This paper presents advanced control methodologies for modular multilevel converters (MMCs) with partially integrated battery energy storage systems (PBESS), specifically optimized for solar inverter applications. The proposed architecture enables efficient energy transfer between DC photovoltaic arrays, AC grids, and distributed storage resources while maintaining operational stability under variable power conditions.
$$P_{dc} – P_{ac} = P_{bat}$$
1. System Configuration and Mathematical Modeling
The three-phase MMC-PBESS topology for solar inverters features:
- Upper arms with capacitive submodules (SMCs)
- Lower arms with battery-integrated submodules (SMBs)
- DC-link voltage: $U_{dc} = NU_B$
Key operational equations for solar inverter integration:
$$2L_a\frac{di_{dcj}}{dt} = U_{dc} – (u_{pj} + u_{nj})$$
$$i_{pj} = \frac{I_{dc}}{3} + \eta i_j$$
$$i_{nj} = \frac{I_{dc}}{3} – (1-\eta)i_j$$
| Parameter | Value |
|---|---|
| Arm inductance ($L_a$) | 2 mH |
| Grid inductance ($L_g$) | 1 mH |
| Capacitance (C) | 10 mF |
| Battery voltage ($U_B$) | 48 V |
2. Hierarchical Control Architecture
The proposed solar inverter control system implements:
$$ID_p = \frac{ID}{2k}$$
$$ID_n = -\frac{(2k-1)ID}{2k}$$
| Operating Mode | Power Ratio (k) | Control Strategy |
|---|---|---|
| Battery Charging | 0 < k < 0.5 | Upper arm current boosting |
| Grid Support | 0.5 ≤ k < 1 | Dual-arm power sharing |
| Full Inversion | k = 1 | Symmetric current distribution |
3. Voltage Balancing Mechanism
Critical for solar inverter reliability:
$$u_{a,p,av} = \frac{1}{N}\sum_{i=1}^N u_{api}$$
$$\Delta u_c = PI(u_{c,ref} – u_{a,p,av})$$
4. Operational Boundaries
Stability constraints for solar inverter applications:
$$|ID_n| \leq |ID_p|$$
$$m = \frac{2U_m}{U_{dc}} \approx 1$$
| Condition | Modulation Index | Efficiency |
|---|---|---|
| k = 0.4 | 0.92 | 96.7% |
| k = 0.6 | 0.95 | 97.2% |
| k = 1 | 1.01 | 98.1% |
5. Simulation Results
Key findings for solar inverter implementation:
$$THD_{ac} < 2.5\%\ (k=1)$$
$$\Delta u_c < 3\%\ (full\ load)$$
The solar inverter-integrated MMC-PBESS demonstrates superior performance in:
- Bidirectional power flow management
- Dynamic response to solar irradiance changes
- Grid code compliance under fault conditions
6. Conclusion
This control strategy enhances solar inverter capabilities through:
- Decoupled arm control without circulating current compensation
- Adaptive power sharing between PV generation and storage
- Stable operation across 0 < k ≤ 1 power ratio range
The modular architecture proves particularly effective for large-scale solar inverters requiring integrated energy storage, achieving 98.1% conversion efficiency while maintaining capacitor voltage balance within 3% deviation.