The integration of renewable energy sources and advanced power electronics in modern grids has heightened the demand for efficient energy storage solutions. Modular multilevel converter-battery energy storage systems (MMC-BESS) have emerged as a critical technology for medium-voltage DC (MVDC) distribution networks. However, periodic power fluctuations in submodules lead to frequent charge-discharge state transitions in battery packs, generating additional charge throughput that accelerates battery degradation. This challenge becomes more pronounced when MMC-BESS interfaces with solar inverters and other renewable energy systems, where bidirectional power flow and variable operating conditions exacerbate charge throughput issues.
System Modeling and Charge Throughput Analysis
The MMC-BESS topology consists of cascaded submodules with embedded battery units, enabling bidirectional power transfer between AC/DC grids. The charge throughput \( Q \) is defined as:
$$ Q = \int_{0}^{T} |i_{\text{bat}}| \, dt $$
where \( i_{\text{bat}} \) is the battery current and \( T \) is the grid cycle period. Key factors influencing \( Q \) include:
- Modulation ratio \( m \)
- Energy storage power ratio \( k = P_{\text{bat}}/P_{\text{ac}} \)
- Circulating current characteristics
For a three-phase MMC-BESS with \( N \) submodules per arm, the arm currents are expressed as:
$$
\begin{cases}
i_{\text{ua}} = I_{\text{cira}} + \frac{I_m}{2}\cos(\omega t + \phi) + \lambda I_m\cos(2\omega t + \theta) \\
i_{\text{la}} = I_{\text{cira}} – \frac{I_m}{2}\cos(\omega t + \phi) + \lambda I_m\cos(2\omega t + \theta)
\end{cases}
$$
where \( \lambda \) and \( \theta \) represent the amplitude and phase angle of injected second-order circulating currents.
Optimal Circulating Current Injection Strategy
The proposed strategy minimizes charge throughput through optimized second-harmonic current injection. The optimal parameters (\( \lambda_{\text{opt}}, \theta_{\text{opt}} \)) are determined by solving:
$$
\min_{\lambda, \theta} \sum_{x=u,l} \int_{0}^{T} |S_x(t)i_x(t)| \, dt
$$
where \( S_x(t) \) represents the switching function of submodules. The solution space for different operating conditions is shown below:
| Operating Mode | \( k \) Range | \( \lambda_{\text{opt}} \) | \( \theta_{\text{opt}} \) (rad) |
|---|---|---|---|
| Battery Charging (Inverter) | 0.2-0.8 | 0.12-0.35 | 0 |
| Battery Discharging (Inverter) | -0.5-0 | 0.25-0.45 | 0 |
| Grid Support (Solar Inverter Mode) | -1.0-1.0 | 0.18-0.32 | \(\pi/6\) |
Simulation and Experimental Validation
The control strategy was tested under multiple scenarios relevant to solar inverter applications:
| Case | \( P_{\text{ac}} \) (MW) | \( k \) | Reduction |
|---|---|---|---|
| Inverter Charging | 5 | 0.2 | 37.6% |
| Inverter Discharging | 5 | -0.2 | 24.5% |
| Solar Inverter Integration | 3 | 0.5 | 31.2% |
The experimental platform with 4 submodules per arm demonstrated:
$$
Q_{\text{reduction}} = \frac{Q_{\text{base}} – Q_{\text{optimized}}}{Q_{\text{base}}} \times 100\% = 31.5\% \text{ (at } k = -0.2)
$$
Implementation Considerations for Solar Inverter Systems
When integrated with solar inverters, the MMC-BESS requires additional adaptations:
- Dynamic \( k \) adjustment based on PV generation
- Harmonic compensation for variable DC-link voltage
- Enhanced SOC balancing for partial shading conditions
The system efficiency when combined with commercial solar inverters follows:
$$
\eta_{\text{total}} = \eta_{\text{MMC}} \times \eta_{\text{inv}} = 97.2\% \times 98.5\% = 95.7\%
$$
Conclusion
The proposed second-harmonic injection strategy effectively suppresses charge throughput in MMC-BESS, particularly in solar inverter applications with variable power flow. Future work will focus on real-time parameter adaptation and integration with multi-port solar inverter topologies.