Grid Forming Converter (GFC) Overview

• Grid-forming converters (GFCs) are power electronic interfaces that act as controllable voltage sources, setting AC voltage magnitude, frequency, and phase without relying on phase-locked loops.
• They employ a variety of control strategies—such as droop, virtual synchronous machine, and dual-port methodologies—to enhance power balance, voltage support, and grid stability.
• Key challenges include managing AC/DC coupling, current limitation, and overload protection under weak-grid conditions, which drive the evolution of adaptive and hybrid control techniques.

Searching arXiv for recent and foundational papers on grid-forming converters to support the article. A grid-forming converter (GFC) is a power electronic interface that behaves as a controllable voltage source capable of establishing AC voltage magnitude, phase, and frequency, rather than merely injecting current into an already-established grid (Gao et al., 2020). In the research literature summarized here, GFCs are treated as key devices for low-inertia and converter-dominated power systems because they can provide voltage support, frequency support, droop behavior, virtual inertia / virtual synchronous machine behavior, black-start and islanding capability, and self-synchronization, while also exposing new control-design problems involving AC/DC coupling, current limitation, weak-grid synchronization, and model fidelity (Tripathy et al., 1 Sep 2025, Chen et al., 2021, Kkuni et al., 2021).

1. Definition and operating role

The distinction between grid-forming and grid-following control is central to the topic. Grid-forming converters are modeled conceptually as an active voltage source behind a series impedance, capable of setting voltage magnitude and frequency and operating without a PLL, whereas grid-following converters are modeled as a current source with parallel impedance, synchronized to the existing grid voltage using a phase-locked loop (Tripathy et al., 1 Sep 2025). In a broader formulation, a GFC is a converter that does not rely on a PLL to synchronize to an already stiff grid; instead, it establishes its own AC voltage magnitude and frequency and synchronizes through power balance (Chen et al., 2021). A closely related statement appears in the offshore-wind literature, where GFCs are described as using voltage-source behavior, controlling terminal voltage rather than behaving as a current source, and providing a frequency reference for the rest of the grid to follow instead of following the existing grid by PLL synchronization (Ghimire et al., 2023).

This operating role is repeatedly motivated by the displacement of synchronous machines. Several papers state that increasing renewable penetration weakens frequency and voltage stability because converters interfaced as renewables do not inherently contribute synchronous-machine inertia and associated electromechanical control structure (Gao et al., 2020, Tayyebi et al., 2020). The resulting low-inertia context is not presented merely as a lack of stored kinetic energy; it is also a loss of the historical machine-governor-excitation structure that shaped primary frequency and voltage control (Tayyebi et al., 2020). This motivates GFCs as functional substitutes for key external behaviors of synchronous machines, including inertia-like response, droop/load sharing, and hierarchical voltage/frequency support (Gao et al., 2020).

A recurrent theme is that “grid forming” should not be reduced to a single canonical control law. One paper explicitly reframes droop control, power synchronization control, virtual synchronous generator control, matching control, dispatchable virtual oscillator control, and many improved variants as special cases of a common multivariable feedback architecture (Chen et al., 2021). Another paper argues even more strongly that a converter can be grid-forming without being a direct analogue of a synchronous machine: active-power balance can be carried by amplitude dynamics, while synchronization can be carried by reactive-power/angle dynamics (Milano, 2024). This suggests that the GFC concept is best understood functionally—as voltage and frequency formation with stable network interaction—rather than as a single machine-emulation template.

2. Canonical control realizations and unifying viewpoints

Several control realizations recur across the cited work. Droop control implements active-power/frequency and reactive-power/voltage regulation directly, with frequency adjusted according to active-power mismatch and voltage magnitude adjusted according to reactive-power mismatch (Gao et al., 2020, Tripathy et al., 1 Sep 2025, Ghimire et al., 2023). Virtual synchronous machine or virtual synchronous generator control introduces swing-equation-like dynamics, typically through a virtual inertia term and damping term, so that frequency or angle evolves with synchronous-machine-like transient behavior (Gao et al., 2020, Tripathy et al., 1 Sep 2025, Ghimire et al., 2023). Dispatchable virtual oscillator control is presented as a nonlinear oscillator-based GFC law capable of synchronization and dispatch to a chosen operating point, in which active-power mismatch modifies phase/frequency evolution and reactive-power mismatch modifies amplitude (Gao et al., 2020). Matching control exploits the similarity between DC-capacitor energy dynamics and synchronous-machine swing dynamics, with frequency generated directly from DC voltage (Chen et al., 2021). Power synchronization loop control is treated as equivalent to droop control with respect to the frequency channel in the generalized multivariable formulation (Chen et al., 2021).

The literature also emphasizes that control structure matters materially. A comparative assessment of three realizations—GFC with cascaded voltage and current control, GFC with inner current control only, and GFC with no inner loop—argues that the defining GFC property of behaving as a voltage source behind an impedance is best preserved by a no-inner-loop design, reasonably preserved by current-control-only designs, and most compromised by cascaded voltage-current control, especially in MW-scale, low-switching-frequency converters (Kkuni et al., 2021). In that paper, the converter without inner loop is described as behaving most like an ideal voltage source behind an impedance, while the cascaded realization behaves like a voltage source behind a time-varying reactance (Kkuni et al., 2021). The same paper also reports that the GFC with cascaded control can only operate stably within a narrow range of network impedances, and that MW level GFC with inner loops could potentially go unstable under weak power system conditions (Kkuni et al., 2021).

A broader unifying view is provided by the generalized multivariable grid-forming architecture, which models the controller as a $3\times 5$ transfer matrix mapping errors in $v_{dc}$, $p$, $\omega_u$, $q$, and $V$ to control variables $i_u$, $\omega_u$, and $E_u$ (Chen et al., 2021). Within that framework, droop control becomes a sparse transfer matrix, VSG becomes a low-order dynamic extension of droop, matching control appears as explicit DC-to-frequency coupling, and dVOC-type formulations are incorporated by nonlinear error signals such as $P_{ref}/V_{ref}^2 - p/V^2$ and $v_{dc}$0 (Chen et al., 2021). The paper’s practical conclusion is that a GFC should not automatically be designed as three isolated loops—DC voltage loop, active-power/frequency loop, and reactive-power/voltage loop—but instead as a coupled MIMO regulation problem (Chen et al., 2021).

3. AC/DC coupling, dual-port operation, and energy-aware formulations

A major strand of GFC research concerns the fact that converter control cannot be treated as purely AC-side waveform generation independent of DC-side energy availability. One paper focuses explicitly on the problem that standard GFC controls such as frequency droop, VSM/VSG, and dVOC are usually built mainly from AC-side feedback variables—power, frequency, voltage, and phase—and therefore may fail to protect the converter’s DC-link voltage under large disturbances (Gao et al., 2020). In the unified averaged model used there,

$v_{dc}$1

with

$v_{dc}$2

so increasing AC power export generally increases the DC-side current demanded by the inverter stage (Gao et al., 2020). The paper’s central observation is that under a large load increase, if the DC current saturates while AC-side control still demands sustained power export, then the deficit is supplied by the DC-link capacitor, whose stored energy

$v_{dc}$3

decreases until DC-link voltage collapse occurs (Gao et al., 2020). The proposed remedy is to inject DC voltage feedback into the frequency-generation mechanism of droop, VSG, and dVOC so that AC-side behavior becomes consistent with available DC-side energy (Gao et al., 2020).

A second line of work goes further by proposing dual-port grid-forming control for converters interconnecting AC and DC subgrids. In one formulation, a dc/ac converter is treated as a two-port device that can simultaneously form AC voltage/frequency and DC voltage behavior, rather than being GFM on one side and GFL on the other (Subotić et al., 2021). The central outer-loop law is

$v_{dc}$4

which means converter AC frequency is shaped by both AC active power deviation and DC voltage deviation (Subotić et al., 2021). The corresponding converter DC-link balance is

$v_{dc}$5

so the AC side is used to restore DC-side power balance (Subotić et al., 2021). The same paper argues that this unifies standard GFL and GFM functions and is backwards compatible with conventional machine-based generation (Subotić et al., 2021).

A closely related MMC-based development proposes dual-port GFM control for interconnecting power converters in “grids of grids” (Groß et al., 2021). There, dual-port GFM means the MMC forms a stable AC terminal voltage, forms a stable DC terminal voltage, and balances its internal stored energy $v_{dc}$6 using both AC and DC terminals (Groß et al., 2021). The internal energy dynamics are

$v_{dc}$7

and two control classes are proposed. The hybrid power/energy droop law is

$v_{dc}$8

$v_{dc}$9

while the energy-balancing controller uses $p$0 directly to form both AC frequency and DC voltage (Groß et al., 2021). That paper argues that dual-port GFM removes the need to assign GFM/GFL roles across IPC terminals and is more resilient to contingencies than state-of-the-art single-port GFM control (Groß et al., 2021).

This body of work suggests a broader implication: in converter-dominated systems, the defining slack variables need not be confined to synchronous-machine analogues. Some designs use DC voltage feedback to make classical droop or VSG energy-aware (Gao et al., 2020); others treat AC frequency and DC voltage as co-regulated port variables (Subotić et al., 2021, Groß et al., 2021). A plausible implication is that future GFC design space is fundamentally hybrid AC/DC, not purely AC.

4. Current limits, overload, and transient stability

Current limitation is one of the most technically consequential issues in GFC research. Several papers emphasize that GFCs are attractive precisely because they behave as voltage sources, but that same voltage-source behavior means they do not stiffly control grid-side active power and therefore require a separate current-limiting mechanism (Kkuni et al., 2021). In wind-farm applications, even a small phase jump of a few degrees, or a modest voltage drop, may trigger overcurrent depending on pre-disturbance loading, because the current response is approximately set by the voltage difference across the impedance between the converter’s internal emf and the grid (Kkuni et al., 2021). The key concern is that many GFCs derive synchronization from measured output power, and once current limiting engages, this loop is effectively broken or desensitized, which can sharply reduce synchronization margin and may cause loss of synchronism (Kkuni et al., 2021, Kkuni et al., 2021).

A particularly clear analytical treatment is given for a GFC represented as an internal voltage $p$1 behind total reactance $p$2, with active and reactive power

$p$3

in the unlimited case (Kkuni et al., 2021). Under a circular current limit $p$4, the active-power characteristic becomes piecewise: $p$5 (Kkuni et al., 2021). The paper’s main claim is that current limiting sharply reduces transient stability margins for phase jumps, RoCoF events, and voltage dips because the peak transferable active power is greatly reduced and the unstable operating point appears at a much lower $p$6 (Kkuni et al., 2021). To mitigate this, the authors propose feeding a virtual active power computed from the unsaturated current reference into the synchronization loop: $p$7 which preserves a meaningful synchronizing signal during saturation while still enforcing actual current limits (Kkuni et al., 2021).

Wind-farm studies reinforce the same mechanism at plant scale. In a 420 MW wind farm with 35 WTGs of 12 MW arranged in 7 strings, a string-aggregated model shows that under a $p$8 phase jump with current limit at 1.2 pu, the most highly loaded string enters current limit first and can lose synchronism, after which its disturbed power output corrupts the response of the remaining strings (Kkuni et al., 2021). The paper concludes that a fully aggregated wind-farm model is adequate only if strings are symmetric in control, electrical parameters, and generation, and that stability margin against phase-jump disturbances must be assessed using the most heavily loaded WTG/string rather than the fully aggregated farm alone (Kkuni et al., 2021).

Overload control has also been studied from an ML-augmented perspective. A 2025 paper considers a droop-controlled voltage-source converter with cascaded inner voltage/current loops under abrupt overload after islanding and proposes a physics-informed neural network that replaces the AC voltage control, AC current limitation, and AC current control while retaining the classical frequency droop (Kumar et al., 27 Mar 2025). In the reported modified IEEE 13-bus microgrid, conventional droop is stable at 5.916 MVA, pf = 0.97, but becomes unstable at 5.918 MVA, pf = 0.97 after islanding, with GFC1 voltage falling below 5% of steady-state voltage and $p$9 reaching $\omega_u$0 (Kumar et al., 27 Mar 2025). At the same load where droop fails, the PINN stabilizes the system, reduces peak voltage deviation to 42.85%, and preserves the post-disturbance operating point in contrast to a current-limitation strategy that changes the active-power setpoint (Kumar et al., 27 Mar 2025). This suggests that overload-aware GFC control increasingly treats protection and synchronization as a coupled design problem rather than as separate layers.

5. Weak-grid interaction, dynamic modeling, and stability analysis

Weak-grid performance is another major axis of GFC research. Offshore wind studies explicitly define a weakly connected WPP by

$\omega_u$1

and use this benchmark to compare droop, VSM, VSM with inner loops, virtual admittance, and PR-control-based GFCs under a 0.2 pu load addition and a grid phase jump of $\omega_u$2 rad (Ghimire et al., 2023). In that study, pure droop is fast but has high ROCOF and under-damped oscillations under phase shift; outer-loop-only VSM captures inertial behavior but shows super-synchronous oscillations with long settling; VSM with inner loops and virtual admittance control are identified as the most promising methods under the chosen weak-grid benchmark and disturbance set (Ghimire et al., 2023). The same paper emphasizes that conclusions are conditional on control tuning and comparison prerequisites, and that more work is needed on small-signal stability, eigenvalue analysis, and more severe disturbance studies (Ghimire et al., 2023).

Control realization also affects weak-grid robustness. The comparative assessment of typical GFC realizations based on voltage-source behavior concludes that the GFC without inner loop behaves as passive impedance in the frequency range of interest and exhibits no observed constraint on network impedance, whereas the current-control-only realization may be non-passive at frequencies determined by feedforward filter and control bandwidth, and the cascaded voltage/current realization may be non-passive around resonant frequency ranges and can only operate stably within a narrow range of network impedances (Kkuni et al., 2021). This is not a minor implementation detail; the paper’s core message is that being “grid-forming” in outer-loop terminology is not sufficient if the inner realization fails to preserve voltage-source-behind-impedance behavior (Kkuni et al., 2021).

Dynamic-phasor modeling has emerged as a key tool for analyzing such interactions. For single-phase GFMCs, one paper argues that the orthogonal signal generation unit used for power measurement introduces nonlinear and dynamic effects that have been ignored in prior work, causing small-signal stability predictions to miss unstable modes (Si et al., 2024). The proposed dynamic phasor model represents the converter voltage as

$\omega_u$3

and derives power measurement dynamics through delayed-signal phasor products such as

$\omega_u$4

(Si et al., 2024). The resulting linearized model predicts instability at $\omega_u$5 that prior models miss, and hardware experiments confirm diverging waveforms at $\omega_u$6 and converging waveforms at $\omega_u$7 (Si et al., 2024).

A more recent dynamic-phasor framework treats a droop-controlled GFC connected to a series-compensated line. It models the GFC in $\omega_u$8-frame DPs with $\omega_u$9 and the network in $q$0-frame DPs with $q$1, includes constant-angle and $q$2-priority current limiters, and supports both time-domain unbalanced-fault simulation and LTI small-signal analysis (Hossain et al., 23 May 2025). The key finding is that with droop active and 83.25% series compensation, the linearized DP model exhibits a very poorly damped 6.54 Hz mode, and participation-factor analysis identifies the converter/POI voltage angle state $q$3 as dominant in that mode (Hossain et al., 23 May 2025). Eigenvalue sensitivity analysis shows that reducing the power–frequency droop coefficient $q$4 is most effective in stabilizing the poorly damped mode, and reducing $q$5 by a factor of 0.98 yields a desired settling time of 15 s (Hossain et al., 23 May 2025). This suggests that GFC stability in compensated networks is not simply a matter of “more damping” in the abstract; it can be directly angle/droop dominated.

6. Emerging directions and conceptual expansions

Recent work has also expanded the conceptual design space of GFCs. One notable proposal is the “dual GFM” converter, which intentionally swaps the conventional association between active power and frequency/angle dynamics and between reactive power and voltage-magnitude dynamics (Milano, 2024). Starting from the lossy synchronous-machine power equations,

$q$6

$q$7

the paper notes a near symmetry and constructs a “dual” model by retaining the $q$8-dependent part instead of the $q$9-dependent part (Milano, 2024). With $V$0, the proposed converter power equations become

$V$1

so $V$2 depends strongly on voltage magnitude $V$3 and $V$4 depends strongly on angle $V$5 (Milano, 2024). The associated dual swing equation is

$V$6

with $V$7 interpreted as “instantaneous bandwidth,” dual to instantaneous frequency $V$8 (Milano, 2024). The paper’s simulations on a modified WSCC 9-bus system and a 1479-bus all-island Irish system are used to argue that active-power balancing does not fundamentally require frequency measurement in the primary power-balancing loop, though the implementation still uses bus frequency for the reactive/frequency loop (Milano, 2024).

Another emerging direction is adaptive or learning-assisted hybridization of classical GFM paradigms. A 2025 paper proposes a mixed-angle controller

$V$9

with heuristic constraints $i_u$0, $i_u$1, and $i_u$2, and formulates a nonlinear program in GAMS/MOSEK to minimize a frequency-error-related MSE objective (Tripathy et al., 1 Sep 2025). The reported optimized coefficients are $i_u$3, $i_u$4, $i_u$5, and $i_u$6, implying a droop-dominant hybrid controller (Tripathy et al., 1 Sep 2025). The same paper augments the framework with ANN and LSTM methods for reference generation under contingencies such as overload, generation outage, fault, load drop, load surge, and microgrid islanding, with the ANN trained by the Levenberg–Marquardt algorithm and reporting a regression coefficient $i_u$7 (Tripathy et al., 1 Sep 2025). Because the paper does not provide a formal benchmark table or full implementation detail, these results are best read as evidence that adaptive hybridization is becoming an explicit research direction rather than as a settled controller class.

A different data-driven direction asks whether the dynamics of a converter-infinite-bus GFC system can be recovered directly from data using SINDy or deep symbolic regression (Javadi et al., 10 Oct 2025). On a benchmark with active power reference change to 0.7 p.u. at $i_u$8 s, reactive power reference change to 0.2 p.u. at $i_u$9 s, and voltage reference change to 0.9 p.u. at $\omega_u$0 s, deep symbolic regression consistently outperforms SINDy in derivative prediction accuracy, while being approximately 11 times more computationally demanding (Javadi et al., 10 Oct 2025). For example, for $\omega_u$1, SINDy yields mean square error 1.2 and $\omega_u$2, whereas DSR yields mean square error 0.002 and $\omega_u$3 (Javadi et al., 10 Oct 2025). This suggests that, alongside analytical and physically structured control design, symbolic data-driven modeling is emerging as a complementary reduced-order representation layer for GFC dynamics.

Finally, there is an operational-systems direction in which GFM capability itself becomes a dispatchable grid service. One scheduling framework treats the GFM penetration level $\omega_u$4 at each wind farm as a continuous decision variable between 0 and 1 and co-optimizes generator commitment, active/reactive reserve constraints for GFM operation, frequency-security constraints, and a small-signal-stability surrogate based on generalized short-circuit ratio (Cui et al., 2023). On a modified IEEE 30-bus system, the paper reports that dynamic optimal GFM allocation yields an average cost $\omega_u$5, compared with $\omega_u$6 for the best fixed GFM penetration case and about $\omega_u$7 for low fixed GFM penetration $\omega_u$8 (Cui et al., 2023). This suggests that, at system level, “how much GFM” is not a static hardware attribute but an operating-point-dependent service allocation problem.

In aggregate, the cited literature depicts the grid-forming converter as neither a single controller nor a settled engineering commodity. It is a family of voltage-forming, power-balancing, and increasingly energy-aware control structures whose defining research questions span machine emulation, AC/DC coupling, overload protection, weak-grid synchronization, dynamic-model fidelity, and system-level deployment. The common thread across these directions is that a GFC must be understood not only by its steady-state droop or swing law, but by the full interaction among waveform formation, internal energy constraints, current limits, network topology, and the specific realization used to expose a voltage-source behavior to the grid (Tayyebi et al., 2020, Chen et al., 2021, Milano, 2024).