Source-linked AI summary
Quantifying Grid-Forming Requirements for System Strength: How Much and Where?
Ambuj Gupta, Balarko Chaudhuri, Mark O'Malley
TL;DR
As IBRs displace synchronous generation, conventional SCR-based measures do not necessarily capture small-signal voltage stiffness, leaving GFM number and placement requirements unclear. The paper uses JVSM to assess system strength across GFM configurations; strength generally rises with GFM count, but placements with the same count can differ substantially. The authors therefore support specifying GFM requirements by resulting system strength rather than by count or penetration alone.
Problem
In IBR-dominated grids, conventional SCR-based measures do not necessarily characterize small-signal voltage stiffness, and the required number and locations of GFM IBRs remain unclear.
Source: §1 · p. 1Method
The paper uses JVSM, derived from frequency-domain Jacobian characteristics, to compare bus-wise strength across GFM numbers and placements.
Source: §1 · p. 1, §3.1 · p. 3Results
JVSM assessments show that more GFM IBRs generally strengthen the system, while configurations with the same count can differ substantially in voltage stiffness and small-signal stability.
Source: §4.3 · p. 5, §5 · p. 6Takeaways & Limitations
GFM requirements should be expressed in terms of achieved system strength, with bus-wise JVSM supporting comparisons of placements and checks of minimum voltage stiffness.
Source: §5 · pp. 6, 8
Abstract
from arXiv · showhide
As power systems transition toward inverter-based resource (IBR)-dominated grids, Grid-ForMing (GFM) IBRs are increasingly expected to provide the voltage-source characteristics required to maintain adequate system strength. However, how many GFM IBRs are required, and where they should be located in the grid, remains unclear. This paper investigates the impact of the number and location of GFM IBRs on small-signal system strength. The Jacobian Voltage Stiffness Metric (JVSM), which quantifies the voltage-magnitude and voltage-phase stiffness from frequency-domain Jacobian characteristics, is used as a system-strength measure. The analysis demonstrates that increasing the number of GFM IBRs generally improves system strength; however, configurations with the same number of GFM IBRs can exhibit significantly different bus-wise system-strength characteristics depending on their locations. Thus, this paper provides a quantitative basis for specifying GFM requirements in terms of the resulting system strength, rather than solely in terms of penetration level or the number of GFM IBRs. Case studies on a modified IEEE 39-bus system demonstrate how JVSM can be used to quantify and compare the system-strength impact of different numbers and locations of GFM IBRs, with the resulting strength assessments validated against small-signal oscillatory stability.
1 Introduction
As IBRs displace synchronous generation, conventional SCR-based measures may not capture small-signal voltage stiffness because IBR controls affect voltage-source behavior. The paper examines how GFM number and location shape system strength and motivates requirements based on the resulting strength.
1 Introduction
- In IBR-dominated grids, conventional SCR-based measures do not necessarily characterize small-signal voltage stiffness because strength depends on IBR dynamics and controls.Synchronous generators traditionally provide voltage-magnitude and phase stiffness; GFM IBRs are expected to provide similar voltage-source characteristics.Source: §1 · p. 1
- GFM requirements depend on both how many units are deployed and where they are located, since control design and electrical location affect system-level contribution.Requirements expressed only as installed capacity, unit count, or GFM penetration do not directly characterize resulting system strength.Source: §1 · p. 1
- Existing approaches leave the combined impact of GFM number and location on bus-wise voltage stiffness insufficiently analyzed.Prior approaches may assume ideal voltage sources or require detailed models, vector fitting, eigenvalue analysis, or reference impedance models.Source: §1 · p. 1
- The paper evaluates bus-wise JVSM across GFM numbers and placements and validates strength assessments against small-signal modal analysis.It also reports that equal-count placements can produce significantly different system-strength characteristics.Source: §1 · pp. 1–2
2 VSBI Characterization of System Strength
VSBI characterizes a device’s or grid’s ability to maintain voltage magnitude and phase around an operating point after disturbances. In IBR grids, this response can be non-ideal and control-dependent, so impedance alone does not determine stiffness.
2 VSBI Characterization of System Strength
- VSBI describes the ability of a device or grid, as seen from a bus, to maintain voltage magnitude and phase around an operating point following disturbances.A rapid, significant power response indicates stronger voltage stiffness; a slower or smaller response indicates weaker VSBI characteristics.Source: §2 · p. 2
- In the mechanical analogy, the wall anchor represents the internal voltage source and the stick length represents impedance Z.An ideal source has a rigid anchor, while a non-ideal, control-dependent source has a weaker anchor; at equal impedance, this can change terminal oscillations.Source: Figure 1 · p. 2, §2 · p. 2
- The frequency-domain Jacobian relates small voltage-magnitude and phase perturbations to active- and reactive-power responses.In high-X/R transmission systems, active-power/phase and reactive-power/magnitude couplings dominate; the other two couplings are not considered here.Source: §2 · p. 2
3 Jacobian Voltage Stiffness Metric
JVSM combines frequency-domain Jacobian characteristics to quantify voltage-magnitude and voltage-phase stiffness. It can compare standalone IBR strength with the bus-wise strength produced by the network and connected devices.
3.1 Metric Definition
- JVSM combines the magnitude and speed of active- and reactive-power responses to voltage disturbances into voltage-magnitude, voltage-phase, and overall stiffness measures.The metric weights faster responses and uses a 5–100 Hz range for the sub-transient to transient time frame; larger component values indicate stronger stiffness.Source: §3.1 · pp. 2–3
- JVSM can be calculated from frequency-domain scans without detailed internal models, reference impedance, prior GFM/GFL classification, or vector fitting.It retains the active-power/phase and reactive-power/magnitude characteristics that dominate in high-X/R transmission systems.Source: §3.1 · p. 3
3.2 Device- and Grid-Level Interpretation of JVSM
- Device-level JVSM measures standalone IBR stiffness, whereas grid-level JVSM measures strength observed from each bus through driving-point characteristics.Grid-level characteristics combine network and connected-device dynamics and can be obtained from whole-system scans or a system admittance representation.Source: §3.2 · p. 3
4 Case Studies: GFM Requirements for System Strength
Across the modified 39-bus study, increasing GFM count generally raises minimum GFL-bus stiffness and damping, while placement changes outcomes even at fixed count. JVSM assessments are compared with small-signal modal characteristics.
4.1 Test System
- The study replaces all ten synchronous generators in the IEEE 39-bus system with IBRs at buses 30–39, varying GFM number and location while holding IBR ratings fixed.The ten locations are grouped into four broad areas for interpreting GFM spatial distribution.Source: §4.1 · p. 3, Figure 2 · p. 3
4.2 JVSM and Modal Assessment
- Bus-wise JVSM identifies weak GFL locations associated with critical oscillatory modes: in the reference case, bus 38 has the lowest JVSM and strongest IBR participation.Across four representative two-GFM configurations, the weakest GFL bus lies in an area without direct GFM support; modal observability corroborates the weak-region assessment.Source: §4.2 · pp. 4–5
4.3 Impact of GFM Number
- Across all placements, median minimum GFL-bus JVSM rises from 19.66 with one GFM to 28.24 with four, while median worst-mode damping rises from −1.15% to 31.83%.All 210 four-GFM configurations are positively damped, but GFM count alone does not determine system strength.Source: §4.3 · p. 5, Figure 5 · p. 5, Figure 6 · p. 6
4.4 Impact of GFM Location
- With three GFMs spread across A1, A2, and A4, worst-mode damping reaches 19.00%, exceeding the 8.73% with four GFMs concentrated in A1 and A2.The three-GFM case has minimum GFL-bus JVSM 23.47; the four-GFM case has 27.10, showing that the two strength and damping measures need not rank these cases alike.Source: §4.4 · p. 6
- Minimum GFL-bus JVSM increases from 22.66 at spread score 1 to 26.48, 28.29, and 36.77 at scores 2–4; median worst-mode damping rises from 10.71% to 39.09%.At scores 2 and 3, minimum JVSM is 26.48 and 28.29, while median damping is 26.45% and 32.46%; placements within a score can still yield different outcomes.Source: §4.4 · p. 6
- Among four-GFM cases, median minimum GFL-bus JVSM rises with spatial spread, but placements within the same spread score can still produce different outcomes.The spread score counts how many of four areas contain at least one GFM; it is a coarse indicator rather than a complete description of electrical placement.Source: §4.4 · p. 6
5 Conclusion
The conclusion argues that system strength depends on both the number and locations of GFM IBRs, so requirements should reflect resulting strength rather than counts or penetration alone. JVSM can screen weak locations and compare placements before detailed stability analysis.
5 Conclusion
- GFM count alone does not determine system strength; placement also shapes voltage stiffness and small-signal stability, so requirements should reflect resulting strength.More spatially distributed GFM IBRs generally strengthen the weakest GFL-connected regions and improve damping.Source: §5 · p. 6
- Fig. 7 assesses three illustrative GFM-location configurations; its normalized participation factors and voltage observability indicate relative values within each case, not absolute cross-case magnitudes.Figs. 8 and 9 show distributions of minimum GFL-bus JVSM and worst-mode damping ratio, respectively, for four-GFM configurations grouped by spread score.Source: Figure 7 · p. 7, Figure 8 · p. 8, Figure 9 · p. 8
- Bus-wise JVSM can screen weak locations, compare candidate GFM placements, and check minimum voltage stiffness across GFL-connected buses before detailed stability analysis.Future work can jointly consider GFM number, capacity, location, device characteristics, and operating conditions.Source: §5 · p. 8