*5.1. Simulation Results*

The simulation model of the three-phase MMC-BESS is built in MATLAB/Simulink (R2016b, Mathworks, Natick, MA, USA). The main parameters are listed in Table 1. To verify the SOC equalization proposed in this paper, the capacity of individual battery is set as 0.3 Ah, so the SOCs can be equalized rapidly.


**Table 1.** Main parameters of the MMC-BESS simulation model.

5.1.1. Rectifier Mode Operation with Proposed Control Strategy Based on Battery Side Capacitor Voltage Control

The simulation waveforms of rectifier mode operation are shown in Figure 13 and the SOC equalization process is shown in Figure 14. The initial SOCs of all 24 SMs are arbitrarily distributed from 61% to 71%. The AC power increases from 0 to 480 kW through a slope reference, then it is transferred to 320 kW at *t* = 0.4 s and 640 kW at *t* = 0.6 s. A 480 kW external DC load is connected to the DC-link at *t* = 0.1 s. Seen from Figure 13, the AC power is indicated by grid currents in Figure 13a; the DC-link voltage is shown in Figure 13b. With the proposed control strategy for rectifier mode operation of MMC-BESS, the DC-link voltage is controlled to the reference value throughout. The capacitor voltages are shown in Figure 13c utilizing the proposed battery side-based capacitor voltage control strategy. Figure 13d shows the circulating currents of three phases. The DC circulating currents

are controlled according to the coefficient in Equation (11) to equalize the SOCs among phases, while the fundamental frequency circulating currents are controlled according to Equation (12) to equalize the SOCs between the upper and lower arms each phase. With the SOCs gradually converging to the same value, the differences among circulating currents in three phases also decrease consequently. The battery currents of four SMs within upper arm of phase A are shown in Figure 13d, where the differences among SMs also decrease gradually during the SOC equalization process. In Figure 14, the SOC equalization of all three levels are illustrated. Figure 14a shows the SOC equalization of all 24 SMs. The SOC equalizations among three phases, between upper and lower arms, and among SMs are shown in Figure 14b–d, respectively. During the rectifier mode operation of MMC-BESS, the simulation results validate the effectiveness of the proposed control strategy based on battery side capacitor voltage control.

**Figure 13.** Simulation waveforms of rectifier mode operation of MMC-BESS. (**a**) Grid currents. (**b**) DC-link voltage. (**c**) Capacitor voltages of upper and lower arm of phase A. (**d**) Circulating currents. (**e**) Battery currents of SMs within upper arm of phase A.

**Figure 14.** Three-level SOC equalization results. (**a**) SOC equalization of all 24 SMs. (**b**) SOC equalization among three phases. (**c**) SOC equalization between upper and lower arms of phase A. (**d**) SOC equalization among SMs within upper arm of phase A.

### 5.1.2. Verification of Proposed Battery Side Capacitor Voltage Control Strategy

The verifications of the proposed battery side capacitor voltage control strategy in steady and dynamic state are shown in Figure 15. Figure 15a is implemented without feedforward component of Equation (23), while this feedforward component is employed in Figure 15b,c. The difference of implementation between Figure 15b,c locates on the capacitor voltage filter scheme. The MAF is implemented in each SM capacitor voltage control in Figure 15b while the proposed common MAF scheme within one phase arm is employed in Figure 15c. At *t* = 0.3 s, the AC power reference is transferred from 480 kW to 960 kW, then at *t* = 0.6 s, the external DC load is transferred from 480 kW to 960 kW. In transient process, the capacitor voltage variation is up to Δ*vc*1 = −16% and the regulation time of battery current is *tr*1 = 0.2 s after *t* = 0.3 s in Figure 15a. While in Figure 15b, with the estimated feedforward component at battery side control, the transient performance is significantly improved with Δ*vc*1 ≈ −2% and *tr*1 = 0.03 s. Similar improvement can be observed from the comparison of Figure 15a,b during 0.6–0.8 s. Hence, the effectiveness of the feedforward component is validated. One the other hand, in steady state in Figure 15b,c, the ripples in capacitor voltage are eliminated from battery current, leaving only DC component, which validate the feasibility of the proposed common MAF scheme within phase arm compared with utilizing MAF each SM.

**Figure 15.** Verification of proposed battery side capacitor voltage control strategy. (**a**) Without estimated feedforward component. (**b**) Utilizing MAF each SM with estimated feedforward component. (**c**) Utilizing proposed common MAF each phase arm with estimated feedforward component.
