As power systems transition toward inverter-based resource (IBR)-dominated grids, traditional system strength definitions and metrics are becoming increasingly inadequate to characterize emerging stability challenges. NERC defines system strength at a bus as the sensitivity of terminal voltage to variations in current injection. Emerging definitions characterize system strength in terms of "voltage source behind impedance (VSBI)" characteristics. Similarly, grid-forming (GFM) IBRs are also expected to contribute to grid voltage stiffness by exhibiting near-constant VSBI characteristics in the sub-transient time frame. Thus, it is essential to assess and quantify VSBI characteristics as a measure of system strength and GFM capability.

VSBI characteristics are defined as the ability of a device to behave like an ideal voltage source behind an impedance in the sub-transient time frame. In the case of a voltage phase angle (or magnitude) jump, the device should exchange an appropriate amount of active (or reactive) power or current with the grid. In the frequency domain, VSBI characteristics can be assessed by comparing admittance spectra (Ydq (s)) or frequency-domain Jacobian (J(s)) spectra to those of an ideal voltage source (IDVS) behind an impedance, i.e., similar P-θ and Q-V characteristics over the frequency range of interest. Building on this framework, a novel “Jacobian Voltage Stiffness Metric (JVSM)” is defined to capture both the speed and magnitude of the response and quantify system strength and grid-forming capability.

The advantages of JVSM over traditional and existing system strength metrics are demonstrated through a structured comparison across four key characteristics: (a) applicability, i.e., which power system stability characteristics the metric captures; (b) practicality and scalability, i.e., whether the metric can be applied to bulk power systems and adopted by system operators; (c) IBR consideration and model dependency, i.e., whether the metric accounts for IBR-dominated grids, the presence of nearby devices, and the need for detailed models; and (d) operating point dependency, i.e., whether the metric varies with the operating point. JVSM is benchmarked against traditional metrics (SCR, gSCR, eSCR), industry-adopted metrics (Dynamic Admittance, nSCR), and recent frequency-domain metrics (Grid Strength Impedance Metric, Admittance Margin, Dynamic Similarity Index, and Forming Index).

EMT-based simulations conducted in PSCAD on the IEEE 39-bus system validate that JVSM more accurately identifies small- signal instability than existing metrics. The case study results confirm that JVSM provides a comprehensive characterization of system strength and GFM capability in IBR-dominated grids.