# Cooperative Multi-Objective Optimization of DC Multi-Microgrid Systems in Distribution Networks

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## Abstract

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## Featured Application

**A cooperative multi-objective optimization model of a DC multi-microgrid that considers across-time-and-space energy transmission of EVs is established to improve the economy of the system, decrease the loss of the distribution network, and reduce carbon emissions.**

## Abstract

## 1. Introduction

- A grid-connected MMGS containing RESs and EVs is constructed, where RESs, EVs, MGs and distribution networks are combined, bidirectional V2G technology is used and the across-time-and-space energy transmission (ATSET) of EVs is thoroughly considered. The effect of the across-time-and-space energy transmission on MMGS economic operation is analyzed to state the potential benefits of cooperative multi-objective optimization.
- A cooperative multi-objective optimization model is established, including the dynamic economic dispatch of RESs, EVs, DC/AC converters, and the reactive power optimization of DC/AC converters in MMGS. The cooperative multi-objective optimization model consists of two loops. The inner-loop model uses the active power output of RESs, EVs, DC/AC converters as variables, and the daily operating cost of MMGS is used as the optimization objective. The outer-loop model uses the reactive power output of the DC/AC converters as the variable to optimize the network loss of the distribution network, thereby reducing network loss cost and carbon emissions cost. The ultimate goal of the cooperative multi-objective is to obtain the optimal daily economic cost.
- The concepts of carbon neutrality and carbon peaking are combined. Through the cooperative multi-objective optimization model, the carbon emissions generated by the operation of the MMGS and the distribution network are effectively reduced. The cooperative multi-objective optimization model not only improves the economy but also reduces the total carbon emissions of MMGS and the distribution network.

## 2. System Structure

#### 2.1. Structure of the DC Multi-Microgrid System

#### 2.2. DC Microgrid

#### 2.3. Bidirectional DC/AC Converter

## 3. Mathematical Model

#### 3.1. Renewable Power Generation

#### 3.1.1. Photovoltaic Module

#### 3.1.2. Wind Turbine

#### 3.2. Electric Vehicles

#### 3.2.1. EVs Model

_{EVm}

_{,n,t}is the remaining power capacity of the n-th EV in the m-th MG in the t-th hour, σ is the self-discharge coefficient. ${P}_{m,n,t}^{EV}$ is the charging or discharging power in the t-th hour of the n-th EV in the m-th MG. If ${P}_{m,n,t}^{EV}$ ≥ 0, EVs are charged. If ${P}_{m,n,t}^{EV}$ < 0, EVs release energy; ∆t = 1 h. η

_{DEV}and η

_{CEV}are the discharging and charging efficiency of EVs to calculate the power actual charging or discharging power of EVs.

#### 3.2.2. Across-Time-and-Space Energy Transmission of EV

#### 3.3. EV Charging/Discharging Infrastructures

## 4. Cooperative Multi-Objective Optimization Model

#### 4.1. Description of the Optimization Model

#### 4.2. Double-Loop Optimization Process

#### 4.3. Cooperative Multi-Objective Optimization Objective Function

_{ETC}is the economic total cost of MMGS. C

_{OTC}is the operating total cost of MMGS, C

_{WTC}is the energy loss cost of the MMGS that is obtained from the outer-loop model, where

_{il}and C

_{co}are the network loss cost and carbon emissions cost caused by the increase in the distribution network loss in the outer-loop model, respectively. E

_{CO}is the carbon emissions generated by the distribution network. ${W}_{S}^{G}$ is the total daily operating network loss of the distribution network when MMGS is integrated into the distribution network and runs.${W}_{S}^{B}$ is the total daily operating network loss when there is no MMGS access, which is a fixed value also called the original baseline loss. k

_{il}, e

_{c}, k

_{c}are fixed factors, k

_{il}is the loss cost coefficient of the distribution network, e

_{c}is the carbon emissions factor, k

_{c}is the carbon cost factor. ∆t = 1 h. E

_{C}is the total carbon emissions of MMGS and the distribution network, E

_{CIm}is the carbon emissions generated by m-th MG in the inner-loop model, M is the number of MGs in the MMGS.

_{OTC}and ${W}_{S}^{G}$ are the optimization targets of the inner-loop model and the outer-loop model, respectively, the objective functions of the inner-loop model and the outer-loop model are set as follows:

_{1}and f

_{2}are the objective functions of the inner-loop model and the outer-loop model, respectively.

#### 4.4. Inner-Loop Optimization

_{OCm}is the operating cost of the m-th MG that is obtained from the inner-loop model. C

_{exm}is the energy transaction cost in the m-th MG. C

_{cim}is the carbon emissions cost due to energy exchange in the inner-loop model.

#### 4.4.1. Energy Transaction Cost

_{resm}is the cost of RESs of the m-th MG in a day, C

_{PVm}, and C

_{WTm}are the cost of PVs and WTs. ${P}_{m,t}^{PV}$ is the power output of PVs in the m-th MG, at t-th hour, ${C}_{m,t}^{PV}$ is the PV power generation cost, ${P}_{m,t}^{WT}$ is the power output of WTs, ${C}_{m,t}^{WT}$ is the WT power generation cost. C

_{evm}is the cost of energy exchange between MMGS and EVs, ${C}_{m,t}^{CEV}$ is the charging price of EVs in m-th MG, ${C}_{m,t}^{DEV}$ is the discharging price, ∆t = 1 h, T = 24 h. C

_{gm}is the energy exchange cost between the MG and the distribution network through the DC/AC converters, ${P}_{m,t}^{G}$ is the active power output between the MG and the distribution network through the DC/AC converters. If ${P}_{m,t}^{G}$ ≥ 0, MG purchases electricity from the distribution network. If ${P}_{m,t}^{G}$ < 0, MMGS sells electricity to the distribution network. ${C}_{m,t}^{G}$ is the electricity price that MG purchases/sells to the distribution network. C

_{cym}is the additional cycle cost of EV batteries, ${C}_{cyn}^{EV}$ is the additional battery charging/discharging cycle cost of n-th EV, k

_{cy}is the number of additional charging/discharging cycles, N is the number of EVs.

#### 4.4.2. Carbon Emissions and Cost

_{2}. To reduce carbon emissions as much as possible and increase the use of RESs, in this paper, the cost of carbon emissions is used as the penalty cost of CO

_{2}generated by the energy exchange between the MMGS and the distribution network [29].

#### 4.5. Constraints of the Inner-Loop Model

#### 4.5.1. EVs Power Constraint

#### 4.5.2. EVs Capacity Constraint

_{EVm}

_{,n,min,}and SOC

_{EVm}

_{,n,max}are the minima and maximum capacity, respectively, of n-th EV in m-th MG.

#### 4.5.3. RESs Output Constraint

#### 4.5.4. System Power Balance Constraint

#### 4.6. Outer-Loop Optimization

_{br}is the number of branches. i, j are the nodes, k

_{i}is the state variable of the i-th branch switch, 1 means closed, 0 means open; R

_{ij}is the resistance of branch ij, P

_{ij}

_{,t}, Q

_{ij}

_{,t}are the active and reactive power of branch ij in the t-th hour, V

_{ij,t}is the voltage,${P}_{ij,t}^{0}$,${Q}_{ij,t}^{0}$ are initially active, reactive power when connected without MMGS. ${P}_{m,t}^{G}$, ${Q}_{m,t}^{G}$ are the active and reactive power through the DC/AC converters injected into node i by the m-th MG connected to node i. To facilitate the calculation of network loss, a day is divided into 12 small periods, with a time interval of 2 h.

#### 4.6.1. Network Loss Cost

#### 4.6.2. Carbon Emissions and Cost

_{2}will be emitted. MMGS will still incur a penalty cost for carbon emissions by the increasing network loss, which differs from the carbon emissions cost due to energy exchange in the inner-loop model.

#### 4.7. Constraints of the Outer-Loop Model

#### 4.7.1. Node Power Flow Constraint

_{Li}

_{,t}and Q

_{Li}

_{,t}are the active and reactive load, V

_{i}

_{,t}and V

_{j}

_{,t}are the voltage of node i and j, G

_{ij}, B

_{ij}, and δ

_{ij}are the conductance, susceptance, and phase angle difference of branch ij.

#### 4.7.2. Node Voltage Constraint

#### 4.7.3. Branch Power Constraint

_{ij}

_{,}

_{max}, Q

_{ij}

_{,max}are the maximum active and reactive power of the branch ij.

#### 4.7.4. Branch Current Constraint

#### 4.7.5. Reactive Output Constraint of DC/AC Converter

_{m}is the rated power of the DC/AC converter in m-th MG, ${Q}_{m,t}^{G}$ is the reactive power that the DC/AC converter can output to the distribution network, ${P}_{m,t}^{G}$ is the active power output by DC/AC converter.

#### 4.8. Particle Swarm Algorithm

#### 4.8.1. Procedure of PSO

#### 4.8.2. Coding

## 5. Case Study and Discussion

#### 5.1. Case Description

#### 5.1.1. Case 1

#### 5.1.2. Case 2

#### 5.1.3. Case 3

#### 5.1.4. Case 4

#### 5.2. Simulation System Construction

#### 5.2.1. System Introduction

#### 5.2.2. Parameters of RESs

#### 5.2.3. Parameters of DC/AC Converter

_{m}= 1000 kW, the power limit is set as [33]:

#### 5.2.4. Parameters of EVs

#### 5.2.5. Other Parameters

#### 5.3. Simulation Results

#### 5.3.1. Inner-Loop Optimization Results

- Case 1

- 2.
- Case 2

- 3.
- Case 3

_{OTC}.

#### 5.3.2. Outer-Loop Optimization Results

_{WTC}and total carbon emissions E

_{C}of MMGS and the distribution network, and cooperating with the inner-loop model to reduce the total economic cost C

_{ETC}of MMGS. The comparison of the results under the four cases is shown in Table 4.

_{il}and the carbon emissions cost C

_{co}derived from the optimization of the outer-loop model are the lowest, which proves that the outer-loop optimization model plays a role in the cooperative optimization of the economic cost of MMGS.

#### 5.3.3. Cooperative Multi-objective Optimization Results

_{ETC}of MMGS is the lowest. The cost of case 4 adopting the cooperative multi-objective model is 16.3% lower than that for case 1, 13.9% lower than that for case 2, 8.6% lower than that for case 3 which only uses the economic dispatch model of the inner-loop without optimizing reactive power output of DC/AC converters. It is proved that the cooperative multi-objective optimization model improves the economy of MMGS.

#### 5.3.4. Further Verification

_{ETC}and the lowest distribution network loss ${W}_{S}^{G}$ are obtained, which further proves the correctness and effectiveness of the model.

## 6. Conclusions

- According to the simulation results, the economic dispatch model of the inner-loop in the cooperative multi-objective optimization can reduce the operating cost of MMGS, which makes full use of the ATSET of EVs. Additionally, the optimization of the output reactive power output of the DC/AC converters of the outer-loop can reduce network loss cost and carbon emissions cost of the distribution network. The two cooperate to realize the improvement of the economy of MMGS and the efficient operation of the distribution network.
- The cooperative multi-objective optimization model not only realizes the optimization of the economic cost of MMGS and the network loss of the distribution network, but also reduces the total carbon emissions of MMGS and the distribution network, which greatly responds to the calls for national carbon neutrality and carbon peak.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

B_{ij} | Susceptance of branch ij in the distribution network. |

C_{ETC} | Economic total cost of MMGS. |

C_{OTC} | Operating total cost of MMGS from the inner-loop model. |

C_{WTC} | Energy loss cost of the MMGS from the outer-loop model. |

C_{il} | Network loss cost. |

C_{co} | Carbon emissions cost. |

C_{OCm} | Operating cost of the m-th MG from the inner-loop model. |

C_{exm} | Energy transaction cost in the m-th MG. |

C_{cim} | Carbon emissions cost in the m-th MG. |

C_{resm} | Cost of RESs of the m-th MG. |

C_{PVm} | Cost of PVs in the m-th MG. |

C_{WTm} | Cost of WTs in the m-th MG. |

${C}_{m,t}^{PV}$ | PV power generation cost in the m-th MG in the t-th hour. |

${C}_{m,t}^{WT}$ | WT power generation cost in the m-th MG in the t-th hour. |

C_{evm} | Cost of energy exchange between the m-th MG and EVs. |

${C}_{m,t}^{CEV}$ | Charging price of EVs in m-th MG in the t-th hour. |

${C}_{m,t}^{DEV}$ | Discharging price of EVs in m-th MG in the t-th hour. |

C_{gm} | Energy exchange cost between the m-th MG and the distribution network. |

${C}_{m,t}^{G}$ | Electricity price that m-th MG purchases/sells to the distribution network in the t-th hour. |

C_{cym} | Additional cycle cost of EV batteries in m-th MG. |

${C}_{cyn}^{EV}$ | Additional battery charging/discharging cycle cost of n-th EV. |

E_{C} | Total carbon emissions of MMGS and the distribution network. |

E_{Cim} | Carbon emissions generated by m-th MG in the inner-loop model. |

E_{CO} | Carbon emissions in the outer-loop model. |

e_{c} | Carbon emissions factor. |

f | The main objective function of the cooperative optimization model. |

f_{1} | The objective functions of the inner-loop model. |

f_{2} | The objective functions of the outer-loop model. |

G_{ij} | Conductance of branch ij in the distribution network. |

${I}_{ij}^{\mathrm{max}}$ | Upper limit of branch ij current carrying capacity in the distribution network. |

i,j | Nodes of the distribution network. |

k_{il} | Loss cost coefficient. |

k_{c} | Carbon cost factor. |

k_{cy} | Number of additional charging/discharging cycles. |

k_{i} | The state variable of the i-th branch switch. |

M | Number of MGs in the MMGS. |

N | Number of EVs in m-th MG. |

N_{br} | Number of branches in the distribution network. |

${P}_{m,n,t}^{EV}$ | Exchanging power in the t-th hour of the n-th EV in the m-th MG. |

${P}_{m,t}^{EV}$ | Exchanging power in the t-th hour of the EVs in the m-th MG. |

${P}_{m,n,t}^{EVCDIs}$ | Power of the EVCDIs of the n-th EV in the m-th MG in the t-th hour. |

${P}_{m,t}^{PV}$ | Power output of PVs in the m-th MG in the t-th hour. |

${P}_{m,t}^{WT}$ | power output of WTs in the m-th MG in the t-th hour. |

${P}_{m,t}^{G}$ | Active power output between the m-th MG and the distribution network in the t-th hour through the DC/AC converters. |

${P}_{m,n,R}^{EVCDIs}$ | Rated power of the EVCDI serving the n-th EV in the m-th MG. |

${P}_{m,t}^{L}$ | Total load of the m-th MG in the t-th hour. |

P_{ij,t} | Active power of branch ij in the t-th hour. |

${P}_{ij,t}^{0}$ | Initially active power of branch ij when connected without MG in the t-th hour. |

${P}_{i,t}^{0}$ | Initial input active power of node i in the t-th hour. |

P_{Li,t} | Active load of node i in the t-th hour. |

P_{ij,max} | Maximum active power of the branch ij. |

Q_{ij,t} | Reactive power of branch ij in the t-th hour. |

${Q}_{ij,t}^{0}$ | Initially reactive power of branch ij when connected without MMGS in the t-th hour. |

${Q}_{m,t}^{G}$ | Reactive power output between the m-th MG and the distribution network in the t-th hour through the DC/AC converters. |

${Q}_{i,t}^{0}$ | Initial input reactive power of node i in the t-th hour. |

Q_{Li,t} | Reactive load of node i in the t-th hour. |

Q_{ij,max} | Maximum reactive power of the branch ij. |

R_{ij} | The resistance of branch ij. |

SOC_{EVm,n,t} | Remaining power capacity of the n-th EV in the m-th MG in the t-th hour. |

SOC_{EVm,n,min} | Minima capacity, respectively, of the n-th EV in the m-th MG. |

SOC_{EVm,n,max} | Maximum capacity, respectively, of the n-th EV in the m-th MG. |

S_{m} | Rated power of the DC/AC converter in the m-th MG. |

T | Scheduling cycle, one day, 24 h. |

V_{ij,t} | Voltage of branch ij in the t-th hour. |

${V}_{i}^{\mathrm{min}}$ | Lower limits of the node i voltage amplitude. |

${V}_{i}^{\mathrm{max}}$ | Upper limits of the node i voltage amplitude. |

${W}_{S}^{B}$ | Original baseline network loss. |

${W}_{S}^{G}$ | Total daily operating network loss of the distribution network. |

${W}_{S}^{I}$ | Daily operating increased network loss of the distribution network. |

σ | Self-discharge coefficient of EV’s battery. |

∆t | Length of the time slot set for the optimization. |

η_{DEV} | Efficiency for EV discharging. |

η_{CEV} | Efficiency for EV charging. |

δ_{ij} | Phase angle difference of branch ij. |

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**Figure 8.**(

**a**) Power output of RESs, EVs, and the DC/AC converter in OBMG; (

**b**) power output of RESs, EVs, and the DC/AC converter in RMG.

**Figure 9.**(

**a**) Power output of RESs, EVs, and the DC/AC converter in OBMG; (

**b**) power output of RESs, EVs, and the DC/AC converter in RMG.

**Figure 10.**(

**a**) Power output of RESs, EVs, and the DC/AC converter in OBMG; (

**b**) power output of RESs, EVs, and the DC/AC converter in RMG.

**Figure 12.**(

**a**) Reactive power output by the DC/AC converter of OBMG in case 4; (

**b**) reactive power output by the DC/AC converter of RMG in case 4.

MG Type | RES Type | Installed Capacity/kW | Power Generation Cost/¥·kWh^{−1} |
---|---|---|---|

OBMG | PV1 | 800 | 0.24 |

WT1 | 800 | 0.38 | |

RMG | PV2 | 400 | 0.24 |

WT2 | 400 | 0.38 |

Case | MGs | C_{ex}Energy Transaction Cost/CNY | C_{ci}Carbon Emissions Cost/CNY | C_{OTC}Total Operating Cost/CNY |
---|---|---|---|---|

Case 1 | RMG | 2760.0 | 16.3 | 2776.3 |

OBMG | 5700.8 | 31.8 | 5732.6 | |

MMGS | 8460.8 | 48.1 | 8508.9 | |

Case 2 | RMG | 2627.8 | 16.3 | 2644.1 |

OBMG | 5609.6 | 32.5 | 5642.1 | |

MMGS | 8237.4 | 48.8 | 8286.2 | |

Case 3 | RMG | 2348.9 | 42.9 | 2391.8 |

OBMG | 5394.6 | 9.5 | 5404.1 | |

MMGS | 7743.5 | 52.4 | 7795.9 |

Case | Case 1 | Case 2 | Case 3 |
---|---|---|---|

The Cost of EVs’ Users/CNY | 211.2 | 173.4 | −410.8 |

Case | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

${W}_{S}^{G}$ Total Network Loss/kW | 14,889.2 | 14,872.5 | 14,876.0 | 13,987.2 |

${W}_{S}^{I}$ Increased Network Loss/kW | 101.3 | 84.6 | 88.1 | −800.7 |

Case | C_{il}Network Loss Cost/CNY | C_{co}Carbon Emissions Cost/CNY | C_{WTC}Energy Loss Cost/CNY |
---|---|---|---|

Case 1 | 75.0 | 1.8 | 76.8 |

Case 2 | 62.6 | 1.5 | 64.1 |

Case 3 | 65.2 | 1.6 | 66.8 |

Case 4 | −592.5 | −14.5 | −607.0 |

Case | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

C_{ETC}Total Economic Cost of MMGS/CNY | 8585.7 | 8350.3 | 7862.7 | 7188.9 |

Case | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

E_{C}Total Carbon Emissions/kg | 237.6 | 239.5 | 257.1 | 180.5 |

Case | MGs | C_{ex}Energy Transaction Cost/CNY | C_{ci}Carbon Emissions Cost/CNY | C_{OTC}Total Operating Cost/CNY |
---|---|---|---|---|

Case 1 | RMG | 2968.9 | 23.4 | 2992.3 |

OBMG | 6446.4 | 48.6 | 6495.0 | |

MMGS | 9415.3 | 72.0 | 9487.3 | |

Case 2 | RMG | 2836.7 | 23.4 | 2860.1 |

OBMG | 6304.5 | 44.6 | 6349.1 | |

MMGS | 9141.2 | 68.0 | 9209.2 | |

Case 3 | RMG | 2574.4 | 48.5 | 2622.9 |

OBMG | 6154.2 | 27.6 | 6181.8 | |

MMGS | 8728.6 | 76.1 | 8804.7 |

Case | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

${W}_{S}^{G}$ Total Network Loss/kW | 14,933.1 | 14,915.8 | 14,919.4 | 14,110.8 |

${W}_{S}^{I}$ Increased Network Loss/kW | 145.2 | 127.9 | 131.5 | −677.1 |

Case | C_{il}Network Loss Cost/CNY | C_{co}Carbon Emissions Cost/CNY | C_{WTC}Energy Loss Cost/CNY |
---|---|---|---|

Case 1 | 107.4 | 2.6 | 110.0 |

Case 2 | 94.6 | 2.3 | 96.9 |

Case 3 | 97.3 | 2.4 | 99.7 |

Case 4 | −501.1 | −12.3 | −513.4 |

Case | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

C_{ETC}Total Economic Cost of MMGS/CNY | 9597.3 | 9306.1 | 8904.4 | 8291.3 |

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## Share and Cite

**MDPI and ACS Style**

Xu, Z.; Chen, C.; Dong, M.; Zhang, J.; Han, D.; Chen, H. Cooperative Multi-Objective Optimization of DC Multi-Microgrid Systems in Distribution Networks. *Appl. Sci.* **2021**, *11*, 8916.
https://doi.org/10.3390/app11198916

**AMA Style**

Xu Z, Chen C, Dong M, Zhang J, Han D, Chen H. Cooperative Multi-Objective Optimization of DC Multi-Microgrid Systems in Distribution Networks. *Applied Sciences*. 2021; 11(19):8916.
https://doi.org/10.3390/app11198916

**Chicago/Turabian Style**

Xu, Zhiwen, Changsong Chen, Mingyang Dong, Jingyue Zhang, Dongtong Han, and Haowen Chen. 2021. "Cooperative Multi-Objective Optimization of DC Multi-Microgrid Systems in Distribution Networks" *Applied Sciences* 11, no. 19: 8916.
https://doi.org/10.3390/app11198916