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

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.

💡 Research Summary

The paper investigates a fundamental source of harmonic instability in virtual‑admittance‑based grid‑forming inverters that employ the virtual admittance‑current controller (VA‑CC) architecture. VA‑CC consists of a virtual admittance (Yv), a current controller (CC), and voltage feed‑forward (VFF). While the virtual admittance is typically realized as a series R‑L network to emulate an inductive source, the interaction between the filter inductance (Lf) and the virtual inductance (Lv) introduces a second‑order term s²LfLv/Kcc,p into the inverter’s equivalent output impedance (Zeq). In the harmonic frequency range this term manifests as a negative resistance (–ω²LfLv/Kcc,p), rendering the overall system non‑passive and causing the return‑ratio Zg/Zeq to cross the critical 180° phase condition, which leads to instability. Importantly, this mechanism is delay‑independent; even when control delays are removed, the non‑passivity persists, contradicting earlier explanations that focused on controller bandwidth or delay.

To mitigate this structural issue without altering the well‑established current controller or VFF, the authors propose augmenting the virtual admittance with a parallel virtual resistor, thereby mimicking the skin‑effect damping that physical inductors exhibit at high frequencies. The modified admittance is expressed as

 Yv,prop(s) =