthened, while the uncertainty and variability of renewables will eventually affect the operation of both systems. Wind power is one of the most important renewable generations in power systems, albeit volatile with significant uncertainties [1]. Due to the uncertainties and power network operating constraints, wind power curtailment occurs [7]; storing the excess power can facilitate the integration of wind power. For that reason, power-to-gas (P2G) technology has been attracting a lot of interest [8,9]. P2G technology produces synthetic natural gas consuming electric energy, which can enhance the flexibility of IPGES. At present, the cost of P2G technology is relatively high, but it is widely considered to be the most suitable scenario for P2G to absorb the excess wind power. P2G technology requires CO2 as the raw material in the process of synthesis of natural gas, which makes it possible to absorb wind and reduce carbon at the same time. Relevant studies have paid little attention to the carbon emission benefit of P2G [10,11], and the incentive space brought by the benefit has not been further explored. After taking into account the wind curtailment and carbon emission benefits of P2G, P2G will have higher economic efficiency.
As the interaction between the power system and the natural gas system increases, on the one hand, the power system needs to consider the reliable and safe supply constraints of the natural gas network when dispatching [12]. On the other hand, the optimized operation of IPGES is the basis for optimizing resource allocation and improving energy utilization efficiency, and is of great significance for improving the comprehensive benefits of the system [13,14]. The power grid and natural gas network, as the carriers of energy transmission, are mainly considered as power flow operation constraints in the model [15,16]. Mirzaei M A et al. [17] present a novel hybrid information gap decision theory stochastic co-optimization problem for integrating electricity and natural gas networks. Moreover, the power-to-gas technology and demand response program are considered in the proposed model for increasing the wind power dispatch. The power generation of renewable energy is random and difficult to predict. Therefore, the entire energy system also faces the challenge of accommodating a large amount of random renewable energy. Two main approaches adopted by many researchers for including uncertainty which are robust optimization and stochastic programing. In [18,19] the stability of the power system is analyzed using robust optimization considering a high level of wind generation. Although robust optimization has been applied to circumvent the challenges of uncertainty of wind generators, the main disadvantage is that it only considers the worst case in the analysis of renewable energy sources (RES) penetration level. The robust optimization framework increases the operating cost that affects the optimal dispatch scheme. In contrast to robust optimization, the stochastic programming approach uses a large number of scenarios to handle uncertainty in RES generation [20,21]. In the scenario generation method, a large number of scenarios are generated through the probability distribution of random variables.
Developing the low carbon power sector is of great economic significance under carbon policies. Carbon trading mechanism is an important way to balance environmental protection and economic benefits, and can stimulate enterprises to reduce carbon emissions independently. It is mainly divided into traditional unified carbon trading and lad-der-type carbon trading [22,23]. In [24,25], low-carbon dispatching models of energy systems based on carbon trading mechanisms have been established respectively, which have guiding significance for the carbon trading cost analysis of integrated energy systems. In [26], a risk-constrained two-stage stochastic dispatch model based on the chance-constrained programming is proposed, in which the carbon capture systems, carbon trading, demand response and renewable generation are considered. Cui et al. [27] analyzed carbon emission and total cost of the system without considering the carbon trading mechanism, considering traditional carbon trading mechanism and considering ladder-type carbon trading mechanism respectively, and proved the rationality of adopting the ladder-type carbon trading mechanism for the low-carbon economic dispatching of the integrated energy system. Zhang et al. [28] propose the concept of reward coefficient, introduce the reward and punishment ladder-type carbon trading into the planning model, and establish an energy center planning model with the goal of minimizing the sum of system investment cost, operation cost and carbon transaction cost. The above studies on the construction of low-carbon economic scheduling model of power system or IPGES based on the background of carbon trading mainly increase the carbon trading cost on the objective function, and do not study the setting of carbon price level for implementing carbon trading in IPGES. The implementation of carbon trading should ensure that it will not bring too high financial burden to the participating sources [29]. If the carbon trading price is too high, it will affect the enthusiasm of power generation enterprises and excessively increase the carbon trading cost of the energy system. If the carbon trading price is too low, it cannot meet the corresponding total carbon emission control requirements. Therefore, in the context of carbon trading, it is necessary to study the optimal tiered carbon price level of IPGES under the requirement of total carbon emission control, so as to provide theoretical guidance for decision makers.
On the basis of the above research, the contributions of this paper are as follows: 1. A reward and punishment ladder-type carbon trading model is constructed, and comparatively analyzed the impact of three carbon price mechanisms of carbon trading on the carbon emission sources in the power system; 2. Comprehensively considering the power system constraints, natural gas system constraints, and coupling element operation constraints, a stochastic optimal dispatching model of IPGES that takes into account the uncertain wind power and carbon trading cost is established. 3. In order to explore the optimal carbon price of IPGES under carbon trading, a bi-level optimization model has been established while taking into account the economics of dispatching and the requirements of carbon emission reduction, which takes the optimal carbon price solution of carbon trading as the outer layer model, and the stochastic optimal dispatching of IPGES as the inner layer model. 4. The solution method of the bi-level optimization model in this paper is proposed.
The paper is organized in seven sections. In the second section, the reward and punishment ladder-type carbon trading model is constructed. In the third section, a bi-level optimization model of IPGES is proposed. The processing and solving methods of the bi-level optimization model in this paper are introduced in the fourth section. The simulation case study is discussed in the fifth section, and the expansion of the model and method is discussed and explained in the sixth section. The overall analysis and conclusions are drawn in the last section. The nomenclature and formulae section is given at the end of the article.

Carbon Trading Cost Model
The purpose of the carbon emission trading (carbon trading) market is to control the total amount of carbon emissions by means of a market regulation mechanism, and its main target is the source of carbon emissions. The specific measure is to allocate a certain carbon emission quota to each carbon emission source. If the carbon emission of the carbon emission source exceeds the quota, the excess quota must be purchased on the market; conversely, if the carbon emission of the carbon emission source is less than the quota, the carbon emission rights can be sold for profit.
Firstly, the regulatory authorities assign duty-free carbon emission quotas to all carbon sources (thermal power generating sets such as CFPP, GFPPG) in the system. In a dispatch cycle (T), the free carbon quota (Q i c ) and the actual carbon emissions (E i ) of generator set i are as follows: where ε is the free carbon emission quota coefficient per unit of electricity allocation, which is obtained by the weighted average of the marginal emission factor of electricity and the marginal emission factor of capacity in the area [26,30]. The carbon trading cost C(E i ) of generator set i is as follows: where p 0 rc is the benchmark carbon emission right price. From Equation (3), we can see that the carbon price of carbon trading (p i rc ) directly affects the cost of carbon trading. Carbon price can be divided into traditional unified carbon price mechanism (UCT) and ladder-type carbon price mechanism (LCT). This paper introduces the reward coefficient [24] on the basis of the ladder-type carbon price mechanism, to give certain incentives and subsidies to energy supply companies whose total carbon emissions are lower than the freely allocated carbon emissions quota. This kind of carbon price carbon trading is called reward and punishment ladder-type carbon trading (RPLCT). The carbon trading price of RPLCT is shown in Equation (8). Figure 1 shows the carbon price of UCT, LCT and RPLCT.

Comparison of the Effects of Different Types of Carbon Trading Mechanisms
Under the carbon trading mechanism, for such thermal power generators (denoted as GH type generators) whose carbon emission intensity is higher than the free carbon emission quota coefficient per unit of electricity allocation, the excess carbon emission cost must be paid. For such thermal power generators whose carbon emission intensity is lower than the free carbon emission quota coefficient per unit of electricity allocation (denoted as GL type generators), the carbon emission rights will be sold in carbon trading market for profit. The difference between UCT and LCT is mainly reflected in the control of the power output of GH type generators, and the difference between LCT and RPLCT is reflected in the incentive effect of the power output of GL type generators.
Under the benchmark carbon price of 10 $/Ton, assuming that the carbon emission of a 100 MW GH type generator forms a ladder at 58 Ton (with a power output of 63 MW), the difference between UCT and LCT can be shown in Figure 2(a). Specifically, Figure 2(a) shows the relationship between the comprehensive unit variable output cost and output power of a GH type generator under UCT and LCT. The comprehensive unit variable output cost is the amount of change in the comprehensive cost required to change a unit of electricity per unit time. The comprehensive cost refers to the sum of carbon transaction costs and unit fuel costs. It can be seen from Figure 2(a) that, unlike UCT, LCT has a comprehensive unit variable output cost segmentation point when the output power is 63 MW. When the on-grid power tariff of the system is 41.2 $/MWh, as long as the output power of GH type generators under UCT is less than 80 MW, they will try to send them to 80 MW to obtain the maximum benefit. At this time, the system has no suppression capability for GH type generator with output power less than 80 MW. Under LCT, when the output power of the GH type generator is less than 63 MW, the system revenue is greater than the comprehensive unit variable output cost of the GH type generator. In order to optimize the system revenue, the system can limit the output of the GH type generator to 63 MW at this time. The emission of carbon dioxide is curbed. When the on-grid power tariff of the system is 42 $/MWh, under the condition of meeting the basic load constraint, as long as the output power of the GH type generator in UCT is greater than 20 MW, the system has no ability to suppress the output power of the GH type generator, which increases the carbon emissions. Under LCT, considering the overall revenue issue, the output power will be limited to 50 MW, and carbon emissions will be suppressed at this time. If the carbon price of UCT is simply increased, the ability to suppress carbon emissions will be improved, but the total cost of the system will rise sharply. Therefore, under certain economic conditions, LCT has a stronger ability to inhibit the carbon emissions of the system, which is conducive to the reduction of carbon emissions.  When the generator output power increases and multiple carbon emission intervals are considered, Figure 2(c) shows the influence of three carbon trading mechanisms on the comprehensive unit variable output cost of coal-fired and GL type generators. The intersections A, B and C are the turning points when the economic benefits of GL type generators are better than that of GH type generators after considering UCT, LCT and RPLCT respectively. Observing points A and B, compared with UCT, the power output of the generator at the turning point under LCT is smaller, that is, the control effect on the output of GH type generators and the stimulation effect on the output of GL type generators have been advanced, but the comprehensive unit variable output cost of the generator is also higher, and the total cost of the system will rise. Observing point C, compared with UCT and LCT, the power output at the turning point under RPLCT is the smallest and the comprehensive unit variable output cost is the lowest, that is, RPLCT has better carbon emission control capabilities and can better balance the total system cost. The impact and comparison of the three carbon trading mechanisms on the entire system will be analyzed in the fifth section of this paper.

Problem Formulation
The integrated power and natural gas energy system is an important carrier for improving wind power consumption and energy efficiency. The structure of IPGES is shown in Figure 3. The carbon trading market is recognized as an effective method that can take into account the economics of energy and power and low-carbon environmental protection. The level of carbon prices directly affects the cost of system carbon trading. A reasonable carbon price level can meet the system's total carbon emission control requirements while taking into account the economics of IPGES. At the same time, the uncertainty of wind power output cannot be ignored in the dispatch of IPGES. To this end, a low-carbon economic bi-level optimal dispatch model of IPGES considering carbon trading is proposed. Among them, the outer layer is the optimal carbon price model of IPGES considering the reward and punishment ladder-type carbon trading, and the inner layer is the stochastic optimal dispatching model of IPGES considering the uncertainty of wind power output. Through the interactive solution of the inner and outer layer model, the optimal benchmark carbon price and optimal dispatching results of IPGES can be obtained under the requirement of total carbon emission control, so as to provide carbon trading price guidance for regulatory decision makers and dispatching strategy for dispatching decision makers.

Power System Operating Constraints
The stochastic optimal dispatch model of IPGES takes into account the power grid security constraints. The power system adopts the DC power flow model [15]. The main constraints are as follows.
(1) Generator output constraint state state ,min , ,max ; 1 (2) Unit climbing constraint up down , 1 , (3) System reserve constraint As wind power output is difficult to accurately predict, the system needs to reserve a certain amount of upward reserve and downward reserve adjustment capabilities to cope with the uncertainty of wind power output.
where P w s,i t represents the random output of wind power in scenario s, which can be obtained by the method described in Section 4.1.

(4) Power flow constraint
For the transmission network level, DC power flow constraint should be adopted for branch power flow. , , ,min , (5) Line safety constraint safe ,max , safe ,max ; 1 T,1  (14) 3.1.3. Natural Gas System Operating Constraints The natural gas system mainly consists of natural gas source, natural gas pipeline, pressure station, gas load and so on. The main operating constraints are as follows.
(1) Supply constraint of natural gas well , ,min , , (2) Natural gas network flow constraints The IPGES involved in this paper is a high-pressure network, so the Weymouth equation of high-pressure pipeline with pressure above 0.7 MPa is used to express the flow equation of the gas network [15]. 2 2 , , , ; 1 T,1 l t mn t mn m t n t m t n t pip , , , (3) Gas flow constraint of the pipeline ,min , (4) Compressor operation constraint In order to simplify the calculation, the consumption characteristics of the compressor are not considered in this paper, and the compression ratio is constant.
in in in S, , S, S, ,max 0 ; 1 T , 1 out out out S, , , S, ,max in out , ,

Electricity and Gas Coupling Constraints
The gas consumption and output active power of gas-fired units are shown in Equation (26), the upper and lower limits of output constraints and climbing constraints are shown in Equations (7) and (8), and the operation constraints of P2G are shown in Equations (27) and (28).

Outer Model: Optimal Carbon Price Solution Model of IPGES
The carbon trading market is recognized as an effective means to take into account the economics of dispatching and low-carbon environmental protection. The benchmark carbon price in the reward and punishment ladder-type carbon trading has a great impact on the total carbon emissions control and carbon trading costs. In this paper, the objective of the solution is to minimize the benchmark carbon price, as shown in Equation (29), and the constraint condition is the total carbon emission control requirement of IPGES, as shown in Equations (30)- (32). The essence of the outer optimal carbon price model is to find the carbon price that makes the total carbon emission of IPGES not higher than the total carbon emission control requirement.
Sub. 0 min rc p (29) S.t. 0 (1 ) where λredu is the carbon emission reduction coefficient; E S0 is the total carbon emission of IPGES without carbon trading; E S and P c i,t are, respectively, the carbon emissions of the system and the dispatching power of carbon trading entities (CFPP, GFPP, P2G) determined by the inner-level IPGES stochastic optimization dispatching model.

Solving Method
For the bi-level optimization model constructed in this paper, the analysis is as follows: (1) The inner layer model has 0-1 nonlinear variables, and it is difficult to convert the two-layer model into a single-layer model through duality, so this paper adopts an iterative method to solve the inner and outer layer model. (2) The inner layer model is a stochastic optimization dispatching problem taking into account the uncertainty of wind power, and the stochastic model needs to be transformed into a deterministic form. (3) Nonlinear terms appear in the objective function and constraint conditions of the inner model, which is difficult to be solved directly. In this paper, the nonlinear terms are transformed into mixed integer linear programming problems. Appendix B shows the process of piecewise linearization.

Uncertainty Processing of Wind Power
According to the proposed internal IGPES stochastic optimization dispatching model, its stochastic form is due to the wind power uncertainty in the constraints, as shown in Equations (9) and (10). In order to obtain certain quantitative results, the current stochastic model must be transformed into a deterministic form. In this paper, a scenario-based approach is adopted to deal with the uncertainty of wind power.

Scenario Generation of Wind Power
Wind power prediction error is uncertain, assuming that the uncertainty wind power error at time t (ΔP t w ) obeys normal distribution. The actual output value of wind power P t w is based on the predicted output value P t w0 plus output error value ΔP t w .
The 800 wind power output prediction error values are generated by Monte Carlo method, and the 800 wind power output scenarios are obtained by combining with the wind power output prediction values, as shown in Figure 4

Scenario Generation and Reduction of Wind Power
Large-scale scenario analysis will increase the computational time, so effective aggregation and reduction of the original scenario set can not only approach the original solution from the perspective of probability, but also further improve the computational efficiency. K-means algorithm is the most common and widely used clustering algorithm, which has the advantages of simplicity and efficiency, and can handle large-scale data. Using the K-means algorithm, the 800 wind power output scenarios were clustered into six typical wind power output scenarios to carry out optimal dispatching calculation of IPGES, typical wind power output scenarios are shown in Figure4(b).

Outer Model Solution
In this paper, the bi-layer optimization model is constructed, in which the inner layer model has 0-1 nonlinear variables and is difficult to be solved by duality conversion into a single-layer model. It is noted that the higher the benchmark carbon price is, the stronger the inhibition effect on the high-emission units is, and the stronger the incentive effect on the low-emission units is, the smaller the carbon emissions of the system will be, and the relationship between carbon price and carbon emissions is monotonically decreasing. Therefore, the outer model can be converted into the solution problem of the equation f (p 0 rc ) = 0 about the independent variable p 0 rc , as shown in Equation (34). In this paper, a dichotomy method is used to solve this equation.
When the optimal carbon price model applies the dichotomy, a benchmark carbon price interval is set, and the midpoint is taken as the benchmark carbon price p 0 rc , which is substituted into the inner model (stochastic optimal dispatching model of IPGES) to solve the problem. Then, the total carbon emission of IPGES obtained from the inner model is transferred to the outer model, which cuts the benchmark carbon price interval in half, and then iterates until the solution accuracy is satisfied. The solution flow chart of dichotomy method adopted in this paper is shown in Appendix A Figure A1

Solving Process
The outer optimal carbon price model is transformed into an equation zero-point solution problem through analysis, and the solution is solved through the dichotomy. The inner model is a stochastic optimal dispatching model of IPGES. The wind power output uncertainty set is generated by the scenario generation method, and the scenario is reduced by the K-means clustering method. Through the mixed integer linear expression of the reward and punishment ladder carbon trading cost, the piecewise linearization of the natural gas pipeline equation and the cost of coal-fired power generation, the inner model is transformed into a mixed integer linear programming problem, and the Gurobi solver is called through MATLAB to solve it. The benchmark carbon price (p 0 rc ) obtained from the solution of the outer model is passed into the inner model as a known quantity, and the carbon emission (E S ) of IPGES obtained from the solution of the inner model is passed into the outer model as a boundary condition. In this way, the interactive iterative solution of inner and outer layer model is carried out until the solution accuracy is satisfied. The whole solution process of the bi-layer optimization model is shown in Figure 5.

Case Description
Based on Sections 2 and 3, a new model was built up to solve the low-carbon economic optimal dispatching and optimal carbon price solution problem of IPGES containing P2G considering wind power uncertainty and carbon trading. This model was developed in the most general form, while various parameters for objectives, constraints, power source structure, network parameters, characteristics of wind power and carbon trading can be set according to the different conditions. Therefore, the proposed model is suitable for most situations. With the thorough development of low-carbon electricity, power dispatching should meet the requirements for carbon emission reduction. In virtue of the proposed model, this study tries to explore how carbon trading affects the optimal dispatching solution of IPGES under wind power uncertainty, to compare the three carbon trading price mechanisms, and to solve optimal carbon price under the requirements of carbon emission reduction.
In this study, an IPGES composed of the modified IEEE39-bus power system and the Belgian 20-node gas system was used as the research object for simulation analysis [31,32], and its structure is shown in Figure 6. The IEEE 39-bus power network has 46 branches, four coal-fired generators (CG), three gas-fired generators (GG) and two wind power units (WT), where the capacity of wind power units accounts for 27% of the total installed capacity of 5500 MW. The modified Belgian high-calorific 20-node gas system has 24 pipelines, four natural gas wells, two natural gas storage stations and two P2Gs.
The parameters of the power system are from [18,32] and the parameters of the natural gas system are from [31,32]. The electric load and gas load are shown in Appendix A Figure A2; the uncertain wind power scenarios set and typical wind power output scenarios are obtained by the method introduced in Section 4.1, as shown in Figure 5; the network structure parameters and units cost parameters of IPGES can be found in [18]; the carbon emission coefficients of the units are shown in Table A1; for other parameters in IPGES, such as natural gas well parameters, natural gas storage parameters and P2G parameters, see Table A2, Table A3 and Table A4 in Appendix A, respectively; The carbon trading parameters are shown in Appendix A Table A5. The optimal scheduling cycle is 24 h, and the optimal step size is 1 h. The set up for the multiple cases for simulation analysis as follows.

Simulation Settings and Results Analysis
(1) Effect of P2G on wind power accommodation and system carbon emission reduction In order to analyze the effect of P2G on the improvement of wind power accommodation and system carbon emission reduction capabilities of IPGES, the following two cases were set up for dispatching of IPGES. There is no P2G in case 1; there is P2G between the power grid and the gas network in case 2. In case 1 and case 2, both of them are in the reward and punishment ladder-type carbon trading with the benchmark carbon price of 20 $/t, and the objective function is to consider only the operation cost without considering the carbon trading cost. Figure 7 is a time sequence diagram of generators output and electrical power of P2G, Figure 8 is a time sequence diagram of natural gas flow for natural gas wells and gas storages, and Figure 9(a) shows the results of the dispatch. In case 2, P2G was considered in IPGES, and its total dispatching cost, wind abandonment amount (wind abandonment amount of case 1 is 1106 MW; wind abandonment amount of case 2 is 46.5 MW), carbon emissions, and carbon tax cost all decreased compared with case 1. As shown in Figures 7 and 8, P2G works during the wind abandonment period (1-7), using H2O and CO2 as raw materials, converting the abandoned wind power into natural gas and injecting it into the natural gas network. It can be seen that the introduction of P2G can improve the wind power accommodation capacity and reduce the carbon emissions of the system, thus reducing the wind abandonment penalty cost and carbon trading cost.  (2) The impact of different carbon trading mechanisms on the carbon emissions of IPGES.
Analyze the situation of the same system under different carbon trading mechanisms(CT), and divide it into the following three cases, the benchmark carbon price of each case is set to 20 $/t, other carbon trading parameters are shown in Appendix A Table A5. P2G is considered in all cases. Case 3, traditional unified carbon trading mechanism(UCT); Case 4, ladder-type carbon trading mechanism(LCT); Case 5, reward and punishment ladder-type carbon trading mechanism(RPLCT). Figure 9(b) shows the dispatch results of the systems under different CT. It can be seen that under the same benchmark carbon price, compared with UCT, the system car-bon emission under LCT is reduced by 5429 ton; compared with LCT, the system carbon emission under PRLCT is reduced by 1562 ton.
In case 3, the total dispatch cost of the system considering CT is the lowest, but the carbon emission control of the system is not obvious. Under the carbon price of 20 $/t, it fails to achieve a good emission reduction control effect, and it can achieve a higher carbon emission control effect by further increasing the carbon price.
Comparing the results of case 4 and case 5, both LCT and RPLCT can suppress the carbon emissions of high-carbon emission units. The latter can also further stimulate the more output of low-emission units in the system, such as gas-fired units, to indirectly weaken the dependence of the system on high-emission units, that is, by increasing the output of gas-fired units to suppress the coal-fired units, so as to reduce the carbon emissions.
The total dispatch cost, carbon emission and carbon trading cost of IPGES under RPLCT are all lower than those under LCT. Due to the introduction of the incentive coefficient, the carbon emission reduction characteristics of P2G can benefit from the reward and punishment ladder-type carbon trading. Under the lower carbon trading cost, the system can achieve better carbon emission reduction effect, indicating the effectiveness of RPLCT in the low carbon economic dispatch of IPGES. Figure 10 shows the electrical output of various types of units and the input electrical power of P2G in each case. The output of gas-fired units with low carbon emission units under UCT, LCT and RPLCT increases sequentially. (3) The optimal carbon price and carbon trading cost of different carbon trading mechanisms under the same emission reduction requirements Case 6 implements UCT; case 7 implements LCT; case 8 implements RPLCT. The carbon emission reduction coefficient of each case is set to 0.15, and P2G is considered in all cases. Carbon trading parameter settings are shown in Appendix A Table A5.
It can be seen from Figure 9(c) that, under the same carbon emission reduction requirements, the optimal carbon prices of UCT, LCT and RPLCT decrease sequentially. Compared with case 6 and case 7, under the optimal baseline carbon price, the total scheduling cost of IPGES under UCT is lower than that under LCT, but the higher benchmark carbon price will reduce the enthusiasm of low-emission units. In contrast, under the total carbon emission control requirements of the system, the optimal benchmark carbon price, the total dispatch cost and the carbon trading cost under RPLCT are the lowest. RPLCT can specifically limit the emission of large emission units, reduce the carbon trading cost of small and medium emission units, and stimulate the system to increase the output of clean units and reduce the carbon emission of the system through the form of incentives. It has the best effect in terms of economy and low carbon.
(4) The impact of carbon trading prices and free carbon emission quota coefficient on low-carbon economic dispatch of IPGES Figure 11 shows the carbon emissions and units dispatching results of IPGES considering unified carbon trading under different carbon trading prices. As the price of carbon trading rises, carbon trading costs account for an increase in the total cost, and the system gradually strengthens the constraints on carbon emissions. The output of high-emission intensity coal-fired units is gradually shifting to low-emission intensity gas-fired units, power generation costs increase, and carbon emissions are reduced. Figure 12 shows the carbon emissions of IPGES considering reward and punishment ladder-type carbon trading under different free carbon emission quota coefficient.
Here, the benchmark carbon price is set at 10 $/MW, and other carbon trading parameters refer to case 5. It can be seen from Figure 12 that as the free carbon emission quota coefficient per unit of electricity allocation increases, the system's carbon emissions increase. This is because the increase in the free carbon emission quota allowance coefficient per unit of power generation means that the weakening of the control of the carbon emission intensity of the generator sets will increase the carbon emissions of the system.

Discussions
(1) The inner stochastic optimal dispatch model provides an optimal hourly dispatch plan for the integrated power and natural gas energy system considering the uncertain wind power and carbon trading costs. Photovoltaic power generation and other types of generators can also be well integrated into this model. Wind power was chosen in this article because of its reverse peak shaving characteristics. In China, the peak period of wind power at night is at a low electricity load, and wind power is difficult to absorb. At the same time, wind power accounts for the highest installed capacity of all renewable power sources in Europe. The natural gas network is the physical constraint of the inner model, and the natural gas network constraint can be ignored in the power system dispatch where the proportion of gas generators is not high.
(2) This paper introduces the carbon trading mechanism into the energy power system with wind power and gas generators. The construction of the bi-layer model can obtain the optimal carbon price of the regional power system under a given carbon emission reduction control target and the day-ahead dispatching plan of the system at this time. It aims to find a carbon trading price and scheduling plan that meets the lowest cost and achieves carbon emission reduction targets. However, the method in this paper can be extended to other regional cases, as follows: The government's regulatory authority sets the carbon emission reduction targets (λredu) of the energy and power systems of the corresponding regions and the free carbon quota (Q i c ) of the carbon emission sources. Whether the allocation object of free carbon emission quota is all generators or carbon emission source generating units in the region, such as thermal power, depends on the local carbon trading policy. The free carbon emission quota is mainly determined by the free carbon emission quota coefficient per unit of electricity allocation (ε), which is obtained by the weighted average of the marginal emission factor of electricity and the marginal emission factor of capacity in the area. When regional clean generators account for a relatively high proportion, such as Europe, the free carbon emission quota per unit of electricity allocation will be lower. Under strong emission reduction requirements, gas-fired generators need to purchase carbon emission rights in the carbon trading market, and cleaner generators such as carbon capture power plants and nuclear power generators will sell carbon emission rights to make profits. Taking the above-mentioned parameters in a specific area as the input of the bi-level model in this article, the optimal carbon price of carbon trading and the day-ahead dispatching plan of the system at this time can be obtained according to the idea of the bi-level model in this article. Realize the reasonable allocation of carbon resources in the regional energy power system under consideration of dispatching economy and total carbon emission control. The method in this article can provide a certain reference, but the application of a specific area should also be combined with the regional policy situation.
(3) Energy and environmental issues are very complex. This paper only considers the carbon emissions of pollutants. Relevant studies also show that the carbon emissions of the power industry and other pollutants such as SO2 have certain roots and simultaneity, and other pollutants can be roughly controlled through the control of CO2 [33,34]. However, in a more in-depth environmental analysis, we should also consider the emissions of other pollutants in power production.

Conclusions
In this paper, firstly, the reward and punishment ladder-type carbon trading model is constructed, and the impact of three carbon price mechanisms of carbon trading on the carbon emission sources in the power system is comparatively analyzed. Secondly, the low-carbon economic stochastic optimization dispatching model of the integrated power and natural gas energy system (IPGES) containing P2G considering wind power uncertainty and carbon trading is established. Finally, an optimal carbon price solution model is proposed for IPGES considering the economics of dispatching and the requirements of carbon emission reduction. From the simulation results, we can get the following conclusions. After considering P2G, the abandoned wind power and carbon emissions of IPGES decreased. Meanwhile, under the reward and punishment ladder-type carbon trading, P2G could obtain more carbon emission reduction benefits due to the introduction of incentive coefficient. Taking carbon trading into consideration in the dispatching of IPGES can reduce the carbon emissions of the system, and the implementation of the reward punishment ladder carbon price has better dispatching economy and low carbon effect compared with the ladder carbon price and the unified carbon price. Under the same total carbon emission control requirements of IPGES, the optimal benchmark carbon price and total dispatch cost are the lowest for reward and punishment ladder-type carbon trading, which enables IPGES to achieve the total carbon emission control requirements at lower carbon trading costs, indicating that the effectiveness of reward and punishment ladder-type carbon trading in the dispatch of IPGES.

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

IPGES
Integrated power and natural gas energy system P2G Power-to-gas facilities CFPP Coal-fired power plant GFPP Gas-fired power plant UCT Unified carbon price mechanism LCT Ladder-type carbon price mechanism RPLCT Reward and punishment ladder-type carbon trading GH/GL type generators Thermal power generators whose carbon emission intensity is higher/lower than the free carbon emission quota coefficient per unit of electricity allocation Parameters t Index of time T Dispatch cycle, this paper is taken 24h Respectively represent the correlation coefficient (all of them are 0 or 1, and 1 means connected) between node i and natural gas wells, gas storage stations, natural gas pipelines, GFPPs, P2G and load nodes in the nature gas network F D t Natural gas load at each node at time t (km 3 /h)