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Mitigation of Structural Harmonic Instability in Virtual Admittance-Based Grid-Forming Inverters via Mimicking Skin Effect

Jaekeun Lee, Jae-Jung Jung, Shenghui Cui

Abstract

The virtual admittance-current controller (VA-CC) scheme is widely employed to emulate an equivalent inductance in front of the internal voltage source of grid-forming inverters. However, recent studies have reported harmonic instabilities associated with VA-CC, motivating the need for a more physically interpretable understanding of their origin. This letter identifies a delay-independent structural mechanism of harmonic instability in the VA-CC scheme, wherein the interaction between the filter and virtual inductances introduces a non-passive second-order transfer-function term exhibiting negative resistance. To address this issue, a simple yet effective modification is proposed by integrating a parallel virtual resistor into the VA structure. This reconfiguration enhances the passivity of VA-CC scheme across the harmonic range by mimicking the skin effect which augments damping in high-frequency range, without altering the wellestablished current controller or voltage feedforward control. Experimental results validate that the proposed method achieves robust harmonic stability, whereas the conventional approach fails under identical grid conditions.

Mitigation of Structural Harmonic Instability in Virtual Admittance-Based Grid-Forming Inverters via Mimicking Skin Effect

Abstract

The virtual admittance-current controller (VA-CC) scheme is widely employed to emulate an equivalent inductance in front of the internal voltage source of grid-forming inverters. However, recent studies have reported harmonic instabilities associated with VA-CC, motivating the need for a more physically interpretable understanding of their origin. This letter identifies a delay-independent structural mechanism of harmonic instability in the VA-CC scheme, wherein the interaction between the filter and virtual inductances introduces a non-passive second-order transfer-function term exhibiting negative resistance. To address this issue, a simple yet effective modification is proposed by integrating a parallel virtual resistor into the VA structure. This reconfiguration enhances the passivity of VA-CC scheme across the harmonic range by mimicking the skin effect which augments damping in high-frequency range, without altering the wellestablished current controller or voltage feedforward control. Experimental results validate that the proposed method achieves robust harmonic stability, whereas the conventional approach fails under identical grid conditions.
Paper Structure (9 sections, 10 equations, 7 figures, 1 table)

This paper contains 9 sections, 10 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Analysis on the Instability of VA-CC
  3. Formulation of Equivalent Output Impedance
  4. Inherent Non-passivity of Conventional VA-CC
  5. Proposed VA with Parallel Virtual Resistor
  6. Physical Rationale and Design of the Proposed VA
  7. Comparison of Conventional and Proposed VA-CC Schemes
  8. Experimental Verification
  9. Conclusion

Figures (7)

  • Figure 1: VA-CC instability: (a) control structure, (b) equivalent circuit of $Z_\text{eq}(s)$, and (c) emergence of the negative resistance term, $s^2 L_\text{v}L_\text{f}$.
  • Figure 2: Proposed VA structure: (a) circuit model of the proposed VA and (b) control implementation of the proposed VA.
  • Figure 3: Experimental setup and control structure.
  • Figure 4: Comparison of $1/Y_\text{v}(s)$ between the conventional and proposed methods.
  • Figure 5: Impedance plot of $Z_\text{eq}(s)$: (a) with the conventional VA and (b) with the proposed VA.
  • ...and 2 more figures