# Research on the Optimization of Energy–Carbon Co-Sharing Operation in Multiple Multi-Energy Microgrids Based on Nash Negotiation

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## Abstract

**:**

## 1. Introduction

## 2. Energy–Carbon Co-Sharing Operation Model of Multiple Multi-Energy Microgrids

#### 2.1. Subsection

#### 2.2. Operation Model of Multiple Multi-Energy Microgrids

#### 2.2.1. Operation Model of P2G

- Electrolyzer:

- Methane reactor:$$\{\begin{array}{l}{P}_{i}^{mr,g}(t)={\eta}_{{}^{mr}}{P}_{i}^{{H}_{2},mr}(t)\\ {P}_{i,\mathrm{min}}^{{H}_{2},mr}\le {P}_{i}^{{H}_{2},mr}(t)\le {P}_{i,\mathrm{max}}^{{H}_{2},mr}\\ \Delta {P}_{i,\mathrm{min}}^{{H}_{2},mr}\le {P}_{i}^{{H}_{2},mr}(t+1)-{P}_{i}^{{H}_{2},mr}(t)\le \Delta {P}_{i,\mathrm{max}}^{{H}_{2},mr}\end{array}$$

- Hydrogen fuel cells:$$\{\begin{array}{l}{P}_{i}^{hfc,e}(t)={\eta}_{e,hfc}{P}_{i}^{{H}_{2},hfc}(t)\\ {P}_{i}^{hfc,h}(t)={\eta}_{h,hfc}{P}_{i}^{{H}_{2},hfc}(t)\\ {P}_{i,\mathrm{min}}^{{H}_{2},hfc}\le {P}_{i}^{{H}_{2},hfc}(t)\le {P}_{i,\mathrm{max}}^{{H}_{2},hfc}\\ \Delta {P}_{i,\mathrm{min}}^{{H}_{2},hfc}\le {P}_{i}^{{H}_{2},hfc}(t+1)-{P}_{i}^{{H}_{2},hfc}(t)\le \Delta {P}_{i,\mathrm{max}}^{{H}_{2},hfc}\end{array}$$

#### 2.2.2. Operation Model of the CHP

#### 2.2.3. Operation Model of the GB

#### 2.2.4. Operation Model of the CCS

#### 2.2.5. Model of Electricity and Heat Load

#### 2.2.6. Operation Model of Energy Storage Devices

## 3. Cost Model of Multiple Multi-Energy Microgrids

#### 3.1. Objective Function

#### 3.1.1. Cost of Buying and Selling Energy

#### 3.1.2. Cost of Demand Response

#### 3.1.3. Cost of Energy Storage Devices

#### 3.1.4. Cost of Carbon Sharing

#### 3.1.5. Cost of Carbon Trading

#### 3.2. Constraints

## 4. Nash Negotiation Method Based on Cooperative Games

#### 4.1. Sub-Model 1: The Model of Maximizing the Benefits of MMEM Alliances

- 1.
- Establish the augmented Lagrange function of the model (29):$${L}_{i}={C}_{i}^{meg}+{\displaystyle \sum _{t=1}^{T}{\lambda}_{i,j}(\tilde{{P}_{i,t}^{j}}-{P}_{j,t}^{i})+{\displaystyle \sum _{t=1}^{T}\frac{{\rho}_{i,j}}{2}}}{\Vert \tilde{{P}_{i,t}^{j}}-{P}_{j,t}^{i}\Vert}_{2}^{2}$$

- 2.
- For each entity, update its own electricity trading strategy through calculation. MEM-j receives the amount of electricity, $\tilde{{P}_{i,t}^{j}}(k)$, which it expected to be purchased from MEM-i, and it updates its decision-making, ${P}_{j,t}^{i}(k+1)$. MEM-i accepts the updated decision-making information, ${P}_{j,t}^{i}(k+1)$, and updates its decision-making, $\tilde{{P}_{i,t}^{j}}(k+1)$;
- 3.
- After completing a round of iterations, update the Lagrange multiplier and update the iteration number, $k=k+1$:

- 4.
- Determine whether the algorithm converges according to Equation (33) and stop the iteration if it is satisfied, otherwise return to step (2) until it is satisfied.

#### 4.2. Sub-Model 2: The Model of Income Distribution within the Alliance

## 5. Case Study

#### 5.1. Basic Data

^{3}. The compensation unit price for reducing the electricity load was RMB 0.03/kWh, the compensation unit price for transferring the electricity load was RMB 0.01/kWh, and the compensation unit price for reducing the heat load was RMB 0.016/kW. The system parameters of the MMEMs are shown in Table 1 [18,22]. The total investment costs of the energy storage device considered in this paper was RMB 1.3 million, with annual operating hours of 8760 h, a service life of 15 years, and an annual depreciation rate of 6.3% [24].

#### 5.2. Results Analysis

#### 5.2.1. Analysis of Energy Sharing Results

#### 5.2.2. Analysis of Carbon Sharing and Carbon Emission Results

#### 5.2.3. Analysis of Renewable Energy Consumption Results

#### 5.2.4. Analysis of Renewable Energy Consumption Results

^{−3}, indicating that the Nash negotiation solution algorithm proposed based on ADMM exhibited a satisfactory convergence.

#### 5.2.5. Analysis of Costs

## 6. Conclusions

- Energy–carbon co-sharing among MMEMs facilitates the complementary and efficient utilization of resources. Through the cooperative games, the renewable energy consumption was enhanced, resulting in increased renewable energy consumption rates of 8.34%, 8.78%, and 8.83% for MEM-1, MEM-2, and MEM-3, respectively.
- Energy–carbon co-sharing among MMEMs based on cooperative games can reduce the overall carbon emissions of MMEM alliances. The carbon emissions of each MEM in the case study were reduced to varying degrees, and the overall carbon emission reduction rate reached 17.81%, which proves that the energy–carbon co-sharing of MMEMs based on the Nash game is effective in reducing carbon emissions.
- The Nash-negotiation-solving algorithm of the MMEM alliance based on ADMM had good convergence, and the convergence accuracy reached 10
^{−3}while also considering the privacy protection of each subject. - The bargaining coefficient method based on energy–carbon co-sharing capacity is helpful in mobilizing the enthusiasm of all subjects to actively participate in the cooperative game. MEMs containing low-carbon units such as CCS and two-stage P2G units can achieve a fairer distribution of benefits compared to scenarios in which bargaining factors are not considered. Microgrids with higher renewable energy generation and more carbon capture can also obtain higher benefits in the energy–carbon co-sharing process.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Electric power balance diagram of MMEM after cooperative game: (

**a**) MEM-1; (

**b**) MEM-2; (

**c**) MEM-3.

**Figure 7.**Carbon dioxide power balance of MMEMs after cooperative game: (

**a**) MEM-1; (

**b**) MEM-2; (

**c**) MEM-3.

**Figure 9.**Comparison of renewable energy consumption in MEM-1 before and after the Nash negotiations: (

**a**) before the Nash negotiations; (

**b**) after the Nash negotiations.

**Figure 10.**Comparison of renewable energy consumption in MEM-2 before and after the Nash negotiations: (

**a**) before the Nash negotiations; (

**b**) after the Nash negotiations.

**Figure 11.**Comparison of renewable energy consumption in MEM-3 before and after the Nash negotiations: (

**a**) before the Nash negotiations; (

**b**) after the Nash negotiations.

**Figure 12.**Iterative convergence results of Sub-model 1: (

**a**) MEM-1; (

**b**) MEM-2; (

**c**) MEM-3; (

**d**) MMEMs.

Parameter | Value/kW | Parameter | Value |
---|---|---|---|

${P}_{i,\mathrm{min}}^{e,el}$, ${P}_{i,\mathrm{max}}^{e,el}$ | 0, 500 | ${\eta}_{e,el}$ | 0.87 |

$\Delta {P}_{i,\mathrm{min}}^{e,el}$, $\Delta {P}_{i,\mathrm{max}}^{e,el}$ | −250, 250 | ${\eta}_{mr}$ | 0.6 |

${P}_{i,\mathrm{min}}^{{H}_{2},mr}$, ${P}_{i,\mathrm{max}}^{{H}_{2},mr}$ | 0, 250 | ${\eta}_{e,hfc}$, ${\eta}_{h,hfc}$ | 0.95, 2.1 |

$\Delta {P}_{i,\mathrm{min}}^{{H}_{2},mr}$, $\Delta {P}_{i,\mathrm{max}}^{{H}_{2},mr}$ | −125, 125 | ${\eta}_{e,chp}$, ${\eta}_{h,chp}$ | 0.92, 2.1 |

${P}_{i,\mathrm{min}}^{{H}_{2},hfc}$, ${P}_{i,\mathrm{max}}^{{H}_{2},hfc}$ | 0, 250 | ${\eta}_{gb}$ | 0.95 |

$\Delta {P}_{i,\mathrm{min}}^{{H}_{2},hfc}$, $\Delta {P}_{i,\mathrm{max}}^{{H}_{2},hfc}$ | −125, 125 | ${\eta}^{abs}$, ${\eta}^{relea}$ | 0.95, 0.96 |

${P}_{i,\mathrm{min}}^{g,chp}$, ${P}_{i,\mathrm{max}}^{g,chp}$ | 0, 600 | ${\mu}_{i}^{c}$ | 0.55 |

$\Delta {P}_{i,\mathrm{min}}^{g,chp}$, $\Delta {P}_{i,\mathrm{max}}^{g,chp}$ | −1000, 1000 | ${\sigma}_{c}$ | 0.9 |

${P}_{i,\mathrm{min}}^{g,gb}$, ${P}_{i,\mathrm{max}}^{g,gb}$ | 0, 600 | ${\gamma}^{ccs}$ | 0.55 |

$\Delta {P}_{i,\mathrm{min}}^{g,gb}$, $\Delta {P}_{i,\mathrm{max}}^{g,gb}$ | −1000, 1000 | ${k}^{e,trans}$ | 0.1 |

${E}_{\mathrm{min}}$, ${E}_{\mathrm{max}}$ | 500, 2500 | ${\varsigma}^{e}$, ${\varsigma}^{g}$ | 1.08, 0.234 |

${P}_{\mathrm{max}}^{grid,buy}$, ${P}_{\mathrm{max}}^{grid,sell}$ | 5000, 2000 | $\alpha $, $\beta $ | 0.5, 0.5 |

${P}_{\mathrm{max}}^{g,buy}$ | 5000 | $\epsilon $ | 0.01 |

Carbon Emission Volume before Cooperation/kg | Carbon Emission Volume after Cooperation/kg | Carbon Emission Volume Reduction/% | |
---|---|---|---|

MEM-1 | 103,381 | 91,503 | 11.49% |

MEM-2 | 123,808 | 86,533 | 30.11% |

MEM-3 | 99,827 | 90,742 | 9.10% |

MMEMs | 327,016 | 268,778 | 17.81% |

Entities | Pre-Cooperation Costs/RMB * | Post-Cooperation Costs/RMB | Revenue Enhancement Value/RMB |
---|---|---|---|

MEM-1 | 104,604.82 | 94,851.47 | 9753.35 |

MEM-2 | 78,344.45 | 51,462.24 | 26,882.21 |

MEM-3 | 259,168.68 | 255,559.07 | 3609.61 |

MMEMs | 442,117.95 | 401,872.78 | - |

Entities | Bargaining Coefficient | Bargaining Proceeds/RMB | Cost after Revenue Distribution/RMB | The Value of the Yield Enhancement after Considering the Bargaining Factor/RMB |
---|---|---|---|---|

MEM-1 | 0.9172 | 2341.27 | 92,510.20 | 12,094.62 |

MEM-2 | 0.8073 | −10,782.2 | 62,244.44 | 16,100.01 |

MEM-3 | 1.2533 | 8437.39 | 247,121.68 | 12,047.00 |

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## Share and Cite

**MDPI and ACS Style**

Yuan, X.; Cui, C.; Zhu, G.; Ma, H.; Cao, H.
Research on the Optimization of Energy–Carbon Co-Sharing Operation in Multiple Multi-Energy Microgrids Based on Nash Negotiation. *Energies* **2023**, *16*, 5655.
https://doi.org/10.3390/en16155655

**AMA Style**

Yuan X, Cui C, Zhu G, Ma H, Cao H.
Research on the Optimization of Energy–Carbon Co-Sharing Operation in Multiple Multi-Energy Microgrids Based on Nash Negotiation. *Energies*. 2023; 16(15):5655.
https://doi.org/10.3390/en16155655

**Chicago/Turabian Style**

Yuan, Xiaoling, Can Cui, Guanxin Zhu, Hanqing Ma, and Hao Cao.
2023. "Research on the Optimization of Energy–Carbon Co-Sharing Operation in Multiple Multi-Energy Microgrids Based on Nash Negotiation" *Energies* 16, no. 15: 5655.
https://doi.org/10.3390/en16155655