Abstract
The integration of grid-forming energy storage inverters (GFIs) in parallel configurations enhances power supply reliability and redundancy for critical loads. However, direct parallel operation of GFIs with LCL filters introduces circulating currents and power frequency oscillations, threatening system stability. This study establishes a state-space model for LCL-filtered GFI systems, identifies the mechanism of circulating resonance, and proposes a damping control strategy using capacitor current feedback to suppress oscillations. Experimental validation confirms the effectiveness of the proposed method in improving system stability and current waveform quality.
1. Introduction
The transition toward renewable energy demands grid-forming inverters (GFIs) capable of autonomous frequency/voltage regulation. Parallel operation of energy storage inverters increases system capacity and improves output current quality, especially when paired with LCL filters. However, inherent resonance in LCL networks amplifies circulating currents between parallel modules, leading to power frequency oscillations. Existing studies focus on standalone LCL-filtered inverters, neglecting challenges in parallel configurations. This work bridges the gap by analyzing resonance mechanisms and proposing a novel damping strategy tailored for parallel GFI systems.
2. Circulating Current and Power Frequency Oscillation Mechanisms
2.1 LCL Filter Characteristics
The LCL filter, compared to traditional L filters, offers superior high-frequency attenuation but introduces resonance risks. Its frequency-domain transfer function is derived as:GLCL(s)=ig(s)ui(s)=1s3CfL1L2+s(L1+L2)GLCL(s)=ui(s)ig(s)=s3CfL1L2+s(L1+L2)1
where L1L1 and L2L2 are inverter-side and grid-side inductances, and CfCf is the filter capacitance. The resonance frequency is:fr=12πL1+L2CfL1L2fr=2π1CfL1L2L1+L2
Table 1 compares key parameters of L and LCL filters.
| Parameter | L Filter | LCL Filter |
|---|---|---|
| Attenuation Slope | -20 dB/dec | -40 dB/dec |
| Resonance Frequency | None | Dependent on L1,L2,CfL1,L2,Cf |
| Stability Risks | Low | High |
2.2 Parallel System Resonance Analysis
In parallel GFI systems, interactions between inverters amplify circulating currents. The equivalent single-phase circuit (Fig. 5 in the original text) yields the circulating current transfer function:Gcirc(s)=icirc(s)ui1(s)=s2CfL1(L1+L2)+L1+L2s3CfL1(L1+L2)+s2(L1+L2+Lg)+⋯Gcirc(s)=ui1(s)icirc(s)=s3CfL1(L1+L2)+s2(L1+L2+Lg)+⋯s2CfL1(L1+L2)+L1+L2
where LgLg is the grid impedance. Resonance peaks coincide with the system’s natural frequencies, causing oscillations that degrade equipment lifespan and grid stability.
3. Damping Control Strategy for Oscillation Suppression
3.1 Traditional Current Control Limitations
Conventional PI-based current control in the dqdq-frame suffers from steady-state errors and poor resonance damping. The control structure (Fig. 8a in the original text) lacks mechanisms to counteract circulating currents.
3.2 Proposed Capacitor Current Feedback
To suppress resonance, a damping term derived from capacitor current feedback is integrated into the current loop (Fig. 8b in the original text). The modified control law becomes:ui=GPI(s)⋅(iref−ig)−Kd⋅icfui=GPI(s)⋅(iref−ig)−Kd⋅icf
where KdKd is the damping gain, and icficf is the capacitor current. The updated transfer function for the LCL filter is:Gdamped(s)=ig(s)ui(s)=1s3CfL1L2+s2CfL1(L1+L2)+s(L1+L2)+KdGdamped(s)=ui(s)ig(s)=s3CfL1L2+s2CfL1(L1+L2)+s(L1+L2)+Kd1
3.3 Parameter Design and Stability Trade-offs
Optimal KdKd selection balances resonance suppression and system stability. Frequency response analysis (Fig. 10 in the original text) shows that Kd=25Kd=25 achieves significant resonance attenuation without destabilizing the system.
4. Experimental Validation
4.1 Test Platform Setup
A prototype with two parallel GFIs was built using the parameters below:
| Parameter | Value |
|---|---|
| DC Input Voltage | 400 V |
| AC Line Voltage | 220 V |
| L1,L2L1,L2 | 3 mH, 6 mH |
| CfCf | 12 μF |
4.2 Results Without Damping
Under conventional control, the grid current (igig) exhibits minor resonance, while circulating currents (icircicirc) and inverter-side currents (iL1,iL2iL1,iL2) show severe oscillations (Fig. 11 in the original text). FFT analysis confirms harmonic alignment between icircicirc and iL1/2iL1/2 (Fig. 12).
4.3 Results With Proposed Damping
Introducing capacitor current feedback reduces circulating currents by 72% and improves grid current THD from 4.8% to 1.2% (Fig. 13). Key metrics are summarized below:
| Metric | Without Damping | With Damping |
|---|---|---|
| Circulating Current (A) | 8.5 | 2.4 |
| Grid Current THD (%) | 4.8 | 1.2 |
| Resonance Peak (dB) | 35 | 12 |
5. Conclusion
This study addresses power frequency oscillations in parallel grid-forming energy storage inverters through a capacitor current feedback-based damping strategy. Key contributions include:
- Mechanism Analysis: Resonance in LCL-filtered GFI systems is linked to circulating currents.
- Control Design: A damping term integrated into the current loop suppresses oscillations without compromising stability.
- Experimental Proof: Prototype tests validate the strategy’s effectiveness in reducing harmonics and enhancing reliability.
Future work will explore adaptive damping gains and scalability for larger multi-inverter systems.