Spatial-Frequency Control Authority of Grid-Forming Inverters over Voltage Waveforms in Distribution Feeders

Overview & Synopsis

This paper develops a spatial-frequency framework to quantify the impact of distributed energy resources with grid-forming inverters (GFMs) on voltage waveforms at different locations along a feeder. An analytical authority function is formulated to characterize how controllability varies with both electrical distance from the point of common coupling (PCC) and frequency. It is shown that the GFM control authority generally decays with both distance and frequency, reflecting the limited ability of inverter actions to influence voltage waveforms at distant points. To better capture controllability near resonance, a relative dominance metric is introduced to compare the influence of inverter-induced and grid-induced voltages at a given location and frequency. These results highlight that waveform controllability is fundamentally a spatial-frequency phenomenon along the feeder. Simulation studies validate the analytical findings by demonstrating both the spatial decay of control effectiveness along the feeder and the frequency-dependent trends in control authority in a realistic electromagnetic transient setting. The proposed framework provides insights into the placement and coordination of GFMs to enable effective waveform-level voltage control across electrical distance along the feeder.