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arxiv: 2607.01616 · v1 · pith:IHFKMADEnew · submitted 2026-07-02 · 📡 eess.SY · cs.SY

A Unified Framework for Hybrid Grid-Forming and Grid-Following Inverter Control

Xiaoyang Wang , Xin Chen This is my paper

Pith reviewed 2026-07-03 08:11 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords inverter controlgrid-forminggrid-followingvirtual oscillator controlmode transitionpre-synchronizationunified frameworksmall-signal stability
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0 comments X

The pith

A unified inverter control framework supports grid-forming and grid-following modes through continuous parameter tuning rather than discrete switching.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes integrating dispatchable virtual oscillator control with reference-following synchronization to create one structure that handles multiple inverter operating modes. These include voltage- and frequency-following (PQ mode), voltage-forming and frequency-following (PV mode), voltage-following and frequency-forming (Qf mode), voltage- and frequency-forming (Vf mode), and a hybrid mode mixing behaviors. The method produces smooth pre-synchronization and seamless transitions simply by adjusting a small set of continuous parameters. Small-signal stability and frequency-domain characteristics are examined for different parameter choices. Electromagnetic transient simulations and hardware-in-the-loop tests confirm effectiveness under varied conditions.

Core claim

Integrating dispatchable virtual oscillator control with reference-following synchronization yields a single control structure that supports PQ, PV, Qf, Vf, and hybrid modes. Smooth pre-synchronization and transitions across these modes occur by tuning continuous parameters instead of switching discrete controllers. The framework adapts inverter dynamics to grid conditions while remaining physically interpretable, with stability verified through small-signal analysis and performance shown in EMT simulations and HIL experiments.

What carries the argument

dispatchable virtual oscillator control integrated with reference-following synchronization, which enables continuous parameter-based selection among forming and following behaviors

If this is right

  • Inverters can move between PQ, PV, Qf, Vf, and hybrid modes without controller reconfiguration.
  • Small-signal stability holds across the examined parameter settings for each mode.
  • Input-output frequency-domain behavior can be shaped directly by the same continuous parameters.
  • Pre-synchronization occurs smoothly before connection to the grid in all supported modes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could reduce the need for multiple separate inverter controllers in microgrid or renewable installations.
  • Real-time parameter adjustment might allow inverters to respond to changing grid stiffness without mode-specific redesign.
  • Extension to larger networks could simplify coordination if the stability margins scale as the small-signal analysis suggests.

Load-bearing premise

The combined controls maintain stability and performance in every listed mode without unmodeled dynamics that would need extra mechanisms.

What would settle it

An EMT simulation or HIL test in which a mode transition produces instability, oscillations, or requires discrete controller changes despite the continuous parameter settings.

Figures

Figures reproduced from arXiv: 2607.01616 by Xiaoyang Wang, Xin Chen.

Figure 1
Figure 1. Figure 1: Typical structure of a voltage-source inverter system. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Linear harmonic oscillator. (a) LC oscillator circuit. (b) Control block [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Andronov-Hopf oscillator. (a) LC oscillation circuit with a controlled [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The proposed unified GFM-GFL controller for a three-phase inverter. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The unified GFM-GFL control in local inverter [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Multiple operating modes enabled by the proposed unified GFM-GFL [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The control block diagram of typical power synchronization methods. [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Equivalent frequency/phase control loop of the proposed unified GFM [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Participation factors under varying voltage feedback gain [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Eigenmode trajectories under varying voltage feedback gain [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: illustrates the control dynamics (µ = 0) in the αβ frame and the corresponding small-signal linearized model in the dgqg frame, where i0 is assumed approximately constant during linearization. The small-signal model explicitly reveals the equivalent negative resistance introduced by the current￾feedback loop, providing further physical insight into and validation of the derived stability boundary. This st… view at source ↗
Figure 15
Figure 15. Figure 15: Eigenmodes trajectories under varying current feedback gain [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Eigenmode trajectories under varying LC filter resistance [PITH_FULL_IMAGE:figures/full_fig_p012_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Participation factors under varying LC filter resistance [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Input-output frequency-domain response. V. ELECTROMAGNETIC TRANSIENT SIMULATION RESULTS In this section, high-fidelity EMT simulations are conducted in MATLAB Simulink under three different test cases. Firstly, an infinite-bus system with a passive impedance load is used to illustrate the characteristics of various operating modes. Secondly, a two-bus system is constructed to demonstrate the dynamic featu… view at source ↗
Figure 20
Figure 20. Figure 20: Dynamic performance of P Q mode under disturbances. 1) PQ Control Mode - Voltage and Frequency Following: Setting ϵ = 0, µ = 0, and η1 = η2 = 10, the inverter operates in P Q mode and tracks the prescribed active and reactive power references. The simulation results are shown in [PITH_FULL_IMAGE:figures/full_fig_p013_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Comparison of initial power responses with and without pre [PITH_FULL_IMAGE:figures/full_fig_p014_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Dynamic performance of [PITH_FULL_IMAGE:figures/full_fig_p014_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Dynamic performance of Qf mode under disturbances. from the grid, both voltage and frequency remain stable. Their steady-state values are determined by the passive load and the f-P and V -Q droop characteristics. Since the passive load is set to 0.5 + j0.25 pu, which is lower than the reference power 1 + j0.5 pu, both voltage and frequency settle above their reference values. The ability to maintain stabl… view at source ↗
Figure 24
Figure 24. Figure 24: Dynamic performance of V f mode under disturbances. As discussed in Section III-D4, in V f mode, setting η1 = η2 = 0 makes the inverter operate with constant voltage magnitude V0 and constant frequency ω0. Under the same disturbance sequence as before, the simulation results for constant-V and constant-f operation are shown in [PITH_FULL_IMAGE:figures/full_fig_p015_24.png] view at source ↗
Figure 26
Figure 26. Figure 26: Dynamic performance of hybrid mode under disturbance. [PITH_FULL_IMAGE:figures/full_fig_p016_26.png] view at source ↗
Figure 29
Figure 29. Figure 29: Seamless mode transition under continuous changes in control [PITH_FULL_IMAGE:figures/full_fig_p016_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Two-inverter test system with a P Q-mode inverter and a V f-mode inverter connected at the PCC. (a) P Q-mode inverter. (b) V f-mode inverter [PITH_FULL_IMAGE:figures/full_fig_p017_30.png] view at source ↗
Figure 32
Figure 32. Figure 32: Two-inverter test system consisting of a [PITH_FULL_IMAGE:figures/full_fig_p017_32.png] view at source ↗
Figure 35
Figure 35. Figure 35: Frequency and power responses under different allocations of [PITH_FULL_IMAGE:figures/full_fig_p018_35.png] view at source ↗
Figure 34
Figure 34. Figure 34: Two-inverter test system for illustrating transitions between [PITH_FULL_IMAGE:figures/full_fig_p018_34.png] view at source ↗
Figure 37
Figure 37. Figure 37: Frequency and power trajectories in time domain under different [PITH_FULL_IMAGE:figures/full_fig_p018_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: Power-frequency trajectories under different frequency-forming [PITH_FULL_IMAGE:figures/full_fig_p019_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: IEEE 39-bus system with proposed unified GFM and GFL control [PITH_FULL_IMAGE:figures/full_fig_p019_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: Dynamic frequency responses of inverter and generator buses under [PITH_FULL_IMAGE:figures/full_fig_p019_40.png] view at source ↗
Figure 43
Figure 43. Figure 43: Reactive power response of inverters and generators under distur [PITH_FULL_IMAGE:figures/full_fig_p020_43.png] view at source ↗
Figure 44
Figure 44. Figure 44: Dynamic responses under different events and operating modes in the hardware-in-the-loop tests. The columns correspond to the [PITH_FULL_IMAGE:figures/full_fig_p021_44.png] view at source ↗
Figure 45
Figure 45. Figure 45: Hardware-in-the-loop implementation of the proposed unified GFM [PITH_FULL_IMAGE:figures/full_fig_p021_45.png] view at source ↗
Figure 46
Figure 46. Figure 46: Reference power defined before and after the filter inductor. [PITH_FULL_IMAGE:figures/full_fig_p021_46.png] view at source ↗
read the original abstract

This paper proposes a novel unified control framework for achieving hybrid grid-forming (GFM) and grid-following (GFL) inverter operation by integrating dispatchable virtual oscillator control with reference-following synchronization. The proposed inverter control method supports multiple operating modes within a unified structure, including voltage- and frequency-following (PQ mode), voltage-forming and frequency-following (PV mode), voltage-following and frequency-forming (Qf mode), voltage- and frequency-forming (Vf mode), and a hybrid mode with mixed GFM and GFL behaviors. In particular, the proposed method achieves smooth pre-synchronization and enables seamless transitions across a spectrum of inverter operating modes by tuning a small set of continuous control parameters, rather than relying on discrete controller switching. This framework provides a flexible and physically interpretable approach for adapting inverter dynamics to varying grid conditions and operational requirements. The small-signal stability and input-output frequency-domain characteristics are further analyzed under different control parameter settings. The effectiveness and robustness of the proposed unified control method are demonstrated through extensive electromagnetic transient (EMT) simulations and hardware-in-the-loop (HIL) experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a unified inverter control framework that integrates dispatchable virtual oscillator control (dVOC) with reference-following synchronization. This structure supports PQ, PV, Qf, Vf, and hybrid GFM/GFL operating modes through continuous tuning of a small set of parameters, enabling smooth pre-synchronization and mode transitions without discrete controller switching. Small-signal stability and input-output frequency-domain analysis are performed for different parameter settings, with validation via EMT simulations and HIL experiments.

Significance. If the central claims on stability across modes and seamless transitions hold under both small- and large-signal conditions, the framework would offer a physically interpretable, flexible alternative to mode-switching approaches, potentially simplifying inverter control design for varying grid conditions. The emphasis on continuous parameters rather than discrete switching is a conceptual strength, though its practical robustness requires stronger evidence than small-signal analysis alone.

major comments (2)
  1. [stability analysis section / abstract] The stability analysis (referenced in the abstract and presumably detailed in the dedicated analysis section) is restricted to small-signal linearization and frequency-domain characteristics. However, the central claim of seamless pre-synchronization and mode transitions relies on nonlinear dynamics; without Lyapunov-based large-signal analysis or explicit coverage of worst-case disturbances (e.g., grid faults during transitions), the no-additional-mechanisms assumption remains unverified.
  2. [validation / EMT and HIL sections] The validation relies on EMT simulations and HIL experiments, but the abstract provides no quantitative metrics (error bounds, settling times, or disturbance scenarios) for the hybrid mode or transition cases. This makes it difficult to assess whether unmodeled interactions violate the unified-structure claim under realistic conditions.
minor comments (1)
  1. [control structure section] Notation for the control parameters and their mapping to the five operating modes should be tabulated for clarity, as the abstract refers to a 'small set' without explicit listing.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and indicate whether revisions will be made.

read point-by-point responses

  1. Referee: [stability analysis section / abstract] The stability analysis (referenced in the abstract and presumably detailed in the dedicated analysis section) is restricted to small-signal linearization and frequency-domain characteristics. However, the central claim of seamless pre-synchronization and mode transitions relies on nonlinear dynamics; without Lyapunov-based large-signal analysis or explicit coverage of worst-case disturbances (e.g., grid faults during transitions), the no-additional-mechanisms assumption remains unverified.

    Authors: The manuscript centers on small-signal linearization and frequency-domain analysis to characterize local stability and input-output behavior across the continuous parameter space. The EMT simulations and HIL experiments, which incorporate the full nonlinear dynamics, explicitly demonstrate pre-synchronization, mode transitions, and operation under disturbances including grid faults. These empirical results support the claim that no additional discrete mechanisms are required. A formal Lyapunov analysis lies outside the paper's scope, which prioritizes the unified structure and its small-signal properties; the simulation evidence is sufficient to substantiate the claims. revision: no

  2. Referee: [validation / EMT and HIL sections] The validation relies on EMT simulations and HIL experiments, but the abstract provides no quantitative metrics (error bounds, settling times, or disturbance scenarios) for the hybrid mode or transition cases. This makes it difficult to assess whether unmodeled interactions violate the unified-structure claim under realistic conditions.

    Authors: We agree that the abstract would benefit from quantitative indicators. In the revised manuscript we will update the abstract to include representative metrics (e.g., settling times and steady-state errors) drawn from the EMT and HIL results for hybrid-mode and transition scenarios. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation rests on proposed integration and external validation

full rationale

The paper defines a new unified controller by integrating dispatchable virtual oscillator control with reference-following synchronization, then tunes continuous parameters to realize PQ/PV/Qf/Vf/hybrid modes and pre-synchronization. Small-signal analysis and EMT/HIL experiments supply independent verification. No equation reduces a claimed result to a fitted input by construction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled via prior work. The central claims therefore remain non-tautological.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on standard control-theory assumptions and introduces a new integration of existing concepts; the small set of continuous control parameters are the primary adjustable elements.

free parameters (1)
  • small set of continuous control parameters
    These are tuned to achieve different modes and seamless transitions; their specific values are not provided in the abstract.
axioms (1)
  • domain assumption Small-signal stability analysis and frequency-domain characteristics accurately reflect system behavior under varying parameter settings.
    Invoked when the abstract states these analyses are performed under different control parameter settings.

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discussion (0)

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