5.1.1. Case 1

In this case, the EVs do not participate in the energy dispatch of the MG. Once they reach the MG, the EVs will be charged until the batteries are fully charged. MMGS does not optimize the reactive power output by DC/AC converters.

### 5.1.2. Case 2

In this case, after EVs are connected to the MG, they participate in the energy management system of each MG. Once they reach the MG, the energy in the EV battery will be dispatched by the MG's energy management system until they leave. When the EVs leave the MG at the end of the dispatching, the energy of EVs should be fully charged. This case takes advantage of the across-time energy transmission of EVs in each independent MG, and the optimization of the reactive power output of DC/AC converters is not considered.

### 5.1.3. Case 3

In this case, only the inner-loop economic dispatch model is used to minimize the total cost of MMGS by optimizing the active power output of RESs, EVs, and DC/AC converters. The ATSET of EV between RMGs and OBMGs is used. However, the reactive power output of DC/AC converters is also not optimized. Case 3 can be used as a reference.

### 5.1.4. Case 4

In this case, cooperative multi-objective optimization combines the inner-loop economic dispatch model and the outer-loop reactive power optimization model. The ATSET of EV between RMG and OBMG is considered. By optimizing the active power output of RES, EVs, and DC/AC converters, the total daily operating cost of MMGS is reduced. By optimizing the reactive power output of DC/AC converters, the loss of the distribution network is reduced, and the total economic cost of MMGS is reduced synergistically.

### *5.2. Simulation System Construction*

### 5.2.1. System Introduction

The modified IEEE 33-node system is used to prove the model, whose structure is shown in Figure 6, and its parameters can be obtained from [32]. According to the principle of distribution [32], OBMG and RMG are set at node 19 and node 20, respectively.

**Figure 6.** Topological diagram of the modified IEEE 33-node system.

### 5.2.2. Parameters of RESs

According to the principle of renewable energy consumption [27], the RESs installed in each MG and the power generation cost are given in Table 1. The optimization time interval is 1 h, and the optimization cycle is 1 day (24 h).


**Table 1.** Installed RESs and the power generation cost.

The daily wind speed, radiation intensity, temperature, and load data are adopted in this area. The renewable energy output and load curves of each MG come from [27].

### 5.2.3. Parameters of DC/AC Converter

Considering the performance of the DC/AC converters of MMGS, *Sm* = 1000 kW, the power limit is set as [33]:

$$0 \le \left| P\_{m,t}^G \right| \le 1000 \text{kW} \tag{53}$$

$$0 \le \left| Q\_{m,t}^G \right| \le 1000 \text{kVar} \tag{54}$$

### 5.2.4. Parameters of EVs

Take a BYD E6 electric vehicle as an example, whose parameters are from [34]. The battery capacity is 80 kWh, and the upper limit of charging and discharging power of EVCDI is 7 kW. The charging and discharging efficiency are all 90% [34]. An EV consumes an average of 8% of electricity per way between RMG and OBMG [31]. The additional battery charging/discharging cycle cost of EV is CNY 50 each time [35]. The minimum power of the battery of EV is not less than 20% [36]. Considering the needs of users, the upper and lower limits for the battery are 100% and 35% [27].

### 5.2.5. Other Parameters

The time-of-use (TOU) energy prices in RMG/OBMG from [31] are shown in Figure 7. The carbon emissions factor *ec* is 86.47 g/kWh [29], and the carbon cost factor *kc* is 0.21 CNY/kg [37]. The loss cost coefficient of the distribution network *kil* is 0.74 CNY/kWh [38].

**Figure 7.** (**a**) Prices of energy exchanging in OBMG; (**b**) prices of energy exchanging in RMG.

### *5.3. Simulation Results*

5.3.1. Inner-Loop Optimization Results

1. Case 1

In this case, when EVs are connected to the MG, they are charged immediately. In case 1, the 24 h curve of RESs, EVs, load, and DC/AC converter active power output in OBMG/RMG is shown in Figure 8. EVs are charged as soon as they reach RMG/OBMG. The active power curve of the DC/AC converter represents the active power output curve of the MG to the distribution network. When it is below the *X*-axis, it means that the MG sells electric energy to the distribution network. When it is above the *X*-axis, it means that the MG purchases electric energy from the distribution network. The power curve of EVs has a similar definition. In Figure 8, RMG will allow EVs to be charged at maximum power from 19:00–20:00, and when RESs are insufficient, MEMS will purchase electricity from the distribution network. OBMG is also charging EVs at 9:00–10:00. The total daily operating cost of RMG is CNY 2776.3, and the total daily operating cost of OBMG is CNY 5732.6. Therefore, the total daily operating cost of MMGS is CNY 8508.9.

**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.

### 2. Case 2

In this case, since EVs can participate in the energy dispatching of independent MGs, their across-time energy transmission is used. When the total generated power of the RESs in the MGs is greater than the load, the MEMS will sell the remaining energy to the distribution network or charge the EVs according to the energy prices. When the total power generation of RES is less than the load, the MEMS will purchase electricity from the distribution network or EVs according to the energy prices. In Figure 9, the active power output of RES, EV and DC/AC converters in OBMG and MG are optimized. In OBMG, due to the high energy prices of the distribution network and EVs from 9:00 to 12:00, MEMS choose to let EVs release electric energy. OBMG lowers costs by selling energy to the distribution network. When energy prices are low between 12:00 and 15:00, MEMS fully charges EVs. In RMG, MEMS chooses to charge EVs at 23:00 when energy prices are low. This is to avoid additional battery charge–discharge cycle costs due to discharge, so EVs are only charged. The across-time energy transmission of the EV in the independent MG is fully utilized. Through optimization model calculation, the total daily operating cost of RMG is CNY 2644.1, and the total daily operating cost of OBMG is CNY 5642.1. Therefore, the total daily operating cost of MMGS is CNY 8286.2. Compared with Case 1, the across-time energy transmission of EVs can reduce the overall operating cost of MMGS.

**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.
