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arxiv: 2604.10129 · v1 · submitted 2026-04-11 · 📡 eess.SY · cs.SY

Analysis and Enhancement of Incremental-Quantity-Based Distance Protection With Grid-Forming Inverters

Henrik Johansson , Qianli Xing , Nathaniel Taylor , Xiongfei Wang This is my paper

Pith reviewed 2026-05-10 15:45 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords grid-forming invertersincremental quantitiesdistance protectiontrip criterioncurrent limiterpower system protectionfault analysistime-domain protection
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The pith

A new trip criterion for incremental-quantity distance protection provides general settings that work reliably with grid-forming inverters.

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

The paper develops an analytical model to examine how grid-forming inverters affect the incremental quantities measured by distance relays. It finds that standard IQ-based protection performs better than quadrilateral methods for close-in faults but is difficult to tune across different inverter behaviors and fault types. To address this, the authors introduce a modified trip criterion that allows straightforward, general settings while preserving dependability and security. This matters because future power grids will rely heavily on inverter-based resources whose nonlinear fault responses challenge traditional protection assumptions. The model is verified through electromagnetic transient simulations.

Core claim

Grid-forming inverters, being nonlinear during faults due to current limiters, still permit the use of incremental-quantity superposition in protection analysis when modeled by fixed operating modes. The proposed trip criterion, derived from this model, enables dependable operation for internal faults and security for external faults with settings that do not require case-by-case adjustment for various GFM sources.

What carries the argument

The analytical model representing GFM inverter current limiter effects on relay incremental quantities, combined with the proposed trip criterion that adjusts the decision logic for improved interoperability.

If this is right

  • Time-domain IQ-based distance protection shows superior dependability for close-in faults compared to quadrilateral distance protection when GFM inverters are present.
  • The proposed settings can be secure for external faults in cases where quadrilateral protection would overreach.
  • Settings become easy to generalize across different GFM inverter current limiters and fault scenarios.
  • Interoperability issues with standard IQ protection are mitigated without losing the advantages of time-domain processing.

Where Pith is reading between the lines

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

  • Such criteria could support protection schemes in highly inverter-dominated networks where phasor-based methods fail due to lack of inertia.
  • Further validation in hardware-in-the-loop tests with real inverter controllers would strengthen confidence in the general settings.
  • Integration with other time-domain protections like traveling-wave methods might offer hybrid solutions for full line coverage.

Load-bearing premise

The GFM inverter current limiter can be modeled with fixed operating modes whose transitions do not break the linearity assumption underlying the incremental-quantity superposition used by the relay.

What would settle it

A simulation or field test of an internal close-in fault with a GFM inverter using a different current limiter mode transition that causes the proposed criterion to fail to trip or to misoperate on an external fault.

Figures

Figures reproduced from arXiv: 2604.10129 by Henrik Johansson, Nathaniel Taylor, Qianli Xing, Xiongfei Wang.

Figure 1
Figure 1. Figure 1: shows the studied power system. It includes a 66 kV GFM inverter at the sending end (left side) and a ∆-Y0 transformer with negligible leakage reactance that raises the voltage to 220 kV. The system frequency is 50 Hz and the nominal power of the GFM inverter is 300 MW. A 100 km transposed overhead line (OHL) transfers the power to the utility grid and is modelled using the frequency-dependent (phase) mode… view at source ↗
Figure 2
Figure 2. Figure 2: and 3 show their control diagrams. Both employ the P-f droop power synchronization control (PSC) and have an inductive output filter, but unlike GFM1, GFM2 separately controls the positive- and negative-sequences. Moreover, their current-limiting control strategies are vastly different: GFM1 applies a 1.2 pu magnitude saturation current limiter (no angle prioritization), while GFM2 applies an adaptive virt… view at source ↗
Figure 3
Figure 3. Figure 3: GFM2 control diagram as shown in [8]. Thorough comparisons of the current limiters implemented in GFM1 and GFM2 are given in [28], [29]. In short, the high control bandwidth of the inner current control loop enables the saturation current limiter of GFM1 to quickly limit [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Time-domain pure-fault network under balanced faults (linear sources). [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Proposed modelling of nonlinear GFM inverter FRT dynamics on the IQs locally measured by the relay during balanced faults. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: PSCAD test system for simulation validation. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Analytical calculations (dashed lines) compared to PSCAD simulations [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: shows the performance of IQ-based distance pro￾tection with GFM inverters as function of ∆Rs and ∆Xs, under various internal balanced faults. The shaded gray area in each subplot corresponds to the area where ψ op ≤ ψ rst , meaning that IQ-based distance protection is not dependable. The colored areas indicate where ψ op > ψrst, meaning the time-domain running sums (7) trend upwards and the distance elemen… view at source ↗
Figure 10
Figure 10. Figure 10: Quadrilateral distance: SIRs = SIRg = 0.3 and Ppre = 1 pu. C. Proposed Trip Criterion for IQ-Based Distance Protection For time-domain IQ-based distance protection, dependabil￾ity and security are heavily affected by where the trip threshold level of the running sums is put, which is not an easy-to-tune or straightforward user-specific setting that can be generalized for applications near GFM inverters, i… view at source ↗
Figure 9
Figure 9. Figure 9: Quadrilateral distance: SIRs = SIRg = 0.3 and Ppre = 1 pu. B. External Fault Security With regards to security against external faults, the an￾alytical calculations always yield ψ op ≤ ψ rst as function of ∆Rs and ∆Ls, even for balanced faults at mf = 0.81 (from solid to high-resistance faults), indicating that IQ-based distance protection demonstrates credible security properties against external faults u… view at source ↗
Figure 12
Figure 12. Figure 12: GFM2: ABCG fault at mf = 90% with Rf = 0 Ω. With regards to GFM1, the proposed IQ-based distance element is dependable up to Rf = 8 Ω at mf = 0.2, and Rf = 5 Ω at mf = 0.7 (better than quadrilateral for close￾in faults but worse near the reach point). Similar to GFM2, the slightly improved dependability compared to the analytical results in [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: GFM2: ABCG fault at mf = 70% with Rf = 5 Ω. Out of the simulated faults, the proposed IQ-based distance element is dependable with GFM2 up to Rf = 15 Ω at mf = 0.45, Rf = 10 Ω at mf = 0.6, and Rf = 8 Ω at mf = 0.75. The slightly enhanced dependability from the sim￾ulations compared to the analytical findings in [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: GFM1: ABCG fault at mf = 50% with Rf = 10 Ω. VI. CONCLUSION This paper proposes a general analytical framework to model the impact of GFM inverters on the relay-measured IQs, uses it to investigate the interoperability of time-domain IQ-based distance protection in the vicinity of GFM inverters [PITH_FULL_IMAGE:figures/full_fig_p009_13.png] view at source ↗
read the original abstract

Grid-forming (GFM) inverters are expected in future inverter-dominated grids. In such grids, time-domain protection schemes, for example those based on instantaneous incremental quantities (IQs), are being advocated as potential solutions to the challenges faced by traditional phasor-based protection schemes, due to their ability to process nonlinear data. However, IQ-based protection uses the superposition principle; thus, linearity is still assumed in their application, while GFM inverters are nonlinear sources during faults. This paper proposes an analytical model to study the impact of GFM inverters on the relay-measured IQs. The model is validated with PSCAD/EMTDC simulations, and is used to investigate the interoperability of time-domain IQ-based distance protection with GFM inverters employing different current limiters. Results show that time-domain IQ-based distance protection demonstrates superior dependability for close-in faults compared to that of quadrilateral distance protection with GFM inverters, and it has the possibility to be secure for external faults when quadrilateral distance protection overreaches; however, tuning of its settings is hard to generalize for various sources and faults. Taking the observed interoperability issues into account, a trip criterion for dependable and secure time-domain IQ-based distance protection is proposed, which facilitates easy-to-tune and general settings for applications with GFM inverters.

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

3 major / 2 minor

Summary. The paper develops an analytical model to characterize how grid-forming (GFM) inverters affect relay-measured incremental quantities (IQs) under different current-limiter implementations. The model is validated against PSCAD/EMTDC EMT simulations for multiple limiter types and fault locations. It shows that conventional IQ-based distance protection offers better dependability than quadrilateral distance protection for close-in faults with GFM inverters, yet its settings are difficult to generalize. The authors then propose a new trip criterion intended to provide easy-to-tune, general settings while preserving dependability for internal faults and security for external faults.

Significance. If the central modeling assumptions hold, the work supplies a first-principles analytical framework for a timely protection problem in inverter-dominated grids. The simulation-validated derivation of IQs and the concrete trip-criterion proposal constitute tangible contributions that could inform practical relay settings; the explicit comparison against quadrilateral protection and the emphasis on tuning generality are particularly useful.

major comments (3)
  1. [§3–4] §3–4: The analytical model represents the GFM inverter current limiter by a fixed set of operating modes and applies the superposition principle to obtain incremental quantities. The derivation therefore presupposes that mode transitions (voltage-to-current limiting, saturation entry/exit) do not occur on the timescale of the fault transient. No explicit analysis or additional simulation cases are provided to bound the validity of this assumption across limiter implementations or network topologies.
  2. [§5] §5: Validation is performed for several limiter types and fault locations, yet the reported cases do not include exhaustive checks for mid-fault mode transitions. Because the proposed trip criterion in §6 is derived directly from the IQ expressions obtained under the fixed-mode assumption, any violation of that assumption directly affects the claimed generality and dependability/security performance.
  3. [§6] §6: The assertion that the new trip criterion “facilitates easy-to-tune and general settings” rests on the analytical expressions; however, the manuscript provides no quantitative sensitivity study (e.g., variation of threshold margins with source strength, fault resistance, or limiter parameters) that would demonstrate reduced tuning effort relative to existing IQ or quadrilateral schemes.
minor comments (2)
  1. [Abstract, §1] The abstract and §1 should qualify statements about “superior dependability” and “secure for external faults” with reference to the specific simulation scenarios examined, to avoid implying unconditional generality.
  2. [§2] Notation for the incremental quantities (e.g., ΔV, ΔI) and the limiter-mode variables should be introduced once in §2 and used consistently thereafter; occasional redefinition in later sections reduces readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments. We address each of the major comments below and have made revisions to the manuscript to strengthen the presentation and address the concerns raised.

read point-by-point responses

  1. Referee: [§3–4] The analytical model represents the GFM inverter current limiter by a fixed set of operating modes and applies the superposition principle to obtain incremental quantities. The derivation therefore presupposes that mode transitions (voltage-to-current limiting, saturation entry/exit) do not occur on the timescale of the fault transient. No explicit analysis or additional simulation cases are provided to bound the validity of this assumption across limiter implementations or network topologies.

    Authors: We agree that the model relies on the assumption of fixed limiter modes during the transient to enable the use of superposition. This assumption is justified for the fault inception and the short time window considered for incremental quantity calculation, as mode transitions typically require some time to develop. In the revised manuscript, we have expanded Section 3 to include a discussion of the validity conditions for this assumption, supported by references to typical GFM control response times. Additionally, we have added simulation cases in Section 5 across different network topologies to illustrate that mode transitions do not occur within the relevant timeframe for the studied limiter implementations. revision: yes

  2. Referee: [§5] Validation is performed for several limiter types and fault locations, yet the reported cases do not include exhaustive checks for mid-fault mode transitions. Because the proposed trip criterion in §6 is derived directly from the IQ expressions obtained under the fixed-mode assumption, any violation of that assumption directly affects the claimed generality and dependability/security performance.

    Authors: We acknowledge the importance of verifying the absence of mode transitions in the validation cases. The original simulations were designed to capture the steady-state post-fault behavior within the incremental quantity window, but we agree that explicit checks are beneficial. In the revised version, we have included plots and analysis in Section 5 showing the limiter operating mode over time for all validation cases, confirming no mid-fault transitions occur. This reinforces the applicability of the derived expressions and the proposed trip criterion. revision: yes

  3. Referee: [§6] The assertion that the new trip criterion “facilitates easy-to-tune and general settings” rests on the analytical expressions; however, the manuscript provides no quantitative sensitivity study (e.g., variation of threshold margins with source strength, fault resistance, or limiter parameters) that would demonstrate reduced tuning effort relative to existing IQ or quadrilateral schemes.

    Authors: The proposed trip criterion is designed such that the threshold setting is determined from the analytical model in a manner that is largely independent of specific system parameters, thereby facilitating general settings. To address the request for quantitative demonstration, we have added a sensitivity analysis in the revised Section 6. This analysis varies source strength, fault resistance, and limiter parameters, showing that the threshold margins remain robust and require less case-specific tuning compared to conventional schemes, as evidenced by the smaller variation in required settings. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation from first-principles circuit equations with external simulation validation

full rationale

The paper constructs an analytical model of relay-measured incremental quantities under GFM inverters directly from circuit equations and the superposition principle, then validates it against independent PSCAD/EMTDC EMT simulations. The proposed trip criterion is subsequently derived from the model's predictions and observed interoperability issues. No fitted parameters are renamed as predictions, no self-citations are load-bearing for the central claims, and no ansatz or uniqueness result is imported from prior author work. The chain remains self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of representing GFM inverters by a small number of discrete current-limiter modes and on the continued applicability of incremental-quantity superposition within each mode. No new physical entities are postulated.

free parameters (1)
  • current-limiter threshold and mode-transition logic
    The model treats limiter behavior as piecewise constant; the exact threshold values and transition rules are taken from the specific inverter implementations tested in simulation.
axioms (1)
  • domain assumption Superposition principle remains usable for incremental quantities once the source is represented by its equivalent circuit in each limiter mode.
    Invoked when the analytical expression for relay-measured IQs is written; the paper itself notes that GFM inverters are nonlinear yet proceeds with this decomposition.

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Reference graph

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