A Distributed Multi-Microgrid Cooperative Energy Sharing Strategy Based on Nash Bargaining

Abstract

With the rapid development of energy transformation, the proportion of new energy is increasing, and the efficient trading mechanism of multi-microgrids can realize energy sharing to improve the consumption rate of new energy. A distributed multi-microgrid cooperative energy sharing strategy is proposed based on Nash bargaining. Firstly, by comprehensively considering the adjustable heat-to-electrical ratio, ladder-type positive and negative carbon trading, peak–valley electricity price and demand response, a multi-microgrid system with wind–solar-storage-load and combined heat and power is constructed. Then, a multi-microgrid cooperative game optimization framework is established based on Nash bargaining, and the complex nonlinear problem is decomposed into two stages to be solved. In the first stage, the cost minimization problem of multi-microgrids is solved based on the alternating direction multiplier method to maximize consumption rate and protect privacy. In the second stage, through the established contribution quantification model, Nash bargaining theory is used to fairly distribute the benefits of cooperation. The simulation results of three typical microgrids verify that the proposed strategy has good convergence properties and computational efficiency. Compared with the independent operation, the proposed strategy reduces the cost by 41% and the carbon emission by 18,490 kg, thus realizing low-carbon operation and optimal economic dispatch. Meanwhile, the power supply pressure of the main grid is reduced through energy interaction, thus improving the utilization rate of renewable energy.

1. Introduction

With the vigorous development of energy transformation, the penetration rate of renewable energy represented by wind power and photovoltaic energy continues to rise, which brings serious consumption problems to the power system [1]. Microgrids are important carriers of absorbing new energy, so it is of great practical significance to establish the energy-sharing pathways for multi-microgrids by using an efficient trading mechanism to realize the low-carbon operation and economic dispatch of the power grid [2].

Countless excellent research results have been achieved in the research of individual microgrids [3,4,5], including the smooth switching technology, which can effectively realize the on-grid and off-grid modes of a microgrid. This improves the flexibility of the system and the consumption rate of new energy [6]. However, with the large-scale development of new energy, research on interconnected multi-microgrids has attracted significant attention as the complementary characteristics of energy to coordinate multi-microgrids can be fully utilized so as to improve the reliability and stability of the system [7,8,9]. The management of multi-microgrids can be simply divided into centralized and distributed types. In the centralized structure [10,11,12], the central coordinator collects the relevant information from each microgrid for centralized calculation and processing so as to obtain the optimal control strategy and ultimately achieve the operational objectives such as economic optimization or minimum network losses. In [10], a centralized energy management framework considering the non-integer-hour energy transmission is designed for pelagic island microgrid groups. In [11], a centralized distributionally robust chance-constrained dispatch model is established for integrated transmission–distribution systems. In [12], the centralized energy storage is used as an energy-type energy storage unit to take part in the peak shaving of the active distribution network. However, as an increasing proportion of new energy leads to an increasing number of microgrids, this centralized structure will face challenges in terms of computational complexity and data privacy risks. Therefore, the distributed structure enables microgrids to trade energy with each other without exchanging information with a central coordinator [13,14,15,16]. In [14], combining the optimal allocation problem with optimal scheduling, an improved snake optimization algorithm is proposed to optimize the capacity of microgrids. In [15], a novel decentralized approach called the primal–dual sub-gradient algorithm is used to clear the designed market without third-party involvement or disclosure of players’ private information. In [16], by integrating with the analytical target cascading (ATC) method, a distributed robust model predictive control framework is implemented through the necessary exchange of information while respecting privacy. As an alternative to ATC, the alternating direction method of multipliers (ADMMs) is also widely applied to achieve distributed optimal energy management [17]. However, the independent trading strategy of each microgrid cannot guarantee the feasibility and global optimization of the whole multi-microgrid system [18]. By comprehensively analyzing the characteristics of a centralized and distributed structure, it is of practical significance to study energy trading and the sharing strategy of multi-microgrids based on the ADMM algorithm to achieve efficient computing and privacy protection.

As a popular energy management strategy, peer-to-peer (P2P) energy trading among microgrids enables them to leverage their complementary strengths among the different types of MGs, and more efficient energy sharing among microgrids can be achieved by introducing an autonomous pricing mechanism [19,20]. A non-iterative decentralized market-clearing method based on game theory is proposed to meet the challenges of computation and communication in an iterative process in [21]. Game theory is a powerful tool to balance the interests of each microgrid and achieve the lowest operating cost of a multi-microgrid system. It can be generally divided into non-cooperative games and cooperative games. This game-theoretic study provides an incentive for energy trading among microgrids in future power grids, based on which a distributed mechanism for energy trading among microgrids is proposed in a competitive market [22]. The non-cooperative game involves the existence of multiple decision-making agencies such that each microgrid tries to maximize its own interests [23]. Among them, the famous Stackelberg game is applied in the power market, which belongs to a typical two-level hierarchical distributed energy management [24]. Due to the lack of consideration of the overall system interests in non-cooperative games, cooperative game theory based on a coalitional game model or Nash bargaining model has attracted significant research attention [25]. The coalition-based game approach was proposed in [26], and the profit is distributed according to the Shapley value. Further, an incentive mechanism based on Nash bargaining was proposed in [27], where the Nash product can guarantee that the benefits of multi-microgrid energy cooperative trading are shared by each microgrid in a fair manner. By analysis, it is challenging to establish a cooperative game model of multi-microgrid energy sharing based on Nash bargaining to realize the efficient operation of the system.

Motivated by this, we propose a comprehensive energy sharing strategy for the established multi-microgrid system, and solve the complex optimization algorithm step by step to realize the low-carbon operation and economic scheduling of multi-microgrids. The main contributions are as follows.

(1)

A multi-microgrid system with wind–solar-storage-load and combined heat and power (CHP) is established. Compared with the conventional microgrids [8,9,27], this paper takes into account various factors such as the adjustable heat-to-electrical ratio, power load, heat load, ladder-type positive and negative carbon trading and peak–valley electricity price, thereby aligning more closely with the actual development needs of the power grid.

(2)

A distributed multi-microgrid cooperative energy sharing strategy is proposed. Compared with other optimal scheduling strategies [19,20,21,22,23,24,26], this strategy establishes a cooperative energy sharing optimization model for multi-microgrids based on Nash bargaining, and divides it into two stages of the cost minimization of multi-microgrids and fair distribution of cooperative benefits, so as to realize low-carbon and economic scheduling, and improve the utilization rate of renewable energy.

(3)

The alternating direction method of multipliers (ADMM) is adopted to address cost minimization and fair distribution problems. Compared with other centralized optimization scheduling methods [10,11,12,14], the ADMM can update and iterate the multipliers according to the constraints of the multi-microgrid system after the objective function of each microgrid is solved by itself, which can fully protect the privacy of each microgrid.

The remainder of this paper is organized as follows. Section 2 establishes the model of multi-microgrid systems, and the multi-microgrid energy sharing strategy and ADMM algorithm are proposed in Section 3. Section 4 performs simulation results and Section 5 concludes this paper.

2. The Modeling of Multi-Microgrid Systems

The multi-microgrid systems (containing n microgrids) is established, as shown in Figure 1, which is suitable for both grid-connected mode and isolated mode. Each microgrid is equipped with renewable energy (wind or solar) generators, a hybrid energy storage system (ESS), combined heat and power (CHP) units, gas boilers (GBs), power load, heat load and management systems consisting of microsource controllers (MCs) and load controllers (LCs), so that the internal optimization strategies of each microgrid can be solved locally, while the multi-microgrid dispatchers of the main grid require only multiplier information for updates and iterations, which fully guarantees the privacy and data security of each microgrid.

Furthermore, each microgrid is interconnected with the main grid through power exchange lines to realize the demand for purchasing and selling electricity from the main grid. Meanwhile, each microgrid interacts with the other through the tie lines to enable power sharing and realize the complementary advantages between the multi-energy microgrids. Assuming that the interactive electricity price is between the sale price and the purchase price of the peak and valley electricity price mechanism, the power sharing between microgrids can be given priority, so as to improve the utilization rate of renewable energy. Inspired by [6,7,8,9], the subsequent sections of the microgrid will be modeled, incorporating adjustable heat-to-electrical ratios, a ladder-type positive and negative carbon trading mechanism and peak–valley electricity price to make the model more suitable for the actual demand.

2.1. Multi-Energy Microgrids

Photovoltaic (PV) power generation is primarily reliant on solar energy. The model for operating and maintenance (O&M) cost, along with its associated constraints, can be established as follows:

$$\begin{array}{c}{C}_i^{pv}=c_{pri}^{pv}{\displaystyle \sum _{t=1}^T}(P_i^{pv}(t))\Delta \tau ,0\le P_i^{pv}(t)\le P_{i,max}^{pre\_pv}(t),\end{array}$$

(1)

where $C_i^{pv}$ and $c_{pri}^{pv}$ are the O&M cost and price per unit of PV, and $P_i^{pv}$ and $P_{i,max}^{pre\_pv}$ represent the PV output and predicted maximum output, respectively. T is the scheduling period and $\Delta \tau$ is the time step.

Wind turbine (WT) power generation is primarily reliant on wind energy. The O&M cost model, along with its associated constraints, can be established as follows:

$$\begin{array}{c}{C}_i^{wt}=c_{pri}^{wt}{\displaystyle \sum _{t=1}^T}(P_i^{wt}(t))\Delta \tau ,0\le P_i^{wt}(t)\le P_{i,max}^{pre\_wt}(t),\end{array}$$

(2)

where $C_i^{wt}$ and $c_{pri}^{wt}$ are the O&M cost and price per unit of WT, and $P_i^{wt}$ and $P_{i,max}^{pre\_wt}$ represent the WT output and predicted maximum output, respectively.

Energy Storage Systems (ESSs) possess the capability to dynamically modulate the relationship between supply and demand through charging and discharging. The battery capacity $S_i^{ess}(t)$ of ESS at time t for the $i_{th}$ microgrid can be described as follows:

$$\begin{array}{c}{S}_i^{ess}(t)=(1-{\eta }_{loss}^{ess})S_i^{ess}(t-1)+{\eta }_{ch}^{ess}{P}_{i,ch}^{ess}(t)-{\eta }_{dis}^{ess}{P}_{i,dis}^{ess}(t),S_{i,min}^{ess}(t)\le S_i^{ess}(t)\le S_{i,max}^{ess}(t),\end{array}$$

(3)

where ${\eta }_{loss}^{ess}$ is the self-loss rate of ESS, ${\eta }_{ch}^{ess}$, and ${\eta }_{dis}^{ess}$, $P_{i,ch}^{ess}$ and $P_{i,dis}^{ess}$ correspond to charging and discharging efficiency and power of ESS, respectively. $S_{i,max}^{ess}$ and $S_{i,min}^{ess}$ are the upper and lower limits of battery capacity. The start-end stored energy balance $S_i^{ess}(1)=S_i^{ess}(24)$ is guaranteed within the dispatching range. Then the cost model and constraints associated with ESS can be established as:

$$\begin{array}{c}{C}_i^{ess}=c_{pri}^{ess}{\displaystyle \sum _{t=1}^T}(P_{i,ch}^{ess}(t)+P_{i,dis}^{ess}(t))\Delta \tau ,\\ 0\le P_{i,ch}^{ess}(t)\le u_{i,ch}^{ess}(t)P_{i,ch\_max}^{ess}(t),0\le P_{i,dis}^{ess}(t)\le u_{i,dis}^{ess}(t)P_{i,dis\_max}^{ess}(t),u_{i,ch}^{ess}(t)+u_{i,dis}^{ess}(t)\le 1,\end{array}$$

(4)

where $C_i^{ess}$ and $c_{pri}^{ess}$ are the O&M cost and price per unit of ESS, respectively. $P_{i,ch\_max}^{ess}$ and $P_{i,dis\_max}^{ess}$ are the maximum charging and discharging power of ESS. The binary variables $u_{i,ch}^{ess}$ and $u_{i,dis}^{ess}$ denote charging and discharging states, which can be restricted to not simultaneously charging and discharging during the optimization scheduling process.

Combined Heat and Power (CHP) systems can effectively meet both power and heat demands by recovering waste heat generated during power production. To further optimize operational efficiency, the CHP systems with adjustable heat-to-electrical ratios can modify their output in response to real-time power and heat requirements. Therefore, the power output $P_{i,e}^{chp}$ and heat output $P_{i,h}^{chp}$ of the CHP systems are as follows:

$$\begin{array}{c}{P}_{i,e}^{chp}(t)={\eta }_e^{chp}Q{V}_{i,e}^{chp\_gas}(t),P_{i,h}^{chp}(t)={\eta }_h^{chp}Q{V}_{i,h}^{chp\_gas}(t),\end{array}$$

(5)

where ${\eta }_e^{chp}$, ${\eta }_h^{chp}$, $V_{i,e}^{chp\_gas}$ and $V_{i,h}^{chp\_gas}$ represent the efficiencies and natural gas consumption for power generation and heat generation in CHP systems, respectively. Q represents the calorific value of natural gas. Then the cost model and constraints associated with CHP can be established as:

$$\begin{array}{c}{C}_i^{chp}=c_{pri}^{chp}{\displaystyle \sum _{t=1}^T}(P_{i,e}^{chp}(t)+P_{i,h}^{chp}(t))\Delta \tau +c_{pri}^{gas}{\displaystyle \sum _{t=1}^T}(V_{i,e}^{gas}(t)+V_{i,h}^{gas}(t))\Delta \tau ,\\ 0\le P_{i,e}^{chp}(t)\le P_{i,e\_max}^{chp}(t),0\le P_{i,h}^{chp}(t)\le P_{i,h\_max}^{chp}(t),{\epsilon }_{i,min}^{chp}(t)\le {\displaystyle \frac{P_{i,h}^{chp}(t)}{P_{i,e}^{chp}(t)}}\le {\epsilon }_{i,max}^{chp}(t),\end{array}$$

(6)

where $C_i^{chp}$, $c_{pri}^{chp}$ and $c_{pri}^{gas}$ are CHP cost, O&M and gas purchase price per unit, respectively. $P_{i,e\_max}^{chp}$ and $P_{i,h\_max}^{chp}$ are the maximum power output and maximum heat output of CHP, and ${\epsilon }_{i,min}^{chp}$ and ${\epsilon }_{i,max}^{chp}$ are the adjustable upper and lower limits of heat-to-electrical ratios.

Gas boilers (GBs) generate heat energy through the combustion of natural gas, so the cost model and associated constraints for GB similar to CHP can be obtained as follows:

$$\begin{array}{c}{P}_{i,h}^{gb}(t)={\eta }_h^{gb}Q{V}_{i,h}^{gb\_gas}(t),0\le P_{i,h}^{gb}(t)\le P_{i,h\_max}^{gb}(t),\\ C_i^{gb}=c_{pri}^{gb}{\displaystyle \sum _{t=1}^T}(P_{i,h}^{gb}(t))+c_{pri}^{gas}{\displaystyle \sum _{t=1}^T}(V_{i,h}^{gb\_gas}(t))\Delta \tau ,\end{array}$$

(7)

where $C_i^{gb}$ and $c_{pri}^{gb}$ are the cost associated with GB and O&M price per unit, respectively. $P_{i,h}^{gb}$ and $P_{i,h\_max}^{gb}$ are the heat output of GB and its maximum capacity, and ${\eta }_h^{gb}$ and $V_{i,h}^{gb\_gas}$ correspond to efficiency and natural gas consumption for heat generation in GB.

2.2. Demand Response

In aligning more closely with actual demand, both electrical and heat loads are considered in each microgrid. Furthermore, these loads have a certain proportion of adjustable characteristics to achieve demand response, aimed at maximizing the utilization of renewable energy sources (RESs). Note that the demand response here only considers the transferable and cuttable loads. The transferable load means that a certain proportion of electricity consumption in each time period can be flexibly adjusted, with the characteristics of interruption and non-sustainability, while maintaining the total electricity consumption amount. The cuttable load means that a certain proportion of load can be reduced in accordance with optimal scheduling requirements, and the heat load only considers cuttable characteristics. Therefore, the electrical load $L_{i,e}^{load}$ and heat load $L_{i,h}^{load}$ are expressed as:

$$\begin{array}{c}{L}_{i,e}^{load}(t)=L_{i,e}^{rig}(t)+L_{i,e}^{tran}(t)-L_{i,e}^{cut}(t),L_{i,e}^{cut}(t)\le {\epsilon }_{i,e}^{cut}(t)L_{i,e}^{load}(t),\\ -{\epsilon }_{i,e}^{tran}(t)L_{i,e}^{load}(t)\le L_{i,e}^{tran}(t)\le {\epsilon }_{i,e}^{tran}(t)L_{i,e}^{load}(t),{\displaystyle \sum _{t=1}^T}{L}_{i,e}^{tran}(t)\Delta \tau =0,\\ L_{i,h}^{load}(t)=L_{i,h}^{rig}(t)-L_{i,h}^{cut}(t),L_{i,h}^{cut}(t)\le {\epsilon }_{i,h}^{cut}(t)L_{i,h}^{load}(t),\end{array}$$

(8)

where $L_{i,e}^{rig}$, $L_{i,h}^{rig}$, $L_{i,e}^{cut}$ and $L_{i,h}^{cut}$ are the rigid and cuttable electrical and heat loads, respectively, while $L_{i,e}^{tran}$ denotes the transferable electrical load. ${\epsilon }_{i,e}^{tran}$, ${\epsilon }_{i,e}^{cut}$ and ${\epsilon }_{i,h}^{cut}$ indicate the proportions of transferable electrical load, cuttable electrical load and cuttable heat load, respectively. Considering that both load transfer and reduction need to give appropriate compensation for users, the costs associated with demand response can be established as:

$$\begin{array}{c}{C}_i^{dr}=c_e^{tran}{\displaystyle \sum _{t=1}^T}(L_{i,e}^{tran}(t))\Delta \tau +c_e^{cut}{\displaystyle \sum _{t=1}^T}(L_{i,e}^{cut}(t))\Delta \tau +c_h^{cut}{\displaystyle \sum _{t=1}^T}(L_{i,h}^{cut}(t))\Delta \tau ,\end{array}$$

(9)

where $C_i^{dr}$ represents the costs of demand response, while $c_e^{tran}$, $c_e^{cut}$ and $c_h^{cut}$ are the compensated unit prices for load transfer and load reduction, respectively.

2.3. Energy Interaction

Energy interaction encompasses the power trading with the main grid, in addition to the power trading among microgrids. The utilization rate of renewable energy can be improved by optimizing energy interaction. The power trading with the main grid is subject to the following constraints:

$$\begin{array}{c}0\le P_i^{buy}(t)\le u_i^{buy}(t)P_{i,max}^{buy}(t),0\le P_i^{sell}(t)\le u_i^{sell}(t)P_{i,max}^{sell}(t),u_i^{buy}(t)+u_i^{sell}(t)\le 1,\end{array}$$

(10)

where $P_i^{buy}$, $P_i^{sell}$, $P_{i,max}^{buy}$ and $P_{i,max}^{sell}$ are the actual amount and maximum limits for power purchased and sold, respectively. Note that $P_{i,max}^{buy}$ should be limited to the load demand, while $P_{i,max}^{sell}$ should be limited by the corresponding generation units within the microgrid. The binary variables $u_i^{buy}$ and $u_i^{sell}$ denote the states of buying and selling, which are subject to the condition that power cannot be simultaneously bought and sold. Taking into account the actual peak–valley electricity price mechanism, the costs associated with power trading with the main grid can be expressed as:

$$\begin{array}{c}{C}_i^{p2m}={\displaystyle \sum _{t=1}^T}(c_i^{buy}(t)P_i^{buy}(t)-c_i^{sell}(t)P_i^{sell}(t))\Delta \tau ,\end{array}$$

(11)

where $C_i^{p2m}$ represents the power trading costs with the main grid, and $c_i^{buy}$ and $c_i^{sell}$ are purchase and sale electricity prices, which follow the peak–valley electricity price mechanism.

The power trading between microgrids adheres to the following constraints:

$$\begin{array}{c}-u_{j,i}^{p2p}(t)P_{max}^{p2p}\le P_{i,j}^{p2p}(t)\le u_{i,j}^{p2p}(t)P_{max}^{p2p}(i\ne j),\\ u_{j,i}^{p2p}(t)+u_{i,j}^{p2p}(t)\le 1,u_i^{buy}(t)+u_{i,j}^{p2p}(t)\le 1,u_i^{sell}(t)+u_{j,i}^{p2p}(t)\le 1,\end{array}$$

(12)

where $P_{i,j}^{p2p}$ and $P_{max}^{p2p}$ are the power traded from microgrid i to microgrid j and the maximum power traded between microgrids, respectively. Note that $P_{max}^{p2p}$ should be limited to the load demand or the relevant generation units within the microgrid. The binary variables $u_{i,j}^{p2p}$ and $u_{j,i}^{p2p}$ denote the states in which MG_i delivers power to MG_j, and MG_j delivers power to MG_i, respectively. Therefore, the power trading costs between microgrids can be expressed as:

$$\begin{array}{c}{C}_i^{p2p}=c_{i,j}^{p2p}{\displaystyle \sum _{t=1}^T}(P_{i,j}^{p2p}(t))\Delta \tau ,(i\ne j),\end{array}$$

(13)

where $C_i^{p2p}$ and $c_{i,j}^{p2p}$ represent the power trading costs and unit price of MG_i, respectively.

Therefore, the heat and power balance of multi-microgrid system can be expressed as:

$$\begin{array}{c}{P}_{i,h}^{chp}(t)+P_{i,h}^{gb}(t)=L_{i,h}^{load}(t),\\ P_i^{pv}(t)+P_i^{wt}(t)+P_{i,dis}^{ess}(t)+P_{i,e}^{chp}(t)+P_i^{buy}(t)=P_{i,ch}^{ess}(t)+L_{i,e}^{load}(t)+P_i^{sell}(t)+P_{i,j}^{p2p}(t).\end{array}$$

(14)

2.4. Ladder-Type Positive and Negative Carbon Trading

The ladder-type positive and negative carbon trading mechanism mainly includes carbon emission quota, actual carbon emission and ladder-type positive and negative carbon emission trading. Each power or heat production unit can buy and sell the carbon emission quota in the carbon trading market according to its own carbon emission quota and actual carbon emission. The ladder-type trading price is divided into different ranges according to the carbon emission quota to be purchased. The more carbon emission quotas to be purchased, the higher the purchase price of the corresponding range, which can effectively suppress carbon emissions and achieve low carbon. Therefore, the carbon emission quota can be expressed as:

$$\begin{array}{c}{E}_i^{quo}={\alpha }_e^{pv}{\displaystyle {\displaystyle \sum _{t=1}^T}}(P_i^{pv}(t))+{\alpha }_e^{wt}{\displaystyle {\displaystyle \sum _{t=1}^T}}(P_i^{wt}(t))+{\alpha }_e^{chp}{\displaystyle {\displaystyle \sum _{t=1}^T}}(P_{i,e}^{chp}(t))+{\alpha }_h^{chp}{\displaystyle \sum _{t=1}^T}(P_{i,h}^{chp}(t))+{\alpha }_h^{gb}{\displaystyle \sum _{t=1}^T}(P_{i,h}^{gb}(t)),\end{array}$$

(15)

where $E_i^{quo}$ is the carbon emission quota, and ${\alpha }_e^{pv}$, ${\alpha }_e^{wt}$, ${\alpha }_e^{chp}$, ${\alpha }_h^{chp}$ and ${\alpha }_h^{gb}$ are the carbon emission quota allocation coefficients for power generation and heat generation from PV, WT, CHP and GB, respectively. Then, the actual carbon emissions can be expressed as:

$$\begin{array}{c}{E}_i^{co2}={\beta }_e^{buy}{\displaystyle \sum _{t=1}^T}(P_i^{buy}(t))+{\beta }_e^{chp}{\displaystyle \sum _{t=1}^T}(P_{i,e}^{chp}(t))+{\beta }_h^{chp}{\displaystyle \sum _{t=1}^T}(P_{i,h}^{chp}(t))+{\beta }_h^{gb}{\displaystyle \sum _{t=1}^T}(P_{i,h}^{gb}(t)),\end{array}$$

(16)

where $E_i^{co2}$ is the actual carbon emissions, and ${\beta }_e^{buy}$, ${\beta }_e^{chp}$, ${\beta }_h^{chp}$ and ${\beta }_h^{gb}$ are the carbon emission coefficients for power generation and heat generation from main grid, CHP and GB, respectively. Therefore, the costs of ladder-type positive and negative carbon trading can be established as:

$$C_i^{co2}=\{\begin{array}{cc}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\dots \dots & \\ c_{neg3}^{co2}(E_i^{co2}-E_i^{quo}+2d)-(c_{neg1}^{co2}+c_{neg2}^{co2})d,& -3d<E_i^{co2}-E_i^{quo}\le -2d;\\ c_{neg2}^{co2}(E_i^{co2}-E_i^{quo}+d)-c_{neg1}^{co2}d,& -2d<E_i^{co2}-E_i^{quo}\le -d;\\ c_{neg1}^{co2}(E_i^{co2}-E_i^{quo}),& -d<E_i^{co2}-E_i^{quo}\le 0;\\ c_{pos1}^{co2}(E_i^{co2}-E_i^{quo}),& 0<E_i^{co2}-E_i^{quo}\le d;\\ c_{pos2}^{co2}(E_i^{co2}-E_i^{quo}-d)+c_{pos1}^{co2}d,& d<E_i^{co2}-E_i^{quo}\le 2d;\\ c_{pos3}^{co2}(E_i^{co2}-E_i^{quo}-2d)+(c_{pos1}^{co2}+c_{pos2}^{co2})d,& 2d<E_i^{co2}-E_i^{quo}\le 3d;\\ c_{pos4}^{co2}(E_i^{co2}-E_i^{quo}-3d)+(c_{pos1}^{co2}+c_{pos2}^{co2}+c_{pos3}^{co2})d,& 3d<E_i^{co2}-E_i^{quo}\le 4d;\\ c_{pos5}^{co2}(E_i^{co2}-E_i^{quo}-4d)+(c_{pos1}^{co2}+c_{pos2}^{co2}+c_{pos3}^{co2}+c_{pos4}^{co2})d,& 4d<E_i^{co2}-E_i^{quo}\le 5d;\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\dots \dots & \end{array}$$

(17)

$$\dots <c_{neg3}^{co2}<c_{neg2}^{co2}<c_{neg1}^{co2},c_{pos1}^{co2}<c_{pos2}^{co2}<c_{pos3}^{co2}<c_{pos4}^{co2}<c_{pos5}^{co2}<\dots ,$$

where $C_i^{co2}$ is the ladder-type positive and negative carbon trading costs, and d is the length of the carbon emission interval. $c_{pos1}^{co2}$, $c_{pos2}^{co2}$, $c_{pos3}^{co2}$, $c_{pos4}^{co2}$, $c_{pos5}^{co2}$, $c_{neg1}^{co2}$, $c_{neg2}^{co2}$ and $c_{neg3}^{co2}$ are the positive and negative carbon emission trading unit prices for each interval, respectively.

Remark 1.

Note that different from existing fixed carbon trading models or ladder carbon trading models [8,12,27], this paper considers the ladder-type positive and negative carbon trading mechanism, in which the modeling of the negative carbon part is improved, so that it is more in line with reality and realizes low carbon demand.

3. Multi-Microgrid Energy Sharing Strategy and ADMM Algorithm

The cooperative game theory is applied to optimize the sharing and trading of renewable energy in distributed multi-microgrids, and fair distribution is achieved through Nash bargaining after the maximum benefits of multi-microgrids are completed. Inspired by [8,27], the multi-variable coupling non-convex nonlinear problem is decomposed into two stages to solve, that is, cost minimization (benefit maximization) of multi-microgrids and fair distribution of cooperation benefits, then solved by ADMM algorithm in turn.

3.1. Cost Minimization of Multi-Microgrids

Firstly, the multi-microgrid energy sharing model based on Nash negotiation theory is established as follows:

$$\begin{array}{c}max{\displaystyle \prod _{i=1}^n}(C_i^{pre}-C_i^{post}),C_i^{pre}-C_i^{post}>0,\end{array}$$

(18)

where $C_i^{pre}$ and $C_i^{post}$ denote the pre-sharing costs and post-sharing costs of MG_i. Then, maximizing the sharing benefits of multi-microgrids is equivalent to minimizing costs. Therefore, according to the above-mentioned model and related constraints of each energy module, the multi-microgrid power cooperation and sharing cost model can be constructed as follows:

$$\begin{array}{c}min{\displaystyle \sum _{i=1}^n}(C_i^{pv}+C_i^{wt}+C_i^{ess}+C_i^{chp}+C_i^{gb}+C_i^{dr}+C_i^{p2m}+C_i^{p2p}+C_i^{co2}).\end{array}$$

(19)

Note that the interactive power $P_{i,j}^{p2p}$ and $P_{j,i}^{p2p}$ are not only the global variables of multi-microgrids, but also the local variables of MG_i and MG_j, respectively. When $P_{i,j}^{p2p}=-P_{j,i}^{p2p}$, it indicates that MG_i and MG_j have reached a consensus on power trading. Therefore, in order to protect the privacy of each microgrid, the steps to solve the cost minimization problem of multi-microgrids based on ADMM algorithm are as follows:

Step 1. 

The augmented Lagrange relaxation method is applied as follows:

$$\begin{array}{c}{L}_i^{cm}=C_i^{pv}+C_i^{wt}+C_i^{ess}+C_i^{chp}+C_i^{gb}+C_i^{dr}+C_i^{p2m}+C_i^{p2p}+C_i^{co2}\\ +{\displaystyle \sum _{j=1}^n}{\displaystyle \sum _{t=1}^T}({\mu }_{i,j}^{cm}(t)(P_{i,j}^{p2p}(t)+P_{j,i}^{p2p}(t)))+{\displaystyle \sum _{j=1}^n}{\displaystyle \frac{{\rho }_i^{cm}}{2}}{\displaystyle \sum _{t=1}^T}({∥P_{i,j}^{p2p}(t)+P_{j,i}^{p2p}(t)∥}_2^2),\end{array}$$

(20)

where ${\mu }_{i,j}^{cm}$ and ${\rho }_i^{cm}$ are Lagrange multiplier and penalty term in cost minimization.

Step 2. 

Each microgrid updates its own power traded locally to protect privacy, so the update strategy of MG_i can be expressed as:

$$\begin{array}{c}{P}_{i,j}^{p2p}(t,k+1)=argmin{L}_i^{cm}({\mu }_{i,j}^{cm}(t,k),P_{i,j}^{p2p}(t,k),P_{j,i}^{p2p}(t,k)),\end{array}$$

(21)

where k denotes the number of iterations. Then the update strategy of MG_j is:

$$\begin{array}{c}{P}_{j,i}^{p2p}(t,k+1)=argmin{L}_j^{cm}({\mu }_{j,i}^{cm}(t,k),P_{i,j}^{p2p}(t,k+1),P_{j,i}^{p2p}(t,k)),\end{array}$$

(22)

and an iteration is not completed until the strategy is updated for each microgrid.

Step 3. 

Then the Lagrange multiplier is updated as follows:

$$\begin{array}{c}{\mu }_{i,j}^{cm}(t,k+1)={\mu }_{i,j}^{cm}(t,k)+{\rho }_i^{cm}(P_{i,j}^{p2p}(t,k+1)+P_{j,i}^{p2p}(t,k+1)),\end{array}$$

(23)

Step 4. 

By calculating the raw residuals of the distributed algorithm, the convergence of the algorithm is judged as follows:

$$\begin{array}{c}{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{i=1}^n}({∥P_{i,j}^{p2p}(t,k+1)-P_{i,j}^{p2p}(t,k)∥}_2^2)\le {\delta }_{rr}^{cm},\end{array}$$

(24)

where ${\delta }_{rr}^{cm}$ is a small constant. Therefore, if the judgment condition (24) is satisfied, the iteration can be stopped; otherwise, go to Step 2. Then, the details are implemented as shown in Algorithm 1.

Algorithm 1 Cost Minimization of Multi-Microgrids

Initialization:

Import new energy and load data, as well as electricity price parameters;

Establish the cost minimization objective function for each microgrid based on (1)–(17);

Set the Lagrange multiplier ${\mu }_{i,j}^{cm}$, penalty term ${\rho }_i^{cm}$ and tolerances ${\delta }_{rr}^{cm}$;

Establish augmented Lagrangian function (20) of cost minimization for multi-microgrids;

Iterative: 1: while ${\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{i=1}^n}({∥P_{i,j}^{p2p}(t,k+1)-P_{i,j}^{p2p}(t,k)∥}_2^2)>{\delta }_{rr}^{cm}$ do 2:    For MGi: Update $P_{i,j}^{p2p}(t,k+1)=argmin{L}_i^{cm}({\mu }_{i,j}^{cm}(t,k),P_{i,j}^{p2p}(t,k),P_{j,i}^{p2p}(t,k))$; 3:    For MGj: Update $P_{j,i}^{p2p}(t,k+1)=argmin{L}_j^{cm}({\mu }_{j,i}^{cm}(t,k),P_{i,j}^{p2p}(t,k+1),P_{j,i}^{p2p}(t,k))$; 4:    if $P_{i,j}^{p2p}(t,k+1)$ and $P_{j,i}^{p2p}(t,k+1)$ of each microgrid are updated then 5:      Update ${\mu }_{i,j}^{cm}(t,k+1)={\mu }_{i,j}^{cm}(t,k)+{\rho }_i^{cm}(P_{i,j}^{p2p}(t,k+1)+P_{j,i}^{p2p}(t,k+1))$; 6:    end if 7: end while 8: Iteration end, and record the number and time of iterations.

Remark 2.

For the adopted ADMM algorithm, by introducing an additional multiplier and penalty term, the original optimization problem is transformed into sub-problems which are easy to solve in a distributed way and processed in parallel on multiple computing nodes, which significantly improves the calculation speed and the solvability of the system, and enables local data errors to be corrected by the global model through multiplier updates. In the fully distributed framework, each subsystem only needs to deal with its local optimization problem and exchange information with neighboring subsystems, without a centralized global control center, which reduces the risk of data leakage.

3.2. Fair Distribution of Cooperative Benefits

After the minimum power sharing costs of multi-microgrids is solved, that is, the maximum benefits are obtained, it is necessary to create a fair benefit distribution according to the contribution of each microgrid. A logarithmic function is adopted to quantify the contribution of different microgrids in power sharing as follows:

$$\begin{array}{c}{d}_i=e^{{\displaystyle \frac{W_i^{sup}}{W_{max}^{sup}}}}-e^{-{\displaystyle \frac{W_i^{rec}}{W_{max}^{rec}}}},\\ W_i^{sup}={\displaystyle \sum _{j=1}^n}{\displaystyle \sum _{t=1}^T}max(0,P_{i,j}^{p2p}(t)),W_i^{rec}=-{\displaystyle \sum _{j=1}^n}{\displaystyle \sum _{t=1}^T}min(0,P_{i,j}^{p2p}(t)),(i\ne j),\end{array}$$

(25)

where $d_i$ represents the contributions of different microgrids in power sharing. $W_i^{sup}$ and $W_i^{rec}$ denote the total supplied power and the total received power of MG_i between microgrids, and $W_{max}^{sup}$ and $W_{max}^{rec}$ denote the maximum supplied power and the maximum received power in each microgrid.

Then, the microgrids negotiate with each other with their own contributions $d_i$ as bargaining power to determine the power trading price among them, so as to achieve fair benefit distribution. Therefore, the benefit distribution model based on the asymmetric bargaining theory is established as follows:

$$\begin{array}{c}max{\displaystyle \prod _{i=1}^n}{(C_i^{pre}-C_i^{post}+C_i^{p2p})}^{d_i},C_i^{pre}-C_i^{post}+C_i^{p2p}>0.\end{array}$$

(26)

Note that the power trading costs $C_i^{p2p}$ are part of the cooperative benefits. Meanwhile, to facilitate the solution, the maximum value problem in (26) is transformed into a minimum value problem by taking the logarithm method as follows:

$$\begin{array}{c}min{\displaystyle \sum _{i=1}^n}-d_{i}ln(C_i^{pre}-C_i^{post}+C_i^{p2p}).\end{array}$$

(27)

Note that the power trading unit prices $c_{i,j}^{p2p}$ and $c_{j,i}^{p2p}$ are not only the global variables of multi-microgrids, but also the local variables of MG_i and MG_j, respectively. Moreover, the traded power price should be limited between the sale price and the purchase price of the peak–valley electricity price mechanism to effectively improve the utilization of renewable energy. When $c_{i,j}^{p2p}=c_{j,i}^{p2p}$, it indicates that MG_i and MG_j have reached a consensus on power trading unit price. Therefore, in order to protect the privacy of each microgrid, the steps to solve the above problem based on ADMM algorithm are as follows:

Step 1. 

The augmented Lagrange relaxation method is applied as follows:

$$\begin{array}{c}{L}_i^{fd}=-d_{i}ln(C_i^{pre}-C_i^{post}+C_i^{p2p})\\ +{\displaystyle \sum _{j=1}^n}{\displaystyle \sum _{t=1}^T}({\mu }_{i,j}^{fd}(t)(c_{i,j}^{p2p}(t)-c_{j,i}^{p2p}(t)))+{\displaystyle \sum _{j=1}^n}{\displaystyle \frac{{\rho }_i^{fd}}{2}}{\displaystyle \sum _{t=1}^T}({∥c_{i,j}^{p2p}(t)-c_{j,i}^{p2p}(t)∥}_2^2),\end{array}$$

(28)

where ${\mu }_{i,j}^{fd}$ and ${\rho }_i^{fd}$ are the Lagrange multiplier and penalty term in a fair distribution.

Step 2. 

Each microgrid updates its own power trading unit price locally to protect privacy, so the update strategy of MG_i can be expressed as:

$$\begin{array}{c}{c}_{i,j}^{p2p}(t,k+1)=argmin{L}_i^{fd}({\mu }_{i,j}^{fd}(t,k),c_{i,j}^{p2p}(t,k),c_{j,i}^{p2p}(t,k)),\end{array}$$

(29)

where k denotes the number of iterations. Then the update strategy of MG_j is:

$$\begin{array}{c}{c}_{j,i}^{p2p}(t,k+1)=argmin{L}_j^{fd}({\mu }_{j,i}^{fd}(t,k),c_{i,j}^{p2p}(t,k+1),c_{j,i}^{p2p}(t,k)),\end{array}$$

(30)

and an iteration is not completed until the strategy is updated for each microgrid.

Step 3. 

Then the Lagrange multiplier is updated as follows:

$$\begin{array}{c}{\mu }_{i,j}^{fd}(t,k+1)={\mu }_{i,j}^{fd}(t,k)+{\rho }_i^{fd}(c_{i,j}^{p2p}(t,k+1)-c_{j,i}^{p2p}(t,k+1)),\end{array}$$

(31)

Step 4. 

By calculating the raw residuals of the distributed algorithm, the convergence of the algorithm is judged as follows:

$$\begin{array}{c}{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{i=1}^n}({∥c_{i,j}^{p2p}(t,k+1)-c_{i,j}^{p2p}(t,k)∥}_2^2)\le {\delta }_{rr}^{fd},\end{array}$$

(32)

where ${\delta }_{rr}^{fd}$ is a small constant. Therefore, if the judgment condition (32) is satisfied, the iteration can be stopped; otherwise, go to Step 2. Then, the details are implemented as shown in Algorithm 2.

Algorithm 2 Fair Distribution of Cooperative Benefits

Initialization:

Calculate Equation (25) based on the optimal interaction results obtained by Algorithm 1;

Establish the benefit distribution model based on the asymmetric bargaining theory (27);

Set the Lagrange multiplier ${\mu }_{i,j}^{fd}$, penalty term ${\rho }_i^{fd}$ and tolerances ${\delta }_{rr}^{fd}$;

Establish augmented Lagrangian function (28) of fair distribution for cooperative benefits;

Iterative: 1: while ${\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{i=1}^n}({∥c_{i,j}^{p2p}(t,k+1)-c_{i,j}^{p2p}(t,k)∥}_2^2)>{\delta }_{rr}^{fd}$ do 2:    For MGi: Update $c_{i,j}^{p2p}(t,k+1)=argmin{L}_i^{fd}({\mu }_{i,j}^{fd}(t,k),c_{i,j}^{p2p}(t,k),c_{j,i}^{p2p}(t,k))$; 3:    For MGj: Update $c_{j,i}^{p2p}(t,k+1)=argmin{L}_j^{fd}({\mu }_{j,i}^{fd}(t,k),c_{i,j}^{p2p}(t,k+1),c_{j,i}^{p2p}(t,k))$; 4:    if $c_{i,j}^{p2p}(t,k+1)$ and $c_{j,i}^{p2p}(t,k+1)$ of each microgrid are updated then 5:      Update ${\mu }_{i,j}^{fd}(t,k+1)={\mu }_{i,j}^{fd}(t,k)+{\rho }_i^{fd}(c_{i,j}^{p2p}(t,k+1)-c_{j,i}^{p2p}(t,k+1))$; 6:    end if 7: end while 8: Iteration end, and record the number and time of iterations.

Remark 3.

The proposed strategy belongs to the day-ahead scheduling-related work, but for the problems of uncertainty, communication delays and potential failures in the real world, we can rely on the optimal scheduling results of this paper, and then achieve real-time accurate control by intra-day scheduling or primary and secondary control [28].

4. Simulation Results

This section constructs a system consisting of three typical microgrids to perform day-ahead optimal scheduling at an interval of one hour based on the wind–solar-load predictive data (assuming the predictive data are relatively accurate), which are shown in Figure 2, with parameters of multi-microgrid systems and simulations given in

Table 1. The parameters of multi-microgrid systems and simulations.

Items	Capacity (kW)	Parameters
PV/WT	$P_{i,max}^{pre\_pv}$ and $P_{i,max}^{pre\_wt}$ are in line with Figure 2a	$c_{pri}^{pv}=0.01$, $c_{pri}^{wt}=0.01$
ESS	$S_{i,min}^{ess}=500$, $S_{i,max}^{ess}=1800$	${\eta }_{loss}^{ess}=0.01$, ${\eta }_{ch}^{ess}=0.95$, ${\eta }_{dis}^{ess}=1/0.96$, $c_{pri}^{ess}=0.1$
CHP	$P_{i,e\_max}^{chp}=5000$, $P_{i,h\_max}^{chp}=10000$, ${\epsilon }_{i,min}^{chp}=0.5$, ${\epsilon }_{i,max}^{chp}=4.1$	${\eta }_e^{chp}=0.35$, ${\eta }_h^{chp}=0.9$, $c_{pri}^{chp}=0.01$, $c_{pri}^{gas}=3.5$
GB	$P_{i,h\_max}^{gb}=800$	${\eta }_h^{gb}=0.9$, $Q=9.7$, $c_{pri}^{gb}=0.01$, $c_{pri}^{gas}=3.5$
	Valley: 1:00–7:00	$c_i^{buy}=0.25$, $c_i^{sell}=0.22$
Price	Normal: 8:00–10:00, 16:00–18:00, 22:00–24:00	$c_i^{buy}=0.53$, $c_i^{sell}=0.42$
	Peak: 11:00–15:00, 19:00–21:00	$c_i^{buy}=0.82$, $c_i^{sell}=0.65$
Demand	$L_{i,e}^{load}$ is in line with Figure 2b	${\epsilon }_{i,e}^{tran}=0.15$, ${\epsilon }_{i,e}^{cut}=0.15$, $c_e^{tran}$ = 0.1, $c_e^{cut}=0.3$
	$L_{i,h}^{load}$ is in line with Figure 2c	${\epsilon }_{i,h}^{cut}=0.15$, $c_h^{cut}=0.16$
Trading	$P_{i,max}^{buy}=1000$, $P_{i,max}^{sell}=1000$, $P_{max}^{p2p}=2000$	$c_i^{buy}$ and $c_i^{sell}$ follow the peak-valley price
Carbon	${\alpha }_e^{pv}={\alpha }_e^{wt}=0.15,{\alpha }_e^{chp}={\alpha }_h^{chp}={\alpha }_h^{gb}=0.45,{\beta }_e^{buy}={\beta }_e^{chp}=0.55,{\beta }_h^{chp}={\beta }_h^{gb}=0.65,d=1000$
	$c_{neg3}^{co2}=1.34$, $c_{neg2}^{co2}=1.72$, $c_{neg1}^{co2}=2.1$, $c_{pos1}^{co2}=1.34$, $c_{pos2}^{co2}=1.72$, $c_{pos3}^{co2}=2.1$, $c_{pos4}^{co2}=2.49$, $c_{pos5}^{co2}=2.81$
ADMM	${\rho }_i^{cm}=1e^{-3}$, ${\delta }_{rr}^{cm}=1e^{-3}$, ${\rho }_i^{fd}=2000$, ${\delta }_{rr}^{fd}=0.23e^{-4}$

. It should be noted that the proposed strategy can be extended to larger-scale microgrids in theory, but it is difficult to achieve efficient calculation in practice due to hardware limitations and other constraints. Therefore, three typical microgrids are constructed to verify the theoretical effectiveness of the proposed strategy.

As seen from Figure 2, MG₁ has sufficient wind power (stable power generation during the day and high power generation at night due to strong winds) and relatively less load, so it represents a kind of energy-rich microgrid, which can not only meet its own low load demand, but also sell power; MG₂ has certain photovoltaic power generation, and its load shows the characteristics of low demand during working hours and high demand in the morning and evening, so it represents a kind of residential microgrid, which needs to purchase power during peak energy consumption, and can sell power during working hours; MG₃ also has a certain amount of photovoltaic power generation, but its load shows a high demand during working hours, so it represents an industrial microgrid, which needs to purchase power to meet the high demand for equipment operation during working hours. Therefore, the multi-microgrid system composed of these three types of typical microgrids can be used to verify the proposed strategy, which can make our results more representative and highlight that the proposed strategy is more practical.

4.1. Optimization Results for Cost Minimization of Multi-Microgrids

According to the above proposed strategy, the cost minimization problem of multi-microgrids is solved by using the yalmip modeling tool and cplex solver (supporting linear programming) in MATLAB R2023a. The iterative convergence process for cost minimization and the power interaction results between microgrids are shown in Figure 3.

As seen from Figure 3a, the proposed strategy achieves convergence up to the 41st iteration with a computation time of about 191s. Therefore, the economic interactive operation strategy of multi-microgrids has good convergence characteristics and computational efficiency. Then, by analyzing the interactive operation results in Figure 3b, it can be seen that the power interaction of each microgrid conforms to its own characteristics. Specifically, the wind energy of MG₁ is rich and supplies power to MG₂ and MG₃ all the time. MG₂ supplies power to MG₃ from 11:00 to 16:00 when the solar energy is rich, while it needs to rely on the power of MG₁ to meet its own load demand in other periods. The solar energy of MG₃ is difficult to meet its large load demand, so it needs the power of MG₁ and MG₂ all the time. Therefore, the detailed power and heat energy distribution of each microgrid is shown in Figure 4 and Figure 5.

As seen from Figure 4 and Figure 5, the three microgrids do not purchase power from the main grid, indicating that the load demand is met through the complementary interaction of energy among microgrids, energy storage charging and discharging and demand response, and the power balance is achieved to make the system stable and reduce the power supply pressure of the main grid, that is, the utilization rate of renewable energy is effectively improved. Meanwhile, the autonomy of multi-microgrids is realized through energy interaction, which increases the revenue of energy-rich microgrids and reduces the operating costs of industrial microgrids, that is, the low-carbon and economic scheduling of multi-microgrids is realized. To avoid generality, it can be seen in the Section 4.4 that power is purchased from the main grid when power balance cannot be achieved through the interaction between microgrids.

4.2. Optimization Results for Fair Distribution of Cooperative Benefits

Based on interaction power solved by the above cost minimization problem, the fair distribution problem of cooperative benefits is solved by using the yalmip modeling tool and mosek solver (supporting exponential cones) in MATLAB. The iterative convergence process of power trading costs for bargaining between microgrids are shown in Figure 6.

As seen from Figure 6, the proposed algorithm achieves convergence up to the 25th iteration with a computation time of about 15 s. Therefore, the proposed asymmetric bargaining algorithm between microgrids has good convergence characteristics and computational efficiency, and it is more fair to obtain the power trading costs according to the interaction power of each microgrid. Specifically, MG₁ supplies power to MG₂ and MG₃, which contribute the most in the interaction, so the benefits of 16,855.4 are the highest. MG₂ relies on MG₁ for power in the interaction, and also supplies power to MG₃, so the benefits of −6311.36 are in the middle. MG₃ has to rely on MG₁ and MG₂ for power, which contributes the least, so the benefits of −10,542.7 are the lowest. Meanwhile, the traded power price obtained by asymmetric bargaining is shown in Figure 7.

As seen from Figure 7, the traded power price through asymmetric bargaining is between the sale price and the purchase price of the peak and valley electricity price mechanism, which can effectively improve the utilization rate of renewable energy and increase the cooperative benefits of each microgrid.

4.3. Comparative Analysis with Independent Operation of Multi-Microgrids

This section further conducts independent operation simulation for the above multi-microgrid system, that is, there is no power interaction between microgrids. Therefore, the advantages of the interactive operation for distributed multi-microgrids in this paper are demonstrated by comparing the total costs and carbon emissions with the previous simulation, as shown in

Table 2. The costs and carbon emissions under different operating modes.

Operating	Cost/Carbon	MG1	MG2	MG3	Total
Independent	Cost/RMB	2155.3	47,998	43,353	93,506.3
	Carbon/kg	17,439	24,514	24,554	66,507
Interactive	Cost/RMB	18,777	21,216	15,422	55,415
	Carbon/kg	20,156	14,271	13,590	48,017

.

As seen from Table 2, the total cost of the multi-microgrid distributed interactive operation using the proposed strategy is 55,415 RMB, which is about 41% lower than the total cost of the independent operation mode of 93,506.3 RMB. By comparing the total carbon emission from 66,507 kg to 48,017 kg, it can be shown that the proposed strategy with ladder-type positive and negative carbon trading mechanism can reduce carbon emission by 18,490 kg. Therefore, it is effectively verified that the proposed multi-microgrid energy interaction strategy can realize the low-carbon operation and economic dispatch of multi-microgrids, and improve the new energy consumption rate.

4.4. Validation of Scenarios with Increased Load of Multi-Microgrids

In this section, to avoid generality, we increase the load of MG₁ by 40% to verify the effectiveness of the proposed strategy when other conditions are unchanged. Therefore, the detailed energy distribution of each microgrid under increased load is shown in Figure 8.

As seen from Figure 8, MG₃ purchases a certain amount of electricity from the main grid during the period of 1:00 to 5:00, which indicates that when the load of MG₁ is increased by 40%, the optimal power scheduling cannot be achieved only by the autonomy among the three microgrids, thus verifying the effectiveness of the interaction with the main grid in the proposed algorithm. Meanwhile, noted that MG₃ only purchases electricity from the main grid during the period of low price, which indicates that the proposed algorithm realizes the optimal economic dispatch under the premise of ensuring the stability of the system power balance.

Comprehensive analysis of Figure 4 and Figure 8 shows that in the case of abundant renewable energy, the proposed algorithm realizes the optimal scheduling through energy interaction to improve the utilization rate of renewable energy, and in the case of poor renewable energy, the proposed algorithm can also achieve optimal scheduling through energy trading with the main grid on the premise of ensuring power balance.

5. Conclusions

In this paper, a distributed multi-microgrid cooperative energy sharing strategy based on Nash bargaining game is proposed, which realizes the low-carbon economic dispatch and the improvement of new energy consumption rate through a two-stage optimization model. Firstly, the adjustable heat-to-electrical ratio, ladder-type positive and negative carbon trading, peak–valley electricity price and demand response were integrated, which was more suitable for the actual needs of the new power system. Secondly, a cooperative game model based on Nash bargaining is established, and the complex optimization problem is decoupled into two-stage solution of multi-microgrid cost minimization and fair distribution of cooperation benefits. Finally, the local objective function solution and global multiplier iterative update mechanism of the ADMM distributed algorithm are used to ensure data security and improve computational efficiency. Compared with the simulation results of independent operation of multi-microgrids, the proposed strategy significantly improves the new energy consumption rate through the complementary collaboration between microgrids, and realizes low-carbon economic operation. In addition, future works need to be extended to the uncertainties of actual multi-microgrid systems and the robustness of the ADMM-based algorithm.