With the increasing integration of renewable energy into power grids, coordinated control of multiple parallel energy storage inverter has become critical. Virtual Synchronous Generator (VSG) algorithms provide grid-forming energy storage systems with damping, inertia support, and stable voltage/frequency regulation. However, challenges such as line impedance differences and State-of-Charge (SOC) imbalance among battery stacks require advanced control strategies for parallel operation.
System Configuration and Modeling
The parallel energy storage system architecture consists of vanadium redox flow batteries (VRBs), two-level power conversion systems (PCS), and AC loads. Each energy storage inverter employs a bidirectional Buck/Boost DC/DC converter and a three-phase voltage-source inverter with LC filters. The mathematical model for parallel operation considers:
$$ J\frac{d\Delta\omega}{dt} = T_m – T_e – D_p\Delta\omega $$
$$ E = U + I(R + j\omega L) $$
Key parameters of the energy storage inverter system are summarized in Table 1.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Rated Power | 10 kW | DC Bus Voltage | 800 V |
| Switching Frequency | 20 kHz | Filter Inductance | 2 mH |
| Filter Capacitance | 50 μF | Line Impedance | 0.02-0.04 Ω |
Enhanced VSG Control Strategy
The proposed improved VSG control integrates adaptive virtual impedance and SOC balancing:
1. Adaptive Virtual Impedance Compensation
The virtual impedance adjustment mechanism addresses line impedance differences:
$$ M_{vi} = -\frac{\Delta X_i + \Delta R_i \cot\phi}{1 + \cot\phi} $$
$$ L_{vi} = -\frac{K_{vi}}{s}\left(\sum_{j=1,j\neq i}^n Q_j – (n-1)Q_i\right) $$
2. SOC-Based Power Allocation
Dynamic power distribution considering battery SOC levels:
$$ \Delta SOC_i = SOC_i – \frac{1}{n}\sum_{j=1}^n SOC_j $$
$$ k_i(t+T_s) = 1 + \frac{\Delta SOC_i(t)}{SOC(t)} $$
$$ P_{ref,i}^* = k_i \cdot P_{ref} $$
Simulation and Validation
The MATLAB/Simulink model demonstrates superior performance in:
- Reactive power sharing accuracy improvement: 92% → 98%
- SOC balancing time reduction: 180s → 65s
- Voltage regulation enhancement: ±3% → ±0.8%
Critical performance metrics are compared in Table 2.
| Metric | Conventional VSG | Improved VSG |
|---|---|---|
| Reactive Power Deviation | 12.8% | 2.4% |
| SOC Convergence Time | 180s | 65s |
| THD (Voltage) | 3.2% | 1.8% |
Conclusion
The proposed energy storage inverter control strategy effectively addresses line impedance variations and SOC imbalances through:
- Adaptive virtual impedance compensation for accurate reactive power sharing
- Dynamic SOC-based power allocation for battery lifespan optimization
- Enhanced stability under load transients (30% step changes)
This approach significantly improves the operational efficiency and reliability of grid-forming energy storage systems, particularly in high-renewable penetration scenarios. Future work will focus on hardware implementation and multi-objective optimization for large-scale energy storage inverter arrays.
$$ \text{System Efficiency} \eta = \frac{P_{out}}{P_{in}} \times 100\% \geq 96.5\% $$
$$ \text{SOC Balancing Error} \epsilon_{SOC} = \max|SOC_i – \overline{SOC}| \leq 1.2\% $$