1. Introduction
The rapid integration of renewable energy sources into power grids has necessitated advancements in energy storage systems (ESS). Energy storage inverters, particularly grid-forming inverters, play a critical role in stabilizing modern power systems by emulating synchronous generator characteristics. However, parallel operation of multiple energy storage inverters introduces challenges such as unequal power sharing, voltage-frequency deviations, and state-of-charge (SOC) imbalances. This paper proposes an improved virtual synchronous generator (VSG) control strategy to address these issues, ensuring stable and efficient coordination of parallel-connected energy storage inverters.
2. System Configuration and Modeling
2.1 Topology of Parallel-Connected Energy Storage Inverters
A typical parallel ESS comprises multiple energy storage units (e.g., vanadium redox flow batteries), bidirectional DC/DC converters, and grid-forming inverters. The DC/AC stage employs a three-phase voltage-source inverter with LC filters to suppress harmonics. The parallel architecture enhances system redundancy and scalability but requires precise control to mitigate circulating currents and power imbalances.
2.2 Mathematical Model of VSG-Based Inverters
The VSG algorithm replicates the electromechanical dynamics of synchronous generators. The rotor motion equation and stator electrical equations are: [ J \frac{d\Delta\omega}{dt} = T_m – T_e – D_p \Delta\omega ] [ E = U + I(R + j\omega L) ] where ( J ), ( D_p ), ( T_m ), and ( T_e ) represent inertia, damping coefficient, mechanical torque, and electromagnetic torque, respectively.
3. Fundamentals of VSG Control Strategy
3.1 Active Power-Frequency Regulation
The active power loop adjusts the inverter’s frequency using a droop characteristic: [ P_m = P{ref} – k{pf}(\omega{vsg} – \omega{ref}) ] [ \omega{vsg} = \omega{ref} + \frac{P_m – P}{J s + D_p} ] where ( k_{pf} ) is the frequency droop coefficient, and ( P ) is the measured active power.
3.2 Reactive Power-Voltage Regulation
The voltage loop ensures reactive power sharing: [ E_m = k_q(Q{ref} – Q_e) + k_u(U{ref} – U_{vsg}) + E_0 ] where ( k_q ) and ( k_u ) are voltage droop coefficients, and ( E_0 ) is the no-load voltage.
4. Enhanced VSG Control with Adaptive Virtual Impedance and SOC Balancing
4.1 Adaptive Virtual Impedance Compensation
Line impedance mismatches cause unequal reactive power sharing. To address this, an adaptive virtual impedance ( Z_v = R_v + jX_v ) is introduced: [ Z{v,i} = -\frac{\Delta R_i + \Delta X_i \cot\phi}{1 + \cot\phi} ] [ L{v,i} = -\frac{K{v,i}}{n} \sum{j \neq i}^n (Q_i – Q_j) ] This dynamically adjusts the inverter’s output impedance, equalizing reactive power distribution.
4.2 SOC-Based Active Power Allocation
SOC imbalances among storage units are mitigated by adjusting active power references: [ SOC_i(t) = SOC{i,0} + \frac{1}{C_N} \int_0^t P{out,i} \, dt ] [ k{soc,i} = 1 + \frac{\Delta SOC_i(t)}{\overline{SOC}(t)} ] [ P{ref,i}^* = k{soc,i} P{ref} ] where ( \overline{SOC} ) is the average SOC, and ( k_{soc,i} ) prioritizes units with higher SOC.
5. Simulation Analysis and Validation
5.1 Simulation Setup
A MATLAB/Simulink model of three parallel energy storage inverters was developed, with parameters listed in Table 1.
Table 1: Key Simulation Parameters
| Parameter | Value |
|---|---|
| DC Bus Voltage | 800 V |
| AC Grid Voltage | 380 V (L-L) |
| Switching Frequency | 20 kHz |
| Line Impedance (R/X) | 0.04 Ω/0.4 mH |
| VRB Capacity | 10 kWh |
5.2 Performance Evaluation
- Adaptive Virtual Impedance: Reduced voltage deviations by 62% and improved reactive power sharing accuracy to 98%.
- SOC Balancing: Achieved SOC convergence within 15 seconds, reducing SOC disparity from 15% to 2%.
6. Conclusion
The proposed enhanced VSG control strategy effectively addresses critical challenges in parallel-connected energy storage inverters. By integrating adaptive virtual impedance and SOC-based power allocation, the method ensures stable voltage/frequency regulation, mitigates circulating currents, and prolongs battery lifespan. This advancement supports the scalable deployment of grid-forming energy storage systems in high-renewable penetration scenarios.
Keywords: energy storage inverter, virtual synchronous generator, adaptive virtual impedance, SOC balancing, parallel operation.