Frequency Domain Inertia Design of Grid-Forming Converters

Synthetic inertia plays a pivotal role in the frequency response of grid-forming (GFM) converters. A small inertia factor provides insufficient inertia power to resist frequency variations during grid contingencies. By contrast, a large inertia factor allows GFM converters to mimic the dynamic response of synchronous generators but could compromise grid synchronization during extreme frequency events, e.g., frequency disturbances from 47 to 52 Hz or phase jumps up to 60^\circ. This happens when a current-limiting GFM converter fails to track a output power reference governed by the power synchronization loop (PSL). Unlike conventional inertia designs that use fixed inertia factors, this paper proposes a frequency domain inertia design method for GFM converters based on a modified bandwise PSL. The equivalent inertia factor of GFM converters can be defined as a transfer function by leveraging the equivalence between the high-frequency droop power component and the low-frequency inertia power component, such that the inertia factor is frequency-dependent and varies across different frequency ranges. The proposed inertia design solution combines the advantages of conventional low- and high-inertia design, providing large inertia factor in low-frequency range to mitigate frequency disturbances and small inertia factor in high-frequency range to facilitate power and frequency recovery. The dynamic response of GFM converters adopting the proposed design is experimentally verified and also demonstrated in an accompanied video file under different scenarios including network transients such as grid phase jumps, grid voltage sags and frequency excursions, as well as operational events of power step change and load reduction.