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REVIEW 2 major objections 5 minor 31 references

Revisiting the Effect of Grid-Following Converter on Frequency Dynamics -- Part I: Center of Inertia

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Grid-following converters do not enter the center of inertia; their equivalent frequency couples to it through a weak, adjustable virtual tie line.

desk verdict Careful GFL swing-equation modeling, but the central no-COI-aggregation claim rests on a sign error in Eq. (21d) that likely does not survive contact with the paper's own Eq. (20). read the letter →

arxiv 2507.15358 v1 pith:ZM7JALK5 submitted 2025-07-21 eess.SY cs.SY

Jiahao Liu , Cheng Wang , Tianshu Bi This is my paper · ORCID
classification eess.SYcs.SY
keywords grid-followingconvertercenterofinertiafrequencydynamicsequivalentphase-lockedlooptyingpowervirtualtielinemulti-generatormodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish where grid-following (GFL) converters sit in the frequency dynamics of a power system. The center of inertia (COI), the inertia-weighted average frequency used in most frequency-stability analyses, has always been formed by aggregating synchronous generators whose inter-machine exchange powers cancel pairwise like springs. The paper claims that when a GFL is present, the power exchanged between it and a synchronous generator does not cancel in the same way, so the converter cannot be folded into the COI; instead, its equivalent frequency couples to the COI through a virtual tie line. If this is correct, the common shortcut of treating a converter as either a constant power source or as extra inertia inside the COI misses the actual mechanism, and converter support for system frequency is weak, time-variable, and adjustable through control parameters.

What carries the argument

The load-bearing object is the tying power between generators: for two synchronous generators the exchange term is $E_iE_jB_{ij}\sin(\delta_i-\delta_j)$ on one side and its exact negative on the other, so the pair cancels and all SGs can be merged into one COI. For an SG and a GFL, the corresponding expression built from the transfer parameter $V^{eq}$ reads $-E_iI_fV^{eq}\cos(\delta_i-\theta_{f})$ on both sides, giving equal magnitudes but the same direction, so the pair does not cancel and the GFL must remain outside the COI. The second piece of machinery is the GFL interface state variable $I^F\angle\theta^{F,I}$, which replaces the synchronous machine's internal EMF as the quantity that couples converter dynamics to the network, and whose dynamics are split into a continuous part governed by equivalent inertia and a discontinuous part governed by the proportional coefficient $L^F$.

What would settle it

Recompute the SG-side and GFL-side tie powers by substituting Eq. (20) into the active-power formula $P=\mathrm{Re}(\dot U\,\overline{\dot I})$ and compare the resulting signs; if the two expressions are negatives of each other, the SG-GFL pair cancels like an SG-SG pair and the paper's central claim fails, while if they are equal in sign the claim is confirmed.

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Extended reading notes

Core claim

The paper's central claim is that grid-following converters and synchronous generators cannot be aggregated into one center of inertia because the tying power between them has equal magnitudes but the same direction, not opposite directions. It develops a multi-generator model in which each GFL's interface state variable is the output-current phasor $I^F\angle\theta^{F,I}$, whose dynamics are shaped by the d-axis power control, the DC boost, and the phase-locked loop; this variable obeys a swing-equation-like relation with an equivalent inertia $H^F$, an equivalent governor transfer function $J^F(s)$, and a proportional step coefficient $L^F$. On the network side, the admittance matrix is rearranged so that active power between SGs and GFLs flows through transfer parameters $V^{eq}$ and $W^{eq}$; because these terms do not cancel pairwise, only synchronous generators form the COI, and the GFL equivalent frequency interacts with the COI frequency through a virtual tie line. The paper further claims that this coupling is weak because the transfer parameters are small, and that the GFL-side equivalent inertia and governor, although they do not add directly to $H^{COI}$, still shape COI dynamics through that tie line and are adjustable via control setpoints.

Load-bearing premise

The central conclusion that a GFL cannot be aggregated into the COI rests entirely on the signs of the two tie-power terms in Eqs. (21d) and (22d): the block-matrix derivation in Eq. (20) yields the GFL-side term as the negative of the SG-side term, yet the printed formulas add to $-2EIV\cos(\delta-\theta)$, and the 'same direction' property comes from that printed sign.

Editorial extensions

If this is right

  • Only synchronous generators define the system center of inertia; a GFL's equivalent inertia and governor reach the COI indirectly through the virtual tie line, not by direct addition to $H^{COI}$.
  • In the paper's test system, the proposed model reduces COI-frequency error to 0.56% and GFL-power error to 4.41%, compared with 6.39% and 11.48% for the SFR-based treatment that ignores converter dynamics.
  • A GFL's equivalent parameters are not fixed machine constants: they vary with active power, reactive power, voltage setpoint, PLL gains, and DC-control gains, so the same converter can look like different inertia values at different operating points.
  • Reducing the PLL integral gain can raise the COI frequency nadir, so slower converter synchronization can actually improve the system frequency response in a low-inertia grid.
  • The GFL equivalent governor provides no steady-state damping; it only contributes an oscillation at frequency $\omega_{Osc}$ that can be tuned through DC-side control gains and is reflected in COI dynamics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the paper's conclusion turns on the sign of the tie-power terms in Eqs. (21d) and (22d), a direct algebraic check of those equations against Eq. (20) would settle whether the cancellation argument extends to SG-GFL pairs; the matrix derivation already supplies a relative negative sign that the printed tie-power formulas do not carry through.
  • The same construction likely transfers to grid-forming converters, whose internal synchronization differs from both SGs and GFLs; the critical test is whether their tying power with synchronous generators cancels pairwise.
  • The paper's finding that the coupling is controlled by $V^{eq}$ and $W^{eq}$ suggests a design extension: frequency support could be shaped by adjusting converter output impedance or network impedance rather than only by tuning converter inertia.
  • Since the case study shows a negative component ($H^{F,Id}$) and a positive component ($H^{F,PLL}$) combining into a positive total equivalent inertia, interpreting a single fitted 'inertia' value could be misleading; an experimental separation of the continuous and discontinuous frequency components would clarify what is actually being measured.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper develops a multi-generator model of a power system containing synchronous generators (SGs) and grid-following converters (GFLs). It derives a swing-equation-like model for the GFL equivalent frequency, including equivalent inertia, equivalent governor, and a proportional coefficient, all expressed in terms of control parameters and operating points. On the network side, it defines tying power between SG and GFL interface state variables and claims that SG-GFL tying powers have equal magnitudes but the same direction, so GFLs cannot be aggregated into the SG center of inertia (COI); instead, GFLs interact with the SG COI through a virtual tie line. Case studies on a modified WECC 9-bus system compare the proposed model with EMT simulations and two existing methods, reporting smaller errors for the proposed model.

Significance. If the central claim were correct, the paper would provide a principled answer to a long-debated question: whether GFL equivalent inertia and governor dynamics can be lumped into a system-wide COI. The paper's derivation of GFL equivalent parameters directly from control parameters and operating points, without fitting to simulation output, and its validation against EMT simulations with small error indices, are genuine strengths. However, the central no-aggregation result rests on a sign error in the tie-power equations. Once the sign is corrected, the SG-GFL tie powers cancel in exactly the same way as SG-SG tie powers, so the proposed virtual-tie-line interpretation and the entire COI aggregation structure collapse. The contribution, as a proof of the stated claim, is therefore not reliable.

major comments (2)
  1. [Section IV-A, Eqs. (21d), (22d), (24)] The sign of the V_eq cos term in Eq. (21d) is inconsistent with the block matrix (20). Expanding (20), the SG-side tie power is Re(E_G conj(T_eq I_F)) = E_G I_F [V_eq cos(δ_G - θ_F) + W_eq sin(δ_G - θ_F)], while the GFL-side tie power is Re(U_F conj(I_F)) = -E_G I_F [V_eq cos(δ_G - θ_F) + W_eq sin(δ_G - θ_F)]. The printed Eq. (21d) uses -V_eq cos(...) + W_eq sin(...), which is the negative of the correct first term, and Eq. (22d) also uses -V_eq cos(...) + W_eq sin(...). Consequently Eq. (24) prints -2 E_G I_F V_eq cos(...), whereas the correctly derived terms sum to zero. Since equation (24) is the sole stated basis for the claim that SG-GFL tie powers are 'equal in magnitude but same direction', the paper's central conclusion that GFLs cannot be aggregated into the SG COI is unsupported. This is a load-bearing error: correcting the sign reverses the conclusion and invalidates the virtual-tie-line model of Eqs. (26e) and (27d).
  2. [Section IV-B.1 and Table III] The claim that the connection between the SG COI and GFLs is 'relatively weak' is not derived in the paper but is inferred from a single numerical case (V_eq' = -0.84 pu versus G_eq' = 2.67 pu in Table III) together with a qualitative statement about the admittance-matrix inversion. No bound, scaling law, or parametric study establishes that V_eq and W_eq are generally small, so the abstract's statement that the impact of GFLs on COI frequency is 'relatively weak' is not supported beyond the specific test system.
minor comments (5)
  1. [Eq. (22c) and Eq. (27c)] The index in the cosine term is repeated: 'θ_{F,I}^{i_F} - θ_{F,I}^{i_F}' should read 'θ_{F,I}^{i_F} - θ_{F,I}^{j_F}'; the same typo appears in Eq. (27c).
  2. [Heading of Section IV-B] The heading contains a typo: 'Frequecny' should be 'Frequency'.
  3. [Section IV-B.2] The notation 'P_{F,M ac}' is inconsistent with 'P_{F,M ec}' used earlier in Eq. (16c); the same symbol should be used throughout.
  4. [Reference [30]] The derivations for the transfer functions J_Id(s), J_Pll(s), the coefficients c_Ei, c_Ep, c_Pll, c_Pi, and the network reduction are relegated to an external URL. The manuscript is not self-contained, which makes it difficult to verify the derivations.
  5. [Eq. (26e), Eq. (27d), and Table III] The coefficients V_eq' and W_eq' appear with a single GFL subscript i_F, whereas the earlier full-network model uses double subscripts i_G, i_F; the definition of these aggregated coefficients is deferred to the appendix and should be stated in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is self-contained and benchmarked against independent EMT simulation.

full rationale

The paper's core derivation chain is not circular. The GFL interface-state model (Eqs. 7-16) is obtained by linearizing the converter controls (DC boost, d-axis power control, PLL) under stated assumptions A1-A4; equivalent inertia H_F, equivalent governor J_F(s), and proportional coefficient L_F are closed-form functions of control gains and operating points, not parameters fitted to the EMT output. The network-side tying powers (Eqs. 21-22) are computed from the admittance matrix via the standard relation P = Re(U conj(I)), and the SG-SG cancellation (Eq. 23) and the SG-GFL non-cancellation (Eq. 24) are presented as derived results rather than assumed conclusions. The model is then tested against detailed EMT simulation on a modified WECC 9-bus system (Sec. V-A, Table II), which is an external benchmark independent of the model's fitted parameters. The appendix citation [30] supplies derivations and coefficient expressions rather than invoking an unverified self-cited uniqueness theorem, so it is not load-bearing circularity. The possible sign inconsistency in Eqs. (21d)/(22d) is a correctness or consistency concern, not a circularity defect: even if Eq. (24) is algebraically wrong, the paper's conclusion would be unsupported but not equivalent to its inputs by construction. No fitted parameter is renamed as a prediction, and no known result is repackaged as the claimed derivation. Hence no circular step is present.

Assumptions & free parameters 0 free parameters · 4 assumptions · 2 invented entities

The central claim rests on no fitted constants: equivalent inertia and governor terms are computed from control settings and operating points. The heavier burden is carried by the linearization, the A1-A4 simplifications, and the sign convention in Eqs. (21d) and (22d), the last of which is not justified in the text.

assumptions (4)
  • domain assumption Synchronous generators are represented by a second-order swing equation with constant EMF amplitude behind a reactance, and SG tie susceptances dominate conductances.
    Used in Section II and Section IV-A to justify aggregating SGs into the COI and to neglect G terms in Eq. (23).
  • ad hoc to paper A1-A4: constant DC input power, constant control setpoints, ideal inner current loops, and constant q-axis voltage, reactive power, and q-axis current during frequency dynamics.
    These assumptions in Section III-A reduce the GFL to DC boost, d-axis power control, and PLL; they are stated but not validated for large disturbances.
  • domain assumption The power system can be linearized around the pre-disturbance operating point, and node elimination with constant-impedance loads yields the block matrices in Eqs. (17)-(20).
    Required for the transfer-function derivation in Sections III-B and III-C and for the sign relations in Eq. (20).
  • ad hoc to paper The sign convention for tie power in Eqs. (21d) and (22d) is the same as for physical branch power.
    The central non-cancellation result in Eq. (24) uses this convention; the paper never states it, and the printed signs appear inconsistent with active-power balance.
invented entities (2)
  • GFL equivalent frequency with continuous and discontinuous components
    purpose: Represents the dynamics of the current-interface state variable in swing-equation form; used to define equivalent inertia, governor, and proportional coefficient.
    It is a mathematical construct from transfer-function manipulation, not directly measurable; the simulation match provides only indirect support.
  • Virtual tie line and virtual tying power between SG COI and GFLs
    purpose: Models the aggregated interaction after SGs are combined into the COI; the paper uses it to quantify a weak coupling.
    A modeling abstraction with no independent falsifiable handle; its parameters are computed from the same network model used to derive it.

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Cite this review

Pith. "Pith review of Revisiting the Effect of Grid-Following Converter on Frequency Dynamics -- Part I: Center of Inertia." pith.science (2026). https://pith.science/paper/ZM7JALK5

@misc{pith2026250715358,
  author       = {Pith},
  title        = {Pith review of: Revisiting the Effect of Grid-Following Converter on Frequency Dynamics -- Part I: Center of Inertia},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZM7JALK5}},
  note         = {Machine review of arXiv:2507.15358}
}
read the original abstract

Understanding the impact of grid-following (GFL) converters on system frequency dynamics is crucial, from both the center of inertia (COI) and frequency spatial variation perspectives. Part I of this series clarifies the mechanisms by which GFLs influence COI frequency dynamics. A multi-generator model of the power system with GFLs is developed, incorporating the local dynamics of GFLs and their interaction with synchronous generators via virtual tie lines. By aggregating the multi-generator model into the COI frame, the interaction between the COI frequency and the equivalent frequency of GFLs is revealed. The equivalent inertia and other components at the GFL side, determined by control parameters and operating conditions, support the COI through virtual tying power. Simulation validates the accuracy of the proposed modeling and demonstrates that the impact of GFLs on COI frequency is relatively weak. The equivalent inertia and other components of GFLs still significantly influence COI frequency dynamics, with their effects being both time-variable and adjustable.

Figures

Figures reproduced from arXiv: 2507.15358 by the authors.

Figure 2
Figure 2. COI frequency dynamics in traditional power systems. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. GFL model in system frequency dynamics time scale. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Multi-generator dynamics in power systems with GFLs. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (7 more)
Figure 6
Figure 6. Figure 6: COI frequency dynamics in power systems with GFLs. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: Model validation with (a) GFL active power and (b) COI frequency. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Phase angle dynamics validation. and the internal angle of the SG. For the SFR-based model, the GFL dynamics are entirely ignored, resulting in constant active power, as depicted in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Dynamics of (a) power, (b) frequency, and (c) state variable. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 12
Figure 12. Figure 12: Summary of time-variable and adjustable characters for (a) GFL inertia, (b) equivalent generator, and (c) proportional coefficient. [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 10
Figure 10. Figure 10: Frequency trend when reducing PLL integral control setting. [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: Frequency trend when reducing proportional and integral control [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]

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Works this paper leans on

31 extracted references · 24 canonical work pages

  1. [24]

    Inertia and primary frequency provisions of pll-synchronized vsc hvdc when attached to islanded ac system,

    M. Zhang, X. Yuan, and J. Hu, “Inertia and primary frequency provisions of pll-synchronized vsc hvdc when attached to islanded ac system,”IEEE Trans. Power Syst., vol. 33, no. 4, pp. 4179–4188, 2018

    2018

  2. [22]

    Modeling of grid-connected vscs for power system small-signal stability analysis in dc-link voltage control timescale,

    H. Yuan, X. Yuan, and J. Hu, “Modeling of grid-connected vscs for power system small-signal stability analysis in dc-link voltage control timescale,” IEEE Trans. Power Syst. , vol. 32, no. 5, pp. 3981–3991, 2017

    work page 2017

  3. [23]

    Inertial and primary frequency response of pll synchronized vsc interfaced energy resources,

    R. Fu, X. Wang, Y . Zhang, and L. Li, “Inertial and primary frequency response of pll synchronized vsc interfaced energy resources,” IEEE Trans. Power Syst., vol. 37, no. 4, pp. 2998–3013, 2022

    work page 2022

  4. [1]

    Frequency control and optimal operation of low-inertia power systems with hvdc and renewable energy: A review,

    K. Yan, G. Li, R. Zhang, Y . Xu, T. Jiang, and X. Li, “Frequency control and optimal operation of low-inertia power systems with hvdc and renewable energy: A review,” IEEE Trans. Power Syst. , vol. 39, no. 2, pp. 4279–4295, 2024

    work page 2024

  5. [2]

    Frequency divider,

    F. Milano and ´A. Ortega, “Frequency divider,” IEEE Trans. Power Syst., vol. 32, no. 2, pp. 1493–1501, 2017

    2017

  6. [3]

    Foundations and challenges of low-inertia systems (invited paper),

    F. Milano, F. D ¨orfler, G. Hug, D. J. Hill, and G. Verbi ´c, “Foundations and challenges of low-inertia systems (invited paper),” in 2018 Power Systems Computation Conference (PSCC) , 2018, pp. 1–25

    2018

  7. [4]

    Review on measurement-based frequency dynamics monitoring and analyzing in renewable energy dominated power systems,

    X. Chen, Y . Jiang, V . Terzija, and C. Lu, “Review on measurement-based frequency dynamics monitoring and analyzing in renewable energy dominated power systems,” Int. J. Elect. Power Energy Syst. , vol. 155, p. 109520, 2024

    2024

  8. [5]

    Modeling of wind turbine generators for power system stability studies: A review,

    X. He, H. Geng, and G. Mu, “Modeling of wind turbine generators for power system stability studies: A review,” Renew. Sustain. Energy Rev., vol. 143, p. 110865, 2021

    work page 2021

Show all 31 references
  1. [6]

    Definition and classification of power system stability - revisited & extended,

    N. Hatziargyriou, J. Milanovic, C. Rahmann, V . Ajjarapu, C. Canizares, I. Erlich, D. Hill, I. Hiskens, I. Kamwa, B. Pal, P. Pourbeik, J. Sanchez- Gasca, A. Stankovic, T. V . Cutsem, V . Vittal, and C. V ournas, “Definition and classification of power system stability - revisi...

    2021

  2. [7]

    Performance comparison of typical frequency response strategies for power systems with high penetration of renewable energy sources,

    L. Xiong, X. Liu, H. Liu, and Y . Liu, “Performance comparison of typical frequency response strategies for power systems with high penetration of renewable energy sources,” IEEE J. Emerg. Sel. Top. Circuits Syst., vol. 12, no. 1, pp. 41–47, 2022

    2022

  3. [8]

    Aggregated sfr model for vsc hvdc interconnected power systems with high penetration of wind power,

    K. Yan, G. Li, R. Zhang, F. Li, T. Jiang, X. Li, and H. Chen, “Aggregated sfr model for vsc hvdc interconnected power systems with high penetration of wind power,” Electr. Power Syst. Res. , vol. 216, p. 109018, 2023

    2023

  4. [9]

    Simultaneous scheduling of multiple frequency services in stochastic unit commitment,

    L. Badesa, F. Teng, and G. Strbac, “Simultaneous scheduling of multiple frequency services in stochastic unit commitment,” IEEE Trans. Power Syst., vol. 34, no. 5, pp. 3858–3868, 2019

    2019

  5. [10]

    A frequency se- curity constrained scheduling approach considering wind farm providing frequency support and reserve,

    Z. Zhang, M. Zhou, Z. Wu, S. Liu, Z. Guo, and G. Li, “A frequency se- curity constrained scheduling approach considering wind farm providing frequency support and reserve,” IEEE Trans. Sustain. Energy , vol. 13, no. 2, pp. 1086–1100, 2022

    2022

  6. [11]

    Frequency security constrained robust unit commitment for sufficient deployment of diversified frequency support resources,

    K. Li, X. Ai, J. Fang, S. Cui, Y . Feng, D. Liu, P. Gu, W. Qiu, and J. Wen, “Frequency security constrained robust unit commitment for sufficient deployment of diversified frequency support resources,” IEEE Trans. Ind. Appl. , vol. 60, no. 1, pp. 1725–1737, 2024

    2024

  7. [12]

    Virtual inertia scheduling (vis) for real-time economic dispatch of ibr-penetrated power systems,

    B. She, F. Li, H. Cui, J. Wang, Q. Zhang, and R. Bo, “Virtual inertia scheduling (vis) for real-time economic dispatch of ibr-penetrated power systems,” IEEE Trans. Sustain. Energy , vol. 15, no. 2, pp. 938–951, 2024

    2024

  8. [13]

    Online inertia allocation for grid-connected renewable energy systems based on generic asf model under frequency nadir constraint,

    Z. Peng, Q. Peng, Y . Zhang, H. Han, Y . Yin, and T. Liu, “Online inertia allocation for grid-connected renewable energy systems based on generic asf model under frequency nadir constraint,” IEEE Trans. Power Syst. , vol. 39, no. 1, pp. 1615–1627, 2024

    2024

  9. [14]

    Photovoltaic system control for power system frequency support in case of cascading events,

    T. Ba ˇskarad, N. Holjevac, and I. Kuzle, “Photovoltaic system control for power system frequency support in case of cascading events,” IEEE Trans. Sustain. Energy, vol. 14, no. 2, pp. 1324–1334, 2023

    2023

  10. [15]

    A two- stage power distribution scheme of multiple wind farms participating in primary frequency regulation,

    C. Zhao, D. Sun, X. Zhang, W. Ke, B. Hu, and H. Nian, “A two- stage power distribution scheme of multiple wind farms participating in primary frequency regulation,” IEEE Trans. Power Syst., vol. 38, no. 6, pp. 5009–5021, 2023

    2023

  11. [16]

    Enhanced frequency- constrained unit commitment considering variable-droop frequency con- trol from converter-based generator,

    Y . Yuan, Y . Zhang, J. Wang, Z. Liu, and Z. Chen, “Enhanced frequency- constrained unit commitment considering variable-droop frequency con- trol from converter-based generator,” IEEE Trans. Power Syst. , vol. 38, no. 2, pp. 1094–1110, 2023

    2023

  12. [17]

    A system-view optimal additional active power control of wind turbines for grid frequency support,

    Y . Zhang, Z. Hao, S. Yang, and B. Zhang, “A system-view optimal additional active power control of wind turbines for grid frequency support,” IEEE Trans. Power Syst., vol. 39, no. 2, pp. 4323–4335, 2024

    2024

  13. [18]

    Photovoltaic system power reserve determination using parabolic approximation of frequency re- sponse,

    T. Baskarad, I. Kuzle, and N. Holjevac, “Photovoltaic system power reserve determination using parabolic approximation of frequency re- sponse,” IEEE Trans. Smart Grid., vol. 12, no. 4, pp. 3175–3184, 2021

    2021

  14. [19]

    Frequency security constraint in unit commitment with detailed frequency response behavior of wind turbines,

    J. Yu, P. Yong, J. Yu, and Z. Yang, “Frequency security constraint in unit commitment with detailed frequency response behavior of wind turbines,” Energy, vol. 313, p. 133735, 2024

    2024

  15. [20]

    Frequency dynamics- constrained parameter design for fast frequency controller of wind turbine,

    J. Huang, Z. Yang, J. Yu, L. Xiong, and Y . Xu, “Frequency dynamics- constrained parameter design for fast frequency controller of wind turbine,” IEEE Trans. Sustain. Energy , vol. 13, no. 1, pp. 31–43, 2022

    2022

  16. [21]

    Optimized auxiliary frequency control of wind farm based on piecewise reduced-order frequency response model,

    X. Zhang, C. Zhao, J. Ma, L. Zhang, D. Sun, C. Wang, Y . Peng, and H. Nian, “Optimized auxiliary frequency control of wind farm based on piecewise reduced-order frequency response model,” J. Mod. Power Syst., vol. 12, no. 3, pp. 791–802, 2024

    2024

  17. [25]

    Synchronization mechanism between power-synchronized vs and pll-controlled cs and the resulting oscilla- tions,

    Y . Zhou, J. Hu, and W. He, “Synchronization mechanism between power-synchronized vs and pll-controlled cs and the resulting oscilla- tions,” IEEE Trans. Power Syst. , vol. 37, no. 5, pp. 4129–4132, 2022

    2022

  18. [26]

    Transient stability of low-inertia power systems with inverter-based generation,

    C. He, X. He, H. Geng, H. Sun, and S. Xu, “Transient stability of low-inertia power systems with inverter-based generation,” IEEE Trans. Energy Convers., vol. 37, no. 4, pp. 2903–2912, 2022

    2022

  19. [27]

    P. M. Anderson and A. A. Fouad, Power system control and stability . John Wiley & Sons, 2003

    2003

  20. [28]

    Characterization of equilibrium and stability in power systems,

    C. J. Tavora and O. J. M. Smith, “Characterization of equilibrium and stability in power systems,” IEEE Trans. Power Appar. Syst., vol. PAS- 91, no. 3, pp. 1127–1130, 1972

    1972

  21. [29]

    Inertia response and frequency control techniques for renewable energy sources: A review,

    M. Dreidy, H. Mokhlis, and S. Mekhilef, “Inertia response and frequency control techniques for renewable energy sources: A review,”Renew. Sust. Energ. Rev., vol. 69, pp. 144–155, 2017

    2017

  22. [30]

    revisiting the effect of grid-following converter on frequency dynamics

    Appendix for “revisiting the effect of grid-following converter on frequency dynamics”. [Online]. Available: https://www.researchgate. net/publication/388122216

  23. [31]

    Analytical method to aggregate multi-machine sfr model with applications in power system dynamic studies,

    Q. Shi, F. Li, and H. Cui, “Analytical method to aggregate multi-machine sfr model with applications in power system dynamic studies,” IEEE Trans. Power Syst., vol. 33, no. 6, pp. 6355–6367, 2018

    2018

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