This paper investigates advanced control strategies for parallel-connected energy storage inverters in islanded AC microgrids, focusing on state-of-charge (SOC) collaborative operation and power distribution accuracy. A novel adaptive virtual impedance method combined with exponential SOC coordination is proposed to address challenges in reactive power sharing and battery lifetime optimization.
1. System Modeling and Control Fundamentals
The mathematical model of energy storage inverters incorporates battery dynamics and power conversion characteristics. The SOC estimation combines Coulomb counting with open-circuit voltage measurement:
$$ \text{SOC}(t) = \text{SOC}_0 – \frac{1}{C_{ ext{nom}}} \int_0^t i_{ ext{bat}}( au)d au $$
Key parameters for the three-phase voltage source inverter are designed as:
| Parameter | Value | Unit |
|---|---|---|
| Filter inductance (L) | 0.77 | mH |
| Filter capacitance (C) | 50 | μF |
| Switching frequency | 10 | kHz |
2. Adaptive Virtual Impedance Control
The improved droop control with adaptive virtual impedance addresses line impedance mismatch:
$$ \begin{cases}
f_i = f_{ ext{ref}} – m_pP_i \\
E_i = E_{ ext{ref}} – nQ_i – Z_{ ext{virt},i}i_o
\end{cases} $$
Virtual impedance adaptation law:
$$ Z_{ ext{virt},i} = \frac{X_{ ext{line},j}Q_{ ext{ref},j} – X_{ ext{line},i}Q_{ ext{ref},i}}{Q_j} – X_{ ext{line},i} $$
3. SOC Collaborative Control Strategy
The exponential SOC coordination mechanism ensures dynamic balance:
$$ m_{p,i} = \frac{m_0}{C_i} \exp(-\alpha( ext{SOC}_i – ext{SOC}_{ ext{ave}})) $$
Small-signal stability analysis reveals system eigenvalues:
$$ \det(sI – J) = s^3 + a_2s^2 + a_1s + a_0 = 0 $$
| Parameter | Effect on Stability |
|---|---|
| α < 30 | Stable operation |
| 30 < α < 60 | Marginally stable |
| α > 60 | Unstable |
4. Multi-Agent Consensus Implementation
The distributed consensus algorithm achieves SOC synchronization:
$$ ext{SOC}_{ ext{ave}}[k+1] = \frac{1}{N}\sum_{j\in\mathcal{N}_i} ( ext{SOC}_j[k] + \epsilon( ext{SOC}_i[k] – ext{SOC}_j[k])) $$
Key performance metrics for energy storage inverters:
| Metric | Proposed Strategy | Conventional Droop |
|---|---|---|
| SOC Convergence Time | 2.8s | N/A |
| Frequency Deviation | <0.2Hz | 0.5Hz |
| Reactive Power Error | <3% | 15% |
5. Case Studies and Validation
Simulation results demonstrate the energy storage inverter’s performance under various scenarios:
$$ \Delta P_{ ext{max}} = \frac{C_i}{\sum C_j} P_{ ext{load}} \pm 2.5\% $$
Plug-and-play capability verification shows:
$$ t_{ ext{recovery}} = \frac{-\ln(0.05)}{\sigma_{\min}(L)} < 500 ext{ms} $$
The proposed control strategy enables energy storage inverters to maintain voltage quality (THD < 2.5%) while achieving SOC balance (ε < 5%) across different capacity configurations. Experimental validation confirms the algorithm’s scalability for systems with 4-8 parallel units.