As a researcher in the field of power electronics and energy storage, I have focused on addressing the challenges associated with modular multilevel converter based battery energy storage system (MMC-BESS) in renewable energy integration. The intermittent nature of renewable sources like wind and solar necessitates advanced energy storage solutions to stabilize grid operations. The battery energy storage system (BESS) plays a pivotal role in smoothing power fluctuations and enhancing grid reliability. However, traditional centralized BESS configurations face issues such as the “bucket effect” due to state of charge (SOC) imbalances among battery cells, which reduce overall efficiency and lifespan. In contrast, the MMC-BESS offers a decentralized approach by distributing battery units across submodules, enabling precise management and improved safety. Despite its advantages, the grid-connected equalization strategies for MMC-BESS are often constrained by power capacity losses and harmonic distortions when SOC distributions are uneven. To overcome these limitations, I propose a reconfigurable off-grid hierarchical equalization control strategy that facilitates internal energy redistribution without external grid connections, thereby optimizing the performance of the battery energy storage system.
The topology of the MMC-BESS consists of three phase units, each with upper and lower arms comprising N submodules (SMs) connected in series with an arm inductor L0. Each SM is a half-bridge circuit with two switches (S1 and S2) and a capacitor C0 paralleled with the battery energy storage unit. In off-grid mode, the MMC-BESS operates independently, allowing energy transfer between battery units within the system. The key equations governing the operation include the output voltages of the upper and lower arms, given by:
$$u_{xp} = \sum_{z=1}^{N} s_{xpz} u_{xpz}$$
$$u_{xn} = \sum_{z=1}^{N} s_{xnz} u_{xnz}$$
where \( u_{xp} \) and \( u_{xn} \) are the total output voltages of the upper and lower arms in phase x, respectively, \( s_{xpz} \) and \( s_{xnz} \) are the switching functions, and \( u_{xpz} \) and \( u_{xnz} \) are the voltages of the z-th SM. The arm currents in off-grid mode are derived as:
$$i_{cx} = \frac{i_{xp} + i_{xn}}{2}$$
and the relationship between DC voltage and arm voltages is expressed as:
$$U_{dc} = u_{xp} + u_{xn} + 2L_0 \frac{di_{cx}}{dt}$$
These equations highlight the internal dynamics that enable off-grid equalization by manipulating circulating currents. The common-mode voltage is defined as \( u_{comx} = u_{xp} + u_{xn} \), and the sum of three-phase circulating currents satisfies \( i_{ca} + i_{cb} + i_{cc} = 0 \), ensuring no net energy exchange with the grid. This foundational analysis sets the stage for implementing the proposed equalization strategy in the battery energy storage system.
The off-grid equalization strategy operates by transferring energy from high-energy battery units to low-energy ones through controlled switching of SMs. To quantify the imbalances, I define the minimum and maximum battery voltages in phase x as:
$$u_{minx} = \min\{u_{xpz}, u_{xnz}\}_{z=1}^{N}$$
$$u_{maxx} = \max\{u_{xpz}, u_{xnz}\}_{z=1}^{N}$$
The total voltage of battery units in phase x is calculated as:
$$u_x = \sum_{z=1}^{N} u_{xpz} + \sum_{z=1}^{N} u_{xnz}$$
and the average three-phase total voltage is:
$$U_{ph} = \frac{u_a + u_b + u_c}{3}$$
The deviation of each phase’s total voltage from the average is \( \Delta u_x = u_x – U_{ph} \). The equalization time for phase x is dynamically adjusted using a weighting coefficient \( k_x \), such that \( T_x = k_x T \), where T is the relative equalization cycle duration. This approach ensures that phases with higher total voltages discharge for longer periods, while those with lower voltages charge more, achieving inter-phase voltage balancing in the battery energy storage system.
In terms of operational modes, the off-grid equalization involves three distinct states where only one SM per phase is active—either the highest or lowest voltage unit—while others are bypassed. For instance, in Mode 1, the highest voltage SM in phase a discharges to the lowest voltage SMs in phases b and c. The equivalent circuit for off-grid equalization includes battery internal resistance \( R_{dci} \), switch on-resistance \( R_{dson} \), arm inductor DCR \( R_0 \), and line resistance \( R_l \). The total resistance per phase is \( R = R_{dci} + 2NR_{dson} + 2R_0 + R_l \), and the circulating current for phase x is derived as:
$$i_{cx} = \frac{U_{dc} – u_{xyz}}{R}$$
where \( u_{xyz} \) is the voltage of the active SM in phase x. This current facilitates energy transfer, and its magnitude depends on voltage differences and circuit resistance. To prevent excessive currents that could damage the battery energy storage system, an active current-limiting control is incorporated, which adjusts switch duty cycles based on current feedback.
The control strategy is divided into single-layer and double-layer approaches. Single-layer equalization focuses on intra-phase voltage differences by selecting SMs with the highest and lowest voltages for fixed-duration cycles. However, this may lead to prolonged equalization times when inter-phase imbalances are significant. Therefore, I propose a double-layer equalization control that combines module-level and phase-level adjustments. The weighting coefficient \( k_x \) is computed as:
$$k_x = \frac{\Delta u_x}{\Delta u_a + \Delta u_b + \Delta u_c}$$
ensuring that \( k_x \) ranges between 0 and 1 based on the phase’s voltage deviation. This dynamic adjustment optimizes equalization times, enhancing the overall efficiency of the battery energy storage system. The active current-limiting control uses a PI controller to maintain currents within safe limits, such as \( i_{cx}^{max} \) for charging and \( i_{cx}^{min} \) for discharging, by modulating the duty cycle D of the switches. The relationship between current and voltage difference is linear when D=1, but becomes non-linear under current limiting, as shown in the control block diagram.
To validate the proposed strategy, I conducted simulations and experiments with parameters summarized in Table 1. The MMC-BESS setup includes three phases with three SMs per arm, each SM containing a battery unit with nominal voltage 12.8 V and capacity 20 Ah. The initial voltages of the battery units were set to create imbalances, as listed in Table 2. The simulation results demonstrate that the double-layer control achieves faster inter-phase voltage balancing compared to single-layer control, as illustrated in the voltage waveforms over time. For example, the inter-phase voltage convergence occurs within 800 seconds with double-layer control, whereas single-layer control takes longer. The experimental waveforms of circulating currents confirm the effectiveness of the current-limiting mechanism, maintaining currents within ±4 A. Additionally, the intra-phase voltage equalization shows all battery voltages converging to a common value, verifying the strategy’s capability to handle both inter and intra-phase imbalances in the battery energy storage system.
| Parameter | Value |
|---|---|
| Number of SMs per arm (N) | 3 |
| Battery unit nominal voltage (U_{bat}) | 12.8 V |
| Battery unit capacity (Q) | 20 Ah |
| Battery internal resistance (R_{dci}) | 20 mΩ |
| MOSFET on-resistance (R_{dson}) | 1.5 mΩ |
| Arm inductance (L_0) | 0.8 mH |
| Arm inductor DCR (R_0) | 35.4 mΩ |
| SM capacitance (C_0) | 1.36 mF |
| Line resistance (R_l) | 26.6 mΩ |
| Max discharge current (i_{disc}^{max}) | -4 A |
| Max charge current (i_{char}^{max}) | 4 A |
| Relative equalization time (T) | 120 s |
| Switching frequency (f) | 5 kHz |
| Submodule | Phase a (V) | Phase b (V) | Phase c (V) |
|---|---|---|---|
| SM1 (Upper) | 10.466 | 13.338 | 13.148 |
| SM2 (Upper) | 12.567 | 13.303 | 13.182 |
| SM3 (Upper) | 13.246 | 13.291 | 10.695 |
| SM1 (Lower) | 13.310 | 13.152 | 13.347 |
| SM2 (Lower) | 13.350 | 12.928 | 12.906 |
| SM3 (Lower) | 13.336 | 11.000 | 13.338 |
The simulation waveforms for double-layer equalization show the circulating currents \( i_{ca} \), \( i_{cb} \), and \( i_{cc} \) varying with the equalization states, consistently staying within the set limits. The experimental results align closely, confirming the practicality of the approach. For instance, in State 1, phase a discharges at -4 A while phases b and c share the charging current. The active current-limiting control effectively regulates currents by adjusting duty cycles, as seen in the PWM signal waveforms. A comparison of calculated, simulated, and experimental currents under full duty cycle conditions reveals minor discrepancies due to parasitic elements, but overall consistency validates the current computation model. Furthermore, the intra-phase voltage equalization waveforms demonstrate all battery voltages converging to approximately 12.8 V, underscoring the strategy’s success in achieving uniformity across the battery energy storage system.
In conclusion, the reconfigurable off-grid hierarchical equalization control strategy for MMC-BESS effectively addresses the limitations of grid-connected methods by enabling internal energy redistribution. The double-layer control dynamically adjusts equalization times based on phase imbalances, while the active current-limiting ensures operational safety. Simulation and experimental results confirm that the strategy achieves both inter-phase and intra-phase voltage balancing, enhancing the energy utilization and longevity of the battery energy storage system. Future work could focus on optimizing the control algorithms for faster convergence in the late stages of equalization, further improving the efficiency of BESS in renewable energy applications.