Cooperative Game-Theoretic Scheduling for Low-Carbon Integrated Energy Systems with P2G–CCS Synergy

Abstract

In the context of the dual-carbon goals, this study proposes a cooperative game-theoretic optimization strategy to enhance the energy utilization efficiency, operational efficiency, and cost-effectiveness of integrated energy systems (IESs) while simultaneously reducing carbon emissions, improving operational flexibility, and mitigating renewable energy variability. To achieve these goals, an IES framework integrating power-to-gas (P2G) technology and carbon capture and storage (CCS) facilities is established to regulate carbon emissions. The system incorporates P2G conversion units and thermal components—specifically, hydrogen fuel cells, electrolyzers, reactors, and electric boilers—aiming to maximize energy conversion efficiency and asset utilization. A cooperative game-theoretic optimization model is developed to facilitate collaboration among multiple stakeholders within the coalition, which employs the Shapley value method to ensure equitable distribution of the cooperative surplus, thereby maximizing collective benefits. The model is solved using an improved gray wolf optimizer (IGWO). The simulation results demonstrate that the proposed strategy effectively coordinates multi-IES scheduling, significantly reduces carbon emissions, facilitates the efficient allocation of cooperation gains, and maximizes overall system utility.

1. Introduction

Amid escalating global energy crises and environmental challenges [1,2,3], IESs have emerged as a critical solution for addressing inefficient energy utilization and high carbon emissions, achieved through the coordinated integration of multi-form energy carriers and optimized cross-sectoral synergy [4,5,6]. The optimized scheduling of IESs not only ensures energy supply–demand equilibrium but also enhances systemic efficiency while mitigating environmental impacts [7,8,9,10].

Current research on IESs has extensively explored optimal operation strategies. The studies in [11,12] adopted supply–demand coordination to develop IES scheduling models that account for coupled cooling, heating, and power demand characteristics. These models demonstrate enhanced economic performance in park-level implementation while facilitating renewable energy integration. The studies in [13,14] focused on system flexibility and economic performance by analyzing multi-energy conversion efficiency encompassing cooling, heating, electricity, and gas. These studies established multi-timescale scheduling frameworks that span day-ahead, intra-day, and real-time operations, highlighting the strengths of IESs in terms of energy complementarity, flow regulation, and operational adaptability, thereby forming a foundational architecture. The studies in [15] proposed a collaborative scheduling model for multi-region integrated energy systems (MIESs). This model establishes a hierarchical thermal energy mechanism to enable cross-system cascaded waste heat utilization, designs dynamic interactive electricity pricing, and develops an adaptive-step regularized alternating direction method of multipliers (AR-ADMM). The approach enhances solution efficiency while preserving participant data privacy. This model demonstrates synergistic benefits between IES operators and users, lowering system energy procurement costs while enhancing operator revenues.

To address wind curtailment arising from insufficient operational flexibility and wind power’s anti-peak shaving nature, P2G technology is incorporated due to its multifunctional capabilities. P2G conversion enables bidirectional electricity-to-gas conversion, provides flexible load regulation, and enhances storage reliability through synergistic operation with gas storage [16]. Existing research has focused on establishing P2G–carbon capture synergy, where the CO₂ captured by CCS serves as feedstock for P2G conversion, forming a closed-loop carbon system [17]. The study in [18] proposed a virtual power plant (VPP) incorporating P2G–CCS coupling and established a stepped carbon trading-based optimal scheduling framework. The study in [19] proposed a wind power-integrated VPP model with P2G–CCS coupling for combined heat and power (CHP) systems. The coordinated operation of ground source heat pumps (GSHPs) and P2G–CCS units in this configuration enhances wind power utilization while reducing carbon emissions and operational costs.

Existing research on integrated energy systems with carbon capture and P2G conversion has predominantly focused on system-wide optimization, often neglecting the substantive exploration of multi-operator collaboration frameworks and their prerequisites. Resolving this challenge requires ensuring the equitable distribution of benefits, with game theory providing essential tools in this context. Consequently, this study employs game theory to address these issues. The study in [20] developed a two-layer optimal scheduling model involving multiple energy sources, establishing a cooperative game framework among VPP members aimed at profit maximization. The study in [21] proposed a non-cooperative game-based bi-level optimization model that minimizes daily costs while maximizing system performance through inter-temporal interaction, resulting in reduced operational expenses and improved energy efficiency. Although the conventional Shapley value method is a canonical benefit allocation mechanism in game theory recognized for its theoretical fairness and rationality, its practical application faces limitations, including computational complexity, operational inefficiency, and contextual constraints. The study in [22] introduced a cooperative allocation approach using an enhanced Shapley value method. This approach first employs Shapley values for the initial distribution, then applies dimension reduction, establishes collaborative indices for refined allocation, and achieves an efficient benefit distribution. Consequently, establishing cooperative alliances using game theory is critical to addressing the economic inefficiency of independently deployed P2G or carbon capture facilities. This approach integrates P2G conversion’s renewable energy accommodation capacity with carbon capture’s deep decarbonization potential, while implementing equitable profit distribution to ensure coalition stability and enhance overall cooperative benefits. Building on this concept, the ADR mechanism in [15] advances the framework through a dual-layer dispatch architecture and dynamic pricing strategies, reducing system peak–valley differentials and further boosting collaborative benefits.

As the scale of multi-energy interconnections expands, system interaction security concerns become prominent. The study in [23] pioneered a cyber–physical contingency (CPC) N-1 assessment framework for integrated electricity–gas systems (IEGSs). This framework (1) establishes a nonlinear partial differential–algebraic equation (PDAE) model characterizing boundary condition changes triggered by CPCs, (2) develops a variable-coefficient analytical method (VC-AM) to circumvent discretization errors inherent in traditional numerical approaches, and (3) reveals how cyber–physical interdependence amplifies failure impacts. This research study provides a foundation for ensuring system security under coordinated operation.

Focusing on an IES incorporating carbon capture, P2G conversion, electric boilers, renewables, and storage, this study proposes a cooperative game-based optimization strategy. The strategy establishes a framework that balances stakeholder interests, employs the IGWO algorithm to resolve benefit allocation and ensure coalition stability, and targets dual optimization for both low-carbon and economic benefits. Through coordinated multi-energy conversion, it achieves synergistic reductions in emissions and efficiency goals. Case studies validate its effectiveness in ensuring equitable profit distribution, optimizing energy conversion efficiency, and realizing system-wide emission reduction–economic synergies.

2. Multi-Agent IES

2.1. IES Architecture

The IES architecture is shown schematically in Figure 1. A regional implementation case study, detailed in Figure 2, comprises three functionally distinct entities: a carbon capture plant (CCP), equipped with CCS systems and P2G conversion facilities; a combined heat and power plant (CHPP) that integrates gas-fired boilers, electric boilers, P2G units, thermal energy storage, and CHP units; and a low-carbon energy supplier (LCES) that comprises photovoltaic arrays, lithium-ion battery banks, and wind turbine clusters. The system loads consist of thermal and electrical loads.

2.2. IES Mathematical Model

2.2.1. P2G Equipment

P2G technology stores surplus electricity through methane synthesis in a two-stage process: (1) hydrogen production via water electrolysis in an electrolyzer, followed by (2) methanation in a reactor, where hydrogen reacts with carbon dioxide to produce CH₄. This study investigated the synergistic integration of P2G and lithium-ion batteries (LIBs) in an IES. LIBs are employed for short-term electricity storage and grid fluctuation smoothing, while P2G technology enables efficient P2G conversion, effectively mitigating LIB overcharge and overdischarge issues. Furthermore, P2G leverages natural gas network infrastructure for large-scale, long-term energy storage and cross-regional energy transmission. The mathematical model with governing constraints is formulated as follows:

$$\left\{\begin{array}{l}{V}_{\mathrm{Gas}}\left(t\right)={\displaystyle \frac{3600{\phi }_{\mathrm{P}2\mathrm{G}}{P}_{\mathrm{P}2\mathrm{G}}\left(t\right)}{K_{\mathrm{Gas}}}}\hfill \\ Q_{\mathrm{P}2\mathrm{G}}\left(t\right)={\lambda }_{{\mathrm{CO}}_2}{\phi }_{\mathrm{P}2\mathrm{G}}{P}_{\mathrm{P}2\mathrm{G}}\left(t\right)\hfill \\ P_{P2G}^{\min }\le P_{\mathrm{P}2\mathrm{G}}\left(t\right)\le P_{P2G}^{\max }\hfill \\ \mathsf{\Delta }{P}_{P2G}^{\min }\le P_{\mathrm{P}2\mathrm{G}}\left(t\right)-P_{\mathrm{P}2\mathrm{G}}\left(t-1\right)\le \mathsf{\Delta }{P}_{P2G}^{\max }\hfill \end{array}\right.$$

(1)

where $Q_{\mathrm{P}2\mathrm{G}}\left(t\right)$ is the amount of ${\mathrm{CO}}_2$ consumed by P2G equipment, t; $V_{\mathrm{Gas}}\left(t\right)$ is the volume of natural gas generated by P2G equipment, $m^3$; $K_{\mathrm{Gas}}$ is the low calorific value of natural gas combustion, $MJ/m^3$; ${\phi }_{\mathrm{P}2\mathrm{G}}$ is the efficiency of the electric-to-gas conversion device; ${\lambda }_{{\mathrm{CO}}_2}$ is the amount of ${\mathrm{CO}}_2$ required to generate natural gas per unit power, t; $P_{\mathrm{P}2\mathrm{G}}\left(t\right)$ is the electrical power consumed in the P2G facility at time t.; $P_{P2G}^{\min }$ and $P_{P2G}^{\max }$ are the minimum and maximum power consumption values of the electric-to-gas conversion device, respectively; and $\mathsf{\Delta }{P}_{P2G}^{\min }$ and $\mathsf{\Delta }{P}_{P2G}^{\max }$ are the lower and upper limits of the ramp-up rate of device power consumption.

2.2.2. CHP Equipment

CHP equipment significantly improves energy efficiency by simultaneously generating electricity and useful heat from natural gas input, utilizing waste heat from power generation and industrial processes.

$$\left\{\begin{array}{l}{P}_{H,\mathrm{CHP}}(t)={\alpha }_{H,\mathrm{CHP}}{P}_{\mathrm{G},\mathrm{CHP}}(t)\hfill \\ P_{\mathrm{E},\mathrm{CHP}}(t)={\alpha }_{\mathrm{E},\mathrm{CHP}}{P}_{\mathrm{G},\mathrm{CHP}}(t)\hfill \\ P_{\mathrm{G},\mathrm{CHP}}^{\min }\le P_{\mathrm{G},\mathrm{CHP}}(t)\le P_{\mathrm{G},\mathrm{CHP}}^{\max }\hfill \\ \begin{array}{l}\mathsf{\Delta }{P}_{\mathrm{G},\mathrm{CHP}}^{\min }\le P_{\mathrm{G},\mathrm{CHP}}(t+1)\\ -P_{\mathrm{G},\mathrm{CHP}}(t)\le \mathsf{\Delta }{P}_{\mathrm{G},\mathrm{CHP}}^{\max }\end{array}\hfill \end{array}\right.$$

(2)

where $P_{\mathrm{G},\mathrm{CHP}}(t)$ is the natural gas power input to the equipment at time t; $P_{H,\mathrm{CHP}}(t)$ is the thermal energy output from the equipment at time t; $P_{\mathrm{E},\mathrm{CHP}}(t)$ is the electrical energy output from the equipment at time t; ${\alpha }_{H,\mathrm{CHP}}$ and ${\alpha }_{\mathrm{E},\mathrm{CHP}}$ are the conversion efficiencies of the thermal and electrical energy of the equipment, respectively; $P_{\mathrm{G},\mathrm{CHP}}^{\max }$ and $P_{\mathrm{G},\mathrm{CHP}}^{\min }$ are the upper and lower limits of the input power of the equipment, respectively; and $\mathsf{\Delta }{P}_{\mathrm{G},\mathrm{CHP}}^{\max }$ and $\mathsf{\Delta }{P}_{\mathrm{G},\mathrm{CHP}}^{\min }$ are the upper and lower limits of the climbing rate of the equipment, respectively.

2.2.3. CCS Facilities

CCS facilities capture, purify, and compress the CO₂ produced in energy or industrial production for storage.

CCS equipment:

$$\left\{\begin{array}{l}{P}_{\mathrm{CCS}}(t)=P_{\mathrm{E},\mathrm{CCS}}(t)+P_{\mathrm{N},\mathrm{CCS}}(t)\hfill \\ P_{\mathrm{CCS}}^{\min }\le P_{\mathrm{CCS}}(t)\le P_{\mathrm{CCS}}^{\max }\hfill \\ \mathsf{\Delta }{P}_{\mathrm{CCS}}^{\min }\le P_{\mathrm{CCS}}(t+1)-P_{\mathrm{CCS}}(t)\le \mathsf{\Delta }{P}_{\mathrm{CCS}}^{\max }\hfill \\ P_{\mathrm{Oc},\mathrm{CCS}}(t)={\lambda }_{\mathrm{C}{\mathrm{O}}_2}{L}_{\mathrm{C},\mathrm{C}{\mathrm{O}}_2}(t)\hfill \\ P_{\mathrm{C},\mathrm{CCS}}(t)=P_{\mathrm{Fc},\mathrm{CCS}}(t)+P_{\mathrm{Oc},\mathrm{CCS}}(t)\hfill \\ \mathsf{\Delta }{P}_{\mathrm{C},\mathrm{CCS}}^{\min }\le P_{\mathrm{C},\mathrm{CCS}}(t+1)\hfill \\ \begin{array}{l}-P_{\mathrm{C},\mathrm{CCS}}(t)\le \mathsf{\Delta }{P}_{\mathrm{C},\mathrm{CCS}}^{\max }\\ L_{\mathrm{D},\mathrm{C}{\mathrm{O}}_2}(t)={\beta }_{\mathrm{C}}{P}_{\mathrm{CCS}}(t)-L_{\mathrm{C},\mathrm{C}{\mathrm{O}}_2}(t)\end{array}\hfill \\ L_{\mathrm{Q},\mathrm{C}{\mathrm{O}}_2}(t)={\beta }_{\mathrm{Q}}{P}_{\mathrm{CCS}}(t)\hfill \end{array}\right.$$

(3)

where $P_{\mathrm{CCS}}(t)$ is the actual power of the carbon capture power plant at time t; $P_{\mathrm{E},\mathrm{CCS}}(t)$ is the power supplied to the carbon capture equipment by the carbon capture power plant at time t; $P_{\mathrm{N},\mathrm{CCS}}(t)$ is the online power of the carbon capture power plant at time t; $P_{\mathrm{CCS}}^{\max }$ and $P_{\mathrm{CCS}}^{\min }$ are the upper and lower limits of the output of the carbon capture power plant, respectively; $\mathsf{\Delta }{P}_{\mathrm{CCS}}^{\max }$ and $\mathsf{\Delta }{P}_{\mathrm{CCS}}^{\min }$ are the upper and lower limits of the creep rate of the carbon capture power plant, respectively; $P_{\mathrm{Oc},\mathrm{CCS}}(t)$ is the energy consumption of the carbon capture equipment in operation at time t; ${\lambda }_{\mathrm{C}{\mathrm{O}}_2}$ is the energy consumption required for the processing of carbon dioxide by the carbon capture equipment; $L_{\mathrm{C},\mathrm{C}{\mathrm{O}}_2}(t)$ is the amount of carbon dioxide captured at time t; $P_{\mathrm{C},\mathrm{CCS}}(t)$ is the electric power consumed by the carbon capture device at time t; $P_{\mathrm{Fc},\mathrm{CCS}}(t)$ is the fixed energy consumption of the carbon capture device at time t; $\mathsf{\Delta }{P}_{\mathrm{C},\mathrm{CCS}}^{\max }$ and $\mathsf{\Delta }{P}_{\mathrm{C},\mathrm{CCS}}^{\min }$ are the upper and lower limits of the creep rate of the carbon capture device, respectively; $L_{\mathrm{D},\mathrm{C}{\mathrm{O}}_2}(t)$ is the amount of carbon dioxide emitted at time t; $L_{\mathrm{Q},\mathrm{C}{\mathrm{O}}_2}(t)$ is the carbon emission quota of the carbon capture plant at time t; and ${\beta }_{\mathrm{C}}$ and ${\beta }_{\mathrm{Q}}$ refer to the carbon intensity of the carbon capture plant and the carbon emission quota of the unit electricity, respectively.

2.2.4. Gas Boilers and Electric Boilers

A gas boiler uses natural gas as fuel to produce high-temperature flue gas, transferring heat energy to a working fluid via a heat exchanger for heating purposes.

Gas boiler:

$$\left\{\begin{array}{l}{P}_{\mathrm{H},\mathrm{GB}}(t)={\alpha }_{H,\mathrm{GB}}{P}_{\mathrm{G},\mathrm{GB}}(t)\hfill \\ P_{\mathrm{G},\mathrm{GB}}^{\min }\le P_{\mathrm{G},\mathrm{GB}}(t)\le P_{\mathrm{G},\mathrm{GB}}^{\max }\hfill \\ \mathsf{\Delta }{P}_{\mathrm{G},\mathrm{GB}}^{\min }\le P_{\mathrm{G},\mathrm{GB}}(t+1)\hfill \\ -P_{\mathrm{G},\mathrm{GB}}(t)\le \mathsf{\Delta }{P}_{\mathrm{G},\mathrm{GB}}^{\max }\hfill \end{array}\right.$$

(4)

where $P_{\mathrm{H},\mathrm{GB}}(t)$ is the thermal energy output of the equipment at time t; ${\alpha }_{H,\mathrm{GB}}$ is the thermal energy conversion efficiency of the equipment; $P_{\mathrm{G},\mathrm{GB}}(t)$ is the natural gas power input of the equipment at time t; $P_{\mathrm{G},\mathrm{GB}}^{\max }$ and $P_{\mathrm{G},\mathrm{GB}}^{\min }$ are the upper and lower limits of the input power of the equipment, respectively; and $\mathsf{\Delta }{P}_{\mathrm{G},\mathrm{GB}}^{\max }$ and $\mathsf{\Delta }{P}_{\mathrm{G},\mathrm{GB}}^{\min }$ are the upper and lower limits of the climbing rate of the equipment, respectively.

Electric boilers are efficient energy conversion devices that use electricity to generate heat.

Electric boiler:

$$\left\{\begin{array}{l}{P}_{\mathrm{H},\mathrm{EB}}(t)={\alpha }_{\mathrm{E},\mathrm{EB}}{P}_{\mathrm{E},\mathrm{EB}}(t)\hfill \\ P_{\mathrm{E},\mathrm{EB}}^{\min }\le P_{\mathrm{E},\mathrm{EB}}(t)\le P_{\mathrm{E},\mathrm{EB}}^{\max }\hfill \\ \mathsf{\Delta }{P}_{\mathrm{E},\mathrm{EB}}^{\min }\le P_{\mathrm{E},\mathrm{EB}}(t+1)\hfill \\ -P_{\mathrm{E},\mathrm{EB}}(t)\le \mathsf{\Delta }{P}_{\mathrm{E},\mathrm{EB}}^{\max }\hfill \end{array}\right.$$

(5)

where $P_{\mathrm{H},\mathrm{EB}}(t)$ is the thermal energy output of the equipment at time t; ${\alpha }_{\mathrm{E},\mathrm{EB}}$ is the thermal energy conversion efficiency of the equipment; $P_{\mathrm{E},\mathrm{EB}}(t)$ is the electrical power input of the equipment at time t; $P_{\mathrm{E},\mathrm{EB}}^{\max }$ and $P_{\mathrm{E},\mathrm{EB}}^{\min }$ are the upper and lower limits of the input power of the equipment, respectively; and $\mathsf{\Delta }{P}_{\mathrm{E},\mathrm{EB}}^{\max }$ and $\mathsf{\Delta }{P}_{\mathrm{E},\mathrm{EB}}^{\min }$ are the upper and lower limits of the climbing rate of the equipment, respectively.

2.2.5. Electrical and Thermal Energy Storage

Electrical and thermal energy storage alleviate the mismatch between load demand and low-carbon energy output, supporting multi-energy complementarity and renewable energy integration. Lithium iron phosphate (LFP) batteries are widely used in energy storage due to their stable chemistry, long lifespan, good thermal stability, and high safety. Therefore, LFP batteries were selected for electrical storage in this study.

(1)

Electrical energy storage:

$$\left\{\begin{array}{l}{S}_{\mathrm{EES}}(t)={\displaystyle \frac{1}{S_{\mathrm{EES}}^{\max }}}({\alpha }_{\mathrm{C},\mathrm{EES}}{P}_{\mathrm{C},\mathrm{EES}}(t)\hfill \\ \begin{array}{l}-{\displaystyle \frac{P_{\mathrm{D},\mathrm{EES}}(t)}{{\alpha }_{\mathrm{D},\mathrm{EES}}}})\mathsf{\Delta }t+S_{\mathrm{EES}}(t-1)\\ 0\le {\eta }_{\mathrm{C},\mathrm{EES}}+{\eta }_{\mathrm{D},\mathrm{EES}}\le 1\end{array}\hfill \\ {\eta }_{\mathrm{D},\mathrm{EES}}{P}_{\mathrm{EES}}^{\min }\le P_{\mathrm{D},\mathrm{EES}}(t)\le {\eta }_{\mathrm{D},\mathrm{EES}}{P}_{\mathrm{EES}}^{\max }\hfill \\ {\eta }_{\mathrm{C},\mathrm{EES}}{P}_{\mathrm{EES}}^{\min }\le P_{\mathrm{C},\mathrm{EES}}(t)\le {\eta }_{\mathrm{C},\mathrm{EES}}{P}_{\mathrm{EES}}^{\max }\hfill \\ S_{\mathrm{EES}}^{\min }\le S_{\mathrm{EES}}(t)\le S_{\mathrm{EES}}^{\max }\hfill \\ S_{\mathrm{EES}}(\infty )=S_{\mathrm{EES}}(1)\hfill \end{array}\right.$$

(6)

where $S_{\mathrm{EES}}(t)$ is the charge state of the lithium battery at moment t; $P_{\mathrm{C},\mathrm{EES}}(t)$ is the charging power of the lithium battery at moment t; $P_{\mathrm{D},\mathrm{EES}}(t)$ is the discharging power of the lithium battery at moment t; ${\alpha }_{\mathrm{C},\mathrm{EES}}$ and ${\alpha }_{\mathrm{D},\mathrm{EES}}$ are the charging and discharging efficiencies of the lithium battery, respectively; ${\eta }_{\mathrm{C},\mathrm{EES}}$ and ${\eta }_{\mathrm{D},\mathrm{EES}}$ are the charging and discharging states of the lithium battery, respectively; $P_{\mathrm{EES}}^{\max }$ and $P_{\mathrm{EES}}^{\min }$ are the maximum and minimum values of the charging and discharging power of the lithium battery, respectively; $S_{\mathrm{EES}}^{\max }$ and $S_{\mathrm{EES}}^{\min }$ are the minimum and maximum charging states of the lithium battery, respectively; and $S_{\mathrm{EES}}(1)$ and $S_{\mathrm{EES}}(\infty )$ refer to the charging state of the lithium battery in the charging and discharging cycle at the initial moment and the final moment, respectively.

(2)

Thermal energy storage:

$$\left\{\begin{array}{l}0\le {\eta }_{\mathrm{C},\mathrm{HES}}+{\eta }_{\mathrm{D},\mathrm{HES}}\le 1\hfill \\ {\eta }_{\mathrm{D},\mathrm{HES}}{P}_{\mathrm{HES}}^{\min }\le P_{\mathrm{D},\mathrm{HES}}(t)\le {\eta }_{\mathrm{D},\mathrm{HES}}{P}_{\mathrm{HES}}^{\max }\hfill \\ {\eta }_{\mathrm{C},\mathrm{HES}}{P}_{\mathrm{HES}}^{\min }\le P_{\mathrm{C},\mathrm{HES}}(t)\le {\eta }_{\mathrm{C},\mathrm{EES}}{P}_{\mathrm{HES}}^{\max }\hfill \end{array}\right.$$

(7)

where ${\eta }_{\mathrm{C},\mathrm{HES}}$ and ${\eta }_{\mathrm{D},\mathrm{HES}}$ are the heat storage and heat release states of the equipment, respectively; $P_{\mathrm{D},\mathrm{HES}}(t)$ and $P_{\mathrm{C},\mathrm{HES}}(t)$ are the heat storage and heat release power of the equipment at time t, respectively; and $P_{\mathrm{HES}}^{\max }$ and $P_{\mathrm{HES}}^{\min }$ are the maximum and minimum values of the heat storage and heat release power of the equipment, respectively.

3. Cooperative Game-Based Multi-Agent Operational Model for IES

IES optimization, the carbon capture plant, integrated heat and power plant, and low-carbon energy supplier are typically separate stakeholders. In a non-cooperative model, the power company sells electricity to the grid at a feed-in tariff, while other participants purchase it at industrial tariffs. In the cooperative model, a direct transaction is established between users and low-carbon energy suppliers, replacing the traditional non-cooperative approach. The grid company collects wheeling charges based on relevant standards. This creates a coalition whose members follow specific allocation principles to ensure efficient energy use. This study employed cooperative game theory to model collaboration among the energy stakeholders.

Cooperation must satisfy two essential conditions:

(1)

Individual rationality: Each participant must receive a higher benefit from cooperation than it would achieve individually.

(2)

Collective rationality: The total benefits of cooperation must exceed the sum of the benefits each participant would achieve acting alone.

Principles of cooperative union operation:

(1)

Renewable energy suppliers joining the cooperative union can sell electricity to the grid, supply power directly to carbon capture and electricity-to-gas facilities at an agreed price, and pay the corresponding over-the-grid charges.

(2)

Carbon capture power plants in the union can purchase electricity directly from renewable energy suppliers to meet the energy needs of their carbon capture equipment, in addition to buying power from the grid. Decisions on electricity procurement are influenced by varying electricity rates at different times of day. The captured CO₂ can also be sold to CCS facilities.

(3)

Cogeneration plants in the union can buy electricity directly from renewable energy suppliers to meet the energy needs of their P2G facilities, in addition to grid power purchases. Purchasing decisions follow time-of-use tariffs.

(4)

Entities not part of the cooperative union are not allowed to transmit electricity to or from other participants. Thermal power plants—which hold a monopoly on heat services within the system—only account for their operating costs, excluding revenues from heat sales.

3.1. Objective Function and Constraints

3.1.1. Optimization Objective

The objective of multi-agent IES optimization is to maximize the net benefit of the cooperative union. The objective function is

$$\min {\displaystyle \sum _{t=1}^T(}{C}_{\mathrm{M}}+C_{\mathrm{CCS}}+C_{\mathrm{Q}}+C_{\mathrm{BUY}}+C_{\mathrm{F}}+C_{\mathrm{P}2\mathrm{G}}+C_{\mathrm{N}}+C_{\mathrm{EB}}+C_{\mathrm{GAS}}-C_{\mathrm{CR}}-C_{\mathrm{ER}})$$

(8)

where $C_{\mathrm{M}}$ is the maintenance cost of new-energy facilities, $C_{\mathrm{CCS}}$ is the system carbon capture cost, $C_{\mathrm{Q}}$ is the cost of abandoned wind and light for the system, $C_{\mathrm{BUY}}$ is the cost of purchasing electricity for the system, $C_{\mathrm{F}}$ is the cost of carbon capture energy input, $C_{\mathrm{P}2\mathrm{G}}$ is the cost of operating the P2G system, $C_{\mathrm{N}}$ is the cost of crossing the grid, $C_{\mathrm{EB}}$ is the cost of operating the electric boiler equipment, $C_{\mathrm{GAS}}$ is the cost of purchasing gas, $C_{\mathrm{CR}}$ is the gain from carbon trading, and $C_{\mathrm{ER}}$ is the gain from selling electricity.

The objective function is

$$\left\{\begin{array}{l}{C}_{\mathrm{M}}={\displaystyle \sum _{t=1}^T\left({\lambda }_{\mathrm{W}}{P}_{\mathrm{W}}(t)+{\lambda }_{\mathrm{pv}}{P}_{\mathrm{pv}}(t)+{\lambda }_{\mathrm{M}}{P}_{\mathrm{C},\mathrm{EES}}(t)\right)}\hfill \\ C_{\mathrm{CCS}}={\alpha }_{\mathrm{CCS}}{\displaystyle \sum _{t=1}^T\left(L_{\mathrm{C},\mathrm{C}{\mathrm{O}}_2}(t)-L_{\mathrm{C}2\mathrm{P}}(t)\right)}\hfill \\ C_{\mathrm{Q}}={\eta }_{\mathrm{W}}{\displaystyle \sum _{t=1}^T\left(F_{\mathrm{W}}(t)-P_{\mathrm{W}}(t)\right)}\hfill \\ +{\eta }_{\mathrm{pv}}{\displaystyle \sum _{t=1}^T\left(F_{\mathrm{pv}}(t)-P_{\mathrm{pv}}(t)\right)}\hfill \\ C_{\mathrm{BUY}}=b_{\mathrm{E}}(t){\displaystyle \sum _{t=1}^T{P}_{\mathrm{BUY}}(t)}\hfill \\ C_{\mathrm{F}}={\displaystyle \sum _{t=1}^T\left(a{P}_{\mathrm{CCS}}^2(t)+b{P}_{\mathrm{CCS}}(t)+c\right)}\hfill \\ C_{\mathrm{P}2\mathrm{G}}={\alpha }_{\mathrm{P}2\mathrm{G}}{\displaystyle \sum _{t=1}^T{P}_{\mathrm{P}2\mathrm{G}}(t)}\hfill \\ +b_{\mathrm{C}{\mathrm{O}}_2}{\displaystyle \sum _{t=1}^T\left(L_{\mathrm{P}2\mathrm{G}}(t)-L_{\mathrm{C}2\mathrm{P}}(t)\right)}\hfill \\ C_{\mathrm{N}}={\displaystyle \sum _{t=1}^T\left({\lambda }_{\mathrm{N}}{P}_{\mathrm{N},\mathrm{P}}^2(t)+{\gamma }_{\mathrm{N}}{P}_{\mathrm{N},\mathrm{P}}(t)\right)}\hfill \\ +{\displaystyle \sum _{t=1}^T\left({\lambda }_{\mathrm{N}}{P}_{\mathrm{N},\mathrm{E}}^2(t)+{\gamma }_{\mathrm{N}}{P}_{\mathrm{N},\mathrm{E}}(t)\right)}\hfill \\ +{\displaystyle \sum _{t=1}^T\left({\lambda }_{\mathrm{N}}{P}_{\mathrm{N},\mathrm{C}}^2(t)+{\gamma }_{\mathrm{N}}{P}_{\mathrm{N},\mathrm{C}}(t)\right)}\hfill \\ C_{\mathrm{EB}}={\alpha }_{\mathrm{EB}}{\displaystyle \sum _{t=1}^T{P}_{\mathrm{H},\mathrm{EB}}(t)}\hfill \\ C_{\mathrm{GAS}}=b_{\mathrm{GAS}}{\displaystyle \sum _{t=1}^T\left(V_{\mathrm{CHP}}(t)+V_{\mathrm{GB}}(t)-V_{\mathrm{GAS}}(t)\right)}\hfill \\ C_{\mathrm{CR}}={\phi }_{\mathrm{CR}}(t)\left(L_{\mathrm{Q},\mathrm{C}{\mathrm{O}}_2}(t)-L_{\mathrm{D},\mathrm{C}{\mathrm{O}}_2}(t)\right)\hfill \\ C_{\mathrm{ER}}=b_{\mathrm{ER}}(t){\displaystyle \sum _{t=1}^T\left(P_{\mathrm{N},\mathrm{CCS}}(t)+P_{\mathrm{E},\mathrm{CHP}}(t)+P_{\mathrm{N},\mathrm{R}}(t)\right)}\hfill \end{array}\right.$$

(9)

where ${\lambda }_{\mathrm{W}}$, ${\lambda }_{\mathrm{pv}}$, and ${\lambda }_{\mathrm{M}}$ are the operation and maintenance cost coefficients of wind and solar power generation and the operation and maintenance cost coefficient of energy storage, respectively; ${\alpha }_{\mathrm{CCS}}$ is the cost coefficient of sequestering carbon dioxide; $L_{\mathrm{C}2\mathrm{P}}(t)$ is the amount of carbon dioxide supplied by carbon capture equipment to electricity-to-gas conversion equipment at moment t; ${\eta }_{\mathrm{W}}$ and ${\eta }_{\mathrm{pv}}$ are the unit penalty cost coefficients for wind and light abandonment, respectively; $F_{\mathrm{W}}(t)$ and $F_{\mathrm{pv}}(t)$ are the predicted output of wind and light at time t, respectively; $P_{\mathrm{W}}(t)$ and $P_{\mathrm{pv}}(t)$ represent the actual outputs of wind and solar power at time t, respectively; $b_{\mathrm{E}}(t)$ is the power purchase price of the grid at time t; $P_{\mathrm{BUY}}(t)$ is the purchased power of the grid at time t; $a$, $b$, and $c$ are the fuel cost coefficients of the carbon capture plant, respectively; ${\alpha }_{\mathrm{P}2\mathrm{G}}$ is the operating cost coefficient of P2G; $b_{\mathrm{C}{\mathrm{O}}_2}$ is the purchasing price of carbon dioxide per unit; $L_{\mathrm{P}2\mathrm{G}}(t)$ is the amount of carbon dioxide consumed by P2G conversion at time t; ${\lambda }_{\mathrm{N}}$ and ${\gamma }_{\mathrm{N}}$ are the conversion factors for over-the-grid fees; $P_{\mathrm{N},\mathrm{P}}(t)$, $P_{\mathrm{N},\mathrm{E}}(t)$, and $P_{\mathrm{N},\mathrm{C}}(t)$ refer to the power supplied by renewable energy suppliers to the P2G equipment, the electric boiler equipment, and the carbon capture equipment, respectively, at time t; ${\alpha }_{\mathrm{EB}}$ is the cost factor for the operation of the electric boiler; $b_{\mathrm{GAS}}$ is the purchase price of natural gas per unit; ${\phi }_{\mathrm{CR}}(t)$ is the price of carbon trading at time t; and $b_{\mathrm{ER}}(t)$ is the average feed-in tariff at time t. The units of the parameters are listed in

Table 1. Parameters of each unit of IES.

Main Body	Parameter	Numerical Value
P2G	Upper limit of output, MW	198
	Lower limit of output, MW	0
	Conversion efficiency	0.62
	CO2 consumption coefficient, (t/MWh)	0.27
CHP	Upper limit of output, MW	135
	Lower limit of output, MW	0
	Low combustion calorific value of natural gas, (MJ/m3)	41
CCS	Energy consumption coefficient, (t/MWh)	0.285
	Carbon emission intensity coefficient, (t/MWh)	0.94
	Carbon emission quota coefficient, (t/MWh)	0.73
EB	Upper limit of output, MW	100
	Lower limit of output, MW	10
	Electrical efficiency	0.8
	Thermal efficiency	0.8
GB	Upper limit of output, MW	100
	Lower limit of output, MW	30
	Gas turbine thermal efficiency	0.69
Lithium battery	Upper limit of charging and discharging power, MW	100
	Lower limit of charging and discharging power, MW	0
	Charging efficiency coefficient	0.94
	Discharge efficiency coefficient	0.94
Price	Cost coefficient of carbon capture power plant, (USD/MW2)	0.00031
	Cost coefficient of carbon capture power plant, (USD/MW)	17.3
	Cost coefficient of carbon capture power plant, USD	970
	Unit natural gas price, (USD/m3)	0.419
	Carbon trading price, (USD/t)	14.286
	Cost coefficient of wind curtailment punishment, (USD/MWh)	40
	Penalty cost coefficient for abandoning light, (USD/MWh)	35
	Carbon sequestration cost coefficient, (USD/t)	4.89
	Unit CO2 price, (USD/t)	120
	P2G cost coefficient, (USD/MWh)	20
	Cost coefficient of internet fees, (USD/MW2)	0.0046
	Cost coefficient of internet fees, (USD/MW)	1.548

Notes on parameter sources: (1) Energy Conversion Technology Standards [24]; (2) cost coefficients: based on Hubei Province 2023 Energy Guidance Prices (Hubei Pricing Bureau Notice No. 12 (2023)); (3) carbon trading price: reflects the 2023 annual average price on the China Emissions Exchange; (4) other technical parameters: derived from engineering measurement data published in References [17,18,22].

.

3.1.2. Restrictive Condition

The optimization of IES operation needs to follow certain constraints to ensure that the system can operate within a safe and reliable range:

(1)

Renewable energy capacity constraints:

$$\left\{\begin{array}{l}{P}_{\mathrm{N}}(t)=P_{\mathrm{W}}(t)+P_{pv}(t)\hfill \\ P_{\mathrm{N}}(t)=P_{\mathrm{CCS},\mathrm{N}}(t)+P_{\mathrm{N},\mathrm{C}}(t)\hfill \\ +P_{\mathrm{N},\mathrm{P}}(t)+P_{\mathrm{N},\mathrm{E}}(t)\hfill \\ 0\le P_{\mathrm{W}}(t)\le F_{\mathrm{W}}(t)\hfill \\ 0\le P_{pv}(t)\le F_{\mathrm{pv}}(t)\hfill \end{array}\right.$$

(10)

(2)

Union operational constraints:

$$\left\{\begin{array}{l}\begin{array}{l}{P}_{\mathrm{E},\mathrm{EB}}(t)=P_{\mathrm{N},\mathrm{E}}(t)+P_{\mathrm{BUY}}(t)\\ P_{\mathrm{C},\mathrm{CCS}}(t)=P_{\mathrm{E},\mathrm{CCS}}(t)+P_{\mathrm{N},\mathrm{C}}(t)\end{array}\hfill \\ P_{\mathrm{P}2\mathrm{G}}(t)=P_{\mathrm{BUY}}(t)+P_{\mathrm{N},\mathrm{P}}(t)\hfill \end{array}\right.$$

(11)

(3)

Electric power balance constraints:

$$\left\{\begin{array}{l}{P}_{\mathrm{CCS}}(t)+P_{\mathrm{N}}(t)+P_{\mathrm{P},\mathrm{CHP}}(t)+P_{\mathrm{D},\mathrm{EES}}(t)+P_{\mathrm{BUY}}(t)=\hfill \\ P_{\mathrm{E},\mathrm{L}}(t)+P_{\mathrm{C},\mathrm{EES}}(t)+P_{\mathrm{C},\mathrm{CCS}}(t)+P_{\mathrm{P}2\mathrm{G}}(t)\hfill \\ P_{\mathrm{E},\mathrm{L}}(t)+P_{\mathrm{C},\mathrm{EES}}(t)=P_{\mathrm{N},\mathrm{T}}(t)+P_{\mathrm{CCS},\mathrm{N}}(t)\hfill \\ +P_{\mathrm{CHP}}(t)+P_{\mathrm{D},\mathrm{EES}}(t)\hfill \end{array}\right.$$

(12)

where $P_{\mathrm{N}}(t)$ is the actual power of renewable energy suppliers at time t, $P_{\mathrm{BUY}}(t)$ is the power purchased from the grid at time t, $P_{\mathrm{E},\mathrm{L}}(t)$ is the electric load at time t, $P_{\mathrm{N},\mathrm{T}}(t)$ is the power of renewable energy feed-in at time t, and $P_{\mathrm{CCS},\mathrm{N}}(t)$ is the power of carbon capture plant feed-in at time t.

3.2. Algorithm and Optimization Solution

3.2.1. Gray Wolf Optimization Algorithm

GWO is a metaheuristic algorithm inspired by the hunting behaviors of gray wolf packs—tracking, encircling, and attacking prey. In GWO, each wolf’s position within a D-dimensional search space represents a candidate solution. The population forms a strict hierarchy based on fitness values: The fittest individual is designated the alpha (α) wolf, the second-best the beta (β) wolf, and the third-best the delta (δ) wolf. The α, β, and δ wolves guide the search, while the remaining wolves (ω) update their positions around the leaders. The expression of the GWO algorithm is

$$\left\{\begin{array}{l}{L}_p=\delta P_p(k)-P(k)\hfill \\ P(k+1)={\displaystyle \frac{1}{3}}{\displaystyle \sum _{p=\alpha ,\beta ,\delta }\left[P_p(k)-\lambda L_p\right]}\hfill \end{array}\right.$$

(13)

where $L_p$ is the distance between the gray wolf and its prey; $k$ is the number of iterations; $P\left(k\right)$ and $P_p\left(k\right)$ are the positions of the gray wolf and prey after the kth iteration, respectively; and $\lambda ,\gamma$ are the synergy coefficients, which are calculated as follows:

$$\left\{\begin{array}{l}\lambda =2\eta r_2-\eta \hfill \\ \eta =2\left(1-{\displaystyle \frac{k}{k_{\max }}}\right)\hfill \\ \gamma =2r_1\hfill \end{array}\right.$$

(14)

where $a$ is the convergence factor, k_max is the maximum number of iterations, and $r_1$ and $r_2$ are random numbers within [0, 1].

3.2.2. Improved Gray Wolf Optimization Algorithm

To address uneven distribution and limited global search from random initialization in standard GWO, tent chaotic mapping is introduced for population initialization. Leveraging its ergodicity and uniformity, this enhances the solution space coverage and strengthens global exploration. Furthermore, to resolve the exploitation–exploration imbalance from the linear convergence factor decay, a nonlinear adaptive strategy is proposed. This establishes a nonlinear relationship between the convergence factor and iteration, intensifying early exploration and late exploitation, thereby improving global convergence probability. The expression is

$$x(k+1)=\left\{\begin{array}{ll}2x(k),\hfill & 0⩽x(k)⩽0.5\hfill \\ 2\left[1-x(k)\right],\hfill & 0.5⩽x(k)⩽1\hfill \end{array}\right.$$

(15)

$$a=2\left[1-\cos \left({\displaystyle \frac{\pi }{2}}\cdot {\displaystyle \frac{k}{k_{\max }}}\right)\right]$$

(16)

The convergence changes of the improved algorithm compared with before the improvement are shown in Figure 3.

Figure 3 demonstrates that conventional GWO becomes trapped in a local optimum after 72 iterations, while IGWO converges to the global optimum in 22 iterations. This result demonstrates the superior computational efficiency and convergence accuracy of IGWO.

Benefit allocation model:

$$\left\{\begin{array}{l}{\phi }_i(V)={\displaystyle \sum _{i\in S}\frac{\left(\left|S_i\right|-1\right)!\left(n-\left|S_i\right|\right)!}{n!}}\mathsf{\Delta }{V}_1\hfill \\ \mathsf{\Delta }{V}_1=\left(V\left(S\right)-V\left(S\backslash \left\{i\right\}\right)\right)\hfill \end{array}\right.$$

(17)

where ${\phi }_i(V)$ is the value of the benefit distribution of the ith subject, $S_i$ is the number of members in the coalition, $V\left(S\right)$ is the operational benefit of the cooperative coalition, and $V\left(S\backslash \left\{i\right\}\right)$ is the operational benefit of the coalition with i removed.

3.2.3. Solution Algorithm and Steps

The proposed IGWO solves the power system scheduling optimization problem. Shapley value calculation is integrated, with the optimal coalition benefit distribution as an objective. The solution procedure is shown in Figure 4.

Step 1: Initialization—A set number of gray wolves are randomly generated as the initial population, each representing a potential solution, such as the Shapley value.

Step 2: Fitness evaluation—The fitness of each wolf is calculated based on the objective function, with higher fitness indicating better solutions.

Step 3: Leader selection—Wolves are ranked by fitness, and the one with the highest fitness is selected as the leader, whose solution is considered optimal.

Step 4: Position update—Each wolf’s position is updated based on the leader’s and its own position, moving closer to the optimal solution.

Step 5: Optimization—The position update is repeated until the stopping conditions are met. In each iteration, the wolves adjust their positions based on the leader’s and their own information.

Step 6: Leader update—The leader is re-selected based on the updated positions and fitness values. If a better solution is found, the leader’s position is replaced.

Step 7: Termination—The algorithm stops when the iteration limit or accuracy requirements are reached, and the leader’s solution is considered the optimal result.

3.2.4. Optimization of the Solution Process

The multi-body IES cooperative operation mode is a cooperative game problem that involves the distribution of interests among multiple individuals, while also ensuring the maximization of the cooperative union’s overall benefits. It aims to determine the optimal energy trading quantity and the corresponding energy trading prices. Based on the established comprehensive energy optimization model, the eigenfunction values for each participant are derived by introducing the improved gray wolf algorithm. The Shapley value method is then applied to allocate the benefits of the cooperative union. To solve the model optimally, the CPLEX business model solver—integrated with MATLAB (R2018a) through Yalmip (R20230622)—is employed. The solution process is outlined in the flowchart shown in Figure 4.

4. Case Study Analysis

A case study was conducted for an IES based on an industrial park in Hubei, China. The model was formulated as a mixed-integer nonlinear programming (MINLP) problem with the standard form

$$\left\{\begin{array}{l}\min D(x)\hfill \\ p_i(x)=0 i=1,2,\dots m\hfill \\ q_j(x)\le 0 j=1,2\dots ,n\hfill \\ x_{\min }\le x\le x_{\max }\hfill \\ x_k\in \left\{0,1\right\}\hfill \end{array}\right.$$

(18)

where $D(x)$ is the objective function, $p_i(x)=0$ is the equality constraint, $q_j(x)\le 0$ is the inequality constraint, and $x_{\max }$ and $x_{\min }$ are the upper and lower limits of the variables, respectively.

Figure 5 and Figure 6 present the day-ahead wind power generation forecast profiles for the IES, along with the operational mechanisms of the time-of-use electricity pricing and feed-in tariff schemes.

4.1. Operation Analysis

This section evaluates the operational results of an IES in five cooperation scenarios, non-cooperative, {CCP, CTPP, LCES} (CTL), {CCP, CTPP} (CT), {CCP, LCES} (CL), and {CTPP, LCES} (TL), as shown in

Table 2. Table of all sub-unions.

	Members	CCP	CTPP	LCES
Type of Union
Union 1		0	0	0
Union 2		1	1	0
Union 3		1	0	1
Union 4		0	1	1
Union 5		1	1	1

. The system comprised three main entities: a CCP, an integrated heat and power plant (CTPP), and a LCES. The costs and benefits for each entity in these scenarios are summarized in

Table 3. Benefits and costs of cooperative unions.

$\times 100$
Type of Union	LCES	CCP	CTPP	Total Profit
Union 1	2748.69	1433.97	−2925.36	1257.30
Union 2	2880.40	1627.55	−3294.24	1213.71
Union 3	2867.91	1713.21	−3234.77	1346.35
Union 4	2957.75	1334.35	−3038.36	1253.74
Union 5	3304.44	1706.51	−3101.62	1909.33

and

Table 4. Annotation table.

TP	Total Profit
CTR	Carbon trading revenue
PES	Proceeds from electricity sales
WCG	Wheeling charge
OC	P2G operating cost
CP	Cost of gas purchases
CSC	Carbon sequestration costs
FC	Fuel cost
WPV	Wind power and photovoltaic abandonment penalties
NEM	New-energy maintenance system maintenance costs
CU	Cooperative union

, where positive values indicate benefits and negative values indicate costs. The analysis aimed to verify the rationality of the proposed model.

Table 3 and

Table 5. Benefits of the units in the system.

×100
CU	NEM	WPV	FC	CSC	CP	OC	WCG	PES	CTR	TP
1	−794.62	−74.18	−1053.23	−142.82	−3575.64	−165.91	0	7157.53	−93.83	1257.3
2	−797.31	−74.18	−1703.81	−148.31	−2928.48	−281.25	0	7165.85	−18.8	1213.71
3	−854.18	−74.18	−1548.72	−191.42	−3158.37	−193.85	−21.63	7193.81	194.89	1346.35
4	−582.21	0	−1354.68	−331.62	−3347.11	−261.68	−99.69	7126.36	104.37	1253.74
5	−582.21	0	−1354.68	−329.46	−2895.07	−243.36	−127.81	7126.36	315.56	1909.33

show that in Union 5 mode, the P2G operating cost increased significantly because it absorbed large amounts of curtailed wind and solar energy. While the total revenue increased due to abandonment penalty costs and lower carbon sequestration expenses, the costs for CO₂ purchasing, electricity for the electric boiler, P2G equipment, and the operation and maintenance of these systems were entirely borne by the integrated heat and power plant. The plant’s revenue primarily came from natural gas production, with the savings being allocated to the LCES and CCP. This reflects a reduction in penalty payments for surplus electricity absorption and lower carbon sequestration costs through carbon reuse. However, this resulted in an increase of USD 13,024 in the cogeneration plant’s costs compared with separate operations, which was not justified. Therefore, a fair distribution of the additional benefits generated by cooperation is required to provide appropriate incentives for all partners.

4.2. Cooperative Union Rationalization Validation

The rationality verification process of Union 5 is as follows: Based on the Shapley value method under the incoming gray wolf algorithm, the allocation process is shown in

Table 6. CCP profit distribution on Shapley values.

$\times 100$
S	$\mathit{V}\left(\mathit{S}\right)$	$\mathit{V}\left(\mathit{S}\backslash \left\{\mathit{C}\mathit{C}\mathit{P}\right\}\right)$	Weighting Factor
$\left\{S_{\mathrm{CCP}}\right\}$	1433.97	0	1/3
$\{S_{\mathrm{CCP}},S_{\mathrm{CTPP}}\}$	−1666.69	−2925.36	1/6
$\{S_{\mathrm{CCP}},S_{\mathrm{LCES}}\}$	4581.12	2748.69	1/6
$\{S_{\mathrm{CCP}},S_{\mathrm{LCES}},S_{\mathrm{CTPP}}\}$	1909.33	−80.61	1/3

,

Table 7. Distribution of CTPP profits on Shapley values.

$\times 100$
S	$\mathit{V}\left(\mathit{S}\right)$	$\mathit{V}\left(\mathit{S}\backslash \left\{\mathit{C}\mathit{T}\mathit{P}\mathit{P}\right\}\right)$	Weighting Factor
$\left\{S_{\mathrm{CTPP}}\right\}$	−2925.36	0	1/3
$\{S_{\mathrm{CTPP}},S_{\mathrm{CCP}}\}$	−1666.69	1433.97	1/6
$\{S_{\mathrm{CTPP}},S_{\mathrm{LCES}}\}$	−80.61	2748.69	1/6
$\{S_{\mathrm{CTPP}},S_{\mathrm{CCP}},S_{\mathrm{LCES}}\}$	1909.33	4581.12	1/3

and

Table 8. Distribution of LCES profits on Shapley values.

$\times 100$
S	$\mathit{V}\left(\mathit{S}\right)$	$\mathit{V}\left(\mathit{S}\backslash \left\{\mathit{L}\mathit{C}\mathit{E}\mathit{S}\right\}\right)$	Weighting Factor
$\left\{S_{\mathrm{LCES}}\right\}$	2748.69	0	1/3
$\{S_{\mathrm{LCES}},S_{\mathrm{CCP}}\}$	4581.12	1433.97	1/6
$\{S_{\mathrm{LCES}},S_{\mathrm{CTPP}}\}$	−80.61	−2925.36	1/6
$\{S_{\mathrm{LCES}},S_{\mathrm{CCP}},S_{\mathrm{CTPP}}\}$	1909.33	−1666.69	1/3

. The daily profits of the CCP and LCES are found to be USD 165,648.5 and USD 310,688, respectively, and the daily operating cost of the CTPP is USD 285,405.

Two basic conditions for cooperative games were analyzed based on Union 5:

(1)

Individual conditions:

$$\left\{\begin{array}{l}{\phi }_{\mathrm{CCP}}=1654.485>V\left(S_{\mathrm{CCP}}\right)=1433.97\hfill \\ {\phi }_{\mathrm{CTPP}}=-2854.05>V\left(S_{\mathrm{CTPP}}\right)=-2925.36\hfill \\ {\phi }_{\mathrm{LCES}}=3106.88>V\left(S_{\mathrm{LCES}}\right)=2748.69\hfill \end{array}\right.$$

(19)

(2)

Conditions of cooperation:

$$\begin{array}{l}\left\{\begin{array}{l}{U}_1:{\phi }_{\mathrm{CCP}}+{\phi }_{\mathrm{CTPP}}+{\phi }_{\mathrm{LCES}}=1909.315\hfill \\ U_2:V\left(S_{\mathrm{CCP}}\right)+V\left(S_{\mathrm{CTPP}}\right)+V\left(S_{\mathrm{LCES}}\right)=1257.3\hfill \end{array}\right.\\ U_1>U_2\end{array}$$

(20)

As shown in Equations (19) and (20) and Figure 7, revenue increased by USD 65,201.50 after the cooperative alliance was formed, compared with independent operation. The revenues of the individual members—CCP, CTPP, and LCES—rose by USD 22,051.5, USD 7131, and USD 35,819, respectively. These results meet the conditions for the cooperative game framework; therefore, this demonstrates the necessity of establishing a cooperative alliance.

4.3. Analysis of Electrochemical Energy Storage Output Results

Based on the comparison of the data in Figure 8 and Figure 9, it is evident that a bottleneck in renewable energy consumption occurred between 1 a.m. and 8 a.m., when the system operated under Union 1 status. Due to the lack of electric boiler equipment and direct power supply channels for the P2G system, the system primarily relied on lithium battery storage devices to consume wind power. However, the limited capacity of these batteries prevented the full consumption of surplus wind energy. In contrast, when operated under Union 5, the electric boiler equipment and P2G system worked together, enabling the full utilization of surplus wind power through the joint operation of the gas-to-heat and electricity-to-gas devices. Compared with independent operations, this cooperation significantly reduced the lithium battery charge/discharge cycles while increasing the operational load of the electric boiler equipment and P2G system. As a result, the wind power consumption rate reached 100%, and the service life of the energy storage equipment was extended by 3–5 years. This synergy arose from the complementary strengths of the two technology routes: lithium batteries managed short-term, high-frequency regulation, while the electric boiler and P2G systems handled the continuous energy conversion needs.

4.4. Optimized Scheduling Analysis

Combined with the analysis of Figure 10, Figure 11 and Figure 12, during the 1:00–7:00 period, the electric load was low, while the wind power output was high. Due to constraints, including heat load demand limits, unit output boundaries, and ramp rate restrictions, the regulation capacity of carbon capture plants and CHP equipment on the generation side was limited. Additionally, the energy storage systems faced charging power constraints, making it impossible to fully integrate surplus wind power, which inevitably led to wind curtailment in Union 1 mode. In contrast, under Union 5’s cooperative operation, the carbon capture devices flexibly shifted loads and collaborated with electric boilers and P2G equipment to utilize curtailed wind. This approach addressed the insufficient absorption capacity caused by low carbon capture operation intensity, reducing wind curtailment costs by USD 9416 compared with Union 1’s standalone operation. This model alleviated energy storage utilization pressure, decreased reliance on lithium batteries, resolved mismatches between renewable energy output and load demand, and achieved effective peak shaving and valley filling.

From 08:00 to 10:00, the system heat load was primarily supplied by CHP units, with a minor contribution from electric boiler units. As the heat load demand declined, the electric boiler units ceased operation, and the CHP units reduced their power output. Concurrently, the increasing electrical load demand caused a rise in the output of carbon capture power plants (CCPPs), resulting in higher energy consumption. Notably, despite this elevated energy demand, CO₂ emissions remained unchanged, as the CCPPs were entirely powered by wind and solar generation during this period.

During the 11:00–18:00 period, reduced heat demand led to a significant decrease in CHP unit output and the deactivation of electric boiler units. The thermal supply was primarily met by TES systems during this interval. Concurrently, the electrical load remained high, requiring the prioritized dispatch of CHP units, PV systems, and wind turbines. Meanwhile, carbon capture plants operated as flexible loads, dynamically modulating their capture rates in response to renewable energy generation fluctuations to enhance grid stability. This coordinated dispatch mechanism demonstrates how flexible carbon capture integration can facilitate the penetration of renewable energy while maintaining grid reliability.

During the 19:00–24:00 period, PV generation dropped sharply, while the wind turbine output increased. The system primarily relied on carbon capture power plants, CHP units, and wind turbines to meet the electrical load demand. When the electrical load decreased, the carbon capture facilities enhanced their sequestration capacity, with wind power being prioritized to supply their energy consumption. This operational strategy reduced system-wide CO₂ emissions and increased the carbon trading revenue; concurrently, the rising heat load demand drove higher output from electric boilers and CHP units to ensure thermal supply adequacy.

4.5. Analysis of Carbon Emission Reduction Results of Cooperative Unions

Through the comprehensive analysis of Figure 13 and Figure 14 and

Table 9. Carbon trading outcome.

Carbon Dioxide	Exhaust, t	Earnings
Union 1	6743.94	−10,485.83
Union 2	5192.41	8352.67
Union 3	4146.38	19,536.42
Union 4	4127.44	−3582.51
Union 5	5772.59	24,785.03

, in the case where the participants operated alone or only the carbon capture power plant and the gas-fired cogeneration plant formed a cooperative union, the energy consumption of the carbon capture facility was completely dependent on the power supply of the carbon capture power plant, which resulted in a limited CO₂ treatment capacity and relatively high CO₂ emissions. However, once low-carbon energy suppliers were involved, the energy consumption of the carbon capture facility could be met by wind and solar power, which not only improved CO₂ treatment efficiency but also effectively reduced CO₂ emissions. When operating in Union 5 mode, CO₂ emissions were reduced by 971.36 tons compared with independent operation, while carbon trading revenues increased by USD 35,271, with most of the energy consumption of the carbon capture facility being supplied by wind and light.

Collectively, carbon pricing and renewable penetration formed a self-reinforcing closed loop via “green electricity-driven emission reduction–benefit feedback for consumption.” When both reached critical threshold values simultaneously, the system achieved concurrent gains in economic efficiency, carbon emission reductions, and operational flexibility. This provides a technical pathway for high-penetration renewable power systems that balances market adaptability with low-carbon transition objectives.

5. Conclusions

This study established a CCS–EB–P2G integrated framework and employed an IGWO algorithm with Shapley value profit allocation to facilitate multi-stakeholder collaboration through a technology–benefit coupling approach. This approach significantly enhances wind power utilization, improves system economics, and reduces carbon emission intensity. It provides a feasible pathway for regional IESs to balance economic efficiency, low-carbon goals, and operational effectiveness. The proposed synergistic operation model and cooperation mechanism are directly applicable to industrial parks or urban energy hubs. The main conclusions are as follows:

• The integrated CCS–EB–P2G system significantly enhances wind power utilization, load management flexibility, and global optimization performance. The IGWO algorithm efficiently solves the complex scheduling problem.
• Adopting an energy entity alliance operation mode and utilizing the Shapley value method for profit distribution substantially improves overall economic benefits compared with those under independent operation, effectively coordinating the conflict between individual rationality and collective interests.
• Deep collaboration among CCS, P2G, and EB within the coalition simultaneously reduces carbon emission intensity and carbon trading costs, achieving synergistic enhancements in environmental and economic performance.

The proposed multi-agent synergistic operation model significantly enhances wind power accommodation, economic efficiency, and carbon reduction. However, two key limitations persist: (1) the model overlooks critical IES network security constraints, particularly within the PS and GS; (2) the collaboration mechanisms are idealized, neglecting real-world factors such as contract enforcement risks or information asymmetry, which could undermine the stability of the alliance. Future work will integrate security-constrained optimization and design default-resistant mechanisms to transform the “economy–low-carbon” synergy from theoretical advantage into sustainable practice.