WT is a device that can convert wind energy into electric power, which can realize RE to replace traditional power generation and effectively realize the goals of peaking CO₂ emissions and carbon neutrality. The blade rotation of the WT drives the generator set to generate electricity. The blade rotation is affected by the wind speed, and the control system adjusts the working state according to the power generated by the wind turbine generator. For example, when the generator output is above 15% of the rated power for 10 min and above 50% of rated power for more than 2 s, the wind speed is lower than 3 m/s and the mechanical brake stops power generation. However, the wind speed is intermittent and uncertain, which changes with the changes of meteorological and topographic factors such as temperature, landform, and atmospheric pressure. The relationship between the actual power generated and the wind speed is shown as follows (Guofa, 2020): P w t = { P r , v r < v < v o u t P r × ( 1 - v r - v v r - v i n ) , v i n < v < v r 0 , o t h e r s (1) where P w t and P r are the actual output and rated output power of the WT, respectively, and v r , v in , and v out are the rated, cut-in, and cut-out wind speed of the WT, respectively. It can be seen from Eq 1 that when the current wind speed is between the cut-in and cut-out wind speed, the WT outputs according to the rated power P r . It outputs according to the given model when the wind speed reaches v in . When v > v out , to avoid damage to the unit equipment due to excessive wind, the WT is in the fault halting work state.

A PV generator is a device that can convert solar energy into electric power. Like the WT, it could reduce carbon emissions. In addition, it has no noise pollution and has free location distribution. It can be installed in buildings, houses, and other places. Similarly, PV output is affected by natural conditions such as light intensity and ambient temperature; under standard temperature and light intensity, the light intensity is less than 20%, PV is in a fault shutdown state, and power generation is stopped. The relationship between actual PV output P p v and light intensity H is shown as (Guofa, 2020) P p v = { P s t c ⋅ H 0 H s t c ⋅ [ 1 + g ( T − T r ) ] , H ≥ 0.2 H s t c 0 , H < 0.2 H s t c , (2) where H s t c is the standard light intensity; P s t c is the maximum output power under standard conditions; T and T r are the actual temperature and reference temperature, respectively; and g is the power temperature coefficient.

FC is a device that converts the chemical energy of fuel and oxidant into electrical power by chemical reaction. Compared with the WT and PV, the FC has the advantages of fast response and stable power supply, while the disadvantage is that it will produce pollution while burning natural gas to provide power. However, the output cost and conversion efficiency will affect the output of FC, as shown by C f c = 1 L H V n g ⋅ C n g ⋅ P f c η f c (3) where C f c is the power generation cost of the FC, P f c is the output power of the FC, C n g is the fuel cost, and L H V n g and η f c are the low calorific value of natural gas fuel and the conversion coefficient, respectively.

The ESS converts power into other forms or the same form through chemical or physical methods, stores it in the equipment, and releases it when necessary. In the power system, the combination of distributed generation and ESS can not only improve the consumption of RE but also overcome the intermittence and uncertainty of RE. When the battery is in use, the charge state is used to represent the electric quantity. The charge state during charge and discharge is shown as S O C t = ( 1 − ξ ) S O C t − 1 + η c P b a t , c Δ t C B E (4) S O C t = ( 1 − ξ ) S O C t − 1 − P b a t , d Δ t η d C B E (5) where S O C t and S O C t − 1 , respectively, represent the state of charge (SOC) of the battery at time t and t − 1 ; ξ is the self-discharging rate; P bat , c and P bat , d , respectively, represent the charging power and discharge power; η c and η d , respectively, represent the charging and discharge efficiency; and C B E is the rated capacity of the battery.

In the fault state, due to the limitations of generator sets and power connecting lines, the EMS of MMG needs to cut off the flexible load to ensure the safety and economy of MG. However, the flexible load curtailment of MG will reduce the satisfaction of MG and affect the user experience and the safety of the MG. The more flexible loads are curtailed, the lower the satisfaction of the MG. Therefore, the satisfaction of the MMG is shown as (Kaijun and Junyong, 2018) y = ∑ i = 1 3 α i ⋅ ( exp ( 1 − D i , t P l o a d , i , t ) − 1 ) (6) where α i , t is the satisfaction coefficient and D i , t and P l o a d , i , t are the power of flexible load curtailment and power demand before removal of MG i at time t . In the fault state, due to the insufficient output on the supply side, the EMS of the MMG needs to cut off the flexible load to ensure the power balance of the MG and the safe operation of the MG. However, the flexible load curtailment will reduce the satisfaction of MG, which is used to measure the capacity of the MG power supply.

The MG is connected through the power connection line. When there is a transaction between MGs, the logic switch of the power connection line is turned on for power transmission; otherwise, it is turned off, which can promote the consumption of RE and reduce the removal of flexible load. The transaction between MGs affects the removal of flexible load and then affects the satisfaction of MG. At the same time, if there are too many energy transactions, it will affect the profit of MG. Therefore, to reflect the fairness of the transaction between MGs, the energy transaction between MGs is carried out using a contribution bargaining game according to the power output information of each unit of MG by the EMS, as follows: max ( γ i , t ⋅ ρ s e l l / b u y , i , t ⋅ P s e l l / b u y , i , t ) ( γ j , t ⋅ ρ s e l l / b u y , j , t ⋅ P s e l l / b u y , j , t ) , P t r a n s , i , t ≠ 0 (7) γ i , t = P t r a n s , i , t P t r a n s , l , t + P t r a n s , i , t (8) P t r a n s , i , t = { P l o a d , i , t − P w t , i , t − P p v , i , t P l o a d , i , t − P w t , i , t − P p v , i , t − P g r i d , i , t − P f c , i , t , , normal fault, (9) where P t r a n s , i , t is the transaction power demand of MG; P t r a n s , i , t ≠ 0 indicates that there is a transaction demand of MG; P t r a n s , i , t = 0 is no transaction demand of MG; ρ s e l l / b u y , i , t and P s e l l / b u y , i , t , respectively, represent the purchase and sale price and purchase and sale energy of MG i at time t ; P l o a d , i , t , P g r i d , i , t , P w t , i , t , P f c , i , t , and P p v , i , t , respectively, represent the load demand, the power purchased by MG from the distribution network, and the output of WT, PV, and FC; and γ i , t is the contribution factor, which is determined according to the P t r a n s , i , t proportion of the demand of MG i at time t . P t r a n s , i , t is divided by the total demand. When P t r a n s , i , t > 0 , it means that the power of MG i is insufficient; on the contrary, there is surplus power. The contribution factors can make the MG with higher output sell more energy. Similarly, when buying energy, those with large demand are allocated more energy. This distribution mechanism not only ensures the enthusiasm of energy surplus MG to sell energy but also enables energy-deficient MG to participate in the transaction.

The MG EMS receives the output information from the MMG EMS, manages the output of FC, WT, PV, and ESS, loads in the MG, and achieves the goal of maximizing its profits. The cost of purchasing reactive power and other auxiliary services from the distribution network is not considered in this paper. The management strategy is shown in Figure 2. The dispatching profit of each MG can be expressed as follows: E i = ρ i , t ( P l o a d , i , t − D i,t ) − ( P p r i c e ⋅ P m g , i , t + a ⋅ P f c , i , t + b ⋅ P w t , i , t + c ⋅ P p v , i , t + d ⋅ P e s , i , t + ρ s e l l / b u y , i , y ⋅ P s e l l / b u y , i , t ) (10) where ρ i , t ( P l o a d , i , t − D i,t ) represents the energy sales revenue from the MG to the consumer; ρ i , t represents the selling price; D i , t is the power of the flexible load curtailment; P m g , i , t , P f c , i , t , P w t , i , t , P p v , i , t , P e s , i , t , and P s e l l / b u y , i , t , respectively, represent the energy purchase from the MG i to the distribution network, the output of FC, WT, PV, and ESS, and the energy purchase and sales between MGs at time t ; P p r i c e represents the purchase and sale price from the distribution network; P p r i c e > 0 represents the purchase; P p r i c e < 0 represents the sale of energy from the distribution network; and a, b, c, and d are the cost factors.

To evaluate the ability of MMG to absorb RE, this paper proposes the utilization rate of RE (URRE) as the evaluation index, which can be defined as follows: U R R E = ∑ i = 1 N ∑ t = 1 96 P w t , i , t + ∑ i = 1 N ∑ t = 1 96 P p v , i , t − ∑ i = 1 N ∑ t = 1 96 P − g r i d , i , t ∑ i = 1 N ∑ t = 1 96 P w t , i , t max + ∑ i = 1 N ∑ t = 1 96 P p v , i , t max (11) where P p v , i , t , P − g r i d , i , t , P w t , i , t max , and P p v , i , t max , respectively, represent the output of WT and PV, the energy sold by the MG to the distribution network, and the actual maximum power generation of WT and PV.

The MG sends the information of each unit to the MMG EMS for optimization. There is no need to transfer information back and forth between the MG EMS and the MMG EMS, as shown in Figure 3. Using the contradictory relationship between the profit of MG and the satisfaction of MMG, a balance point needs to be found between the individual profit of MG and the overall satisfaction of MMG to ensure their rationality. Therefore, the objective function can be expressed as follows: min ⁡ ln ( ( y i , t a f t e r − y i , t b e f o r e ) ∏ i = 1 ` 3 ( E i , t a f t e r − E i , t b e f o r e ) ) (12) where y i , t a f t e r and y i , t b e f o r e , respectively, represent the satisfaction after and before load curtailment and E i , t a f t e r and E i , t b e f o r e , respectively, represent the profit of the MG after and before load curtailment. The decision variables are P m g , i , t , P f c , i , t , P w t , i , t , P p v , i , t , P e s , i , t , P s e l l / b u y , i , t , and D i , t , and the constraint conditions meet Eqs. 13–21 in the manuscript.

The EMS of MMG considers not only the flexible load curtailment of each MG but also the transaction balance constraints between MGs. Eqs. 13, 14 are the flexible load curtailment constraints of each MG: 0 ≤ D i , t ≤ τ i ⋅ P l o a d , i , t (13) P m g , i , t max + P f c , i , t max + P p v , i , t max + P e s , i t max + P s e l l / b u y , i , t max ≥ P l o a d , i , t − D i , t (14) where, τ i is the proportion of flexible load.

Eqs. 15–17 are the power purchase and sale constraints between MGs, that is, the energy purchase and sale shall be within the maximum acceptable range of MG, to prevent simultaneous purchase and sale of energy and earn intermediate profit: P s e l l / b u y , i , t + P s e l l / b u y , j , t ≤ P t r a n s , l , t (15) P s e l l / b u y , i , t ≤ P t r a n s , i , t (16) P s e l l , i , t ⋅ P b u y , i , t = 0 (17)

Eq 18 is the balance constraint. The power balance of MG is the basic condition to ensure system safety and user experience, which includes the energy purchase from the distribution network and FC, WT, and PV generator output limits: P w t , i , t + P p v , i , t + P e s , i , t + P s e l l / b u y , i , t + P f c , i , t + P g r i d , i , t + D i , t = P l o a d , i , t (18)

To ensure the service life, safety, and reliability of the battery during use, it must also be restrained as follows: S O C t min ≤ S O C t ≤ S O C t max (19) 0 ≤ P b a t , c , i , t , P b a t , d , i , t ≤ P b a t r (20) P b a t , c , i , t ⋅ P b a t , d , i , t = 0 (21) where P b a t , c , i , t , P b a t , d , i , t , P b a t r , S O C t min , and S O C t max , respectively, represent the charge power, discharge power, rated power, and minimum and maximum SOC of ESS. Eq 21 ensures that the ESS cannot charge and discharge at the same time.

This paper takes MG1, MG2, and MG3 as the research objects, which are composed of industrial, residential, and commercial loads, respectively. These loads have different demand characteristics, in which the industrial load includes 10% flexible load and the commercial load includes 20% flexible load. According to the importance of load, the satisfaction sensitivity of the three loads is also different. The industrial load sensitivity is the highest, the commercial load is the second, and the residential load is the last. The 15 min load active power demand curve is shown in Figure 4. The commercial load peak is 09:00–18:00, the residential load peak is 18:00–23:45, and the industrial load peak is 08:00–18:00. The wind speed and light intensity conditions of the three MGs are quite different. The 15 min PV and WT output curves are shown in Figure 5. The intermittent RE of MG 1 occurs at 10:00–15:00, resulting in the fault shutdown of the WT and PV generator. The installed capacity of each unit of MG is shown in Table 1. The experimental environment uses Intel (R) Core (TM) i7-6700hq CPU @ 2.60GHz, Matlab (2020) commercial fmincon solver.

According to the satisfaction of MMG and the balance of MG profit, the flexible load is cut off, as shown in Figure 6. At 10:00–15:00 MG1, the RE is intermittent, resulting in the fault shutdown of WT and PV. To ensure the safety constraints and economy of each MG, the flexible load of each MG is cut off. MG1 supplies the industrial load. At this time, the energies purchased from the distribution network, the use of FC, and the energies purchased from other MGs reach the limit. At this time, the satisfaction with the MG has been very low, so the load is restored to the limit value of 124.57kw. MG2 supplies the residential load. During this period, it belongs to the flat valley period of power consumption. In other periods, when the energy is insufficient, it is necessary to purchase energies from the distribution network or use FC to meet the load demand. Therefore, the flexible load is cut off to ensure the profit of each MG2. The supply of commercial load by MG3 belongs to the peak period of power consumption at this time. However, in order to improve the satisfaction of MG1, it is necessary to sell power to MG1, resulting in a shortage of RE. Like MG2, it is necessary to use FC or purchase energies from the distribution network to meet the load demand and ensure its own profit.

The dispatching of each MG in the fault state is shown in Figures 7–9. MG1 faults during peak power generation of WT and PV, resulting in no surplus energy for MG to sell energies to other MGs. Although there is surplus RE at 03:30, 03:45, and 04:15–04:45, other MGs also have surplus RE at this time and do not trade energy. At 0:00–2:15, 05:00–06:15, and 21:45–23:45, MG1 purchases energy from MG3 and MG2, respectively, to meet their own load demand.

MG2 has surplus RE at 04:15–07:30, and at 03:00–04:45, other MGs also have surplus RE. At this time, MG2 charges the power storage. Due to the limitation of the power of the ESS, it cannot fully absorb the RE, so it sells the excess RE to the distribution grid, and at 05:00–07:30, it gives priority to selling energies to other MGs; after other MGs meet the load demand, they charge the ESS and finally sell energies to the distribution network. At 07:15–07:30, the bargaining transaction distribution mode, the energy sales to MG1 and MG3 tend to be evenly distributed. At 05:45, 06:30, and 06:45, MG3 wants to buy a large number of energies. If most RE is sold to MG3 at this time, the energy purchase revenue of MG1 will be reduced, the principle of fair bargaining is destroyed, and the negotiation breaks down. Only after the energy purchase of MG1 is satisfied, MG3 can purchase a large amount of purchase. At 00:00–00:45, MG3 has surplus RE, but the energy of MG3 cannot fully meet the demand of MG2. The ESS is used to discharge to meet the load demand. At 08:00–09:00 and 14:30–16:15, other MGs have no surplus RE and MG2 uses the energy stored by the ESS. At 21:45–23:45, MG2 is short of energy, but MG3 has surplus energy, so energy is purchased from MG3 to meet the demand of the load. From 10:00 to 15:00, to meet the load demand of MG1, MG2 sells RE to MG1 and meets its load demand through FC or purchasing energies from the distribution network.

MG3 has surplus RE at 00:00–05:30 and 21:45–23:45. Among them, 00:00–02:00 and 21:45–23:45 are insufficient, and MG3 sells energies to them. Similarly, it tends to be evenly distributed before one party fails to meet the energy purchase demand. A lot of energy can be purchased only after MG3 meets the demand, such as at 23:45. At 2:30–04:45, the energy of MG1 and MG2 can meet their own needs. At this time, MG3 charges the excess energy to the ESS; at 08:00–10:15, RE cannot fully meet the load demand, and ESS has a priority to releasing power to meet the load demand. After 10:00–15:00, MG1 fails and MG3 sells energies to MG1, and the FC is used to meet its own load demand in order to balance MG3 satisfaction and profit.

As shown in Figure 6 and Table 2, taking 23:00 and 23:45 as examples, at this time, MG3 has surplus RE, and the total number of RE is less than the sum of the demand for MG1 and MG2. MG1 needs a large number of RE. If MG3 sells a large number of RE to MG1 (strategy 1), MG2 has a small energy purchase and energy purchase income, which violates the fairness of bargaining, and the bargaining negotiation breaks down. At the time of 23:45, MG3 has surplus RE, and the total number of RE is greater than the sum of the demand for MG1 and MG2. Due to power restrictions, MG2 needs a little energy, so MG1 obtains more energy. This bargaining distribution model can reasonably distribute the MG3 surplus RE to other MGs.

As shown in Table 3, during the fault period, since the load curtailment of MG1 reaches the constraint boundary, both the strategy in this paper and the complete removal strategy reach the limit value. Although the dispatching of MG1 is in a loss state, the removal number of such flexible load can make MG1 the most satisfactory. When MG2 and MG3 are fully restored, no load is cut off to achieve the most satisfaction because their profits are sacrificed to improve the satisfaction of MMG. The strategy of this paper is to obtain more profits by balancing satisfaction and income and reducing satisfaction.

The utilization rate of renewable energy is shown in the Table 4. The transaction between MG not only reduces the removal of load but also increases the utilization rate of renewable energy. Due to the fault of MG1 during the peak period of renewable energy power generation, the energy utilization rate is the highest and the wind and light abandonment are the least; MG2 and MG3 sell surplus renewable energy to MG1, increasing the consumption of renewable energy. Their energy utilization rates reached 99.81%, 98.73%, and 98.91% respectively.