In modern power systems, the integration of renewable energy sources such as wind and solar has been growing rapidly. However, the inherent intermittency and fluctuation of these sources pose significant challenges to grid stability and power quality. The modular multilevel converter based battery energy storage system (MMC-BESS) has emerged as a promising solution to mitigate these issues by providing large-scale energy storage and power regulation capabilities. Traditional equalization control strategies for MMC-BESS are often designed for grid-connected operation, which may suffer from limitations when the state-of-charge (SOC) dispersion among submodules is large, leading to reduced capacity utilization and increased harmonic distortion. To address these limitations, we propose a reconfigurable off-grid hierarchical equalization control strategy that can effectively balance the voltages of battery energy storage units both between phases and within phases, thereby enhancing the energy utilization rate and operational safety of the battery energy storage system.
This paper first analyzes the topology and off-grid operating characteristics of MMC-BESS, where the absence of grid connection forces energy to be redistributed internally among submodules. The proposed strategy consists of a top-layer control that dynamically adjusts the discharge equalization time for each phase based on inter-phase voltage differences by modifying phase weighting coefficients, and a bottom-layer control that selects appropriate cross-phase equalization targets using a module-level voltage sorting algorithm to address intra-phase voltage imbalances. Additionally, an active current-limiting mechanism is incorporated to prevent excessive equalization currents, ensuring safe operation. A detailed simulation model is built in MATLAB/Simulink, and experimental validation is carried out on a hardware platform. The results demonstrate that the proposed control strategy can achieve effective inter-phase and intra-phase voltage equalization in the battery energy storage system, significantly improving the overall performance of the energy storage system.
Introduction
The rapid development of renewable energy generation technologies, represented by wind and solar power, has greatly increased the penetration of renewable energy in the power grid. However, the volatile, intermittent, and anti-peaking characteristics of renewable energy output impose tremendous pressure on transmission and distribution networks. Battery energy storage systems (BESS), especially those using lithium-ion batteries, have become dominant in new energy storage products due to their high conversion efficiency, low self-discharge rate, and long cycle life. By integrating BESS with renewable energy sources, it is possible to smooth power fluctuations, achieve peak shaving and valley filling, and significantly reduce curtailment of wind and solar power.
Conventional BESS often employs a centralized structure to achieve high capacity and power. However, such configurations suffer from the “bucket effect” when large numbers of cells are connected in series and parallel, as variations in cell voltage, temperature, and cycle life lead to inconsistent state-of-charge (SOC). Managing thousands of cells with a centralized BMS becomes challenging, both in terms of monitoring and thermal management. Moreover, the power conversion system (PCS) directly influences the output power quality, construction cost, and operational reliability of the energy storage system.
The modular multilevel converter based battery energy storage system (MMC-BESS) distributes battery cells into individual submodules, avoiding direct series/parallel connection of large numbers of cells. This segmentation allows finer control and enhances safety. The MMC-BESS topology features a common DC bus that facilitates energy exchange between the DC side, the storage units, and the AC side. Due to differences in switching characteristics of submodules and variations among battery cells, the SOC of storage units in different submodules inevitably diverges during charging and discharging cycles. Without proper equalization, high-SOC cells may become overcharged during charging, while low-SOC cells may become over-discharged during discharging, degrading battery health and reducing overall energy utilization. Therefore, developing effective equalization methods is crucial.
Most existing MMC-BESS equalization control strategies are designed for grid-connected operation and have certain limitations. For example, when the SOC distribution of battery energy storage units is highly dispersed, the power capacity of the MMC-BESS is reduced, and active power distribution among submodules becomes unbalanced, leading to increased harmonic content in the output current. In virtual power plant dispatch scenarios, some MMC-BESS units may remain idle. Utilizing this idle time for off-grid voltage equalization can improve the grid-connected quality when these units are later put into operation and reduce the required equalization time during grid connection. Since the currents in the upper and lower arms of an off-grid MMC-BESS are equal, it is impossible to transfer power between the upper and lower arms using conventional three-level voltage equalization strategies designed for grid connection. Hence, a new off-grid voltage equalization strategy is needed.
To overcome the limitations of grid-connected equalization, we propose a reconfigurable off-grid hierarchical equalization control strategy that operates in two layers. The top layer addresses inter-phase voltage differences by adjusting the discharge equalization time dynamically via phase weighting coefficients. The bottom layer addresses intra-phase voltage differences by dynamically selecting cross-phase equalization targets through a module-level voltage sorting algorithm. We analyze the equivalent circuit of off-grid equalization and the influence of circuit resistance on equalization current. An active current-limiting control is added to maintain currents within safe limits. We build a simulation model and an experimental platform to verify the effectiveness of the proposed strategy.
MMC-BESS Topology and Off-Grid Operation
Topology Description
The MMC-BESS topology studied in this paper is shown in the conceptual diagram. It consists of three phase units, each comprising an upper arm and a lower arm. Each arm contains N identical submodules (SMs) connected in series with an arm inductor L0. Each SM uses a half-bridge circuit with two switches (S1 and S2) and a capacitor C0 in parallel with the battery energy storage unit. When grid-connected, the system is linked to the grid via filter inductors Ls, enabling bidirectional energy flow. In off-grid mode, the system is disconnected from the grid, and energy circulates internally among the battery modules.
Off-Grid Operating Characteristics
For any submodule, the output voltage is denoted as uxyz and the switching function as sxyz, where x = a, b, c; y = p (upper), n (lower); z = 1,2,…,N. The total output voltage of the upper and lower arms can be expressed as:
$$ u_{xp} = \sum_{z=1}^{N} s_{xpz} \cdot u_{xpz} $$
$$ u_{xn} = \sum_{z=1}^{N} s_{xnz} \cdot u_{xnz} $$
In grid-connected MMC-BESS, the output current isx is equally shared between the upper and lower arms. However, in off-grid MMC-BESS, there is no external energy exchange. The arm circulating current can be expressed as:
$$ i_{cx} = i_{xp} = i_{xn} $$
Neglecting arm resistance, the relationship between phase voltage, submodule voltages, and arm inductance is:
$$ U_{dc} = u_{xp} + u_{xn} + 2L_0 \frac{di_{cx}}{dt} $$
The common-mode voltage is defined as:
$$ u_{comx} = u_{xp} + u_{xn} $$
From Kirchhoff’s current law for the three phases:
$$ i_{ca} + i_{cb} + i_{cc} = 0 $$
Therefore, the DC voltage Udc can be further expressed by:
$$ U_{dc} = u_{coma} + 2L_0 \frac{di_{ca}}{dt} $$
$$ U_{dc} = u_{comb} + 2L_0 \frac{di_{cb}}{dt} $$
$$ U_{dc} = u_{comc} + 2L_0 \frac{di_{cc}}{dt} $$
Off-Grid Equalization Working Principle
Basic Principle of Equalization
In off-grid mode, the battery energy storage system does not exchange energy with the external system. Equalization transfers energy from submodules with higher stored energy to those with lower stored energy. Let us define the minimum and maximum voltage of the battery energy storage units in phase x:
$$ u_{xmin} = \min\{u_{xpz}, u_{xnz}\}_{1 \leq z \leq N} $$
$$ u_{xmax} = \max\{u_{xpz}, u_{xnz}\}_{1 \leq z \leq N} $$
Define the total voltage of phase x as:
$$ u_x = \sum_{z=1}^{N} (u_{xpz} + u_{xnz}) $$
Define the average total voltage of the three phases as:
$$ U_{ph} = \frac{u_a + u_b + u_c}{3} $$
The deviation of phase x from the average is:
$$ \Delta u_x = u_x – U_{ph} $$
Define the equalization time for phase x as:
$$ T_x = k_x T $$
where kx is the phase equalization weighting coefficient and T is the relative equalization time representing one cycle of equalization state.
Because the current in each phase is the same for all series-connected submodules, it is impossible to transfer power within a phase. Our proposed reconfigurable off-grid equalization method selects only one submodule with the highest or lowest voltage per phase during each operating mode, while all other submodules are bypassed, thus avoiding simultaneous charging/discharging of all submodules within a phase.
Off-Grid Equalization Operating Modes
Three operating modes are illustrated conceptually. In Mode 1, the phase with the highest voltage battery cell (e.g., phase a) is selected to discharge to the two phases with the lowest voltage cells (phases b and c). In Mode 2, another phase with the highest voltage cell discharges to the other two phases with lowest voltage cells. In Mode 3, the remaining phase with the highest voltage cell discharges to the other two phases. The selection is based on a voltage sorting algorithm that identifies SMmaxx and SMminx for each phase. Under equal weighting coefficients, the relationship between target submodules and time is periodic.
Proposed Reconfigurable Off-Grid Hierarchical Equalization Control Strategy
Single-Layer Equalization Control
Single-layer equalization does not consider inter-phase voltage differences; only intra-phase voltage differences are addressed. By using a voltage sorting algorithm, we select the submodules that need charging or discharging and cycle with a fixed duration. When all submodule voltages within a phase become equal, both inter-arm and intra-arm voltage equalization are achieved. In this case, the weighting coefficients are equal for all three phases:
$$ k_a = k_b = k_c = \frac{1}{3} $$
Consequently, the equalization times for each phase are identical:
$$ T_a = T_b = T_c = \frac{T}{3} $$
Under Mode 1, for example, the submodule with the highest voltage in phase a (SMmaxa) is selected to discharge, while the submodules with the lowest voltage in phases b and c (SMminb, SMminc) are selected to charge. All other submodules are bypassed. The common-mode voltages are:
$$ u_{coma} = u_{maxa}, \quad u_{comb} = u_{minb}, \quad u_{comc} = u_{minc} $$
When switching transitions occur, the arm inductors suppress the rate of rise of circulating current. In steady state, the circulating current is DC, and only the DC resistance (DCR) affects it. The equivalent circuit of off-grid equalization can be simplified as shown in Table 1.
| Parameter | Symbol | Value/Expression |
|---|---|---|
| DC internal resistance of battery cell | Rdci | 20 mΩ |
| MOSFET on-resistance (per switch) | Rdson | 1.5 mΩ |
| Arm inductor DCR | R0 | 35.4 mΩ |
| Line resistance | Rl | 26.6 mΩ |
| Number of series switches per phase path | 2N | 6 (when N=3) |
| Total resistance per phase | R | R = Rdci + 2NRdson + 2R0 + Rl |
The sum of the three phase circulating currents is zero. Writing KVL for each phase and using the condition that the sum of currents is zero yields:
$$ \frac{U_{dc} – u_{ayz}}{R} + \frac{U_{dc} – u_{byz}}{R} + \frac{U_{dc} – u_{cyz}}{R} = 0 $$
$$ \Rightarrow U_{dc} = \frac{u_{ayz} + u_{byz} + u_{cyz}}{3} $$
Therefore, the circulating current of phase x is:
$$ i_{cx} = \frac{U_{dc} – u_{xyz}}{R} = \frac{(u_{ayz} + u_{byz} + u_{cyz})/3 – u_{xyz}}{R} $$
Thus, the equalization current is proportional to the voltage difference between the phase and the average of the three selected cell voltages, and inversely proportional to the total resistance.
Double-Layer Equalization Control
When the inter-phase voltage difference is small, the completion times of inter-phase and intra-phase equalization are similar. However, when inter-phase imbalance is high, the single-layer strategy may result in intra-phase equalization without achieving inter-phase balance. For example, if the voltages of all cells in one phase are generally low, the highest voltage cell in that phase might discharge a very small current or even become charged. To solve this problem, we propose a hierarchical double-layer control strategy that dynamically adjusts phase weighting coefficients based on inter-phase imbalance.
The weighting coefficient kx for phase x is calculated as:
$$ k_x = \frac{|\Delta u_x|}{|\Delta u_a| + |\Delta u_b| + |\Delta u_c|} + \frac{1}{3} $$
$$ \text{with condition: } \Delta u_a + \Delta u_b + \Delta u_c = 0 $$
When the total voltage of a phase is higher than the average, its weighting coefficient is increased to lengthen discharge time and shorten charge time. Conversely, when it is lower, the coefficient is decreased. This ensures that inter-phase equalization is maintained without over- or under-equalization.
The double-layer equalization steps are:
- Sort the voltages of all battery energy storage units in each phase and identify the minimum and maximum voltage submodules.
- Calculate equalization times Tx for each phase using the weighting coefficients.
- Turn on the selected submodules and bypass all others.
An active current-limiting control is added to ensure the equalization current stays within a safe range. The maximum allowed charging and discharging currents are defined as icharmax and idiscmax. The error between the actual current and the limit is processed by a PI controller to adjust the duty cycle D of the selected submodule’s switches. When the current is within limits, D=1; when it exceeds the limit, D is reduced to clamp the current. The relationship between the equalization current icx and duty cycle is:
$$ i_{cx} = \frac{(u_{ayz} + u_{byz} + u_{cyz})/3 – u_{xyz} \cdot D}{R} $$
The active current-limiting control block diagram uses the minimum of the charging and discharging current errors to generate the duty cycle command.
Simulation and Experimental Verification
Parameters and Setup
To validate the proposed control strategy, a simulation model was built in MATLAB/Simulink using the parameters listed in Table 2. An experimental platform was also constructed with identical parameters. The battery energy storage units consist of four 20 Ah lithium iron phosphate cells in series. The main controller is STM32G474VET6, and the PWM signals are generated via FPGA EP4CE6E22C8N. Three LA25-NP current sensors measure phase currents.
| Parameter | Value |
|---|---|
| Number of SMs per arm N | 3 |
| Rated voltage of each battery unit Ubat | 12.8 V |
| Rated capacity Q | 20 Ah |
| Battery DC internal resistance Rdci | 20 mΩ |
| MOSFET on-resistance Rdson | 1.5 mΩ |
| Arm inductance L0 | 0.8 mH |
| Arm inductor DCR R0 | 35.4 mΩ |
| Submodule capacitance C0 | 1.36 mF |
| Line resistance Rl | 26.6 mΩ |
| Maximum discharge equalization current idiscmax | -4 A |
| Maximum charge equalization current icharmax | 4 A |
| Relative equalization time T | 120 s (simulation 1.2 s for faster testing) |
| Switching frequency f | 5 kHz |
The initial voltages of all battery energy storage units before equalization are given in Table 3.
| Submodule | Phase a | Phase b | Phase c |
|---|---|---|---|
| Upper arm 1 | 10.466 | 13.338 | 13.148 |
| Upper arm 2 | 12.567 | 13.303 | 13.182 |
| Upper arm 3 | 13.246 | 13.291 | 10.695 |
| Lower arm 1 | 13.310 | 13.152 | 13.347 |
| Lower arm 2 | 13.350 | 12.928 | 12.906 |
| Lower arm 3 | 13.336 | 11.000 | 13.338 |
Double-Layer Equalization Results
Simulation results of the double-layer equalization control strategy show the equalization currents and the state transition over time. Initially, the weighting coefficients calculated from the initial voltages are ka=0.175, kb=0.500, kc=0.325, leading to equalization times Ta=21 s, Tb=60 s, Tc=39 s (for the long simulation). The current waveforms indicate that in Mode 1, phase a current is clamped at -4 A (discharge) while phases b and c share a total of 4 A charging current. After two more modes, the cycle repeats with updated weighting coefficients. The experimental results closely match the simulation, confirming that the proposed double-layer control effectively redistributes energy.
Active Current-Limiting Results
The active current-limiting control was tested under three scenarios: without limit, with 10 A / -10 A limit, and with 5 A / -10 A limit. When no limit is applied, the equalization currents can reach high values. By setting appropriate limits, the currents are constrained. Experimental waveforms show that when the charging limit is 2 A and discharging limit is -2 A, the pulse-width-modulated (PWM) signals adjust to maintain the current within bounds. Similarly, for 4 A / -4 A limits, the duty cycle changes accordingly. This verifies the effectiveness of the active current-limiting scheme.
Verification of Equalization Current Calculation
Comparison of the equalization currents measured in experiments, simulated values, and calculated values from the theoretical formula shows a good match, confirming the accuracy of the current calculation method.
Inter-Phase Voltage Equalization
To observe the equalization effect over a long period, the battery capacity was reduced to 0.2 Ah and relative equalization time to 1.2 s. The simulation waveforms of phase total voltages under single-layer and double-layer control are compared. The double-layer control achieves inter-phase voltage equalization much faster than single-layer control. At around 600 s, slight imbalance appears in the double-layer case due to residual intra-phase differences, but by 800 s the voltages converge.
Intra-Phase Voltage Equalization
Simulation and experimental waveforms of intra-phase voltages show that all cell voltages gradually approach a common value under the double-layer control strategy. Throughout the process, the highest voltage cell in each phase always discharges, while the lowest voltage cell always charges; cells with intermediate voltages remain bypassed. The final steady state indicates successful intra-phase equalization.
Conclusion
We have proposed a reconfigurable off-grid hierarchical equalization control strategy for modular multilevel converter based battery energy storage system (MMC-BESS) to overcome the limitations of grid-connected equalization when battery energy storage unit voltages are widely dispersed. The strategy integrates a top-layer control that dynamically adjusts phase equalization durations based on inter-phase voltage differences and a bottom-layer control that uses voltage sorting to select cross-phase equalization targets for intra-phase balancing. An active current-limiting mechanism ensures safe operation by limiting equalization currents to preset ranges. Simulation and experimental results demonstrate that the strategy effectively achieves both inter-phase and intra-phase voltage equalization, thereby improving the energy utilization rate of the battery energy storage system. The proposed method is especially suitable for idle MMC-BESS units that can be utilized in off-grid mode to prepare for grid-connected operation. Future work may focus on improving the equalization current at the later stage to further accelerate equalization.