A frequency-based screening method distinguished grid-forming (GFM) and grid-following (GFL) inverter control models in simulations, but it also exposed oscillations and negative damping in some configurations. The results suggest that measuring an inverter's response across frequencies can reveal behavior missed by a one-cycle power-response criterion.
The study's central tool is dynamic droop, a frequency-dependent measure. Its active-power form, mP, uses gain and phase to describe an inverter-based resource's response to active-power oscillations.
A frequency response instead of a single snapshot
In the proposed identification procedure, the model is separately exposed to sinusoidal changes in the alternating-current source's frequency and voltage magnitude, and the analysis waits for a periodic steady state. Amplitudes and phases are then recovered from Fourier-series coefficients in voltage, angle, active-power and reactive-power signals.
The reported analyses use electromagnetic-transient simulations of common grid-following and grid-forming controls, plus vendor-provided models. The analysis is restricted to 0.01 hertz to 40 hertz.
For frequency-control services, the proposed mP rules require a match to steady-state droop at 0.01 hertz, a bounded transient droop gain, and a tenfold fall in gain for each tenfold rise in perturbation frequency in the region representing rate-of-change and inertia-like support. For the active-power GFM screen, phase is limited to 90 degrees plus a small allowance to avoid incorrect-sign droop.
The voltage-support rules apply the same approach to reactive power and voltage. They call for low-frequency matching to steady-state reactive-power and voltage droop, transient gain and phase limits, and a high-frequency option with phase no greater than 90 degrees plus a small allowance and gain no higher than 1 per unit.
The gap widened at higher frequencies
In tests of prototypical controls, GFM and GFL responses converged at low frequency. As frequency increased, the GFM gain decreased while the GFL gain increased, reducing damping. Their time-domain responses matched at 0.1 hertz, but at 30 hertz both reached a 90-degree phase shift. The simulated frequency deviations were large for GFL control and small for GFM control.
A modified GFL model representing the 18 to 20 hertz oscillation studied for the Kaua'i Island Power System delivered steady-state and transient droop but no rate-of-change support. It failed the proposed high-frequency GFM screen and showed a 180-degree phase reversal near 19 hertz, indicating negative damping, a response that can reinforce an oscillation instead of reducing it. This was a model simulation, not a field-attribution test.
Vendor models did not all behave alike
The first vendor model was rated at 3.4 megavolt-amperes and 600 volts. Its GFM configuration used steady-state reactive and active droop values of 0.18 and 0.016, respectively, and aligned with the proposed specifications at thresholds of 0.2, 1 and 5 hertz. Its GFL configuration lay outside those bounds.
The second vendor plant was rated at 107 megavolt-amperes and 220 kilovolts and could be configured as GFL, GFM A or GFM B. With steady-state frequency droop off and in voltage-control mode, GFM B broadly aligned with the proposed active-power specifications at 0.05, 0.25 and 2.5 hertz, but violated the proposed reactive-power gain bound because of limited voltage-control bandwidth.
GFM A showed a different problem. Its reactive-power response violated the proposed phase bound from 0.4 to 1.5 hertz and reached a 180-degree shift near 0.8 hertz, reported in the analysis as significant negative damping. In a simulated loss of the last synchronous machine, all the models supplied 90 percent of the active-power deficit within one cycle, yet the GFL configuration did not survive. GFM A showed a significant 0.8 hertz oscillation, and its frequency slowly moved away from the nominal value without steady-state frequency droop.
A model screen with clear limits
The paper presents dynamic droop as a way to formulate GFM specifications and screen model responses. Its examples are model-based electromagnetic-transient simulations and vendor-model scans, so they do not provide hardware or field validation.
The frequency analysis covers only 0.01 to 40 hertz. The proposed thresholds and droop constants are intended to depend on system-operator requirements and operating conditions, while the study reports no statistical uncertainty estimates or replicate count.
The supplied document is an arXiv preprint, version 1, dated 26 August 2026. The work was supported by the U.S. Department of Energy's Office of Critical Minerals and Energy Innovation under the Integrated Energy Systems Office, Award Number 38637.
Paper data and sources
Original title: Dynamic droop specifications for Grid-Forming Inverter-Based Resources
Authors: Jennifer T. Bui, Dominic Groß, Deepak Ramasubramanian
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text