Research on Multi-Microgrid Electricity–Carbon Collaborative Sharing and Benefit Allocation Based on Emergy Value and Carbon Trading

Abstract

In response to climate change, the proportion of renewable energy penetration is increasing daily. However, there is a lack of flexible energy transfer mechanisms. The optimization effect of low-carbon economic dispatch in a single park is limited. In the context of the sharing economy, this study proposes a research method for multi-park electricity sharing and benefit allocation based on carbon credit trading. Firstly, a framework for multi-park system operation is constructed, and an energy hub model is established for the electrical, cooling, and heating interconnections with various energy conversions. Secondly, a park carbon emission reduction trading model is established based on the carbon credit mechanism, further forming an optimal economic and environmental dispatch strategy for multi-park electricity sharing. Matlab+Gurobi is used for solving. Then, based on asymmetric Nash bargaining, the comprehensive contribution rate of each park is calculated by considering their energy contribution and carbon emission reduction contribution, thereby achieving a fair distribution of cooperation benefits among multiple parks. The results show that the proposed method can effectively reduce the overall operational cost of multiple parks and decrease carbon emissions, and the benefit allocation strategy used is fair and reasonable, effectively motivating the construction of new energy in parks and encouraging active participation in cooperative operations by all parks.

1. Introduction

Constructing a new energy system is the inevitable path for China to move towards a green and sustainable future. It is crucial to achieving the “dual-carbon” goals and promoting ecological civilization [1]. In 2023, China’s installed capacity for renewable energy generation historically surpassed that of thermal power. The annual new installed capacity contributes over half of the global total, reaching a cumulative capacity of 1.45 billion kilowatts and a total power generation exceeding 30 trillion kilowatt-hours. In the future, for the application of renewable energy, low-carbon development requires coupling the electricity and carbon markets in the energy industry to promote its healthy development. Furthermore, it entails coordinating and managing multi-complementary energy systems centered around energy storage, establishing pathways for energy sharing in microgrids, and thereby enhancing the consumption capacity of renewable energy generation [2,3,4,5,6].

There have been several previous studies on the coordinated operation of the electricity and carbon markets. Batista et al. [7] proposed a physical options theory approach to consider the uncertainty in estimating carbon emissions reductions and the incremental revenue in carbon markets for renewable energy generation projects. They further incorporated the stochastic nature of certified carbon emission reduction (CCER) trading prices to develop investment plans for clean development projects. Wang et al. [8] designed a carbon-oriented demand response mechanism for electricity consumption, where the carbon emissions and corresponding costs for individual users were determined through traceability. There are various aspects to consider in the design of the electricity–carbon market transmission mechanism. One key aspect is clarifying the linkage between renewable energy generation companies, such as wind and solar, participating in both green electricity trading in the power market and CCER trading in the carbon market. Additionally, it is important to remove the limitations on the offset ratio between green electricity and CCER trading in carbon emission reductions and devise a mechanism for mutual recognition and offset of green electricity and CCER trading [9]. Du, X. et al. [10] adopted the improved cuckoo search algorithm to optimize the power dispatching scheme of a multi-microgrid, aiming at promoting the economic benefit of the system and the consumption of renewable energy. Aghmadi, A. et al. [11] investigated multi-microgrid systems, including DC microgrids, renewable energy, and energy storage units, and verified that the multi-microgrid systems are more robust than the single-microgrid system in the face of pulse loads and variable loads.

The dual carbon goals have facilitated the flourishing development of distributed renewable energy, addressing challenges such as the stochastic behavior of demand-side users, difficulties in energy management, and low equipment utilization efficiency. To fully leverage demand-side flexibility, the concept of energy sharing in microgrids has emerged as a new distributed operational paradigm. In the face of growing load demand, energy sharing in microgrids encourages participants to contribute their idle high-quality production/regulation capacity, optimizing the allocation of existing resources in the power sector, which includes natural resources like wind and solar, as well as storage and electric vehicle resources, to achieve energy sharing [12]. Numerous scholars have conducted research on energy sharing. Dai et al. [13] summarized the development and utilization of shared energy storage, emphasizing the need to quantify the benefits of shared energy storage and establish optimization models to encourage the use of non-battery long-term energy storage. Attention should also be given to shared mobile energy storage. In addition to shared energy storage, distributed energy sharing, or multi-energy sharing, in microgrids is an important means of achieving optimized resource allocation. Li et al. [14,15] focused on the characteristics of distributed energy deployment in community microgrids and the energy consumption patterns of different users. They proposed an energy-sharing cloud model to enable energy and power mutual assistance in community microgrids and established hierarchical planning and operation models for producer–consumer users based on the energy-sharing cloud. The upper-level management system assists cloud users in obtaining the optimal capacity allocation for renewable energy generation and storage systems on a monthly basis, while the lower-level management system aims to minimize total operating costs and maximize electrical comfort for cloud users through daily power dispatch optimization. Zhu et al. [16] used a greedy algorithm to create an energy sharing system among adjacent buildings, promoting energy consumption matching among households and reducing energy losses.

The energy sharing scheduling in a multi-microgrid system can be viewed as a holistic approach that enables unified management and global optimization, thus improving overall energy utilization. However, within the multi-microgrid system, each microgrid belongs to different stakeholders, resulting in uneven internal energy distribution and varying operational conditions, objectives, and user demands. Microgrids are often driven by internal benefits. Therefore, redistributing benefits through game theory is an important aspect of enhancing the active participation of individual microgrids in multi-microgrid energy sharing [17,18]. Peer-to-peer (P2P) energy trading between microgrids is typically modeled using cooperative game theory or Nash bargaining (NB) models. Zhang Tao et al. [19] improved carbon emissions and wind–solar consumption in multiple zones by employing a carbon–green certificate mechanism. They subsequently selected the power interaction contribution as the weight for the Shapley value in cooperative game theory, achieving cost–benefit equilibrium among different zones. Hu et al. [20] considered the uncertainty in the energy output of multi-microgrids and established a two-stage robust optimization model. They used the Alternating Direction Method of Multipliers (ADMM) to enable efficient energy interaction among microgrids under worst-case scenarios. They also considered the contributions of microgrid energy, changes in load status, and carbon reduction, and utilized an improved Nash bargaining approach for asymmetric bargaining to allocate cooperative benefits and complete transaction payments. This ensures the robustness, economic efficiency, and fairness of the benefit distribution of multi-microgrids. Du et al. [21] creatively constructed a multi-microgrid energy sharing model based on deceptive game theory. They further considered the uncertainty in electricity prices and employed robust optimization to mitigate the adverse effects of multiple uncertainties in energy sharing. Subsequently, they analyzed fraudulent behavior in energy trading and proposed a fraudulent equilibrium mechanism based on an intermediary trading mechanism. By employing ADMM for solving, they guarantee stable cooperative energy sharing and maximize benefits in multi-microgrid energy sharing. Wang, H. et al. [22] introduced carbon capture and P2G technology to reduce carbon emissions and proposed a multi-microgrid electric–thermal sharing strategy based on Nash negotiation to reduce the total cost and distribute the profit.

Cross-district energy sharing is an important approach to achieving the dual carbon goals. It requires a clear understanding of various energy production models and output patterns in multi-microgrid energy sharing, as well as delineating different ways in which users participate in energy sharing. This involves aggregating and optimizing the various energy devices and load resources within microgrids through interconnection, with industrial park microgrids as the core. It also involves detailed modeling of renewable energy, micro gas turbines, and various types of energy storage, taking into account the energy consumption characteristics and low-carbon performance of each microgrid. The goal is to establish an overall operational strategy for energy sharing in user park areas, with the maximization of clean energy absorption and societal welfare as objectives. Furthermore, it is necessary to properly allocate benefits to strengthen user collaboration and improve energy utilization efficiency.

However, the occurrence of climate issues is not only related to excessive carbon emissions but also closely linked to the loss of other ecosystem services, which leads to the destruction of environmental sustainability. Although using carbon emissions as an environmental assessment indicator is beneficial for verifying the root causes, it is not comprehensive enough to accurately express the true environmental sustainability of various energy system construction projects, and carbon trading markets cannot truly reflect the flow of clean sustainability. For distributed energy systems in industrial parks, sustainability evaluation indicators should include five dimensions: energy saving, low carbon, environmental protection, emission reduction, and ecological design [23]. The concept of emergy, first proposed by H. T. Odum, provides a solution for comprehensive sustainability assessment, effectively measuring the overall environmental support for microgrid energy systems. Emergy theory has been widely studied in multi-energy planning. Shao et al. [24] proposed a dual-layer planning model for comprehensive energy system coupling equipment, with the upper layer aiming to minimize the annual cost of the integrated energy system’s coupling equipment location and selection and the lower layer targeting the maximization of emergy output rate to provide the best operating data for the upper layer. Wang et al. [25] proposed an integrated optimization method for solar building co-generation systems based on emergy, which evaluates the system’s multifaceted performance using energy flow and optimizes equipment capacity allocation to minimize the annual emergy consumption. Mitigating climate change is urgent, and research on the emergy theory in energy optimization scheduling is also beginning to develop, seeking synchronous economic and sustainable development on a short-term scale. Tian Litin, Qian Jiaxin, Han Juntao, and others [26,27,28] have used the emergy method to assess the sustainability of multi-energy system operation schemes. Ye et al. [29] further proposed a distributed multi-energy system considering shared energy storage, initially using bi-objective optimization for optimal capacity planning and operational scheduling, then using Nash bargaining to equitably allocate benefits from the distributed multi-energy system, and finally using emergy analysis to evaluate the sustainability of different schemes. However, the energy scheduling process in the above literature did not actually consider emergy sustainability, and the decoupling of sustainability and economic viability can easily lead to the neglect of sustainability issues in subsequent scheduling. Even if Nash bargaining is used for equitable benefit distribution, the true sustainability contribution of energy system operation schemes does not correspond to the real sustainability contributions of each stakeholder.

To address the above issues, this paper proposes a profit allocation model for multi-microgrid asymmetric bargaining based on emergy sustainability contributions. As emergy is measured in solar energy joules (sej), renewable energy, fossil fuels, commodities, services, and even information, all of which consume energy in the operation of distributed energy systems in multi-microgrids, the emergy theory can be used to evaluate the multifaceted performance of multi-microgrid systems and guide the rational and effective allocation of microgrid benefits and sustainability distribution based on emergy indicators. To further promote the coordinated development of electricity and carbon, this paper takes the optimization dispatch of a multi-microgrid electric–carbon joint sharing economy as a premise, sharing electricity and bundling carbon emissions among multiple microgrids. Due to the lack of consideration for the overall situation in non-cooperative games and the Nash bargaining process in cooperative games, which often neglects the contribution of different microgrid subjects, this paper then allocates the benefits of multiple microgrids based on the energy value index and asymmetric Nash bargaining, reflecting the fairness of profitability corresponding to different levels of environmental sustainability and promoting the realization of microgrid energy construction without sacrificing environmental ecosystem services. The main contributions of this paper are as follows:

(1) In response to the lack of sustainability evaluation in multi-microgrid dispatch, a multi-microgrid energy value evaluation index is established.

(2) According to the different subjects in the carbon trading market, a unified carbon trading object is established, and a multi-microgrid carbon credit trading model is designed based on carbon emission reductions.

(3) A benefit allocation method based on the joint contribution of electric–carbon–energy value sustainability and asymmetric Nash bargaining is proposed.

The content of this paper is organized as follows: Section 2 identifies different types of multi-microgrid energy systems, outlines the energy value flow of multi-microgrid energy systems, and constructs a multi-microgrid energy value assessment model. Section 3 establishes a multi-microgrid carbon credit trading model based on different user subjects’ types of carbon assets, followed by the establishment of a multi-microgrid electric–carbon joint sharing economy optimization dispatch model. Section 4 develops a multi-microgrid asymmetric bargaining profit allocation model based on electric–carbon–energy value sustainability, along with an overview of the solution methods. Section 5 conducts case studies based on the multi-microgrid electric–carbon joint sharing economy dispatch model and the asymmetric bargaining profit allocation model to determine the coordinated operation scheme of electricity and carbon for multi-microgrids and achieve fair and sustainable profit distribution. Finally, Section 6 summarizes the content of this paper.

2. The Energy Valuation Model of a Microgrid

2.1. The Energy System Model of a Multi-Microgrid

A multi-microgrid consists of various types of campus microgrids. In the comprehensive energy system of a single campus microgrid, the external energy supply is sourced from the superior power utility company $P_{\mathrm{e},\mathrm{buy}}$, coal suppliers $P_{coal}$, natural gas companies $P_g$, and shared electricity from other campus microgrids $P_{\mathrm{e}\_\mathrm{share}}$. The internal energy supply also includes self-built photovoltaic generation $P_v$ and wind power generation $P_w$. Energy demand arises from electrical load $L_e$, heat load $L_h$, and cooling load $L_c$. The exported energy comes from excess photovoltaic generation $P_v$, wind power generation $P_w$, and cogeneration units $P_e^{CHP}$, which cannot be accommodated internally after balancing. Coupled equipment includes cogeneration units, gas boilers, air conditioning, and absorption chillers. The main energy storage equipment used is battery storage.

The energy flow diagram of a single-campus microgrid’s energy hub (EH) is shown in Figure 1.

The constructed model of the energy hub for a single-campus microgrid is as follows:

$$\begin{array}{l}\left[\begin{array}{c}{\mathit{L}}_{\mathit{e}}\\ {\mathit{L}}_{\mathit{h}}\\ {\mathit{L}}_{\mathit{c}}\end{array}\right]=\left[\begin{array}{cc}{\alpha }_1& {\alpha }_1{\beta }_1{\eta }_e^{CHP}\\ {\alpha }_2{\eta }_h^{AC}{\mu }_1& ({\alpha }_2{\beta }_1{\eta }_e^{CHP}{\eta }_h^{AC}+{\beta }_1{\eta }_h^{CHP}+{\beta }_2{\eta }_{GB}){\mu }_1\\ {\alpha }_2^{\prime }{\eta }_c^{AC}& ({\alpha }_2^{\prime }{\beta }_1{\eta }_e^{CHP}{\eta }_c^{AC}+{\beta }_1{\eta }_h^{CHP}+{\beta }_2{\eta }_{GB}){\mu }_2{\eta }_{AR}\end{array}\begin{array}{c} \\ \\ \end{array}\begin{array}{c}{\alpha }_1{\eta }_e^{CHP}\\ ({\alpha }_2{\eta }_e^{CHP}{\eta }_h^{AC}+{\eta }_h^{CHP}){\mu }_1\\ ({\alpha }_2^{\prime }{\eta }_e^{CHP}{\eta }_c^{AC}+{\eta }_h^{CHP}){\mu }_2{\eta }_{AR}\end{array}\right]\\ \times \left[\begin{array}{c}({\mathit{P}}_{\mathit{e},buy}+{\mathit{P}}_{\mathit{v}}+{\mathit{P}}_{\mathit{w}}-{\mathit{P}}_{\mathit{e},sell}+{\mathit{P}}_{\mathit{e},buy}^{share}-{\mathit{P}}_{\mathit{e},sell}^{share})\\ \begin{array}{l}{\mathit{P}}_{\mathit{g}\mathit{a}\mathit{s}}\\ {\mathit{P}}_{\mathit{c}\mathit{o}\mathit{a}\mathit{l}}\end{array}\end{array}\right]-\left[\begin{array}{c}{\mathit{P}}_{\mathit{s}}\\ 0\\ 0\end{array}\right]\end{array}$$

(1)

In the equation, ${\mathit{L}}_{\mathit{e}}$, ${\mathit{L}}_{\mathit{h}}$, and ${\mathit{L}}_{\mathit{c}}$ represent the predicted values of electrical load, heat load, and cooling load, respectively. ${\mathit{P}}_{\mathit{e},buy}$ represents the electricity input from the superior power grid. ${\mathit{P}}_{\mathit{v}}$ and ${\mathit{P}}_{\mathit{w}}$ represent the power generation from photovoltaic power plants and wind farms within the park, respectively. ${\mathit{P}}_{\mathit{e},sell}$ represents the electricity sold to the superior power grid. ${\mathit{P}}_{\mathit{e},buy}^{share}$ represents the electricity input from other electricity-sharing and carbon-sharing microgrids within the park. ${\mathit{P}}_{\mathit{e},sell}^{share}$ represents the electricity output from other electricity-sharing and carbon-sharing microgrids. ${\mathit{P}}_{\mathit{g}\mathit{a}\mathit{s}}$ represents the natural gas input from the natural gas network. ${\mathit{P}}_{\mathit{c}\mathit{o}\mathit{a}\mathit{l}}$ represents the coal consumption input. ${\mathit{P}}_{\mathit{s}}$ represents the charging/discharging of electrical energy storage devices. ${\alpha }_1$, ${\alpha }_2$, and ${\alpha }_2^{\prime }$ represent the electrical energy dispatch factors. ${\alpha }_1$ represents the distribution coefficient of electrical energy directly supplied to users. ${\alpha }_2$ represents the distribution coefficient for winter heating electrical energy from air conditioning. ${\alpha }_2^{\prime }$ represents the distribution coefficient for summer cooling electrical energy from air conditioning. When studying summer scenarios, ${\alpha }_2=0,{\alpha }_1+{\alpha }_2^{\prime }=1$, and when studying winter scenarios, ${\alpha }_2^{\prime }=0,{\alpha }_1+{\alpha }_2=1$. ${\beta }_1$ and ${\beta }_2$ represent the natural gas dispatch factors. ${\beta }_1$ represents the distribution coefficient of natural gas for combined heat and power units. ${\beta }_2$ represents the distribution coefficient of natural gas for gas boilers, and ${\beta }_1+{\beta }_2=1$. ${\mu }_1$ and ${\mu }_2$ represent the heat energy dispatch factors. ${\mu }_1$ represents the distribution coefficient of heat energy directly supplied to users. ${\mu }_2$ represents the distribution coefficient of heat energy for absorption chillers, and ${\mu }_1+{\mu }_2=1$.

The multi-microgrid consists of a main grid and three microgrids for industrial, commercial, and residential areas, respectively. Each microgrid has different energy equipment, coupling devices, and load demands. Setting the scenario for air conditioning cooling, it satisfies ${\alpha }_2=0,{\alpha }_1+{\alpha }_2^{\prime }=1$. The composition of the designed microgrid EH for each area is as follows:

Industrial Area Microgrid EH1: The heavy industrial area comprises wind power generation equipment, photovoltaic power generation equipment, coal/gas combined heat and power units, gas boilers, batteries, and heavy industrial electrical, thermal, and cooling loads.

$$\begin{array}{l}\left[\begin{array}{c}{\mathit{L}}_{\mathit{e}\_1}\\ {\mathit{L}}_{\mathit{h}\_1}\\ {\mathit{L}}_{\mathit{c}\_1}\end{array}\right]=[\begin{array}{cc}{\alpha }_{1\_1}& {\alpha }_{1\_1}{\beta }_{1\_1}{\eta }_{e\_1}^{CHP}\\ 0& {\mu }_{1\_1}({\beta }_{1\_1}{\eta }_{h\_1}^{CHP}+{\beta }_{2\_1}{\eta }_{GB\_1})\\ {\alpha }_{2\_1}^{\prime }{\eta }_c^{AC}& ({\alpha }_{2\_1}^{\prime }{\beta }_{1\_1}{\eta }_{e\_1}^{CHP}+{\beta }_{1\_1}{\eta }_{h\_1}^{CHP}+{\beta }_{2\_1}{\eta }_{GB\_1}){\mu }_{2\_1}{\eta }_{AR\_1}\end{array}\begin{array}{c} \\ \\ \end{array}\begin{array}{c}{\alpha }_{1\_1}{\eta }_{e\_1}^{CHP}\\ {\mu }_{1\_1}{\eta }_{h\_1}^{CHP}\\ ({\alpha }_{2\_1}^{\prime }{\eta }_{e\_1}^{CHP}+{\eta }_{h\_1}^{CHP}){\mu }_{2\_1}{\eta }_{AR\_1}\end{array}]\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times \left[\begin{array}{c}({\mathit{P}}_{\mathit{e}\_1,buy}+{\mathit{P}}_{\mathit{v}\_1}+{\mathit{P}}_{\mathit{w}\_1}-{\mathit{P}}_{\mathit{e}\_1,sell}+{\mathit{P}}_{\mathit{e}\_1,buy}^{share}-{\mathit{P}}_{\mathit{e}\_1,sell}^{share})\\ \begin{array}{l}{\mathit{P}}_{\mathit{g}\mathit{a}\mathit{s}\_1}\\ {\mathit{P}}_{\mathit{c}\mathit{o}\mathit{a}\mathit{l}\_1}\end{array}\end{array}\right]-\left[\begin{array}{c}{\mathit{P}}_{\mathit{s}\_1}\\ 0\\ 0\end{array}\right]\end{array}$$

(2)

Commercial Area Microgrid EH2: It includes photovoltaic power generation equipment, wind power generation equipment, gas cogeneration units, gas boilers, batteries, and commercial electrical, thermal, and cooling loads.

$$\begin{array}{l}\left[\begin{array}{c}{\mathit{L}}_{\mathit{e}\_2}\\ {\mathit{L}}_{\mathit{h}\_2}\\ {\mathit{L}}_{\mathit{c}\_2}\end{array}\right]=\left[\begin{array}{cc}{\alpha }_{1\_2}& {\alpha }_{1\_2}{\beta }_{1\_2}{\eta }_{e\_2}^{CHP}\\ 0& {\mu }_{1\_2}({\beta }_{1\_2}{\eta }_{h\_2}^{CHP}+{\beta }_{2\_2}{\eta }_{GB\_2})\\ {\alpha }_{2\_2}^{\prime }{\eta }_{c\_2}^{AC}& ({\alpha }_{2\_2}^{\prime }{\beta }_{1\_2}{\eta }_{e\_2}^{CHP}+{\beta }_{1\_2}{\eta }_h^{CHP}+{\beta }_{2\_2}{\eta }_{GB\_2}){\mu }_{2\_2}{\eta }_{AR\_2}\end{array}\right]\\ \times \left[\begin{array}{c}({\mathit{P}}_{\mathbf{e}\_2,buy}+{\mathit{P}}_{\mathit{v}\_2}+{\mathit{P}}_{\mathit{w}\_2}-{\mathit{P}}_{\mathbf{e}\_2,sell}+{\mathit{P}}_{\mathbf{e}\_2,buy}^{share}-{\mathit{P}}_{\mathbf{e}\_2,sell}^{share})\\ {\mathit{P}}_{\mathit{g}\mathit{a}\mathit{s}\_2}\end{array}\right]-\left[\begin{array}{c}{\mathit{P}}_{\mathit{s}\_2}\\ 0\end{array}\right]\end{array}$$

(3)

Residential Area Microgrid EH3: It comprises photovoltaic power generation equipment, wind power generation equipment, energy storage batteries, and residential electricity and cooling loads.

$$\left[\begin{array}{c}{\mathit{L}}_{\mathit{e}\_3}\\ {\mathit{L}}_{\mathit{c}\_3}\end{array}\right]=({\mathit{P}}_{\mathit{e}\_3,buy}+{\mathit{P}}_{\mathit{v}\_3}+{\mathit{P}}_{\mathit{w}\_3}-{\mathit{P}}_{\mathit{e}\_3,sell}+{\mathit{P}}_{\mathit{e}\_3,buy}^{share}-{\mathit{P}}_{\mathit{e}\_3,buy}^{share}-{\mathit{P}}_{\mathit{s}\_3})\times \left[\begin{array}{c}{\alpha }_{1\_3}\\ {\alpha }_{2\_3}^{\prime }{\eta }_{c\_3}^{AC}\end{array}\right]$$

(4)

According to the equipment and load composition of each microgrid in the residential area, the overall energy system framework for multiple microgrids is illustrated in Figure 2.

2.2. Multi-Microgrid Energy Value Analysis Method

The steps to analyze the energy value of the microgrid distributed energy system in the park are as follows:

(1) Primary data collection. Inputs of the park microgrid distributed energy system: renewable resources (R), non-renewable resources (N), economic feedback inputs (F), etc. System outputs: electrical energy (Y_E), heat energy (Y_H), cooling energy (Y_C), carbon emissions (W_cb), and economic returns (S).

(2) Energy value analysis diagram drawing. Taking a single-park microgrid as an example, according to Section 2.1, the energy structure and energy flow distribution of the park microgrid, the system energy illustration of the outer boundary of the distributed energy system, and the components within the system are formed as shown in Figure 3.

(3) List the energy value analysis table. The general model of energy value input and output of the distributed energy system of the park microgrid is shown in Equations (5) and (6), and the energy value of each category of energy and substance of the park microgrid needs to be calculated specifically according to the energy value conversion rate and the relationship between diversion and joint supply.

$$E_{\mathrm{m}\_\mathrm{in}}=E{T}_r$$

(5)

$$E_{\mathrm{m}\_\mathrm{out}}={\displaystyle \sum _i{E}_i{T}_{r,i}}$$

(6)

In the formulas: $E_{\mathrm{m}\_\mathrm{in}}$ represents the energy value of the input substance, measured in sej; $E$ stands for the energy of the input substance, measured in J, g, or ¥; $T_r$ denotes the energy conversion rate of the input substance, measured in sej/J, sej/g, or sej/¥; $E_{\mathrm{m}\_\mathrm{out}}$ represents the energy value of the output substance, measured in sej; $E_i$ represents the energy of the ith input substance, measured in J, g, or ¥; and $T_{r,i}$ stands for the energy conversion rate of the ith input substance, measured in sej/J, sej/g, or sej/¥.

(4) Calculation of energy sustainability indicators. Calculate the energy sustainability indicators of each microgrid in accordance with the energy value analysis table.

(5) Analysis and evaluation. Through the analysis of energy value indicators and quantitative analysis of system structure functions, discuss the contribution of each microgrid in the residential area to the sustainable benefit distribution of multi-microgrid electricity and carbon sharing. Achieve both economic and sustainable energy scheduling for multi-microgrid systems.

2.3. Multi-Microgrid Energy Value Evaluation Index

By summarizing the energy and material flows as well as the fund flows of the microgrid in Figure 3, the system energy value inputs can be categorized as follows: local renewable resources R (solar energy, wind energy, 40% human labor); land use loss N; purchasing resources from the external environment, including renewable materials F_R (26% tap water), non-renewable materials F_N (74% tap water, natural gas, coal, etc.), human labor services 60% F_L, equipment operation and maintenance costs (90% F_ERc, 10% F_ENc), grid electricity purchases F_Ne, and carbon trading costs F_Cc (when the value is negative, it is considered as carbon trading revenue S_Cc); system outputs, including electrical energy Y_E, thermal energy Y_H, cooling energy Y_C, carbon emissions W_cb, and electricity sold to the grid Se. Energy evaluation indicators for the microgrid are established based on classifications, as seen in Formulas (7)–(9).

(1) Microgrid electricity emergy yield ratio, Me_EYR

Me_EYR is the ratio of the amount of energy consumed by the park microgrid, the combined output of electricity and carbon, to the amount of energy input from the feedback of the electricity-producing economy, showing the effectiveness of the purchased resources to actually produce electricity. The higher the ratio, the more the investment per unit of energy helps the economy.

$$\{\begin{array}{l}Me\_EYR={\displaystyle \frac{E}{F_E}}\\ E=Y_{E1}+Y_{E2}+W_{cb}+S_e+S_{Cc}\\ F_E=F_e+F_{Cc}+F_{\mathrm{L}}+F_{\mathrm{ERc}}+F_{\mathrm{ENc}}+F_{Ne}+{\alpha }_1{\beta }_1{F}_{N1}{\eta }_2+{\alpha }_1{F}_{N2}{\eta }_2\end{array}$$

(7)

where E is the energy value of the park’s microgrid production power output.

(2) Microgrid environmental loading ratio, M_ELR

M_ELR represents the ratio of the overall non-renewable energy value to the renewable energy value of the park microgrid, reflecting the potential environmental impact and ecological pressure of the energy conversion process of the park microgrid. The larger the value, the worse the sustainability.

$$M\_ELR={\displaystyle \frac{{\displaystyle \sum _{i=1}^7{N}_i}+{\displaystyle \sum _{j=1}^4{F}_{N,j}}+F_{ENc}}{{\displaystyle \sum _{k=1}^6{R}_k}+F_{ERc}}}$$

(8)

(3) Microgrid emergy sustainability index, M_ESI

M_ESI is a potential process-loaded contribution to the park microgrid environment, reflecting the sustainability of the park microgrid’s electrical energy production process and carbon reduction.

$$M\_ESI={\displaystyle \frac{Me\_EYR}{M\_ELR}}$$

(9)

3. Multi-Microgrid Electric–Carbon Joint Sharing Model

3.1. Multi-Micro Network Carbon Credit Trading Model

If a certain park microgrid, EH, has a significant number of high-carbon emitting units, it is prone to encountering a shortage of carbon quotas during the electricity generation process. In such cases, it needs to purchase additional carbon quotas from the carbon market or from other park microgrids. Conversely, there may be some park microgrids where the proportion of new energy generation is higher, resulting in surplus carbon quotas or certified emission reductions (CCERs). In this scenario, they can choose to sell the surplus carbon quotas and CCERs to generate certain profits. When there is an imbalance in carbon quotas, there is a possibility of trading between different park microgrids when a favorable carbon price is proposed by EH entities.

Currently, non-key emitting units in industries and businesses are not allocated carbon quotas and do not need to participate in the carbon emissions trading market. However, they can choose to participate in the Chinese Certified Carbon Emission Reduction (CCER) market. Residents can accumulate carbon reduction credits by adopting various carbon reduction measures to participate in the carbon-inclusive market. In order to promote carbon sharing among industrial, commercial, and residential park microgrids, parks of various types should have unified trading targets based on carbon reduction credits. They should encourage microgrids to actively reduce carbon emissions from various aspects and design a multi-microgrid carbon credit trading model. Microgrid carbon credits that are positive can be sold to obtain profits, while negative carbon credits require costs to purchase.

The carbon credit trading model includes the park microgrid’s external electricity purchase and the electricity–heat carbon quota benchmark model issued by power/heat units, the park microgrid’s carbon emissions model based on historical emission intensity, the park microgrid’s carbon-inclusive emission reduction model, the carbon credit trading model, and the grid-connected renewable energy fluctuation carbon penalty model. The specific details of the carbon trading models are as follows:

(1) Benchmarking model for electricity–heat carbon allowances issued by the park’s microgrid for purchased electricity and electricity/heat supply units

$$E_i^{\mathrm{L}}={\kappa }_e^{\mathrm{GRID}}{\delta }_{\mathrm{re}}{\displaystyle \sum _{t=1}^{\mathrm{T}}{P}_{i,t}^{\mathrm{GRIDb}}}\Delta t+{\displaystyle \sum _{t=1}^{\mathrm{T}}({\chi }_i^{CHP·e}{P}_{i,t}^{CHP·e}}+{\chi }_i^{CHP·h}{P}_{i,t}^{CHP·h})\Delta t+{\displaystyle \sum _{t=1}^{\mathrm{T}}({\chi }_i^{GB·h}{P}_{i,t}^{GB·h}})\Delta t$$

(10)

In the equation, $E_i^{\mathrm{L}}$ represents the daily carbon emission quota of park microgrid i, measured in kgCO₂; t denotes the current time interval, with a time scale of 1 h, where T equals 24 h; ${\kappa }_e^{\mathrm{GRID}}$ stands for the average carbon emission factor of the grid, measured in kgCO₂/kWh; ${\delta }_{\mathrm{re}}$ represents the carbon quota reduction factor for externally purchased electricity, with values ranging from 0 to 1; $P_{i,t}^{\mathrm{GRIDb}}$ represents the power purchased by park microgrid i from the grid at time t, measured in kW; ${\chi }_i^{CHP·e}$, ${\chi }_i^{CHP·h}$, and ${\chi }_i^{GB·h}$, respectively, denote the carbon emission benchmarks for power supply from cogeneration units, heat supply from cogeneration units, and heat supply from gas boilers in park microgrid i, measured in kgCO₂/kWh; $P_{i,t}^{CHP·e}$, $P_{i,t}^{CHP·h}$, and $P_{i,t}^{GB·h}$, respectively, stand for the electricity output from cogeneration units, heat output from cogeneration units, and heat output from gas boilers in park microgrid i at time t, measured in kW.

(2) Carbon emission modeling for park microgrids based on historical emission intensity

Considering the carbon footprint factor of renewable energy units and based on the historical emission intensity of the park microgrid, the park microgrid carbon emission model is established as follows:

$$E_i^{\mathrm{m}}={\displaystyle \sum _{t=1}^{\mathrm{T}}{\mathrm{E}}_{i,t}^{\mathrm{m}}}={\displaystyle \sum _{t=1}^{\mathrm{T}}\left[\begin{array}{l}{\kappa }_e^{\mathrm{GRID}}{u}_{i,t}^{\mathrm{GRIDb}}{P}_{i,t}^{\mathrm{GRIDb}}\Delta t+{\kappa }_i^{\mathrm{coal}}{P}_{i,t}^{\mathrm{coal}}\Delta t+{\kappa }^{\mathrm{gas}}{P}_{i,t}^{\mathrm{gas}}\Delta t\\ \hspace{1em}+({\kappa }_i^{\mathrm{RE}}-{\kappa }_e^{\mathrm{GRID}})P_{i,t}^{\mathrm{RE}}\Delta t -{\kappa }_{e,i}^{\mathrm{IES}}{u}_{i,t}^{\mathrm{GRIDs}}{P}_{i,t}^{\mathrm{GRIDs}}\Delta t\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+{\kappa }_{e,j}^{\mathrm{IES}}{u}_{i-j,t}^{\mathrm{GRIDb}}{P}_{j-i,t}^{\mathrm{SHAREb}}\Delta t-{\kappa }_{e,i}^{\mathrm{IES}}{u}_{i-j,t}^{\mathrm{GRIDs}}{P}_{i-j,t}^{\mathrm{SHAREs}}\Delta t\end{array}\right]}$$

(11)

$${\kappa }_{e,i}^{\mathrm{IES}}={\displaystyle \frac{{\displaystyle \sum _{t_{\mathrm{be}}=1}^{{\mathrm{T}}_{\mathrm{be}}}{\displaystyle \sum _k{\phi }_{i,k}{P}_{i,k,t_{\mathrm{be}}}^{\mathrm{IES}}\Delta t_{\mathrm{be}}}}}{{\displaystyle \sum _{t_{\mathrm{be}}=1}^{{\mathrm{T}}_{\mathrm{be}}}{\displaystyle \sum _{i,k}{P}_{i,k,t_{\mathrm{be}}}^{\mathrm{IES}}\Delta t_{\mathrm{be}}}}}}$$

(12)

$$u_{i,t}^{\mathrm{GRIDs}}+u_{i,t}^{\mathrm{GRIDb}}=1$$

(13)

$$u_{i-j,t}^{\mathrm{SHAREb}}+u_{i-j,t}^{\mathrm{SHAREs}}=1$$

(14)

In the equation, $E_i^{\mathrm{m}}$ represents the total daily carbon emissions of microgrid i in the park, measured in kgCO₂; $E_{m,t}$ represents the total carbon emissions of microgrid i at time t, measured in kgCO₂; $u_{i,t}^{\mathrm{GRIDb}}$ and $u_{i,t}^{\mathrm{GRIDs}}$ are binary variables, each taking the value of either 0 or 1; ${\kappa }_i^{\mathrm{coal}}$ represents the carbon emission factor of coal purchased by microgrid i when combusted completely, measured in kgCO₂/kWh; $P_{i,t}^{\mathrm{coal}}$ represents the coal consumption of microgrid i at time t, measured in kW; ${\kappa }^{\mathrm{gas}}$ represents the carbon emission factor of natural gas purchased by microgrid i when combusted completely, measured in kgCO₂/kWh; $P_{i,t}^{\mathrm{gas}}$ represents the amount of natural gas input by microgrid i at time t, measured in kW; ${\kappa }_i^{\mathrm{RE}}$ represents the carbon footprint factor of renewable energy generation units in microgrid i, measured in kgCO₂/kWh; $P_{i,t}^{\mathrm{RE}}$ represents the electricity generation capacity of renewable energy generation units in microgrid i at time t, measured in kW; ${\kappa }_{e,i}^{\mathrm{IES}}$ and ${\kappa }_{e,j}^{\mathrm{IES}}$ represent the historical carbon emission intensity of microgrids i and j, respectively, measured in kgCO₂/kWh; $P_{i,t}^{\mathrm{GRIDs}}$ represents the electricity sold by microgrid i to the grid at time t, measured in kW; $P_{i-j,t}^{\mathrm{SHAREs}}$ and $P_{j-i,t}^{\mathrm{SHAREb}}$ represent the electricity sold and purchased between microgrids i and j, respectively, measured in kW; $u_{i-j,t}^{\mathrm{SHAREb}}$ and $u_{i-j,t}^{\mathrm{SHAREs}}$ are binary variables, each taking the value of either 0 or 1; t_be represents historical time intervals, with a time scale of 1 h, and T_be represents the total historical duration, which is greater than or equal to 24 h; ${\phi }_{i,k}$ represents the carbon emission factor of each type of power generation unit k in microgrid i, measured in kgCO₂/kWh; $P_{i,k,t_{\mathrm{be}}}^{\mathrm{IES}}$ represents the electricity generation capacity of power generation unit k in microgrid i at historical time t_be, measured in kW.

(3) Modeling of carbon-inclusive emission reductions in parks

$$E_i^{\mathrm{R}}={\displaystyle \sum _{t=1}^{\mathrm{T}}{E}_{i,t}^{\mathrm{R}}}={\displaystyle \sum _{t=1}^{\mathrm{T}}\left[E{r}_{i,t}^{\mathrm{pe}}+E{r}_{i,t}^{\mathrm{ve}}+E{r}_{i,t}^{\mathrm{me}}+E{r}_{i,t}^{\mathrm{eco}}\right]}$$

(15)

where $E_i^{\mathrm{R}}$ represents the daily carbon offset amount of microgrid i in the park, measured in kgCO₂; $E_{i,t}^{\mathrm{R}}$ represents the total carbon offset amount of microgrid i at time t, measured in kgCO₂; $E{r}_{i,t}^{\mathrm{pe}}$, $E{r}_{i,t}^{\mathrm{ve}}$, $E{r}_{i,t}^{\mathrm{me}}$, and $E{r}_{i,t}^{\mathrm{eco}}$, respectively, represent the carbon offset amounts of individual activities, transportation, material usage, and forestry of microgrid i at time t, measured in kgCO₂.

(4) Carbon Credit Trading Model

$$C_i^{{\mathrm{CO}}_2}=(E_i^{\mathrm{m}}-E_i^{\mathrm{L}}-E_i^{\mathrm{R}})\times f_{\mathrm{cc}}$$

(16)

where $C_i^{{\mathrm{CO}}_2}$ is the daily park microgrid i carbon cost in ¥; $f_{\mathrm{cc}}$ is the carbon credit unit price in ¥/kgCO₂.

3.2. Multi-Microgrid Electricity–Carbon Joint Sharing Economy Dispatch Model

(1) Object function

The total operating cost of the multi-microgrid includes the maintenance cost of equipment units in each microgrid within the park (${\mathrm{C}}_{i,t}^{\mathrm{IES},\mathrm{op}}$), the cost of purchasing electricity from the grid (${\mathrm{C}}_{i,t}^{\mathrm{GRIDb}}$), the cost of purchasing gas (${\mathrm{C}}_{i,t}^{\mathrm{gas}}$), the cost of purchasing coal (${\mathrm{C}}_{i,t}^{\mathrm{coal}}$), the cost of electricity exchange (${\mathrm{C}}_{i,t}^{P2P}$), the revenue obtained from selling electricity to the grid (${\mathrm{C}}_{i,t}^{\mathrm{GRIDs}}$), the cost of wind and solar curtailment carbon penalties ($C_{i,t}^{\mathrm{ab},\mathrm{pm}}$), the cost of peak–valley grid integration carbon rewards and penalties ($C_{i,t}^{\mathrm{pu},\mathrm{pm}}$), and the cost of carbon trading (${\mathrm{C}}_i^{{\mathrm{CO}}_2}$). The optimization objectives are as follows:

$$\min C={\displaystyle \sum _i{\mathrm{C}}_i}={\displaystyle \sum _i{\displaystyle \sum _t{\mathrm{C}}_{i,t}}}={\displaystyle \sum _i{\displaystyle \sum _{t=1}^{\mathrm{T}}\left[\begin{array}{r}{\mathrm{C}}_{i,t}^{\mathrm{IES},\mathrm{op}}+{\mathrm{C}}_{i,t}^{\mathrm{GRIDb}}{+\mathrm{C}}_{i,t}^{\mathrm{gas}}{+\mathrm{C}}_{i,t}^{\mathrm{coal}}{+\mathrm{C}}_{i,t}^{\mathrm{P}2\mathrm{P}}\\ -{\mathrm{C}}_{i,t}^{\mathrm{GRIDs}}+C_{i,t}^{\mathrm{ab},\mathrm{pm}}+C_{i,t}^{\mathrm{pu},\mathrm{pm}}\end{array}\right]+{\displaystyle \sum _i{\mathrm{C}}_i^{{\mathrm{CO}}_2}}}}$$

(17)

The model for the cost of electricity exchange in a multi-microgrid is as follows:

$${\mathrm{C}}_{i,t}^{\mathrm{P}2\mathrm{P}}={\tau }_{j,t}{u}_{i-j,t}^{\mathrm{SHAREb}}{P}_{j-i,t}^{\mathrm{SHAREb}}-{\tau }_{i,t}{u}_{i-j,t}^{\mathrm{SHAREs}}{P}_{i-j,t}^{\mathrm{SHAREs}}$$

(18)

In the equation, C represents the total daily cost of the multi-microgrid, measured in RMB (Chinese Yuan); $C_i$ represents the total daily cost of microgrid i in the park, measured in RMB; ${\mathrm{C}}_{i,t}$ represents the total daily cost of microgrid i at time t in the park, measured in RMB; ${\mathrm{C}}_{i,t}^{\mathrm{IES},\mathrm{op}}$ represents the operation and maintenance cost of the equipment units in microgrid i at time t, measured in RMB; ${\mathrm{C}}_{i,t}^{\mathrm{GRIDb}}$ represents the cost of purchasing electricity from the grid for microgrid i at time t, measured in RMB; ${\mathrm{C}}_{i,t}^{\mathrm{gas}}$ represents the cost of purchasing gas for microgrid i at time t, measured in RMB; ${\mathrm{C}}_{i,t}^{\mathrm{coal}}$ represents the cost of purchasing coal for microgrid i at time t, measured in RMB; ${\mathrm{C}}_{i,t}^{\mathrm{P}2\mathrm{P}}$ represents the cost of energy exchange between microgrid i and the grid at time t, measured in RMB; ${\mathrm{C}}_{i,t}^{\mathrm{GRIDs}}$ represents the revenue from selling electricity to the grid from microgrid i at time t, measured in RMB; $C_{i,t}^{\mathrm{ab},\mathrm{pm}}$ represents the penalty cost for wind and solar power curtailment in microgrid i at time t, measured in RMB; $C_{i,t}^{\mathrm{pu},\mathrm{pm}}$ represents the carbon incentive or penalty cost for peak–valley grid connection in microgrid i at time t, measured in RMB; ${\tau }_{i,t}$ and ${\tau }_{j,t}$ represent the selling price of electricity from microgrids i and j to other microgrids in RMB/(kW·h).

(2) Constraints

• Power balance constraints

• Electric power balance constraint

$$L_{i,t}^e=\left[\begin{array}{l}{\alpha }_1(P_{i,t}^{\mathrm{GRIDb}}+P_{i,t}^{\mathrm{v}}+P_{i,t}^{\mathrm{w}}-P_{i,t}^{\mathrm{GRIDs}}+P_{j-i,t}^{\mathrm{SHAREb}}-P_{i-j,t}^{\mathrm{SHAREs}})\\ \hspace{1em}+{\alpha }_1{\beta }_1{\eta }_e^{CHP}{P}_{i,t}^{\mathrm{gas}}+{\alpha }_1{\eta }_e^{CHP}{P}_{i,t}^{\mathrm{coal}}-P_{i,t}^{\mathrm{s}}\end{array}\right]$$

(19)

• Thermal power balance constraint

$$L_{i,t}^h=\left[\begin{array}{l}{\alpha }_2{\eta }_h^{AC}(P_{i,t}^{\mathrm{GRIDb}}+P_{i,t}^{\mathrm{v}}+P_{i,t}^{\mathrm{w}}-P_{i,t}^{\mathrm{GRIDs}}+P_{j-i,t}^{\mathrm{SHAREb}}-P_{i-j,t}^{\mathrm{SHAREs}})\\ \hspace{1em}+\left({\alpha }_2{\mu }_1{\beta }_1{\eta }_e^{CHP}+{\mu }_1{\beta }_1{\eta }_h^{CHP}+{\mu }_1{\beta }_2{\eta }_{GB}\right)P_{i,t}^{\mathrm{gas}}+\left({\alpha }_2{\mu }_1{\eta }_e^{CHP}+{\mu }_1{\eta }_h^{CHP}\right)P_{i,t}^{\mathrm{coal}}\end{array}\right]$$

(20)

• Cold power balance constraint

$$L_{i,t}^c=\left[\begin{array}{l}{\alpha }_2^{\prime }{\eta }_c^{AC}(P_{i,t}^{\mathrm{GRIDb}}+P_{i,t}^{\mathrm{v}}+P_{i,t}^{\mathrm{w}}-P_{i,t}^{\mathrm{GRIDs}}+P_{j-i,t}^{\mathrm{SHAREb}}-P_{i-j,t}^{\mathrm{SHAREs}})\\ \hspace{1em}+({\alpha }_2^{\prime }{\mu }_2{\beta }_1{\eta }_e^{CHP}+{\mu }_2{\beta }_1{\eta }_h^{CHP}+{\mu }_2{\beta }_2{\eta }_{GB}){\eta }_{AR}{P}_{i,t}^{\mathrm{gas}}+({\alpha }_2^{\prime }{\mu }_2{\eta }_e^{CHP}+{\mu }_2{\eta }_h^{CHP}){\eta }_{AR}{P}_{i,t}^{\mathrm{coal}}\end{array}\right]$$

(21)

In the equation, $L_{i,t}^e$, $L_{i,t}^h$, and $L_{i,t}^c$, respectively, represent the predicted electrical load, heat load, and cooling load of microgrid i in the park at time t; $P_{i,t}^{\mathrm{v}}$ represents the power generation of the photovoltaic generator units in microgrid i at time t, measured in kW; $P_{i,t}^{\mathrm{w}}$ represents the power generation of the wind turbine units in microgrid i at time t, measured in kW; $P_{i,t}^{\mathrm{s}}$ represents the charging or discharging power of the energy storage system in microgrid i at time t, measured in kW.

2.

Equipment constraints

$$0\le P_{i,k,t}\le P_{i,k}^{\max }$$

(22)

$$P_{i,k}^d\le P_{i,k,t}-P_{i,k,t-1}\le P_{i,k}^u$$

(23)

In the equation, $P_{i,k,t}$ represents the output power of equipment k in microgrid i at time t, measured in kW; $P_{i,k}^{\max }$ represents the rated power of equipment k in microgrid i; $P_{i,k}^d$ and $P_{i,k}^u$ represent the down-slope and up-slope rates of equipment k in microgrid i.

3.

Multi-microgrid P2P power trading constraints

The electricity sold or purchased between microgrids during time t should be within the range of the maximum transmission power $P_{i-j,\max }^{\mathrm{P}2\mathrm{P}}$ of the interconnection line:

$$\left|P_{i-j,t}^{\mathrm{SHAREb}}\right|\le P_{i-j,\max }^{\mathrm{P}2\mathrm{P}}$$

(24)

$$\left|P_{i-j,t}^{\mathrm{SHAREs}}\right|\le P_{i-j,\max }^{\mathrm{P}2\mathrm{P}}$$

(25)

Multi-microgrids need to meet the constraints of electricity sharing balance and payment balance:

$${\displaystyle \sum _i{P}_{i,t}^{\mathrm{P}2\mathrm{P}}=0}$$

(26)

$${\displaystyle \sum _i{C}_{i,t}^{\mathrm{P}2\mathrm{P}}=0}$$

(27)

In the formula, $P_{i,t}^{\mathrm{P}2\mathrm{P}}$ represents the total electricity consumption of microgrid i in the park participating in multi-microgrid carbon sharing transactions during time t, in kW.

4. Multi-Microgrid-Based Asymmetric Nash Bargaining Method for Sharing the Benefits of Electricity and Carbon

4.1. Basic Principles of Nash Negotiation

Nash bargaining belongs to a typical cooperative game, which can lead to an overall increase in total benefits after cooperation among the parties involved. The Nash bargaining model, as shown in Formula (28), yields the equilibrium solution of the Nash bargaining model, and this Nash bargaining solution ensures that all members of the cooperative alliance achieve Pareto-optimal benefits.

$$\{\begin{array}{l}\max \underset{i}{\Pi }(U_i-U_i^0)\\ \mathrm{s}.\mathrm{t}. U_i\ge U_i^0\end{array}$$

(28)

In the equation, $U_i$ represents the payoff after cooperative negotiation, and $U_i^0$ represents the payoff before cooperative negotiation, i.e., the bargaining fallback position. The equation presents a multi-variable coupled, non-convex, and non-linear problem. Therefore, the above model is decomposed and transformed into two sub-problems: the minimization of joint sharing costs for multi-microgrid carbon union (Q1) and the asymmetric bargaining interest allocation based on energy value and carbon trading (Q2), which are solved sequentially.

4.2. Minimizing the Cost of Joint Sharing of Electricity and Carbon in Multiple Microgrids

This article uses Nash negotiation theory to construct a multi-microgrid carbon sharing model:

$$\{\begin{array}{l}\max \underset{i}{\Pi }({\mathrm{C}}_i^0-{\mathrm{C}}_i)\\ \mathrm{s}.\mathrm{t}{. \mathrm{C}}_i\le {\mathrm{C}}_i^0\end{array}$$

(29)

In the equation, ${\mathrm{C}}_i^0$ represents the total operating cost for microgrid i in the park before participating in electric–carbon sharing.

As Formula (29) represents a non-linear optimization problem, it cannot be directly solved. It is known that the objective function ${\mathrm{C}}_i^0$, before participating in electric–carbon sharing, can easily be reduced to a constant value, so minimizing ${\mathrm{C}}_i$ will facilitate problem solving. In other words, maximizing the cooperative benefits of multi-park microgrid electric–carbon sharing is equivalent to minimizing costs. The transformation of the aforementioned multi-microgrid electric–carbon sharing model is as follows:

$$\{\begin{array}{l}\min {\displaystyle \sum _i{\mathrm{C}}_i(P_{i,t}^{\mathrm{P}2\mathrm{P}})}\\ \mathrm{s}.\mathrm{t}. (19)-(26)\end{array}$$

(30)

The payment equilibrium constraint Formula (27) indicates that $C_{i,t}^{\mathrm{P}2\mathrm{P}}$ can be ignored when solving the minimum sharing cost problem, i.e., $C_{i,t}^{\mathrm{P}2\mathrm{P}}=0$. Since the electricity sharing balance constraint Formula (26) is multi-coupled among all park microgrids, auxiliary variables $P_{i-j,t}^{\mathrm{P}2\mathrm{P}}$ and $P_{j-i,t}^{\mathrm{P}2\mathrm{P}}$ are introduced to decouple it, transforming the sub-problem of minimizing the joint sharing costs for multi-microgrid electric–carbon union (Q1) into a double-coupled model as follows:

$$P_{i-j,t}^{\mathrm{P}2\mathrm{P}}+P_{j-i,t}^{\mathrm{P}2\mathrm{P}}=0$$

(31)

In the equation, $P_{i-j,t}^{\mathrm{P}2\mathrm{P}}$ represents the electricity traded between microgrids i and j within the campus microgrid; $P_{j-i,t}^{\mathrm{P}2\mathrm{P}}$ represents the electricity traded between microgrids j and i; and when $P_{i-j,t}^{\mathrm{P}2\mathrm{P}}=-P_{j-i,t}^{\mathrm{P}2\mathrm{P}}$, it indicates the realization of electric–carbon sharing between microgrids i and j.

After decoupling, the sub-problem Q1 for minimizing the joint carbon-sharing cost of multiple microgrids is solved in a distributed manner using the ADMM algorithm. The specific steps are as follows:

1.

Establish an augmented Lagrangian function for subproblem Q1.

$$L_i^{Q1}=C_i+{\displaystyle \sum _j{\displaystyle \sum _{t=1}^T{\lambda }_{i-j,t}^{Q1}\left(P_{i-j,t}^{\mathrm{P}2\mathrm{P}}+P_{j-i,t}^{\mathrm{P}2\mathrm{P}}\right)}}+{\displaystyle \sum _j\frac{{\rho }_{i,t}^{Q1}}{2}{\displaystyle \sum _{t=1}^T{\Vert P_{i-j,t}^{\mathrm{P}2\mathrm{P}}+P_{j-i,t}^{\mathrm{P}2\mathrm{P}}\Vert }_2^2}}$$

(32)

In the formula, ${\lambda }_{i-j,t}^{Q1}$ is the Lagrange multiplier; ${\rho }_{i,t}^{Q1}$ is the penalty factor, set to 10⁻⁴.

2.

Let k represent the iteration count. Initialize the iteration count as k = 1, variables $P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k)=0$, $P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k)=0$, and Lagrange multiplier ${\lambda }_{i-j,t}^{Q1}(k)=0$.

3.

Decision variables $P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k)$ and $P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k)$ update to $P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k+1)$ and $P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k+1)$.

Update of park microgrid i:

$$P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k+1)=\arg \min L_i^{Q1}({\lambda }_{i-j,t}^{Q1}(k),P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k),P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k))$$

(33)

Park microgrid j update $P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k+1)$ based on $P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k+1)$:

$$P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k+1)=\arg \min L_i^{Q1}({\lambda }_{j-i,t}^{Q1}(k),P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k+1),P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k))$$

(34)

Repeat Formulas (33) and (34) until each microgrid in the park updates the interactive electricity consumption for carbon-sharing in this iteration.

4.

After one iteration, update the Lagrange multiplier.

$${\lambda }_{i-j,t}^{Q1}(k+1)={\lambda }_{i-j,t}^{Q1}(k)+{\rho }_{i,t}^{Q1}\left[P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k+1)+P_{j-i,t}^{\mathrm{P}2\mathrm{P}}(k+1)\right]$$

(35)

5.

Update the number of iterations k = k + 1, and repeat the execution of Formulas (33)–(35).

6.

Judging convergence

$$\{\begin{array}{l}{\displaystyle \sum _i{\displaystyle \sum _{t=1}^T{\Vert P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k+1)-P_{i-j,t}^{\mathrm{P}2\mathrm{P}}(k)\Vert }_2\le \zeta }}\\ \hspace{1em}or\hspace{1em}k>k_{\max }\end{array}$$

(36)

In the equation, $\zeta$ represents the convergence precision; $k_{\max }$ represents the maximum number of iterations.

If the convergence condition in Equation (36) is met, the iteration process terminates; otherwise, return to step 3 and enter the next iteration until the algorithm converges below the set precision or reaches the maximum number of iterations.

4.3. Asymmetric Bargaining Profit Distribution Based on Emergy and Carbon Trading

The symmetrical Nash bargaining theory distributes benefits equally among cooperating participants, but the equal division method fails to reflect the different contributions of participants to cooperation, leading to a certain degree of unfairness in symmetrical Nash bargaining. Asymmetric bargaining refers to the different bargaining abilities of each cooperating participant in the game due to information or positional asymmetry. In this section, different campus microgrids have different contributions to electric–carbon sharing, considering the transfer of electricity and carbon emissions as well as the sustainable energy scheduling of the campus microgrids. Based on the representation of sustainability and the interactive electricity volume of different campus microgrids, a model for asymmetric bargaining based on emergy value and carbon trading is proposed for benefit allocation.

(1) Improved contribution based on emergy value and carbon trading

$$d_i={\displaystyle \frac{{\displaystyle \sum _t\frac{Me\_ES{I}_i}{{\kappa }_{e,i}^{IES}}\cdot \left|P_{i,t}^{P2P}\right|}}{{\displaystyle \sum _i{\displaystyle \sum _t\frac{Me\_ES{I}_i}{{\kappa }_{e,i}^{IES}}\cdot \left|P_{i,t}^{P2P}\right|}}}}$$

(37)

(2) Profit distribution model

$$\{\begin{array}{l}\max {\displaystyle \prod _i({\mathrm{C}}_i^0-}{\mathrm{C}}_i-{\mathrm{C}}_i^{P2P}{)}^{d_i}\\ s.t.{ \mathrm{C}}_i^0-{\mathrm{C}}_i-{\mathrm{C}}_i^{P2P}>0 \forall \mathrm{i}\\ \left(17\right),\left(25\right)\end{array}$$

(38)

The objective function in Formula (38) aims to maximize the benefits of participating in carbon sharing in the park microgrid compared to not participating, and it ensures that each park microgrid can receive benefits. Due to the fact that the natural logarithm is a strictly monotonically increasing convex function, the objective function in Formula (38) can be logarithmically transformed to transform the problem of finding the maximum value into a problem of finding the minimum value, making it easier to solve. After transformation, Formula (39) is obtained.

$$\min {\displaystyle \sum _i-d_i\ln ({\mathrm{C}}_i^0-{\mathrm{C}}_i-{\mathrm{C}}_i^{P2P})}$$

(39)

Solving Equations (38) and (39) is necessary for solving the non-linear logarithmic problem. Since the pre-sharing benefits ${\mathrm{C}}_i^0$ and post-sharing benefits ${\mathrm{C}}_i$ of microgrid i are obtained as constant values through previous solutions, directly using the fmincon function in MATLAB can effectively solve this problem.

5. Case Study

The case study in this section conducts research on the coordinated economic dispatch of multi-district microgrids for industrial, commercial, and residential areas and the asymmetric bargaining profit allocation based on emergy value and carbon trading. The simulation analysis was carried out using the Yalmip modeling tool in Matlab R2016a to establish the electric–carbon joint sharing model of multi-district microgrids and to solve the constrained cost optimization problem Q1 using the Gurobi 11.0 solver. The profit allocation problem Q2 was solved using the fmincon solver. The simulation was performed on an Intel^® Core™ i7-10870H CPU @ 2.20GHz with a 2.21GHz processor.

The case study in this section consists of two test scenarios.

Scenario S1: Without considering electric–carbon sharing, the operating costs, electricity purchase and sale quantities, and carbon emissions of each microgrid in the districts are calculated.

Scenario S2: Considering electric–carbon sharing, the total operating costs of multi-district microgrids and the electric–carbon interaction quantities between multiple microgrids are calculated.

5.1. Algorithm Parameterization

Carbon credit trading parameters are shown in

Table 1. Carbon credit trading parameters.

Carbon Credit Trading Mechanism Parameters	Parameter Values
Historical carbon emission intensity of industrial park microgrid power generation ${\kappa }_{e,1}^{\mathrm{IES}}$ (kgCO2/kWh)	0.705
Historical carbon emission intensity of microgrid power generation in commercial parks ${\kappa }_{e,2}^{\mathrm{IES}}$ (kgCO2/kWh)	0.685
Historical carbon emission intensity of microgrid power generation in residential parks ${\kappa }_{e,3}^{\mathrm{IES}}$ (kgCO2/kWh)	0.359
Carbon footprint factor for renewable energy units ${\kappa }_i^{\mathrm{RE}}$ (kgCO2/kWh)	0.025
Industrial park microgrid carbon universal emission reduction (kg CO2)	510
Commercial park microgrid carbon universal emission reduction (kg CO2)	320
Carbon universal emission reduction in residential parks (kg CO2)	850
Unit Price $f_{\mathrm{cc}}$ (¥/kgCO2)	0.09

. The rated capacity of each device in the multi-campus microgrid is shown in

Table 2. Rated capacity of the equipment.

Equipment Rated Capacity/kW (kWh)		Park Micro Network Type
		Industrial Park Microgrid 1	Commercial Park Microgrid 2	Residential Park Microgrid 3
Equipment type	Coal-fired cogeneration unit	1000	0	0
	Gas-fired cogeneration unit	1000	500	0
	Gas-fired boiler	1000	500	0
	Electrical storage device	1000 (kWh)	500 (kWh)	1000 (kWh)

.

The day is divided into T = 24 equal time intervals. According to the energy hub (EH) model of each district microgrid, electric energy dispatch factors, natural gas allocation coefficients, and thermal energy dispatch factors are set for each time interval. The demand loads for electricity, heat, and cooling are set for each time interval, and the predicted solar power $P_{v,t}^{\max }$ and wind power $P_{v,t}^{\max }$ of the microgrids are input into the electric–carbon joint sharing model. The power variations in the three district microgrids are illustrated in Figure 4.

5.2. Electricity/Carbon Volume Analysis

(1) Campus microgrids not participating in multi-microgrid electric–carbon sharing

The output situation of devices not participating in the multi-microgrid electricity–carbon sharing in the industrial, commercial, and residential microgrid areas is illustrated in Figure 5. With the premise of meeting the load demands of each microgrid area, the three microgrid areas ensure the lowest individual operation costs by prioritizing the absorption of wind and solar power with low costs and low carbon emissions, facilitated by energy storage participation for most periods. When the generation capacity within the microgrid areas is insufficient, electricity is purchased to achieve supply–demand balance. The daily electricity purchases for the three microgrid areas are 12,068.04 kWh, 31,342.55 kWh, and 7153.11 kWh, totaling 50,563.70 kWh. Additionally, the industrial microgrid area sells 2605.18 kWh to the grid from 12:00 to 15:00 due to the high output of photovoltaics. The residential microgrid area sells a small portion of excess wind power to the grid at 2:00 and 5:00, totaling 538.47 kWh. However, the commercial microgrid area, due to insufficient capacity from its generating units, needs to purchase electricity from the grid at all times to meet its load demands.

The carbon emissions and carbon trading costs for the microgrids not participating in the electricity–carbon joint sharing are presented in

Table 3. Carbon emissions and carbon transaction costs when each park microgrid operates separately.

Carbon Market Situation	Industrial Park Microgrid 1	Commercial Park Microgrid 2	Residential park Microgrid 3	Multi-Micro Network Total
Carbon quota amount (kgCO2)	14,543.35	23,084.34	4573.70	42,201.38
Carbon emissions (kgCO2)	13,992.52	24,262.32	5306.18	43,561.03
Carbon benefit quantity (kgCO2)	510.00	320.00	850.00	1680.00
Carbon emission reduction (kgCO2)	1060.83	−857.99	117.52	320.36
Transaction cost of carbon credit points (RMB)	−95.47	77.22	−10.58	−28.83
Penalty cost of abandoning wind and light carbon (RMB)	0.00	0.00	0.00	0.00
Reward and punishment cost of peak–valley grid-connected carbon (RMB)	28.08	0.00	−12.92	15.17
Carbon trading cost (RMB)	−67.39	77.22	−23.50	−13.67

“−” in each cost indicates benefits.

We used the minus sign, which may have been a mischaracterization due to the font. The commercial microgrid area, which procures a significant amount of external electricity, exceeds the carbon quota due to the constraint of the carbon quota reduction factor. Taking into account the carbon offset quantity, the carbon emissions still exceed the quota, requiring the purchase of carbon credits worth 77.22 yuan for offsetting. In addition, the industrial and residential microgrid areas, due to the substantial integration of wind and solar power, have carbon emissions lower than the carbon quota, resulting in positive carbon emission reductions. They can sell the surplus carbon credits, and after accounting for carbon penalty costs, they respectively obtain total carbon market revenues of 67.39 yuan and 23.50 yuan.

(2) Multi-Microgrid Electric–Carbon Joint Sharing

The interactive electricity exchange shared by various microgrid carbon collaborations in different zones is illustrated in Figure 4, Figure 5 and Figure 6, while the electricity purchase and sales, as well as equipment output situations of the microgrid carbon collaborations in various zones, are shown in Figure 7. Based on Figure 6a,b, it can be observed that from 2:00 to 6:00, Industrial Park Microgrid 1 mainly supplies electricity to Residential Park Microgrid 3, and from 10:00 to 15:00, Industrial Park Microgrid 1 transitions from selling electricity to the grid to primarily supplying electricity to Commercial Park Microgrid 2 to meet the electricity demand of Microgrid 2. Under this scheme, the total purchased electricity for Microgrids 1–2 amounts to 2757.44 kWh, while the total sold electricity amounts to 10,054.55 kWh; for Microgrids 1–3, the total purchased electricity amounts to 6237.52 kWh, while the sold electricity is almost the same at 6435.31 kWh; for Microgrids 2–3, the purchased electricity is 257.28 kWh, and the sold electricity is 2309.89 kWh. Therefore, in the context of multiple microgrid carbon collaborations, Microgrid 1 contributes the most to electricity output.

However, by combining Figure 7 with Figure 5, it can be observed that the multi-microgrids, through joint cost minimization and carbon sharing between microgrids, maximize the benefits of transferring electricity and carbon emissions to the grid while engaging in electricity transactions. Taking the period from 2:00 to 6:00 as an example, while Microgrids 1–3 in the park engage in energy exchange, Microgrid 1, with a historical carbon emission intensity of 0.705 (kgCO₂/kWh), purchases electricity from the grid, and Microgrid 3, with a historical carbon emission intensity of 0.359 (kgCO₂/kWh), sells electricity to the grid. Contrasting with the grid carbon emission factor of 0.695 (kgCO₂/kWh), under this interaction scheme, optimal joint cost sharing for low off-peak electricity prices and clean power carbon trading is achieved. In summary, under the electricity and carbon sharing scheme, the total electricity sold to the grid by the three microgrids amounts to 9200.80 kW, which is 2.93 times the total electricity sold by the three microgrids operating independently at 3143.65 kWh. Furthermore, compared to the total carbon emission reduction of 320.36 kgCO₂ when the three microgrids operate independently, under the joint electricity and carbon sharing scheme, the total carbon emission reduction in the three microgrids correspondingly increases to 875.33 kgCO₂, a 2.73-fold increase. Additionally, grid-connected electricity sales during peak periods result in the carbon penalty and reward costs for Microgrid 1 changing from a cost of 28.08 yuan to a gain of 77.73 yuan, and for Microgrid 3, the expanded carbon penalty and reward change from 10.57 yuan to 143.02 yuan.

(3) Operational cost analysis of campus microgrids before and after participation in electric–carbon joint sharing.

The operational costs before and after the participation of the park microgrids in the electric–carbon joint sharing are shown in

Table 4. Carbon emissions of different park microgrid before and after the transaction.

Microgrid Type	Carbon Trading Cost (RMB)		Total Operating Cost (RMB)
	before Sharing	after Sharing	before Sharing	after Sharing
Industrial park microgrid 1	−67.39	−712.01	14,521.03	17,050.17
Commercial park microgrid 2	77.22	384.78	29,169.19	23,379.47
Residential park microgrid 3	−23.50	27.69	5408.68	6033.68
Multi-micro network total	−13.67	−299.54	49,098.90	46,463.32

. Industrial Park Microgrid 1 increased its carbon trading revenue by 10.56 times through the joint sharing of electricity and transferring correspondingly high-carbon emissions between microgrids. However, to meet the load demand, it had to increase the purchased electricity from the grid, leading to a total increase in operational costs of 2529.14 yuan. Commercial Park Microgrid 2 received more high-carbon emission electricity from Microgrid 1 and a small portion of low-carbon emission electricity from Microgrid 3, which reduced its purchased electricity costs, resulting in a decrease of 5789.72 yuan in operational costs despite an increase of 307.56 yuan in carbon trading costs. Residential Park Microgrid 3, with the lowest carbon emission intensity, transferred low-emission electricity to other microgrids and the grid, requiring the use of high-emission electricity to meet its internal load demand. As a result, its revenue turned into costs in carbon market trading, and its operational costs increased by 625 yuan. However, after the participation of the multiple microgrids in the electric–carbon joint sharing, the total carbon trading revenue increased by 285 yuan, and the total operational costs decreased by 2635.58 yuan. In the electric–carbon joint sharing mode, Industrial Park Microgrid 1 shared the most electricity and transferred the highest carbon emissions from power generation. Commercial Park Microgrid 2, whose unit-rated capacity cannot meet the load demand, obtained the most electricity in the sharing, resulting in a significant reduction in operational costs primarily based on purchased electricity. Residential Park Microgrid 3 shared low-emission electricity but needed to supplement its load demand with high-carbon emission electricity, leading to increases in both carbon trading costs and operational costs. In the next step, profit distribution for the multiple microgrids should be based on their contributions of electricity and carbon emissions, ensuring that the operational costs of each microgrid are minimized to make the sharing scheme sustainable.

5.3. Operational Sustainability Analysis

The energy value baseline is 12.0 × 1024 sej/yr. Here, based on a typical daily electric–carbon joint sharing operation scenario for the multiple microgrids, the corresponding energy was converted into annual averages before calculating the energy value. The resulting energy value analysis is presented in Table 4 and

Table 5. Emergy analysis table of the multi-microgrids with the sharing of electricity and carbon.

Code Name	Name	Energy Value			Unit /yr	Emergy Transformity the sej/(Unit)	Energy Value (sej/yr)
		Microgrid 1	Microgrid 2	Microgrid 3			Microgrid 1	Microgrid 2	Microgrid 3
R1	Solar energy	7.74 × 107	2.32 × 107	4.64 × 107	MJ	1.00 × 106	7.74 × 1013	2.32 × 1013	4.64 × 1013
R2	Wind energy source	6.03 × 1011	2.01 × 1011	4.02 × 1011	MJ	5.89 × 107	3.55 × 1019	1.18 × 1019	2.37 × 1019
FR1, FN1	Fresh water is used for gas-fired boilers	2.19 × 106	2.19 × 106	0	kg	4.61 × 108	1.01 × 1015	1.01 × 1015	0
FR2, FN2	Fresh water is used for coal-fired generating units	1.72 × 108	0	0	kg	4.61 × 108	7.93 × 1016	0	0
R3	Oxygen for gas boilers	1.67 × 105	8.34 × 104	0	kg	5.16 × 1010	8.61 × 1015	4.30 × 1015	0
R4	Oxygen is used for the gas turbines	7.15 × 104	3.58 × 104	0	kg	5.16 × 1010	3.69 × 1015	1.84 × 1015	0
R5	Oxygen for coal-fired units	2.58 × 105	0	0	kg	5.16 × 1010	1.33 × 1016	0	0
R6	Manpower and sustainable service	9.20 × 103	7.88 × 103	1.31 × 103	h	2.50 × 1013	2.30 × 1017	1.97 × 1017	3.29 × 1016
N1	Coal-fired units cover land space and damage	1.77 × 102	0	0	m2	2.02 × 1010	3.58 × 1012	0	0
N2	Gas turbine footprint loss	1.77 × 102	8.87 × 10	0	m2	2.02 × 1010	3.58 × 1012	1.79 × 1012	0
N3	Gas boiler footprint loss	4.50 × 10	4.50 × 10	0	m2	2.02 × 1010	9.09 × 1011	9.09 × 1011	0
N4	The fan covers an area of loss	2.25 × 102	7.50 × 10	1.50 × 102	m2	2.02 × 1010	4.55 × 1012	1.52 × 1012	3.03 × 1012
N5	Photovoltaic covers an area of loss	1.40 × 104	1.20 × 103	0	m2	2.02 × 1010	2.83 × 1014	2.42 × 1013	0
N6	The refrigerator floor area is damaged	1.00 × 102	1.00 × 102	0	m2	2.02 × 1010	2.02 × 1012	2.02 × 1012	0
N7	Energy storage covers an area of loss	1.30 × 102	7.50 × 10	1.30 × 102	m2	2.02 × 1010	2.63 × 1012	1.52 × 1012	2.63 × 1012
FN3	Buy natural gas	2.51 × 107	1.48 × 107	0	MJ	1.46 × 1011	3.67 × 1018	2.16 × 1018	0
FN4	Buy coal	2.36 × 105	0	0	kg	1.11 × 1012	2.62 × 1017	0	0
FNe	Buy electricity	3.75 × 107	4.78 × 107	2.50 × 107	MJ	1.12 × 1012	4.20 × 1019	5.36 × 1019	2.80 × 1019
FCc	Carbon transaction costs	0	1.40 × 105	1.01 × 104	first	2.81 × 1011	0	3.95 × 1016	2.84 × 1015
FERc	Operation and maintenance of the recyclable equipment	4.94 × 105	2.01 × 105	2.02 × 105	first	2.81 × 1011	1.39 × 1017	5.63 × 1016	5.68 × 1016
FENc	Non-recyclable equipment operation and maintenance	5.49 × 104	2.23 × 104	2.24 × 104	first	2.81 × 1011	1.54 × 1016	6.26 × 1015	6.31 × 1015
FL	Manual paid service	6.13 × 103	5.26 × 103	8.76 × 102	h	2.50 × 1013	1.53 × 1017	1.31 × 1017	2.19 × 1016
YE1	Electrical load	4.67 × 107	3.88 × 107	2.59 × 107	MJ		3.31 × 1019	3.33 × 1019	2.07 × 1019
YE2	Output electricity	2.59 × 107	6.66 × 106	1.64 × 107	MJ		1.84 × 1019	5.71 × 1018	1.31 × 1019
YH	Thermal load	1.68 × 107	8.34 × 106	0	MJ		9.78 × 1017	5.56 × 1017	0
YC	Cooling load	2.80 × 107	1.58 × 107	2.49 × 107	MJ		2.62 × 1019	2.13 × 1019	1.55 × 1019
Wcb	Carbon emission	5.11 × 106	8.86 × 106	1.94 × 106	kg		3.62 × 1018	7.60 × 1018	1.55 × 1018
Se	Electricity sales income	6.50 × 105	0	1.20 × 106	first		4.61 × 1017	0	9.55 × 1017
SCc	Carbon trading earnings	2.60 × 105	0	0	first		1.84 × 1017	0	0

. In terms of the magnitude of the calculated energy values, the energy flows that contribute the most energy value are purchased electricity, wind energy, and purchased natural gas. It can be observed that external energy inputs serve as the primary support in multi-microgrid electric–carbon joint sharing.

Based on the energy structure of the multiple microgrids and the situation of energy distribution and co-supply, combined with the energy value conversion rates of various input materials and Formulas (5) and (6), the energy values of the respective output materials for the multiple microgrids were calculated. It can be observed that the energy material outputs are ranked in descending order of energy value magnitude as follows: electric load, cooling load, electrical energy output, heating load, carbon emissions, electricity sales revenue, and carbon trading revenue. Therefore, it can be inferred that secondary energy production requires more energy input to achieve economic benefits. Furthermore, based on the energy values of the output materials for the multiple microgrids shown in Table 5, their corresponding energy value conversion rates were calculated, as presented in

Table 6. Emergy transformity of material or energy output from multi-microgrids.

Code Name	Name	Emergy Transformity			Unit/yr
		Microgrid 1	Microgrid 2	Microgrid 3
YE1	Electrical load	7.09 × 1011	8.58 × 1011	7.98 × 1011	sej/MJ
YE2	Output electricity	7.09 × 1011	8.58 × 1011	7.98 × 1011	sej/MJ
YH	Thermal load	5.82 × 1010	6.67 × 1010	0	sej/MJ
YC	Cooling load	9.35 × 1011	1.35 × 1012	6.24 × 1011	sej/MJ
Wcb	Carbon emission	7.09 × 1011	8.58 × 1011	7.98 × 1011	sej/kg
Se	Electricity sales income	7.09 × 1011	0	7.98 × 1011	sej/first
SCc	Carbon trading earnings	7.09 × 1011	0	0	sej/first

. The bundling effect of the multi-microgrid electric–carbon joint sharing results in electrical energy, carbon emissions, and electric–carbon revenue having the same energy value conversion rate. However, due to the fact that the power generation units of Commercial Park Microgrid 2 do not meet the park’s electricity demand, it still requires substantial external electrical support, resulting in the highest energy value conversion rate for its electricity and carbon. This can be understood as requiring more energy input to produce one unit of electricity.

Furthermore, by calculating the energy value indicators for each park microgrid participating in the electric–carbon joint sharing of the multiple microgrids using Formulas (7)–(9), the results are presented in

Table 7. Emergy index comparison table of multi-microgrids.

	Microgrid 1	Microgrid 2	Microgrid 3
M e_EYR	1.30	0.86	1.29
M_ELR	1.28	4.61	1.18
M_ESI	1.02	0.19	1.10

. The energy sustainability index (M_ESI) of the park microgrids is directly proportional to the electricity energy yield rate (Ee_EYR) and inversely proportional to the environmental load rate (M_ELR). Industrial Park Microgrid 1 and Residential Park Microgrid 3 have power generation units with significant capacity, leading to higher Ee_EYR values. Microgrid 3 solely relies on renewable energy generation units, resulting in the lowest M_ELR due to the primary operation based on input from renewable solar and wind energy sources. In contrast, Commercial Park Microgrid 2 has lower capacity in its power generation units and a limited rooftop area for renewable energy generation, leading to the lowest Ee_EYR and highest M_ELR among the three microgrids. Finally, the energy sustainability index (M_ESI) for the multiple microgrids was calculated. Microgrid 1 has an M_ESI slightly greater than 1, indicating that the industrial park microgrid with a high proportion of renewable energy generation units possesses primary sustainability. Microgrid 2 with an M_ESI less than 1 suggests that the commercial park microgrid focused on self-owned thermal power generation units lacks sustainability. On the other hand, Microgrid 3 exhibits the highest M_ESI, showcasing the highest sustainability in energy usage due to its 100% renewable energy generation unit configuration.

5.4. Comparative Analysis of the Distribution of Benefits

Section 5.2 indicates that the total operating cost for the multiple microgrids running independently is 49,098.90 yuan, while the total operating cost for the multiple microgrids after participating in electric–carbon joint sharing is 46,463.32 yuan, resulting in a reduction of 2635.58 yuan in total operating costs.

Table 8. Profit distribution and cost analysis of multi-microgrids with the sharing of electricity and carbon.

Cost Classification		Microgrid 1	Microgrid 2	Microgrid 3
Total cost before sharing (yuan)		14,521.03	29,169.19	5408.68
Total cost after joint sharing of electricity and carbon (yuan)		17,050.17	23,379.47	6033.68
Nash bargaining	Negotiated cost (RMB)	−2529.14	3155.44	−626.30
	Total allocation cost (RMB)	14,521.03	26,534.92	5407.37
	Interest enhancement (RMB)	0.00	2634.28	1.30
Electric energy contribution of asymmetric bargaining	Negotiated cost (RMB)	−3725.69	5068.09	−1342.40
	Total allocation cost (RMB)	13,324.48	28,447.57	4691.27
	Interest enhancement (RMB)	1196.55	721.63	717.40
Electric–carbon joint contribution to asymmetric bargaining	Negotiated cost (RMB)	−3470.46	5203.56	−1733.10
	Total allocation cost (RMB)	13,579.71	28,583.03	4300.58
	Interest enhancement (RMB)	941.32	586.16	1108.10
Electric–carbon sustainable contribution to asymmetric bargaining	Negotiated cost (RMB)	−3635.45	5661.71	−2026.26
	Total allocation cost (RMB)	13,414.71	29,041.19	4007.42
	Interest enhancement (RMB)	1106.32	128.01	1401.26

provides the operating cost situation for the multiple microgrids participating in electric–carbon joint sharing and under different benefit allocation methods.

The Nash bargaining, without considering the contributions of each microgrid in the parks, results in an increase of 2634.28 yuan in the benefits of Commercial Park Microgrid 2 compared to before participating in electric–carbon joint sharing. However, Industrial Park Microgrid 1, which provides more electricity among the multiple microgrids, does not experience a benefit increase, and Residential Park Microgrid 3 only gains a marginal increase of 1.3 yuan in benefits. Under the Nash bargaining allocation method, the microgrids that are capable of providing electricity do not receive incentives and lack the willingness to participate in sharing. Considering the asymmetrical bargaining profit distribution based on the contributions of the multiple microgrids, solely based on electricity contribution, the benefit increase rates among the three park microgrids are 45.40%, 27.38%, and 27.22%, respectively. This is because Microgrid 1, which provides the most electricity among the multiple microgrids, receives the highest benefit increase. When considering the joint contribution based on electric–carbon cooperation, the benefit increase rates among the three park microgrids change to 35.72%, 22.24%, and 42.04%, respectively, based on their carbon emission intensities. This indicates that Residential Park Microgrid 3, with its low carbon emissions intensity, can gain more low-carbon benefits from participating in sharing.

Based on the joint contribution of electricity, carbon emission intensity, and energy value sustainability indicators, the benefit increases for industrial, commercial, and residential park microgrids are 1106.32 yuan, 128.01 yuan, and 1401.26 yuan, respectively, accounting for 41.98%, 4.86%, and 53.17% shares, respectively. Under this mode, the costs of all microgrids are reduced so that the willingness to cooperate can be effectively assured. In addition, it can be found that the interest enhancement of the residential park microgrid is the highest compared with the other bargaining methods. This is because its M_ESI is the highest, 1.10, as shown in Table 7. For the commercial park microgrid, although its cost is lower than the original cost, its interest enhancement is the lowest of the three microgrids because of the lowest M_ESI, 0.19. That is to say, the level of a microgrid’s M_ESI is positively related to its interest enhancement. This indicator represents the sustainability level of the microgrid. It is conceivable that when the microgrid strengthens its sustainable level of construction, its indicator can be increased, so that the benefit enhancement can also be increased, and finally the dual benefits of environment and economy can be realized. Therefore, in this model, the three park microgrids can exhibit a stable and trustworthy cooperative willingness while also incentivizing each microgrid to further enhance the cleanliness and sustainability of their internal power generation systems. Specific measures include increasing the capacity of renewable energy units and battery storage devices, improving unit system layouts, using low-carbon energy materials, and enhancing management levels, among others.

6. Conclusions

In response to climate change, the penetration of new energy is increasing daily, but there is a lack of flexible energy transfer mechanisms. The optimization effect of low-carbon economic scheduling within a single park is limited. In the context of the sharing economy, this paper proposes a research method for multi-park electric–carbon joint sharing and benefit distribution based on energy value and carbon credit trading. Firstly, a framework for the operation of multi-microgrid energy systems is constructed, and a model of an energy hub with electrical, cooling, and heating interconnections for multiple energy conversions is established. Secondly, based on the energy conversion relationships of the energy hub model, an energy value analysis method for multi-microgrid is formulated, and an improved energy value index for multi-microgrid is established. Subsequently, a carbon credit trading model for parks is established based on the carbon emission reduction mechanism, further forming an optimal dispatch strategy for the economic and environmental benefits of multi-microgrid electric–carbon joint sharing, and solved using Matlab+Gurobi. Then, based on asymmetric Nash bargaining, combined with the energy contribution, carbon emission reduction contribution, and energy value sustainability contribution of each park, the comprehensive contribution rate of each park is calculated to achieve a fair distribution of cooperative benefits among multiple parks. The results show that the proposed method can effectively reduce the total operating cost of multi-microgrids and reduce carbon emissions, and the adopted benefit distribution strategy can achieve sustainable and equitable profit allocation, effectively incentivizing the construction of new energy in multi-microgrids and promoting active participation of various park microgrids in cooperative operations.