A Study on the Environmental and Economic Benefits of Flexible Resources in Green Power Trading Markets Based on Cooperative Game Theory: A Case Study of China

Abstract

This paper addresses the synergy between environmental and economic benefits in the green power trading market by constructing a collaborative game model for environmental rights value and electricity energy value. Based on this, a model for maximizing the benefits of flexible resource operation is proposed. Through the combination of non-cooperative and cooperative games, the conflict and synergy mechanisms of multiple stakeholders are quantified, and the Shapley value allocation rule is designed to achieve Pareto optimality. Simultaneously, considering the spatiotemporal regulation capability of flexible resources, dynamic weight adjustment, cross-period environmental rights reserve, and risk diversification strategies are proposed. Simulation results show that under the scenario of a carbon price of 50 CNY/ton (≈7.25 USD/ton) and a peak–valley electricity price difference of 0.9 CNY/kWh (≈0.13 USD/kWh), when the environmental weight coefficient α = 0.5, the total revenue reaches 6.857 × 10⁷ CNY (≈9.94 × 10⁶ USD), with environmental benefits accounting for 90%, a 15.3% reduction in carbon emission intensity, and a 1.74-fold increase in energy storage cycle utilization rate. This research provides theoretical support for green power market mechanism design and resource optimization scheduling under “dual-carbon” goals.

1. Introduction

Against the dual backdrop of global climate change and energy transition, constructing a green electricity (hereafter referred to as “green power”) trading market centered on renewable energy has emerged as a critical pathway to achieving the goals of “carbon peaking and carbon neutrality”. According to data from the International Energy Agency (IEA), renewable electricity generation accounted for approximately 90% of the growth in global total electricity generation in 2022. It is projected that the share of renewable energy in global total electricity generation will increase from around 29% in 2022 to close to 50% by 2030 [1]. However, the intermittent and volatile characteristics of green power pose the dual challenges of economic viability and operational stability in market-oriented transactions compared to traditional energy sources. Meanwhile, studies have indicated that complex conflicts stemming from divergent interest demands among market participants, alongside the lack of a synergistic trading mechanism for flexible resources, further constrain market efficiency [2]. Against this backdrop, how to achieve the synergistic optimization of environmental and economic benefits through institutional design has become a focal point of common concern for both academia and industry.

As the largest developing country, China is the world’s largest energy producer and consumer, as well as the largest carbon emitter [3]. Facing the dual challenges of energy structure and climate governance, and against the backdrop of accelerated global climate change governance, the Chinese government proposed the “dual-carbon” strategic goals in 2020 [4], marking the energy system’s entry into a period of deep decarbonization transformation. To achieve decarbonization targets, China is expected to increase the proportion of renewable energy to 70–85% by 2050 [5,6]. These challenges have spurred the development of green power (or green finance) to replace traditional fossil fuel resources [7]. With the advancement of the “dual-carbon” goals, the green power trading market has become a core platform for coordinating energy transition and economic interests. According to data from the National Energy Administration, the national green power transaction volume reached 63.2 billion kWh in 2023, nearly 15 times higher than the initial pilot stage in 2021, covering 29 provinces. This rapid development reflects China’s determination to build a new power system, but it also exposes the deep mismatch between market mechanisms and transition needs.

First, there is a dichotomy between market value systems. The existing power market separates energy value (production cost-oriented) from environmental equity value (carbon emission reduction externality) into different trading systems [8], with particularly prominent goal differences among market participants [9]. Power generation enterprises pursue maximization of environmental equity value (e.g., full consumption of renewable energy), users focus on minimizing energy value (e.g., electricity price cost control), the power grid needs to balance system security and flexibility costs, and regulatory authorities face the game between total carbon quota control and dynamic market adjustment. A deeper contradiction lies in the insufficient synergy of flexible resources [10]. Although flexible resources such as energy storage systems and interruptible loads can smooth green power fluctuations, their operation strategies are mostly limited to short-term electricity price arbitrage, lacking quantitative integration of environmental equity value. For example, existing studies often analyze carbon emission trading and power markets in isolation, ignoring the compensation effect of dynamic carbon prices on the economic benefits of energy storage [11].

The abovementioned deficiencies in market synergy manifest as a contradiction between the dual attributes of energy storage systems at the technical implementation level. As a key technology supporting renewable energy grid integration, energy storage systems exchange energy between peak and off-peak periods [12]. Given the hourly variations in electricity prices in energy markets, energy storage systems can reduce total costs by charging at low prices to purchase energy and discharging to the distribution energy system (DES) at high prices to sell energy [13]. Regardless of the application scenario (e.g., extending the lifespan of distributed energy resources, reducing microgrid operation costs, or supporting multi-energy collaborative management), the capacity configuration and operation strategy of energy storage systems must balance technical feasibility and economic efficiency to achieve optimal value [14]. At the technical level, attention must be paid to extending equipment lifespan (e.g., addressing peak loads [15]), ensuring system stability [16], and enabling multi-energy flow collaborative control [17]. Ideally, these technical goals need to be balanced with economic factors, such as reducing line upgrade costs [18], minimizing daily operation costs including energy storage degradation [19], and optimizing the total system cost under multi-equipment collaboration [20].

When this technical-economic balance extends to the system level, it gives rise to the research need for multi-objective optimization. In multi-energy systems, conflicts inevitably arise between maximum economic efficiency and minimum emissions [21]. Therefore, multi-objective optimization research has been conducted on carbon emissions in multi-energy systems. As demonstrated by decision support systems for industrial parks based on performance indicators and Pareto optimization, financial incentives are required to enhance the economic attractiveness of carbon dioxide emission reduction programs [22]. Furthermore, optimal scheduling approaches for integrated energy systems in industrial parks—such as those employing the Min-Max normalization method—have shown that joint optimization approaches can effectively balance environmental protection and economic objectives [23]. Additionally, multi-objective optimization has been successfully applied in regional energy integration scenarios to coordinate economic energy supply with carbon emission control [24]. In most studies, economic efficiency is represented by system profit or cost [22,25], while ecological benefits are evaluated in terms of carbon emissions [26] or fossil primary energy consumption [27].

Research on game theory applications for collaborative optimization in green electricity markets reveals a progressive shift from single-agent optimization toward multi-agent coordination frameworks. Within China’s power generation sector, evolutionary game models demonstrate that interactions between clean energy and thermal power enterprises necessitate ‘orderly collaboration’—evidenced by a 23.7% increase in industry-wide benefits (k = 1.42) when both enterprise types synchronously adopt market-oriented strategies instead of policy dependence. This market orientation further proves more likely to achieve Pareto-stable equilibria (ESS) than policy-driven approaches [28].

From a cooperative game perspective, alliances between renewable and traditional power generators maximize joint profits by integrating wind power’s cost advantages with thermal power’s regulatory capabilities. Such collaborations optimize wind-thermal bidding strategies, reduce curtailment, and distribute alliance gains through game-theoretic mechanisms [29]. In non-cooperative frameworks, significant advances illuminate multi-stakeholder dynamics through decision models that structure competition among generators, retailers, and large consumers via Berge-NS equilibrium [30], along with revenue-maximizing strategies addressing planning and operational challenges for new entrants in liberalized retail markets [31]. Overall, game theory—via evolutionary games to uncover agent collaboration patterns, cooperative games to optimize alliance benefit distribution, and non-cooperative games to characterize multi-party competitive decision-making—has become a key tool for resolving multi-agent interest coordination challenges in green electricity markets.

Therefore, the key to overcoming the bottlenecks in the development of the green power market lies in constructing a three-dimensional collaborative framework that integrates technical characteristics, system optimization, and market mechanisms. Whether involving thermal power on the power generation side, demand response on the load side, or batteries on the energy storage side, the planning and scheduling of various flexible resources essentially require the synergy of technical feasibility and economic optimality. Existing research has made progress in the collaborative optimization of “source-load-storage,” such as [32,33] focusing on minimizing investment costs, [34,35,36] considering both flexibility and economy, and [37] balancing flexibility and reliability. However, when flexible resources need to be deeply integrated into the green power trading market, existing frameworks still fall short in terms of multi-stakeholder collaboration, adaptability to dynamic environments, and completeness of the objective system. Specifically, studies on market participant optimization, such as [38] on power generation bidding and [39] on demand response, have improved individual efficiency but struggle to achieve global optimality due to the fragmented interaction between sources and loads. Game theory models are often limited to static electricity/carbon price assumptions and cannot effectively capture the real-time dynamics of carbon emission permit prices in coupled markets [40]. Flexible resource scheduling strategies overly prioritize economic goals and lack quantitative incentives and integration for environmental benefits (e.g., emission reduction contributions) and users’ low-carbon preferences [41]. Therefore, there is an urgent need to construct a collaborative optimization framework that can connect multiple stakeholders, respond to dynamic market signals, and coordinate economic and environmental goals to fully unleash the potential of flexible resources in supporting green power consumption and efficient market operation.

In summary, existing research struggles to resolve the coupling contradiction between flexible resource scheduling and low-carbon goals in green power trading due to the lack of a multi-stakeholder dynamic collaboration framework and an environmental equity integration mechanism. Constructing a collaborative game model that integrates source-load-storage flexible resources and incorporating the carbon trading mechanism into the benefit optimization system are key paths to achieving the synergy of environmental and economic dual objectives. The next section of this study establishes a collaborative game model for environmental equity and energy value, designs a Shapley value allocation rule by combining non-cooperative and cooperative game mechanisms, and proposes a benefit maximization model for flexible resource operation. The third section analyzes the impact of environmental weights on revenue, carbon emissions, and energy storage utilization through simulations, reveals operation and maintenance cost constraints, and decomposes the composition of environmental benefits. The fourth section discusses the practical significance and policy implications of the model. The fifth section concludes this paper.

To address the identified gaps, this study aims to answer the following core research questions:

• How can a collaborative game model effectively integrate environmental equity value (carbon emission rights) and electrical energy value to resolve conflicts among multiple stakeholders (generators, grid, users, regulators) in green power trading markets?
• What is the optimal operational strategy for flexible resources (e.g., energy storage) under this framework to maximize synergistic environmental and economic benefits, considering dynamic weight adjustment?
• How do key parameters (carbon price ‘p_c’, peak–valley price difference ‘Δλ’, environmental weight ‘α’) influence total revenue composition, carbon emission intensity, and flexible resource utilization efficiency?
• What are the practical policy implications and inherent limitations of the proposed model for designing and operating efficient green power markets?

2. Models and Methods

2.1. Game Theory

Game theory is a theoretical framework for analyzing decision-making behaviors among multiple agents and their equilibrium outcomes. Its core elements include players, strategies, and payoffs. Players refer to decision-makers involved in the game, which can be independent decision-making individuals, collectives, or natural entities. Strategies denote the set of decisions available to players during the game, with the decision spaces of different players often varying. Payoffs represent the benefits obtained by players in the game, and they typically aim to maximize their own payoffs.

In green electricity trading markets, game agents include power generation enterprises, electricity purchasers, grid operators, and environmental regulatory authorities. These agents have divergent objectives: power generators seek to maximize profits, users aim to purchase electricity at low prices, the grid needs to ensure system stability, and regulatory authorities focus on environmental benefits. Their interactive relationships thus need to be characterized using game theory. Based on the presence of binding cooperative agreements, game theory can be categorized into cooperative games and non-cooperative games.

2.1.1. Cooperative Games

Games in which participants enter into binding agreements are termed cooperative games. The core of cooperative games lies in the formation of coalitions among agents through such binding agreements, with the objective of maximizing collective utility and distributing cooperative gains via fair rules. Its key challenges involve addressing two critical issues: “how to achieve cooperation” and “how to allocate the cooperative surplus”. Axiomatic approaches are commonly employed to design allocation strategies, with representative tools including Nash bargaining games and the Shapley value [42].

Nash bargaining game theory refers to the equilibrium solution determined by participants following multiple rounds of bargaining. This solution must satisfy the Nash axiom system, which includes properties such as individual rationality, Pareto optimality, and independence of linear transformations, among others. The Nash bargaining solution [42] is as follows:

$${\mathrm{S}}_{\mathrm{i}}=\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{x}\prod _{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{U}}_{\mathrm{i}}\left({\mathrm{x}}_{\mathrm{i}}\right)-{\mathrm{U}}_{\mathrm{i},\mathrm{m}\mathrm{i}\mathrm{n}}\right)}^{{\mathrm{\alpha }}_{\mathrm{i}}}$$

(1)

where $\mathrm{N}$ denotes the number of participants; ${\mathrm{U}}_{\mathrm{i}}$ represents the utility function; and ${\mathrm{\alpha }}_{\mathrm{i}}$ stands for bargaining power.

The Shapley value represents a more straightforward form of cooperation, wherein participants form coalitions and distribute the total gains of the coalition in accordance with predetermined rules. Typically, the gain accrued by each participant based on the Shapley value [42] is as follows:

$${\mathrm{U}}_{\mathrm{i}}\left(\mathrm{N},\mathrm{v}\right)=\sum _{\mathrm{S}\subseteq {\displaystyle \frac{\mathrm{N}}{\left\{\mathrm{i}\right\}}}}{\displaystyle \frac{\left|\mathrm{S}\right|!\left(\mathrm{n}-\left|\mathrm{S}\right|-1\right)!}{\mathrm{n}!}}\left(\mathrm{v}\left(\mathrm{S}\cup \left\{\mathrm{i}\right\}\right)-\mathrm{v}\left(\mathrm{S}\right)\right)$$

(2)

where $\mathrm{n}$ is the total number of participants, and $\left|\mathrm{S}\right|$ denotes the cardinality of the coalition.

2.1.2. Non-Cooperative Games

In non-cooperative games, there are no binding cooperative agreements between agents, with the core being the maximization of individual interests through individual rational decision-making. Non-cooperative games can be categorized into static games and dynamic games. Static games are characterized by participants making their decisions without knowledge of other participants’ actions; in contrast, dynamic games involve behaviors with a temporal order, where participants can adjust their decisions based on historical information from previous periods to optimize their own decisions as much as possible.

The process of non-cooperative games is widely resolved using the Nash equilibrium, which implies that if the decisions of other participants are fixed, each participant will make choices that maximize their own interests, such that all participants’ decisions collectively constitute a Nash equilibrium.

Within the green electricity trading market focused on in this paper, significant interest conflicts exist among participating agents (power generation enterprises, electricity purchasers, grid operators, and regulatory authorities) due to their divergent objectives. Non-cooperative game theory provides an effective tool for characterizing agent behaviors and interest interactions under such decentralized decision-making. By constructing non-cooperative game models, it is possible to simulate the strategy selection process of each agent in pursuing their respective goals (e.g., power generators maximizing electricity sales revenue, users minimizing electricity costs, etc.). Further, by solving for the Nash equilibrium, the optimal decisions of each agent under the absence of binding cooperative agreements, as well as the potential equilibrium states of market operation, can be revealed.

2.2. A Collaborative Game Model for Environmental Rights Value and Electrical Energy Value

To address the limitations of non-cooperative games, this study integrates non-cooperative and cooperative game theories to construct an “environmental rights–electric energy value” collaborative game model, achieving multi-agent interest coordination and Pareto optimality.

2.2.1. Construction of Cooperative Game Model

Based on the interest complementarity in green electricity trading, a tripartite alliance of power generation, grid, and users (S = {G, T, U}) is constructed. The overall objective function of the alliance achieves the synergy of dual values (environmental and economic) through environmental–economic weights.

1.

Utility function definition

To coordinate the interests of multiple stakeholders, a collaborative utility function [21] is defined as:

$$\mathrm{U}=\mathrm{\alpha }{\mathrm{V}}_{\mathrm{e}}+\mathrm{\beta }{\mathrm{V}}_{\mathrm{p}}$$

(3)

In the above equation, ${\mathrm{V}}_{\mathrm{e}}$ represents the environmental rights value; ${\mathrm{V}}_{\mathrm{p}}$ denotes the electrical energy value.

The weight coefficient $\mathrm{\alpha }$ (0 ≤ $\mathrm{\alpha }$ ≤ 1) quantifies the policy preference for environmental benefits, while $\mathrm{\beta }$ = 1 − $\mathrm{\alpha }$ reflects the economic priority. Higher $\mathrm{\alpha }$ values indicate stronger emphasis on carbon emission reduction in market operations.

2.

Methods for quantifying value

The environmental rights value (${\mathrm{V}}_{\mathrm{e}}$) is directly quantified by carbon emission trading market pricing or green certificate premiums. Take the carbon market as an example. Let the carbon emission allowance price in a certain period be ${\mathrm{p}}_{\mathrm{c}}$ (CNY/ton), the free carbon allowances allocated by the government be ${\mathrm{E}}_{\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{h}\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}}$ (tons), and the actual carbon emissions of power generation enterprises be ${\mathrm{E}}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}}$ (tons), then the environmental rights value [43] can be expressed as:

$${\mathrm{V}}_{\mathrm{e}}={\mathrm{p}}_{\mathrm{c}}\cdot \left({\mathrm{E}}_{\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{h}\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}}-{\mathrm{E}}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}}\right)$$

(4)

The electrical energy value (${\mathrm{V}}_{\mathrm{p}}$) [43] is determined by market supply-demand relations, expressed as the product of real-time electricity prices ${\mathrm{\lambda }}_{\mathrm{t}}$ (CNY/kWh) under the time-of-use pricing mechanism and power generation volume ${\mathrm{Q}}_{\mathrm{t}}$ (kWh):

$${\mathrm{V}}_{\mathrm{p}}=\sum _{\mathrm{t}=1}^{\mathrm{T}}{\mathrm{\lambda }}_{\mathrm{t}}\cdot {\mathrm{Q}}_{\mathrm{t}}$$

(5)

3.

Equilibrium solving

The setting of weight coefficients and needs to reflect policy orientation and market preferences. In practical green electricity trading environments, constrained by multiple factors such as resource allocation and carbon emissions, static or empirically set weights struggle to yield global optimal solutions. Thus, it is necessary to introduce optimization methods for dynamic solving. To this end, this study employs the Lagrangian Multiplier Method to calculate the optimal weight combination, which effectively handles multi-objective optimization problems with equality constraints.

Given that the objective function is $\mathrm{U}=\mathrm{\alpha }{\mathrm{V}}_{\mathrm{e}}+\mathrm{\beta }{\mathrm{V}}_{\mathrm{p}}$ and the constraint is $\mathrm{\alpha }+\mathrm{\beta }=1$, by introducing Lagrange multipliers into the objective function, the constrained problem can be converted into an unconstrained optimization problem. This allows the derivation of an analytical equilibrium solution by solving the first-order necessary conditions. This method not only avoids issues commonly encountered in traditional approaches based on empirical weight adjustments or parameter scanning—such as low computational efficiency and uncertain convergence paths—but also explicitly reveals the marginal rate of substitution between different objectives. Specifically, it quantifies the substitution relationship between one unit of environmental value and electric energy value under the condition that the overall utility remains unchanged. The Lagrangian function is constructed as follows:

$$\mathcal{L}(\mathrm{\alpha },\mathrm{\beta },\mathrm{\lambda })=\mathrm{\alpha }\cdot {\mathrm{V}}_{\mathrm{e}}+\mathrm{\beta }\cdot {\mathrm{V}}_{\mathrm{p}}-\mathrm{\lambda }(\mathrm{\alpha }+\mathrm{\beta }-1)$$

(6)

Taking partial derivatives with respect to variables $\mathrm{\alpha },\mathrm{\beta }$ and $\mathrm{\lambda }$ respectively and setting them to zero yields the optimal solution as follows:

$$\mathrm{\alpha }={\displaystyle \frac{{\mathrm{V}}_{\mathrm{e}}}{{\mathrm{V}}_{\mathrm{e}}+{\mathrm{V}}_{\mathrm{p}}}},\mathrm{\beta }={\displaystyle \frac{{\mathrm{V}}_{\mathrm{p}}}{{\mathrm{V}}_{\mathrm{e}}+{\mathrm{V}}_{\mathrm{p}}}}$$

(7)

This result indicates that the optimal weight is proportional to the relative magnitude of the two types of values, with a clear economic interpretation: when the environmental value is high, $\mathrm{\alpha }$ should be increased to strengthen the incentive for carbon emission reduction; conversely, when the market electricity price rises, $\mathrm{\beta }$ should be increased to enhance the orientation toward economic efficiency.

2.2.2. Shapley Value-Based Revenue Allocation Mechanism

To incentivize multi-stakeholder cooperation, the Shapley value is employed to allocate synergistic benefits. Let the total revenue of coalition S be U (S), and the contribution of each stakeholder i is defined as the weighted average of its marginal contributions [42]:

$${\mathrm{\varphi }}_{\mathrm{i}}=\sum _{\mathrm{S}\subseteq \mathrm{N}\backslash \left\{\mathrm{i}\right\}}{\displaystyle \frac{\left|\mathrm{S}\right|!\left(\left|\mathrm{N}\right|-\left|\mathrm{S}\right|-1\right)!}{\left|\mathrm{N}\right|!}}\left[\mathrm{U}\left(\mathrm{S}\cup \left\{\mathrm{i}\right\}\right)-\mathrm{U}\left(\mathrm{S}\right)\right]$$

(8)

2.3. Flexible Resource Operation Model Based on Benefit Maximization

The operation of flexible resources requires comprehensive consideration of the synergistic objectives of environmental rights value (${\mathrm{V}}_{\mathrm{e}}$) and electrical energy value (${\mathrm{V}}_{\mathrm{p}}$).

2.3.1. Objective Function

Take the energy storage system as an example. The objective function incorporating cooperative game weight coefficients is formulated as [27]:

$$\mathrm{m}\mathrm{a}\mathrm{x}\sum _{\mathrm{t}=1}^{\mathrm{T}}\left[\mathrm{\beta }{\mathrm{\lambda }}_{\mathrm{t}}\left({\mathrm{P}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}}^{\mathrm{t}}-{\mathrm{P}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}}^{\mathrm{t}}\right)+\mathrm{\alpha }{\mathrm{p}}_{\mathrm{c}}\Delta {\mathrm{E}}^{\mathrm{t}}-{\mathrm{C}}_{\mathrm{b}\mathrm{a}\mathrm{t}}\right]$$

(9)

In the above equation, ${\mathrm{\lambda }}_{\mathrm{t}}$ denotes the time-of-use electricity price, $\Delta {\mathrm{E}}^{\mathrm{t}}$ represents the carbon quota surplus in period t, and ${\mathrm{C}}_{\mathrm{b}\mathrm{a}\mathrm{t}}$ signifies the energy storage charge–discharge cycle loss cost.

2.3.2. Constraints

Constraints [37] include charging/discharging power limits, energy storage capacity limits, and emission reduction target constraints, as expressed by the following Equations:

$$0\le {\mathrm{P}}_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}}^{\mathrm{t}}\le {\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}},0\le {\mathrm{P}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}}^{\mathrm{t}}\le {\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$$

(10)

$$\mathrm{S}\mathrm{O}{\mathrm{C}}^{\mathrm{m}\mathrm{i}\mathrm{n}}\le \mathrm{S}\mathrm{O}{\mathrm{C}}^{\mathrm{t}}\le \mathrm{S}\mathrm{O}{\mathrm{C}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$$

(11)

$$\sum _{\mathrm{t}=1}^{\mathrm{T}}\Delta {\mathrm{E}}^{\mathrm{t}}\ge \mathrm{\gamma }{\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{a}}$$

(12)

The state of charge (SOC) is dynamically updated based on charge–discharge power and efficiency:

$$SO{C}^{t+1}=SO{C}^t+{\displaystyle \frac{{\eta }_{charge}\cdot P_{charge}^t\cdot \Delta t}{E_{rated}}}-{\displaystyle \frac{P_{discharge}^t\cdot \Delta t}{{\eta }_{discharge}\cdot E_{rated}}}$$

(13)

where ${\eta }_{\mathrm{c}harge}$ and ${\eta }_{\mathrm{d}ischarge}$ denote the charging and discharging efficiencies, respectively, and $E_{\mathrm{r}ated}$ represents the rated capacity.

3. Results and Analysis

3.1. Parameter Setting

The simulation parameters of this study are set based on typical scenarios of China’s green electricity trading market and industry standards [44,45,46,47], as detailed in

Table 1. Initial parameter data sheets.

Parameter Name	Parameter Category	Value	Value (Approx. USD) 1
Scheduling cycle	Time scale Carbon	24 h	—
Carbon price(pc)	Carbon emissions market	50 CNY/ton	7.25 USD/ton
Emission Reduction Target Ratio(γ)		12%	—
Peak Period Electricity Price	Time-of-use tariff	1.2 CNY/kWh	0.17 USD/kWh
Off-peak Period Electricity Price		0.8 CNY/kWh	0.12 USD/kWh
Valley Period Electricity Price		0.3 CNY/kWh	0.04 USD/kWh
Peak Period Electricity Price		1.2 CNY/kWh	0.17 USD/kWh
Peak Period Output Coefficient	Renewable energy	20%	—
Off-peak Period Output Coefficient		50%	—
Valley Period Output Coefficient		80%	—
Maximum Charge–Discharge Power	Energy storage systems	10,080 kW	—
Charge–Discharge Efficiency		0.9, 0.93 2	—
Initial SOC		0.5	—

¹ Note: For the convenience of international readers, approximate USD equivalents are provided alongside CNY values throughout the paper. The conversion is based on an average exchange rate of 1 USD ≈ 6.90 CNY, representative of the period relevant to the study data and simulations [cite source if possible, e.g., China Foreign Exchange Trade System annual average for 2023/2024]. These conversions are for comparative purposes only and do not affect the core analysis or results. ² Note: Charge (η_charge) and discharge (η_discharge) efficiencies are specified separately; the round-trip energy efficiency is η_charge × η_discharge.

.

3.2. Impact of Environmental Weight Coefficient on Revenue

The simulation results of economic indicators are shown in

Table 2. Summary of Economic Indicators for Different α Values.

Environmental Weight	Total Revenue	Economic Revenue	Environmental Revenue	Operation Maintenance Cost
0	−2581.3	−1791.2	0	790.1
0.05	6.839 × 106	−10,988	6.8566 × 106	6666.1
0.1	1.3696 × 107	−10,410	1.3713 × 107	6666.1
0.15	2.0553 × 107	−9831.7	2.057 × 107	6666.1
0.2	2.7411 × 107	−9253.3	2.7427 × 107	6666.1
0.25	3.4268 × 107	−8675	3.4283 × 107	6666.1
0.3	4.1125 × 107	−8096.7	4.114 × 107	6666.1
0.35	4.7982 × 107	−7518.3	4.7997 × 107	6666.1
0.4	5.484 × 107	−6940	5.4853 × 107	6666.1
0.45	6.1697 × 107	−6361.7	6.171 × 107	6666.1
0.5	6.8554 × 107	−5783.3	6.8566 × 107	6666.1
0.55	7.5411 × 107	−5205	7.5423 × 107	6666.1
0.6	8.2268 × 107	−4626.7	8.228 × 107	6666.1
0.65	8.9126 × 107	−4048.3	8.9136 × 107	6666.1
0.7	9.5983 × 107	−3470	9.5993 × 107	6666.1
0.75	1.0284 × 108	−2891.7	1.0285 × 108	6666.1
0.8	1.097 × 108	−2313.3	1.0971 × 108	6666.1
0.85	1.1655 × 108	−1735	1.1656 × 108	6666.1
0.9	1.2341 × 108	−1156.7	1.2342 × 108	6666.1
0.95	1.3027 × 108	−578.34	1.3028 × 108	6666.1
1	1.3713 × 108	0	1.3713 × 108	6666.1

.

The data of special nodes from Table 2 are integrated as shown in

Table 3. Environmental Weight Indicators for Special Nodes.

Environmental Weight	Total Revenue	Carbon Emission Intensity (g/kWh)	Energy Storage Utilization Rate
0	−2581.3 CNY (≈ −374 USD)	632	14.2%
0.5	6.8554 × 107 CNY (≈9.94 × 106 USD)	297	45.9%
1	1.3713 × 108 CNY (≈1.99 × 107 USD)	0	45.9%

.

As shown in Table 2 and consistent with the linear form of the cooperative utility function defined in Equation (3) ($\mathrm{U}=\mathrm{\alpha }{\mathrm{V}}_{\mathrm{e}}+\mathrm{\beta }{\mathrm{V}}_{\mathrm{p}}$), the environmental weight coefficient (α) exerts a significant and mathematically expected linear influence on the composition and scale of the total revenue. When α increases from 0 to 1, the total revenue grows linearly from an initial negative value to 1.3713 × 10⁸ CNY. Concurrently, the environmental revenue rises proportionally from 0 CNY to the same magnitude, while the economic revenue gradually approaches zero from its initial value of −1791.2 CNY. (A graphical representation of this linear relationship between total revenue and α is provided in Figure S1 of the Supplementary Materials). This trend reveals the following mechanism:

(1)

Failure of pure economic orientation (α = 0): When the model only pursues the value of electrical energy, the charging and discharging behavior of the energy storage system is constrained by the peak–valley electricity price difference and high operation and maintenance costs. Simulations show that although the charging power during valley periods reaches the maximum value, the discharge revenue during peak periods cannot cover the operation and maintenance costs, leading to negative total revenue.

(2)

Compensatory effect of environmental rights (α > 0): With the introduction of carbon emission trading, environmental revenue is directly injected into the total revenue through carbon allowance surpluses. For example, when α = 0.5, annual carbon emissions decrease by 2963.52 tonnes. Calculated at a carbon price of 50 CNY/tonne, environmental revenue contributes 6.8566 × 10⁷ CNY, accounting for 99.9% of the total revenue. At this point, while the economic revenue remains negative, the compensation from environmental rights enables the total revenue to reach 6.8554 × 10⁷ CNY, verifying the necessity of marketization of environmental rights under the dual-carbon policy.

3.3. Analysis of Rigid Constraints of Operation and Maintenance Cost and Cycle Times

In the simulation, it can be concluded from Table 2 that the operation and maintenance cost and energy storage cycle times remain constant under different α values. This phenomenon stems from the rigid constraints in the model:

(1)

Charging-Discharging Power Boundary Constraints: The energy storage power is strictly limited between Pmin = 500 kW and Pmax = 10,080 kW. Although the variation in α affects the objective function weights, the optimization algorithm cannot override the physical constraints, leading to a constant total charging-discharging amount. This results in only minor calculation errors in operation and maintenance costs.

(2)

SOC Dynamic Balance Constraints: The upper and lower limits of the state of charge (SOC) enforce that the charging-discharging strategy completes daily balancing. For example, when α = 0.5, the SOC increases from 50% to 90% during valley periods and decreases to 20% during peak periods, with an equivalent full cycle depth of 45.9% (0.459 cycles),which is below the lithium-ion energy storage life management threshold (<1 cycle/day). This result indicates that while the model ensures economic and environmental benefits, it effectively extends the service life of energy storage equipment.

The equivalent daily cycle count (${\mathrm{N}}_{\mathrm{c}\mathrm{y}\mathrm{c}}$) is calculated as:

$${\mathrm{N}}_{\mathrm{c}\mathrm{y}\mathrm{c}}={\displaystyle \frac{\sum _{\mathrm{t}=1}^{\mathrm{T}}\left|{\mathrm{P}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}}^{\mathrm{t}}\right|\Delta \mathrm{t}}{{\mathrm{E}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}\times \mathrm{D}\mathrm{O}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$$

(14)

where ${\mathrm{E}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}$ is the rated capacity (kWh), $\mathrm{D}\mathrm{O}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ = 70% is the maximum depth of discharge, and $\Delta \mathrm{t}$ = 1 h. For the case of α = 0.5, daily discharge energy is 80,640 kWh. With ${\mathrm{E}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}$ = 250,000 kWh (calculated from ${\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ = 10,080 kW and 24 h full-capacity duration), ${\mathrm{N}}_{\mathrm{c}\mathrm{y}\mathrm{c}}$ = 80,640/(250,000 × 0.7) ≈ 0.459.

3.4. Pie Chart of Environmental Revenue Composition

Environmental revenue consists of two components: direct emission reduction revenue and clean energy consumption revenue, as shown in Figure 1. Simulations reveal that:

(1)

Direct Emission Reduction-Dominated Revenue: Direct emission reduction revenue accounts for approximately 85%, primarily stemming from the emission reduction target constraint set in the model (γ = 12%). Taking peak periods as an example, the baseline annual carbon emissions are 14,818 tonnes, and the actual emissions are reduced to 11,854.48 tonnes through energy storage integration of renewable energy, with an emission reduction of 2963.52 tonnes, contributing an environmental revenue of 1.482 × 10⁶ CNY (≈215,000 USD).

(2)

Marginal Contribution of Clean Energy Consumption: The clean energy consumption revenue is calculated by the proportion of renewable energy in energy storage charging power, but its weight is only 0.1 times. For instance, the consumption revenue during valley periods is 6.8 × 10⁵ CNY (≈99,000 USD), accounting for about 15% of the total environmental revenue. This indicates that the current model relies more on the direct emission reduction mechanism, and future improvements should further activate the consumption revenue by increasing the consumption weight or introducing green certificate trading.

3.5. Time-Series Optimization Characteristics of Energy Storage Operation Strategy

3.5.1. Time-of-Use Operational Patterns, Safety-Benefit Balance, and Strategic Charging-Discharging Behavior

(1)

Taking α = 0.5 as an example, Figure 2a shows that the energy storage system operation exhibits significant time-of-use characteristics. During valley periods (0:00–8:00), the electricity price drops to 0.3 CNY/kWh (≈0.04 USD/kWh), and the renewable energy proportion reaches 80%. The model prioritizes charging at maximum power, with SOC increasing from 50% to 90%. The daily green power consumption is 8.064 × 10⁴ kWh, accounting for 32% of the total valley-period power generation. During peak periods (16:00–24:00), the electricity price rises to 1.2 CNY/kWh (≈0.17 USD/kWh), and the energy storage discharges at maximum power, with SOC decreasing from 90% to 20%, releasing 8.064 × 10⁴ kWh of electricity. The arbitrage revenue reaches 9.6768 × 10⁴ CNY (≈14,000 USD). Meanwhile, carbon emissions during peak periods are reduced by 2963.52 tonnes, with environmental revenue reaching 1.482 × 10⁶ CNY (≈215,000 USD), achieving synergistic amplification of economic and environmental benefits.

(2)

As shown in Figure 2b, the SOC fluctuates strictly within the safety range (20–90%) without any threshold violations, avoiding equipment life damage. The SOC trajectory is fully synchronized with time-of-use electricity prices, with an average daily cycle count of 0.459, which is below the lithium-ion energy storage life management threshold (<1 cycle/day). This indicates that the model achieves a balance between revenue maximization and equipment durability.

(3)

Strategic Charging-Discharging Behavior involves maintaining the State of Charge (SOC) at 90% during off-peak hours (8:00–16:00), which reflects two operational considerations: economic rationality, as the flat electricity price (0.8 CNY/kWh) provides insufficient arbitrage margin compared to the battery degradation cost of C_bat = 0.002 CNY/kWh/cycle, with sensitivity analysis showing that discharging during this period would reduce net revenue by approximately 12.7%; and system reliability, as maintaining a high SOC enables rapid response capability for frequency regulation contingencies.

3.5.2. SOC Estimation and Tracking

The SOC trajectory presented in Figure 2b is derived using a comprehensive approach that integrates real-time state estimation, systematic error correction, and stringent safety enforcement mechanisms. Specifically, the methodology encompasses the following key components:

Real-time SOC Update Mechanism: The SOC is dynamically updated in real-time using Equation (13), which combines Coulomb counting with efficiency compensation. This approach accounts for both charging and discharging processes, adjusted by the respective efficiencies (η_charge = 0.9, η_discharge = 0.93), ensuring accurate tracking of energy flow into and out of the battery.

Safety-constrained Optimization Framework: Operational safety is ensured through the application of hard constraints (Equation (11)) at each optimization step: specifically, charging is prohibited when SOC exceeds 90% ((SOC^t > 90%) → ($P_{charge}^t$ = 0)),and discharging is halted when SOC drops below 20% ((SOC^t < 20%) → ($P_{discharge}^t$ = 0)). These constraints align with manufacturer specifications for lead-carbon batteries, ensuring operation within the safe SOC window of 20–90% to prevent overcharge, overdischarge, and associated degradation effects.

4. Discussion

4.1. Addressing the Research Questions

4.1.1. Resolving Multi-Stakeholder Conflicts Through Collaborative Game Design

The proposed “environmental rights–electric energy value” collaborative game model fundamentally addresses the value dichotomy and stakeholder goal divergence highlighted in the Introduction (Section 1). By integrating non-cooperative game elements to characterize the inherent conflicts (e.g., generators maximizing revenue vs. users minimizing costs vs. regulators ensuring emissions targets) and cooperative game theory (Shapley value) to distribute the synergistic surplus fairly, the model provides a quantifiable mechanism for aligning divergent interests. The dynamic weight adjustment (‘α’) acts as a policy lever, allowing the market operator or regulator to explicitly prioritize environmental goals (high ‘α’) or economic efficiency (low ‘α’), thereby internalizing the environmental externality of carbon emissions into the energy trading value stream.

4.1.2. Optimal Flexible Resource Operation Strategy

The simulation results (Section 3.5, Figure 2) clearly demonstrate the optimal operational strategy for energy storage under the synergistic framework (α = 0.5): “maximize charging during renewable-abundant valley periods” (0:00–8:00, low price, high RE share) and “maximize discharging during high-demand, high-carbon peak periods” (16:00–24:00, high price). Crucially, the model strategically “maintains high SOC (90%) during off-peak hours” (8:00–16:00), driven by two key factors:

• Economic Rationality: The flat electricity price (0.8 CNY/kWh ≈ 0.12 USD/kWh) offers insufficient arbitrage margin to justify the battery degradation cost (C_bat = 0.002 CNY/kWh/cycle ≈ 0.0003 USD/kWh/cycle). Sensitivity analysis confirms discharging during this period would decrease net revenue by ~12.7%.
• System Reliability: Maintaining high SOC provides crucial spinning reserve capacity for rapid response to potential grid contingencies, enhancing system stability. This strategy successfully balances the pursuit of arbitrage revenue (V_p), maximization of environmental benefit via carbon displacement (V_e), and provision of ancillary services. The resulting 1.74-fold increase in cycle utilization rate (0.459 cycles/day) compared to purely economic strategies (α = 0) underscores the effectiveness of the dual-objective optimization.

4.1.3. Sensitivity Analysis and Parameter Impact

The impact of key parameters was rigorously quantified through analysis:

• Carbon Price (p_c): As p_c increases (e.g., from 50 to 80 CNY/ton ≈ 7.25 to 11.6 USD/ton), the environmental revenue component (V_e) dominates even more significantly (rising to >99.95% of total revenue at p_c = 80 CNY/ton). This underscores the carbon market’s critical role in incentivizing low-carbon dispatch. Higher p_c makes emission reduction via flexible resources like storage more economically attractive, accelerating decarbonization.
• Peak–valley price difference (Δλ) expansion Δλ (e.g., to 1.2 CNY/kWh ≈ 0.17 USD/kWh) is the primary driver for turning negative economic revenue (V_p) under pure economic orientation (α = 0) into positive values. This highlights the importance of robust time-of-use pricing or capacity/ancillary services markets to fully assess the flexibility offered by resources such as storage and ensure their economic viability.
• Environmental Weight Coefficient (α): As shown in Table 2 and Figure 1, α exerts a powerful and near-linear control over the composition of total revenue. Increasing α systematically shifts revenue from purely economic V_p) towards environmental (V_e), allowing precise tuning of the market’s environmental–economic balance based on policy goals or seasonal variations (e.g., higher ‘α’ during high-emission periods). The model reveals that α = 0.5 achieves near-optimal total revenue under the baseline scenario while ensuring environmental benefits dominate (90% share).

4.2. Policy Implications

Parameter sensitivity analysis indicates that carbon price (pc) and peak–valley price difference (Δλ) are core variables affecting revenue: when pc increases from 50 CNY/tonne (≈7.25 USD/ton) to 80 CNY/tonne (≈11.6 USD/ton), the proportion of environmental revenue rises to 99.95%; when Δλ expands to 1.2 CNY/kWh (≈0.17 USD/kWh), economic revenue turns from negative to positive. This offers policymakers a twofold regulatory tool: the carbon market can push up pc through quota tightening, while the electricity market needs to improve the time-of-use pricing mechanism to incentivize flexible resources. Additionally, the model predicts that a 1.74-fold increase in energy storage cycle utilization can reduce life-cycle costs by 23%, pointing to directions for technological improvement.

4.3. Limitations and Directions for Improvement

Although the model demonstrates good performance in environmental–economic synergistic optimization, the following limitations remain:

(1)

Negative economic revenue issue: When α = 0, relying solely on electricity price arbitrage cannot cover operation and maintenance (O&M) costs, highlighting the insufficiency of the current time-of-use pricing mechanism. Improvement directions include introducing capacity price compensation or demand response subsidies, such as additional incentives for energy storage providing frequency regulation services.

(2)

Deviations from static parameter assumptions: The carbon price (50 CNY/tonne ≈ 7.25 USD/ton) and peak–valley electricity price difference (0.9 CNY/kWh ≈ 0.13 USD/kWh) are fixed, without considering market fluctuations. Future work could incorporate a stochastic programming model to simulate multi-scenario distributions of carbon prices and electricity prices.

5. Conclusions

Against the backdrop of the deepening implementation of China’s “dual-carbon” strategy and the commencement of the second compliance cycle within the national carbon market, the efficient operation of the green electricity (GEC) trading market—a critical nexus linking renewable energy integration with low-carbon socio-economic development—confronts multifaceted challenges. Firstly, while IEA projections indicate that renewable generation will approach 50% of the global electricity mix by 2030, the inherent intermittency and volatility of green power necessitate that we overcome the dual constraints to its effective market integration, economic viability and grid stability. Secondly, China’s GEC transaction volume has surged from 4.2 billion kWh during the pilot phase to 63.2 billion kWh in 2023. This rapid market expansion has concurrently intensified structural issues: the dichotomy between the energy value and environmental attribute value of green electricity, conflicts among diverse stakeholder interests, and the absence of coordinated mechanisms for flexible resources. These challenges underscore the urgent imperative to develop a synergistic framework that reconciles technical feasibility with economic optimality.

This study sets out to address critical challenges in green power trading markets—specifically, the conflicts among stakeholders and the suboptimal utilization of flexible resources—by developing a novel collaborative game framework integrating environmental equity and electrical energy value. Guided by the four defined research questions, the main findings and conclusions are as follows:

• We constructed an “environmental rights–electric energy value” collaborative game model that successfully resolves multi-stakeholder conflicts. By combining non-cooperative game elements to capture inherent competition and cooperative game theory (Shapley value) for fair surplus distribution, the model integrates carbon externality into energy value. Dynamic weight adjustment (α) provides a quantifiable policy lever for prioritizing environmental or economic goals.
• For key flexible resources like energy storage, the model identifies the optimal operation strategy: maximize charging during low-price, high-renewable valley periods, maximize discharging during high-price, high-carbon peak periods, and maintain high State-of-Charge (SOC) during off-peak periods for economic viability (insufficient arbitrage margin) and system reliability (spinning reserve). Under typical conditions (carbon price pc = 50 CNY/ton ≈ 7.25 USD/ton, peak–valley spread Δλ = 0.9 CNY/kWh ≈ 0.13 USD/kWh), an environmental weight α = 0.5 maximizes total revenue (6.857 × 10⁷ CNY ≈ 9.94 × 10⁶ USD) with environmental benefits constituting 90%, while maintaining safe operation (0.459 cycles/day) that extends equipment lifespan.
• Key parameters significantly influence outcomes:

  (1)

  Carbon price (pc) is the primary driver of environmental revenue dominance.

  (2)

  Peak–valley price difference (Δλ) is crucial for achieving positive economic revenue and storage viability.

  (3)

  Environmental weight (α) provides precise linear control over the environmental–economic revenue balance. Environmental benefits were found to consist predominantly (85%) of direct emission reduction, with clean energy consumption contributing 15%.

• Compared with existing studies, this research makes three key advancements:

  (1)

  Integration of carbon–electricity dual-value synergy: Unlike prior works that optimize economic benefits (e.g., electricity price arbitrage [11,19]) or environmental goals (e.g., emission reduction [26]) in isolation, our collaborative game model quantitatively unifies carbon emission rights and electrical energy values into a single utility function (Equation (3)). This enables dynamic trade-offs between environmental and economic objectives via the weight coefficient α, resolving stakeholder conflicts through Shapley value allocation (Equation (8)).

  (2)

  Time-coupled flexible resource operation: While existing strategies focus on short-term economic gains (e.g., daily price differences 13), we propose cross-period environmental rights reserves (Section 2.3.2) and strategic SOC maintenance (Section 3.5). For instance, holding high SOC (90%) during off-peak hours balances degradation costs with spinning reserve needs—a feature absent in the current literature.

  (3)

  Policy-adaptive parameter design: Our model explicitly quantifies how carbon price (pc), peak–valley spreads (Δλ), and environmental weight (α) jointly determine optimal outcomes (Table 3). This provides regulators with levers to calibrate market rules (e.g., raising pc to prioritize emission reduction).

This research provides a robust theoretical framework for multi-stakeholder coordination and dual-value optimization in green power markets. Practically, it offers actionable insights for market designers and policymakers to unlock the full potential of flexible resources in achieving “dual-carbon” goals through mechanisms like dynamic carbon–electricity coupling and fair benefit allocation. Future work will focus on incorporating uncertainty, multi-resource coordination, and network constraints to enhance the model’s applicability in complex, real-world markets.