**1. Introduction**

Since the national carbon neutrality and carbon peak requirements have been put forward [1], low carbon emissions and new energy have become hot research topics [2,3]. It is a trend to replace petrol vehicles with electric vehicles (EVs) and replace regional largescale power grids with microgrids (MGs) containing renewable energy sources (RESs) [4,5]. As the output of RESs is intermittent and uncertain, the MGs need to coordinate with the distribution network to centrally regulate the RESs, which is a challenge to the operation mode of the traditional power system. With the popularity of EVs, the burden of the distribution network will greatly be increased. Additionally, the safe operation of the distribution network will be threatened if EVs are charged in the distribution network without control.

The research on the charging and discharging dispatching strategy of EVs is mainly from the view of the economy [6,7]. Many studies have considered charging/discharging strategies of EVs but overlooked the energy storage characteristics of EVs. Through the bidirectional Vehicle-to-grid (V2G) technology, EVs can also deliver electrical energy to the grid by discharging, and improve the operation of the grid [8–10].

**Citation:** 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

Academic Editor: Marcos Tostado-Véliz

Received: 7 August 2021 Accepted: 21 September 2021 Published: 24 September 2021

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Some research combines EVs with distributed RESs in the MG. In [11], an optimization method for the operation route and charging/discharging time of EVs is proposed, which uses the timely charging/discharging of EVs to consume the output of RESs and reduce the volatility of the equivalent load. In [12], the MG energy management strategy is discussed from the perspective of system operating cost and the consumption efficiency of RESs, and V2G technology has been applied. In [13], the structure and parameter design of the system have been discussed, and the actual MG system using V2G technology has been studied. However, most of the energy scheduling in MGs and the distribution network is to adjust the output of active power.

Some research focuses on the economic dispatch of the multi-microgrid system. In [14], an interconnected multi-microgrids (IMMGs) system using various complementary power sources effectively coordinates the energy sharing/trading among the MGs and the main grid to improve energy efficiency. In [15], A probabilistic modeling of both small-scale energy resources (SSERs) and load demand at each microgrid (MGs) is performed to determine the optimal economic operation of each MG with minimum cost based on the power transaction between the MGs and the main grid. The above does not consider the reactive power exchange between MMG and the main grid.

In the current research on reactive power exchange and network loss, most studies focus on the reactive power of a single distribution network. In [16], the trend of reactive power demand in the distribution network is evaluated. Reactive power demand management plays an important role in the cost-effectiveness and stable operation of the distribution network. A multi-objective planning algorithm for reactive power compensation of radial distribution networks is proposed in [17], which uses unified power quality conditioner (UPQC) compensation for load reactive power to reduce network loss. In [18], the solid-state transformer (SST) is used to supply the load reactive power demand and inject reactive power into the grid, which reduces network losses in a radial distribution network.

Some research focuses on the impact of reactive power optimization on the loss of MG. In [19], a distributed, leaderless and randomized algorithm is proposed, which controls the microgenerators in the island-operated MG system to compensate for reactive power and reduce power distribution loss in MG. A generalized approach for probabilistic optimal reactive power planning is proposed in [20], which can reduce the annual energy losses of the grid-connected MG system.

These papers mentioned above give less consideration to the collaborative optimization of MG clusters and the distribution network. To solve the above problems, a cooperative multi-objective optimization model of a DC multi-microgrid system (MMGS) including RESs, EVs, and DC/AC converters is established. The goal of the model is to obtain the optimal MMGS economic cost and the network loss of the distribution network. The main contributions of this paper are as follows:


cost. The ultimate goal of the cooperative multi-objective is to obtain the optimal daily economic cost.

3. 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*

The MMGS discussed in this paper includes multiple relatively independent MGs in space. The DC multi-microgrid energy management system (MMGEMS) manages all energy transactions in MMGS. Each MG is integrated into the distribution network through power electronic devices and exchanges energy with the distribution network. Each MG contains RESs and EVs charging/discharging infrastructures (EVCDIs). There are two main types of MGs in the MMGS: MGs located in residential areas (RMG) and MGs located in office areas (OBMG). The structure of the MMGS is shown in Figure 1.

**Figure 1.** Structure of a DC multi-microgrid system.

The control of the system is mainly conducted by the collaboration of the MG energy management system (MEMS) and the EVs management system (EVMS). The MEMS is responsible for the energy dispatching of photovoltaics (PVs), wind turbines (WTs), and EVs in MGs, and the EVMS manages the charging and discharging behaviors of EVs. A DC multi-microgrid control system is shown in Figure 2.

### *2.2. DC Microgrid*

The basic structure of the DC microgrid is shown in Figure 3. Each MG is connected to the distribution network through a transformer and a DC/AC converter, which can exchange energy with the distribution network. A connection switch is installed in the grid-connected circuit, which can switch the MG between island operation mode and grid-connected operation mode.

**Figure 2.** Structure of a DC multi-microgrid control system.

**Figure 3.** Structure of a DC microgrid.
