Low‐carbon economic operation for integrated energy system considering carbon trading mechanism

Carbon trading mechanism is an effective means to control greenhouse gas emissions. This paper focuses on the low‐carbon economic operation of the integrated energy system under carbon trading mechanism in China. The integrated energy system includes the energy storage, ground source heat pump, and other equipment. The objective of this paper was to minimize the annual total cost of the system considering the carbon trading cost and study the operation modes under different carbon trading prices by commercial optimization software. The simulation results show the operation modes in summer are changed obviously with the increase of the carbon trading prices, while the operation modes in winter basically are not changed with the fluctuation of the carbon trading prices; under the carbon trading mechanism, the integrated energy system can not only reduce the carbon emissions, but also reduce the annual total cost through carbon trading, which shows its advantages and good development prospect. In addition, the setting of the carbon emission quota has a direct impact on the economy of the enterprises. Furthermore, the ground source heat pump and the electric refrigeration units can stabilize the fluctuation of the equipment output caused by the change of natural gas prices in this integrated energy system.


| INTRODUCTION
The growing demand for energy poses a great challenge to the global environment, and the way of energy utilization is crucial for the sustainable development in future. 1 The energy demands present a trend of diversification and distribution. 2 The integrated energy system (IES) is a new type of energy system which can meet the users' various energy needs and promote an efficient energy use in the forms of cold, heat, and electricity/gas energy supplies. The IES has the advantages of decentralized layout and nearby utilization, 3 which has received widespread attention. Modeling, planning, 4 operation optimization, [5][6][7][8] and performance evaluation 9 of the IES are hot topics in the academic circles.
The IES can realize energy cascade utilization, which has great potential in reducing the greenhouse gas emissions, [10][11][12][13] and will become one of the most important means to control the carbon dioxide emissions in the next 20 years. 14 The introduction of the carbon trading mechanism is also an effective way to control the CO 2 emissions. This mechanism contributing to the energy transformation and upgrading will make more use of the clean energy such as natural gas. 15 Since the first global carbon trading market was launched in EU in 2005, the scale of the international carbon market has been expanding. 16 China's national carbon trading system has been pilot since 2013 and is expected to become the world's largest carbon trading market. 17 After 9 years' pilot work, China's carbon market officially began online trading on 16 July 2021.
At present, the research on the IES considering the carbon trading mechanism mainly focuses on the large-scale IES composed of the gas turbine, cogeneration, and wind turbine units with large installed capacity. [18][19][20][21][22] A significant portion of this literature focuses on the issue of the renewable energy consumption under the carbon trading mechanism. [23][24][25][26][27] Studying the effectiveness of the laddertype carbon trading price on reducing the carbon emissions is also one of the popular researches. 27 The existing literature on the diversification of the internal equipment and miniaturized IES under the carbon trading mechanism is relatively little. Although some scholars have done some researches in this aspect, for example, Chu et al 28 established a nonlinear optimization model with three objectives of the economic benefit, environmental sustainability, and energy efficiency in the consideration of the carbon trading policy, which was solved by the particle swarm optimization. In the case study, with this optimal system operation strategy, the reducing cost percentage of five different types of public buildings increased with the carbon trading prices growth under different carbon emission quotas. The authors showed the energy system was more economical to take the carbon trading policy into account than not when adopting the prescribed carbon emission quotas. Li et al 29 studied on the effects of the carbon trading and feed-in electricity tariff policies on the performance of the IES in different operation strategies, which was solved by genetic algorithm, and obtained a best choice under different circumstances. Their studies indicated the energy system can convert the CO 2 emission reduction and surplus electricity into the economic benefits through the carbon trading and electricity trading according to the incentive policy described by the authors. However, the existing literature lacked the research on the optimal operation modes of the IES at different carbon trading prices. Improper operation modes will cause practical operating mode to deviate from the optimal operating one. 30 Therefore, the motivation of this work is to begin to address this research gap. The main contributions of this work are as follows.
• An IES model considering the carbon trading mechanism is established. The single equipment is modeled and controlled to ensure the control accuracy. • The effects of the carbon emission quotas and energy storage on the annual total cost are analyzed, which can provide constructive suggestions for the carbon trading development in China. • The carbon emissions and operation modes of the research object at different carbon trading prices are analyzed. • The natural gas prices and carbon trading prices on the equipment output are studied, which can provide reference for the equipment configuration of IES.
F I G U R E 1 Sketch map of the integrated energy system 2 | EQUIPMENT AND MODELING

| Description of the integrated energy system
The sketch map of the IES is shown in Figure 1. The system includes the gas internal combustion engine (ICE) units, absorption lithium bromide (ALB) units, ground source heat pump (GSHP) units, energy storage pool, electric refrigeration (ER) units, gas boilers, and plate heat exchanger (PHE). This system can gain the power from the grid, but cannot transmit the power to the grid.
As shown in Figure 1, natural gas, as a primary energy, is converted into the electric and thermal power to meet the users' needs through the energy production link, and the waste heat is converted into the cold and heat energy required by the users through the energy recovery link. In addition, through secondary conversion, such as the ER and GSHP units, which can realize the conversion from the electricity to the cold and heat energy to meet the users' needs. The energy storage system (ESS) can decouple the production and consumption of the energy in time, including the heat storage (HS) and cold storage (CS).

| Model of energy production equipment
The energy production subsystem consists of the ICE units and boilers.
Referring to the ICE samples provided by the manufacturer, the formula is obtained by using the Origin Software, the relationship between the partial input power ratio of the natural gas and the partial load ratio of the ICE is shown as follows: where G in represents the natural gas input power, kW; G max in represents the maximum natural gas input power, kW; G PL in is defined as the partial input power ratio of the natural gas; P PL ICE is the partial load ratio of the ICE; P ICE is the power generation of the ICE, kW; and P e ICE is the rated power of the ICE, kW. The above nonlinear model will increase the difficulty of solving; therefore, the nonlinear curve is piece-wise linearized, as shown in Figure 2.
Using the method reported in the literature, 31 the linearization function is expressed as follows: where K i is the slope of the segment i; M i is the intercept of the segment i; P PL ICE,i is the i-th segment point, where P PL ICE,1 corresponds to the minimum partial load ratio of the ICE, P PL ICE,n corresponds to the maximum partial load ratio of the ICE; the value range of B i is 0-1, which indicates the position in the segmentation area; Equation (7) guarantees it must be a piece-wise continuous linearization from left to right without skipping.
The natural gas consumption of the ICE is expressed as follows: (1) Piece-wise linearizing of the partial input power ratio of natural gas where V ICE represents the natural gas consumption of the ICE, m 3 /h; H is 35.3 MJ/m 3 as the low calorific value of the natural gas. The calculation formulas of the exhaust heat power and cylinder liner water heat power of the ICE are as follows: where Q PL ICE,eg is defined as the partial exhaust gas waste heat recovery rate of the ICE; Q ICE,eg is the exhaust gas waste heat power of the ICE, kW; Q max ICE,eg is the maximum exhaust gas waste heat power of the ICE, kW; Q PL ICE,cyl is defined as the partial cylinder liner water waste heat recovery rate of the ICE; Q max ICE,cyl is the maximum cylinder liner water waste heat power of the ICE, kW; Q ICE,cyl is the cylinder liner water waste heat power of the ICE, kW.
The same method will be adopted to linearize in formula (10) and (11).
The heat production of the boiler is related to the boiler's efficiency and gas consumption as shown in Equation (14).
where Q H GB represents the heating capacity of the boiler, kW; V GB represents the gas consumption of the boiler, m 3 /h; GB represents the efficiency of the boiler.

| Model of energy recovery equipment
The model of the cooling and heating capacity of the ALB can be shown as follows: where Q C ALB represents the refrigerating capacity of the ALB in summer, kW; Q H ALB represents the heating capacity of the ALB in winter, kW; C ALB represents the efficiency of the ALB in summer; H ALB represents the efficiency of the ALB in winter.
The model of the PHE's heating capacity is: where Q H PHE represents the heating capacity of the PHE in winter, kW; H PHE represents the efficiency of the PHE in winter.

| Model of energy conversion equipment
Combining the traditional combined cooling heating and power system and GSHP into the IES will be conducive to realizing the cascade utilization of the ICE's waste heat. The use of the ICE's waste heat improves the design temperature of the ground source side of the GSHP, avoids the shutdown protection problem caused by the low water temperature of the ground source side when the GSHP units are operating under extreme conditions in winter, and further improves the heating performance coefficient of the GSHP in winter.
Referring to the GSHP samples provided by the manufacturer, the formula is obtained by using the Origin Software. The refrigerating and heating capacity of the GSHP can be calculated as follows: where Q C GSHP represents the refrigerating capacity of the GSHP in summer, kW; Q H GSHP represents the heating capacity of the GSHP in winter, kW; P C GSHP represents the input electric power of the GSHP in summer, kW; P H GSHP represents the input electric power of the GSHP in winter, kW; C GSHP represents the efficiency of the GSHP in summer; H GSHP represents the efficiency of the GSHP in winter; Q C GSHP,e represents the rated refrigerating capacity of the GSHP in summer, kW; and Q H GSHP,e represents the rated heating capacity of the GSHP in winter, kW.
The refrigerating capacity of the ER can be calculated as: where Q C ER represents the refrigerating capacity of the ER in summer, kW; P ER represents the input electric power of the ER in summer, kW; C ER represents the efficiency of the ER in summer.

| Model of energy storage equipment
The model of the energy storage device is established as: where SOC(t + 1) is the state of charge at the moment t + 1; SOC(t) is the state of charge at the moment t; cha is the charging efficiency; dis is the discharging efficiency; B is the capacity of the ESS, kWh; is the self-discharge rate; P cha (t) is the stored power at the moment t, kW; P dis (t) is the discharged power at the moment t, kW.

| Description of carbon trading mechanism
The government allocates the carbon emission quotas to the enterprises and encourages them to participate in carbon emission quotas market trading. The mode is as follows: when the actual carbon emissions of the enterprises are less than the amount allocated by the government, the enterprises can choose to sell the excess emission amount into the carbon market; when the actual carbon emissions exceed the amount allocated by the government, the enterprises need to buy the missing amount from the carbon market, otherwise they will have to pay high fines.

| Carbon emission calculation
The calculation of the carbon emissions of this IES is mainly divided into two parts: one is the CO 2 emissions from the equipment using natural gas as the primary energy, the other is the CO 2 emissions generated by the purchased power.
The facilities consuming natural gas in the IES are the ICE units and boilers. The formula of CO 2 emissions of the natural gas from the IES is calculated as: where E CO 2 ,gas is the CO 2 emissions of the natural gas, kg; N 1 represents the numbers of the ICE units; P ICE,j (t) represents the power generation of the j-th ICE at the moment t, kW; N 2 represents the numbers of the boilers; Q GB,k (t) presents the heating capacity of the k-th boiler at the moment t, kW; ICE,j represents the efficiency of the j-th ICE; and F CO 2 ,gas is the CO 2 emission factor of the natural gas based on the minimum heat value which can be set to 5.62 × 10 −7 kg/kJ. 32 The formula of the CO 2 emissions from the purchased power is: where E CO 2 ,E is the CO 2 emissions from the purchased power, kg; P buy (t) represents the power purchased from the grid at the moment t, kW; and F CO 2 ,E is the average emission factor of the regional power grid which can be set to 0.8647 kg/kWh. 33 Therefore, the formula of the total CO 2 emissions of the IES is expressed as:

| Carbon trading cost model
The carbon trading market of China is in its infancy, and the allocation policies of various regions are not unified. This paper calculates the initial carbon emission quota according to the load served by the IES. The formula is as follows: where E CO 2 ,q represents the initial carbon emission quota for free; Q E (t) represents the electric load served by the IES at the moment t, kW; Q H (t) is the heat load served by the IES at the moment t, kW; and E represents the quota coefficient of the unit electricity emission, which refers to the baseline carbon emission factor of the regional power grid. 34 This paper sets the quota coefficient of the unit electricity emission at the project site to 0.40 kg/kWh. H represents the quota coefficient of the unit heat emission, which refers to carbon emission baseline for heating in China. 35 The quota coefficient of the unit heat emission at the project site is assumed to be 0.20 kg/kWh. These two quota coefficients are also analyzed by taking other data in this paper subsequently. The cooling load served by the IES is converted into the electric load according to the average COP of the cooling equipment and then substituted into formula (27).
Considering that the actual carbon emissions of the system are greater or less than the allocated carbon emission quotas, the carbon trading cost should be written as: where CO 2 represents the unit carbon trading price, ¥/t.

| Objective
The optimization objective is to minimize the annual total cost considering the carbon trading cost, and the objective function can be written as: where C represents the annual total cost, ¥; C H O is the operating cost in winter, C C O is the operating cost in summer, ¥; C E,t is the electricity price at the moment t, ¥/kWh; C M is the maintenance cost, ¥; M 1 are the numbers of the ALB units, M 2 are the numbers of the ER units, M 3 are the numbers of the GSHP units; f is the equipment maintenance cost coefficient, ¥/kW. The minimum load rate of all the equipment is set to 0.5.

Climbing constraint of internal combustion engine
The output power of the ICE is not abrupt, so there is a climbing constraint: where P down ICE and P up ICE are the maximum downhill rate and the maximum climbing rate of the ICE output, kW/h. Both the maximum downhill and climbing rate are set to 200 kW/h.

| Model solution
The solution process of the optimization model of the IES established is shown in Figure 3.
Using the commercial optimization software LINGO 19.0 to write a model program and ask the global solver to tackle it. In order to ensure the control accuracy, the unit commitment problem is considered in the programming. Use @if statement to define whether the equipment is running or not: when the equipment is running, the output must be greater than the critical point of the start-up and stop; otherwise, the equipment will be shut down. In this way, it can avoid introducing 0-1 integer variables into the optimization model and thus reduce the difficulty of solving.

| Energy demand profiles
This paper takes a residential community in northern China as the research object. The hourly load of a typical day is simulated by using the dynamic simulation software and the results are shown in Figure 4. 24 hours is a scheduling cycle, and the unit scheduling time is 1 hour. The heating and cooling season all last for 120 days each year.

| Energy price and parameters of equipment
The energy price parameters are shown in Table 1.
The parameters of the energy supply equipment and energy storage equipment in the case are shown in Tables 2 and 3.

F I G U R E 3
Flowchart of the optimization model

| Analysis of the annual total cost and carbon emissions
This paper uses the following eight cases to simulate the impact of the carbon trading prices and the energy storage on the carbon emissions and the annual total cost of the IES. The carbon trading price of the project in recent two years is about ¥40/t and ¥80/t respectively, which fluctuates wildly. For simplicity, the initial carbon trading price is defined at ¥40/t, progressing at ¥40/t intervals.
Case 1: The carbon trading mechanism is not taken into account in the IES, without the energy storage; Case 2: The carbon trading mechanism is taken into account in the IES and the carbon trading price is ¥40/t, without the energy storage; Case 3: The carbon trading mechanism is taken into account in the IES and the carbon trading price is ¥80/t, without the energy storage; Case 4: The carbon trading mechanism is taken into account in the IES and the carbon trading price is ¥120/t, without the energy storage; Case 5: The energy storage is taken into account in the IES, without the carbon trading mechanism; Case 6: Both the energy storage and the carbon trading mechanism are taken into account in the IES, and the carbon trading price is ¥40/t; Case 7: Both the energy storage and the carbon trading mechanism are taken into account in the IES, and the carbon trading price is ¥80/t; Case 8: Both the energy storage and the carbon trading mechanism are taken into account in the IES, and the carbon trading price is ¥120/t; The results of different cases are shown in Table 4. The unit's start and stop status of Case 8 is shown in Table 5, × means stop, √ means start.
As shown in Table 4, which shows with or without energy storage, along with the increase of carbon trading price, the carbon emissions of the IES have been decreased or invariable. The increase of the carbon trading prices will lead to the increase of the carbon trading cost and the annual total cost. After adding the energy storage equipment, it will help to cut down the carbon emissions and reduce the cost of carbon trading, thus the annual total cost. By analyzing the above cases, it can be seen that with the energy storage equipment and the carbon trading mechanism is the most conducive to reducing the carbon emissions of the IES. Figure 5 depicts the change in annual carbon emissions at different carbon trading prices. As shown in Figure 5, when the carbon trading price is between ¥0/t and ¥80/t, the change of carbon emissions is not obvious. However, when the carbon trading price is between ¥80/t and ¥160/t, the carbon emissions show a significant reduction trend. When the carbon trading price is greater than ¥160/t, the decline of the carbon emissions slows down dramatically. Therefore, when the carbon trading price is set at 80 to ¥160/t, the trend of the carbon emission reduction is more obvious.
In addition to the carbon trading price, the quota coefficients of the unit electricity and heat emission play an important role in the economic operation of the IES. Taking Case 6 as an example, the influence of their values on the annual total cost is shown in Figure 6. The change trend is the same at different carbon trading prices.
As can be seen from Figure 6, the annual total cost will be decreased with the increase of the quota coefficients of the unit electricity and heat emission. When the carbon transaction cost is negative, the enterprise will be in a profitable state; thus, the higher the carbon trading price is, the less the annual total cost is, which will bring more profit to the enterprise. Nowadays, coal accounts for a large proportion in China's primary energy structure, resulting in low energy efficiency and high carbon emissions. The cost of natural gas power generation in China is higher than that of coal, the enterprises using natural gas have high energy supply cost and poor economy when their power generation cannot be sold through the power grid. The introduction of the carbon trading mechanism and the establishment of differentiated carbon emission quotas for enterprises using different types of primary energy and unit size will help to alleviate this problem.

| Operation mode in summer
Under different carbon trading prices, after optimization, the equipment output in the IES on a typical day in summer is shown in Figure 7.
It can be seen that the energy storage equipment basically stores energy when the electricity prices are low, and releases energy when the load is large. The ALB units are in full load operation all day, and the ER and the GSHP units share most of the cooling load.
However, with the increase of the carbon trading prices, the operation modes on a typical day in summer have changed dramatically. When the carbon trading price reaches ¥120/t, the GSHP units will completely replace the ER units in the periods 1-5 and 23 at low electricity prices. The reason is that the refrigerating economy of the GSHP units is better and close to full load operation during these periods.

| Operation mode in winter
Under different carbon trading prices, after optimization, the equipment output in the IES on a typical day in winter is shown in Figure 8.
It can be seen that the outputs of the GSHP units and the boilers are more in winter; the outputs of the ALB units and the PHE are less, which play the roles of auxiliary heating. In the periods 10-15, when the electricity prices are high, the heating mainly depends on the boilers, which consume the primary energy natural gas. At this time, the GSHP units' refrigeration is not economical.
Differing from summer, with the increase of the carbon trading prices, the operation strategies of the system in winter are not changed significantly; while only the outputs of the GSHP units and the boilers have a slight change. The reason is that in winter operation, no matter how the carbon trading prices change, the main equipment has been basically in the best operation mode, and there is little room for the optimization.

| Impact of natural gas prices on the outputs
The ALB, ER, and GSHP units are the main output equipment on a typical day in summer, and the boilers, ALB, and GSHP units are the main output equipment on a typical day in winter (in a cycle of the optimized operation, the net output of the ESS is 0).
Defining the initial natural gas price at ¥2.25/m 3 , with a 20% increase, the percentage of different equipment output on the typical days in winter and summer varies with the natural gas prices and the carbon trading prices, which is shown in Figure 9. From Figure 9A, it can be seen that the outputs of the ER units decrease when the carbon trading price reaches ¥120/t in summer, and the outputs change little at the same carbon trading price. From Figure 9B, it can be seen that the outputs of the GSHP units in summer are maximum when the carbon trading price reaches ¥120/t, and they are not significantly affected by the change of natural gas prices at the same carbon trading price.
As can be seen from Figure 9C,D, the outputs of the boilers are more affected by the change of the natural gas prices in winter. With the rise of the carbon trading prices, the outputs of the boilers decrease, and the outputs of the GSHP units gradually increase (the output ratio of ALB units are relatively small). It follows that the GSHP and ER units can stabilize the fluctuation of the outputs caused by the natural gas prices change in the IES.

| CONCLUSIONS
The following conclusions can be drawn.
1. The carbon trading mechanism adopts the economic regulation means of rewarding the low emissions and punishing the high emissions. In the case of high-cost natural gas power generation in China, the carbon trading mechanism provides an effective way for the low-carbon economic operation of the IES. Under the carbon trading mechanism, the IES can not only reduce the carbon emissions, but also reduce the annual total cost through the carbon trading when the carbon transaction cost is negative, which shows its advantages and good development prospect.
With the energy storage equipment and the carbon trading mechanism, it is the most conducive to reducing the carbon emissions of the IES.
The setting of the carbon emission quota has a direct impact on the economy of the enterprises, and the fuel type and the unit size should also be taken into account. have changed greatly. When the carbon trading price reaches ¥120/t, the GSHP units will completely replace the ER units in the periods 1-5 and 23 at low electricity prices. Differing from summer, with the increase of the carbon trading prices, the operation strategies of the system are not changed significantly in winter. 3. The outputs of the GSHP units are not significantly affected by the change of the natural gas prices in summer, but the outputs are more affected by the natural gas prices in winter, because in winter, the outputs of the GSHP units and boilers are in the opposite direction. The GSHP and ER units can stabilize the fluctuation of the outputs caused by the change of the natural gas prices in the IES.
The construction of China's carbon trading market is at its initial stage, the optimizing measures and constructive suggestions should be encouraged. The calculation standard of carbon emissions and carbon emission quotas allocation policy for the IES still needs further study.