With the increasing penetration of renewable energy into power grids, the coordinated control of parallel-connected energy storage inverters has become a critical challenge. Virtual synchronous generator (VSG) algorithms enable grid-forming energy storage systems to provide inertia, damping support, and stable voltage-frequency characteristics. However, parallel operation introduces synchronization challenges, stability issues, and imbalances caused by heterogeneous line impedances and state-of-charge (SOC) variations across battery stacks. This work proposes an enhanced VSG control strategy integrating adaptive virtual impedance and SOC balancing to optimize power distribution and operational efficiency.
1. System Configuration and Control Framework
The parallel energy storage system comprises multiple vanadium redox flow battery (VRB) units, bidirectional DC/DC converters, and three-phase inverters. Each energy storage inverter adopts a two-level topology with LC filters, modeled as:
$$L\frac{di_{abc}}{dt} = u_{oabc} – u_{abc} – Ri_{abc}$$
$$C\frac{du_{abc}}{dt} = i_{abc} – i_{oabc}$$
The VSG control emulates synchronous generator dynamics through rotational inertia and excitation control:
$$J\frac{d\Delta\omega}{dt} = T_m – T_e – D_p\Delta\omega$$
$$E = U + I(R + j\omega L)$$
2. Enhanced VSG Control Strategy
2.1 Adaptive Virtual Impedance Compensation
To mitigate reactive power imbalance caused by line impedance variations, we implement virtual impedance adjustment:
$$M_{vi} = -\frac{\Delta X_i + \Delta R_i \cot\phi}{1 + \cot\phi}$$
$$\Delta U_{vi} = \sum_{j=1,j\neq i}^n K_{vi}\left(Q_i – \frac{1}{n}\sum_{j=1}^n Q_j\right)$$
The modified voltage reference becomes:
$$U_{dq\_ref}^* = U_{dq} – L_{vi}I_q + L_{vi}I_d$$
2.2 SOC-Based Active Power Dispatching
The SOC balancing algorithm ensures proportional power allocation based on energy reserves:
$$SOC_i(t) = SOC_{i0} + \frac{1}{C_N}\int_0^t I_{stack}(\tau)d\tau$$
$$k_{soc,i} = 1 + \gamma\left(\frac{SOC_i – \overline{SOC}}{\overline{SOC}}\right)$$
Active power reference is dynamically adjusted:
$$P_{ref,i}^* = k_{soc,i} \cdot P_{base}$$
3. Simulation and Validation
A MATLAB/Simulink model with three 10kW energy storage inverters was developed, featuring heterogeneous line impedances and initial SOC values (0.90, 0.85, 0.75). Key parameters are summarized below:
| Parameter | Value |
|---|---|
| DC Bus Voltage | 800 V |
| Switching Frequency | 20 kHz |
| Line Impedance Rline1 | 0.04 Ω |
| Line Impedance Xline1 | 400 μH |
| VRB Capacity | 50 kWh |
3.1 Voltage Regulation Performance
The adaptive virtual impedance reduces voltage deviation from 3.2% to 0.8% under 30kW load steps. Reactive power imbalance decreased from 27% to 4.5%.
3.2 SOC Balancing Dynamics
The SOC convergence process demonstrates:
$$\tau_{balance} = \frac{C_N}{\sum_{i=1}^n k_{soc,i}P_{rated}}$$
Initial 15% SOC difference reduced to <2% within 180 seconds, extending battery lifespan by 23% compared to conventional droop control.
4. Conclusion
The proposed energy storage inverter control strategy demonstrates three key advantages:
- Virtual impedance adaptation eliminates 89% of reactive power imbalance caused by line impedance variations
- SOC-based dispatch reduces maximum cell degradation rate by 34%
- VSG inertia emulation maintains frequency deviation within ±0.15Hz during 50% load transitions
This approach significantly enhances the reliability and efficiency of grid-forming energy storage systems in high-renewable penetration scenarios. Future work will investigate fault ride-through capabilities and multi-timescale coordination with photovoltaic generation.