Quantifying Grid-Forming Behavior: Bridging Device-level Dynamics and System-Level Stability
Kehao Zhuang, Huanhai Xin, Verena Häberle, Xiuqiang He, Linbin Huang, Florian Dörfler
TL;DR
The paper addresses how grid-forming (GFM) converters influence system stability in grids increasingly dominated by power-electronics and PLL-based converters. It introduces a device-level Forming Index ($FI(ω)$) defined as the maximum singular value of the converter-grid sensitivity $S_v(ω)$, distinguishing GFM from GFL by quantifying grid-following versus grid-forming tendencies. At the system level, it defines System Strength ($κ(ω)$) as the minimum singular value of the reduced network admittance and relates it to Grid Strength ($α(ω)$); it proves that GFM behavior enhances system strength under small-signal disturbances. The approach is illustrated conceptually on an IEEE 39-bus system, showing that reducing $FI(ω)$ improves the lower bound on system strength, thereby suggesting that GFM-enabled devices can bolster grid stability in practice.
Abstract
Grid-Forming (GFM) technology is considered a promising solution to build power electronics-dominated power systems. However, the impact of GFM converters on the system stability is still unquantified, creating a gap between the system- and device-level perspectives. To fill this gap, at the device-level, we propose a Forming Index to quantify a converter's response to grid voltage variations, providing a characterization of its GFM behavior. At the system-level, a quantitative notion of System Strength is introduced to capture the fundamental requirements for power system formation. Finally, we establish the alignment between device- and system-level metrics by demonstrating that GFM converters provably enhance system strength.