Quantifying Grid-Forming Behavior: Bridging Device-level Dynamics and System-Level Strength

Grid-forming (GFM) technology is widely regarded as a promising solution for future power systems dominated by power electronics. However, a precise method for quantifying GFM converter behavior and a universally accepted GFM definition remain elusive. Moreover, the impact of GFM on system stability is not precisely quantified, creating a significant disconnect between device and system levels. To address these gaps from a small-signal perspective, at the device level, we introduce a novel metric, the Forming Index (FI) to quantify a converter's response to grid voltage fluctuations. Rather than enumerating various control architectures, the FI provides a metric for the converter's GFM ability by quantifying its sensitivity to grid variations. At the system level, we propose a new quantitative measure of system strength that captures the multi-bus voltage stiffness, which quantifies the voltage and phase angle responses of multiple buses to current or power disturbances. We further extend this concept to grid strength and bus strength to identify weak areas within the system. Finally, we bridge the device and system levels by formally proving that GFM converters enhance system strength. Our proposed framework provides a unified benchmark for GFM converter design, optimal placement, and system stability assessment.