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Dynamic droop specifications for Grid-Forming Inverter-Based Resources
Jennifer T. Bui, Dominic Groß, Deepak Ramasubramanian
TL;DR
The retirement of synchronous generators and heterogeneous IBR controls create a need to understand and specify IBR dynamics for grid stability and interoperability. The paper develops a data-enabled dynamic droop model and gain-phase bounds for GFM IBRs, then illustrates them with controls and OEM models. The resulting specifications characterize subsynchronous small-signal behavior, support screening for potential adverse interactions, and clarify frequency-control services including IBR inertia response.
Problem
Heterogeneous IBR controls and the replacement of synchronous generators make it important to characterize IBR behavior for power-grid stability and reliability.
Method
The paper develops frequency-dependent dynamic droop coefficients from IBR small-signal behavior, formulates GFM gain-phase specifications, and uses experiments, simulations, and OEM models for illustration.
Results
The specifications characterize IBR response below nominal frequency and are illustrated as a screening tool for potential adverse interactions across common GFL and GFM controls and OEM models.
Takeaways & Limitations
Dynamic droop coefficients provide a functional, data-enabled basis for specifying GFM capabilities and frequency-control ancillary services, including a generalized IBR inertia response.
Abstract
from arXiv · showhide
The large-scale retirement of synchronous generators requires additional capabilities from inverter-based resources (IBRs) to ensure the stability and reliability of power grids. With the heterogeneous controls of IBRs, it is especially important to understand their behavior on the grid. This work proposes a simple data-enabled dynamic model to capture the small-signal dynamics of IBRs and formulate specifications for grid-forming (GFM) IBRs. The dynamic droop model is complementary to well-studied impedance models and extends the common definition of steady-state droop coefficients to dynamic droop coefficients that fully characterize the IBR small-signal response below the nominal line frequency (e.g., subsynchronous oscillations). We propose bounds on the gain and phase of the dynamic droop coefficients to encode minimum requirements for GFM IBRs to promote interoperability and minimize adverse interactions. The resulting specifications also provide some insights into the much-debated question of how to certify an IBR as GFM. Moreover, we also provide dynamic droop specifications for frequency control ancillary services that, e.g., clarify and generalize the notion of an IBR inertia response. Finally, common grid-following (GFL) and GFM controls as well as original equipment manufacturer (OEM) models are used to illustrate the results and showcase the use of dynamic droop coefficients as a tool to screen IBR dynamics for potential adverse interactions.
I. INTRODUCTION
Increasing use of heterogeneous inverter-based resources changes power-system dynamics and raises stability, reliability, and interoperability concerns. The paper introduces dynamic droop coefficients as a data-enabled way to characterize IBR small-signal behavior and formulate GFM specifications.
- Motivation: Heterogeneous IBR dynamics and interactions create major interoperability concerns as power systems replace synchronous generators with power-electronic resources.The transition affects renewable generation, storage, HVDC transmission, and large loads.
- Motivation: GFL controls depend on stable grid voltage waveforms, whereas GFM controls aim to impose self-synchronizing AC voltage dynamics at their terminals.The passage identifies droop, virtual synchronous machine, and dispatchable virtual oscillator controls as established GFM approaches.
- Motivation: Existing GFM definitions based on stiff voltage sources or implementation details do not fully capture self-synchronization or provide architecture-agnostic specifications.The paper motivates definitions verifiable solely from input-output data.
- Contribution: Dynamic droop coefficients extend steady-state droop coefficients to frequency-dependent quantities that characterize IBR small-signal response below nominal line frequency.They complement impedance models, which are described as insightful at or above nominal line frequency.
- Method: The model represents frequency-domain gain and phase responses to active- and reactive-power oscillations and can be obtained from hardware experiments or black-box simulations.For common GFM controls away from limits, the model has low dependence on operating point.
- Scope: At frequencies below roughly 5–10 Hz, cross-coupling terms are often negligible, motivating a simplified model using only the active- and reactive-power dynamic droop coefficients.The paper explicitly scopes specifications for off-diagonal droop coefficients out of the work.
B. Experimental Identification
The paper identifies dynamic droop coefficients by perturbing an IBR with an AC voltage source, measuring settled periodic responses, and recovering frequency-domain gains at the IBR terminal.
- Sinusoidal frequency or magnitude perturbations are injected into an AC voltage source to excite the IBR dynamics.Perturbation amplitudes must excite the dynamics while keeping the IBR within current, power, and modulation limits.
- Measurements capture three-phase voltage and current at a reference point that may be located before or after an included transformer.The reference point is determined by the measurement location rather than the perturbation-source bus.
- The dynamic droop model can be recovered at any perturbation frequency fp from experiments or simulations after the signals reach periodic steady state.Frequency and magnitude perturbations are conducted separately before coefficient recovery.
- Fourier coefficients at the perturbation frequency recover the amplitude and phase of voltage, angle, active-power, and reactive-power oscillations.These oscillation representations provide the complex deviations used to calculate dynamic droop coefficients.
- The approach recovers the transfer function at the IBR terminal independently of perturbation-source impedance.This avoids the instability and accuracy trade-off associated with frequency scans using separated input and output buses.
C. Example: Comparison of a GFL and a GFM IBR
The example compares dynamic droop responses of prototypical GFM and GFL IBRs across frequency and relates those responses to time-domain behavior and complementary impedance models.
- At fp →0, GFL and GFM dynamic droop coefficients converge, indicating the same slow dynamic response in the example.Both controls use 5% steady-state P-f and Q-V droop in the EMT comparison.
- As frequency increases, GFM dynamic-droop gain decreases, whereas GFL retains high gain in the illustrated comparison.The differing gains distinguish their responses to higher-frequency active-power oscillations.
- At 30 Hz, both controls reach a ±90° phase shift, causing the frequency deviation to have the wrong sign during half the power oscillation.At 0.1 Hz, the GFL and GFM frequency responses are the same and follow the standard droop sign relationship.
- The high GFL gain can destabilize the system in this case, while the low GFM gain ensures stiff frequency control.
- Dynamic-droop specifications fully characterize small-signal response and can address interoperability more broadly than scenario-specific time-domain specifications.Impedance models instead naturally describe fast dynamics, while dynamic droop is more insightful and less operating-point-dependent for slow dynamics below line frequency.
III. FUNCTIONAL CAPABILITIES OF GFM IBRS AND STABILITY REQUIREMENTS
The paper restricts dynamic-droop specifications to 0.01–40 Hz and divides this range into regions covering quasi-steady-state, transient, rate-of-change, and higher-frequency behavior.
- The relevant specification range is restricted to 0.01 Hz to 40 Hz because lower frequencies show little GFM–GFL difference and higher frequencies contribute less to system-wide interaction.
- The first frequency region parameterizes the quasi-steady-state response, followed by a region for transient droop response.
- A subsequent region parameterizes rate-of-change support, including inertia-like behavior.
- Frequencies beyond the GFM reference bandwidth characterize responses dominated by fast controls and circuit dynamics such as current control and LCL filters.This region is identified as crucial for distinguishing GFM and GFL dynamics.
- The specifications derive from functional or performance requirements and decentralized small-signal frequency-stability conditions.For higher frequencies, these conditions can be expressed as either low-gain or passivity requirements, depending on the GFM architecture.
B. Frequency Control Ancillary Services
The paper specifies dynamic active-power droop across steady-state, transient, and rate-of-change response ranges, linking the high-frequency decrease in gain to an inertia response.
- IBRs with energy storage or resource reserves can provide steady-state droop, low-frequency oscillation damping, and inertia response services.
- As fp →0.01 Hz, steady-state droop requires |mP (j2πfp)| ≈m⋆P.
- On transient timescales, |mP (j2πfp)| is bounded by the transient droop gain m′′P to provide sufficiently stiff frequency.
- Between the transient and rate-of-change regions, gain decreases ten times per ten times increase in fp, encoding an increasingly stiff frequency response.
- For a GFM VSM, the inertia constant H and steady-state droop m⋆P determine the rate-of-change-response transition.
- The transient upper bound m′′P is selected to enforce existing primary-frequency-control prequalification requirements, including bounds on step response.
C. Frequency Synchronization and High-Frequency Stiffness
The dynamic droop specifications constrain active-power synchronization responses through gain and phase bounds, while allowing alternative high-frequency conditions for different GFM architectures.
- The specification permits PI active-power-frequency droop that enables GFM synchronization without steady-state droop while meeting the transient droop gain bound.
- The phase condition |∠mP (j2πfp)| ≤90 + ϵ1 prevents a droop response with incorrect average sign over an oscillation cycle.
- Beyond f ′′′p, the specifications trade off gain and phase conditions.
- The passive high-frequency specification allows |mP (j2πfp)| to increase ten times for a ten times increase in fp, accounting for output impedance in voltage-source-behind-impedance control.
- PI current and voltage control architectures often fall into the low-gain category for high-frequency behavior.
D. GFM Voltage Support
The voltage-support specifications require low-frequency Q-V droop behavior and constrain higher-frequency reactive-power responses through phase and gain conditions.
- At low frequencies, mQ(j2πfp) must closely match the steady-state Q-V droop specification, with |mQ(j2πfp)| ≈m⋆Q and phase approaching zero near 0.01 Hz.
- Between defined transition frequencies, reactive-power gain is bounded by the transient droop gain m′′Q.
- Below f ′′′p, |∠mQ(j2πfp)| ≤90 + ϵ1 prevents an incorrectly signed average droop response.
- If step-response deviation must remain within a specified percentage of steady state, either passivity or a small-gain condition can be used.
- The passive high-frequency specification restricts phase to |∠mQ(j2πfp)| ≤90+ϵ1 and gain to 1 p.u., accommodating output impedance effects.
- For a Thevenin equivalent grid reactance Xg in p.u., preliminary results give mlow ≈f0/f ′′′p when arbitrary phase is permitted at higher frequencies.
E. Parameter Ranges and Operating Conditions
The specifications separate system-operator-selected frequency boundaries from IBR droop parameters and relate high-frequency dynamic droop to voltage-source-behind-impedance behavior.
- System operators are envisioned to specify f ′p and f ′′′p from prevailing frequency- and voltage-control timescales.
- IBRs may need to comply with steady-state droop constants and transient droop bounds updated for operating and system conditions.
- Compliance with the entire applicable range of droop constants and bounds should be established before commissioning using the stated method.
- A stiff voltage source behind an impedance offers higher-frequency insight but conflicts directly with self-synchronization through droop.
- For small ρ < 1/10, mP (j2πfp) ≈jXofp/f0 over [f ′′′p, f0], giving tenfold gain growth per tenfold frequency increase and 90° phase.
- The high-frequency active-power asymptote shifts upward when output reactance Xo increases.
- For reactive power, the specification |mQ(j2πfp)| ≤1 p.u. requires Xo ≤1 p.u., precluding unreasonably high output reactance.
B. Kaua‘i Island Power System 18-20 Hz Oscillations
The dynamic droop coefficient identifies a GFL inverter whose response contributes to the observed 18–20 Hz oscillation. Its phase reversal near 19 Hz indicates negative damping and failure to satisfy proposed GFM specifications.
- The GFL IBR provides steady-state and transient droop but no rate-of-change support, failing the proposed high-frequency GFM specifications.Its dynamic droop response was obtained from an EMT model modified to reproduce the Kaua‘i oscillation.
- A 180° phase shift at approximately 19 Hz indicates negative damping because the P-f droop effectively flips sign.
- The IBR therefore does not qualify as GFM under the proposed specifications, and its dynamics were identified as the source of the 18–20 Hz oscillation.
C. Battery Energy Storage System (OEM 1)
OEM 1 models show that dynamic droop specifications distinguish GFM and GFL behavior more effectively than a fast power-response criterion alone. The GFM model satisfies the proposed specifications and survives loss of the last synchronous machine.
- The OEM 1 GFM model aligns with the proposed specifications in its active- and reactive-power dynamic droop responses.
- The GFM model survives loss of the last synchronous machine, whereas the GFL model does not.
- Both models supply 90% of the lost generation within one cycle, so that criterion does not distinguish their GFM and GFL responses.
D. Battery Energy Storage System (OEM 2)
OEM 2 configurations exhibit distinct relationships between dynamic droop specifications and transient behavior. GFM B mostly satisfies the specifications, GFM A shows a low-frequency negative-damping issue, and GFL fails the loss-of-synchronous-machine test.
- The OEM 2 plant model evaluates GFL, GFM A, and GFM B configurations using active- and reactive-power dynamic droop coefficients.The plant is a 107 MVA, 220 kV model with steady-state frequency droop disabled for this study.
- GFM B largely aligns with the proposed specifications above 2.5 Hz but violates the reactive-power gain bound because of insufficient voltage-control bandwidth.
- GFM B’s approximately 90° reactive-power phase response implies incorrect gain without significant negative damping in the affected range.
- GFM A violates the reactive-power phase bound from 0.4 to 1.5 Hz and exhibits a 180° phase shift near 0.8 Hz, indicating significant negative damping.
- The GFL configuration largely lies outside the specifications and does not survive the loss of the last synchronous machine.
- All configurations provide 90% of the active-power deficit within one cycle, while GFM A exhibits a significant 0.8 Hz oscillation linked to its reactive-power phase shift.