the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Mar 2025
PLL-Reinforced Damping for Interoperability Enhancement of Independently Designed Grid-Forming Wind Turbines in Weak Grids
Abstract. Interoperability of grid-forming (GFM) converters is crucial for the stability and efficiency of modern power systems, particularly when two independently designed GFM converters with different control architectures are connected to a common weak AC network. In this context, the interoperability of such GFM-based generation sources is examined in this paper in terms of power and frequency oscillations during both steady-state and transient cases. Based on this analysis, a novel method of oscillation mitigation via frequency-power reference (ω − P*) droop-based feedback control in the power control loops is proposed. This method significantly improves the interoperability of grid-connected GFM converters during both steady-state and fault conditions. Furthermore, due to the generality of the control structures, the proposed method benefits different applications irrespective of the generation sources, such as offshore wind power plants (OF WPPs), GFM-HVDC converters, and battery energy storage systems (BESS). Additionally, the proposed method could reinforce standard power controller designs, such as virtual synchronous machines (VSM) or PI-controller-based power control loops.
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RC1: 'Comment on wes-2025-18', Anonymous Referee #1, 01 Apr 2025
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AC2: 'Reply on RC1', Sulav Ghimire, 15 Dec 2025
Dear reviewer,
The authors would like to thank the reviewers for taking their valuable time to review the manuscript and providing invaluable feedback and comments on the work. Here, the authors have answered the questions posed by the reviewers, provided explanations, and updated the manuscript content, where relevant.
Reviewer: This work proposes two methods of oscillation mitigation via frequency-power reference feedback control in the power control loops.
Some questions and recommendations:
1. The abstract is short and not clear for easy understanding.
Authors: The authors have updated the abstract.2. I recommend to expand the literature review in Introduction. The authors are encouraged to avoid self-citation (unless extremely necessary).
Authors: The authors have expanded the introduction where possible. However, the topic under study is very specific, and the current manuscript is one of the very few works that exist on this topic, so there is a lack of relevant literature in the field. Furthermore, there is an extreme necessity of self-citation as the control architectures, their tunings, analyses which led to the choice of the control architectures used in this manuscript, the analysis and elaboration on the issue of control interactions and oscillations, were performed in the previous works performed by the author. Due to the limited scope of this work and the consideration of coherence to the topic and plan for this manuscript, these details had to be omitted from this paper. However, to make it easy for the readers to refer to the whole picture of the work, some self-citations became a necessity.3. Could you please explain what do you mean by "solution of a general nature" on lines 23-24?
Authors: This sentence has been reformulated for clarity. It now reads "The second option is to propose a solution where it is not necessary to re-tune the existing GFM device controls where the manufacturers have performed extensive research on; however, a general solution which can be applied to any GFM units irrespective of their control architectures without explicit knowledge of the control design." in the reviewed manuscript.4. The authors are encouraged to revise the verb conjugation throughout the text. E.g., line 95, "$V_{c1,2}$ represent"
Authors: $V_{c1,2}$ is a vectorized notation of $V_{c1}$ and $V_{c2}$, thus the choice of verb base form (V1) here. The authors have checked and corrected any such grammatical errors.5. Are $\DeltaP$ and $\Deltaf$ symbols for oscillations or deviations? For example, this quantities can be constant and nonzero in steady-state? If yes, I recommend change the terminology to power and frequency deviations (or similar word). If not, I recommend changing the symbols of $\DeltaP$ and $\Deltaf$, since $\Delta$ is commonly associated with deviation (or error), not oscillations.
Authors: Yes, $\DeltaP$ and $\Deltaf$ are symbols for oscillations or deviations. These quantities are not necessarily constant and nonzero in steady-state, they depend on the per-unit power and frequency fluctuations between the two GFM units under study. The authors agree that $\Delta$ is commonly associated with deviation, however, to represent the oscillation between two devices, this was the most logical choice, as it is given by the per-unit difference in the power dispatched and frequency reference provided by the two GFM units as shown in equations (11) and (12).6. The Section 3. Proposed Solution - I: Additional Damping uses around 60% of the paper length, but it lacks stability for non-rated frequency scenarios. The scenario of rated-frequency operation in power grids is idealistic. Therefore less emphasis should be put in this section (unless the authors can find a way to stabilize the control without PLL).
Authors: This question is addressed in part in section 3.3.4 Grid-RoCoF and in the Section 4. Proposed Solution - II: PLL-Reinforced Damping where issues about frequency deviation from the nominal following a grid RoCoF are addressed. However, for larger frequency deviations (for example 49.5<f>50.5) from the nominal for longer time, it is irrelevant to further the stability studies as this leads to converter tripping. For non-ideal grid frequencies within the safe frequency range, the converter stabilizes due to the action of the PLL-based damping as elaborated here.7. I recommend to move Section 4 to Section 3 as a subsection.
Authors: The authors have accepted this recommendation.8. The Section 5. Proposed Solution - II: PLL-Reinforced Damping proposes an improvement in the method presented in Section 3 to enable operation during steady-state changes in grid frequency. This solution should be emphasized since, among the proposed methods, it is the only stable solution for non-rated grid frequency scenarios. To put in perspective, the authors use around only 12% of the page length in Section 5. I recommend the authors to carry out a stability analysis of this solution, including an stability analysis of the PLL considering weak-grid scenarios.
Authors: The section Proposed Solution - II: PLL-Reinforced Damping, when linearized around the operating point, yields the same small signal model as the section Proposed Solution - I explores. Thus the stability analysis presented in the section Proposed Solution - I also holds for Proposed Solution - II. The only missing part in this section would be the impact of the PLL on stability, which has been omitted in the study. This has been clarified in the revised version of the manuscript.Citation: https://doi.org/10.5194/wes-2025-18-AC2
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AC2: 'Reply on RC1', Sulav Ghimire, 15 Dec 2025
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RC2: 'Comment on wes-2025-18', Anonymous Referee #2, 06 Sep 2025
This paper addresses a very well known subject on the topic of grid forming and it is quite difficult to be original.
2 different GFM controls are proposed on Figure 1. The authors should explain why they choose these 2 different controls since it seems that the difference is hidden in Figure 2 which is quite symmetric.
More over, Figure 2 is a very simplified representation of the system since the internal dynamics are neglected. This simplified model should be verified.
The choice of the parameters of the control is not explained.
J = 1 s : means that D is also in per unit A damping value of 50 is quite small and it can explain the origin of the oscillations
The proposed solution (Fig 4) is quite strange. In fact, it consists in adding an another damping factor to the existing damping factor.
In Table A.1 Kwp = 1.8 Dp meaning that the sum of Kwp + Dp = 180 which is quite a classical value for the damping in GFM
Why not just setting Dp to 180?
What is the interest of adding a fist order filter to this damping? From a stability point of view, it is quite unusual that adding a first order filter improves the stability.
The proposed scheme in Figure 17 is very close to a classical VSM with a PLL. Again adding a first order filter is rarely a good idea.
At the end, it is quite difficult to find a real added value to this paper
Citation: https://doi.org/10.5194/wes-2025-18-RC2 -
AC1: 'Reply on RC2', Sulav Ghimire, 15 Dec 2025
Dear reviewer,
The authors would like to thank the reviewers for taking their valuable time to review the manuscript and providing invaluable feedback and comments on the work. Here, the authors have answered the questions posed by the reviewers, provided explanations, and updated the manuscript content, where relevant.
Reviewer: This paper addresses a very well known subject on the topic of grid forming and it is quite difficult to be original.
Reviewer: 2 different GFM controls are proposed on Figure 1. The authors should explain why they choose these 2 different controls since it seems that the difference is hidden in Figure 2 which is quite symmetric.
Authors: The choice of these two GFM controls is based on previous works of the authors (Ghimire, et. al., 2023), and the first author's PhD thesis. The explanation has been added to the manuscript.
Reviewer: More over, Figure 2 is a very simplified representation of the system since the internal dynamics are neglected. This simplified model should be verified.
Authors: Figure 2 is merely a representation of the voltage sources, measurement points, impedances, and the power oscillation with their electrical positioning/connection. It is not a model used for the study, that would be Figure 1. It was briefly mentioned in line 98, and now is further clarified in the figure caption.
Reviewer: The choice of the parameters of the control is not explained.
J = 1 s : means that D is also in per unit A damping value of 50 is quite small and it can explain the origin of the oscillationsAuthors: The detailed explanation of the choice of control parameters, control structure, and tuning is not in the scope of the work as the primary scope is to investigate and provide solutions to oscillations between GFM converters. Lines 67-71 show the reference to the works from which the control methods and their parameters are adapted from.
Reviewer: The proposed solution (Fig 4) is quite strange. In fact, it consists in adding an another damping factor to the existing damping factor.
In Table A.1 Kwp = 1.8 Dp meaning that the sum of Kwp + Dp = 180 which is quite a classical value for the damping in GFM
Why not just setting Dp to 180?Authors: An explanation is added in lines 64-67 about this. In a real power system with multiple independently designed GFM devices connected, the internal control architectures of the GFM units are not disclosed to each other due to intellectual property concerns. To represent such a system and to explore the methods for interoperability enhancement in such a system, we have refrained from re-tuning or re-structuring the control architecture. This includes setting Dp to 180. Instead, a generic solution is provided where individual GFM devices can add the PLL-based power controller reinforcement block to achieve interoperability. This allows both GFM-1 and GFM-2 to retain the confidential information about their control architectures, reduce the need for control-retuning, thus offerring a generic solution to any GFM control architecture.
Reviewer: What is the interest of adding a fist order filter to this damping? From a stability point of view, it is quite unusual that adding a first order filter improves the stability.
The proposed scheme in Figure 17 is very close to a classical VSM with a PLL. Again adding a first order filter is rarely a good idea.
Authors: The first order filter prevents the power controller to respond to fast events. Although the PLL and the Kwp damping terms are added to enhance the interoperability and stability of the interconnected system, it must be noted that the power controller need not respond to all fast changes in the system frequency, but only on those changes arising from multiple GFM converters' interactions. Thus the first order LPF enables that by slowing down the overall response of the feedback loop. Without the filter, the power controller will de-stabilize as it will respond to all fast frequency changes (as seen from the Vpcc,q changes,) which leads to the power reference and the frequency and the phase reference to the converter to vary accordingly.Reviewer: At the end, it is quite difficult to find a real added value to this paper
Authors: The real added value of the paper, as mentioned in lines 301-304 is on the contribution of a simple yet reliable method to alleviate control interactions of multiple independently designed GFM units connected together without the need to know the internal control architectures. The authors agree that this was not clearly established, so we will clarify it in the revised manuscript.Citation: https://doi.org/10.5194/wes-2025-18-AC1
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AC1: 'Reply on RC2', Sulav Ghimire, 15 Dec 2025
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This work proposes two methods of oscillation mitigation via frequency-power reference feedback control in the power control loops.
Some questions and recommendations:
1. The abstract is short and not clear for easy understanding.
2. I recommend to expand the literature review in Introduction. The authors are encouraged to avoid self-citation (unless extremely necessary).
3. Could you please explain what do you mean by "solution of a general nature" on lines 23-24?
4. The authors are encouraged to revise the verb conjugation throughout the text. E.g., line 95, "$V_{c1,2}$ represent"
5. Are $\DeltaP$ and $\Deltaf$ symbols for oscillations or deviations? For example, this quantities can be constant and nonzero in steady-state? If yes, I recommend change the terminology to power and frequency deviations (or similar word). If not, I recommend changing the symbols of $\DeltaP$ and $\Deltaf$, since $\Delta$ is commonly associated with deviation (or error), not oscillations.
6. The Section 3. Proposed Solution - I: Additional Damping uses around 60% of the paper length, but it lacks stability for non-rated frequency scenarios. The scenario of rated-frequency operation in power grids is idealistic. Therefore less emphasis should be put in this section (unless the authors can find a way to stabilize the control without PLL).
7. I recommend to move Section 4 to Section 3 as a subsection.
8. The Section 5. Proposed Solution - II: PLL-Reinforced Damping proposes an improvement in the method presented in Section 3 to enable operation during steady-state changes in grid frequency. This solution should be emphasized since, among the proposed methods, it is the only stable solution for non-rated grid frequency scenarios. To put in perspective, the authors use around only 12% of the page length in Section 5. I recommend the authors to carry out a stability analysis of this solution, including an stability analysis of the PLL considering weak-grid scenarios.