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arxiv: 2604.12804 · v2 · submitted 2026-04-14 · 📡 eess.SY · cs.SY

Grid-Forming Characterization in DC Microgrids

Jovan Krajacic , Ognjen Stanojev , Mario Schweizer , Orcun Karaca , Gabriela Hug , Vladan Lazarevi\'c This is my paper

Pith reviewed 2026-05-10 14:54 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords DC microgridsgrid-formingimpedance-based indicesvoltage regulationconverter controlstabilityvoltage-forming behaviorcurrent-forming behavior
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The pith

Three impedance-based indices quantify voltage-forming and current-forming behavior in DC microgrids to improve voltage regulation.

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

The paper develops three new indices based on impedance to measure whether a converter in a DC microgrid behaves more as a voltage source or a current source. This addresses the lack of a clear way to evaluate and compare the many proposed control methods for keeping DC bus voltage stable in applications like data centers. A sympathetic reader would care because better classification could lead to controls that prevent voltage deviations more reliably. Simulations apply the indices to common strategies to compare their performance.

Core claim

This paper introduces three novel impedance-based indices that quantify the voltage-forming and current-forming behavior of a converter. The indices provide a basis for defining the desired converter behavior that yields superior DC-bus voltage regulation performance.

What carries the argument

Three novel impedance-based indices for quantifying voltage-forming and current-forming behavior of a converter.

If this is right

  • These indices enable classification and comparison of different converter control algorithms.
  • They support defining target converter behavior for improved DC-bus voltage regulation.
  • Simulations of representative controls illustrate the framework and reveal strengths and limitations of each strategy.

Where Pith is reading between the lines

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

  • The indices could be used to develop standardized guidelines for converter selection in DC microgrid design.
  • They might extend to assessing interactions in multi-converter systems for overall stability.
  • Experimental validation on physical hardware would test if the indices predict real-world performance accurately.

Load-bearing premise

The impedance-based indices accurately reflect the physical behavior of the converters and directly lead to superior voltage regulation performance when applied to define desired behavior.

What would settle it

An experiment showing that converters tuned according to the proposed indices do not achieve better DC-bus voltage regulation than those using traditional methods under varying load conditions.

Figures

Figures reproduced from arXiv: 2604.12804 by Gabriela Hug, Jovan Krajacic, Mario Schweizer, Ognjen Stanojev, Orcun Karaca, Vladan Lazarevi\'c.

Figure 1
Figure 1. Figure 1: Illustration of a source DC/DC (bidirectional boost) converter con [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Small-signal circuit of a source converter connected to a DC microgrid. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: DC microgrid with a boost-type source converter (left) supplying two [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Converter forming characterizition indicies for different boost converter control algorithms: a) Output-Impedance Index (OII), b) Current-Forming Index [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: DC bus voltage response to a load increase for different boost converter [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

DC microgrids are converter-based electrical networks that are increasingly being used in various applications, including data centers and industrial distribution systems. A central challenge in their operation is maintaining the DC-bus voltage within predefined limits while ensuring overall system stability. Although a wide variety of converter control algorithms has been proposed to achieve these objectives, the literature lacks a clear and physically interpretable framework for evaluating their effectiveness and for classifying and comparing them. Moreover, the grid-forming versus grid-following distinction that exists in AC systems has largely been unexplored in DC microgrids. To address this gap, this paper introduces three novel impedance-based indices that can be used to quantify the voltage-forming and current-forming behavior of a converter. The indices also provide a basis for defining the desired converter behavior that yields superior DC-bus voltage regulation performance. Simulation results illustrate the application of the framework to several representative control strategies and highlight the strengths and limitations of these control algorithms.

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

0 major / 2 minor

Summary. The paper introduces three novel impedance-based indices to quantify the voltage-forming and current-forming behavior of converters in DC microgrids. These indices provide a framework for classifying controls and defining desired behaviors that yield superior DC-bus voltage regulation performance, with simulations demonstrating application to representative control strategies.

Significance. If the indices are shown to be physically grounded and predictive, the work supplies a standardized, interpretable tool for evaluating and designing converter controls in DC microgrids, extending AC grid-forming concepts to DC systems. This addresses a clear literature gap and could improve voltage regulation in practical applications such as data centers. The reliance on standard impedance modeling and simulation-based validation are strengths.

minor comments (2)
  1. The abstract states that simulations illustrate the framework, but the manuscript should explicitly link each index value to observed voltage regulation metrics in the results section to strengthen the performance claim.
  2. Ensure all simulation parameters (e.g., line impedances, load steps) are tabulated for reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. We appreciate the recognition that the proposed impedance-based indices address a clear literature gap and offer a standardized, interpretable tool for evaluating converter controls in DC microgrids.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces three novel impedance-based indices derived from standard small-signal impedance models to quantify voltage-forming versus current-forming converter behavior in DC microgrids. These indices are defined directly from physical impedance characteristics and used to specify desired behavior for voltage regulation, without reducing to fitted parameters, self-referential definitions, or load-bearing self-citations. The abstract and claim structure show an independent modeling framework applied to representative controls via simulation, with no enumerated circular patterns (self-definitional, fitted-input-as-prediction, or ansatz smuggling) present in the stated derivation. The chain is self-contained against external benchmarks of impedance analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities used to derive the indices.

pith-pipeline@v0.9.0 · 5473 in / 1036 out tokens · 49007 ms · 2026-05-10T14:54:25.467149+00:00 · methodology

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Exploring Converter Control Duality in Microgrids: AC Grid-Forming vs DC Droop Control

    eess.SY 2026-04 unverdicted novelty 6.0

    AC grid-forming and DC droop controls are duals in small-signal models, current control structure, power-sharing mechanisms, and disturbance responses.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    DC mi- crogrids—Part II: A review of power architectures, applications, and standardization issues,

    T. Dragi ˇcevi´c, X. Lu, J. C. Vasquez, and J. M. Guerrero, “DC mi- crogrids—Part II: A review of power architectures, applications, and standardization issues,”IEEE Transactions on Power Electronics, vol. 31, no. 5, pp. 3528–3549, 2016

    work page 2016

  2. [2]

    Hierarchical control of droop-controlled AC and DC microgrids—a gen- eral approach toward standardization,

    J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. de Vicuna, and M. Castilla, “Hierarchical control of droop-controlled AC and DC microgrids—a gen- eral approach toward standardization,”IEEE Transactions on Industrial Electronics, vol. 58, no. 1, pp. 158–172, 2011

    work page 2011

  3. [3]

    DC- INDUSTRIE2 System Concept,

    Open DC Alliance (ODCA), J. Austermann, and H. Stammberger, “DC- INDUSTRIE2 System Concept,” Open DC Alliance (ODCA), Feb. 2024

    work page 2024

  4. [4]

    Comparative stability analysis of droop control approaches in voltage-source-converter-based DC microgrids,

    F. Gao, S. Bozhko, A. Costabeber, C. Patel, P. Wheeler, C. I. Hill, and G. Asher, “Comparative stability analysis of droop control approaches in voltage-source-converter-based DC microgrids,”IEEE Transactions on Power Electronics, vol. 32, no. 3, pp. 2395–2415, 2017

    work page 2017

  5. [5]

    Comparative admittance-based analysis for different droop control approaches in DC microgrids,

    Z. Jin, L. Meng, and J. M. Guerrero, “Comparative admittance-based analysis for different droop control approaches in DC microgrids,” in Proc. IEEE Second Int. Conf. on DC Microgrids, 2017, pp. 515–522

    work page 2017

  6. [6]

    A decentralized current-sharing controller endows fast transient response to parallel DC–DC converters,

    H. Wang, M. Han, R. Han, J. M. Guerrero, and J. C. Vasquez, “A decentralized current-sharing controller endows fast transient response to parallel DC–DC converters,”IEEE Transactions on Power Electronics, vol. 33, no. 5, pp. 4362–4372, 2018

    work page 2018

  7. [7]

    An inertia and damping control method of DC–DC converter in DC microgrids,

    X. Zhu, F. Meng, Z. Xie, and Y . Yue, “An inertia and damping control method of DC–DC converter in DC microgrids,”IEEE Transactions on Energy Conversion, vol. 35, no. 2, pp. 799–807, 2020

    work page 2020

  8. [8]

    Inertia emulation in droop-based DC microgrids with equivalent converter impedance reshaping,

    F. Deng, L. Zhang, Z. Xiao, Z. Yao, and Y . Tang, “Inertia emulation in droop-based DC microgrids with equivalent converter impedance reshaping,”IEEE Transactions on Power Electronics, vol. 39, no. 11, pp. 15 206–15 216, 2024

    work page 2024

  9. [9]

    Admittance- type RC-mode droop control to introduce virtual inertia in DC mi- crogrids,

    Z. Jin, L. Meng, R. Han, J. M. Guerrero, and J. C. Vasquez, “Admittance- type RC-mode droop control to introduce virtual inertia in DC mi- crogrids,” in2017 IEEE Energy Conversion Congress and Exposition (ECCE), 2017, pp. 4107–4112

    work page 2017

  10. [10]

    Virtual DC machine control strategy of energy storage converter in DC microgrid,

    S. Tan, G. Dong, H. Zhang, N. Zhi, and X. Xiao, “Virtual DC machine control strategy of energy storage converter in DC microgrid,” in2016 IEEE Electrical Power and Energy Conference (EPEC), 2016, pp. 1–6

    work page 2016

  11. [11]

    A virtual inertia and damping control to suppress voltage oscillation in islanded DC microgrid,

    G. Lin, J. Ma, Y . Li, C. Rehtanz, J. Liu, Z. Wang, P. Wang, and F. She, “A virtual inertia and damping control to suppress voltage oscillation in islanded DC microgrid,”IEEE Transactions on Energy Conversion, vol. 36, no. 3, pp. 2134–2144, 2021

    work page 2021

  12. [12]

    Power-loop-free virtual DC machine control with differential compensation,

    N. Zhi, X. Ming, Y . Ding, L. Du, and H. Zhang, “Power-loop-free virtual DC machine control with differential compensation,”IEEE Transactions on Industry Applications, vol. 58, no. 1, p. 413, 2022

    work page 2022

  13. [13]

    Ensuring stability in DC microgrids through application of the passivity principle,

    V . ˇZ. Lazarevi´c, M. Schweizer, D. Pejovski, and A. Antoniazzi, “Ensuring stability in DC microgrids through application of the passivity principle,” in2025 IEEE Seventh International Conference on DC Microgrids (ICDCM), 2025, pp. 1–6

    work page 2025

  14. [14]

    A small-signal stability analysis method for DC microgrids based on immittance phases,

    B. He, J. Xu, M. Wu, C. Guo, and C. Zhao, “A small-signal stability analysis method for DC microgrids based on immittance phases,”IEEE Trans. on Power Electronics, vol. 40, no. 10, pp. 14 271–14 275, 2025

    work page 2025

  15. [15]

    Resistive–capacitive output impedance shaping for droop-controlled converters in DC microgrids with reduced output capacitance,

    G. Liu, P. Mattavelli, and S. Saggini, “Resistive–capacitive output impedance shaping for droop-controlled converters in DC microgrids with reduced output capacitance,”IEEE Transactions on Power Elec- tronics, vol. 35, no. 6, pp. 6501–6511, 2020

    work page 2020

  16. [16]

    A dynamic similarity index for assessing voltage source behaviour in power systems,

    O. Alican, D. Moutevelis, J. Ar ´evalo-Soler, C. Collados-Rodriguez, J. Amor ´os, O. Gomis-Bellmunt, M. Cheah-Ma ˜ne, and E. Prieto-Araujo, “A dynamic similarity index for assessing voltage source behaviour in power systems,”IEEE Transactions on Power Systems, pp. 1–14, 2025

    work page 2025

  17. [17]

    Characterization of the grid- forming function of a power source based on its external frequency smoothing capability,

    M.-S. Debry, G. Denis, and T. Prevost, “Characterization of the grid- forming function of a power source based on its external frequency smoothing capability,” in2019 IEEE Milan PowerTech, 2019, pp. 1–6

    work page 2019

  18. [18]

    Quantifying grid-forming behavior: Bridging device- level dynamics and system-level stability,

    K. Zhuang, H. Xin, V . H ¨aberle, X. He, L. Huang, and F. D ¨orfler, “Quantifying grid-forming behavior: Bridging device- level dynamics and system-level stability,” 2025. [Online]. Available: https://arxiv.org/abs/2503.24152

    work page internal anchor Pith review arXiv 2025

  19. [19]

    Model-based current control of AC ma- chines using the internal model control method,

    L. Harnefors and H.-P. Nee, “Model-based current control of AC ma- chines using the internal model control method,”IEEE Transactions on Industry Applications, vol. 34, no. 1, pp. 133–141, 1998

    work page 1998

  20. [20]

    R. W. Erickson and D. Maksimovi ´c,Fundamentals of Power Electronics, 2nd ed. Boston, MA: Springer, 2001

    work page 2001

  21. [21]

    Bao and P

    J. Bao and P. L. Lee,Process Control: The Passive Systems Approach, ser. Advances in Industrial Control. London: Springer, 2007

    work page 2007