Dual-frames-impedance-based Analysis of Dynamic Phase Difference Effect on Grid-Forming Converter with Different Power Synchronization Controls

The grid-forming converters (GFMs) have been widely employed to support the power grid. Yet, the phase difference effect (PHE) caused by active power control (APC) on the system's design and stability is still inexplicable. This paper comprehensively investigates the PHE in the GFM under six APCs in terms of the developed impedance models. We observed that GFM exhibits nearly equal dq-frame impedance across six APCs when the PHE is disregarded. However, when accounting for PHE, the impedance of GFM with P-δ droop-based APCs differs significantly from that with P-ω droop- and virtual synchronous generator (VSG)-based APCs. Additionally, the sequence impedance of GFM with P-ω droop- and VSG-based APCs appears to be largely decoupled, whereas P-δ droop-based APCs introduce substantial sequence impedance coupling. Stability and coupling analyses indicate that the P-δ droop-based GFM must work in a weaker grid for stable operation compared to other APC-based GFM. Furthermore, the resulting frequency coupling leads to a higher amplitude of the coupled frequency (2f1-f) than the dominant frequency (f). Lastly, theoretical analysis is verified by experiments, providing new insights into the future research and design guidelines of GFM.