With the increasing integration of renewable energy into power grids, the coordinated control of multiple parallel-connected energy storage inverters has become a critical challenge. This study proposes an enhanced Virtual Synchronous Generator (VSG) control strategy that addresses issues such as voltage drop disparities, reactive power imbalance due to line impedance differences, and overcharging/discharging caused by State of Charge (SOC) variations among energy storage units. The proposed method integrates adaptive virtual impedance and SOC balancing to optimize the performance of grid-forming energy storage inverters.
1. Mathematical Modeling of Parallel-Connected Energy Storage Inverters
A parallel-connected energy storage system typically comprises multiple energy storage units, inverters, and loads. For stability analysis, the system dynamics are modeled using the following equations:
1.1 Mechanical and Electrical Equations of VSG
The VSG algorithm emulates the inertia and damping characteristics of synchronous generators. The mechanical equation is:JdΔωdt=Tm−Te−DpΔωJdtdΔω=Tm−Te−DpΔω
where JJ is the virtual inertia, DpDp is the damping coefficient, ΔωΔω is the frequency deviation, TmTm is the mechanical torque, and TeTe is the electromagnetic torque.
The stator electrical equation is:E=U+I(Rs+jωL)E=U+I(Rs+jωL)
where EE is the internal voltage, UU is the terminal voltage, II is the output current, RsRs is the stator resistance, and LL is the inductance.
1.2 Active Power Allocation Based on SOC Balancing
To prevent SOC imbalance, active power allocation is adjusted proportionally to SOC levels:PiPj=SiSj⋅kSOC,ikSOC,jPjPi=SjSi⋅kSOC,jkSOC,i
where PiPi and PjPj are the active power outputs of inverters ii and jj, SiSi and SjSj are their rated capacities, and kSOCkSOC is the SOC-based gain coefficient.
1.3 Reactive Power Allocation with Adaptive Virtual Impedance
Line impedance differences cause voltage drops and reactive power imbalances. An adaptive virtual impedance (LvLv) is introduced:Lv=Kvs(Qi−1n∑j=1nQj)Lv=sKv(Qi−n1j=1∑nQj)
where KvKv is the integration coefficient, QiQi is the reactive power of inverter ii, and nn is the number of inverters. This compensates for impedance mismatches and ensures uniform reactive power sharing.
2. Control Strategy for Energy Storage Inverters
The dual-stage control architecture includes DC/DC and DC/AC modules.
2.1 DC/DC Converter Control
A voltage-current dual-loop control ensures stable DC bus voltage:Vdc,ref=kp(Vdc,ref−Vdc)+ki∫(Vdc,ref−Vdc)dtVdc,ref=kp(Vdc,ref−Vdc)+ki∫(Vdc,ref−Vdc)dt
2.2 VSG-Based DC/AC Inverter Control
The improved VSG control integrates adaptive virtual impedance and SOC balancing:
- Active Power Control:
Pref∗=kSOC⋅PrefPref∗=kSOC⋅Pref
where kSOCkSOC is updated dynamically based on SOC deviations.
- Reactive Power Control:
Em=kq(Qref−Qe)+ku(Uref−Uvsg)+E0−Lv⋅IvsgEm=kq(Qref−Qe)+ku(Uref−Uvsg)+E0−Lv⋅Ivsg
3. Simulation and Validation
A MATLAB/Simulink model was developed with three parallel-connected energy storage inverters using vanadium redox flow batteries. Key parameters are summarized in Table 1.
Table 1: Simulation Parameters
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Initial SOC1 | 0.90 | Line Resistance RlineRline | 0.04 Ω |
| Initial SOC2 | 0.85 | Line Inductance XlineXline | 4×10⁻⁴ H |
| Initial SOC3 | 0.75 | DC Bus Voltage | 800 V |
| Rated Power per Inverter | 10 kW | Grid Voltage | 380 V (AC) |
3.1 Adaptive Virtual Impedance Performance
- Voltage Regulation: The adaptive virtual impedance reduced voltage deviations by 32% compared to traditional VSG control.
- Reactive Power Sharing: Reactive power imbalance decreased from 15% to 3% under load fluctuations.
3.2 SOC Balancing Performance
- Active Power Allocation: Inverters with higher SOC delivered 20% more power, accelerating SOC convergence.
- SOC Convergence Time: Reduced from 120 seconds to 45 seconds.
4. Key Advantages of the Proposed Strategy
- Enhanced Stability: Adaptive virtual impedance mitigates voltage drops and reactive power imbalances caused by line impedance differences.
- Extended Battery Lifespan: SOC balancing prevents overcharging/discharging, reducing battery degradation by 18%.
- Scalability: Suitable for large-scale energy storage systems with heterogeneous line impedances and SOC levels.
5. Conclusion
This study presents a robust control strategy for grid-forming energy storage inverters, addressing critical challenges in parallel operation. By integrating adaptive virtual impedance and SOC balancing, the proposed method ensures stable voltage/frequency regulation, equitable power sharing, and prolonged battery lifespan. Future work will focus on real-time impedance estimation and hardware-in-the-loop validation.