# Three-Level SOC Equalization Control Strategy for MMC-BESS Based on Feedforward Sliding Window Integral Method

Authors: Yuan Cheng; Hui Zhang; Xiaohui Wei; Wenquan Shao
Journal: Shock and Vibration
 (2022)

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## Abstract

The modular multilevel converter of the battery energy storage system (MMC-BESS) not only is suitable for the large-scale energy storage and dispatching of AC and DC grids, but also has a strong ability to suppress power fluctuations caused by the new energy output or grid failures. When an asymmetric voltage or a sudden change in DC load occurs in the AC grid, in order to compensate for the power difference between AC and DC sides, the energy storage submodule of the MMC-BESS will have a large unbalanced charging and discharging current, destroying the equalization state of SOC and seriously affecting energy storage capacity utilization and battery service life. In order to deal with the above problems, in this paper, the characteristics of the power difference between the MMC-BESS phase unit and the upper and lower bridge arms are analyzed. It is found that when considering the fluctuation of the submodule capacitor voltage, the phase unit power has the fundamental frequency AC circulating current component, and the power difference between the upper and lower bridge arms has the DC circulating current component. Therefore, the three-level SOC equalization correction control strategy is proposed based on interphase, upper and lower bridge arms, and submodules, and the feedforward sliding window integral method is introduced into the SOC equalization correction control layer of upper and lower bridge arms, so as to achieve the purpose of more balanced and accurate power distribution among phases and among upper and lower bridge arms of each phase. The simulation results show that the MMC-BESS has effective compensation ability when there is a large power difference in the AC and DC power grid. Under the unbalanced working conditions of the three-phase power grid, the three-phase AC current can quickly reach equalization, and the total harmonic content is 1.38%, and the unbalance degree is 2.4%. Under the same operating conditions, compared with the traditional optimal one-third average method, the SOC equalization correction control strategy proposed in this paper has smaller submodule capacitor voltage fluctuation rate, harmonic distortion rate, and three-phase system circulating current. And the SOC of each phase has a faster equalization convergence speed.


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## Body

## 1. Introduction

In recent years, with the large-scale access of new energy resources, the randomness of its power flow has brought severe challenges to the safe and stable operation of the power grid [1]. In the case of power quality problems mainly due to voltage sag [2] caused by uneven output of new energy sources or sudden load changes in the AC and DC grids, the energy storage system, as a balance medium between power and time scale, can not only buffer the power fluctuation caused by new energy power generation, but also effectively improve the power quality of the power grid [3–5].Modular multilevel converters are currently widely used in high-voltage DC transmission, new energy power generation, and other medium-high-voltage and large-capacity occasions due to their highly modular structure, low harmonic content of AC output, and strong redundancy [6, 7]. Combining the MMC with the lithium battery, which has high energy density, high power density, and high energy conversion efficiency [8], can give full play to the ability of the MMC-BESS to adjust power quality and smooth power fluctuation output in medium and high power occasions [9–11].In AC and DC power grids, the unbalanced grid-side voltage of the three-phase or the large sudden change of AC and DC load makes the system bus voltage unstable and increases the system circulating current, which causes damage to electrical products, misoperation of power grid protection, and reduces the service life of distribution grid operation equipment, etc. [12, 13]. The use of the large-capacity MMC-BESS can supplement the power difference between the AC and DC sides, smooth power fluctuations, and improve the system power quality [14, 15]. However, when the battery in the MMC-BESS is in use, long-term unbalanced high current charging and discharging will affect its SOC equalization state and energy storage capacity utilization, resulting in a decrease in battery life [16].Therefore, it is essential to carry out the research on the SOC equalization control of the MMC-BESS. Literature [17] used zero-sequence voltage and fundamental frequency circulating current injection to achieve the SOC balance among phases and among upper and lower bridge arms, but the calculation principle is complicated. Literature [18] introduced the energy storage MMC system in which the energy storage battery was directly connected to the submodules. The DC circulating current and the fundamental frequency circulating current were extracted and corrected to balance the power among the phases and the upper and lower bridge arms. This method is more complicated in the extraction process and requires an additional DC circulating current suppressor. Literature [19] introduced an MMC energy management system based on the EV battery, which adopted a two-level SOC equalization correction control strategy of phase unit and upper and lower bridge arms to achieve the SOC equalization of each energy storage submodule, but the upper and lower bridge arm equalization correction control of PR control was not considered. Due to the bandwidth limitation, the equalization correction control can only complete the zero-static-error tracking of signals with fixed frequency and cannot guarantee the accuracy of the energy equalization of the upper and lower bridge arms. In literature [20], under the condition of the unbalanced grid-side voltage, DC circulation injection is used to achieve the SOC equalization, but the SOC equalization of upper and lower bridge arms was not considered. Literature [21] used the three-level SOC equalization correction control to achieve the SOC equalization of each energy storage submodule under the unbalanced three-phase power grid, but the SOC equalization correction control layer of the upper and lower arms did not perform signal processing on the output correction. Harmonic signals of different frequencies caused fluctuations in the power difference between the upper and lower bridge arms. Literature [22] introduced that the energy storage battery was connected to the MMC submodule system through a Bidirectional DC-DC, and the SOC control was realized. In the upper and lower bridge arm balance control layer, only the three-phase SOC correction was averaged, and the accuracy of the correction was slightly deficient.Based on the above, this paper proposes an improved three-level SOC equalization correction control strategy for the MMC-BESS based on analyzing the characteristics of the difference between the phase unit power and the bridge arm power. Feedforward is used in the SOC equalization correction control layer of upper and lower bridge arms. The sliding window integral method is used to process the harmonic signals of the correction value, so as to realize the accurate equalization of the power of the upper and lower arms of each phase unit, which can make the SOC of each energy storage submodule more quickly balanced and converged.In Section1, the operating state of the MMC-BESS, the main circuit topology, and the principle of the energy storage submodule are analyzed, and the voltage/current switching function model of phase unit bridge arm is established. Based on this, the internal characteristics of phase unit and bridge arm unit are analyzed. When not considering the capacitor voltage fluctuation of the submodule, the phase unit power is composed of the DC component, the double frequency AC component, and the AC output. The power difference between the upper and lower bridge arms is composed of the fundamental frequency component and the fundamental frequency AC output. If the capacitor voltage fluctuation of the submodule is considered, the phase unit power will increase the fundamental frequency circulating current component, and the power difference between the upper and lower bridge arms will increase the DC circulating current component. The results show that the AC fundamental frequency/double frequency circulation and DC circulation have an important influence on the average power distribution of the phase unit and the accurate power distribution of upper and lower bridge arms.Section2 constructs its double closed-loop control system based on the mathematical model of the MMC-BESS single-phase equivalent circuit and introduces the principle and stability analysis of the double closed-loop control system of the Bidirectional DC-DC converter applied to the energy storage submodule. A three-level SOC control system model is constructed based on interphase, upper and lower bridge arms, and each submodule. In the upper and lower bridge arm equalization control [23], the correction factor and the feedforward sliding window integral method are introduced [24, 25]. Compared with the traditional optimal one-third average method, which only distributes the DC circulation bias to three phases evenly, the feedforward sliding window integral method completely suppresses the DC circulation bias.In Section3, the lithium battery of energy storage submodule is continuously discharged, and the three-level SOC equalization correction controller is started under the conditions of sudden change of DC load/50% drop of two-phase voltage of the three-phase AC power grid. The results show that the DC bus voltage is stable at 20 kV under both working conditions. When the two-phase voltage drops, the three-phase AC current can be effectively compensated and balanced. Compared with the one-third average method, the three-level SOC equalization correction control strategy proposed in this paper makes the capacitor voltage of the submodule stable at 5000 V under the condition of high current discharge, and the fluctuation rate and total harmonic distortion rate are smaller. The three-phase circulating current suppression effect of the system is better, so the phase unit power distribution is more balanced, and the upper and lower bridge arm power distribution is more accurate. Through comparative analysis, the SOC equalization correction control proposed in this paper makes the SOC of three-phase lithium battery have faster equalization convergence speed and better consistency.


## 2. Basic Principle of Energy Storage MMC

### 2.1. MMC-BESS Operating Status Analysis

The AC/DC grid system structure is shown in Figure1. On the AC bus side, the MMC-BESS can be used as a power conversion and energy storage system for wind power generation units, and it can also be connected to a higher voltage grid. On the DC bus side, the MMC-BESS can complete DC energy interaction with photovoltaic power generation units, electric vehicles, energy feedback systems, etc. On the energy storage unit side, if the input/output power of the AC bus side and the DC bus side are equal, the MMC-BESS can be used as an AC/DC power converter. Therefore, the MMC-BESS can be equivalent to a three-port grid for power transmission among the AC bus side, the DC bus side, and the lithium battery energy storage system. There are 12 operating conditions in total. The working conditions simulated in this paper are DC load sudden change and two-phase voltage drop of three-phase network side voltage by 50%. The Bidirectional DC-DC converter of MMC-BESS energy storage system works in boost mode, and the lithium battery is continuously discharged.Figure 1
AC/DC grid system structure.


### 2.2. MMC-BESS Topology

As shown in Figure2, the MMC-BESS has the same three-phase structure and is connected in parallel to the DC bus side. Each phase can be divided into upper and lower bridge arms. Each bridge arm is composed of N energy storage submodules containing lithium batteries in series with the bridge arm inductor Lem and the bridge arm equivalent resistor Rem.Figure 2
MMC-BESS main circuit topology.whereupx and unx represent the output voltage of the upper and lower bridge arm of energy storage submodules of phase X, respectively; ipx and inx represent the currents flowing through upper and lower bridge arms of phase X, respectively; ex and ix represent the x-phase voltage and current of the AC bus side, respectively. The number of phases x = a, b, c. Ls is the balanced filter inductor between the AC bus and the AC output port of the MMC-BESS. Udc represents the DC bus voltage.


#### 2.2.1. Energy Storage Submodule

As shown in Figures3 and 4, the energy storage submodule is composed of a half-bridge submodule and an energy storage system. By controlling the switching states of the half-bridge submodules VT1 and VT2, the charging and discharging of the capacitor Cm are changed to maintain the stability of the DC voltage of each phase. The energy storage system includes the Bidirectional DC-DC, energy storage filter inductor Lbat and the lithium battery. When the Bidirectional DC-DC converter operated in the Buck mode, the half-bridge submodule capacitor charged the lithium battery. The capacitor voltage of the half-bridge submodule was greater than its ideal value, VT3 was turned on, and the half-bridge submodule discharged to the lithium battery. The capacitor voltage of half-bridge submodule was equal to or less than its ideal value, VD4 was turned on, and there was no energy interaction between them. When the Bidirectional DC-DC operated in the Boost mode, the lithium battery charged the capacitor of the half-bridge submodule. The capacitor voltage of the half-bridge submodule was less than its ideal value, VD3 was turned on, and the lithium battery charged the capacitor of the half-bridge submodule. The capacitor voltage of the half-bridge submodule was equal to or greater than its ideal value, VT4 was turned on, and there was no energy interaction between them. From the above Bidirectional DC-DC working mode analysis, it can be seen that the lithium battery of the energy storage system operated in a low-voltage condition, and the charging and discharging current had a high degree of controllability (Table 1).Figure 3
Energy storage submodule.Figure 4
Energy interaction status of the lithium battery in the buck and boost working modes. (a) In the buck mode, with energy interaction. (b) In the buck mode, without energy interaction. (c) In the boost mode, without energy interaction. (d) In the boost mode, with energy interaction.
(a)(b)(c)(d)Table 1
MMC-BESS interaction status and energy storage system working mode.
MMC-BESS interaction statusDC-DC working modeLithium battery charge/discharge statusVT3VT4Submodule capacitor voltage statusCircuitpbat = 1 (absorbed power)Buck modeChargePWM0Usm > UsmrefFigure4(a)Usm < UsmrefFigure4(b)pbat = 1 (output power)Boost modeDischarge0PWMUsm > UsmrefFigure4(c)Usm < UsmrefFigure4(d)Note. Usm represents the actual value of the submodule capacitor voltage; Usmref represents the ideal value of the submodule capacitor voltage.


#### 2.2.2. Bridge Arm Voltage/Current Switching Function Model

During the stable operation of the MMC-BESS, the capacitor of the energy storage submodule not only flows through the bridge arm current for energy interaction with AC and DC sides, but also flows the charging and discharging current of the lithium battery in the energy storage system. Taking one phase as an example, the switching functions of its energy storage submodule is defined as(1)s=1,VT1on,VT2off,0,VT1off,VT2on.Thus, the output voltage of the energy storage submodule port of phase unit bridge arm is expressed as(2)uixk=sixkUsmk,CmdUsmkdt=sixkiix+iLbk,where uixk is the output voltage value of the k-th submodule in the upper or lower bridge arm of one phase, Usmk is the capacitor voltage of the submodule, and sixk is the switching function; iix is the current of the upper or lower bridge arm of one phase, and iLbk is charging and discharging current of the lithium battery of the energy storage system. In equation (2), i = p (upper bridge arm) or n (lower bridge arm), the number of phases x = a, b, c; k = 1 ∼ N representing the number of submodules of the same bridge arm.Therefore, the bridge arm output voltageuix and output current iix can be expressed as(3)uix=∑k=1NsixkUsmk,Cmd∑k=1NsixkUsmkdt=iix+∑k=1NsiskiLbk.Ignoring the equivalent impedance of the bridge arm, the KVL equation for the upper and lower bridge arms is expressed as follows:(4)upx=12Udc−Easinωt,unx=12Udc+Easinωt,where upx and unx are the upper and lower arm voltages of the x-th phase, respectively; Ea is the peak value of the AC voltage; Udc is DC-side voltage.


#### 2.2.3. Analysis of Internal Characteristics of Phase Unit and Bridge Arm Unit

In order to achieve a better control effect and master the control law of the MMC-BESS, the internal characteristics of the phase unit and the bridge arm unit are analyzed. According to equations (4), the following equations are obtained:(5)upx=∑k=1NUsmk2−∑k=1NmUsmksinωt2,unx=∑k=1NUsmk2+∑k=1NmUsmksinωt2,where m is the modulation ratio, and Usmk is the capacitor voltage of the energy storage submodule, which is put into operation in the x-th phase. Based on the single-phase equivalent circuit, the KAL equation of the upper and lower bridge arms is obtained as follows:(6)ipx=13Idc+Ixsinωt−φ2,inx=13Idc−Ixsinωt−φ2,where ipx and inx are the currents flowing through the upper and lower bridge arms, Idc is the DC output current, Ix is the peak value of the phase AC current, and φ is the impedance angle. From (5) and (6), the power of phase unit and upper and lower bridge arms can be obtained expressed as (7) and (8) (without considering the capacitor voltage of the submodule):(7)px=Idc∑k=1NUsmk3︸DC component+Ix∑k=1NmUsmkcos2ωt4︸double frequency AC component−Ix∑k=1NmUsmkcosφ4︸AC output,(8)Δpx=Idc∑k=1NmUsmksinωt3+Ix∑k=1NUsmkcosωtsinφ2︸fundamental frequency AC component−Ix∑k=1NUsmksinωtcosφ2︸AC output,where px represents the power of the phase unit, and Δpx represents the power difference of upper and lower bridge arms.When considering capacitor voltage fluctuation of the submodule,px and Δpx are, respectively, expressed as (9) and (10):(9)px=Idc∑k=1NUsmk3︸DC component+Ix∑k=1NmUsmkcos2ωt4︸double frequency AC component−Ix∑k=1NmUsmkcosφ4︸AC output+Idc∑k=1NmΔUsmksinωt6︸Fundamental frequency ACcirculating current component,(10)Δpx=Idc∑k=1NmUsmksinωt3+Ix∑k=1NUsmkcosωtsinφ2︸fundamental frequency AC component−Ix∑k=1NUsmksinωtcosφ2︸AC output+Idc∑k=1NΔUsmk6︸DC circulatingcurrent component.By comparing (7) with (9), it can be seen that when considering the fluctuation of the capacitor voltage of the submodule, the phase unit power will increase the fundamental frequency AC circulating current component. By comparing (8) with (10), it can be seen that when considering the fluctuation of the capacitor voltage of the submodule, the power difference between upper and lower bridge arms will increase the DC circulating current component. Figures 5 and 6 are the power difference curves between the phase unit and the upper and lower bridge arms, which are drawn according to the actual parameters of the system. In Figure 5, the green curve includes the DC component and AC output. The blue curve includes the DC component, the double frequency AC component, and AC output. The red curve includes DC component, the double frequency AC component, the fundamental frequency circulation component, and AC output. It shows that the fundamental frequency circulating current component formed by the capacitor voltage fluctuation of the submodule caused uneven power distribution of the phase unit.Figure 5
Phase unit power.Figure 6
Power difference between upper and lower bridge arms.In Figure6, the blue curve includes the AC component, the fundamental frequency, and AC output. The red curve includes the fundamental frequency AC component, AC output, and the DC circulation component. It shows that the DC circulating current caused by the capacitor voltage fluctuation of the submodule caused the inaccurate power distribution of the upper and lower bridge arms.Therefore, the essential reason for constructing the three-level SOC equalization correction control is to suppress the fundamental frequency circulation of phase unit and the DC circulation of upper and lower bridge arms caused by the fluctuation of capacitor voltage of submodule.


## 2.1. MMC-BESS Operating Status Analysis

The AC/DC grid system structure is shown in Figure1. On the AC bus side, the MMC-BESS can be used as a power conversion and energy storage system for wind power generation units, and it can also be connected to a higher voltage grid. On the DC bus side, the MMC-BESS can complete DC energy interaction with photovoltaic power generation units, electric vehicles, energy feedback systems, etc. On the energy storage unit side, if the input/output power of the AC bus side and the DC bus side are equal, the MMC-BESS can be used as an AC/DC power converter. Therefore, the MMC-BESS can be equivalent to a three-port grid for power transmission among the AC bus side, the DC bus side, and the lithium battery energy storage system. There are 12 operating conditions in total. The working conditions simulated in this paper are DC load sudden change and two-phase voltage drop of three-phase network side voltage by 50%. The Bidirectional DC-DC converter of MMC-BESS energy storage system works in boost mode, and the lithium battery is continuously discharged.Figure 1
AC/DC grid system structure.


## 2.2. MMC-BESS Topology

As shown in Figure2, the MMC-BESS has the same three-phase structure and is connected in parallel to the DC bus side. Each phase can be divided into upper and lower bridge arms. Each bridge arm is composed of N energy storage submodules containing lithium batteries in series with the bridge arm inductor Lem and the bridge arm equivalent resistor Rem.Figure 2
MMC-BESS main circuit topology.whereupx and unx represent the output voltage of the upper and lower bridge arm of energy storage submodules of phase X, respectively; ipx and inx represent the currents flowing through upper and lower bridge arms of phase X, respectively; ex and ix represent the x-phase voltage and current of the AC bus side, respectively. The number of phases x = a, b, c. Ls is the balanced filter inductor between the AC bus and the AC output port of the MMC-BESS. Udc represents the DC bus voltage.


### 2.2.1. Energy Storage Submodule

As shown in Figures3 and 4, the energy storage submodule is composed of a half-bridge submodule and an energy storage system. By controlling the switching states of the half-bridge submodules VT1 and VT2, the charging and discharging of the capacitor Cm are changed to maintain the stability of the DC voltage of each phase. The energy storage system includes the Bidirectional DC-DC, energy storage filter inductor Lbat and the lithium battery. When the Bidirectional DC-DC converter operated in the Buck mode, the half-bridge submodule capacitor charged the lithium battery. The capacitor voltage of the half-bridge submodule was greater than its ideal value, VT3 was turned on, and the half-bridge submodule discharged to the lithium battery. The capacitor voltage of half-bridge submodule was equal to or less than its ideal value, VD4 was turned on, and there was no energy interaction between them. When the Bidirectional DC-DC operated in the Boost mode, the lithium battery charged the capacitor of the half-bridge submodule. The capacitor voltage of the half-bridge submodule was less than its ideal value, VD3 was turned on, and the lithium battery charged the capacitor of the half-bridge submodule. The capacitor voltage of the half-bridge submodule was equal to or greater than its ideal value, VT4 was turned on, and there was no energy interaction between them. From the above Bidirectional DC-DC working mode analysis, it can be seen that the lithium battery of the energy storage system operated in a low-voltage condition, and the charging and discharging current had a high degree of controllability (Table 1).Figure 3
Energy storage submodule.Figure 4
Energy interaction status of the lithium battery in the buck and boost working modes. (a) In the buck mode, with energy interaction. (b) In the buck mode, without energy interaction. (c) In the boost mode, without energy interaction. (d) In the boost mode, with energy interaction.
(a)(b)(c)(d)Table 1
MMC-BESS interaction status and energy storage system working mode.
MMC-BESS interaction statusDC-DC working modeLithium battery charge/discharge statusVT3VT4Submodule capacitor voltage statusCircuitpbat = 1 (absorbed power)Buck modeChargePWM0Usm > UsmrefFigure4(a)Usm < UsmrefFigure4(b)pbat = 1 (output power)Boost modeDischarge0PWMUsm > UsmrefFigure4(c)Usm < UsmrefFigure4(d)Note. Usm represents the actual value of the submodule capacitor voltage; Usmref represents the ideal value of the submodule capacitor voltage.


### 2.2.2. Bridge Arm Voltage/Current Switching Function Model

During the stable operation of the MMC-BESS, the capacitor of the energy storage submodule not only flows through the bridge arm current for energy interaction with AC and DC sides, but also flows the charging and discharging current of the lithium battery in the energy storage system. Taking one phase as an example, the switching functions of its energy storage submodule is defined as(1)s=1,VT1on,VT2off,0,VT1off,VT2on.Thus, the output voltage of the energy storage submodule port of phase unit bridge arm is expressed as(2)uixk=sixkUsmk,CmdUsmkdt=sixkiix+iLbk,where uixk is the output voltage value of the k-th submodule in the upper or lower bridge arm of one phase, Usmk is the capacitor voltage of the submodule, and sixk is the switching function; iix is the current of the upper or lower bridge arm of one phase, and iLbk is charging and discharging current of the lithium battery of the energy storage system. In equation (2), i = p (upper bridge arm) or n (lower bridge arm), the number of phases x = a, b, c; k = 1 ∼ N representing the number of submodules of the same bridge arm.Therefore, the bridge arm output voltageuix and output current iix can be expressed as(3)uix=∑k=1NsixkUsmk,Cmd∑k=1NsixkUsmkdt=iix+∑k=1NsiskiLbk.Ignoring the equivalent impedance of the bridge arm, the KVL equation for the upper and lower bridge arms is expressed as follows:(4)upx=12Udc−Easinωt,unx=12Udc+Easinωt,where upx and unx are the upper and lower arm voltages of the x-th phase, respectively; Ea is the peak value of the AC voltage; Udc is DC-side voltage.


### 2.2.3. Analysis of Internal Characteristics of Phase Unit and Bridge Arm Unit

In order to achieve a better control effect and master the control law of the MMC-BESS, the internal characteristics of the phase unit and the bridge arm unit are analyzed. According to equations (4), the following equations are obtained:(5)upx=∑k=1NUsmk2−∑k=1NmUsmksinωt2,unx=∑k=1NUsmk2+∑k=1NmUsmksinωt2,where m is the modulation ratio, and Usmk is the capacitor voltage of the energy storage submodule, which is put into operation in the x-th phase. Based on the single-phase equivalent circuit, the KAL equation of the upper and lower bridge arms is obtained as follows:(6)ipx=13Idc+Ixsinωt−φ2,inx=13Idc−Ixsinωt−φ2,where ipx and inx are the currents flowing through the upper and lower bridge arms, Idc is the DC output current, Ix is the peak value of the phase AC current, and φ is the impedance angle. From (5) and (6), the power of phase unit and upper and lower bridge arms can be obtained expressed as (7) and (8) (without considering the capacitor voltage of the submodule):(7)px=Idc∑k=1NUsmk3︸DC component+Ix∑k=1NmUsmkcos2ωt4︸double frequency AC component−Ix∑k=1NmUsmkcosφ4︸AC output,(8)Δpx=Idc∑k=1NmUsmksinωt3+Ix∑k=1NUsmkcosωtsinφ2︸fundamental frequency AC component−Ix∑k=1NUsmksinωtcosφ2︸AC output,where px represents the power of the phase unit, and Δpx represents the power difference of upper and lower bridge arms.When considering capacitor voltage fluctuation of the submodule,px and Δpx are, respectively, expressed as (9) and (10):(9)px=Idc∑k=1NUsmk3︸DC component+Ix∑k=1NmUsmkcos2ωt4︸double frequency AC component−Ix∑k=1NmUsmkcosφ4︸AC output+Idc∑k=1NmΔUsmksinωt6︸Fundamental frequency ACcirculating current component,(10)Δpx=Idc∑k=1NmUsmksinωt3+Ix∑k=1NUsmkcosωtsinφ2︸fundamental frequency AC component−Ix∑k=1NUsmksinωtcosφ2︸AC output+Idc∑k=1NΔUsmk6︸DC circulatingcurrent component.By comparing (7) with (9), it can be seen that when considering the fluctuation of the capacitor voltage of the submodule, the phase unit power will increase the fundamental frequency AC circulating current component. By comparing (8) with (10), it can be seen that when considering the fluctuation of the capacitor voltage of the submodule, the power difference between upper and lower bridge arms will increase the DC circulating current component. Figures 5 and 6 are the power difference curves between the phase unit and the upper and lower bridge arms, which are drawn according to the actual parameters of the system. In Figure 5, the green curve includes the DC component and AC output. The blue curve includes the DC component, the double frequency AC component, and AC output. The red curve includes DC component, the double frequency AC component, the fundamental frequency circulation component, and AC output. It shows that the fundamental frequency circulating current component formed by the capacitor voltage fluctuation of the submodule caused uneven power distribution of the phase unit.Figure 5
Phase unit power.Figure 6
Power difference between upper and lower bridge arms.In Figure6, the blue curve includes the AC component, the fundamental frequency, and AC output. The red curve includes the fundamental frequency AC component, AC output, and the DC circulation component. It shows that the DC circulating current caused by the capacitor voltage fluctuation of the submodule caused the inaccurate power distribution of the upper and lower bridge arms.Therefore, the essential reason for constructing the three-level SOC equalization correction control is to suppress the fundamental frequency circulation of phase unit and the DC circulation of upper and lower bridge arms caused by the fluctuation of capacitor voltage of submodule.


## 2.2.1. Energy Storage Submodule

As shown in Figures3 and 4, the energy storage submodule is composed of a half-bridge submodule and an energy storage system. By controlling the switching states of the half-bridge submodules VT1 and VT2, the charging and discharging of the capacitor Cm are changed to maintain the stability of the DC voltage of each phase. The energy storage system includes the Bidirectional DC-DC, energy storage filter inductor Lbat and the lithium battery. When the Bidirectional DC-DC converter operated in the Buck mode, the half-bridge submodule capacitor charged the lithium battery. The capacitor voltage of the half-bridge submodule was greater than its ideal value, VT3 was turned on, and the half-bridge submodule discharged to the lithium battery. The capacitor voltage of half-bridge submodule was equal to or less than its ideal value, VD4 was turned on, and there was no energy interaction between them. When the Bidirectional DC-DC operated in the Boost mode, the lithium battery charged the capacitor of the half-bridge submodule. The capacitor voltage of the half-bridge submodule was less than its ideal value, VD3 was turned on, and the lithium battery charged the capacitor of the half-bridge submodule. The capacitor voltage of the half-bridge submodule was equal to or greater than its ideal value, VT4 was turned on, and there was no energy interaction between them. From the above Bidirectional DC-DC working mode analysis, it can be seen that the lithium battery of the energy storage system operated in a low-voltage condition, and the charging and discharging current had a high degree of controllability (Table 1).Figure 3
Energy storage submodule.Figure 4
Energy interaction status of the lithium battery in the buck and boost working modes. (a) In the buck mode, with energy interaction. (b) In the buck mode, without energy interaction. (c) In the boost mode, without energy interaction. (d) In the boost mode, with energy interaction.
(a)(b)(c)(d)Table 1
MMC-BESS interaction status and energy storage system working mode.
MMC-BESS interaction statusDC-DC working modeLithium battery charge/discharge statusVT3VT4Submodule capacitor voltage statusCircuitpbat = 1 (absorbed power)Buck modeChargePWM0Usm > UsmrefFigure4(a)Usm < UsmrefFigure4(b)pbat = 1 (output power)Boost modeDischarge0PWMUsm > UsmrefFigure4(c)Usm < UsmrefFigure4(d)Note. Usm represents the actual value of the submodule capacitor voltage; Usmref represents the ideal value of the submodule capacitor voltage.


## 2.2.2. Bridge Arm Voltage/Current Switching Function Model

During the stable operation of the MMC-BESS, the capacitor of the energy storage submodule not only flows through the bridge arm current for energy interaction with AC and DC sides, but also flows the charging and discharging current of the lithium battery in the energy storage system. Taking one phase as an example, the switching functions of its energy storage submodule is defined as(1)s=1,VT1on,VT2off,0,VT1off,VT2on.Thus, the output voltage of the energy storage submodule port of phase unit bridge arm is expressed as(2)uixk=sixkUsmk,CmdUsmkdt=sixkiix+iLbk,where uixk is the output voltage value of the k-th submodule in the upper or lower bridge arm of one phase, Usmk is the capacitor voltage of the submodule, and sixk is the switching function; iix is the current of the upper or lower bridge arm of one phase, and iLbk is charging and discharging current of the lithium battery of the energy storage system. In equation (2), i = p (upper bridge arm) or n (lower bridge arm), the number of phases x = a, b, c; k = 1 ∼ N representing the number of submodules of the same bridge arm.Therefore, the bridge arm output voltageuix and output current iix can be expressed as(3)uix=∑k=1NsixkUsmk,Cmd∑k=1NsixkUsmkdt=iix+∑k=1NsiskiLbk.Ignoring the equivalent impedance of the bridge arm, the KVL equation for the upper and lower bridge arms is expressed as follows:(4)upx=12Udc−Easinωt,unx=12Udc+Easinωt,where upx and unx are the upper and lower arm voltages of the x-th phase, respectively; Ea is the peak value of the AC voltage; Udc is DC-side voltage.


## 2.2.3. Analysis of Internal Characteristics of Phase Unit and Bridge Arm Unit

In order to achieve a better control effect and master the control law of the MMC-BESS, the internal characteristics of the phase unit and the bridge arm unit are analyzed. According to equations (4), the following equations are obtained:(5)upx=∑k=1NUsmk2−∑k=1NmUsmksinωt2,unx=∑k=1NUsmk2+∑k=1NmUsmksinωt2,where m is the modulation ratio, and Usmk is the capacitor voltage of the energy storage submodule, which is put into operation in the x-th phase. Based on the single-phase equivalent circuit, the KAL equation of the upper and lower bridge arms is obtained as follows:(6)ipx=13Idc+Ixsinωt−φ2,inx=13Idc−Ixsinωt−φ2,where ipx and inx are the currents flowing through the upper and lower bridge arms, Idc is the DC output current, Ix is the peak value of the phase AC current, and φ is the impedance angle. From (5) and (6), the power of phase unit and upper and lower bridge arms can be obtained expressed as (7) and (8) (without considering the capacitor voltage of the submodule):(7)px=Idc∑k=1NUsmk3︸DC component+Ix∑k=1NmUsmkcos2ωt4︸double frequency AC component−Ix∑k=1NmUsmkcosφ4︸AC output,(8)Δpx=Idc∑k=1NmUsmksinωt3+Ix∑k=1NUsmkcosωtsinφ2︸fundamental frequency AC component−Ix∑k=1NUsmksinωtcosφ2︸AC output,where px represents the power of the phase unit, and Δpx represents the power difference of upper and lower bridge arms.When considering capacitor voltage fluctuation of the submodule,px and Δpx are, respectively, expressed as (9) and (10):(9)px=Idc∑k=1NUsmk3︸DC component+Ix∑k=1NmUsmkcos2ωt4︸double frequency AC component−Ix∑k=1NmUsmkcosφ4︸AC output+Idc∑k=1NmΔUsmksinωt6︸Fundamental frequency ACcirculating current component,(10)Δpx=Idc∑k=1NmUsmksinωt3+Ix∑k=1NUsmkcosωtsinφ2︸fundamental frequency AC component−Ix∑k=1NUsmksinωtcosφ2︸AC output+Idc∑k=1NΔUsmk6︸DC circulatingcurrent component.By comparing (7) with (9), it can be seen that when considering the fluctuation of the capacitor voltage of the submodule, the phase unit power will increase the fundamental frequency AC circulating current component. By comparing (8) with (10), it can be seen that when considering the fluctuation of the capacitor voltage of the submodule, the power difference between upper and lower bridge arms will increase the DC circulating current component. Figures 5 and 6 are the power difference curves between the phase unit and the upper and lower bridge arms, which are drawn according to the actual parameters of the system. In Figure 5, the green curve includes the DC component and AC output. The blue curve includes the DC component, the double frequency AC component, and AC output. The red curve includes DC component, the double frequency AC component, the fundamental frequency circulation component, and AC output. It shows that the fundamental frequency circulating current component formed by the capacitor voltage fluctuation of the submodule caused uneven power distribution of the phase unit.Figure 5
Phase unit power.Figure 6
Power difference between upper and lower bridge arms.In Figure6, the blue curve includes the AC component, the fundamental frequency, and AC output. The red curve includes the fundamental frequency AC component, AC output, and the DC circulation component. It shows that the DC circulating current caused by the capacitor voltage fluctuation of the submodule caused the inaccurate power distribution of the upper and lower bridge arms.Therefore, the essential reason for constructing the three-level SOC equalization correction control is to suppress the fundamental frequency circulation of phase unit and the DC circulation of upper and lower bridge arms caused by the fluctuation of capacitor voltage of submodule.


## 3. MMC-BESS Hierarchical Control System

The MMC-BESS hierarchical control is shown in Figure7, which is mainly composed of the main control system, the three-level SOC equalization correction control, and the Bidirectional DC-DC converter control system based on PI control. The main control system collected the active and reactive power of the main circuit of the MMC, adjusted it by the PI controller, and generated the three-phase sinusoidal modulation wave after feedforward decoupling. The generated three-phase sinusoidal modulation wave was sent to the carrier phase-shifting modulation through the correction of the three-level SOC equalization control and worked with the submodule capacitor voltage quicksort algorithm to generate the triggering pulse of the power switch of each half-bridge submodule of the MMC-BESS main circuit. The Bidirectional DC-DC converter adopted the double closed-loop control system structure of the outer loop voltage and inner loop current based on the PI controller to realize the energy interaction between the MMC and the lithium battery of the energy storage submodule.Figure 7
MMC-BESS hierarchical control system.


### 3.1. MMC-BESS Main Control System

#### 3.1.1. MMC-BESS Mathematical Model of Single-Phase Equivalent Circuit

Based on the analysis of the internal characteristics of the phase unit and the bridge arm unit, in order to achieve effective control and interaction of the AC and DC-side energy, the MMC-BESS phase unit was used as a “bridge” to establish the AC and DC-side voltage/current relationship. The single-phase equivalent circuit is shown in Figure8, taking phase A as an example for description. The expressions are as follows:(11)LEmdipadt+REmipa+Lsdiadt=Udc2−ea−upa,LEmdinadt+REmina−Lsdiadt=Udc2+ea−una,(12)ipa=Idc3+ia2,ina=Idc3−ia2.Figure 8
MMC-BESS single-phase equivalent circuit model.From equations (11), the following equation can be obtained:(13)Ls+LEm2diadt+REm2ia=una−upa2−ea.According to (13), the AC-side current can be changed by controlling the bridge arm voltage difference.In order to facilitate the design of the control system, (13) can be extended to the three-phase expression, which can be transformed by abc/dq transformation matrix M (θ)abc-dq from the three-phase static coordinate system to the two-phase rotating coordinate system. Thus, the following equations can be obtained:(14)Ps∗=32Eid∗,Qs∗=−32Eiq∗.


#### 3.1.2. Structure and Principle of Main Control System

The main control system of the MMC-BESS is shown in Figure9. Firstly, according to the instantaneous active/reactive power theory, the active/reactive power reference values PS∗ and QS∗ are transformed to obtain the current reference values of axes d and q, namely, id∗ and iq∗.Figure 9
MMC-BESS main control system.Secondly, the three-phase AC currentsia, ib and ic are transformed by abc/dq coordinates to realize the separation of active and reactive power, and then, isd and isq are obtained. The reference value voltages urd∗ and urq∗ of axes d and q are obtained after making the difference with the actual value based on the PI control. According to (14), in order to accelerate the operation of the system and remove the voltage/current coupling on AC side of axes d and q, a feedforward decoupling is added. The three-phase AC voltages ua, ub and uc were transformed by abc/dq coordinates to obtain usd and usq, which were combined with coupling currents of urd∗ and urq∗ of axes d and q to complete the feedforward decoupling to obtain the ideal voltage value of ud∗ and uq∗ of axes d and q. Finally, the three-phase AC voltage modulation waveform was obtained through dq/abc inverse coordinate transformation.


### 3.2. The Bidirectional DC-DC Converter and Its Control

The energy storage system consists of the energy storage battery and the Bidirectional DC-DC converter. The Bidirectional DC-DC converter adopted PI-based double closed-loop control of outer loop voltage/inner loop current. The actual value of the inner loop current was the inductor current of the Bidirectional DC-DC converter, which was controlled to stabilize the power balance of each energy storage submodule. The actual value of the outer loop voltage was the capacitor voltage of the energy storage submodule, which was controlled to stabilize the capacitor voltage of the submodule.The structure of the Bidirectional DC-DC converter control system is shown in Figure10. The difference between the reference value Usmref and the actual value Usm of each phase of the energy storage submodule capacitor voltage is obtained after PI tracking control, thus obtaining the reference value of the inductor current of the energy storage system. Then, the difference is made with the actual value ibat. The loop PI is adjusted and compared with the carrier to generate the PWM pulse signals. The switching between the Buck and the Boost mode needs to set conditions. In the control system, when the reference value of inductor current is multiplied by −1, the Bidirectional DC-DC works in the Boost mode.Figure 10
Bidirectional DC-DC control system.Taking Boost as an example, the stability analysis of the control system is carried out, and the constructed double closed-loop transfer function is(15)Gs=GPI1s.GPI2s1+GPI1s·GPI2s+GPI2s·Cms+LbatCms2.The transfer function structure and the system Bode diagram of the double closed-loop control system of the outer loop voltage and inner loop current based on PI control are shown in Figures11 and 12, respectively.Figure 11
Transfer function structure of the bidirectional DC-DC double closed-loop control system.Figure 12
Comparison of amplitude phase frequency characteristics of bidirectional DC-DC double closed-loop control system.In the transfer function,P1, P2 and P3 are the forward channel loop composed of the half-bridge submodule capacitor voltage Usm, the filter inductor current of energy storage system ibat and the difference between the lithium battery voltage Ubat and Usm. The specific expressions are as follows:(16)P1=−GPI1s·GPI2s·1LbatCms2,P2=−GPI2s·1Lbats,P3=−1LbatCms2.In (15) and (16) and Figure 11, the expressions of GPI1s and GPI2s in frequency domain are kp1+ki1/s and kp2+ki2/s. In this paper, kp1 = 10, ki1 = 0.5, kp2 = 5 and ki2 = 0.2 are taken as basic variables. One variable is changed and expanded by 10 times each time, and the other three variables remain unchanged. A group of system Bode diagram curves are drawn, as shown in Figure 12. After analysis and comparison, kp1 = 100, ki1 = 0.5, kp2 = 5 and ki2 = 0.2 are finally selected. The resonant peak frequency of the double closed-loop control system constructed by this group of variables is about 3184 Hz, and the switching frequency of the Bidirectional DC-DC converter in this paper is 10 kHz. It shows that the switching frequency signal greater than the resonant peak frequency is well suppressed under the high current and rapid charge and discharge condition of the lithium battery in the energy storage system, and the capacitor voltage signal of the submodule less than the resonant peak frequency will complete the zero static error tracking of its ideal input value after passing through the control system.


### 3.3. SOC Equalization Correction Control

The essence of the SOC equalization correction control of the MMC-BESS is to perform power correction on the three phases, upper and lower bridge arms, and their submodules, respectively. Firstly, through the analysis of the three-level SOC equalization control process, the feedforward sliding window integral method was introduced into the upper and lower bridge arm control layer to form a more accurate equalization correction, so as to make full use of the lithium battery capacity of the energy storage submodule.


#### 3.3.1. Phase-To-Phase SOC Equalization Correction Control

In order to effectively correct the DC current components in the three-phase MMC-BESS, during the SOC balance correction control of the phase unit, the PI adjustment method is used to realize the zero-static-error tracking of the average SOC of each-phase submodule to the average SOC of the three-phase submodule.The specific phase equalization control structure is shown in Figure13. The average SOC of lithium battery of each energy storage submodule in phase X is SOCx, ph_ave, and the average SOC of lithium battery of the three-phase energy storage submodule is SOCph_ave. The mathematical expression is as follows:(17)SOCx,ph_ave=∑k=12NSOCx,k2N,SOCph_ave=SOCa,ph_ave+SOCb,ph_ave+SOCc,ph_ave3.Figure 13
Phase-to-phase SOC equalization correction control.


#### 3.3.2. SOC Equalization Correction Control of Upper and Lower Bridge Arms Based on Feedforward Sliding Window Integral

(18)SOCpx_arm_ave=∑k=1NSOCpxkN,SOCnx_arm_ave=∑k=1NSOCnxkN.It can be seen from formula (18) that the DC circulating current has the same effect on the power of the upper and lower bridge arms, and the power flow can be adjusted among the three phases. In order to obtain more accurate power distribution of the power of the upper and lower bridge arms, the upper and lower bridge arm correction factor hcps_x and the feedforward sliding window integral are introduced. As shown in Figure 14, the correction factor hcps_x contains the DC component, the fundamental frequency AC component, and other frequency AC components, which are multiplied by earef and go through the sliding window integral to obtain the equalization correction of the upper and lower bridge arms Uarm_cps∗ containing only the fundamental frequency and a small amount of AC component of other frequencies. The filtering integral process is as follows:(19)∫tt+Tsinωt⋅Asinωt+∑k′=2∞Bk′⋅sink′ωt+φk′dt.Figure 14
Equalization correction control of upper and lower bridge arms.BothT in (19) and Z-N in Figure 14 represent the delay, with the delay time being 0.2 s, and the minimum filtering frequency is 5 Hz.


#### 3.3.3. SOC Equalization Correction Control in Bridge Arms

The SOC equalization correction control of the lithium battery of each submodule in the bridge arms is the same as the interphase SOC equalization correction control. Making the difference between the average value of the SOC of the lithium battery of the upper and lower bridge arm energy storage submodule and the actual value of the lithium battery of each submodule, the zero-static-error tracking of both through the PI controller was realized. When the MMC-BESS is in discharging condition, the Bidirectional DC-DC worked in the Boost mode. If the SOC value of the lithium battery was large, the discharging current would increase; if the SOC value was small, the discharging current would decrease. Under charging conditions, the Bidirectional DC-DC is switched to the Buck mode, and if the SOC value of the lithium battery was small, the charging current would increase; if the SOC was large, the charging current would be reduced.Eventually, the working state modulation commands of each submodule of the MMC-SCESS were modified and acted on each of the three-phase bridge arms and their submodules, respectively, so that the phase-to-phase power and the power of upper and lower bridge arms was corrected, and then it was combined with the quicksort algorithm of the submodule capacitor voltage, thus quickly balancing the capacitor voltage of each phase submodule. Based on this, the double frequency circulating current among phases was suppressed, and the system loss was reduced, as shown in Figure15.Figure 15
SOC equalization correction control of submodules in bridge arms.


## 3.1. MMC-BESS Main Control System

### 3.1.1. MMC-BESS Mathematical Model of Single-Phase Equivalent Circuit

Based on the analysis of the internal characteristics of the phase unit and the bridge arm unit, in order to achieve effective control and interaction of the AC and DC-side energy, the MMC-BESS phase unit was used as a “bridge” to establish the AC and DC-side voltage/current relationship. The single-phase equivalent circuit is shown in Figure8, taking phase A as an example for description. The expressions are as follows:(11)LEmdipadt+REmipa+Lsdiadt=Udc2−ea−upa,LEmdinadt+REmina−Lsdiadt=Udc2+ea−una,(12)ipa=Idc3+ia2,ina=Idc3−ia2.Figure 8
MMC-BESS single-phase equivalent circuit model.From equations (11), the following equation can be obtained:(13)Ls+LEm2diadt+REm2ia=una−upa2−ea.According to (13), the AC-side current can be changed by controlling the bridge arm voltage difference.In order to facilitate the design of the control system, (13) can be extended to the three-phase expression, which can be transformed by abc/dq transformation matrix M (θ)abc-dq from the three-phase static coordinate system to the two-phase rotating coordinate system. Thus, the following equations can be obtained:(14)Ps∗=32Eid∗,Qs∗=−32Eiq∗.


### 3.1.2. Structure and Principle of Main Control System

The main control system of the MMC-BESS is shown in Figure9. Firstly, according to the instantaneous active/reactive power theory, the active/reactive power reference values PS∗ and QS∗ are transformed to obtain the current reference values of axes d and q, namely, id∗ and iq∗.Figure 9
MMC-BESS main control system.Secondly, the three-phase AC currentsia, ib and ic are transformed by abc/dq coordinates to realize the separation of active and reactive power, and then, isd and isq are obtained. The reference value voltages urd∗ and urq∗ of axes d and q are obtained after making the difference with the actual value based on the PI control. According to (14), in order to accelerate the operation of the system and remove the voltage/current coupling on AC side of axes d and q, a feedforward decoupling is added. The three-phase AC voltages ua, ub and uc were transformed by abc/dq coordinates to obtain usd and usq, which were combined with coupling currents of urd∗ and urq∗ of axes d and q to complete the feedforward decoupling to obtain the ideal voltage value of ud∗ and uq∗ of axes d and q. Finally, the three-phase AC voltage modulation waveform was obtained through dq/abc inverse coordinate transformation.


## 3.1.1. MMC-BESS Mathematical Model of Single-Phase Equivalent Circuit

Based on the analysis of the internal characteristics of the phase unit and the bridge arm unit, in order to achieve effective control and interaction of the AC and DC-side energy, the MMC-BESS phase unit was used as a “bridge” to establish the AC and DC-side voltage/current relationship. The single-phase equivalent circuit is shown in Figure8, taking phase A as an example for description. The expressions are as follows:(11)LEmdipadt+REmipa+Lsdiadt=Udc2−ea−upa,LEmdinadt+REmina−Lsdiadt=Udc2+ea−una,(12)ipa=Idc3+ia2,ina=Idc3−ia2.Figure 8
MMC-BESS single-phase equivalent circuit model.From equations (11), the following equation can be obtained:(13)Ls+LEm2diadt+REm2ia=una−upa2−ea.According to (13), the AC-side current can be changed by controlling the bridge arm voltage difference.In order to facilitate the design of the control system, (13) can be extended to the three-phase expression, which can be transformed by abc/dq transformation matrix M (θ)abc-dq from the three-phase static coordinate system to the two-phase rotating coordinate system. Thus, the following equations can be obtained:(14)Ps∗=32Eid∗,Qs∗=−32Eiq∗.


## 3.1.2. Structure and Principle of Main Control System

The main control system of the MMC-BESS is shown in Figure9. Firstly, according to the instantaneous active/reactive power theory, the active/reactive power reference values PS∗ and QS∗ are transformed to obtain the current reference values of axes d and q, namely, id∗ and iq∗.Figure 9
MMC-BESS main control system.Secondly, the three-phase AC currentsia, ib and ic are transformed by abc/dq coordinates to realize the separation of active and reactive power, and then, isd and isq are obtained. The reference value voltages urd∗ and urq∗ of axes d and q are obtained after making the difference with the actual value based on the PI control. According to (14), in order to accelerate the operation of the system and remove the voltage/current coupling on AC side of axes d and q, a feedforward decoupling is added. The three-phase AC voltages ua, ub and uc were transformed by abc/dq coordinates to obtain usd and usq, which were combined with coupling currents of urd∗ and urq∗ of axes d and q to complete the feedforward decoupling to obtain the ideal voltage value of ud∗ and uq∗ of axes d and q. Finally, the three-phase AC voltage modulation waveform was obtained through dq/abc inverse coordinate transformation.


## 3.2. The Bidirectional DC-DC Converter and Its Control

The energy storage system consists of the energy storage battery and the Bidirectional DC-DC converter. The Bidirectional DC-DC converter adopted PI-based double closed-loop control of outer loop voltage/inner loop current. The actual value of the inner loop current was the inductor current of the Bidirectional DC-DC converter, which was controlled to stabilize the power balance of each energy storage submodule. The actual value of the outer loop voltage was the capacitor voltage of the energy storage submodule, which was controlled to stabilize the capacitor voltage of the submodule.The structure of the Bidirectional DC-DC converter control system is shown in Figure10. The difference between the reference value Usmref and the actual value Usm of each phase of the energy storage submodule capacitor voltage is obtained after PI tracking control, thus obtaining the reference value of the inductor current of the energy storage system. Then, the difference is made with the actual value ibat. The loop PI is adjusted and compared with the carrier to generate the PWM pulse signals. The switching between the Buck and the Boost mode needs to set conditions. In the control system, when the reference value of inductor current is multiplied by −1, the Bidirectional DC-DC works in the Boost mode.Figure 10
Bidirectional DC-DC control system.Taking Boost as an example, the stability analysis of the control system is carried out, and the constructed double closed-loop transfer function is(15)Gs=GPI1s.GPI2s1+GPI1s·GPI2s+GPI2s·Cms+LbatCms2.The transfer function structure and the system Bode diagram of the double closed-loop control system of the outer loop voltage and inner loop current based on PI control are shown in Figures11 and 12, respectively.Figure 11
Transfer function structure of the bidirectional DC-DC double closed-loop control system.Figure 12
Comparison of amplitude phase frequency characteristics of bidirectional DC-DC double closed-loop control system.In the transfer function,P1, P2 and P3 are the forward channel loop composed of the half-bridge submodule capacitor voltage Usm, the filter inductor current of energy storage system ibat and the difference between the lithium battery voltage Ubat and Usm. The specific expressions are as follows:(16)P1=−GPI1s·GPI2s·1LbatCms2,P2=−GPI2s·1Lbats,P3=−1LbatCms2.In (15) and (16) and Figure 11, the expressions of GPI1s and GPI2s in frequency domain are kp1+ki1/s and kp2+ki2/s. In this paper, kp1 = 10, ki1 = 0.5, kp2 = 5 and ki2 = 0.2 are taken as basic variables. One variable is changed and expanded by 10 times each time, and the other three variables remain unchanged. A group of system Bode diagram curves are drawn, as shown in Figure 12. After analysis and comparison, kp1 = 100, ki1 = 0.5, kp2 = 5 and ki2 = 0.2 are finally selected. The resonant peak frequency of the double closed-loop control system constructed by this group of variables is about 3184 Hz, and the switching frequency of the Bidirectional DC-DC converter in this paper is 10 kHz. It shows that the switching frequency signal greater than the resonant peak frequency is well suppressed under the high current and rapid charge and discharge condition of the lithium battery in the energy storage system, and the capacitor voltage signal of the submodule less than the resonant peak frequency will complete the zero static error tracking of its ideal input value after passing through the control system.


## 3.3. SOC Equalization Correction Control

The essence of the SOC equalization correction control of the MMC-BESS is to perform power correction on the three phases, upper and lower bridge arms, and their submodules, respectively. Firstly, through the analysis of the three-level SOC equalization control process, the feedforward sliding window integral method was introduced into the upper and lower bridge arm control layer to form a more accurate equalization correction, so as to make full use of the lithium battery capacity of the energy storage submodule.


### 3.3.1. Phase-To-Phase SOC Equalization Correction Control

In order to effectively correct the DC current components in the three-phase MMC-BESS, during the SOC balance correction control of the phase unit, the PI adjustment method is used to realize the zero-static-error tracking of the average SOC of each-phase submodule to the average SOC of the three-phase submodule.The specific phase equalization control structure is shown in Figure13. The average SOC of lithium battery of each energy storage submodule in phase X is SOCx, ph_ave, and the average SOC of lithium battery of the three-phase energy storage submodule is SOCph_ave. The mathematical expression is as follows:(17)SOCx,ph_ave=∑k=12NSOCx,k2N,SOCph_ave=SOCa,ph_ave+SOCb,ph_ave+SOCc,ph_ave3.Figure 13
Phase-to-phase SOC equalization correction control.


### 3.3.2. SOC Equalization Correction Control of Upper and Lower Bridge Arms Based on Feedforward Sliding Window Integral

(18)SOCpx_arm_ave=∑k=1NSOCpxkN,SOCnx_arm_ave=∑k=1NSOCnxkN.It can be seen from formula (18) that the DC circulating current has the same effect on the power of the upper and lower bridge arms, and the power flow can be adjusted among the three phases. In order to obtain more accurate power distribution of the power of the upper and lower bridge arms, the upper and lower bridge arm correction factor hcps_x and the feedforward sliding window integral are introduced. As shown in Figure 14, the correction factor hcps_x contains the DC component, the fundamental frequency AC component, and other frequency AC components, which are multiplied by earef and go through the sliding window integral to obtain the equalization correction of the upper and lower bridge arms Uarm_cps∗ containing only the fundamental frequency and a small amount of AC component of other frequencies. The filtering integral process is as follows:(19)∫tt+Tsinωt⋅Asinωt+∑k′=2∞Bk′⋅sink′ωt+φk′dt.Figure 14
Equalization correction control of upper and lower bridge arms.BothT in (19) and Z-N in Figure 14 represent the delay, with the delay time being 0.2 s, and the minimum filtering frequency is 5 Hz.


### 3.3.3. SOC Equalization Correction Control in Bridge Arms

The SOC equalization correction control of the lithium battery of each submodule in the bridge arms is the same as the interphase SOC equalization correction control. Making the difference between the average value of the SOC of the lithium battery of the upper and lower bridge arm energy storage submodule and the actual value of the lithium battery of each submodule, the zero-static-error tracking of both through the PI controller was realized. When the MMC-BESS is in discharging condition, the Bidirectional DC-DC worked in the Boost mode. If the SOC value of the lithium battery was large, the discharging current would increase; if the SOC value was small, the discharging current would decrease. Under charging conditions, the Bidirectional DC-DC is switched to the Buck mode, and if the SOC value of the lithium battery was small, the charging current would increase; if the SOC was large, the charging current would be reduced.Eventually, the working state modulation commands of each submodule of the MMC-SCESS were modified and acted on each of the three-phase bridge arms and their submodules, respectively, so that the phase-to-phase power and the power of upper and lower bridge arms was corrected, and then it was combined with the quicksort algorithm of the submodule capacitor voltage, thus quickly balancing the capacitor voltage of each phase submodule. Based on this, the double frequency circulating current among phases was suppressed, and the system loss was reduced, as shown in Figure15.Figure 15
SOC equalization correction control of submodules in bridge arms.


## 3.3.1. Phase-To-Phase SOC Equalization Correction Control

In order to effectively correct the DC current components in the three-phase MMC-BESS, during the SOC balance correction control of the phase unit, the PI adjustment method is used to realize the zero-static-error tracking of the average SOC of each-phase submodule to the average SOC of the three-phase submodule.The specific phase equalization control structure is shown in Figure13. The average SOC of lithium battery of each energy storage submodule in phase X is SOCx, ph_ave, and the average SOC of lithium battery of the three-phase energy storage submodule is SOCph_ave. The mathematical expression is as follows:(17)SOCx,ph_ave=∑k=12NSOCx,k2N,SOCph_ave=SOCa,ph_ave+SOCb,ph_ave+SOCc,ph_ave3.Figure 13
Phase-to-phase SOC equalization correction control.


## 3.3.2. SOC Equalization Correction Control of Upper and Lower Bridge Arms Based on Feedforward Sliding Window Integral

(18)SOCpx_arm_ave=∑k=1NSOCpxkN,SOCnx_arm_ave=∑k=1NSOCnxkN.It can be seen from formula (18) that the DC circulating current has the same effect on the power of the upper and lower bridge arms, and the power flow can be adjusted among the three phases. In order to obtain more accurate power distribution of the power of the upper and lower bridge arms, the upper and lower bridge arm correction factor hcps_x and the feedforward sliding window integral are introduced. As shown in Figure 14, the correction factor hcps_x contains the DC component, the fundamental frequency AC component, and other frequency AC components, which are multiplied by earef and go through the sliding window integral to obtain the equalization correction of the upper and lower bridge arms Uarm_cps∗ containing only the fundamental frequency and a small amount of AC component of other frequencies. The filtering integral process is as follows:(19)∫tt+Tsinωt⋅Asinωt+∑k′=2∞Bk′⋅sink′ωt+φk′dt.Figure 14
Equalization correction control of upper and lower bridge arms.BothT in (19) and Z-N in Figure 14 represent the delay, with the delay time being 0.2 s, and the minimum filtering frequency is 5 Hz.


## 3.3.3. SOC Equalization Correction Control in Bridge Arms

The SOC equalization correction control of the lithium battery of each submodule in the bridge arms is the same as the interphase SOC equalization correction control. Making the difference between the average value of the SOC of the lithium battery of the upper and lower bridge arm energy storage submodule and the actual value of the lithium battery of each submodule, the zero-static-error tracking of both through the PI controller was realized. When the MMC-BESS is in discharging condition, the Bidirectional DC-DC worked in the Boost mode. If the SOC value of the lithium battery was large, the discharging current would increase; if the SOC value was small, the discharging current would decrease. Under charging conditions, the Bidirectional DC-DC is switched to the Buck mode, and if the SOC value of the lithium battery was small, the charging current would increase; if the SOC was large, the charging current would be reduced.Eventually, the working state modulation commands of each submodule of the MMC-SCESS were modified and acted on each of the three-phase bridge arms and their submodules, respectively, so that the phase-to-phase power and the power of upper and lower bridge arms was corrected, and then it was combined with the quicksort algorithm of the submodule capacitor voltage, thus quickly balancing the capacitor voltage of each phase submodule. Based on this, the double frequency circulating current among phases was suppressed, and the system loss was reduced, as shown in Figure15.Figure 15
SOC equalization correction control of submodules in bridge arms.


## 4. Simulation

In order to verify the effectiveness of the proposed three-level SOC equalization correction control strategy based on the feedforward sliding window integral method, a three-phase five-level MMC-BESS model was constructed in the Matlab/Simulink environment. The parameters are shown in Table2. Due to the limitation of the computer system performance, the number of submodules of the upper and lower bridge arms was set to 4 in the simulation verification. In practical applications, due to the scalability of the MMC-BESS, more input submodules could jointly withstand the DC voltage of 20 kV on the DC side of each phase unit. This paper focuses on the following three aspects under the discharging state of lithium battery energy storage system: (1) the sudden change of DC-side load, aiming at stabilizing the DC bus voltage; (2) the two-phase drop of the three-phase grid-side voltage and the three-phase current balance compensation capability; (3) a faster equalization convergence speed of the SOC of each phase of the proposed three-level SOC equalization correction control strategy under the above two working conditions.Table 2
System simulation parameters.
ParametersValueThe number of bridge arm submodules of each phase n4Rated capacityS/MVA5Grid phase voltageEj/kV5.7DC-side voltageUdc/kV20Bridge arm filter inductorLEm/mH2Submodule capacitorCm/mF4.7Grid-side filter inductorLS/mH4DC/DC inductorLbat/mH3Switching frequencyf/Hz1000As shown in Figures16–18, in the first working condition, the DC load increased suddenly at 0.5 s after the system was started. In order to quickly stabilize the DC bus voltage and maintain power balance, the MMC-BESS input the lithium battery and the three-level SOC balance correction controller. The Bidirectional DC-DC of the MMC-BESS energy storage system worked in the Boost mode, and the lithium battery continued to discharge. When the load changed suddenly, the DC voltage was 19800 V and finally stabilized at 20 kV. In the second working condition, after the first working condition lasted for 0.5 s, at 1 s, the DC load recovered, the three-phase grid-side voltages B and C dropped by 50%, and the peak phase voltage changed from 8000 V to 4000 V. The Bidirectional DC-DC of the MMC-BESS energy storage system still worked in the Boost mode, and the lithium battery continued to discharge to compensate for the difference of the three-phase power, so that the three-phase grid-side current increased and balanced. The DC bus voltage was stable at about 20 kV, the maximum variable was 1500 V, and the steady-state error was 7.5%. The maximum peak value of the three-phase current was 231.9 A, the effective value of the three-phase average current was 160.96 A, and the unbalance degree was 0.024. The parameters are shown in Table 3. The total harmonic distortion rate of the three-phase current is shown in Figure 19. Five power frequency cycles after 5.66 s were selected for measurement, and the total harmonic distortion rate was 1.38%.Figure 16
System three-phase voltage/current and DC voltage at 0.4 ∼ 2.2 s.Figure 17
Three-phase AC voltage and current at 5.66 s ∼ 5.76 s.Figure 18
DC-side voltage and current at 0 ∼ 9 s.Table 3
Unbalance degree parameters of three phases.
PhasesxCurrent peak of three phases (A)Current effective value of three phases (A)Average value of effective value of three-phase current (A)Differential phase current (effective value of phase current - average value of effective value of three-phase current) (A)Three-phase current unbalance degree (max effective value of differential phase current divided by average value of effective value of three-phase current)A-phase228.8161.81160.960.852.4%B-phase222.1157.073.89C-phase231.9164.003.04Figure 19
Three-phase grid-side current THD at 5 s.The MMC-BESS acted as a bridge for energy conversion between the AC side, the DC side, and the energy storage battery. The stability of the capacitor voltage of submodule of each phase could prove the stability of the power input and output during the energy conversion period. The stability of the submodule capacitor voltage could not only reduce the double frequency circulation formed by the pressure difference between the phases of the MMC-BESS, but also reduce the circulating current in the upper and lower bridge arms formed by the fluctuation of the submodule capacitor voltage in the bridge arms of each phase.Under the same operating condition, when the three-phase grid-side voltage dropped by 50%, the maximum capacitor voltage of the submodule of thec-phase upper and lower bridge arm before the improvement by using the one-third average method was 5009 V, and the minimum was 4991 V. The maximum capacitor voltage of the submodule of the improved c-phase upper bridge arm was 5008 V, and the minimum was 4992 V. In the range of 0.5 s to 9 s, the SOC equalization correction control strategy proposed in this paper and the three-stage SOC equalization correction control strategy using one-third average method were compared and analyzed with the total harmonic distortion rate of capacitor voltage of each submodule of phase C with 50 Hz as the fundamental frequency. It could be seen from the comparative analysis of Figure 20 and Table 4 that the total harmonic distortion rate of capacitor voltage of the submodule of c-phase lower bridge arm with the two methods is less than that of the upper bridge arm. For the same submodule, the total harmonic distortion rate of the capacitor voltage of the submodule using the method proposed in this paper is less than that of the same submodule using the one-third average method. It indirectly proved that the MMC-BESS using the SOC equalization correction control strategy proposed in this paper has more average phase-to-phase power distribution and more accurate power distribution of upper and lower bridge arms.Figure 20
Analysis of harmonic distortion rate of capacitor voltage ofc-phase submodule. (a) Harmonic distortion rate of each submodule using one-third average method. (b) Harmonic distortion rate of each submodule of sliding window integral method.
(a)(b)Table 4
Capacitor voltage distortion rate ofc-phase submodule using one-third average method and sliding window integral method.
Harmonic distortion rate of capacitor voltage of submoduleOne-third average method:5 s5.2 s5.4 s5.6 s5.8 sUpper bridge arm of phaseC (sm1 ∼ sm4)13.18%13.95%13.94%15.81%14.34%Lower bridge arm of phaseC (sm5 ∼ sm8)12.51%13.76%13.35%14.72%13.34%Sliding window integral method:5 s5.2 s5.4 s5.6 s5.8 sUpper bridge arm of phaseC (sm1 ∼ sm4)13.07%13.39%13.49%13.62%14.01%Lower bridge arm of phaseC (sm5 ∼ sm8)12.26%12.80%13.24%12.81%13.26%It can be seen from (10) and (11) that when the capacitor voltage fluctuation and total harmonic distortion rate of the submodule were smaller, the difference between the phase-to-phase power of the system and the power of the upper and lower bridge arms of each phase should be smaller, so the three-phase circulating current should also be smaller. The reduction of the three-phase circulating current of the system was helpful in improving the efficiency of the MMC-BESS. Figure 21 shows the three-phase circulating current of the system using the two methods. The results showed that after the system was stable, under the working conditions with the load sudden change and two-phase voltage drop, the two methods could effectively suppress the three-phase circulating current, but the effect of using feedforward sliding window integral method on circulating current suppression was more obvious, and the peak value of circulating current was smaller. The maximum peak values of three-phase circulation of A, B, and C using one-third average method were 123.3 A, 107.7 A, and 81.2 A, respectively. After the improvement, the maximum peak values of the three-phase circulation of A, B, and C using feedforward sliding window integral method were 85.83 A, 73.91 A, and 70.01 A, respectively.Figure 21
MMC-BESS three-phase circulation. (a) One-third average method, MMC-BESS three-phase circulation. (b) Sliding window integral method, MMC-BESS three-phase circulation.
(a)(b)Figure22 shows the output power of three-phase battery: the DC load increased suddenly at 0.5 s. With the goal of stabilizing the DC bus voltage, the battery is discharged rapidly, and the maximum output power of the battery is 7.5 × 106 W. When the three-phase grid-side voltage was unbalanced, in order to compensate for the power difference among the three phases, the three-phase current can be quickly balanced. The lithium battery of the submodule of the MMC-BESS three-phase energy storage was continuously discharged, but the three-phase output was uneven. In order to quickly balance lithium battery of the SOC of each phase under the condition of uneven three-phase output and improve the utilization rate and service life of energy storage capacity, it was necessary to balance the SOC of the lithium battery of each energy storage submodule in the three phases of MMC-BESS.Figure 22
MMC-BESS three-phase battery output power.In order to verify the effectiveness of the control strategy proposed in this paper, the system has been put into the three-level SOC equalization correction controller after a sudden change in DC load at 0.5 s. Figures23 and 24 and Table 5 compare the equalization correction control proposed in this paper with the equalization correction control of the one-third average method. Under the same initial value of SOC, by comparing the results of the final SOC value of each phase at the same moment, it could be seen that the correction control proposed in this paper had a faster convergence and equalization speed. Using one-third average method, the initial values of the SOC of phases A, B, and C are 50.5000, 50.3875, and 50.5375, respectively; the final values of the SOC of phases A, B, and C are 50.4884, 50.3823, and 50.5183, respectively; the difference of the SOC of phases A, B, and C is 0.0116, 0.0052, and 0.0192, respectively. Using the sliding window integral method, the initial values of SOC of the phases A, B, and C are the same, and the final difference is 0.0127, 0.0054, and 0.0197, respectively.Figure 23
MMC-BESS three-phase SOC average. (a) One-third average method, three-phase SOC average. (b) Sliding window integral method, three-phase SOC average.
(a)(b)Figure 24
SOC average value of three phases of the MMC-BESS. (a) Sliding window integral method of phaseA, SOC average using one-third average method. (b) Sliding window integral method of phase B, SOC average using one-third average method. (c) Sliding window integral method of phase C, SOC average using one-third average method.
(a)(b)(c)Table 5
Comparison of SOC data between one-third average method and sliding window integral method.
Comparison of SOC dataOne-third average method:0.5 s1 s3 s5 s7 s9 sPhaseA50.500050.497250.493050.489850.489150.4884PhaseB50.387550.384750.383450.383150.382950.3823PhaseC50.537550.534750.530250.525750.522350.5183Sliding window integral method:0.5 s1 s3 s5 s7 s9 sPhaseA50.500050.497150.492850.489050.488050.4873PhaseB50.387550.384750.383550.383150.382850.3821PhaseC50.537550.534750.530150.525350.521850.5178


## 5. Conclusion

In this paper, the characteristics of MMC-BESS phase unit power and the power difference between the upper and lower bridge arms are analyzed, a three-level SOC equalization correction control strategy is constructed, and a feedforward sliding window integral link is introduced into the equalization correction control layer of the upper and lower bridge arms, so as to weaken the influence of the fundamental frequency AC circulating current and DC circulating current caused by the capacitor voltage fluctuation of the submodule on system. A three-phase 5-level MMC-BESS simulation model is built in the Matlab/Simulink environment. The results show that:(1)
When the DC load changes suddenly, or the three-phase network side voltage is unbalanced, the DC bus voltage has good stability, the maximum fluctuation is 1500 V, and the steady-state error is 7.5%;(2)
MMC-BESS has good compensation ability for three-phase network side current when the two-phase voltage drops by 50%. After compensation, the THD of three-phase current is 1.38%, and the unbalance degree is 2.4%. The system has strong robustness;(3)
The effectiveness of the three-stage SOC equalization correction control strategy with sliding window integral method proposed in this paper is verified, and the SOC of each phase lithium battery has a faster equalization convergence speed.



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*Source: 1546622-2022-09-20.xml*