Low Carbon Economic Dispatch of a Multi-Principal Integrated Energy System Considering CCS and P2G

1  Introduction

In recent years, carbon emissions have produced a greenhouse effect due to rapid economic and social development, leading to global climate change [1]. Amidst accelerating global efforts toward sustainable development, the adoption of decarbonized energy systems has emerged as a critical priority for both current and future economic paradigms. The development of IES, marked by the seamless coordination of generation, grid, demand, and storage components alongside cross-energy synergies, serves as a cornerstone strategy for advancing toward sustainable, low-carbon energy economies. IES interconnects diverse energy networks, dynamically transforming electricity, thermal, cooling, and gas resources to optimize energy distribution while seamlessly integrating decentralized renewable energy generation [2]. Advancing energy efficiency optimization and driving sustainable energy transitions represent pivotal research priorities with profound implications for future innovation and policy development.

P2G technology facilitates the bidirectional conversion between electrical energy and hydrogen within IES, enhancing energy flexibility and storage capabilities. Reference [3] analyzed the principle of power-to-gas, electrolysis of water to obtain hydrogen, to achieve the conversion and storage of energy. CCS plays a key role in reducing carbon emissions from IES, and CCS technology captures, sequesters, and uses CO2 emitted from the energy sector [4,5]. References [6,7] verify the effectiveness of CCS retrofits in decarbonizing power systems in real cases. However, the application of either P2G technology or CCS technology alone is not ideal in terms of economics [8]. The integration of CCS and P2G technologies enables the repurposing of captured CO2 for methane synthesis, achieving dual outcomes: a substantial reduction in IES carbon emissions and the production of renewable synthetic fuel [9]. Introducing P2G technology into the cogeneration scheduling model in IES effectively improves energy utilization and economy [10]. Reference [11] feeds captured CO2 from a gas-fired cogeneration plant to a P2G plant, and the generated gas is supplied to a gas-fired cogeneration plant. The above references lack consideration of the need for CO2 feedstock for methane production. Reference [12] established an integrated wind-light-hydrogen energy model and a coupled CCS and P2G model, which provides an effective way for IES renewable energy to adapt to a reliable hydrogen supply. Reference [13] proposed an operational framework including carbon capture, hydrogen fuel cells, and P2G technology. Through analysis of carbon valorization pathways, results confirmed improved eco-economic efficiency when operating under a stepped carbon trading policy. The literature largely excludes transactional market structures from multi-stakeholder operational models and employs fixed-rate carbon trading systems that fail to evolve toward more nuanced emission mitigation paradigms. Tensions among market participants arising from transactional disagreements risk eroding their willingness to actively engage in commercial exchanges.

Recent practical research reveals that the power trading mechanism is showing significant dynamic evolution characteristics, and the composition of the participating subjects in its marketization process has broken through the traditional single form and transformed into a multi-dimensional industrial synergy network. Under the new power system architecture, power generation companies, power sales companies, and load aggregators are forming a complex ecology of competition through long-term agreement alliances and spot market bidding. In the face of this asymmetric information environment, the construction of game models for strategy derivation has become an inevitable choice for market players to optimize their decision-making—equilibrium analysis can effectively deconstruct the conflict of interests of multiple parties, while game theory provides quantitative support for dynamic strategy adjustment, which provides a key methodological framework for solving the dilemma of the market power game under the new power system. Since the master-slave game is an important method for solving the dispute of interests of multiple decision-making subjects and studying the strategy choice, it is now widely used in the field of optimal scheduling of IESs [14]. In IES, the system operator formulates an appropriate price strategy based on the load demand and supply-demand relationship, and the suppliers and consumers respond according to the price information given by the operator, there is a sequential order in the game process, which is in line with the dynamic game situation between master and slave [15]. Reference [16] proposes a game-theoretic optimization framework for regional multi-energy systems, integrating load demand responsiveness to maximize combined economic and operational efficiency. Reference [17] proposes a two-level cooperative control strategy model based on multi-intelligence deep reinforcement learning for an “electricity-heat-gas” integrated energy system, which improves energy efficiency and reduces the cost of the integrated energy system. Reference [18] proposes a dual-phase optimization framework for combined heat and power systems, integrating strategic tariff adaptation and operational policy refinement to balance energy efficiency gains with cost minimization. Reference [19] incorporates a carbon trading mechanism, establishes a hierarchical decision-making model between energy suppliers and load-side stakeholders, and incentivizes user participation in low-carbon demand-side management through dynamic pricing strategies and flexible generation scheduling. This approach facilitates synergistic optimization of energy efficiency and emission reduction within IES. The study confirms that the introduction of master-slave game analysis tools can not only quantify the loss of game efficiency due to market power abuse but also provide a computable theoretical framework for institutions to design market power suppression mechanisms, which opens up a new path to solve the prevalent strategic offer and market manipulation problems in the power system. However, the solution methodology and other trading mechanisms are not comprehensively considered, and the extent of the IES carbon reduction potential is not deep enough.

Building on this context, the study introduces a coordinated optimization mechanism for multi-stakeholder interactions within a hierarchical decision-making framework. Firstly, the model of IES including CCS and P2G, and the market trading mechanism are introduced. Then, the payoff model and game framework of each subject are constructed separately. Subsequently, a distributed solving algorithm that protects the privacy of each subject is used to realize the balance between information privacy and market competition by the upper leader formulating a price strategy and the lower follower responding according to the price information provided. Scenario-based evaluations conclusively demonstrate the practical efficacy of the methodology introduced in this study.

Our work establishes the main innovations:

1.    A multi-energy coupled IES optimal scheduling model based on a master-slave game is established. By describing the behaviors of each subject of interest in IES, the problem of conflicting interests among each other is solved, and the interests of each subject are maximized.

2.    A refined CCS and P2G coupling model is constructed, as well as CET and GCT mechanisms are added to deeply explore the carbon reduction potential of IES.

3.    In this paper, a distributed solution algorithm is proposed, aiming to cope with the severe challenge of competition in the electricity market, while protecting the information privacy of each subject of interest. Unlike the traditional Stackelberg game approach, the algorithm does not need to disclose sensitive information such as participants’ objective functions, equipment parameters, or energy use preferences, which are regarded as trade secrets. The core mechanism of the algorithm is that the upper-tier leaders formulate pricing strategies, while the lower-tier followers make decisions based on the received price information, thus maintaining the fairness and stability of the market competition while safeguarding the information privacy.

2  IES Structure

The architecture of IES is shown in Fig. 1. Energy is supplied by wind turbine (WT), photovoltaic (PV), grid, and natural gas. The IES device mainly includes a gas boiler (GB), electric boiler (EB), micro turbine (MT), heat recovery boiler (HRB), absorption chiller (AC), hydrogen fuel cell (HFC), electric refrigeration unit (ERU). Within the combined cooling, heating, and power (CCHP), it consists of MT, HRB, and AC. IESO acts as a bridge between energy supply and demand, connecting the supply side, storage side and load side, and realizes the integrated operation of source, network, load and storage.

Figure 1: Structure of integrated regional energy system

The strategic behavior of IESO, ES, ESO and LA in the process of energy trading can be regarded as a kind of game, in which they formulate trading strategies and optimize the internal operation state according to their interests and environmental effects, respectively. The IESO is the coordinator and leader of the entire IES, assuming the three-way energy mobility and decision-making ability of source-load-storage, setting the energy purchase and sale prices according to the supply-demand relationship and market conditions, and purchasing the energy produced by the ES and selling it to the LA and the ESOs to earn profits. ES, as the energy supplier of IES, provides electricity, heat and cold energy to the system through multiple energy supply equipment. Aligning with the IESO’s established energy pricing framework, the ES dynamically optimizes the IES’s operational strategy to maximize profitability. ES also participates in the GCT and CET markets, taking the initiative to bear carbon emission penalties. LA re-optimizes load demand and reduces energy purchasing expenditures. ESO buys energy at a lower price to store it during low energy use periods and sells it at a higher price during peak energy use periods to make a profit.

3  System Model

3.1 CCS and P2G Coupling Model

CCS constitute climate mitigation frameworks that integrate post-combustion capture technologies with geological sequestration, targeting anthropogenic CO2 emissions from industrial flue streams and power generation units through mineralogical trapping mechanisms. The procedure begins with purifying flue gas by removing contaminants. A chemical solvent then interacts with CO2 in an absorption tower, isolating it from the gas stream. The pure CO2 is separated and transported by compression to a designated location, where it can be sequestered or used in the P2G process [20,21]. In the P2G process, the electrolysis cell (EL) and methane reactor (MR) are two key components. The EL utilizes electrical energy to break down water into hydrogen and oxygen, while the MR reacts CO2 with hydrogen to produce methane gas [22,23].

The advantage of coupling CCS with P2G is that it enables more efficient carbon cycling and emission reduction, thereby minimizing external carbon procurement expenditures and the risk of CO2 transportation. In addition, the energy expenditure of CCS systems is categorized into two primary components: fixed energy consumption and operational energy consumption. Fixed energy consumption refers to the energy and resources required to build the CCS equipment, which does not change with CCS operation. Operational energy consumption, on the other hand, exhibits a direct proportionality to the captured CO2 mass flow rate. In the coupled system, the CCS first captures and sequesters the CO2 released from the gas boilers and CCHP equipment in the system, and then uses the captured CO2 directly in the P2G process. In this way, it not only realizes CO2 reduction but also contributes to sustainable development. The coupled model of P2G and CCS is shown below:

{PCCSt=PCCS,ft+PCCS,otPCCS,ot=εCCSSCCStSCCSt=ηCCS(SGBt+SCCHPt)SELt=ηELPELtSMRt=ηMRPMR,H2tPMR,CO2t=φPMR,H2tmH2t=SELt/HH2mCH4t=SMRt/HCH4mMR,CO2t=mCH4tMCO2/MCH4SCCSt=mMR,CO2t+ms,CO2t(1)

where PCCSt, PCCS,ft, PCCS,ot are the total, fixed, and operational consumption of CCS at moment t, respectively; εCCS is the energy consumption factor for CCS; SCCSt is the amount of CO2 captured by the CCS at moment t; ηCCS is the efficiency of CO2 capture by CCS; SGBt, SCCHPt are the amount of CO2 produced by the gas boiler and CCHP unit at moment t, respectively; SELt, PELt are the hydrogen production power and power consumption power of the electrolysis cell at moment t, respectively; SMRt, PMR,H2t, PMR,CO2t are the power of gas production, hydrogen and carbon dioxide consumption of the methane reactor at moment t, respectively; ηEL, ηMR are the conversion efficiencies of the electrolysis cell and methane reactor, respectively; φ is the coefficient of utilization of carbon dioxide; mH2t, mCH4t are the masses of H2 and CH4, respectively, at moment t; HH2, HCH4 are the calorific values of H2 and CH4, respectively; MCO2, MCH4 are the molar masses of CO2 and CH4, respectively; mMR,CO2t, ms,CO2t are the CO2 supplied by the CCS to the methane reactor and the CO2 to be sequestered at moment t, respectively.

The operational power constraints and climb constraints for carbon capture are:

{0≤PCCSt≤PCCSmax∣PCCSt−PCCSt−1∣≤PCCSup(2)

where t denotes the moment; PCCSmax is the upper power limit of the CCS; PCCSup is the upper climb limit of the CCS.

P2G systems involve hydrogen generation through electrolytic cells as the initial stage of the energy conversion sequence. The operating power constraints and creep constraints of the electrolysis cell are:

{0≤PELt≤PELmax∣PELt−PELt−1∣≤PELup(3)

where t denotes the moment; PELmax is the upper power limit of the electrolysis cell; PELup is the upper climb limit of the electrolysis cell.

Methanation is the next step, and the methane reactor is operated with power constraints and climb constraints:

{0≤PMRt≤PMRmax∣PMRt−PMRt−1∣ ≤PMRup(4)

where t denotes the moment; PMRmax is the upper power limit of the methane generator; PMRup is the upper climb limit of the methane generator.

3.2 CCHP Model

CCHP unit integrates three core components—a gas turbine, waste heat recovery boiler, and absorption chiller—to simultaneously generate cooling, heating, and electricity through optimized natural gas utilization. This multi-functional design enhances energy efficiency while significantly reducing operational carbon footprints and energy waste. The mathematical model is shown below:

{PCCHPt=(QCH4,CCHPt+QH2,CCHPt)ηCCHPPHCCHPt=(QCH4,CCHPt+QH2,CCHPt)ηCCHPHCCCHPt=(QCH4,CCHPt+QH2,CCHPt)ηCCHPCQCH4,CCHPt=SCH4,CCHPtαCH4QH2,CCHPt=SH2,CCHPtαH2(5)

where ηCCHPP, ηCCHPH, ηCCHPC are the electrical, thermal and cooling efficiencies, respectively; PCCHPt, HCCHPt, CCCHPt are the electrical, thermal and cooling powers generated by the micro gas turbine, the waste heat recovery boiler and the absorption chiller at the moment t, respectively; QCH4,CCHPt, QH2,CCHPt are the powers corresponding to the natural gas and hydrogen consumed by the CCHP at the moment t, respectively; SCH4,CCHPt, SH2,CCHPt are the consumptive quantities of natural gas and hydrogen in the CCHP at the moment t, respectively; and αCH4, αH2are the natural gas and hydrogen power conversion coefficients.

CCHP running power constraints and climbing power constraints are:

{QCCHPmin⩽QCCHPt⩽QCCHPmaxQCCHPdown⩽QCCHPt−QCCHPt−1⩽QCCHPup(6)

where t denotes the moment; QCCHPmax, QCCHPmin are the upper and lower limits of the CCHP outflow, respectively; QCCHPup, QCCHPdown are the upper and lower limits of the CCHP climb rate, respectively.

3.3 Models of Energy Conversion Equipment

3.3.1 Gas Boiler Model

GB generates thermal energy through the combustion of natural gas, and the model for this high-carbon emission device is as follows:

{HGBt=ηGB(QCH4,GBt+QH2,GBt)QGBmin⩽QGBt⩽QGBmaxQGBdown⩽QGBt−QGBt−1⩽QGBupQCH4,GBt=SCH4,GBtαCH4QH2,GBt=SH2,GBtαH2(7)

where ηGB is the heat conversion efficiency of the gas boiler; HGBt is the heat production power of the boiler at the moment t; QCH4,GBt, QH2,GBt are the corresponding power of hydrogen and natural gas consumed by the gas boiler at the moment t, respectively; QGBmax, QGBmin are the upper and lower limits of the heat output of the gas boiler; QGBup, QGBdown are the upper and lower limits of the climb of the gas boiler; SCH4,GBt, SH2,GBt are the consumption of natural gas and hydrogen in GB at the moment t, respectively.

3.3.2 Electric Heating Boiler Model

Through electrothermal conversion, the boiler elevates water to steam or high-temperature liquid states to supply heat, which is modeled as follows:

{HEBt=ηEBPEBtPEBmin⩽PEBt⩽PEBmaxPEBdown⩽PEBt−PEBt−1⩽PEBup(8)

where HEBt, PEBt are the heat-producing and power-consuming power of the electric heating boiler at the moment t; ηEB is the energy conversion efficiency of the electric heating boiler; PEBmax, PEBmin are the upper and lower limits of the electric heating boiler’s output; and PEBup, PEBdown are the upper and lower limits of the electric heating boiler’s climb.

3.3.3 Model of Electric Refrigerator

Through a series of compression, expansion and other processes, the electric refrigeration machine realizes the refrigeration of air or other media, converting electrical energy into cooling capacity, which is modeled as follows:

{CERUt=ηERUPERUtPERUmin⩽PERUt⩽PERUmaxPERUdown⩽PERUt−PERUt−1⩽PERUup(9)

where CERUt, PERUt are the cold power and power consumption power generated by the electric cooler at moment t; ηERU is the energy conversion efficiency of the electric cooler; PERUmax, PERUmin are the upper and lower limits of the output power of the electric cooler; PERUup, PERUdown are the upper and lower limits of the climb of the electric cooler.

3.3.4 Photovoltaic Unit Model

Photovoltaic systems transform sunlight into electrical energy. During operation, the generated power of PV panels correlates linearly with solar irradiance intensity. The output power of the photovoltaic unit is modeled as follows:

{PPVt=PSTCSSSTC[1+λ(TC−TSTC)]PPV,pt=PPVt+PPV,at0⩽PPVt⩽PPV,pt(10)

where PPVt, PPV,pt, PPV,at are the actual output power, predicted power, and abandoned the power of the PV unit at moment t, respectively; PSTC is the maximum output power under the standard conditions (light intensity of 1000 W/m2 and ambient temperature of 25°C); S is the actual light intensity during the operation cycle of the PV unit; SSTC is the light intensity of the PV panels under the standard conditions; λ is the temperature coefficient of the power; TC is the temperature of the PV panels’ surface; TSTC is the temperature of the PV panels’ surface under the standard conditions.

3.3.5 Wind Turbine Model

Wind power generation hinges on wind speed, but its variability demands rigorously defined operational limits (cut-in/cut-out speeds), which structure the model’s technical framework:

PWTt={0,νt<νwiνt3−νwi3νo3−νwi3Po,νwi≤νt≤νoPo,νo≤νt≤νwo0,νt>νwo(11)

{PWT,pt=PWTt+PWT,at0⩽PWTt⩽PWT,pt(12)

where PWTt, PWT,pt, PWT,at are the actual output power, predicted power, and abandoned power of the WT at moment t, respectively; νt is the wind speed at moment t; νwi is the cut-in wind speed; νwo is the cut-out wind speed; νo is the rated wind speed; Po is the rated output power of the wind turbine.

3.3.6 Hydrogen Fuel Cell Model

A hydrogen fuel cell converts the energy produced by burning hydrogen into electrical output and also produces a large amount of heat, which is modeled as follows:

{PHFCt=ηHFCePH2,HFCtHHFCt=ηHFChPH2,HFCtPH2,HFCmin≤PH2,HFCt≤PH2,HFCmaxΔPH2,HFCmin≤PH2,HFCt−PH2,HFCt−1≤ΔPH2,HFCmaxκHFCmin≤PHFCt/HHFCt≤κHFCmax(13)

where PHFCt, HHFCt are the electric and thermal power generated by the fuel cell at moment t, respectively; ηHFCe, ηHFCh are the electric and thermal power produced by the fuel cell, respectively; PH2,HFCt is the hydrogen power consumed by the fuel cell at moment t; PH2,HFCmax, PH2,HFCmin are the upper and lower limits of the hydrogen power supplied to the hydrogen fuel cell by the electrolysis cell; ΔPH2,HFCmin, ΔPH2,HFCmax are the upper and lower limits of the creeping power of the hydrogen fuel cell; κHFCmin, κHFCmax are the upper and lower limits of the thermoelectricity ratio of the hydrogen fuel cell.

3.4 Models of Energy Storage Device

The energy storage device includes hydrogen storage tank (HST), thermal storage tank (TST), electric energy storage (EES), and cold storage tank (CST), which are similar in the process of energy charging and discharging but differ in capacity storage. Attaining optimized energy storage and adaptive allocation demands coordinated integration of multi-energy systems to ensure equilibrium between energy generation and consumption. The mathematical model is as follows:

{STSTt=STSTt−1(1−δTST)+(HTSTt,chηTSTch−HTSTt,disηTSTdis)ΔtSEESt=SEESt−1(1−δEES)+(PEESt,chηEESch−PEESt,disηEESdis)ΔtSCSTt=SCSTt−1(1−δCST)+(CCSTt,chηCSTch−CCSTt,disηCSTdis)ΔtSHSTt=SHSTt−1(1−δHST)+(PHSTt,chηHSTch−PHSTt,disηHSTdis)Δt(14)

where STSTt, SEESt, SCSTt, SHSTt indicate the capacity of heat storage, electricity storage, cold storage and hydrogen storage equipment at the moment t, respectively; δTST, δEES, δCST, δHST indicate the self-loss coefficient of heat storage, electricity storage, cold storage, and hydrogen storage equipment, respectively; HTSTt,ch, HTSTt,dis indicate the charging and discharging heat power of heat storage equipment at the moment t; PEESt,ch, PEESt,dis indicate the charging and discharging power of electricity storage equipment at themomentt; CCSTt,ch, CCSTt,dis indicate the charging and discharging cold power of cold storage equipment at the moment t; PHSTt,ch, PHSTt,dis denote the charging and discharging hydrogen power of the hydrogen storage equipment at the moment t; ηTSTch, ηTSTdis denote the thermal energy charging and discharging efficiency; ηEESch, ηEESdis denote the electrical energy charging and discharging efficiency; ηCSTch, ηCSTdis denote the cold energy charging and discharging efficiency; and ηHSTch, ηHSTdis denote the hydrogen energy charging and discharging efficiency.

The constraints are the same for heat, electricity, cold, and hydrogen storage equipment, so only the heat storage constraints are described, and the same for electricity, cold, and hydrogen storage equipment constraints, which are as follows:

{STSTmin≤STSTt≤STSTmax0≤HTSTt,ch≤uTSTt,chHTSTch,max0≤HTSTt,dis≤uTSTt,disHTSTdis,max0≤uTSTt,dis+uTSTt,ch≤1STST1=STST24(15)

where STSTmax, STSTmin for the upper and lower limits of heat storage capacity; HTSTch,max, HTSTdis,max for the maximum charging and discharging power of the heat storage equipment; uTSTt,ch, uTSTt,dis for the charging and discharging state of the equipment at the moment t, for the 0–1 variable, not working at 0, working at 1; STST1 for the initial capacity of the heat storage equipment; STST24 for the capacity of the heat storage equipment at the end of the most important moment.

4  Market Trading Mechanisms

4.1 Carbon Trading Mechanism

In compliance with China’s established carbon quota management scheme, carbon emission allowances have become an important trading asset in the market and can be freely traded in various carbon markets. In China, the initial allocation of allowances is generally done on a free-of-charge basis, and the government regularly accounts for the carbon emissions of enterprises to make timely adjustments to the allowances [24]. When there is a discrepancy between the actual production of the enterprise and the pre-quota, the government department will make up for the discrepancy according to the actual situation, to ensure the accuracy of the enterprise’s carbon emission quota [25,26]. The carbon emission allowances discussed in this paper cover three major categories: power purchase allowances, CCHP allowances, and GB allowances. Carbon allowance distribution for power procurement is proportional to the volume of electricity sourced from external grids, which predominantly rely on fossil-fuel-based generation. In the study, the CET mechanism is refined to the hour, and each hour is optimized to record the carbon quota and the corresponding carbon emission, and then liquidated by the hour at the end of a cycle. The expression is as follows:

EW=EB+ECCHP+EGB(16)

{EB=χeΣt=1TPE.buytECCHP=χg[Σt=1T(PCCHPt+μheHCCHPt+μhcCCCHPt)]EGB=χgΣt=lTHGBt(17)

where EW is the unremunerated carbon emission quota of the integrated energy system; EB, ECCHP, EGB are the unremunerated carbon emission quota of purchased electricity, CCHP and GB, respectively; PE.buyt is the purchased interactive power at moment t; χe, χg are the carbon emission right quota coefficients of natural gas consumption per unit of electricity, specifically 0.728 and 0.3672, respectively; μhe, μhc are the electricity-heat and cold-heat conversion coefficients, specifically 6 and 3.6, respectively.

The IES’s net carbon footprint aggregates direct emissions from CCHP and GB operations, indirect emissions linked to electricity procurement, and deducts emissions mitigated through P2G conversion processes. The expression is as follows:

Eair=EB−a+ECCHP−a+EGB−a−EP−a(18)

{EB−a=εeΣt=1TPE.buytECCHP−a=εglΣt=1TQCH4,CCHPtEGB−a=εg2Σt=1TQCH4,GBtEP−a=ξCO2Σt=1TPMR,H2t(19)

where Eair, EB−a, ECCHP−a, EGB−a, EP−a are the actual total carbon emissions of the integrated energy system, the equivalent CO2 generated by the actual power purchase, the CO2 generated by the actual CCHP operation process, the CO2 generated by the actual GB operation process, and the CO2 handled by the P2G, respectively; εe is the calculation coefficient of the carbon emissions of the thermal power purchased from the grid, which is specifically 1.08; εgl, εg2 are the carbon emission coefficients of the natural gas-fired energy supply of CCHP and GB, which are specifically 0.789 and 0.25, respectively; ξCO2 is the parameter of CO2 absorption by the P2G equipment, which is specifically 0.9.

Net carbon emissions E are actual carbon emissions minus compliance allowances allocated:

E=Eair−EW(20)

This study proposes a laddering carbon trading framework that imposes hierarchically defined emission constraints through segmented emission thresholds, contrasting with conventional homogeneous trading systems, thereby establishing compliance costs based on differentiated allowance allocation across defined carbon intensity brackets. The calculation model of CET is as follows:

CCET={−χ(2+3θ)L+χ(1+3θ)(E+2L),E≤−2L−χ(1+θ)L+χ(1+2θ)(E+L),−2L<E≤−Lχ(1+θ)E,−L<E≤0χE,0<E≤LχL+χ(1+θ)(E−L),L<E≤2Lχ(2+θ)L+χ(1+2θ)(E−2L),2L≤E(21)

where χ is the carbon trading base price of 120 CNY/t; L is the length of the carbon emission interval 15; θ is the carbon trading price growth rate of 0.25; CCET is the systematic carbon trading cost, and the coefficients are positive for buying and negative for selling.

4.2 Green Certificate Trading Mechanism

The GCT mechanism is based on the renewable energy generation quota, when the actual renewable energy power produced by the system fails to meet the established quota requirements, obligated entities procure green certificates to make up the difference, to achieve the renewable energy quota target. If the quota requirements are exceeded, it is possible to make a profit from the sale of green certificates. Analogous to laddered carbon trading, the study uses a laddered GCT mechanism. The model for GCT is as follows:

Sres=κgcΣt=1TPLoadt(22)

SN=Σt=1T(SPVt+SWTt)1000(23)

EGCT=Sres−SN(24)

CGCT={−xGCT(2+d)U+xGCT(1+2d)(EGCT+2U),EGCT≤−2U−xGCTU+xGCT(1+d)(EGCT+U),−2U<EGCT≤−UxGCTEGCT,−U<EGCT≤0xGCT(1+d)EGCT,0<EGCT≤UxGCT(1+d)U+xGCT(1+2d)(EGCT−U),U<EGCT≤2UxGCT(2+3d)U+xGCT(1+3d)(EGCT−2U),2U<EGCT(25)

where Sres for the green certificate quota index; κgc for the green certificate quota coefficient; PLoadt for the t moment of the electric load power; SN for the actual consumption; SPVt, SWTt respectively in t moment of photovoltaic and wind power consumption; EGCT for the participation of the green certificate of the trading volume; xGCT for the green certificate base price of 60 CNY; U for the green certificate trading interval length of 100; d for the green certificate price growth rate of 0.25; CGCT for the green certificate transaction costs, coefficients for the positive representative of the purchase, and a negative coefficient represents a sale.

5  Modeling the Benefits of System’s Subjects

Due to the geographic location of the IES in the study, cooling is supplied to users from May to October, and heating is supplied to users from November to April. Although there is a difference in the way heat energy and cold energy are converted, the transaction mode is roughly the same, and this paper chooses to analyze the heat supply mode.

5.1 Integrated Energy System Operator Revenue Model

The IESO formulates bid-based energy pricing through continuous monitoring of generation-demand balances and market conditions, and when there is an imbalance between energy supply and demand in IES, IESO needs to interact with the main grid. The objective function of IESO mainly includes the trading revenue, operational expenditures for purchasing energy, and the cost of interacting with the higher level of the electricity, heat, and gas grids. The specific expressions are as follows:

{maxIIESO=Σt=1T(RIESO.Et+RIESO.Ht+RIESO.Gt−CIESO.Et−CIESO.Ht−CIESO.Gt)RIESO.Et=cE.selltQE.sellt−cE.buytQE.buytRIESO.Ht=cH.selltQH.sellt−cH.buytQH.buytRIESO.Gt=cG.selltQG.sellt−cG.buytQG.buytCIESO.Et=cE.timetPE.buyt+cE.nettPE.selltCIESO.Ht=cH.maxtPH.buyt+cH.mintPH.selltCIESO.Gt=cG.maxtSG.buyt+cG.mintSG.sellt(26)

where IIESO is the revenue of IESO; RIESO.Et, RIESO.Ht, RIESO.Gt are the net revenues from electricity, heat and gas transactions at moment t, respectively; CIESO.Et, CIESO.Ht, CIESO.Gt are the costs of the operator’s interactions with the higher-level grid, the heat grid, and the gas grid at moment t, respectively; cE.sellt, cH.sellt, cG.sellt are the prices at which the electricity, heat and gas energy are sold at moment t, respectively; cE.buyt, cH.buyt, cG.buyt are the prices at which the electricity, heat and gas energy are purchased at moment t, respectively; QE.sellt, QH.sellt, QG.sellt are the power of electricity, heat and gas energy sold at moment t; QE.buyt, QH.buyt, QG.buyt are the power of electricity, heat and gas energy purchased at moment t, respectively; cE.nett, cE.timet are the feed-in tariff and time-of-day tariff at moment t, respectively; cH.mint, cH.maxt are the lower and upper limits of the heat price at moment t, respectively; cG.mint, cG.maxt are the lower and upper limits of the gas price at moment t, respectively; PE.buyt, PE.sellt are the purchased and sold power from the higher-level grid at moment t, respectively; PH.buyt, PH.sellt are the purchased and sold power from the higher-level heat grid at moment t, respectively; and SG.buyt, SG.sellt are the purchased and sold volume of gas from the higher-level gas grid at moment t, respectively.

To avoid LAs and ESOs trading directly with the main grid, the IESO shall establish procurement rates exceeding feed-in tariff benchmarks while implementing selling rates below the dynamic pricing structure of the time-of-use grid tariffs. To satisfy their interests, the purchase price of electricity should be smaller than the time-of-use grid tariffs and the sale price of electricity should be larger than the feed-in tariff. At the same time, the prices for purchasing and selling thermal energy are within a reasonable market price range, respectively, with the following constraints:

{cE.nett⩽cE.sellt⩽cE.timetcE.nett⩽cE.buyt⩽cE.timetcH.mint⩽cH.sellt⩽cH.maxtcH.mint⩽cH.buyt⩽cH.maxtcG.mint⩽cG.sellt⩽cG.maxtcG.mint⩽cG.buyt⩽cG.maxt(27)

The IES is identical to the different forms of energy interaction constraints and only the grid interaction constraints are described. It is specified as follows:

{0≤PE.buyt≤ωbuytPE.max0≤PE.sellt≤ωselltPE.max(28)

where ωbuyt, ωsellt are the binary sign coefficients for purchasing and selling electricity at moment t, respectively; PE.max is the upper limit of the amount of electricity interacting with the higher grid.

5.2 Energy Supplier Revenue Model

Guided by the IESO’s pricing framework and demand conditions, the ES optimizes unit generation levels to enhance profitability through strategic operational adjustments. The ES maximum target revenue function is as follows:

{maxIES=Σt=1T(RES.sellt−CCET−CGCT−Cc−Cr)RES.sellt=cE.buytPES.pι+cH.buytHES.pt+cG.buytSMRt−cE.selltPES.ct−cG.selltSES.ctCc=aE(PCCHPt)2+bEPCCHPt+dE+aH(HGBt+HCCHPt)2+bH(HGBt+HCCHPt)+dHCr=Σi=1IKiPitPES.pt=PPVt+PWTt+PCCHPt+PHFCtHES.pt=HGBt+HEBt+HCCHPt+HHFCtPES.ct=PCCSt+PELt+PEBtSES.ct=SCH4,GBt+SCH4,CCHPt(29)

where IES is the revenue from ES; RES.sellt is the net revenue from energy sales at moment t; CCET, CGCT are the CET and GCT costs, respectively; Cc, Cr are the O&M and fuel costs, respectively; PES.pt, HES.pt are the electric and thermal power produced at moment t, respectively; PES.ct, SES.ct are the electric power and gas consumption consumed at moment t, respectively; aE, bE, dE (aH, bH, dH) are the fuel cost coefficients; and Ki is the coefficient of the energy conversion equipment (CCS, P2G, CCHP, GB, EB) operation and maintenance cost coefficients; Pit is the output power of the energy conversion equipment at moment t before the day.

5.3 Energy Storage Operator Revenue Model

Following the pricing signals set by the IESO for electricity transactions, the ESO optimizes energy storage charge/discharge patterns to balance supply-demand peaks and valleys, thereby generating revenue through grid stabilization. The ESO’s maximum target revenue function is as follows:

{maxIESO=Σt=1T(RESO.Et+RESO.Ht+RESO.HSTt−CESOt)RESO.Et=cE.buytQESO.Et−cE.selltEESO.EtRESO.Ht=cH.buytQESO.Ht−cH.selltEESO.HtRESO.HSTt=cE.buytPHFCt+cH.buytHHFCt+cH2QHST.selltCESOt=Σt=1T[KEES(PEESt,ch+PEESt,dis)+KTST(HTSTt,ch+HTSTt,dis)+KHST(PHSTt,ch+PHSTt,dis)](30)

where IESO is the ESO’s revenue; RESO.Et, RESO.Ht, RESO.HSTt, CESOt are the ESO’s net revenues from electricity storage, net revenues from heat storage, net revenues from hydrogen storage, and O & M costs, respectively; QESO.Et, EESO.Et are the electricity sold and purchased by electricity storage; QESO.Ht, EESO.Ht are the heat sold and purchased by heat storage; QHST.sellt is the amount of hydrogen sold by hydrogen storage; cH2 is the price of hydrogen; KEES, KTST, KHST are the operation and maintenance factors for the charging and discharging of the electricity, heat, and hydrogen storage.

5.4 Load Aggregator Revenue Model

LA can regulate its flexible load distribution based on energy prices set by the IESO with the following maximum objective benefit function:

{maxILA=Σt=1T(yut−RLA.buyt)yut=[wELe.trt+wHLh.trt−vE2(Le.cutt)2−vH2(Lh.cutt)2]ΔtRLA.buyt=cE.selltQLA.Et+cH.selltQLA.HtQLA.Et=Le.orit+Le.trt−Le.cuttQLA.Ht=Lh.orit−Lh.trt−Lh.cutt(31)

where ILA is the LA’s revenue; yut is the user satisfaction function; RLA.buyt is the cost of purchased energy; wE, vE are the preference coefficients for users’ consumption of electrical energy; wH, vH are the preference coefficients for users’ consumption of thermal energy; QLA.Et, QLA.Ht are the power of electrical and thermal energy purchased by the load aggregator, respectively; Le,orit, Le,cutt, Le,trt are the base load, curtailable load, and shifted load for electrical load, respectively; Lh,orit, Lh,cutt, Lh,trt are the base load, curtailable load, and shifted load for thermal load, respectively.

In the case of electrical loads, the constraints on the shifted loads are as follows:

{0⩽Le.trt⩽Le.tr.maxtΣt=1TLe.trtΔt=WFL.E(32)

where Le.tr.maxt is the upper limit of the transferable load; WFL.E is the total amount of transferable load.

In the case of electrical loads, the constraints on the curtailable loads are as follows:

{ηmin≤Σt=1Tηt≤ηmax0≤Σt=kk+Nmax−1ηt≤NmaxTmin≤Σμ=1μ+TC−1Le.cutt≤Tmax(33)

where ηmin, ηmax are the minimum and maximum number of load cuts, and Nmax is the maximum number of continuous cuts limit. TC is the length of load cuts, and Tmax, Tmin are the upper and lower limits of the maximum and minimum continuous load cuts length.

6  Master-slave Game Framework for Integrated Energy Systems

6.1 Game Model

In the IES, the multi-subject master-follower game describes the decision-making process in which IESO, ES, ESO and LA pursue the optimization of their respective objectives. ES, ESO and LA act as followers, optimizing their own strategies according to the price strategies of the IESO, the upper-level leader, and finally obtaining the optimal solution of the game equilibrium.

The formalized analytical structure representing the game’s dynamics is detailed below:

{ϕ={P;S;I}P={PIESO;PES;PESO;PLA}S={SIESO;SES;SES0;SLA}I={IIESO;IES;IESO;ILA}(34)

where P, S, and I are the participants, strategy sets, and payoffs of the master-slave game, respectively; PIESO, PES, PESO, PLA are the four participants, which are the participant IESO, the participant ES, the participant ESO, and the participant LA, respectively; SIESO, SES, SESO, SLA are the four strategies, which are the sets of IESO, ES, ESO, and LA, respectively.

The specific set of strategies is listed below:

{SIESO={cE.sellt,cH.sellt,cG.sellt,cE.buyt,cH.buyt,cG.buyt}SES={PPVt,PWTt,PCCHPt,PHFCt,HGBt,HEBt,HCCHPt,HHFCt,PCCSt,PELt,PEBt,SCH4,GBt,SCH4,CCHPt,SMRt}SESO={QESO.Et,QESO.Ht,EESO.Et,EESO.Ht}SLA={Le.trt,Lh.trt,Le.cutt,Lh.cutt}(35)