3. Case 3

In this case, EVs can transfer energy among multiple MGs, and EVs participate in MMGS energy dispatching. For OBMG, the energy price of the distribution network and the discharging price of EVs are both high, and the difference between the energy price of the distribution network and the discharging price of EV is much higher than that of RMG. Therefore, MMGS's energy management system will discharge almost all EVs as much as possible when EVs are connected to OBMG, and earn more profits. For RMG, its advantage is that the charging price is lower, so MMGEMS will try its best to allow almost all EVs to be charged during the low energy price of RMG to reduce the charging cost of EVs. In Figure 10, EVs are discharged as much as possible in OBMG and then charged as much as possible in RMG. After optimization model calculation, the total daily operating cost of RMG is CNY 2391.8, and the total daily operating cost of OBMG is CNY 5404.1. Therefore, the total daily operating cost of MMGS is CNY 7795.9. However, compared with case 1 case 2, by using the across-time-and-space energy transmission of EVs, the total daily operating cost of the MMGS is the lowest in this case.

**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.

Table 2 is the comparison of the results of the inner-loop economic dispatch in the three cases. Since case 4 and case 3 use the same inner-loop economic dispatch model, their inner-loop output conditions are the same. Here, the effectiveness of the inner-loop economic dispatch model is mainly discussed, so there is no need to show the results in case 4.

In case 1, EVs do not participate in the energy dispatching of the MG, and MMGS has the highest total operating cost. In case 2, the across-time energy transmission of EVs in the independent MG is used to reduce the cost. In case 3 and case 4, the across-time-and-space energy transmission of EVs is considered to further reduce the total daily operating cost of MMGS, which achieves the lowest daily operating cost *COTC*.


**Table 2.** Comparison of operating cost in three cases.

Figure 11 is the remaining capacity curve of EVs, which proves that EVs meet the power constraint in the four cases. It is also verified that the charging and discharging behaviors analyses of EVs in the three cases are correct.

**Figure 11.** Remaining capacity of EVs in three cases.

Table 3 is the cost of EVs' users. Among the three cases, the user cost of case 3 is the lowest. In case 1, EVs do not participate in dispatching, and the cost of users is the highest. In case 2, the cost of users is reduced by the across-time energy transmission. In case 3, the inner-loop economic dispatch is adopted, which makes full use of the across-time-and-space energy transmission of EVs. Additionally, the cost of users is further reduced. Combining with the lowest daily operating cost of MMGS, the inner-loop economic dispatch model using ATSET of EVs achieved a win–win situation for MMGS and EVs' users.

**Table 3.** The cost of EVs' users in three cases in one day.


5.3.2. Outer-Loop Optimization Results

In case 1, case 2, and case 3, the reactive power output of the DC/AC converters is not optimized. In case 4, the outer-loop reactive power optimization model is used to optimize the reactive power output of the DC/AC converters. The optimized reactive power output of the DC/AC converters of RMG and OBMG in case 4 is shown in Figure 12. The converters will absorb or output a certain amount of reactive power to the distribution network at every moment, which is used to optimize the operating network loss of the distribution network, thereby reducing the energy loss cost *CWTC* and total carbon emissions *EC* of MMGS and the distribution network, and cooperating with the inner-loop model to reduce the total economic cost *CETC* of MMGS. The comparison of the results under the four cases is shown in Table 4.

**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.

**Table 4.** Comparison of network loss in the four cases.


By analyzing the distribution network loss under the above different cases, it can be concluded that the reactive power output of the DC/AC converters to the distribution network will affect the distribution network loss. When MMGS is not integrated into the distribution network to work, the original baseline loss *W<sup>B</sup> <sup>S</sup>* of the distribution network is 14,787.9 kW. The distribution network loss under the first three cases is all greater than *W<sup>B</sup> <sup>S</sup>* , while the distribution network loss under case 4 is less than *<sup>W</sup><sup>B</sup> <sup>S</sup>* and lower than the first three cases. Case 3 and case 4 are a set of comparisons. Under the common premise of using the inner-loop optimization model, case 4 that uses reactive power optimization has lower network loss. Figure 13 is the increased network loss diagram for each period of the distribution network which further proves that intelligently optimizing the reactive power output of DC/AC converters through the outer-loop model can effectively reduce the daily network loss of the distribution network.

Table 5 is the network loss cost and energy loss cost in four cases. Among the four cases, the network loss cost *Cil* and the carbon emissions cost *Cco* 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.

**Figure 13.** Increased network loss in four cases.



### 5.3.3. Cooperative Multi-Objective Optimization Results

It can be concluded from Table 6 that, under the cooperative multi-objective optimization model, the total daily economic cost *CETC* 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.

**Table 6.** The final economic cost of MMGS in four cases.


It can be concluded by analyzing the carbon emissions data in Table 7 that the total carbon emissions of the MMGS and distribution network with cooperative multi-objective optimization are the lowest among the four cases, which is 24.0% lower than that for case 1, 24.6% lower than that for case 2, and 29.8% lower than that for case 3, which does not optimize the reactive power. The economic cost of MMGS, the network loss of the distribution network, and the total carbon emission of MMGS and the distribution network were all optimized, which fully proves that the cooperative multi-objective optimization achieved the effect.

**Table 7.** Total carbon emissions in the four cases.

