A Coordinated Operation Optimization Model for Multiple Microgrids and Shared Energy Storage Based on Asymmetric Bargaining Negotiations

Abstract

The promotion of local renewable energy consumption and stable power gird (the latter is referred to as PG) operation have emerged as the primary objectives of power system reform. The integration of multiple microgrids with distinct characteristics through the utilization of shared energy storage (the following is referred to as SES) facilitates coordinated operation. This approach enables the balancing of energy across temporal and spatial domains, contributing to the overall reliability and security of the energy network. The proposed model outlines a methodology for the coordinated operation of multiple microgrids and SES, with a focus on asymmetric price negotiation. Initially, cost and revenue models for microgrids and SES power plants are established. Secondly, an asymmetric pricing method based on the magnitude of each entity’s energy contribution is proposed. A profit optimization model is also established. The model can be decomposed into two distinct subproblems: the maximization of overall profit and the negotiation of transaction prices. The model can be solved by employing the alternating direction method of multipliers (ADMM). Finally, a series of case studies were conducted for the purpose of validating the operation optimization model that was previously constructed. These studies demonstrate that the model enhances collective operational efficiency by 44.69%, with each entity’s efficiency increasing by at least 12%. At the same time, cooperative benefits are distributed fairly according to each entity’s energy contribution.

1. Introduction

As new energy sources are developed on a large scale, the establishment of a safe, economical, and efficient energy system has gradually become a priority in the energy sector [1,2]. In this context, the construction of different types of microgrids that conduct power transactions with each other has become an important means of realizing local consumption of new energy sources and promoting regional grid balance [3,4].

The integration of SES facilitates the interconnectedness of multiple microgrids, thereby establishing a microgrid cluster. This configuration enables the dynamic allocation of resources to meet the varied demands of the constituent microgrids. This, in turn, contributes to enhancing the whole operational efficiency of the system. Reference [5] addresses issues such as main entity coordination management, the randomness of new energy output, and privacy protection for various entities encountered in actual system operation. It proposes a robust two-stage multi-integrated energy microgrid–SES coordinated operation optimization strategy. As stated in reference [6], the concerns regarding the operation of oilfield microgrids in island mode, significant discrepancies between oil production load demands and renewable energy output, and the proposal of a collaborative scheduling strategy for isolated oilfield microgrid clusters that consider SES are addressed. References [7,8]’s proposed approach involves the implementation of a game mechanism based on end-to-end transactions for SES and microgrid clusters. As stated in reference [9], the operational economics and carbon emission environmental benefits of microgrid clusters are thoroughly examined. The study proposes an interactive microgrid cluster low-carbon day-ahead scheduling model based on distributed SES. As stated in reference [10,11], the challenge of coordinating the complexity of multi-party power interaction with the economic viability of SES is addressed. To this end, a two-layer scheduling optimization model is constructed. Reference [12] addresses the optimization of hydrogen SES configuration and benefit analysis in integrated energy microgrid clusters. To this end, a two-layer optimization configuration model for research is constructed.

A number of studies have recently employed asymmetric bargaining methods in the context of energy system optimization scheduling. Reference [13] employed an asymmetric bargaining method to quantify the contribution of entities transactions and utilized it as a bargaining factor. The strategy involved regional PG electricity–carbon joint multilateral transaction optimization scheduling. Reference [14] provides a quantitative assessment of the correlation between renewable energy generation and load among entities, as well as their contribution to peer-to-peer resource sharing, which are considered as bargaining factors. The study establishes a multi-integrated energy system coordination optimization scheduling model that accounts for the dynamic supply and demand curves of carbon–green certificates. Reference [15] employs asymmetric Nash bargaining games to price electricity insurance services for IESs, thereby establishing an IES electricity insurance service model. Reference [16] utilizes a two-stage asymmetric Nash bargaining method for energy sharing, constructing an optimized model for alliance-based collaborative market participation. Reference [17] utilizes the ADMM to address the payment benefit maximization problem under asymmetric bargaining conditions, thereby establishing a heat-electricity sharing transaction model for multi-service providers. Reference [18] employs an asymmetric Nash bargaining method predicated on pre-day and intra-day contribution weighting coefficients, to ascertain the revenue distribution among entities in regions characterized by low-grade heat sources. Reference [19] employs an asymmetric Nash bargaining approach to reasonably allocate system benefits across multiple regions, thereby enhancing the proactive participation of subsystems in cooperative mechanisms. Reference [20] proposes an asymmetric Nash negotiation method based on the differing bargaining capabilities of each entity within a building cluster business alliance. This approach is intended to achieve a fair and reasonable distribution of alliance benefits.

In summary, extant research on the coordinated operation of SES and multiple microgrids primarily focuses on interaction mechanisms. In instances where game theory is employed to address issues concerning benefit allocation, contributions from individual entities frequently receive inadequate consideration. Instead, the benefits are often distributed equally among all participants. The utilization of asymmetric pricing methodologies within energy systems is found to be limited, particularly in the context of coordinated operations involving SES and multiple microgrids. In summary, to enhance the economic efficiency of SES and the coordinated operation of multiple microgrids, achieve fair profit distribution, and improve the satisfaction of all participating entities, this paper constructs three microgrids with different characteristics and introduces SES as a connecting element, proposing an optimization model for the coordinated operation of multiple microgrids and SES. The asymmetric pricing negotiation model is employed, with the objective of maximizing overall benefits. A nonlinear energy mapping function is utilized to quantify the contribution size of each entity during the electricity sharing process. Asymmetric pricing is applied based on the contribution size of each entity, and the proposed model is solved using the alternating direction method of multipliers.

2. Methods

2.1. Cooperative Operating Architecture

This paper constructs three microgrids with distinct characteristics, each connected to the external PG and gas network, and interconnected via SES to facilitate power transmission. The microgrids differ in terms of power generation unit types, renewable energy generation capacity, and load characteristics, with varying degrees of coordination and complementarity among electricity, heat, natural gas, and hydrogen. Microgrid 1 is a commercial building cluster-type microgrid with significant electricity and heat load demands and typical diurnal fluctuations, requiring energy exchange with the external PG to achieve supply–demand balance. Microgrid 2 is an industrial park-type microgrid with high thermal and electrical load demands, but relatively stable peak–valley characteristics, and includes multiple new hydrogen production and utilization enterprises, resulting in overall high hydrogen load demands. Microgrid 3 is a microgrid primarily composed of renewable energy generation, with a large-scale electricity production and energy storage capacity, primarily serving the function of renewable energy supply. Basic modeling of microgrid equipment and shared energy storage can be found in reference [21,22]. The range of technologies encompasses wind power, photovoltaic power, electricity-to-gas conversion equipment, electric boilers, gas boilers, gas turbines, electrolytic cells, thermal storage tanks, and hydrogen storage tanks, among others. The operational framework is illustrated in Figure 1.

When a single microgrid is operational, integrated response technology can be utilized to assist the PG in flexible regulation. The loads within the microgrid can be categorized based on their energy consumption characteristics into base loads, shiftable loads, peak-reducing loads, and off-peak load increases. Through the implementation of various demand response measures, the scheduling of electricity consumption plans can be rendered more flexible, contingent on electricity prices during disparate time periods. This, in turn, serves to effectively alleviate operational pressure on the microgrid, thereby reducing energy expenditures and ensuring safe operation.

The integration of SES and the coordination of microgrid operations through the alliance facilitates the sale of excess electricity from microgrids to SES during periods of surplus generation. In periods of insufficient generation, microgrids procure electricity from SES at predetermined prices. The interaction between microgrids, resource trading, and allocation can be leveraged to optimize benefits.

2.2. Microgrid and SES Operation Optimization Model

2.2.1. Microgrid Operation Optimization Model

(1)

Objective function

The objective is to optimize microgrid profits.

$$\max V_i=R_i-C_i$$

(1)

where $V_i$ is the profit of the microgrid; $R_i$ is the total revenue of the microgrid; and $C_i$ is the total cost of the microgrid.

(1) Revenue analysis model

Each microgrid maximizes operating revenue by coordinating the output of its controllable units and exchanging power with SES and the PG.

$$R_i=R_i^{ne}+R_i^{GT}+R_i^{C{O}_2}+R_i^{IDR}$$

(2)

where $R_i^{ne}$ is the revenue from external electricity sales and green electricity sales of new energy units; $R_i^{GT}$ is the revenue from external electricity and heat sales of gas-fired units; $R_i^{C{O}_2}$ is the revenue from carbon reduction sales; $R_i^{IDR}$ is the revenue from demand response; and $i$ is a microgrid.

(a) Microgrid New Energy Generator Set External Electricity Sales and Green Electricity Revenue

A microgrid’s new energy power generation units not only generate, consume, and store their own electricity, but also sell surplus electricity to external parties, thereby generating not only electricity sales revenue but also green electricity sales revenue.

$$R_i^{ne}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j=1}^J}}({\lambda }_{i,j,t}^{sell,ne}+{\lambda }_{green,j}^{ne})P_{i,j,t}^{sell,ne}\Delta T$$

(3)

where ${\lambda }_{i,j,t}^{sell,e}$ is the electricity price at which renewable energy unit $j$ sells electricity to the outside; ${\lambda }_{green,j}^{ne}$ is the green electricity premium price for green electricity $j$ (wind power or photovoltaic power), i.e., the additional electricity price by which green electricity exceeds the benchmark price of coal-fired power; $P_{i,j,t}^{sell,ne}$ is the green electricity power sold by renewable energy unit j to other microgrids or the PG; $t$ is a certain moment in time; and $\Delta T$ is the time interval.

(b) Microgrid gas generator set for external electricity sales revenue

In addition to self-use and self-storage, microgrid gas generator sets can sell surplus electricity to generate revenue from electricity sales.

$$R_i^{GT}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{n=1}^N{\lambda }_{i,n,t}^{GT,sell,e}{P}_{i,n,t}^{GT,sell,e}\Delta T}}$$

(4)

where ${\lambda }_{i,n,t}^{GT,sell,e}$ is the electricity price at which gas turbine n sells electricity to the external grid, and $P_{i,n,t}^{GT,sell,e}$ is the power at which gas turbine n sells electricity to the external grid.

(c) Microgrid load demand response external ancillary service revenue

Microgrids can earn compensation income by participating in demand response.

$$R_i^{dr}={\displaystyle \sum _{l=1}^L}{\displaystyle \sum _{t=1}^T({\lambda }_{AD}}\left|L_{i,l,t}^{AD}\right|+{\lambda }_{CD}\left|L_{i,l,t}^{CD}\right|+{\lambda }_{ID}\left|L_{i,l,t}^{ID}\right|)$$

(5)

where $l$ is the type of load; $L$ is the total of load types; ${\lambda }_{AD}$ is the price compensation coefficient for each type of load participating in load-shifting demand response; ${\lambda }_{CD}$ is the price compensation coefficient for each type of load participating in load reduction demand response; ${\lambda }_{ID}$ is the price compensation coefficient for each type of load participating in load increase demand response; $L_{i,l,t}^{AD}$ is the total amount of shifting loads; $L_{i,l,t}^{CD}$ is the total amount of reducible loads; and $L_{i,l,t}^{ID}$ is the total amount of increasable loads.

(d) Microgrid carbon reduction revenue

Microgrids are defined as entities that generate their own electricity from novel energy sources for self-consumption purposes. This results in a reduction in electricity purchased from the PG, consequently generating carbon reduction compensation income.

$$R_i^{C{O}_2}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j=1}^J}}{\lambda }^{c{o}_2}{k}^{grid,c{o}_2}{P}_{i,j,t}^{self,ne}\Delta T$$

(6)

where ${\lambda }^{c{o}_2}$ is the carbon trading unit price; $k^{grid,c{o}_2}$ is the carbon factor of the distribution network; and $P_{i,j,t}^{self,ne}$ is the power corresponding to the self-generation and self-consumption of new energy, which also corresponds to the reduction in purchased PG power.

(2) Cost analysis model

Each microgrid minimizes operating costs by coordinating the output of its controllable units.

$$C_i=C_i^{buy,es}+C_i^{buy,grid}+C_i^{ge}+C_i^{C{O}_2}+C_i^{dr}+C_i^{buy,C{H}_4}+C_i^{selfpro,C{H}_4}$$

(7)

where $C_i^{buy,es}$ is the purchasing cost from SES; $C_i^{buy,grid}$ is the cost of purchasing electricity from the PG; $C_i^{ge}$ is the power generation cost of various types of units; $C_i^{c{o}_2}$ is the carbon emission cost; $C_i^{buy,C{H}_4}$ is the external gas purchase cost; $C_i^{dr}$ is the demand response cost; and $C_i^{selfpro,C{H}_4}$ is the gas self-production cost.

(a) Purchasing cost from SES

The microgrid acquires electricity from SES to satisfy its own demand, and it remunerates SES with the appropriate fees.

$$C_i^{buy,es}={\displaystyle \sum _{t=1}^T({\lambda }_{i,t}^{buy,es}+{\lambda }_i^{trans,micgrid})P_{i,t}^{buy,es}\Delta T}$$

(8)

where $C_i^{buy,es}$ is the electricity purchase cost from SES; ${\lambda }_{i,t}^{buy,es}$ is the price at which microgrid $i$ purchases electricity from SES; ${\lambda }_i^{trans,micgrid}$ is the distribution price that microgrid $i$ needs to pay for purchasing SES; and $P_{i,t}^{buy,es}$ is the power that microgrid $i$ purchases from the SES system.

(b) Purchasing cost from PG

Microgrids procure electricity from the PG to satisfy their own load requirements and remunerate the PG accordingly.

$$C_i^{buy,grid}={\displaystyle \sum _{t=1}^T({\lambda }_{i,t}^{buy,grid}+{\lambda }_i^{trans,grid})P_{i,t}^{buy,grid}}\Delta T$$

(9)

where ${\lambda }_{i,t}^{buy,grid}$ is the price of electricity purchased from the PG; $P_{i,t}^{buy,grid}$ is the power purchased from the PG; and ${\lambda }_i^{trans,grid}$ is the price at which microgrid $i$ purchases electricity from the PG.

(c) Operating costs of each unit

The operating costs for each unit within the microgrid are as follows:

$$C_i^{ge}={\displaystyle \sum _{t=1}^T{k}_{i,j,t}^{ge,ne}{P}_{i,j,t}^{ge,ne}\Delta T}$$

(10)

where $k_{i,j,t}^{ge,ne}$ is the cost coefficient of unit $j$, and $P_{i,j,t}^{ge,ne}$ is the operating power of unit $j$.

(d) Microgrid demand response costs

It is imperative that microgrids allocate financial resources to compensate participants for various demand response loads in accordance with the following expression:

$$C_i^{dr}={\displaystyle \sum _{l=1}^L}{\displaystyle \sum _{t=1}^T(k_{AL}}\left|L_{i,l,t}^{AL}\right|+k_{CL}\left|L_{i,l,t}^{CL}\right|+k_{IL}\left|L_{i,l,t}^{IL}\right|)\Delta T$$

(11)

where $k_{AL}$ is the unit cost for each load type participating in shifting demand response; $k_{CL}$ is the unit cost for each load type participating in reducing demand response; and $k_{IL}$ is the unit cost for each load type participating in increasing demand response.

(e) External gas purchase costs of microgrid

Microgrids purchase gas from external gas networks to meet their own needs.

$$C_i^{buy,C{H}_4}={\displaystyle \sum _{t=1}^T{\lambda }^{buy,C{H}_4}}{V}_{i,t}^{buy,C{H}_4}$$

(12)

where $V_{i,t}^{buy,C{H}_4}$ is the amount of natural gas purchased, and ${\lambda }^{buy,C{H}_4}$ is the natural gas price.

(f) Microgrid gas production costs

The cost expression for producing natural gas through microgrids using electricity-to-gas conversion devices is as follows:

$$C_i^{selfpro,C{H}_4}=C_i^{pro,H_2}+C_i^{CC,c{o}_2}+C_{i,t}^{MR,C{H}_4}$$

(13)

$$C_i^{pro,H_2}={\displaystyle \sum _{t=1}^T{\lambda }_{i,t}^{EL,e,in}}{P}_{i,t}^{EL,e,in}$$

(14)

$$C_i^{CC,c{o}_2}={\displaystyle \sum _{t=1}^T{\lambda }_{\mathrm{i},t}^{CC,e,in}}{P}_{\mathrm{i},t}^{CC,e,in}$$

(15)

$$C_{i,t}^{\mathrm{MR},C{H}_4}={\displaystyle \sum _{t=1}^T{\lambda }_{i,t}^{MR,e,in}}{P}_{i,t}^{MR,e,in}$$

(16)

where $C_i^{pro,H_2}$ is the cost of hydrogen production via water electrolysis; $C_i^{CC,c{o}_2}$ is the carbon capture cost; $C_{i,t}^{MR,C{H}_4}$ is the cost of synthesizing methane from hydrogen and carbon dioxide; ${\lambda }_{i,t}^{EL,e,in}$ is the unit cost of the input power to the electrolyzer; $P_{i,t}^{EL,e,in}$ is the input power to the electrolyzer; $P_{\mathrm{i},t}^{CC,e,in}$ is the input power of the carbon capture device; ${\lambda }_{\mathrm{i},t}^{CC,e,in}$ is the unit cost of the carbon capture device; $P_{i,t}^{MR,e,in}$ is the input power for the synthesis of methane from hydrogen and carbon dioxide; ${\lambda }_{i,t}^{MR,e,in}$ is the unit cost corresponding to the input power of the methanation device.

(g) Microgrid carbon emission costs

The generation of power by microgrids results in the emission of carbon dioxide, which is subject to carbon penalty fees.

$$C_i^{c{o}_2}={\displaystyle \sum _{t=1}^T}{\lambda }^{c{o}_2}(k^{GB,c{o}_2}{P}_{i,t}^{GB,c{o}_2}+k^{GT,c{o}_2}{P}_{i,t}^{GT,c{o}_2}+k^{grid,c{o}_2}{P}_{i,t}^{buy,grid})\Delta \mathrm{T}$$

(17)

where $k^{GB,c{o}_2}$ is the carbon dioxide generated per unit of heat produced by the gas boiler; $P_{i,t}^{GB,c{o}_2}$ is the heat power generated by the gas boiler; $k^{GT,c{o}_2}$ is the carbon dioxide generated per unit of heat produced by the gas turbine; and $P_{i,t}^{GT,c{o}_2}$ is the heat power generated by the gas turbine.

(2)

Operating constraints

(1) Power balance

Power balance constraints between electricity, heat, gas, and hydrogen must be maintained during microgrid operation.

$$\begin{array}{l}{P}_{i,t}^{WT,e,self}+P_{i,t}^{PV,e,self}+P_{i,t}^{GT,e,self}+P_{i,t}^{buy,e}\\ =P_{i,t}^{EB,e,in}+P_{i,t}^{EL,e,in}+P_{i,t}^{CC,e,in}+P_{i,t}^{MR,e,in}+L_{i,t}^e\end{array}$$

(18)

$$P_{i,t}^{GT,h,self}+P_{i,t}^{GB,h,self}+P_{i,t}^{EB,h,self}+P_{i,t}^{TS,h,out}=L_{i,t}^h+P_{i,t}^{TS,h,in}$$

(19)

$$V_{i,t}^{buy,C{H}_4}+V_{i,t}^{MR,C{H}_4}=V_{i,t}^{GT,in,C{H}_4}+V_{i,t}^{GB,in,C{H}_4}+L_{i,t}^{C{H}_4}$$

(20)

$$V_{i,t}^{EL,H_2,out}+V_{i,t}^{HT,H_2,out}=L_{i,t}^{H_2}+V_{i,t}^{HT,H_2,in}$$

(21)

where $P_{i,t}^{WT,e,self}$ and $P_{i,t}^{PV,e,self}$ are the actual power generation of the wind turbine and the photovoltaic, respectively; $P_{i,t}^{GT,e,self}$ is the power output of the gas turbine; $P_{i,t}^{buy,e}$ is the amount of electricity purchased from external sources; $P_{i,t}^{EB,e,in}$ is the power input to the electric boiler; $L_{i,t}^e$ is the electricity load after demand response; $P_{i,t}^{GT,h,self}$ and $P_{i,t}^{GB,h,self}$ are the thermal power output from the gas turbine and the gas boiler, respectively; $P_{i,t}^{EB,h,self}$ is the heating power of the electric boiler; $P_{i,t}^{TS,h,in}$ and $P_{i,t}^{TS,h,out}$ are the heating and release power of the thermal storage tank, respectively; $L_{i,t}^h$ is the thermal load after demand response; $V_{i,t}^{MR,C{H}_4}$ is the volume of natural gas generated by the methane production unit; $V_{i,t}^{GT,in,C{H}_4}$ and $V_{i,t}^{GB,in,C{H}_4}$ are the volume of natural gas input into the gas turbine and the gas boiler, respectively; $L_{i,t}^{C{H}_4}$ is the gas load after demand response; $V_{i,t}^{EL,H_2,out}$ is the hydrogen output from the electrolyzer; $V_{i,t}^{HT,H_2,in}$ and $V_{i,t}^{HT,H_2,out}$ are the hydrogen charge and discharge capacity of the hydrogen storage tank, respectively; and $L_{i,t}^{H_2}$ is the hydrogen load after demand response.

(2) Demand response

(a) Shifting load

Shiftable loads must satisfy the following constraints: total load remains unchanged, upper and lower limits of shiftable loads, upper and lower limits of shifts in and out, and mutual exclusion of shift-in and shift-out states.

$$\left\{\begin{array}{l}{\displaystyle \sum _{t=1}^{T_i^{AL}}(u_{i,t}^{AL,in}{L}_{i,t}^{AL,in}}-u_{i,t}^{AL,out}{L}_{i,t}^{AL,out})=0\\ L_{i,t,\min }^{AL,in}\le L_{i,t}^{AL,in}\le L_{i,t,\max }^{AL,in}\\ L_{i,t,\min }^{AL,out}\le L_{i,t}^{AL,out}\le L_{i,t,\max }^{AL,out}\\ u_{i,t}^{AL,in}+u_{i,t}^{AL,out}=1\\ u_{i,t}^{AL,in}=0 or 1\\ u_{i,t}^{AL,out}=0 or 1\end{array}\right.$$

(22)

where $L_{i,t}^{Al,in}$ is the power input of various shifting loads; $L_{i,t}^{Al,out}$ is the power output of various shifting loads; $L_{i,t,\min }^{Al,in}$ is the minimum power input of various shifting loads; $L_{i,t,\max }^{Al,in}$ is the maximum inflow power of various types of shifting loads; $L_{i,t,\min }^{Al,out}$ is the minimum outflow power of various types of shifting loads; $L_{i,t,\max }^{Al,out}$ is the maximum output power of various types of shifting loads; $T_i^{Al}$ is the minimum continuous operating time of various types of shifting loads; $u_{i,t}^{Al,in}$ is the power-in status flag for all types of shifting loads; and $u_{i,t}^{Al,out}$ is the power-out status flag for all types of shifting loads.

(b) Reducible load

The reducible load must meet the upper and lower limits of load, maximum continuous reduction time, and reduction frequency constraints.

$$\left\{\begin{array}{l}{L}_{i,t}^{CL,\min }\le L_{i,t}^{CL}\le L_{i,t}^{CL,\max }\\ {\displaystyle \sum _t^{t+T_i^{CL}}(1-u_{i,t}^{CL})\ge 1}\\ {\displaystyle \sum _{t=1}^T{u}_{i,t}^{CL}\le M_i^{CL}}\\ u_{i,t}^{CL}=0 or 1\end{array}\right.$$

(23)

where $L_{i,t}^{CL,\min }$ is the minimum of the reducible load capacity; $L_{i,t}^{CL,\max }$ is the maximum of the reducible load capacity; $u_{i,t}^{CL}$ is the reduction status flag for the reducible load capacity; $T_i^{CL}$ is the maximum reduction time; and $M_i^{CL}$ is the maximum number of reductions.

(c) Increasable load

Increasable load must meet the upper and lower limits of the load, the maximum continuous increase time, and the frequency constraints.

$$\left\{\begin{array}{l}{L}_{i,t}^{IL,\min }\le L_{i,t}^{IL}\le L_{i,t}^{IL,\max }\\ {\displaystyle \sum _t^{t+T_i^{IL}}(1-u_{i,t}^{IL})\ge 1}\\ {\displaystyle \sum _{t=1}^T{u}_{i,t}^{IL}\le M_i^{IL}}\\ u_{i,t}^{IL}=0 or 1\end{array}\right.$$

(24)

where $L_{i,t}^{IL,\min }$ is the minimum of the increasable load capacity; $L_{i,t}^{IL,\max }$ is the maximum of the increasable load capacity; $T_i^{IL}$ is the maximum continuous duration; $M_i^{IL}$ is the maximum number of times that the load can be increased; and $u_{i,t}^{IL}$ is the increase status flag for loads.

(3) Interaction with PG and gas networks

Microgrids interacting with the outside world must satisfy constraints such as upper and lower interaction limits and mutual state exclusion.

$$\left\{\begin{array}{l}0\le P_{i,t}^{buy,e,grid}\le {\mu }_{i,t}^{buy,e,grid}{P}_{i,t,\max }^{buy,e,grid}\hfill \\ 0\le P_{i,t}^{sell,e,grid}\le {\mu }_{i,t}^{sell,e,grid}{P}_{i,t,\max }^{sell,e,grid}\hfill \\ {\mu }_{i,t}^{buy,e,grid}+{\mu }_{i,t}^{sell,e,grid}\le 1\hfill \\ {\mu }_{i,t}^{buy,e,grid}=0 or 1\\ {\mu }_{i,t}^{sell,e,grid}=0 or 1\\ 0\le V_{i,t}^{buy,C{H}_4}\le V_{i,\max }^{buy,C{H}_4}\hfill \end{array}\right.$$

(25)

where $P_{i,t,\max }^{buy,e,grid}$ is the maximum power purchased from the PG; $P_{i,t,\max }^{sell,e,grid}$ is the maximum power sold to the PG; ${\mu }_{i,t}^{buy,e,grid}$ is the status flag for purchasing power from the PG; ${\mu }_{i,t}^{sell,e,grid}$ is the status flag for selling power to the PG; and $V_{i,\max }^{buy,C{H}_4}$ is the maximum amount of gas purchased.

(4) Equipment operation

Microgrid devices need to meet upper and lower power limits and ramping constraints.

$$P_i^{j,\min }\le P_{i,t}^{j,\mathrm{act}}\le P_i^{j,\max }$$

(26)

$$\Delta P_{i,\min }^{j,act}\le P_{i,t}^{j,act}-P_{i,t-1}^{j,act}\le \Delta P_{\mathrm{i},\max }^{j,act}$$

(27)

where $P_{i,t}^{j,\mathrm{act}}$ is the actual output of unit $j$; $P_i^{j,\min }$ and $P_i^{j,\max }$ are the minimum and maximum output power of unit $j$, respectively; and $\Delta P_{i,\min }^{j,act}$ and $\Delta P_{\mathrm{i},\max }^{j,act}$ are the minimum and maximum ramping power of unit $j$, respectively.

2.2.2. SES Operation Optimization Model

(1)

Objective function

The objective is to optimize SES profits.

$$\max V_{es}=R_{es}-C_{es}$$

(28)

where $V_{es}$ is the profit of the SES; $R_{es}$ is the total revenue of the SES; and $C_{es}$ is the total cost of the SES.

(1) Revenue analysis model

The primary revenue stream for SES is the sale of electricity to external entities.

$$R_{es}={\displaystyle \sum _{t=1}^T({\lambda }_{i,t}^{buy,es}{P}_{i,t}^{buy,es}}+{\lambda }_t^{sell,grid,es}{P}_t^{sell,grid,es})\Delta T$$

(29)

where ${\lambda }_t^{sell,grid,es}$ is the price at which the SES sells electricity to the PG, and $P_t^{sell,grid,es}$ is the power that is sold to the PG.

(2) Cost analysis model

The main costs of SES are electricity purchase costs and operation and maintenance costs.

$$C_{es}=({\lambda }_{i,t}^{sell,es}+{\lambda }^{run,es})P_{i,t}^{sell,es}+({\lambda }_t^{buy,grid,es}+{\lambda }^{run,es})P_t^{buy,gird,es}+{\lambda }^{main,es}{E}_{es}$$

(30)

where ${\lambda }_{i,t}^{sell,es}$ is the price at which microgrid $i$ sells electricity to the SES system; $P_{i,t}^{sell,es}$ is the power at which microgrid $i$ sells electricity to the SES system; ${\lambda }_t^{buy,grid,es}$ is the purchase price of electricity from the PG; $P_t^{buy,gird,es}$ is the purchase power of electricity from the PG; ${\lambda }^{run,es}$ is the unit operating cost of SES; $E_{es}$ is the capacity of the SES system; and ${\lambda }^{main,es}$ is the daily maintenance cost coefficient of SES.

(2)

Operating constraints

(1) SES operation constraints

SES operation needs to meet the upper and lower limits for input and output power, variable mutual state exclusion constraints, initial and equivalent state constraint, etc.

$$\left\{\begin{array}{l}{P}_{es,t}=P_{es,t-1}+P_{es,t}^{in}{\eta }_{es}^{in}-P_{es,t}^{out}/{\eta }_{es}^{out}\\ 0\le P_{es,t}^{in}\le u_{es,t}^{in}{P}_{es}^{in,\max }\\ 0\le P_{es,t}^{out}\le u_{es,t}^{out}{P}_{es}^{out,\max }\\ u_{es,t}^{in}+u_{es,t}^{out}\le 1\\ P_{es}^{\min }\le P_{es,t}\le P_{es}^{\max }\\ P_{es,0}=P_{es,T}\end{array}\right.$$

(31)

where $P_{es,t}$ is the capacity of the SES system; $P_{es,t}^{in}$ and $P_{es,t}^{out}$ are the charging and discharging power, respectively; ${\eta }_{es}^{in}$ and ${\eta }_{es}^{out}$ are the charging and discharging efficiency, respectively; $u_{es,t}^{in}$ and $u_{es,t}^{out}$ are the charging and discharging state variables, respectively; $P_{es}^{\max }$ and $P_{es}^{\min }$ are the maximum and minimum values of the capacity, respectively; and $P_{es,0}$ and $P_{es,T}$ are the capacity at the start and end, respectively.

(2) Interactive power constraints

The interaction of an SES system with the outside world needs to meet the upper and lower limits on interaction volume.

$$\begin{array}{l}{P}_{i,t}^{sell,micgrid,es}\le P_{i,\max }^{es,micgrid}\\ P_{i,t}^{buy,micgrid,es}\le P_{i,\max }^{es,micgrid}\end{array}$$

(32)

$$\begin{array}{l}{P}_t^{sell,grid,es}\le P_{i,\max }^{es,grid}\\ P_t^{buy,grid,es}\le P_{i,\max }^{es,grid}\end{array}$$

(33)

where $P_{i,\max }^{es,micgrid}$ is the maximum power value for interaction between the SES system and microgrid $i$, and $P_{i,\max }^{es,grid}$ is the maximum power value for interaction between the SES system and the PG.

2.3. Multiple Microgrids and SES Coordinated Optimization Model

2.3.1. Symmetric Bargaining Model

Each microgrid and SES system functions as an autonomous and rational entity, and the interests of the various parties involved are subject to intricate interactions. A balanced strategy is required to optimize both collective and individual benefits. Therefore, this paper employs Nash bargaining to simultaneously consider individual and collective benefits, ensuring that all participating entities achieve a Pareto optimal outcome.

The symmetric Nash bargaining negotiation model is as follows:

$$\left\{\begin{array}{l}\max \left(V_{es,0}-V_{es}\right){\displaystyle \prod _{i=1}^3}\left(V_{i,0}-V_i\right)\\ \mathrm{s}.\mathrm{t}.V_{es}\le V_{es,0}\\ \hspace{1em} V_i\le V_{i,0}\end{array}\right.$$

(34)

where $V_{i,0}$ and $V_i$ represent the profits of microgrid $i$ before and after participation in the cooperation, respectively, and $V_{es,0}$ and $V_{es}$ represent the profits of SES before and after participation in the cooperation, respectively.

The negotiation model is decomposed into two easily solvable subproblems: the profit maximization problem of the alliance and the negotiation problem of SES and electricity prices between microgrids. The original problem can be obtained by iteratively solving the two subproblems. The conversion process is referenced in [5].

Sub-question 1: The problem of maximizing alliance profits

$$\max (V_{es}^{\text{'}}+{\displaystyle \sum _{i=1}^3{V}_i^{\text{'}})}$$

(35)

where $V_{es}^{\text{'}}$ is the profit from SES after participating in the cooperation without considering interaction with the microgrid, and $V_i^{\text{'}}$ is the profit of microgrid $i$ after participating in the cooperation without considering interaction with SES.

Sub-question 2: Negotiating transaction prices between SES and microgrids

$$\left\{\begin{array}{l}\max -\left[{\displaystyle \sum _{i=1}^3}\mathrm{In}(V_{i,0}-V_i^{\ast }+V_{i,es})+\mathrm{In}(V_{es,0}-V_{es}^{\ast }+V_{es,i})\right]\\ s.t.\begin{array}{c}{V}_{i,0}\ge V_i^{\ast }-V_{i,es}\\ V_{es,0}\ge V_{es}^{\ast }-V_{es,i}\end{array}\end{array}\right.$$

(36)

where $V_i^{\ast }$ is the optimal profit of microgrid $i$ after participating in the cooperation without considering interaction with SES; $V_{es}^{\ast }$ is the optimal profit of SES after participating in the cooperation without interaction with the microgrid; $V_{i,es}$ is the additional profit generated by microgrid $i$ after participating in the cooperation and interacting with SES; and $V_{es,i}$ is the additional profit generated by SES after participating in the cooperation and interacting with microgrid $i$.

2.3.2. Asymmetric Bargaining Model

In the context of actual operational cooperation, various microgrids and SES systems contribute distinctively to the system. Consequently, these entities should possess disparate levels of influence and bargaining power in the context of negotiations. Therefore, this paper utilizes a nonlinear function based on natural logarithms to quantify the contributions of different entities in cooperation, thereby enabling asymmetric bargaining.

Set microgrid $i$ to have a positive contribution value when receiving and supplying electrical energy. Microgrids obtain higher contribution values when supplying electricity than when receiving it. The specific expression is as follows:

$${\gamma }_i={\displaystyle \frac{e^{E_i^{supply}/E_{\max }^{supply}}-e^{-E_i^{demand}/E_{\max }^{demand}}}{{\displaystyle \sum _{i=1}^3(e^{E_i^{supply}/E_{\max }^{supply}}-e^{-E_i^{demand}/E_{\max }^{demand}})}}}$$

(37)

where $E_i^{supply}$ and $E_i^{demand}$ are the electricity supplied and received by microgrid $i$, respectively; $E_{\max }^{supply}$ and $E_{\max }^{demand}$ are the maximum electricity supplied and received by the microgrid, respectively; and ${\gamma }_i$ is the bargaining factor in the negotiations of microgrid $i$.

SES exhibited a high level of participation in all power exchanges within the collaborative framework, contributing significantly to the overall results. The bargaining factor was set to be equal to the sum of the bargaining factors of the three microgrids. That is to say, the bargaining factor of SES was 1.

Substituting the aforementioned bargaining factors into Equation (36), and converting it into a logarithmic form, the improved expression for sub-question 2 is as follows:

$$\left\{\begin{array}{l}\max -\left[{\displaystyle \sum _{i=1}^3}{\gamma }_i\mathrm{In}(V_{i,0}-V_i^{\ast }+V_{i,es})+\mathrm{In}(V_{es,0}-V_{es}^{\ast }+V_{es,i})\right]\\ s.t.\begin{array}{c}{V}_{i,0}\ge V_i^{\ast }-V_{i,es}\\ V_{es,0}\ge V_{es}^{\ast }-V_{es,i}\end{array}\end{array}\right.$$

(38)

2.3.3. Model Solution

The alternating direction method of multipliers (ADMM) is a set of methodologies that can be used to divide a given problem into a number of sub-questions. These sub-questions can then be solved in a concurrent manner by employing a process known as decoupling. The utilization of distributed algorithms has been demonstrated to enhance computational speed and convergence. Consequently, this paper implements an ADMM algorithm to address the two sub-questions. In the initial phase, the resolution of sub-question 1 facilitates the calculation of optimal power interaction between microgrids and SES, and optimal output schemes for microgrid units as scheduling variables. In the subsequent stage, sub-question 2 is resolved in accordance with the power interaction ascertained in sub-question 1, and pricing is conducted.

(1)

Solutions to the problem of maximizing alliance profits

Initially, it is necessary to decouple sub-question 1. To do so, the following steps must be taken. First, auxiliary variables ${\widehat{P}}_{i,t}$, Lagrange multipliers ${\delta }_{i,t}$, and penalty factors ${\rho }_1$must be introduced. Then, the augmented Lagrange function is as follows:

$$L_1^i=\min \left[V_i^{\text{'}}+\sum _{t=1}^T{\delta }_{i,t}({\widehat{P}}_{i,t}-P_{i,t}^{sell,es})+\sum _{t=1}^T{\displaystyle \frac{{\rho }_1}{2}}{\parallel {\widehat{P}}_{i,t}-P_{i,t}^{sell,es}\parallel }^2\right]$$

(39)

$$L_1^{es}=\min \left[V_{es}^{\text{'}}+\sum _{i=1}^3\sum _{t=1}^T{\delta }_{i,t}({\widehat{P}}_{i,t}-P_{i,t}^{buy,es})+\sum _{i=1}^3\sum _{t=1}^T{\displaystyle \frac{{\rho }_1}{2}}{\parallel {\widehat{P}}_{i,t}-P_{i,t}^{buy,es}\parallel }^2\right]$$

(40)

The algorithmic solution process for sub-question 1 is as Figure 2:

(2)

Solutions to the problem of electricity price negotiations

Initially, it is necessary to decouple sub-question 2. To do so, the following steps must be taken. First, auxiliary variables ${\widehat{\lambda }}_{i,t}$, Lagrange multipliers ${\phi }_{i,t}$, and penalty factors ${\rho }_2$must be introduced. Then, the augmented Lagrange function is as follows:

$$\left\{\begin{array}{c}{L}_2^i=\min -{\displaystyle {\displaystyle \sum _{i=1}^3}\left[\begin{array}{l}{\gamma }_i\ln [V_{i,0}-V_i^{\ast }+{\displaystyle {\displaystyle \sum _{t=1}^T}{\widehat{\lambda }}_{i,t}{P}_{i,t}^{sell,es}}]\\ +{\displaystyle \sum _{t=1}^T}{\phi }_{i,t}({\widehat{\lambda }}_{i,t}-{\lambda }_{i,t}^{sell,es})+{\displaystyle \sum _{t=1}^T}\frac{{\rho }_2}{2}{\parallel {\widehat{\lambda }}_{i,t}-{\lambda }_{i,t}^{sell,es}\parallel }^2\end{array}\right]}\\ \mathrm{s}.\mathrm{t}.V_{i,0}-V_i^{\ast }+{\displaystyle {\displaystyle \sum _{t=1}^T}{\widehat{\lambda }}_{i,t}{P}_{i,t}^{sell,es}}\ge 0\end{array}\right.$$

(41)

$$\left\{\begin{array}{c}{L}_2^{ES}=\min -\left[\begin{array}{l}\ln [V_{es,0}-V_{es}^{\ast }+{\displaystyle \sum _{t=1}^T{\widehat{\lambda }}_{i,t}{P}_{i,t}^{sell,es}}]\\ +{\displaystyle \sum _{i=1}^3{\displaystyle \sum _{t=1}^T{\phi }_{i,t}({\widehat{\lambda }}_{i,t}-{\lambda }_{i,t}^{buy,es})}}+{\displaystyle \sum _{i=1}^3{\displaystyle \sum _{t=1}^T\frac{{\rho }_2}{2}{\parallel {\widehat{\lambda }}_{i,t}-{\lambda }_{i,t}^{buy,es}\parallel }^2}}\end{array}\right]\\ \mathrm{s}.\mathrm{t}.V_{es,0}-V_{es}^{\ast }+{\displaystyle {\displaystyle \sum _{t=1}^T}{\widehat{\lambda }}_{i,t}{P}_{i,t}^{sell,es}}\ge 0\end{array}\right.$$

(42)

The algorithmic solution process for sub-question 2 is as Figure 3:

2.4. Excess Profit Distribution Satisfaction Model

To calculate the satisfaction level of each entity with the distribution of excess profits after cooperative operation, the following satisfaction model is constructed:

$${\omega }_x={\displaystyle \frac{V_x-V_{x,0}}{V_1-V_0}}$$

(43)

where ${\omega }_x$ is the satisfaction level of entity $x$ with the distribution of benefits; $V_{x,0}$ is the cost of entity $x$ before cooperation; $V_x$ is the cost of entity $x$ after cooperation; $V_1$ is the total cost of the alliance after cooperation; $V_0$ is the total cost of the alliance before cooperation.

3. Results

3.1. Basic Data

This paper utilizes the alliance illustrated in Figure 1 as a case study for numerical analysis. The optimization scheduling time should be set to 24 h, with a time interval of 1 h. The maximum of the power interaction between each microgrid and the PG is 2000 kW. The maximum natural gas purchase is 500 m³. The maximum of the power interaction with SES is 2000 kW. The parameters of distinct microgrid equipment are enumerated in

Table 1. The parameters of distinct microgrid equipment.

Equipment	Microgrid 1	Microgrid 2	Microgrid 3	Operating Costs
WP	400 kW	1000 kW	1800 kW	0.013 yuan/kW
PV	400 kW	400 kW	800 kW	0.014 yuan/kW
GT	/	500 kW	400 kW	0.053 yuan/kW
GB	400 kW	500 kW	400 kW	0.037 yuan/kW
EB	300 kW	/	/	0.046 yuan/kW
EL	/	500 kW	/	0.125 yuan/m3
CC	300 m3	500 m3	500 m3	0.015 yuan/m3
MR	300 m3	500 m3	500 m3	0.141 yuan/m3
HT	/	100 m3	/	0.012 yuan/m3
TS	200 kW	200 kW	200 kW	0.018 yuan/kW

, while the pertinent price parameters are detailed in

Table 2. The pertinent price parameters.

Category	Time Period	Price
Distribution network electricity sales price	23:00–07:00	0.4
	08:00–11:00, 15:00–18:00	0.75
	12:00–14:00, 19:00–22:00	1.2
Distribution network electricity purchase price	All day	0.2
Natural gas price	All day	1.8
Carbon emission factor	All day	0.047
Shiftable load compensation coefficient	All day	0.2
Reducible load compensation factor	All day	0.35
Increasable load compensation coefficient	All day	0.25

. The calculations in this paper are implemented by MATLAB2024b.

3.2. Results Analysis

3.2.1. Operation Results

When the alliance is operating, the operational status of each microgrid and the optimization results of SES interaction are shown in Figure 4, Figure 5 and Figure 6, respectively.

As shown in Figure 4, microgrid 1 has significant load demands with distinct temporal patterns, but its own power generation capacity is insufficient. After collaborative operation, it must purchase electricity from a SES facility throughout the day to meet the load demands within the microgrid.

As shown in Figure 5, Microgrid 2 has a relatively strong power generation capacity. There is high electricity demand during the day and low demand at night. Additionally, the presence of hydrogen and other energy demands exacerbates the daytime electricity shortage. Therefore, Microgrid 2 must purchase electricity from the shared energy storage system during peak periods to meet its needs. During off-peak periods, Microgrid 2 transfers excess electricity to the shared energy storage system. More specifically, during the periods from 00:00 to 07:00 and from 22:00 to 24:00, the various loads within Microgrid 2 are relatively low, but wind power generation is high. At this point, the excess wind power that cannot be absorbed by Microgrid 2 is transmitted to the SES system; during the 08:00–21:00 time period, the demand for various loads in Microgrid 2 surges. On one hand, within the microgrid, part of the electricity, heat, natural gas, and hydrogen loads are adjusted through comprehensive demand response. For example, during the 13:00–15:00 time period, there is a shortage of electricity resources within the microgrid, and the electricity price is at peak-hour levels; At this point, the cost of producing hydrogen within the microgrid is high, so hydrogen loads are significantly reduced and transferred, while electricity and natural gas, which are relatively cheaper, are used as substitutes to reduce the microgrid’s operating costs. On the other hand, during this period, Microgrid 2 purchases electricity from SES to meet load demands.

As shown in Figure 6, microgrid 3 has a surplus of renewable energy generation. After meeting own power supply needs, it transmits electricity to Microgrids 1 and 2, which have electricity shortages, through the SES facility.

The results of energy interaction between each microgrid and the PG before cooperative operation are shown in Figure 7, and the interaction between the SES system and each microgrid and the PG after cooperative operation are shown in Figure 8.

As shown in Figure 7, prior to collaborative operation, Microgrid 1 purchased electricity from the PG throughout the day due to power shortages, while Microgrids 2 and 3 sold electricity to the PG during periods of power surplus. From the overall transaction behavior perspective, during low-price periods, the microgrids exhibited a net electricity sales trend, whereas during high-price periods, they exhibited a net electricity purchase trend, thereby limiting the overall operational economic efficiency. As shown in Figure 8, after cooperative operation, the SES system purchases electricity during certain off-peak price periods (01:00, 04:00, 05:00, 23:00) and when each microgrid has excess generation capacity, it is stored to meet the load demand during periods of electricity shortage in each microgrid. As a result, the overall economic efficiency improves.

3.2.2. Algorithm Convergence

Taking the convergence of subproblem 2 in an asymmetric negotiation as an example, its convergence is shown in Figure 9.

As shown in Figure 9, the proposed algorithm converges after only 41 iterations, demonstrating rapid convergence with a relatively small number of iterations. This indicates that the distributed solution algorithm for the asymmetric negotiation of transaction prices based on ADMM, as proposed in this paper, has good convergence characteristics. It can achieve distributed and efficient solutions while protecting the private information of all parties.

3.2.3. Electricity Price Negotiation Comparison

The electricity trading prices negotiated between SES and various microgrids are shown in Figure 10.

As shown in Figure 10, after asymmetric price negotiations, the electricity transaction prices ultimately negotiated for the whole day are all within the range of the PG’s electricity sales and purchase prices. Therefore, microgrids can, through SES, sell electricity to each other at a price higher than the selling price to the PG and can purchase electricity from other microgrids at a price lower than the purchasing price from the PG, effectively guiding microgrid interaction and enhancing collective benefits.

In the context of the conventional symmetric pricing model, the disparities in energy contributions among entities are not taken into consideration, leading to cost reductions that are distributed relatively uniformly, resulting in an average allocation. However, this approach does not account for differences in contributions. The adoption of the asymmetric pricing method outlined in this paper results in Microgrid 3 supplying electricity to Microgrids 1 and 2 through SES, contributing a substantial amount of energy and consequently receiving a greater share of the cooperative benefits. Conversely, Microgrid 1 primarily receives electricity, while Microgrid 2 supplies electricity to SES during periods of excess electricity generation and receives electricity during peak load periods. However, its overall interaction volume with SES is comparatively negligible in relation to microgrids 1 and 3. This results in a propensity to allocate fewer cooperative benefits to this microgrid. The SES functions as the connecting link for interactions within the microgrid cluster, overseeing all electricity interactions within the cluster and contributing the most to the system. According to Formula (37), the bargaining factors for each microgrid and shared energy storage are calculated to be 0.3088, 0.1234, 0.5678, and 1, respectively.

When operating independently, the profits of each microgrid are calculated based on their individual interactions with the external power grid and gas network. After cooperative operation, the profits of each microgrid and shared energy storage are calculated separately under symmetric and asymmetric pricing scenarios using the model described earlier and the calculated pricing factors. The results are shown in

Table 3. The profit results for each microgrid entity and shared storage.

Scenario	Microgrid 1 (Yuan)	Microgrid 2 (Yuan)	Microgrid 3 (Yuan)	SES (Yuan)
non-cooperative operation	−17,454.76	−6823.58	468.52	/
symmetric cooperative bargaining	−14,796.58	−4149.958	3108.33	2669.20
asymmetric cooperative bargaining	−16,247.67	−5975.345	3742.65	5307.68

.

As shown in Table 3, after the cooperation, the overall profit of the alliance increased by 44.69%, and the profits of all entities increased under both bargaining scenarios.

According to Equation (43), the results of satisfaction with excess profit distribution under symmetric and asymmetric bargaining conditions after cooperation among the various entities are shown in

Table 4. Excess profit distribution satisfaction.

Scenario	Microgrid 1	Microgrid 2	Microgrid 3	SES
symmetric cooperative bargaining	0.249809883	0.251261088	0.248083511	0.250845518
asymmetric cooperative bargaining	0.113478864	0.079742807	0.307801866	0.498976463

.

As shown in Table 4, under symmetric bargaining, the satisfaction levels of all parties with the distribution of excess profits are basically consistent, meaning that an average distribution is achieved. However, under asymmetric bargaining, Microgrid 1 and Microgrid 2, which have lower system contribution levels, receive fewer cooperative benefits, resulting in lower satisfaction levels with the distribution of excess profits compared to symmetric bargaining. In contrast, Microgrid 3 and the shared energy storage system, which have higher contribution levels, receive more cooperative benefits, leading to higher satisfaction levels with the distribution of excess profits. Therefore, transaction payments based on asymmetric bargaining negotiations can reasonably allocate cooperative benefits according to differing levels of cooperative contribution.

4. Discussion

This paper considers the energy contribution to cooperation of different entities and proposes an optimization model for the coordinated operation of multiple microgrids and SES based on asymmetric bargaining negotiations. Through case analysis, the following conclusions are reached:

(1)

After group coordination, SES interacts with the PG and various microgrids to achieve dynamic responses to the differentiated needs of microgrids, promoting the local consumption of new energy in the microgrids and effectively improving the operational efficiency of all entities.

(2)

Asymmetric pricing based on energy contribution enables the reasonable allocation of cooperative benefits, maintaining the enthusiasm of all entities to participate in group cooperation. Microgrids with higher renewable energy generation can obtain higher benefits during the allocation process, thereby encouraging microgrid entities to further expand their installed renewable energy capacity.