Revisiting the Voltage-Source Behavior: Why Impedance Magnitude of Grid-Forming Converter Rises Near Fundamental Frequency?

TL;DR

This paper explains the unexpected impedance peak in grid-forming converters near the fundamental frequency as a result of active power control dynamics involving integrative action, impacting impedance evaluation standards.

Contribution

It reveals the physical origin of impedance anomalies in GFM converters and proposes a quantitative index for impedance-based voltage-source assessment.

Findings

Impedance peak caused by active power control dynamics.

Exclusion bandwidth around fundamental frequency is governed by power-frequency dynamics.

Proposed index offers a theoretical criterion for impedance standardization.

Abstract

Grid-forming (GFM) converters are generally expected to exhibit low impedance near the fundamental frequency due to their voltage-source behavior. However, an impedance peak and a negative-resistance region are consistently observed in this range, which contradicts this expectation and lacks a clear physical explanation. This paper reveals that these phenomena originate from the inherent dynamics of the active power control loop, where the mapping from power disturbance to the synchronous angle inherently involves an integrative action, intrinsically preventing a positive-resistance characteristic near the fundamental frequency. This finding explains why existing grid codes in China, the United States, and Europe exclude a narrow band around the fundamental frequency in impedance-based evaluations. It is further shown that the width of the excluded frequency band (e.g., +/- 3~5 Hz) is governed by the power-to-frequency dynamics. Based on this insight, a quantitative index is proposed to determine the exclusion bandwidth from the corner frequencies of the impedance magnitude curve. The proposed index provides a concise and theoretically grounded criterion for voltage-source assessment and impedance standardization of GFM converters.