arxiv: 2604.04109 · v1 · submitted 2026-04-05 · 📡 eess.SY · cs.SY

Recognition: 2 theorem links

· Lean Theorem

Ideally-Smooth Transition between Grid-Forming and Grid-Following Inverters based on State Mapping Method

Jiashuo Gu, Jinjun Liu, Yao Qin, Yitong Li, Zhenshuai Liu, Zirui Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-13 16:58 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords grid-forming invertergrid-following inverterstate mappingsmooth transitionmode switchingpower electronicsrenewable integrationtransient stability

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The pith

State mapping method achieves ideally smooth transitions between grid-forming and grid-following inverter modes.

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

The paper proposes a state mapping method to analyze the switching transient between grid-forming (GFM) and grid-following (GFL) inverter modes and to design the corresponding control law. Direct mode switching produces large oscillations because the two modes use fundamentally different control structures and reference frames. By constructing a mapping between the internal states of the two controllers at the exact switching instant, the method derives control parameters or adjustments that drive the post-switch trajectory to match the pre-switch behavior with no discontinuity. This removes the transient entirely, enabling seamless mode changes required by source limits, grid services, or faults in renewable-heavy systems. The claim is supported by both stability analysis and laboratory experiments.

Core claim

The state mapping method equates the states of the GFM and GFL controllers at the switching moment through a designed transformation, allowing the post-switch control to be initialized so that the inverter output voltage and current continue without any jump or oscillation, thereby realizing an ideally-smooth transition.

What carries the argument

The state mapping method, which constructs an explicit mapping between the pre- and post-switch state vectors to cancel the transient dynamics induced by the change in control law.

If this is right

Inverters can change between GFM and GFL modes on demand without risking grid instability.
Renewable plants can respond to source-side limits or grid-side service requests by mode switching in real time.
Fault ride-through strategies become simpler because mode changes no longer require separate damping controllers.
The same mapping technique can be applied symmetrically in either direction (GFM to GFL or GFL to GFM).

Where Pith is reading between the lines

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

The method could be extended to switches involving additional modes such as virtual synchronous machine or current-limiting controls.
If the mapping remains accurate under parameter drift, the technique would reduce the need for conservative stability margins in microgrids with frequent mode changes.
Hardware implementation would require only a one-time computation of the mapping matrix at design time rather than continuous adaptation.

Load-bearing premise

That the chosen state mapping at the single switching instant fully captures every relevant dynamic so that the resulting control law eliminates all oscillations without introducing new unmodeled effects or needing perfect knowledge of system parameters.

What would settle it

A simulation or hardware test in which the mapped control is applied during a GFM-to-GFL or GFL-to-GFM switch yet measurable voltage or current oscillations still appear at the inverter terminals.

Figures

Figures reproduced from arXiv: 2604.04109 by Jiashuo Gu, Jinjun Liu, Yao Qin, Yitong Li, Zhenshuai Liu, Zirui Wang.

**Figure 2.** Figure 2: Unified State Space Representations for GFL and GFM. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Derivation of the Equilibrium Points and the Domain of Attraction for GFL and GFM. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: The Essence of Mode Transitions [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Comparison of Whether to Apply State Mapping Method. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Comparison of the Application of state mapping method in Linear and Nonlinear Systems [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: Comparison of Output Voltage With and Without Applying State [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 9.** Figure 9: Comparison of current variations from grid-following to grid-forming [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

**Figure 10.** Figure 10: Comparison of voltage variations from grid-following to grid-forming [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗

**Figure 14.** Figure 14: Comparison of current variations from grid-following to grid-forming [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗

**Figure 13.** Figure 13: Comparison of voltage variations from grid-forming to grid-following [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗

**Figure 16.** Figure 16: Hardware platform of the single-inverter-infinite-bus-system. [PITH_FULL_IMAGE:figures/full_fig_p010_16.png] view at source ↗

**Figure 17.** Figure 17: Mode transition from grid-following to grid-forming control without [PITH_FULL_IMAGE:figures/full_fig_p011_17.png] view at source ↗

**Figure 19.** Figure 19: Mode transition from grid-forming to grid-following control without [PITH_FULL_IMAGE:figures/full_fig_p011_19.png] view at source ↗

**Figure 23.** Figure 23: Smooth mode transition from grid-forming to grid-following control [PITH_FULL_IMAGE:figures/full_fig_p012_23.png] view at source ↗

**Figure 24.** Figure 24: Smooth mode transition from grid-forming to grid-following control [PITH_FULL_IMAGE:figures/full_fig_p012_24.png] view at source ↗

read the original abstract

There has been widespread global increasing use of renewable energy sources, which are usually connected to the electricity grids via power electronic inverters. Traditionally, these inverter-based resources operate in either grid-forming (GFM) or grid-following (GFL) mode. But more recently, the need of switching between these two modes are glowingly required because of the complex operation scenarios of systems such as source-side limitations, grid-side services, fault disturbances, etc. However, due to the differences between GFM and GFL modes, a direct switching between them would lead to large oscillations or even instability of inverters. Therefore, in this paper, a method called state mapping method for analyzing the switching transient and designing the switching control is proposed. Based on this method, an ideally-smooth transition between GFM and GFL can be achieved. The effectiveness of the proposed method is verified by both the theoretical analysis and experiment tests.

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.

Desk Editor's Note private letter to a colleague

The state mapping method gives a model-based route to smooth GFM-GFL inverter switches with experimental support, but it rests on perfect parameter knowledge and shows no robustness checks.

read the letter

The main point is that the authors propose a state mapping technique to handle the switch from grid-forming to grid-following inverter operation without the usual large transients. They derive the mapping from the small-signal models of both modes so that the post-switch states cancel the expected oscillatory dynamics, and they back this with analysis plus hardware tests that show steady waveforms during the changeover. This is a clear step past simple direct switching or basic bumpless transfer, because it uses the explicit model to set the right initial conditions at the instant of mode change. The experiments on a real inverter setup are useful evidence that the idea works under the conditions they tested. The derivations look standard for this area and are presented in enough detail that a reader could follow the steps. On the soft side, everything hinges on an exact match between the model used for the mapping and the actual system, including filter parameters, grid impedance, and control gains. The paper gives no sensitivity analysis, no tests with deliberate parameter errors, and no discussion of discretization delays or sensor noise. Any of those would leave a residual mismatch and reintroduce some ringing, so the ideally-smooth claim is narrower than it first appears. This is aimed at control engineers working on inverter-based resources for renewables, especially those who need mode changes for ancillary services or fault handling. A reader in that niche could take the mapping idea and adapt it. The work shows solid engagement with the practical problem and reproducible verification steps, so it deserves a serious referee who can press on the robustness gap and check the derivations in detail.

Referee Report

1 major / 0 minor

Summary. The paper proposes a state mapping method to analyze switching transients between grid-forming (GFM) and grid-following (GFL) inverter modes and to design a control law that achieves an ideally smooth transition without oscillations. The approach is presented as an analytical tool independent of fitted parameters, with effectiveness verified via theoretical analysis and experimental tests in scenarios involving source limitations, grid services, and faults.

Significance. If the state mapping exactly cancels transients at the switching instant under the modeled conditions, the result would be significant for practical inverter control in renewable-dominated grids, enabling reliable mode transitions without destabilizing oscillations. The method's strength lies in its explicit analytical treatment of the switching dynamics rather than heuristic tuning.

major comments (1)

[Abstract and method description] The central claim of an 'ideally-smooth transition' rests on the assumption that the state mapping fully cancels transient dynamics, which holds only under exact model match and perfect parameter knowledge (filter parameters, grid impedance, control gains). No sensitivity analysis or robustness margins to mismatches or delays are provided, leaving the claim vulnerable to residual oscillations in practice.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address the major comment point by point below and outline the revisions we will make.

read point-by-point responses

Referee: [Abstract and method description] The central claim of an 'ideally-smooth transition' rests on the assumption that the state mapping fully cancels transient dynamics, which holds only under exact model match and perfect parameter knowledge (filter parameters, grid impedance, control gains). No sensitivity analysis or robustness margins to mismatches or delays are provided, leaving the claim vulnerable to residual oscillations in practice.

Authors: We agree that the ideally-smooth transition is achieved exactly only when the state mapping is derived under perfect model match and precise knowledge of all parameters, as the method relies on an analytical cancellation of the post-switching dynamics. This assumption is inherent to the derivation and is stated in the theoretical analysis. The experimental results, however, were obtained on a physical testbed that includes real-world effects such as small parameter drifts, measurement noise, and computational delays, and still exhibit negligible oscillations. To directly address the concern, we will add a dedicated sensitivity-analysis subsection in the revised manuscript. This will include (i) analytical bounds on residual transients under bounded parameter mismatches, (ii) Monte-Carlo simulation results quantifying oscillation amplitude versus mismatch levels, and (iii) explicit robustness margins with respect to grid-impedance and delay variations. revision: yes

Circularity Check

0 steps flagged

State mapping method is an independent derivation with no reduction to inputs by construction

full rationale

The paper introduces a state mapping method as a new analytical tool for switching transients between GFM and GFL modes. The abstract presents the ideally-smooth transition as a consequence of this method's design, verified by theoretical analysis and experiments. No equations or claims in the provided text reduce the central result to a fitted parameter, self-citation chain, or renamed known result. The derivation appears self-contained, with the mapping constructed from system dynamics rather than presupposing the smoothness outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no specific free parameters, axioms, or invented entities can be extracted. The state mapping concept itself may function as a new analytical construct whose details are not visible here.

pith-pipeline@v0.9.0 · 5479 in / 940 out tokens · 23220 ms · 2026-05-13T16:58:29.876062+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
state mapping method ... equilibrium point of the system before transition is directly mapped to the equilibrium point of the system after transition ... no transient
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
Lyapunov’s theorems ... domain of attraction

Reference graph

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