The interior of DIEM is composed of three layers: the energy supply side, conversion and coupling side, and demand side [10], forming a system architecture oriented toward multi-energy complementarity as shown in Figure 1. Compared with traditional microgrids, DIEM has three technical advantages: improving the local consumption capacity of renewable energy through electricity-heat-hydrogen multi-energy coupling; integrating Carbon Capture, Utilization and Storage (CCUS) and Power-to-Gas (P2G) technologies to form a closed-loop carbon cycle path; and possessing flexible trading capabilities to participate in both the electricity market and carbon trading market, realizing the joint optimization of economic and low-carbon objectives. Through the coordinated operation of internal multi-energy coupling equipment, DIEM constructs an integrated operation system of “production-conversion-storage-trading”; externally, by interfacing with the carbon trading market, it achieves multi-energy complementarity and explicit quantitative accounting of carbon costs, providing a physical carrier and market mechanism support for the low-carbon operation of microgrids under the new power system.

Figure 1. Architecture design of DIEM.

Based on the equipment operation and energy conversion mechanisms, mathematical descriptions are established for the core equipment in DIEM, including Combined Heat and Power (CHP), Gas Boiler (GB), Power to Gas (P2G), Hydrogen Fuel Cell (HFC), Carbon Capture, Utilization, and Storage (CCUS), and Energy Storage System (ESS) By constructing energy input-output mapping functions, the conversion efficiency characteristics, operational boundary constraints, and multi-energy flow coupling relationships are comprehensively considered, providing a physical layer constraint foundation for the optimal operation of microgrids.

2.2.1. CHP

CHP unit is a device that produces both electricity and thermal energy. It uses fuels such as natural gas for combustion to generate thermal energy, which is then converted into electricity. Meanwhile, the waste heat generated during the power generation process is utilized for heating, cooling, or industrial production processes.

P t C H P , H t C H P —Power generation power and heat generation power of CHP.

H 0 C H P —Heat power corresponding to the minimum power generation power of CHP.

k min , k max —Electrical-thermal conversion coefficients of CHP unit corresponding to the minimum and maximum output power.

k l —Linear supply slope of electrical and thermal power of CHP.

η E C H P , η l o s s C H P —Power generation efficiency and loss coefficient of CHP.

P h —Cogeneration factor.

N t C H P —Natural gas consumption of CHP.

L H V C H 4 —Low heating value of natural gas, i.e., the heat released when unit mass of CH₄ is completely burned.

P min C H P , P max C H P —Upper and lower limits of power generation power of CHP.

2.2.2. GB

GB is a heating equipment that uses gaseous fuels such as natural gas or liquefied petroleum gas. Compared with traditional coal-fired boilers, it generally has higher combustion efficiency, enabling more sufficient release of thermal energy, and at the same time, the exhaust gas generated during its combustion contains fewer pollutants.

H t G B —Heat generation power of GB.

N t G B —Natural gas consumption of GB.

η G B —Heat generation efficiency of GB.

H m i n G B , H m a x G B —Upper and lower limits of heat generation power of GB.

2.2.3. P2G

P2G equipment can realize two types of energy conversion: it converts electrical energy into hydrogen in an electrolyzer (EL); part of the hydrogen is used for hydrogen energy supply, and the other part reacts with CO₂ in a methane reactor (MR) to produce methane.

P t , H 2 EL —Hydrogen production power of EL.

η EL —Operating efficiency of EL.

P t EL —Electrical energy input power of EL.

P t , H 2 P 2 G —Hydrogen production power of P2G equipment used for hydrogen energy supply.

P t , H 2 MR —Hydrogen input power of MR.

N t , CH 4 MR —Methane production volume of MR.

η MR —Operating efficiency of MR.

P min E L , P max E L —Upper and lower limits of electrical energy input power of EL.

P H 2 , min M R , P H 2 , max M R —Upper and lower limits of hydrogen input power of MR.

Δ P min E L , Δ P max E L —Upper and lower limits of ramp rate of EL.

Δ P H 2 , min M R , Δ P H 2 , max M R —Upper and lower limits of ramp rate of MR.

2.2.4. HFC

Hydrogen energy can be converted into electrical energy and thermal energy through HFC equipment.

P t , e HFC —Electrical energy power generated by HFC.

η e HFC —Electrical conversion efficiency of HFC.

P t , H 2 HFC —Hydrogen power consumed by HFC.

H t , h HFC —Thermal energy power generated by HFC.

η h HFC —Thermal conversion efficiency of HFC.

P H 2 , max HFC —Maximum hydrogen power consumed by HFC.

k min HFC , k max HFC —Upper and lower limits of the electrical-thermal ratio of HFC.

2.2.5. CCUS

A post-combustion capture system is adopted to capture CO₂ generated from the combustion of natural gas in CHP systems and GB. Part of the captured CO₂ is transported to the P2G system for methane production, and the other part is sequestered to reduce carbon emissions. Uncaptured CO₂ is emitted into the atmosphere.

E t C H P , E t G B —Carbon emissions generated by CHP and GB.

μ C H P , μ G B —Carbon emission factors of CHP and GB.

E t —Carbon emissions generated by DIEM.

E t o u t —Carbon emissions released into the atmosphere without capture.

η c C C U S —Carbon capture efficiency of CCUS technology.

E t , c C C U S —Carbon emissions captured by CCUS.

E t , C O 2 P 2 G —CO₂ captured by CCUS used for methane production.

E t , s C C U S —CO₂ captured by CCUS used for storage.

λ C O 2 M R —Carbon consumption coefficient of MR for methane production.

P t C C U S —Total energy consumption of CCUS.

λ c C C U S , λ s C C U S —Power consumption coefficients for unit carbon capture and storage.

P t , min C C U S , P t , max C C U S —Upper and lower limits of CCUS power.

Δ P min C C U S , Δ P max C C U S —Upper and lower limits of CCUS ramp rate.

2.2.6. ESS

Three types of energy storage devices are considered, namely batteries, heat storage tanks, and hydrogen storage tanks, and the State of Charge (SOC) variable is introduced to describe the state of each system.

1) When the system is in the charging state:

2) When the system is in the discharging state:

S O C ESS , t e / h / H 2 —SOC of the electricity/heat/hydrogen storage systems.

P ESS , t , chr e / h / H 2 , P ESS , t , d i s e / h / H 2 —Charging/discharging power of electricity/heat/hydrogen.

η ESS , c h r e / h / H 2 , η ESS , d i s e / h / H 2 —Charging/discharging efficiency of the electricity/heat/hydrogen storage systems.

C ESS e / h / H 2 —Capacity of the electricity/heat/hydrogen storage systems.

S O C ESS , min e / h / H 2 , S O C ESS , max e / h / H 2 —Upper and lower limits of the SOC.

P ESS , c h r ,min e / h / H 2 , P ESS , c h r ,max e / h / H 2 , P ESS , d i s , m i n e / h / H 2 , P ESS , d i s ,max e / h / H 2 —Upper and lower limits of charging and discharging power.

Δ P ESS , c h r ,min e / h / H 2 , Δ P ESS , c h r ,max e / h / H 2 , Δ P ESS , d i s ,min e / h / H 2 , Δ P ESS , d i s ,max e / h / H 2 —Upper and lower limits of the ramp rate of ESS.

Among them, k ESS , c h r e / h / H 2 and k ESS , d i s e / h / H 2 are flag coefficients for charging and discharging states, which are 0 - 1 variables. If the value is 1, it indicates charging; if the value is 0, it indicates discharging. Therefore, ESS cannot perform charging and discharging simultaneously

At present, China’s carbon trading market is in a stage of accelerated construction and improvement, with remarkable results achieved in pilot projects in many regions. Based on the consumption-side accounting principle, the mechanism for DIEM to participate in the carbon trading market is modeled, following the basic principle of “who emits, who bears”. The carbon emission responsibility boundary is defined as follows: 1) As a terminal energy producer and consumer, DIEM assumes full responsibility for operational carbon emissions; 2) Indirect carbon emissions caused by DIEM’s external power purchase shall be uniformly calculated in accordance with the regional power grid benchmark emission factor announced by the state; 3) ESS and HFC only involve energy conversion, do not directly consume fossil energy, and do not generate additional carbon emissions during operation, so they are not included in the carbon emission accounting boundary.

Under this mechanism, the regulatory authority provides DIEM with free initial carbon emission allowances. When DIEM’s actual carbon emissions are lower than the allowances, the remaining allowances can be sold in the carbon trading market for profit; otherwise, it is required to purchase allowances for the excess emission part. This carbon trading mechanism mainly consists of three parts: initial allocation of carbon emission rights, actual carbon emissions, and ladder-type carbon trading costs [11][12].

2.3.1. Initial Allocation Model of Carbon Emission Rights

Carbon allowances are allocated free of charge to incentivize DIEM to save energy and reduce emissions. According to the definition of carbon emission boundaries, the main sources of DIEM’s carbon emissions include: 1) Indirect carbon emissions caused by DIEM purchasing electricity from the main grid (consumption-side accounting); 2) Direct carbon emissions generated by equipment such as CHP and GB consuming natural gas. Therefore, the initial carbon allowance model is as follows:

E 0 —Carbon quota for DIEM.

E e , b u y 0 —Carbon quota for DIEM’s electricity purchase from the upper-level grid.

E C H P 0 —Carbon quota for CHP.

E G B 0 —Carbon quota for GB.

p t b u y —Electricity purchase volume of DIEM from the upper-level grid.

χ e —Carbon quota per unit power consumption of coal-fired units.

χ h —Carbon quota per unit natural gas consumption of natural gas-fired units.

2.3.2. Actual Carbon Emission Model

Considering that the electricity purchased from the upper-level grid comes from coal-fired power units, and CCUS can capture CO₂ and generate methane in P2G, the actual carbon emission model based on the carbon emission responsibility boundary is as follows:

E f —Actual carbon emissions of DIEM.

E e , b u y , f —Indirect carbon emissions from DIEM’s electricity purchase from the upper-level grid.

E t o t a l , f C H P , G B —Direct carbon emissions of CHP and GB.

E C C U S , f —CO₂ capture volume of CCUS.

ϖ —Capture parameter.

a 1 / b 1 / c 1 , a 2 / b 2 / c 2 —Carbon emission calculation parameters for coal-fired units and natural gas-fired units.

2.3.3. Reward-Punishment Incentive-Based Ladder-Type Carbon Trading Model

To strengthen the incentive and constraint functions of the carbon market, a reward-punishment incentive-based ladder-type carbon trading mechanism is introduced. Based on a segmented increasing price strategy, an incentive mechanism characterized by “increasing costs for excess emissions and increasing returns for surplus allowances” is formed.

The carbon trading volume of DIEM is expressed as follows:

The mathematical model of the ladder-type carbon trading for DIEM is as follows:

C C O 2 —Carbon trading cost.

l —Carbon emission interval length.

ε —Price compensation coefficient for surplus interval.

ν —Price growth coefficient for excess interval.

The DIEM aims to minimize its own comprehensive operational cost, which includes external interaction costs, unit operation and maintenance costs, wind and solar curtailment costs, operation and maintenance costs of energy storage systems, and carbon trading costs (see Section 2.3.3 for details, which will not be repeated here).

F D I E M —Benefits of DIEM.

C u t i l i t y —External interaction costs.

C u n i t s —Unit operation and maintenance costs.

C c u t —Wind and solar curtailment costs.

C E S S —Operation and maintenance costs of energy storage systems.

λ t C H 4 —Natural gas purchase price.

α 1 ~ α 6 , β 1 ~ β 2 —Unit operation cost coefficients.

λ c u r —Wind and solar curtailment cost coefficient.

ς —Degradation cost per unit energy for charging and discharging.

3.2.1. Energy Supply-Demand Balance Constraint

3.2.2. Exchange Power Constraint

3.2.3. Natural Gas Flow Balance Constraint

3.2.4. Carbon Emission Flow Balance Constraint

The basic data in this paper is derived from the actual operational data of the Shanghai Caojing Integrated Energy Center. Among them, the multi-energy load data and renewable energy output data are directly obtained from this center. The parameters of the carbon trading mechanism are set as shown in Table 1, and the multi-energy loads and forecast of renewable energy outputs are detailed in Figure 2.

Table 1. Parameters of the carbon trading mechanism.

Figure 2. Multi-energy loads and forecast of renewable energy outputs.

The mixed-integer linear programming model established in this paper is solved by the CPLEX solver based on the MATLAB platform. The key solver parameters are set as follows: the duality gap tolerance is set to 1.00e−04, and the number of parallel computing threads is set to 28. All calculations are implemented on a standard desktop computer with the following hardware configuration: Intel (R) Core (TM) i7-14700HX processor, Windows 11 (64-bit) operating system, and MATLAB R2024b. The total computation time for the whole process to achieve optimal convergence is only 0.13 seconds.

Figure 3 reveals the typical output characteristics of renewable energy in DIEM: PV output presents an obvious unimodal distribution, reaching the peak power during the midday period from 11:00 to 15:00; wind power output exhibits stronger randomness and intermittency. Such differentiated output characteristics lead to power surplus in the system during the midday period when PV generation is high; while there is a power supply gap during the evening peak load period from 19:00 to 22:00.

To further analyze the impact of the carbon trading mechanism on the multi-energy operation of DIEM, two comparative scenarios are set as follows:

Scenario 1: The carbon trading mechanism is not considered, with the sole objective of minimizing the economic operation cost;

Scenario 2: The ladder-type carbon trading mechanism is considered, i.e., the carbon trading cost is included in the optimization model.

Figure 3. Renewable energy generation output.

With the results shown in Figure 4. At the power level, Scenario 1 features frequent and high-level unit output, leading to power surplus in multiple periods but high carbon emissions; by contrast, Scenario 2 reduces the proportion of high-carbon power generation, emphasizes environmental constraints, cuts down power-selling behavior significantly, and moves toward load self-balance. In thermal dispatch, Scenario 1 requires increased CHP cogeneration heat output to match its continuous operation, resulting in obvious thermal energy redundancy, while Scenario 2 shortens CHP operation time, compensates by raising GB heat output, and uses thermal energy storage to smooth heat load fluctuations, thus achieving flexible and economically matched thermal dispatch. In the hydrogen energy path, the P2G system is more effectively utilized in Scenario 2—during the midday peak of renewable energy output, electricity is allocated to P2G for hydrogen production, which improves local power consumption efficiency and enhances hydrogen reserve adjustability—whereas in Scenario 1, HFC is only used to convert hydrogen into electricity and heat during demand peaks.

Figure 4. Energy optimization operation results of DIEM under Scenario 1 and Scenario 2.

Figure 5 illustrates the carbon emission distribution of DIEM under the two scenarios, and the results indicate that the carbon trading mechanism exerts a significant guiding effect on carbon emission behaviors. Since Scenario 1 does not consider carbon cost constraints, the system operation strategy is mainly oriented toward economic objectives, which leads to the priority activation of conventional high-carbon units such as CHP to meet load demands and thus results in relatively high carbon emissions. After the introduction of the conventional stepped carbon trading mechanism in Scenario 2, DIEM realizes the capture and storage of CO₂ during peak carbon emission periods by virtue of CCUS technologies, while reasonably controlling the output of high-carbon equipment. Consequently, the net carbon emissions decrease significantly, which demonstrates the regulatory flexibility and emission reduction guiding capability based on the stepped carbon trading mechanism.

Figure 5. Carbon emissions distribution of the DIEM under Scenario 1 and Scenario 2.

To verify the synergistic effects of economic benefits and environmental performance under different carbon emission strategies, a comparative analysis is conducted on the two typical scenarios. The results are presented in Table 2: Scenario 2 incurs a carbon trading cost of 408.11 CNY, with carbon emissions reduced from 3211.17 kg to 2467.56 kg. On the basis of achieving a 23.16% carbon emission reduction rate, the comprehensive operation cost increases by approximately 4.71%, which reflects the restrictive effect of explicit carbon cost on system operation strategies. The above results indicate that the proposed carbon trading mechanism possesses both carbon regulation flexibility and price guiding capability, providing effective support for DIEM to achieve the dual optimization goals under carbon constraint conditions.

Table 2. Comparison of benefits before and after implementing the ladder-type carbon trading mechanism.

As shown in Figure 6, to investigate the impact of policy stringency on the low-carbon economic operation of the DIEM, a sensitivity analysis is conducted on two key parameters of the ladder-type carbon trading mechanism: interval length l and price growth coefficient v.

For interval length l, when l is in the range of (0.5, 2], the interval length is relatively small, and the system purchases carbon emission rights quotas at ladder prices for most periods, resulting in high carbon trading costs and thus low carbon emissions. When l is in the range of (2, 5], the interval length is relatively large; due to the inherent load demand of the DIEM, with the increase of l, the volume of carbon emission rights quotas purchased at high-gradient prices decreases, leading to lower carbon trading costs. As the carbon emission cost gradually decreases, the system’s carbon emissions increase accordingly. When l is in the range of (5, 8], carbon emissions are all traded at the benchmark price and the first gradient price, and the impact of l on carbon emissions is minor, so carbon emissions reach stability; with the further increase of l, the system’s carbon trading cost decreases continuously, and the total operation cost also decreases gradually.

For price growth coefficient v, when v is in the range of [0, 0.4), with the increase of v, the carbon trading cost increases accordingly. To reduce the carbon trading cost, the system adjusts the output distribution of internal equipment to reduce carbon emissions, resulting in a gradual decrease in carbon emissions and a continuous increase in total operation cost. When v is in the range of [0.4, 0.8], the output of internal equipment has been adjusted to the optimal low-carbon operation state, and the impact of v on carbon emissions is relatively small, so carbon emissions tend to be stable; with the further increase of v, the carbon trading cost and total operation cost continue to rise. Overall, interval length mainly regulates the tightness of carbon emission quotas, while price growth coefficient dominates the incentive intensity of carbon prices, and both parameters jointly determine the trade-off between carbon emissions and economic operation of the DIEM.

Figure 6. Sensitivity analysis of key parameters.