Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper investigates modeling and control strategies for a Triple Active Bridge (TAB) DC–DC converter, focusing on improving the decoupling control of power flow between ports while ensuring system stability and dynamic performance. The topic is highly relevant to the field of power electronics and control engineering, particularly with the growing importance of multiport isolated converters in renewable integration and energy storage systems. 

I have no significant remarks but the following:

• Some key modeling assumptions can be explicitly presented.

• The GAM and ROM derivations could be supported with intermediate steps or diagrams to enhance clarity.

• The tuning process for the observer gains and bandwidth parameters can be described in sufficient detail.

• Computational cost and controller complexity are mentioned qualitatively, but quantitative performance can improve the analysis.

The manuscript offers an objective and technically significant contribution to the modeling and control of multiport converters. It will be of interest to researchers in power electronics, control theory, and energy management systems.

Author Response

Reviewer 1

General Comments: The paper investigates modeling and control strategies for a Triple Active Bridge (TAB) DC–DC converter, focusing on improving the decoupling control of power flow between ports while ensuring system stability and dynamic performance. The topic is highly relevant to the field of power electronics and control engineering, particularly with the growing importance of multiport isolated converters in renewable integration and energy storage systems. The manuscript offers an objective and technically significant contribution to the modeling and control of multiport converters. It will be of interest to researchers in power electronics, control theory, and energy management systems. I have no significant remarks but the following: We thank the reviewer for taking the time to assess our manuscript and provide insightful suggestions and comments, which we have duly addressed below and in the revised manuscript.

1.1 — Some key modeling assumptions can be explicitly presented.

Reply: Table 1 was added to the manuscript to clarify the assumptions and other characteristics for each modeling technique.

1.2 — The GAM and ROM derivations could be supported with intermediate steps or diagrams to enhance clarity.

Reply: Considering the length of the paper, the addition of more equations could reduce the engagement of the reader. Therefore, some details of the model derivation, which are not the main contribution of this paper, were left out. However, the paper clearly directs the reader to papers where the models’ derivation is well-detailed. For instance, in the last paragraph of Section 3.2, the readers are redirected to references [17] and [18] for more details on the GAM model derivation. Furthermore, in Section 3.3, paragraph 1, the readers are redirected to reference [38] for more details on the dual active bridge reduced order model (outside of the scope of this paper), to further understand how its principles are applied to the TAB converter reduced order model.

1.3 — The tuning process for the observer gains and bandwidth parameters can be described in sufficient detail.

Reply: In Section 4.2.3, the impact of the observer and controller bandwidths is investigated, which further clarifies the impact of those design parameters on the performance and stability margin of the LADRC. Practical considerations are also included in the last paragraph, where the authors mentioned the trade-off between observer bandwidth and noise sensitivity, and the fact that controller bandwidth is selected based on the settling time required, which is a common and general concept in controller design. Furthermore, the reader is redirected to well-established literature on state observer design. For instance, in Section 4.2.1, paragraph 3, readers are redirected to reference [51] for more details on state observer design.

1.4 — Computational cost and controller complexity are mentioned qualitatively, but quantitative performance can improve the analysis.

Reply: The main contribution of this paper is focused on the comparison of different models and control strategies for the TAB converter. Practicalities and implementation issues are left out of the paper since the validation was merely on simulation. Further work and details on the real implementation of the controllers will be made in future work, where computational burden and implementation complexity will be assessed.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents an original comparison of models (switching, generalized average, reduced-order) and three control strategies (IDM, LADRC, SMC-LESO) applied to the TAB converter. The analysis of large signals and the influence of interport couplings constitutes a new contribution compared to previous publications limited to small-signal models. The novelty is high, especially in the context of an integrated model-control approach.

The paper is substantively strong, but its educational value and clarity could be improved by better model illustration, a more complete justification of parameter selection, and an expanded comparative analysis. With these improvements, the work will be fully complete and even more useful to the scientific community.

1. Consider the following improvements:
   Add a block diagram for each of the three models (switching, GAM, reduced-order) to help the reader understand the conceptual differences.
2. Supplement the methods section with a table comparing the model features (number of equations, assumptions, advantages/disadvantages).
3. In the results section, consider adding a table comparing control quality parameters (e.g., settling time, overshoot, disturbance sensitivity).
4. Expand or include in an appendix the full form of the linear GAM model, which is crucial for PI and IDM controller design.
5. Add a detailed justification for the controller parameter selection, especially in LADRC and SMC-LESO strategies (e.g., the impact of ω₀, ω_c, α, β on stability and dynamics).
6. Consider presenting a stability analysis (e.g., based on eigenvalues ​​or phase margin) to reinforce the theoretical aspect.
7. Improve the readability of the graphs – increase color contrast, thicken the lines, and add short descriptions in the legends (e.g., "Port 2 voltage," "Port 3 power").
8. Introduce relative error labels (e.g., percentage deviation from the reference model) directly in the comparative graphs.
9. Include a parameter sensitivity analysis for LADRC and SMC-LESO to quantitatively confirm the robustness of these methods.
10. Expand the discussion to include an analysis of the computational complexity and possible implementation limitations of the individual control methods.
11. Indicate the possibilities for experimental verification of the simulation results or plan for such verification in future work.
12. In the summary, clarify under which operating conditions (e.g., different loads, voltage asymmetry) each method is optimal.
13. Shorten very long sentences in the theoretical sections; this will simplify the reading.
14. Standardize symbols (e.g., φ₁₂ vs. ϕ₁₂) and unit notations.
15. Add several recent resources (2024–2025) regarding TAB converter control using hybrid or AI-based control methods.

Comments on the Quality of English Language

Minor editorial comments concern only punctuation (e.g., excessive commas) and occasional ambiguities in long, complex sentences. However, this does not affect the readability or professional character of the text.

Author Response

Reviewer 2

General Comments: This paper presents an original comparison of models (switching, generalized average, reduced-order) and three control strategies (IDM, LADRC, SMC-LESO) applied to the TAB converter. The analysis of large signals and the influence of interport couplings constitutes a new contribution compared to previous publications limited to small-signal models. The novelty is high, especially in the context of an integrated model-control approach. The paper is substantively strong, but its educational value and clarity could be improved by better model illustration, a more complete justification of parameter selection, and an expanded comparative analysis. With these improvements, the work will be fully complete and even more useful to the scientific community. We thank the reviewer for taking the time to assess our manuscript and provide insightful suggestions and comments, which we have duly addressed below and in the revised manuscript.

2.1 — Add a block diagram for each of the three models (switching, GAM, reduced-order) to help the reader understand the conceptual differences.

Reply: The authors of this paper consider that Figures 1 and 4 provide sufficient details for the switching model and the reduced order model. Furthermore, Figure 4 was improved both in resolution and description. On the other hand, it is somehow cumbersome to produce a graphical representation of the full-order GAM model. Therefore, this aspect of the paper is left as it is.

2.2 — Supplement the methods section with a table comparing the model features (number of equations, assumptions, advantages/disadvantages).

Reply: Thank you for the suggestion. Indeed, a table is a useful resource to complement and summarize the analysis made in Section 3. Therefore, Table 1 was added to the manuscript to clarify the assumptions and other characteristics for each modeling technique.

2.3 — In the results section, consider adding a table comparing control quality parameters (e.g., settling time, overshoot, disturbance sensitivity).

Reply: The authors consider that Figures 18 to 20 present enough evidence of the performance of the control strategy under study, especially the differences between IDM and LADRC/SMC- LESO. However, to further clarify the performance differences between LADRC and SMC-LESO, the mentioned Figures (18 to 20) were improved, and a zoomed view provides additional and clearer evidence of how SMC-LESO is slightly better than LADRC. With these changes in the figure, the settling time differences are clear. Additionally, the improved figures show that the overshoot is negligible in the three cases.

2.4 — Expand or include in an appendix the full form of the linear GAM model, which is crucial for PI and IDM controller design.

Reply: The small-signal linear model is added in equation A4, included in the appendix. Furthermore, the first paragraph of Section 4.1.1. was modified to direct the reader’s attention to this detail. ”The linearized small-signal model is presented in (A4), and a more detailed derivation can be found in [17] and [22].”

2.5 — Add a detailed justification for the controller parameter selection, especially in LADRC and SMC-LESO strategies (e.g., the impact of ωo, ωc, α, β on stability and dynamics).

Reply:

• Subsection 4.2.3 was added to highlight the Impact of the controller and Observer Bandwidths (ωo, ωc) on the system performance.

• A justification for the chosen sliding coefficients (α, β) is also provided in Subsection 4.3.1. ”It is worth noting that the sliding coefficients αij and βij were tuned empirically to balance the fundamental trade-off between response speed, robustness, and chattering mitigation.”

2.6 — Consider presenting a stability analysis (e.g., based on eigenvalues or phase margin) to reinforce the theoretical aspect.

Reply: In Section 4.2.3, the impact of the observer and controller bandwidths is investigated, which further clarifies the impact of those design parameters on the performance and stability margin of the LADRC. This is explicitly mentioned in the next paragraph: ”Figure 14 corroborates this relationship, showing that a higher ωci increases the stability margin and accelerates the tracking speed.” These additional aspects reinforce the theoretical analysis of the stability and robustness of the LADRC. Since the same observer is used in the SMC-LESO, this bandwidth analysis is valid for the stability of the SMC-LESO. Furthermore, since the SMC is a nonlinear controller, the Lyapunov stability definitions are defined in equations (61) to (63).

2.7 — Improve the readability of the graphs – increase color contrast, thicken the lines, and add short descriptions in the legends (e.g., ”Port 2 voltage,” ”Port 3 power”).

Reply:

• Figure 1 resolution was improved.

• Figure 4 was replaced with a higher quality figure.

• Figure 18 was replaced with a higher quality and more detailed figure.

• Figure 19 was replaced with a higher quality and more detailed figure.

• Figure 20 was replaced with a higher quality and more detailed figure.

• Figure 21 was replaced with a higher quality and more detailed figure.

2.8 — Introduce relative error labels (e.g., percentage deviation from the reference model) directly in the comparative graphs.

Reply: The authors of this paper tried to implement this suggestion. However, after seeing the result, we consider that it does not improve the readability or clarity of the results. Furthermore, the figures with such an amount of information could be visually intense for the reader. Therefore, the figures comparing the models are left as they were.

2.9 — Include a parameter sensitivity analysis for LADRC and SMC-LESO to quantitatively confirm the robustness of these methods.

Reply: Since the critical parameter b0i = n1i ∗vdc1 /(ωsw ∗Lij ∗Ci) depends on circuit parameters (see Section 4.2, right after equation (42)), a sensitivity analysis of b0 was performed implicitly by varying the inductance L2. The results presented in Figure 20 demonstrate the performance of the three designed controllers when the parameter L2 varies and Lnew 2 = 2L2. The results show that all three controllers remain stable, demonstrating a certain degree of robustness. However, the LADRC and SMC show much better performance compared to IDM, as in the rest of the tests. This was clearly stated in the last paragraph of Section 4.4.

2.10 — Expand the discussion to include an analysis of the computational complexity and possible implementation limitations of the individual control methods.

Reply: A discussion has been added to Section 4.4, in the last paragraph, analyzing the computational burden and real-world deployment constraints of each control scheme. The added text is as follows: ”Among the three methods, IDM imposes the highest computational load due to its reliance on real-time matrix inversion, which scales poorly and is highly sensitive to model errors. On the other hand, LADRC is more efficient, leveraging a simple LESO, but its performance is constrained in practice by sensor noise and the choice of b0i. Additionally, SMC-LESO implementation is challenged by control chattering, forcing a trade-off between robustness and smoothness that complicates tuning. Thus, for real-time systems, LADRC typically offers a better balance of efficiency and performance. SMC-LESO provides superior disturbance rejection at the cost of greater tuning effort, and inverse decoupling is the least suitable for resource-constrained applications.”

2.11 — Indicate the possibilities for experimental verification of the simulation results or plan for such verification in future work.

Reply: A comment on future work on experimental validation was added to Section 5 (last paragraph). ”Additionally, an experimental setup is under development and will be used in experimental validation of the control strategies presented in this study.”

2.12 — In the summary, clarify under which operating conditions (e.g., different loads, voltage asymmetry) each method is optimal.

Reply: The IDM can suffer from operating point deviations. To mitigate this issue, lookup tables can be used to update the decoupling matrix in terms of the operating conditions. However, this increases the computational burden and memory requirements of this method, limiting its practical implementation to applications with limited power flow modes.

2.13 — Shorten very long sentences in the theoretical sections; this will simplify the reading.

Reply: The manuscript was revised in detail, with improvements made to weak and unclear sentences.

2.14 — Standardize symbols (e.g., φ12 vs. ϕ12) and unit notations.

Reply: The manuscript was revised in detail, looking for these kinds of mismatches. All the symbols were unified, including the example that this reviewer provided.

2.15 — Add several recent resources (2024–2025) regarding TAB converter control using hybrid or AI-based control methods.

Reply: Three new relevant references were added regarding these AI-based control methods.

• Buticchi, G.; Farjudian, A.; Oh, J.; Tarisciotti, L. An ANN-Assisted Control for the Power Decoupling of a Multiple Active Bridge DC-DC Converter. 48th Annual Con- ference of the IEEE Industrial Electronics Society, IECON 2022, Brussels, Belgium; 17–20 October 2022.

• M. Liao, H. Li, P. Wang, T. Sen, Y. Chen and M. Chen, “Machine Learning Meth- ods for Feedforward Power Flow Control of Multi-Active-Bridge Converters,” in IEEE Transactions on Power Electronics, vol. 38, no. 2, pp. 1692–1707, Feb. 2023.

• Rongxin Qiu, Chunyang Gu, Jing Li, Jiajun Yang, A Simplified ANN Based Power De- coupling Method of MAB Converters”, IEEE 8th International Electrical and Energy Conference (CIEEC 2025), Changsha, China, 16-18 May 2025.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I congratulate the authors for their interesting research and proper analysis of the topic. This paper can be considered for publication after a minor revision.

My review comments are as follows:

I. The term decoupling in the title needs to be detailed further, especially in the abstract, and the necessary explanations in the main text of the paper should be emphasized.

II. The authors are invited to present an efficiency analysis under the proposed controller system.

III. The authors are invited to include a table where new-generation controller systems, such as AI-based ones, are compared with their research results in terms of complexity, accuracy, feasibility, compatibility with PC programs, cost, etc. https://ieeexplore.ieee.org/abstract/document/10818659
 is a sample paper that I suggest using as a reference.

IV. The authors are invited to present a THD analysis for the system under the proposed control model.

V. Other parts of the paper have been prepared properly.

Author Response

Reviewer 3

General Comments: I congratulate the authors for their interesting research and proper analysis of the topic. This paper can be considered for publication after a minor revision. My review comments are as follows: We thank the reviewer for taking the time to assess our manuscript and provide insightful sug- gestions and comments, which we have duly addressed below and in the revised manuscript.

3.1 — The term decoupling in the title needs to be detailed further, especially in the abstract, and the necessary explanations in the main text of the paper should be emphasized.

Reply: This was included in the abstract section. Indeed, the reviewer had a really good point that the power flow coupling that occurs in the triple active bridge converter was not mentioned before the decoupling goal was introduced. Furthermore, in Section 4, Figure 10 was improved and its description was extended to explain further the cross-coupling effect in the converter.

3.2 — The authors are invited to present an efficiency analysis under the proposed controller system.

Reply: This work is based on software simulations performed in MATLAB/Simulink. Unlike other simulation tools, MATLAB/Simulink is limited in the information it provides regarding switching or conduction losses in power converter simulations. Therefore, the efficiency analysis could not be done.

3.3 — The authors are invited to include a table where new-generation controller systems, such as AI-based ones, are compared with their research results in terms of complexity, accuracy, feasibility, compatibility with PC programs, cost, etc. https://ieeexplore.ieee.org/abstract/document/ is a sample paper that I suggest using as a reference.

Reply: The authors of this paper consider that a theoretical comparison that includes AI-based controllers is out of the scope of this work. Moreover, P. Koohi, et. al. already presented a similar analysis in a theoretical way. This was stated in the literature review in Section 2. However, the literature review was extended, and new AI-based approaches for controlling the triple active bridge or similar topologies were included. To further clarify this point, the authors of this paper consider that, since the main objective of this paper was to provide clear derivation procedures for models and controllers, and a simulation-based comparison, including AI-based controllers would require additional procedures and simulations.

3.4 — The authors are invited to present a THD analysis for the system under the proposed control model. The authors of this paper consider that this is out of the scope of this work. The main reason is that harmonic distortion analysis is more relevant for AC grid studies, and this work only deals with the DC integration of the triple active bridge. 

Author Response File: Author Response.pdf