氢能源背景下应用博弈论的管理科学与工程专业文献综述

… game-theoretic framework for structuring a novel hydrogen market is introduced in this research, with an emphasis on hydrogen refueling for hydrogen … A cooperative game coalition first …

The uncertainty of renewable energy source (RES) and load may bring huge challenge to the operation of power systems. In order to meet the balance of supply and demand, a game bidding strategy considering uncertainty is proposed for the electric-hydrogen shared energy storage system (SESS). Firstly, based on Wasserstein distance in extreme scenarios, a reduced scale fuzzy set is constructed for the uncertainty of supply and demand. Secondly, Vickrey-Clarke-Groves (VCG) mechanism is introduced to deal with the misreporting and valuation behavior of microgrids (MGs). Then a two-stage distributed robust optimization (DRO) game model is designed for SESS—MGs through game bidding. The aim of Stage I can maximize the benefits of SESS, while the social welfare of each microgrid (MG) may be maximized in Stage II, which can achieve a unique Stackelberg equilibrium. So the DRO model is transformed into a solvable mathematical model by taking advantage of dual theory and adaptive McCormick algorithm. Finally, the case studies are simulated by using the IEEE 33 node power grid together with a 20 node hydrogen network, which can validate the effectiveness of the proposed model.

… energy generation system (HREGS) and hydrogen energy … of renewable energy hydrogen production and hydrogen vehicles… renewable energy hydrogen production industry, hydrogen …

… This study develops a game-theoretic framework to evaluate the market dynamics, financial risks, and economic viability of hydrogen-based energy storage … Hydrogen energy storage …

Compared to traditional charging infrastructure, electric–hydrogen integrated charging stations (EHICSs) involve complicated traffic-coupled hydrogen delivery, increasingly diverse energy transaction paradigms, and heightened gaming complexity. To address these challenges, this article proposes a mixed game-theoretic scheduling method for urban EHICSs considering hydrogen transportation. First, an EHICS model containing electric–hydrogen coupling devices is established, with a focus on multi-energy conversion and management. This model fully incorporates hydrogen procurement from the hydrogen production plant (HPP), electricity trading with the grid, and inter-EHICS electricity trading, providing a generalized modeling paradigm for EHICSs. Second, a unified HPP model is developed to synergistically optimize price-responsive energy management, time-sensitive hydrogen delivery scheduling, traffic-adaptive trailer route planning, and game-based hydrogen pricing. Then, the HPP and EHICS models are structured in a hierarchical mixed game-theoretic framework, which captures the complex economic interactions between EHICSs and the HPP, power grid, and new energy vehicle owners. Specifically, the framework employs a Stackelberg game solved by a bi-section-based iterative algorithm to govern hydrogen trading between the HPP and EHICSs while adopting an asymmetric Nash bargaining solved by the alternating direction method of multiplier (ADMM) algorithm for inter-EHICS electricity trading. This multi-agent mixed game integrates the aforementioned considerations by incorporating coordinated electric–hydrogen production, storage utilization, market-driven trading mechanisms, dynamic pricing, and hydrogen transportation under spatiotemporal constraints of road classifications and time-varying traffic conditions. Finally, the proposed method is rigorously validated through comparative case studies across two distinct urban systems. Simulation results substantiate that the model can effectively characterize the operations of the HPP and EHICSs and develop optimal strategies to reduce their economic costs, thereby verifying the methodological validity, implementation feasibility, and economic superiority of the method.

This study examines the pricing and assesses resilience methods in hydrogen supply chains by thoroughly analyzing two main disruption scenarios. The model examines a scenario in which a hydrogen production company depends on a Renewable Power plant (RP) for its electricity supply. Ensuring a steady and efficient hydrogen supply chain is crucial, but outages at renewable power sources provide substantial obstacles to sustainability and operational continuity. Therefore, in the event of disruptions at the RP, the company has two options for maintaining resilience: either sourcing electricity from a Fossil fuel Power plant (FP) through a grid network to continue hydrogen production or purchasing hydrogen directly from another company and utilizing third-party transportation for delivery. Using a game theoretic approach, we examine how different methods affect demand satisfaction, cost implications, and environmental sustainability. The study employs sensitivity analysis to evaluate the impact of different disruption probabilities on each scenario. In addition, a unique sensitivity analysis is performed to examine the resilience of transmission security to withstand disruptions. This study evaluates how investments in security measures affect the strength and stability of the supply chain in various scenarios of disruption. Our research suggests that the first scenario offers greater reliability and cost-effectiveness, along with a higher resilience rate compared to the second scenario. Furthermore, the examination of the environmental impact shows that the first scenario has a smaller amount of CO2 emissions per kg of hydrogen. This study offers important insights for supply chain managers to optimize resilience measures, hence improving reliability, reducing costs, and minimizing environmental effects.

… hydrogen charging facility and PV panels will be favorable to the smooth progress of the partnership. Reasonable hydrogen … developments of HPVs and solar PV hydrogen production. …

The coupling of electricity, heat, and hydrogen subsystems together with carbon capture technologies introduces complex operational interactions in modern multi-energy systems. Existing game-based scheduling studies mainly focus on electricity–heat or electricity–heat–gas coupling, often neglecting hydrogen blending, carbon capture integration, and strategic coordination among heterogeneous stakeholders. To address these gaps, this study develops a game-theoretic hierarchical optimization framework for electricity–heat–hydrogen integrated energy systems incorporating carbon capture. Compared with conventional multi-energy game models, the proposed framework integrates hydrogen blending and carbon capture into a unified electricity–heat–hydrogen–carbon coupling structure, enabling coordinated low-carbon operation. A Stackelberg leader–follower structure is adopted, where the upper-level operator determines electricity and heat prices, and lower-level participants optimize generation dispatch and demand response accordingly. The bi-level model is transformed into an equivalent single-level formulation using Karush–Kuhn–Tucker conditions and solved through a hybrid particle swarm optimization–mathematical programming approach. Simulation results based on an extended IEEE 30-bus system demonstrate improved coordination, enhanced scheduling flexibility, and reduced operating costs and carbon emissions. Compared with centralized optimization, the proposed framework enables the integrated energy operator and energy supplier to achieve revenues of 3.18 × 105 CNY and 3.95 × 105 CNY, respectively, while reducing the load aggregator’s cost by 41.71%, confirming its effectiveness for coordinated low-carbon IES scheduling.

Green hydrogen is essential for advancing the energy transition, as it is regarded as a CO 2 -neutral, flexible, and storable energy carrier. Particularly in steel production, which is known for its high energy intensity, hydrogen has great potential to replace conventional energy sources. In a game-theoretic, bi-level optimization model involving a power plant operator and a steel company, we investigate in which situations the production and use of green hydrogen is advantageous from an economic and ecological point of view. Through an extensive case study based on a real-world scenario, we can observe that hydrogen production can serve as a profitable and flexible secondary income opportunity for the power plant operator, and help avoid curtailment and spot market losses. On the other hand, the steel manufacturer can reduce CO 2 emissions and associated costs while also meeting the growing customer demand for low-carbon products. However, our findings also highlight important trade-offs and uncertainties. While lower electricity generation costs or improved electrolyzer efficiency enhance hydrogen’s competitiveness, increases in coal and CO 2 emission prices do not always result in greater hydrogen adoption. This is due to the persistent reliance on a non-replaceable share of coal in steel production, which raises the overall cost of both low-carbon and carbon-intensive steel. The model further shows that consumer demand elasticity plays a critical role in determining hydrogen uptake. These insights underscore the importance of not only reducing hydrogen costs, but also designing supportive policies that address market acceptance and the full cost structure of green industrial products.

As subsidies for renewable energy are progressively reduced worldwide, electric vehicle charging stations (EVCSs) powered by renewable energy must adopt market-driven approaches to stay competitive. The unpredictable nature of renewable energy production poses major challenges for strategic planning. To tackle the uncertainties stemming from forecast inaccuracies of renewable energy, this study introduces a peer-to-peer (P2P) energy trading strategy based on game theory for solar-hydrogen-battery storage electric vehicle charging stations (SHS-EVCSs). Firstly, the incorporation of prediction errors in renewable energy forecasts within four SHS-EVCSs enhances the resilience and efficiency of energy management. Secondly, employing game theory’s optimization principles, this work presents a day-ahead P2P interactive energy trading model specifically designed for mitigating the variability issues associated with renewable energy sources. Thirdly, the model is converted into a mixed integer linear programming (MILP) problem through dual theory, allowing for resolution via CPLEX optimization techniques. Case study results demonstrate that the method not only increases SHS-EVCS revenue by up to 24.6% through P2P transactions but also helps manage operational and maintenance expenses, contributing to the growth of the renewable energy sector.

The off‐grid system (OGS) has relatively low voltage and frequency requirements, making it suitable for renewable energy generation modes such as wind and solar power. However, due to the large volatility of the power from the generation side and the upper‐bound constraints on its energy supply capacity, OGS faces issues such as low energy utilization efficiency, weak generation‐load power matching, and poor system economic performance. To address these challenges, flexible management on the load side is necessary to achieve optimal operation of generation‐load power balance. This paper establishes a bi‐level optimization model for OGS, incorporating renewable energy power plant (REPP), shared energy storage plant (SESP), and load aggregator (LA), based on master‐slave game theory. The model is solved using a combination of Adaptive Differential Evolution (ADE) algorithm and the CPLEX solver. Through simulation examples, the results show that the integration of SESP into the system alleviates the issue of generation‐load power mismatch, reducing the OGS's curtailment of electricity by 34.15%. This significantly improves the energy utilization efficiency, while the net profit of the REPP increases by 68.62% and the net profit of the LA rises by 6.59%, effectively achieving a win‐win situation among all the stakeholders. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

… This study presents a game theory-based model to analyze the decision-making processes … hydrogen. The model incorporates uncertain parameters such as revenue from hydrogen …

… period of hydrogen energy to regulate, store and convert energy by … game theory, the wind turbine, photovoltaic and hydrogen storage system are taken as the three parties of the game, …

… energy utilization rate of wind-solar-hydrogen energy system is low, and the traditional capacity optimization is modeled based on the fixed hydrogen … the change of hydrogen production …

With the rapid development of society, global energy is in short supply. China has put forward an integrated energy system focusing on interconnecting energy resources and harnessing their complementary advantages to address the energy crisis, thus no longer pursuing the production, transportation and supply of a single source of energy. In the continuous development of integrated energy systems, the elements of participation and interaction are becoming more complex. Game theory, which can effectively solve the problems arising from multi-agent trading, is naturally introduced to the integrated energy system. This paper provides a comprehensive overview of the introduction of game theory into the integrated energy system. First, the development of integrated energy is briefly introduced, game scenarios in integrated energy systems is proposed, and game scenarios considering the energy supply side, distribution network, demand side and common planning and dispatching problems in integrated energy systems are summarized. Secondly, main game theory models in the integrated energy system are summarized, such as cooperative game theory model, the non-cooperative game theory model and the Stackelberg game theory model. Finally, the future prospect and challenge for the application of game theory in integrated energy systems is proposed. The new game models are introduced to the integrated energy system, and a mixed game is considered to solve related problems. It is hoped that this work can serve as a reference for the researchers in this field.

… -based strategy is proposed for a single HIP to jointly optimize pricing, EH … game-based strategy is proposed to minimize coalition costs through distributed optimization of hydrogen …

Confronted with the increasing penetration of renewable energy and hydrogen-powered vehicles (HVs), energy and transportation systems need to be optimized coordinately to improve the economy and reduce carbon emissions. However, the effect of dynamic hydrogen pricing on the optimization performance of energy and transportation systems is scarcely investigated. To realize the low-carbon and economic operation of energy and transportation systems, a hierarchical game between the distributed energy station (DES) and HVs under dynamic hydrogen pricing is put forward. First, a novel dynamic hydrogen pricing mechanism related to the proportion of renewable energy in the energy supply is presented and incorporated into the game optimization, which will promote hydrogen production using renewable energy and minimize the DES operation cost. At the game equilibrium, the HVs completing equivalent aggregation realize balanced hydrogen refueling at the guidance of dynamic hydrogen pricing. Meanwhile, the raised routing optimization method can select a minimum cost route for HVs to refuel based on traffic information. Finally, the effectiveness of the proposed hierarchical game optimization strategy and model is verified by simulations.

… hydrogen from nearby on-site stations. This HRS system is a micro hydrogen supply chain that includes hydrogen … HRS system using a multi-level game model, given that on-site and off-…

… paper constructs a multi-layer game model for HFCV dispatch based on … game that enables HFCV users to independently select HPRS, a Stackelberg game for strategic optimization …

… Secondly, based on the Stackelberg game theory, the game relationships … optimization, this study proposes a "Dual-IDR + V2G" multi-agent game-theoretic collaborative optimization …

Renewable Energy Off-Grid Hydrogen Production Systems (NEOHPS) are characterized by significant source-side power fluctuations, low energy utilization efficiency, weak source-load power matching capability, and poor economic performance. Therefore, flexible load-side management is required to achieve optimal source-load coordinated operation. This paper establishes and solves an optimization model of NEOHPS incorporating a Renewable Energy Power Plant (REPP), a Shared Energy Storage Power Station (SESP), and a Load Aggregator (LA) based on cooperative game theory. Simulation results demonstrate that the integration of SESP alleviates source-load power mismatch, reduces curtailed electricity by 7.7%, and significantly improves energy utilization efficiency. Meanwhile, the net profit of REPP increases by 14.4%, and that of LA increases by 67.5%, achieving both economic and environmental benefits.

In the hydrogen‐based integrated energy system (HIES), there exists a hydrogen trading market where hydrogen producers and consumers are distinct stakeholders. Current research in hydrogen trading predominantly focuses on high‐cost green hydrogen (GH), which is not aligned with the current trend of utilizing hydrogen from multiple sources. To address this, this paper proposes a hydrogen trading strategy between the virtual hydrogen plant (VHP) and electro‐hydrogen energy system (EHES) based on a bi‐level model, considering the synergy of GH produced from electrolyzers and blue hydrogen (BH) derived from natural gas in the HIES. In the VHP level, the objective is to maximize profit from hydrogen sales, allowing for the determination of hydrogen prices. In the EHES level, the goal is to minimize the cost of energy supply, leading to the formulation of GH and BH purchasing plans based on hydrogen prices. Additionally, this paper incorporates a risk‐averse model from the information gap decision theory (IGDT) to account for the impact of wind power output uncertainties in the VHP level. Subsequently, leveraging the Karush–Kuhn–Tucker (KKT) conditions of the EHES level, the bi‐level problem is transformed into a solvable single‐level mathematical program with equilibrium constraints (MPEC), with the non‐linear equilibrium constraints linearized. The proposed bi‐level optimization model is validated through case studies encompassing industrial and residential hydrogen utilization within the HIES. The outcomes confirm the rationality of the proposed model, demonstrating that, in comparison to exclusively trading GH, the coordinated GH and BH trading can increase the profit of the VHP by 2.7% and reduce the costs of the EHES by 8.5%.

… hydrogen production technologies. When all the participators cooperate, the influence of typical factors on the project is evaluated using the evolutionary game … for hydrogen production …

… Low-carbon hydrogen is a promising option for energy … Cooperation among hydrogen supply chain (HSC) agents is … resources using systems and cooperative game theory. This work is …

… differential game model that draws on and extends the literature on hydrogen supply chain … Therein, state variables include the hydrogen retail price and carbon emission trading price, …

The German government attributes a crucial role to green hydrogen in the energy transition, as it has the potential to reduce greenhouse gas emissions when used as an energy carrier. However, currently, green hydrogen is not yet competitive. On the one hand, its production is costly, and on the other, current electrolysis capacities are insufficient to meet the potential demand. Therefore, at least during a transitional period, green hydrogen must compete with gray hydrogen produced from fossil energy sources. In this paper, we examine three government instruments aimed at increasing the market share of green hydrogen: taxes on gray hydrogen, subsidies for the green retailer, and financial support for expanding green hydrogen production capacities. In a bi-criteria, game-theoretic model, in which the government acts as the Stackelberg leader, we observe that all three measures can improve the position of green hydrogen on the market. Notably, the state’s sole intervention can significantly increase the sales volume of green hydrogen. However, if the state’s main focus is on balancing its net gain from hydrogen market interventions, it should concentrate on taxes. If finances and the sales volume of green hydrogen are equally important, the state will increasingly focus on positive measures and support capacity expansions. In contrast, if the state’s expenditures do not matter, the additional use of subsidies leads to maximizing the market share of green hydrogen.

… In the pathway toward decarbonization, hydrogen is … design and management of the hydrogen supply chain (HSC) is … mathematical model of the Stackelberg game. The solution strategy …

This study focuses on hydrogen production capacity planning for wind-solar-hydrogen-storage integrated systems. A bi-level optimization model based on Stackelberg game theory is proposed. The leader (project planner) aims to maximize the net present value (NPV) over the project's life-cycle by determining the optimal number of electrolyzers. The follower (system operator) optimizes the dispatch strategy under a given electrolyzer scale to maximize annual operational profits and feeds back key operational metrics to the leader. The model incorporates technical constraints such as power balance, state of charge (SOC) of energy storage, minimum load and on/off constraints of electrolyzers, and grid interaction ratios. Economic parameters, including investment costs, operation and maintenance expenses, and financing structures, are also integrated. To validate the model, data from a real-world project in northwest China are used as input. Sensitivity analyses are conducted on hydrogen market price, subsidy rate, and discount rate. The solution framework employs a genetic algorithm for the leader's decision variables and mixed-integer linear programming (MILP) for the follower, achieving coordination between long-term investment decisions and short-term operational optimization. This approach provides a theoretical foundation and quantitative analysis tool for capacity configuration in wind-solar-hydrogen-storage systems.

… Although these studies confirm the enabling role of digitalization across the hydrogen supply chain, they offer limited insight into its dynamic penetration mechanism and the evolving …

… hydrogen energy requires the supply chain to have dynamic restructuring capabilities; on the other hand, the risk of energy supply chain … the effectiveness of the game enhanced GA in …

… through hydrogen. … supply chain, this study uses a game-theoretic framework, a common approach for studying decision-making [28], [29]. Game theory is established in supply chain …

… parks via a combined hydrogen production station, … game-based carbon intensity pricing mechanism is developed for inter-regional hydrogen trading between the combined hydrogen …

… a Stackelberg game-based pricing incentive strategy to … links charging stations and hydrogen refueling stations to capture … to optimize orderly charging, refueling, and discharging load …

… Game): FCEV users determine their hydrogen refueling strategies based on the hydrogen price set by HRSO and their refueling … and hydrogen pricing based on the electricity price from …

With the increasing integration of transportation and energy systems, highway energy replenishment facilities are gradually evolving into hybrid refueling stations that integrate photovoltaic generation, energy storage, battery charging, and hydrogen refueling. However, due to differences in resource conditions across stations, independently operated hybrid refueling stations find it difficult to simultaneously improve overall economic performance and renewable energy utilization. To address this issue, this paper investigates the coordinated operation and distributed optimization of highway hybrid refueling stations. First, an inter-station hydrogen–carbon–green certificate trading framework is established, and a trading model for a cluster of hybrid refueling stations is then developed on this basis. Then, the inter-station trading problem is decomposed into two subproblems: symmetric trading volume determination and asymmetric Nash bargaining-based price determination. These two subproblems are solved in a distributed manner using the alternating direction method of multipliers. In addition, a hydrogen transportation model is developed to translate trading decisions into feasible transportation arrangements under highway network and hydrogen tube trailer scheduling constraints. Finally, the case study demonstrates that the proposed model enables multi-resource sharing among hybrid refueling stations, reduces the overall system cost by 21.30%, and achieves a fairer distribution of benefits among stations.

… the EV charging and HV hydrogen refueling for the CPTS. … However, the generalized Nash game is difficult to analyze … the joint pricing issue, we defer the complicated competitive game …

This paper proposes a novel two-level electricity and hydrogen market framework for multi-microgrids (MMGs) coupled with offsite hydrogen refueling stations (HRSs), aiming to strengthen the synergy between electricity and hydrogen. The local hydrogen market among the MMG and HRSs is modeled by multi-leader multi-follower Stackelberg game theory, in which microgrids play the role of leaders to adjust hydrogen prices while HRSs participate as followers to determine their hydrogen purchase scheme. Moreover, to deal with economic and technical issues of the MMG in a holistic manner, Nash bargaining theory is used to model the electricity transaction among microgrids. A distributed algorithm is developed to solve such games, thus reducing the cost of information communication and the risk of privacy exposure. The case study demonstrates that this market mechanism guarantees benefits for all parties and boosts the independence of MMGs by reducing transactions with the main grid.

Nowadays, with the rapid development of hydrogen powered vehicles, the demand for hydrogen refueling stations (HRSs) in the transportation field is growing. The renewable energy, e.g., wind energy, is used to produce and store hydrogen on site for HRSs, which may be a relatively cheap and clean solution. Considering the wind farm (WF) and HRSs belong to different entities, a new cooperative operation model of the WF-HRSs combined system is proposed. Specifically, the robust optimization methods are implemented to characterize the uncertainties of wind power and market electricity price, respectively, to alleviate risk. To ensure the fairness of profit allocation, the bargaining power is measured by various contribution levels of each stakeholder based on the Nash–Harsanyi bargaining game theory. Furthermore, the model is transformed into two sequential subproblems: energy trading problem (SP1) and the payment bargaining problem (SP2). Accordingly, a solving technique adopting column and constraint generation algorithm is provided to solve the SP1. In addition, for the sake of privacy protection, a distributed approach based on data-centric mode is developed to solve SP2. Finally, the numerical results can validate the effectiveness and scalability for the proposed scheme and algorithms.

… operator (EPSO) and the hydrogen system operator (H2SO) … Stackelberg game, aims to minimize the electricity‑hydrogen … marginal price (DLMP) profile of electricity and hydrogen, as …

Current technical approaches find it challenging to reduce hydrogen production costs in combined cooling, heating, and power (CCHP) microgrids integrated with hydrogen refueling stations (HRS). Furthermore, the stability of such systems is significantly impacted by multiple uncertainties inherent on both the source and load sides. Therefore, this paper proposes a two-stage robust optimization for bi-level game-based scheduling of a CCHP microgrid integrated with an HRS. Initially, a bi-level game structure comprising a CCHP microgrid and an HRS is established. The upper layer microgrid can coordinate scheduling and the step carbon trading mechanism, thereby ensuring low-carbon economic operation. In addition, the lower layer hydrogenation station can adjust the hydrogen production plan according to dynamic electricity price information. Subsequently, a two-stage robust optimization model addresses the uncertainty issues associated with wind turbine (WT) power, photovoltaic (PV) power, and multi-load scenarios. Finally, the model’s duality problem and linearization problem are solved by the Karush–Kuhn–Tucker (KKT) condition, Big-M method, strong duality theory, and column and constraint generation (C&CG) algorithm. The simulation results demonstrate that the strategy reduces the cost of both CCHP microgrid and HRS, exhibits strong robustness, reduces carbon emissions, and can provide a useful reference for the coordinated operation of the microgrid.

The operation and scheduling of taxi fleets remain a key application area of the Internet of Things (IoT) technologies. However, the operational strategies for new energy taxis—particularly hydrogen-powered and hydrogen-electric hybrid vehicles—are still underexplored. This article investigates the deployment of plug-in hybrid hydrogen and electric taxis (PH2ETs) in ride-hailing services and proposes a bilevel optimization framework that jointly addresses PH2ETs’ hybrid charging decisions and the pricing strategy of integrated electricity charging and hydrogen refueling stations (IEHSs). PH2ETs determine charging options based on energy prices and time costs, while IEHSs dynamically adjust pricing in response to aggregate charging behaviors. To reduce the prediction error caused by the uncertain behavior of drivers in actual scenarios, the model incorporates algorithm aversion, capturing drivers’ reluctance to follow platform-generated recommendations. An improved whale optimization algorithm (WOA) is developed to solve the multiobjective problem. The simulation results validate the effectiveness of the proposed charging strategy and demonstrate that incorporating algorithm aversion significantly improves the pricing performance of IEHSs over conventional approaches.

Abstract Lack of hydrogen refueling stations (HRSs) has hindered the diffusion of hydrogen fuel cell vehicles (HFCVs) in the Chinese transport market. By combining the agent-based model (ABM) and the experience weighted attraction (EWA) learning algorithm, this paper explores the impact of government subsidy strategy for HRSs on the market diffusion of HFCVs. The actions of the parties (government, HRS planning department and consumers) and their interactions are taken into account. The new model suggests dynamic subsidy mode based on EWA algorithm yields better results than static subsidy mode: HFCV purchases, HRS construction effort, total number of HRSs and expected HRS planning department profits all outperform static data by around 27%. In addition, choosing an appropriate initial subsidy strategy can increase the sales of HFCVs by nearly 40%. Early investment from government to establish initial HRSs can also increase market diffusion efficiency by more than 76.7%.

… , a wholesale hydrogen market, a power supply system, a hydrogen distribution system (HDS), and hydrogen refueling stations (HRSs). It leverages an AI circular hydrogen economist …

This paper proposes a multi-energy trading framework for a hybrid-renewable-to-H2 provider (HP) to coordinate the interaction and trading of electricity and H2 while promoting the efficient accommodation of renewable energy resources (RESs). In this framework, the HP can harvest hybrid RESs for green H2 production based on electrochemical effects of biomass electrolysis, and procure stacked profits from both the electricity and H2 markets by the flexibility of electricity-H2 conversion. A Vickrey auction-based pricing mechanism is developed to determine the trading price and quantity of H2 while eliciting truthful offers and bids in a competitive H2 market. Then, a single-leader-multiple-follower Stackelberg game with an iterative solution algorithm is formulated to capture the interactions between the H2 auctioneer and hydrogen fueling stations (HFSs) for achieving the win-win goal. Furthermore, a hybrid-renewable-to-H2 production and control method is proposed for the HP to raise the production efficiency of green H2 and suppress large fluctuations in electrolysis current caused by RES uncertainties. Comparative studies have validated the superiority of the proposed methodology on economic performance and RES accommodation.

The interest conflict among entities in the integrated energy system (IES) has a great challenge to operation decisions of IES. With regards to this, an optimal dispatching model of electric‐heat‐hydrogen IES based on Stackelberg game is proposed. Firstly, an energy producer (EP) model is formulated which considered the full utilization of hydrogen energy and involved the conversion of hydrogen energy to electricity and heat energy. Meanwhile, the demand response amount is integrated into the objective function of load aggregator (LA) in order to encourage consumers to adjust their consumption behaviour. Secondly, by analyzing the characteristics of price information interaction among EP, energy system operator (ESO), and LA, the payoffs of each entity in IES are reformulated. Finally, a Stackelberg game model is established with ESO as the dominator guiding price information, EP and LA as the followers whose private information is confidential. Genetic algorithm and quadratic programming algorithm (GA‐QP) are employed to solve the developed model. Numerical experiments are carried out on an actual park‐level IES in northern China to demonstrate the effectiveness of the proposed model in promoting the benefit equilibrium among various entities.

This paper develops an optimal energy bidding mechanism for the regional integrated electricity–hydrogen system (RIEHS) considering complex electricity–hydrogen energy flow and further presents an electricity–hydrogen optimization management strategy based on Stackelberg game. The transaction mode of the RIEHS is first introduced, and the optimization models for the three market game participants are established. Then, the Stackelberg game-based bidding mechanism is formulated, where the electricity–hydrogen operator (EHO) is the leader and the regional electricity–hydrogen prosumer (REHP) and load aggregator (LA) are the followers. The EHO dominates the game through energy bidding, and REHP and LA respond to the bidding decision. The Stackelberg equilibrium of the formulation is obtained by applying the differential evolutionary algorithm combined with quadratic programming (DEA-QP). Finally, a demonstration case is studied to analyze the market behavior of the three market players and further validate the effectiveness of the proposed strategy. The proposed strategy is able to produce additional economic benefits to REHP and LA and improve the utilization of hydrogen.

… based on Stackelberg-Nash bargaining for multiple IMES. Specifically, hydrogen is flexibly … pricing incentives is developed based on a Stackelberg game model. In addition, a peer-to-…

Hydrogen energy storage serves as a pivotal technology for integrating high proportions of renewable energy, yet its development faces constraints due to substantial investment requirements and imperfect market mechanisms. Green Asset-Backed Notes (ABNs) offer potential to alleviate financing constraints; however, their synergistic effects with hydrogen storage market strategies remain unexplored. This paper constructs a two-layer Stackelberg game model integrating ABN financing with day-ahead trading. Multi-scenario analysis reveals that ABN financing costs significantly influence the operational economics of energy storage: low-cost financing enhances hydrogen storage’s price responsiveness and arbitrage capabilities, whereas high costs suppress its market participation. The research provides quantitative evidence for leveraging financial instruments to enhance hydrogen storage competitiveness.

Integrated energy system (IES) is an advanced configuration that combines electrical energy, thermal energy, and renewable energy, into a unified system. In recent years, the architecture of IES has gradually changed from vertical integration to interactive competition, and its distributed characteristics have become increasingly evident. Therefore, traditional centralized optimization strategies can no longer meet the current practical situation. In this paper, a low-carbon optimization dispatch for IES based on Stackelberg game and kriging metamodel is proposed. In order to address this problem, firstly, three typical models containing hydrogen blending gas technology and a kind of ladder-type carbon trading mechanism considering reward and punishment (RP-LCTM) are established. Secondly an integrated energy manager (IEM) is introduced and a Stackelberg game model with the IEM as the leader and three typical IESs as followers is established. Finally, the kriging metamodel is used to optimize the transaction electricity price. During the game process, the IPSO algorithm is used to optimize electricity prices in key price regions. At last, an experimental example is utilized to demonstrate the effectiveness of the proposed method.

… growing demand for hydrogen energy due to the low economy of hydrogen energy production… photovoltaic hydrogen production system based on the Stackelberg game mechanism was …

The increasing penetration of photovoltaic (PV) resources and the emergence of Power-to-X (P2X) technologies have fundamentally reshaped the operational and economic dynamics of modern energy systems. This paper develops a unified framework for strategic bidding optimization in distributed multi-energy markets, where decentralized agents equipped with PV, battery storage, electrolyzers, and thermal conversion technologies compete and coordinate across electricity, hydrogen, and heating markets. To account for renewable uncertainty, we formulate the bidding problem as a scenario-based stochastic game, where each agent determines its optimal spatiotemporal bidding strategy under incomplete information and uncertain market conditions. The resulting interactions are modeled using a bilevel Stackelberg–Nash equilibrium structure: the upper level represents the system operator enforcing dispatch feasibility and market rules, while the lower level captures decentralized agent best-responses under a finite scenario tree. Each agent’s optimization problem is solved using KKT-based reformulations, allowing the full game to be tractably recast as a mixed complementarity problem. Simulation results demonstrate that intertemporal bidding strategies with cross-market conversion significantly improve profit robustness, system efficiency, and bid clearing rates under high PV variability. Furthermore, the analysis reveals how agent portfolio heterogeneity and market coupling structure influence equilibrium convergence, strategy diversity, and overall coordination performance. This work provides three main contributions: (1) a novel scenario-based stochastic game formulation for multi-energy bidding in sector-coupled PV systems; (2) a bilevel equilibrium modeling and solution framework with realistic intertemporal and inter-market dynamics; and (3) quantitative insights into how flexibility assets, conversion capabilities, and scenario diversity jointly shape system-level outcomes and agent-level profitability in decentralized energy markets.

To address the economic conflicts and operational coordination challenges among independently operated entities such as Wind Power Hydrogen Production (WPHP) and Seawater Desalination (DE) within a seaport Integrated Energy Microgrid (IEMG), this paper proposes an optimal scheduling strategy based on a Stackelberg game. The strategy establishes a one-leader, multi-follower game model, with the IEMG operator acting as the leader and the WPHP and DE operators as followers. The leader (IEMG operator) aims to minimize its total operating cost by formulating and announcing day-ahead dynamic electricity prices. In response, the followers (WPHP and DE operators) optimize their respective production and operational schedules based on the leader's price signals to maximize their individual economic profits. A hybrid iterative algorithm combining a Genetic Algorithm (GA) with the CPLEX solver is designed to solve this bi-level optimization model. Case study results demonstrate that the proposed game-theoretic strategy successfully establishes a stable market equilibrium and effectively guides the energy consumption behavior of the followers. This research provides an effective market-based coordination mechanism for integrated energy systems with multiple stakeholders, holding significant theoretical and practical value for promoting renewable energy accommodation and enhancing overall system economic efficiency.

Green hydrogen from renewable energy is a promising option to satisfy the growing refueling demand of hydrogen fuel cell vehicles (HFCVs). However, the intermittency of renewable energy and the random integration of HFCVs may result in a supply–demand mismatch in the hydrogen transportation systems. This may bring down system operation efficiency and deteriorate user experience. This article proposes a dynamic collaborative pricing mechanism for managing the refueling demand of HFCVs to minimize the operating cost of the system. First, based on a leader–follower game, we design a hydrogen trading mechanism between hydrogen generation stations (HGSs) and offsite refueling stations. Then, we propose a locational marginal hydrogen pricing method based on the duality theory. This method can determine the refueling stations’ spatiotemporal retail prices. Based on this dynamic pricing mechanism, we further develop a refueling navigation strategy for HFCVs that incorporates the practical multitrip chains to manage their refueling demand. Finally, numerical experiments validate that the proposed method can maximize the total social surplus and reduce the total travel cost of HFCVs by optimizing the trading strategies and spatiotemporal distribution of the refueling demand.

… , large capacity, and resource-sharing advantages, has become a … cooperation, thereby reducing overall system efficiency. To address this issue, this study develops a quantum game-…

… welfare via energy sharing of electricity and hydrogen. From … ) We propose a novel cooperative game model that considers … considers electricity and hydrogen trading and contributes to …

Integrated energy microgrids (IEMs) can effectively improve energy efficiency through multi-energy synergy. However, clustering IEMs in the same distribution area triggers complex interest games regarding electrical interaction, necessitating strategies for low-carbon, economic operation. Therefore, this paper constructs a cooperative game model for multi-microgrids considering green certificate-carbon equivalent interaction and hydrogen blending. First, a natural gas hydrogen blending system and a two-stage power-to-gas (P2G) model comprising electrolyzers and methanation reactors are introduced to finely describe deep hydrogen utilization. Second, a green certificate-carbon emission equivalent interaction mechanism is introduced to constrain carbon emissions. Furthermore, conditional value at risk (CVaR) is employed to quantify energy trading risks caused by renewable energy uncertainty. The model is solved via the alternating direction method of multipliers (ADMM) to minimize coalition costs while protecting privacy, and an improved Shapley value method based on green certificate contributions is used for fair benefit allocation. Case studies verify that the proposed strategy effectively promotes the low-carbon economic operation of the system.

In order to promote the consumption of new energy and the low-carbon economic operation in microgrid cluster, under the background of sharing economy, a low-carbon collaborative optimization operation method of microgrid with shared hydrogen energy storage (SHES) based on cooperative game is proposed to give consideration to the benefits of SHES and microgrid cluster. Firstly, a framework for energy interaction and operation of SHES and microgrid cluster is proposed. Subsequently, with the goals of maximizing the operational benefits of SHES and minimizing the operational costs of each microgrid, a cooperative game-based model for the coordinated operation of electric hydrogen energy is established. Then, considering the privacy of each subject, the ADMM algorithm is used to solve the model in a distributed manner. Finally, the numerical simulation shows that the collaborative operation of SHES and various microgrids can effectively improve the operation of various entities, promote the on-site consumption of new energy, and reduce carbon emissions.

To address the problem of cost sharing among multiple economic agents participating in microgrid capacity planning, it is proposed that the formulation of binding agreements is the key to the cooperative game that can be realized ultimately. Firstly, the conditions that need to be satisfied by the cost sharing strategy of cooperative game in islanded wind-photo-hydrogen storage microgrid system are given, i.e., overall rationality, coalition rationality and individual rationality. Secondly, four cost-sharing strategies are used to cost-share the total economic cost in the fully cooperative game, and the acceptance degree of each game participant in the cooperative game process is measured by the MDP (modified disruption propensity, MDP) index. Finally, taking the actual wind speed and light intensity of a place in Northwest China as an example, it is verified that the cost sharing strategy based on equal MDP index and Shapley value is more attractive to all parties and belongs to the core set, which is a binding cost sharing strategy.

… of the multiplication of sharing economy, hydrogen energy storage (HES) shared calls for … micro-grids from the sharing perspective. The evolution game model is utilized for conflict of …

… sharing mode embodies the cooperative concept of risk … on shared energy storage has gradually expanded beyond the scope of single electrical storage systems, and shared hydrogen …

… hydrogen utilization efficiency is deeply intertwined with carbon market dynamics, we propose a novel dynamic hydrogen … The overall solution method is a two-stage cooperative game …

… Game theory guides Farm A to maximize agrivoltaics energy production for its needs, while Farm B seeks reliable electricity and benefits from green hydrogen-… -scale energy-sharing in …

As global energy systems transition towards greater reliance on renewable energy sources, the integration of energy storage systems (ESSs) becomes increasingly critical to managing the intermittency and variability associated with renewable generation. This paper provides a comprehensive review of the application of evolutionary game theory (EGT) to optimize ESSs, emphasizing its role in enhancing decision-making processes, operation scheduling, and multi-agent coordination within dynamic, decentralized energy environments. A significant contribution of this paper is the incorporation of negotiation mechanisms and collaborative decision-making frameworks, which are essential for effective multi-agent coordination in complex systems. Unlike traditional game-theoretic models, EGT accounts for bounded rationality and strategic adaptation, offering a robust tool for modeling the interactions among stakeholders such as energy producers, consumers, and storage operators. The paper first addresses the key challenges in integrating ESS into modern power grids, particularly with high penetration of intermittent renewable energy. It then introduces the foundational principles of EGT and compares its advantages over classical game theory in capturing the evolving strategies of agents within these complex environments. A key innovation explored in this review is the hybridization of game-theoretic models, combining the stability of classical game theory with the adaptability of EGT, providing a comprehensive approach to resource allocation and coordination. Furthermore, this paper highlights the importance of deliberative democracy and process-based negotiation decision-making mechanisms in optimizing ESS operations, proposing a shift towards more inclusive, transparent, and consensus-driven decision-making. The review also examines several case studies where EGT has been successfully applied to optimize both local and large-scale ESSs, demonstrating its potential to enhance system efficiency, reduce operational costs, and improve reliability. Additionally, hybrid models incorporating evolutionary algorithms and particle swarm optimization have shown superior performance compared to traditional methods. The future directions for EGT in ESS optimization are discussed, emphasizing the integration of artificial intelligence, quantum computing, and blockchain technologies to address current challenges such as data scarcity, computational complexity, and scalability. These interdisciplinary innovations are expected to drive the development of more resilient, efficient, and flexible energy systems capable of supporting a decarbonized energy future.

… This indicates that while hydrogen-coupled dispatch models provide essential physical foundations for low-carbon integrated energy systems, they remain insufficient for analyzing multi-…

… hydrogen production chain to construct a hierarchically nested day-ahead distributionally robust game … hybrid bilevel game optimal dispatch method that considers hydrogen–carbon …

Shared energy storage provides a promising solution for the operation of microgrid clusters. This paper explores a hybrid electric–hydrogen shared energy storage model within microgrid clusters, aiming for clean energy generation and economical energy supply despite renewable energy’s unpredictability and complex stakeholder interactions. First, the proposed method features a shared energy storage operator that hosts electric storage and power-to-gas, enabling multi-microgrids energy sharing. To address market dynamics, a hybrid game theory approach using Nash bargaining and Stackelberg games is employed to manage interactions among the shared energy storage operator, microgrid operators, and internal end-users, while accounting for their differing interests. Second, to address uncertainty in renewable energy output, a distributionally robust optimization model is implemented with conditional value at risk, focusing on risk in extreme scenarios. The Adaptive Alternating Direction Method of Multipliers algorithm and Karush–Kuhn–Tucker conditions are used to solve the optimal decision scheme for each entity. Finally, a case study is used to verify the model’s effectiveness. Simulation results show that hybrid electric–hydrogen energy sharing improves resource utilization, leading to significant revenue increases for microgrids and higher profitability for shared energy storage operator. The game-theory-based approach ensures equitable revenue distribution and a 9.86% increase in coalition revenue. It provides a flexible approach to balance economic efficiency and system robustness by allowing decision-makers to adjust risk preference parameters and use historical sample data for informed decision-making.

… game is employed to coordinate the interests of the IP, HRS, and RE stations, thereby improving system economy while maintaining robustness. The … demand and dispatch idle batteries …

This paper proposes a collaborative optimal scheduling strategy based on asymmetric Nash bargaining for the integrated electricity–heat–hydrogen multi-microgrid system, which can minimize the overall system operation cost while guaranteeing the dynamic fairness of multi-microgrids energy transactions with full consideration of wind–solar uncertainty. First, a scenario generation method based on temporally correlated Latin hypercube sampling and Wasserstein probability distance-based scenario reduction is adopted to construct representative wind–solar uncertainty scenarios, which effectively mitigates the operational risks arising from wind and solar power output fluctuations in the coordinated dispatch of multi-microgrids. Then, an asymmetric Nash bargaining-based cooperative game model for energy trading is established, with each microgrid’s optimal independent operation cost as the negotiation breakdown point. The alternating direction method of multipliers is used for a distributed solution to obtain the optimal scheme that balances total system cost and trading fairness. Simulation results verify that the proposed strategy can effectively suppress operation risks from renewable uncertainty, significantly cut total system cost by 36.85%, and fully ensure trading fairness among multi-microgrid entities, with favorable engineering application value.

… and robustness under uncertain hydrogen demand. … -follower Nash equilibrium game, confirming that hydrogen system … spatially coordinate hydrogen demand and electrolyzer dispatch …

To enhance the economy and decrease the carbon emission of multi-park integrated energy systems (IESs), an optimal multi-park IESs dispatch method is proposed considering electricity-hydrogen-ammonia (E-H-A) coupling. First, a cooperative game framework for a multi-park IESs dispatch is formulated considering E-H-A coupling and electricity-carbon trading. Then, a dispatch optimization model is established to minimize total system costs, which integrates green electricity for hydrogen production, ammonia synthesis, and carbon capture cycling. Finally, the optimization problem is decomposed into two subproblems, including multi-park IESs cost minimization and optimal cost allocation, which are solved by the Alternating Direction Method of Multipliers (ADMM) and Nash bargaining respectively. Case studies show that the proposed method can reduce 15.03% operating costs and 23.56% carbon emissions for multi-park IESs. The method boosts local renewable consumption through inter-park electricity complementarity and promotes green hydrogen-to-ammonia conversion, increasing ammonia production.

The high energy demand driven by industrial development has transformed the power system from a single energy source to multiple energy systems (MESs). These systems, which involve thermal generators, combined heat-and-power (CHP) units, electrolyzers, fuel cells, etc., with realistic forecast uncertainty, are very operationally challenged. This paper proposes a Distributionally Robust Optimization (DRO) based on a Wasserstein-metric ambiguity set, which simultaneously optimizes the annual maintenance schedules and short-term operational dispatch across MESs. The ambiguity set is constructed using joint samples of forecast errors for the three carriers’ demand, allowing for a data-driven worst-case distribution approach that mitigates the excessive conservatism typically associated with conventional robust optimization (CRO). The penalties are explicitly enforced for load and renewable energy curtailments across each of the MESs with source-specific value-of-lost-load coefficients. The Wasserstein radius is improved by sensitivity analysis, obtaining a θ value of 0.20 as the cost reduction radius for a 40% RES penetration. Five RES penetration levels are implemented here on the IEEE 39-bus New England network, with CHP, electrolyzer, fuel cell, thermal storage, and hydrogen storage. The DRO reduces the total annual system cost by 56% compared to CRO, while reducing the unbalanced energy.

With the increasing penetration of wind power, enhancing the renewable energy accommodation rate and reducing the carbon footprint of the IES, this study proposes a comprehensive evaluation method to assess the impact of a novel dynamic Green Certificate Trading (GCT) and Green Hydrogen Certificate Trading (GHCT) joint mechanism. First, considering the integration of the IES into the carbon trading market, a coupled dynamic GCT-GHCT framework is established. This framework links dynamic green electricity certificate revenues with green hydrogen certificate revenues, leveraging cross-subsidization to incentivize renewable energy consumption. Subsequently, an optimal operation model for the IES is formulated with the objective of minimizing comprehensive costs, which encompass energy procurement, green certificates, carbon trading, and wind curtailment penalties. A piecewise linearization approach is applied to transform the optimization model into a Mixed-Integer Linear Programming problem for efficient solving. Furthermore, based on the dispatch results, a multidimensional evaluation index system is constructed, extracting key indicators from economic, technical, and environmental perspectives. To ensure the rationality of the evaluation, a dynamic reward–penalty asymmetric cloud matter-element (ACME) comprehensive evaluation method based on game theory combinatorial weighting is introduced to calculate the index weights and the final comprehensive evaluation value. Finally, multi-scenario simulations are conducted to verify the superiority of the integrated GCT-GHCT trading framework. The results reveal that the proposed approach not only maximizes renewable energy integration but also provides a robust decision-making tool for the low-carbon transition of multi-energy systems.

To improve the energy utilization rate and realize the low-carbon emission of a park integrated energy system (PIES), this paper proposes an optimal operation strategy for multiple PIESs. Firstly, the electrical power cooperative trading framework of multiple PIESs is constructed. Secondly, the hydrogen blending mechanism and carbon capture system and power-to-gas system joint operation model are introduced to establish the model of each PIES. Then, based on the Nash bargaining game theory, a multi-PIES cooperative trading and operation model with electrical power cooperative trading is constructed. Then, the alternating direction method of multipliers algorithm is used to solve the two subproblems. Finally, case studies analysis based on scene analysis is performed. The results show that the cooperative operation model reduces the total cost of a PIES more effectively compared with independent operation. Meanwhile, the efficient utilization and production of hydrogen are the keys to achieve carbon reduction and an efficiency increase in a PIES.

… hydrogen source fluctuations pose severe challenges to the stable operation of electricity-hydrogen… proposes a distributionally robust chance-constrained economic dispatch model (…

Renewable hydrogen production systems involve tightly coupled planning and operational decisions because equipment sizing affects dispatch flexibility, while renewable generation uncertainty significantly influences daily operation. This paper proposes a two-stage distributionally robust optimization framework for a grid-connected wind-photovoltaic hydrogen production system equipped with battery storage, electrolyzers, hydrogen compressors, and hydrogen tanks. In the first stage, the capacities of key hydrogen-side components are determined by jointly considering equivalent daily investment cost and the operational impact of uncertainty. In the second stage, an intra-day dispatch strategy is derived to minimize operating cost under worst-case probability distributions while accounting for the interaction between electricity and hydrogen subsystems and the flexibility of electrical loads. Historical wind and photovoltaic data are clustered into representative scenarios, based on which a data-driven ambiguity set is constructed to capture distributional uncertainty. The resulting model is solved by an iterative decomposition method. Case studies show that the proposed approach produces a practically reasonable capacity configuration and supports coordinated electricity-hydrogen operation under uncertain renewable generation. The proposed framework provides a useful decision-making tool for the joint planning and operation of renewable hydrogen production systems.

… , and weak scheduling robustness under uncertainty. To … economic dispatch strategy based on an electricity-hydrogen-… hybrid games or multi-stage nash-based robust optimization …

The electricity-hydrogen coupled system enhances flexibility and efficiency, but designing market mechanisms that enable multiple entities to collaboratively participate in electricity, hydrogen markets, achieving value linkage across energy-transportation-environment systems, remains a key research challenge. This paper proposes an integrated electricity-hydrogen joint market model based on the synergy of ”hydrogen energy storage aggregators, distribution networks, hydrogen networks, and carbon costs”. The model constructs a multi-agent, cross-market sequential joint clearing mechanism: charging stations act as proactive price setters, optimizing tariffs based on real-time charging power to drive demand response; then participating in coupled grid and hydrogen network clearing via bidding functions, with carbon costs internalizing environmental expenses. An iterative algorithm solves this multi-layer coupled problem, achieving market equilibrium. Simulation results demonstrate that: (1) carbon price pass-through is highly asymmetric, with hydrogen price rising by 23.6% but electricity price by only 0.48% when the carbon price doubles, while social welfare declines by 9.73%, indicating an optimal carbon price interval exists; (2) the deterministic model is unbiased (deviations within 4% for most outputs), yet social welfare exhibits significant downside risk (extreme deviation of 8.1%); (3) electricity price is highly robust (coefficient of variation 0.65%) compared to carbon price (15.7%); (4) the joint market demonstrates structural robustness under uncertainty, with all parameter combinations converging to unique equilibrium. This study provides a market solution for integrating hydrogen into urban energy systems, offering theoretical and practical value for promoting multi-energy collaboration and low-carbon transition.

… in Uniform +25GW/Tech scenario, while hydrogen dispatch varies from 0.5 GWh to over 33 … presents a robust bi-level optimisation framework that integrates a long-term game-theoretic …

… -Nash game framework for AFV-integrated microgrids … Nash equilibrium games are established to capture competitive interactions among charging stations (CSs) and among hydrogen …

… in renewable energy integration, high carbon emissions, and vulnerability to extreme disasters. To address these challenges, this study proposes an optimal hydrogen energy storage (…

To address the challenges of renewable energy curtailment under normal conditions and severe power outages under extreme scenarios, this paper proposes a hydrogen-integrated comprehensive energy system (H-IES) configuration method aimed at enhancing the resilience of distribution networks. The proposed method improves energy utilization efficiency while achieving a balance between economic performance and resilience. First, an operational model of the H-IES is established considering the operating characteristics of distribution networks under extreme conditions. On this basis, a Nash bargaining-based equilibrium model is developed, where economic performance and resilience act as game participants negotiating toward equilibrium. By applying the particle swarm optimization algorithm, the Nash equilibrium solution is obtained, realizing a Pareto-optimal trade-off between the two objectives. Finally, case studies demonstrate that the proposed configuration improves the resilience index by 3.13% and reduces total cost by 10.86% compared with mobile battery energy storage. Under the Nash bargaining framework, the equilibrium configuration increases renewable energy utilization and provides up to 21.6% higher resilience compared with an economy-only optimization scheme.

Coordinating multiple electric–hydrogen regional energy systems (EHRESs) under renewable uncertainty while ensuring rational benefit allocation remains a significant challenge. To address this issue, this paper proposes a cooperative energy mutual-assistance strategy for multiple EHRESs. An electric–hydrogen coupled operational framework integrating power-to-hydrogen technology is established, and a tiered carbon trading mechanism is incorporated to curb carbon emissions. Renewable-generation uncertainty is modeled using chance constraints. To solve the coordinated operation problem in a distributed manner, the cooperative model is decomposed into two tractable subproblems and solved using ADMM. In addition, an asymmetric Nash bargaining-based payoff allocation method incorporating aggregated contribution rates is developed to reflect heterogeneous participant contributions. Case studies are conducted to evaluate convergence, economic performance, emission reduction, and payoff allocation. The results show that the proposed method supports contribution-aware energy trading and benefit sharing among EHRESs while reducing carbon emissions by 8.54% and operating costs by up to 17.17%.

The cooperative interconnection of multi-microgrid systems offers significant advantages in enhancing energy utilization efficiency and economic performance, providing innovative pathways for promoting sustainable development. To establish a fair energy trading mechanism for electricity–hydrogen sharing within multi-energy multi-microgrid (MEMG) systems, this study first analyzes the operational architecture of MEMG energy sharing and establishes a multi-energy coordinated single-microgrid model integrating electricity, heat, natural gas, and hydrogen. To achieve low-carbon operation, carbon capture systems (CCSs) and power-to-gas (P2G) units are incorporated into conventional combined heat and power (CHP) systems. Subsequently, an asymmetric Nash bargaining-based optimization framework is proposed to coordinate the MEMG network, which decomposes the problem into two subproblems: (1) minimizing the total operational cost of MEMG networks, and (2) maximizing payment benefits through fair benefit allocation. Notably, Subproblem 2 employs the energy trading volume of individual microgrids as bargaining power to ensure equitable profit distribution. The improved alternating direction multiplier method (ADMM) is adopted for distributed problem-solving. Experimental results demonstrate that the cost of each MG decreased by 5894.14, 3672.44, and 2806.64 CNY, while the total cost of the MEMG network decreased by 12,431.22 CNY. Additionally, the carbon emission reduction ratios were 2.84%, 2.77%, and 5.51% for each MG and 11.12% for the MEMG network.