This study investigates the coordinated control of parallel-connected energy storage inverters in islanded AC microgrids. A novel adaptive virtual impedance method and state-of-charge (SOC) balancing strategy are proposed to address power distribution inaccuracies and SOC imbalance challenges.
1. System Modeling and Control Framework
The mathematical model of energy storage inverters is established considering battery characteristics and power conversion dynamics. The SOC estimation combines open-circuit voltage measurement with coulomb counting:
$$ \text{SOC} = \text{SOC}_0 – \frac{1}{C_{\text{nom}}} \int_{0}^{t} i_{\text{bat}} dt $$
Key parameters for the three-phase inverter with LC filter are designed as:
| Parameter | Symbol | Value |
|---|---|---|
| Filter Inductance | Lf | 0.77 mH |
| Filter Capacitance | Cf | 50 μF |
| Switching Frequency | fsw | 10 kHz |
2. Enhanced Droop Control with Adaptive Virtual Impedance
The conventional droop control is improved by introducing adaptive virtual impedance to mitigate line impedance mismatch:
$$ \begin{cases}
f_i = f_{\text{ref}} – mP_i \\
E_i = E_{\text{ref}} – nQ_i – Z_{\text{vir},i}I_{o,i}
\end{cases} $$
Where the adaptive virtual impedance is calculated as:
$$ Z_{\text{vir},i} = \frac{X_{\text{line},j}Q_{\text{ref},j} – X_{\text{line},i}Q_{\text{ref},i}}}{Q_j} $$
3. SOC Coordination Strategy
An exponential SOC balancing algorithm is proposed for energy storage inverters with different capacities:
$$ f_i = f_{\text{ref}} – \frac{mP_i}{C_i} \exp[-\alpha(\text{SOC}_i – \overline{\text{SOC}})] $$
The stability analysis through small-signal modeling reveals:
$$ \Delta \dot{\text{SOC}}_i = -\frac{m\alpha}{C_i^2U_{\text{bat}}} \Delta P_i $$
| Parameter | Range | Optimal Value |
|---|---|---|
| Droop Coefficient (m) | 0.1-1.0 mHz/W | 0.5 mHz/W |
| Coordination Factor (α) | 10-50 | 30 |
| Virtual Impedance Ratio | 0.5-2.0 p.u. | 1.2 p.u. |
4. Multi-Agent Consensus Implementation
A distributed consensus algorithm enables SOC information sharing without central controller:
$$ \text{SOC}_{\text{ave}}^{(k+1)} = \frac{1}{N} \sum_{j\in\mathcal{N}_i} a_{ij}\text{SOC}_j^{(k)} $$
Where the adjacency weights are determined by:
$$ a_{ij} = \frac{1}{n_i + n_j + 1} $$
5. Performance Validation
The proposed strategy demonstrates superior performance in:
- Reactive power sharing error reduction (≤3%)
- Frequency deviation limitation (±0.15Hz)
- SOC convergence time acceleration (2.8s for 90% balance)
$$ \varepsilon_{\text{SOC}} = \frac{\text{max}|\text{SOC}_i – \overline{\text{SOC}}|}{\overline{\text{SOC}}} \times 100\% < 5\% $$
The energy storage inverter coordination scheme effectively addresses the challenges of distributed energy management in modern microgrids, demonstrating remarkable adaptability to various operating conditions and system configurations.