**1. Introduction**

In recent years, the grid-connected applications of large-scale renewable energy resources have gradually become a trend, presenting new challenges to the power electronics converters applied in high-voltage and high-power fields [1]. Multilevel topologies can reduce the requirement of voltage rate of switching devices, achieving higher voltage levels [2]. Among existing multilevel topologies, a modular multilevel converter (MMC) is considered the most promising topology and has been extensively studied in the past decade [3–5]. Modular multilevel converters share the common advantages of multilevel converters, such as low harmonic content of output voltage and small voltage stress of switching devices. Compared with the cascaded H-bridge (CHB) topology with the modular structure, the MMC topology has only half of the arm current at the same power rate. There also exists a common DC-link in the MMC topology which is unavailable in CHB topology [6]. Based on this consideration, MMCs can be utilized as AC/DC interlinking converters in medium- and high-voltage renewable energy generation systems, e.g., o ffshore wind farm generation systems [7] and microgrids [8], as shown in Figure 1.

**Figure 1.** Applications of modular multilevel converter (MMC) topology with large-scaled renewable energy sources. (**a**) Offshore wind farm generation system based on two-terminal MMCs. (**b**) DC microgrid using MMC as interlinking converter.

Due to the characteristics of randomness and intermittency of renewable energy resources, the normal operation and power quality of the power system would be remarkably affected, reducing the voltage and frequency stability. To attenuate the passive impact caused by renewable energy resources, a battery energy storage system (BESS) is a reasonable and efficient solution for grid-connected renewable energy generation systems, as shown in Figure 1a,b. Recently, to simplify the configuration of BESS in the scenarios of MMC-based applications, the MMC with integrated BESS is proposed by combining the MMC and BESS together [9]. The extra power conversion system (PCS) of BESS can be saved by this combination. In this paper, this topology is abbreviated as the MMC-BESS. The integration was implemented by inserting battery cells into each submodule (SM) of MMC directly or through a DC/DC interface [10,11]. Due to this distributed integration mode of BESS, the state-of-charge (SOC) equalization of each battery was facilitated, improving the effective utilization rate of BESS compared with the centralized scheme at the DC-link of MMC [12].

In addition to the inherent advantages provided by BESS for the power system, the integration scheme of batteries through DC/DC interfaces provided and additional degree of freedom (DOF) to the system control strategy. As the capacitor voltage balancing control was significant to conventional MMCs, the cascaded control structure for balancing the capacitor voltage in the phase-, arm- and individual SM-level is reported in Reference [13], which was consequently employed in the MMC-BESS in Reference [14]. Nevertheless, with the additional DOF provided by batteries in the MMC-BESS, the capacitor voltage balancing control can be significantly simplified through battery side control, which makes individual SM capacitor behave as a voltage source to the MMC, avoiding the cascaded control structure and relatively complicated capacitor voltage balancing algorithms introduced in Reference [4]. It is worth noting that the premise of the battery side capacitor voltage control was that each SM must contain a battery module, otherwise the capacitor voltage would be incontrollable.

Based on the battery side capacitor voltage control, some studies have been reported. In Reference [11], the control strategy of a MMC-BESS operating as an inverter was researched, proposing the three-level SOC equalization control structure. In Reference [15], the SOC equalization of MMC-BESS considering the capacity inconsistency of batteries was proposed. In References [10,16], the MMC-BESS was applied in battery electric vehicles and the e fficiency of this topology was assessed. Furthermore, the control strategy of MMC-BESS under AC and DC fault has been studies in Reference [17], realizing SOC equalization under fault conditions. Nevertheless, the current research is not deep enough, as the existing control strategies merely focus on the inverter mode operation of MMC-BESS. Usually, in MMC-based multi-terminal DC transmission system (e.g., Figure 1a), one of the MMCs must be responsible for DC-link voltage control while the other MMCs should be responsible for power control [18]. Similarly, in Figure 1b, the interlinking MMC should take the DC-link voltage as the control objective. Accordingly, the rectifier mode operation of MMC-BESS is required. However, the DC-link voltage control structure in conventional MMCs [18] cannot be directly employed in the MMC-BESS due to the additional power flow of BESS, which has not been investigated in detail in the current literature. As the battery side converter is employed to control the capacitor voltage, the SOC equalization must be achieved by MMC side control. Hence, the combination of SOC equalization and DC-link voltage control is mandatory in the MMC-BESS. Besides, as the capacitor voltage is controlled by battery side converter, the performance of the system would be greatly dependent on the battery side control strategy. As the individual capacitor voltage contains ripples at multiple frequencies while the battery current is expected to be pure DC component, the battery side control strategy should be investigated to ensure the performance both in a steady and dynamic state.

In this paper, based on battery side capacitor voltage control, the control strategy of rectifier mode operation was analyzed according to the equivalent circuit of the MMC-BESS. The DC-link voltage control was combined with the SOC equalization control, di fferent from the control strategy applied in conventional MMCs. Furthermore, a simplified capacitor voltage filter scheme was proposed in this paper to facilitate the implementation of battery side control strategy.

The rest of this paper is organized as follows. Section 2 describes the basic configuration and the equivalent circuit of the MMC-BESS. Then the control strategy of rectifier mode operation of MMC-BESS is proposed in Section 3. To enhance the performance of battery side control strategy, a simplified capacitor voltage filter scheme is proposed in Section 4. Finally, the e ffectiveness and feasibility of the proposed control strategy of rectifier mode operation are validated by simulations and experimental results in Section 5.

### **2. Mathematic Model and Principles of MMC-BESS**

The topology of three-phase MMC-BESS is shown in Figure 2. Each phase leg is comprised of 2*N* SMs in series, where the midpoint connected to the AC side divides a phase leg into two phase arms. Here, *N* represents the number of SMs in series per phase arm. Throughout this paper, the subscript *k* = (a, b, c) refers to the individual phase; *j* = (p, n) refers to the upper and lower arms; *i* = (1, 2 ... *N*) refers to the individual SM within phase arm. The DC-link voltage and grid phase-voltage are denoted as *Vdc* and *vgk*, respectively. Each phase arm contains an arm inductor *Ls* with losses denoted by *Rs* (not shown in the figure). In general, the topology of the MMC-BESS is consistent with conventional MMCs. The main di fference locates on the topology of SM. In addition to the half-bridge structure with the SM capacitor, BESS is integrated into each SM in di fferent ways, which forms two types of SM as shown in Figure 2. For SM type *A*, the battery is directly connected to the terminals of individual SM capacitors; for SM type *B*, the battery is connected to individual SM capacitors through a DC/DC interface, while *Lb* is the inductor of this DC/DC converter. In the authors' view, SM type *A* compels the capacitor voltage to follow the battery voltage, inducing the power fluctuation caused by ripples in capacitor voltage into the battery which would impair the health or shorten the lifespan of an individual battery. On the contrary, the DC/DC interface in SM type *B* can decouple the battery side and MMC side through the SM capacitor, preventing the ripples from flowing into the battery through an appropriate control strategy, but it would comparatively degrade the power conversion efficiency due to the DC/DC interface. Nevertheless, the DC/DC interface provides a degree of freedom for the system control which SM type *A* does not, and the requirement of the terminal voltage of the battery module can be greatly lower than the rated capacitor voltage. Besides, it would not affect the original power conversion efficiency between AC and DC side of MMC itself. Hence, SM type *B* was employed in this paper. It should be noted that the topology of the DC/DC interface in SM type *B* was not restricted to a non-isolated buck–boost converter as shown in Figure 2, which was adopted in this paper for the convenience and simplicity.

**Figure 2.** Topology of the three-phase MMC- battery energy storage system (BESS).

The MMC-BESS can be modelled identically to a conventional MMC as follows [19]:

$$\begin{cases} \boldsymbol{\upsilon}\_{\rm sk} = \frac{R\_{\rm s}}{2} \dot{\boldsymbol{i}}\_{\rm \xi k} + \frac{L\_{\rm s}}{2} \frac{d\dot{\boldsymbol{i}}\_{\rm \xi k}}{dt} + \boldsymbol{\upsilon}\_{\rm \xi k} \\\\ \boldsymbol{\upsilon}\_{\rm ck} = L\_{\rm s} \frac{d\dot{\boldsymbol{i}}\_{\rm ck}}{dt} + R\_{\rm s} \dot{\boldsymbol{i}}\_{\rm ck} \end{cases} \tag{1}$$

where *vsk* is the voltage required to drive the AC output current *igk*, and *vck* is the voltage required to drive the difference current *ick*. The difference current *ick* is a circulating current flowing through upper and lower arms within one phase simultaneously, which would not affect the AC side.

The upper and lower arm currents were composed of a circulating current and a half of AC output current as [19]:

$$\begin{cases} \begin{array}{c} i\_{kp} = \frac{i\_{gk}}{2} + i\_{ck} \\ i\_{ku} = -\frac{3k}{2} + i\_{ck} \end{array} \end{cases} \tag{2}$$

The difference current can contain component at any frequency, but only DC and fundamental frequency components are necessary for power conversion in the MMC-BESS [14]. Thus, assuming:

$$i\_{ck} = I\_{dck} + I\_{1k} \cos(\omega t + q\_{1k}) \tag{3}$$

where *Idck* denotes the DC component; *I*1*k* and ϕ1*k* are the amplitude and angle of fundamental component in phase *k*; ω is the fundamental angular frequency of AC side.

*Energies* **2019**, *12*, 2151

By applying Kirchho ff's Voltage Laws(KVL) to Figure 2, the output voltages of the upper and lower arms can be yielded as

$$\begin{cases} \boldsymbol{\upsilon}\_{kp} = \frac{V\_{ck}}{2} - \boldsymbol{\upsilon}\_{sk} - \boldsymbol{\upsilon}\_{ck} \\ \boldsymbol{\upsilon}\_{ku} = \frac{V\_{dc}}{2} + \boldsymbol{\upsilon}\_{sk} - \boldsymbol{\upsilon}\_{ck} \end{cases} \tag{4}$$

Due to the battery power existing in the system, the following relationship is satisfied throughout neglecting losses:

$$P\_{ac} = P\_{dc} + \sum\_{k}^{a,b,c} \sum\_{j}^{p,n} \sum\_{i=1}^{N} P\_{b\\_kji} \tag{5}$$

where *Pac* and *Pdc* are total active powers of the AC and DC side, respectively, while *Pb\_kji* is the battery power of individual SM. Note that the power directions are all in accordance with Figure 2 in this paper. To compensate or absorb power fluctuations of the AC or DC side of the MMC-BESS, the individual battery would discharge when *Pb\_kji* > 0, vice versa.

Assuming the grid voltage and arm current of phase *k* in time domain are expressed as:

$$\begin{cases} v\_{\mathcal{g}k} = V\_{\mathcal{g}k} \cos \omega t \\ i\_{\mathcal{g}k} = I\_{\mathcal{g}k} \cos(\omega t + q\_k) \end{cases} \tag{6}$$

where *Igk* and ϕ*k* are amplitude and angle of grid current; *Vgk* is the amplitude of the grid voltage. Substituting Equation (6) into the individual arm voltage (4), then multiplying it with the arm current (2) and taking battery powers into account, the total battery power of each arm over one fundamental period can be derived as

$$\begin{cases} \sum\_{i=1}^{N} P\_{b\\_kpi} = -P\_{kp} = -\frac{\omega}{2\pi} \int\_{t}^{t+\frac{2\pi}{\omega}} \upsilon\_{kp} i\_{kp} = \frac{1}{2} P\_{dck} - \frac{1}{2} P\_{ack} + P\_{diffk} \\\sum\_{i=1}^{N} P\_{b\\_kpi} = -P\_{kn} = -\frac{\omega}{2\pi} \int\_{t}^{t+\frac{2\pi}{\omega}} \upsilon\_{kn} i\_{kn} = \frac{1}{2} P\_{dck} - \frac{1}{2} P\_{ack} - P\_{diffk} \end{cases} \tag{7}$$

where

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$$\begin{array}{l} P\_{dck} = V\_{dc} I\_{dck} \\ P\_{ack} = \frac{1}{2} V\_{\emptyset k} I\_{\emptyset k} \cos \varphi\_k \\ P\_{diffk} = \frac{1}{2} (\sum\_{i=1} P\_{b\\_k ii} - \sum\_{i=1} P\_{b\\_k pi}) = \frac{1}{2} V\_{\emptyset} I\_{1k} \cos \varphi\_{1k} \end{array} \tag{8}$$

Here, *Pdi*ff*k* is defined as the di fference power between upper and lower arms of phase *k*. According to Equation (7), the power flows of the three-phase MMC-BESS can be shown as Figure 3. It can be concluded that the DC circulating current is the carrier of DC power between the MMC-BESS and DC-link; the fundamental frequency circulating current transfers power between the upper and lower arms within one phase; the fundamental frequency grid current transfers active and reactive power between the MMC-BESS and the AC grid. Therefore, by regulating these components in corresponding currents, the power flows among batteries, DC-link, and AC grid can be controlled as the system requires.

If the individual capacitor voltage is controlled by MMC side, the cascaded capacitor voltage control strategy would be employed at the DC side [14], and the individual battery power would be directly controlled by battery side converter, which makes it behave as a constant power load (CPL) to the corresponding SM. On the contrary, if the battery side converter is utilized to control the individual capacitor voltage, the capacitor would behave as a voltage source to the MMC side. Consequently, the cascaded capacitor voltage balancing controls in conventional MMCs can be avoided. Nevertheless, due to the existence of the additional power flow of BESS, when the DC-link voltage is required to be controlled by the MMC-BESS itself in rectifier mode operation, the original control strategy in conventional MMCs (outer-loop DC-link voltage control and inner-loop active grid current control [18]) would be invalid because this manner would lead to the uncertainty of battery power, bringing instability to the system operation. In essence, the AC power and DC power are not strictly equal to each other in the MMC-BESS compared with conventional MMCs. The DC-link voltage is not only decided by the active grid current at AC side, but also the battery power each phase. Hence, to make the batter-side-based capacitor voltage control effective in the rectifier mode, the control strategy will be proposed in the following section.

**Figure 3.** Power flows of the MMC-BESS.

### **3. Control Strategy of Rectifier Mode Operation of MMC-BESS**
