A typical topology of ring medium voltage DC distribution system is shown in Figure 1, where three medium voltage AC (MVAC) distribution systems are connected to a DC distribution system via hybrid modular multilevel converters (MMC). Compared with traditional voltage source converter (VSC), MMC can output power with higher quality (Meng et al., 2015). On the other hand, the MMC with hybrid topology has DC fault ride-through capability. The ±10 kV DC bus derived from MMC is looped to connect the EV charging stations, ESSs, PV, WT and multitype loads. All units are located in different locations. The MVDC-DS can get stable power from the three MVAC distribution systems that have stable voltage and frequency.

It is worth mentioning that, in the proposed MVDC-DS, EV charging stations are equipped with independent energy storage equipment. They can adjust the charging and discharging power of EV and energy storage equipment. By this way, the dispatching instructions can be executed accurately. In this process, the control center does not need to consider whether there is EV charging in the station. Therefore, the uncertainty of EV does not affect the execution of dispatching instructions.

When the MVDC-DS operates in the normal state, the control center makes scheduling plans based on the obtained forecast data, and dispatches instructions to the units controlled by control center. Then, the local controller of units receives and executes the instructions in the specified time.

The stability of DC bus voltage is the key to ensure the security and stability of the DC distribution system. However, the proposed MVDC-DS has complex and diverse characteristics. Therefore, appropriate control strategies of all units including MMCs should be properly selected to ensure the stability of DC bus voltage. Master-slave (M-S) control, as a typical coordinated control strategy (Xie et al., 2021), is adopted in this system. The master converter adopts constant voltage control to stabilize the DC bus voltage. In the MVDC-DS mentioned in Figure 1. MMC1 is set as the master converter. The slave MMC generally adopts constant power control. However, the MMC with this control cannot respond to the fluctuations and uncertainties of RESs and loads quickly. Therefore, it is more suitable to apply droop control to slave MMC in this MVDC-DS. The control modes of other units, such as EV charging stations, ESSs and RESs are set as constant power control.

The droop control can keep voltage and power near the given reference value. The expression of traditional droop control is shown in Eq. 1. The detailed introductions of the traditional droop control principles can be obtained in Ref. (Zhu et al., 2018). P − P r e f P r e f = V − V r e f k d r o o p V r e f (1) where k _droop is the droop coefficient, P and V are the real values of power and voltage respectively, P _ref and V _ref are the reference values of power and voltage respectively.

During the operation of MVDC-DS, when the demand of loads or the output of RESs fluctuates slightly, the system can operate stably under the traditional droop control, the deviations of power and voltage are small. When the demand of loads or the output of RESs changes greatly, as shown in the Figure 2, the slave MMC operates at the point P _a, the voltage will be lower than the allowable lower limit of DC voltage, affecting the safety of the MVDC-DS operation.

In order to improve the sensitivity of droop control to voltage deviation when there is a large fluctuation, the slopes of droop function at the positions deviating from reference voltage should be increased. The tan-function and exp-function are used in this paper to improve the traditional droop control. The droop functions modified by the tan-function and exp-function can be expressed as: P − P r e f P r e f = tan ( V − V r e f k d r o o p V r e f ) (2) P − P r e f P r e f = 1 2 ( ( exp ( V − V r e f k d r o o p V r e f ) − 1 ) − ( exp ( − V − V r e f k d r o o p V r e f ) − 1 ) ) (3)

The three different droop curves are shown in Figure 2. Under the conditions of small fluctuations, the curves of the two improved controls and the traditional droop control almost coincide, the control effects are similar. When the demand of loads or the output of RESs changes greatly, the DC voltage of slave MMC deviates too much from the reference value. At this time, the MMC adopted these two different improved droop controls will increase the output power and tend to constant voltage control mode. The tan-droop control is more sensitive to voltage deviation than exp-droop control due to its higher slope. However, when the value of V − V r e f k d r o o p V r e f is near π 2 or - π 2 , the tan-function diverges and there will be no continuity of output variables in actual control process.

The characteristics of these three different controls are summarized as follow.

1) When the power fluctuation is small, the dynamic responses of the three controls are similar.

Therefore, it is more suitable to apply exp-droop control to slave MMC.

Based on the long time forecast data of PV, WT and loads, the reference optimization optimizes the dispatching instructions of each MMC, ESS and EV charging station aiming at minimizing the cost. Based on the short time forecast data, the coefficient optimization optimizes the droop coefficients. In addition, the droop control functions are improved, so that MVDC-DS can respond to the uncertainties and fluctuations of RESs and loads quickly. The input and output of different optimizations and the dual-time scale framework are illustrated in Figure 3.

Noted that, in this paper, the reference optimization is triggered at interval (Wang et al., 2019; Jin et al., 2020; Zhu et al., 2021), which is defined as “optimization interval” T_opt. The time point when the control center makes and sends dispatching instructions to MMC, ESSs and EV charging stations is defined as “dispatching time point”. The time interval between each two adjacent dispatching time points is defined as “dispatching interval” ∆ t L . This interval is also the interval at which the coefficient optimization is triggered. The time points within the dispatching interval are defined as the “intermediate time points”. The time interval between each two adjacent intermediate time points is defined as “intermediated time interval”. In this paper, the dispatching interval is set to 10min and the intermediate time interval is set to 1 min. The relationship of “dispatching time point”, “dispatching interval” and “intermediate time point” are shown in Figure 3.

In this paper, the total duration of reference optimization is set as the sum of three contract periods of EV charging stations, and the optimization interval is set as 1 h. In order to balance the accuracy and speed of solution, according to the property that “the short time forecast data is more accurate than the long time forecast data” (Li et al., 2019b), the optimization period of long time scale is divided into “accurate forecast period” and “other periods”, and the “accurate forecast period” is set to the 1 h near to the “dispatching time point”.

In this paper, the reference optimization minimizes the total cost of the MVDC-DS in long term operation. The total cost function is shown in Eq. 4. f M M C L = ∑ i = 1 N M M C ∑ m = 1 N t L p M M C , i m c m ∆ t L + ∑ i = 1 N M M C ∑ h = 1 N t h p M M C , i h c h ∆ t h (4) where f M M C L is the total cost of purchasing power for N M M C MMCs in long time scale, N t L is the number of dispatching intervals contained in precise period in the reference optimization, N t h is the number of optimized intervals contained in other periods, m and h represents the mth and hth dispatching time point, p M M C is the electric power purchased by MMC, c m and c h are the price at different stages.

The constraint of power balance is shown in Eq. 5. ∑ i = 1 N M M C p M M C , i t + ∑ i = 1 N R E S p R E S , i t = ∑ i = 1 N b r a n c h p b r a n c h , i t + ∑ i = 1 N l o a d p l o a d , i t + ∑ i = 1 N E V p E V , i t + ∑ i = 1 N E S S p E S S , i t (5) where p b r a n c h , i t , p l o a d , i t , p E V , i t , p E S S , i t and p R E S , i t represent line loss power, load power, charging power of EV charging station, charge and discharge power of ESS and RES power respectively.

Considering the operation safety of ESS, the constraints on the state of charge (SOC) are shown in Eqs 6–8. S O C m C E S S + ∆ E E S S m = S O C m + 1 C E S S (6) ∆ E E S S m = { p E S S m η c h ∆ t L   i f   p E S S m > 0 p E S S m η d i s c h ∆ t L   i f   p E S S m < 0 (7) S O C min ≤ S O C m ≤ S O C max (8) where ∆ E E S S m is the total amount of charging at dispatching interval, η c h is the charge efficiency, η d i s c h is the discharge efficiency, C E S S is the capacity of ESS, S O C min and S O C max are the upper and lower limits of SOC respectively.

Considering the contract of EV charging stations, the constraints of them is shown in Eq. 9. ∑ m = 1 N T c o n u p E V , i m ∆ t L = E c o n t r a c t u ,   u = 1 , ⋯ , N c o n t r a c t (9) where, N T c o n u and E c o n t r a c t u are the number of dispatching intervals and specified charging quantity contained in the uth contract period, N c o n t r a c t is the number of contract periods.

In the short time scale, the droop coefficients of each slave MMC are optimized according to the short time forecast data of RESs and loads. The objective function is shown in Eq. 10. f M M C S = ∑ i = 1 N M M C ∑ n = 1 N t S p M M C , i n c n ∆ t S (10) where f M M C S is the total cost of purchasing power for N M M C MMCs in short time scale, N t S is the number of intermediate time points contained in the dispatching interval.

Coefficient optimization is subject to the same constraints of the reference optimization. In addition, there are the droop control constraints of MMC at each intermediate time point. The constraint functions under different droop control functions are shown in Eqs 11, 12. p M M C , i m − p M M C , i n p M M C , i m = v M M C , i m − v M M C , i n k d r o o p , i m v M M C , i m (11) p M M C , i m − p M M C , i n p M M C , i m = 1 2 ( ( exp ( v M M C , i m − v M M C , i n k d r o o p , i m v M M C , i m ) − 1 ) − ( exp ( − v M M C , i m − v M M C , i n k d r o o p , i m v M M C , i m ) − 1 ) ) (12) where v M M C , i n and p M M C , i n represent the real voltage and real power of MMC at the nth intermediate time point, v M M C , i m and p M M C , i m represent the reference voltage and reference power of MMC at the mth intermediate time point, k d r o o p , i m is the optimized droop coefficient.

The first term of the Taylor expansion of Eq. 12 is the same as Eq. 11. Therefore, the k d r o o p , i m in Eq. 12 can adopt the optimized k d r o o p , i m of Eq. 11.

The distribution system used to test the proposed energy management and control strategy is shown in Figure 1, which is a ring medium-voltage DC distribution system. The voltage level is ±10 kV. The line lengths of branches are shown in Table 1, where the resistivity is 0.075 Ω/km. As is shown in Figure 4, the test distribution system has four kinds of loads with different characteristics. LD1 is a sensitive industry load, which has high requirements on power reliability and power quality. LD2 is a new microgrid with high penetrated RESs. The value of LD2 is the net load considering the local consumption. When its value is negative, it means the RESs generate too much power and the extra power is sent to the MVDC-DS. LD3 is a residential load with high flexibility. LD4 is a data center, whose main tasks are large-scale data processing and web searching. It has similar characteristics with LD1. The curves of the aforementioned multiple types of loads and the PV, WT covering 24 h are shown in Figure 5.

The characteristics of each MMC, ESS and EV charging station are set in Table 2. The capacity of ESS is 7 M W × 4 h . In this paper, the initial value of SOC is set to 20%, SOC _min to 10%, SOC _max to 90%, and both charge and discharge efficiency to 90%. According to the system proposed in this paper, the control center dispatches ESS instructions according to the rolling energy optimization management. Therefore, this system does not need to consider the constraint that the SOC of ESS remains unchanged at the beginning and end of the dispatching period. The contracts signed by MVDC-DS and EV charging stations are shown in Table 3, where the fourth contract period specifies the next day(D2) response requirements.

Based on the system described above, the traditional particle swarm optimization is used to solve the dual-time scale energy management problem of the ±10 kV ring MVDC-DS. Then, the results of energy management optimization are taken as the known parameters in the simulation. In the end, the simulation of MVDC-DS is carried out based on the MATLAB/Simulink platform. The economic benefits and the security performances of the proposed energy management and coordinated control strategy are illustrated in the remaining content.

According to the different control modes of slave MMC and ESS configuration, 4 scenarios are set in this paper, as shown in Table 4.

Scenario (1): The slave MMC adopts constant power control.

Scenario (2): The slave MMC adopts traditional droop control with optimized coefficients.

Scenario (3): ESS is not operating, and the slave MMC adopts traditional droop control with optimized coefficients.

Scenario (4): The slave MMC adopts exp-droop control with optimized coefficients.

This section is used to verify the effectiveness of dual-time scale energy management method. The total cost of purchasing power and the total line loss under the four scenarios are shown in Table 5. It can be seen from this table that there is little difference in system economy between Scenario (1), Scenario (2) and Scenario (4). By comparing the cost in Scenario (1) and Scenario (2), we can find that, the improvement of droop control can help system to further reduce the electricity purchasing cost. The detailed analysis of the system economy will be introduced from the impact of ESS on the MVDC-DS and the contract responses of EV charging stations.

The economy of the MVDC-DS in steady-state operation has been analyzed. This section focuses on the power quality and dynamic response characteristics of this system.