A MPC and Novel 3D-SVPWM Modulation Coordinated Strategy for Zero-Sequence Circulating Current Suppression in Three-Phase Four-Leg Parallel-Inverter Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Overall, the idea of injecting a scalar adjustment factor into the zero-vector dwell times to regulate the zero-sequence duty difference is interesting; however, the paper in its current form need significant revision.

1. The abstract claims the method “improves output current quality” and “enhances system efficiency,” but the paper only presents simulation waveforms of ZSCC and load voltage and a qualitative statement of improvement. There is no efficiency calculation, no loss model, no switching-loss comparison, and no quantified THD/current-quality metrics.
2. Coordination of MPC and improved 3D-SVPWM” is too broad. It is not clear what is new relative to existing SVPWM-based ZSCC suppression and MPC-based circulating current control.
3. The abstract should explicitly state: (i) what control variable MPC outputs (ii) where it is injected (zero-vector dwell-time asymmetry), and (iii) why this is superior .
4. MPC performance hinges on cost function, constraints, and horizons, yet the abstract gives none

5. The intro lists several approaches (hardware impedance filters, hybrid modulation, feedforward nonlinear control, interleaving PWM, etc.), but it does not clearly articulate: what each method cannot do (e.g., computational burden, dependence on accurate parameters, increased switching losses, limited robustness),and exactly which gap your method fills.

6. The contribution paragraph uses broad phrases , but does not specify what was measured or how.
7. abc-frame 3D-SVPWM reduces computational burden, but then introduce MPC online optimization, which may dominate computation

8. Equations (7)–(8) tie ZSCC to zero-sequence voltage difference and inductances. However, it is not explicit: whether capacitor dynamics, ESR, or line impedance are neglected, whether the neutral leg dynamics are included, whether the derived transfer function remains valid under unbalanced loads and non-linear loads.

9. The MPC section reads like a textbook description, but the actual controller design is not fully specified.Missing MPC design specification.
10. Missing MPC design specification
11. Only simulations; no experimental validation for more information here is the updated litertaure doi.org/10.3390/math12203257.
12. The paper targets practical parallel inverter systems, but provides no HIL or prototype results. This is a major limitation for a control/modulation contribution.

Author Response

Thank you for your valuable suggestions. I have made certain improvements to the paper based on your advice. For a detailed response, please see the attachment.

                             

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper provides a generally sound introduction to the concept of zero-sequence circulating current (ZSCC) in three-phase four-leg parallel inverter systems, and the physical origin of ZSCC is correctly attributed to zero-sequence voltage differences between parallel inverters. However, the description of ZSCC would benefit from clearer conceptual outlining and stronger sensitivity. There are some revision comments raised for this paper to improve the content and representation:

• While the mathematical derivation linking zero-sequence voltage difference to circulating current is presented, the physical explanation of how practical factors such as modulation mismatch, dead-time effects, or sampling delays as zero-sequence voltage differences in real systems should be extended.
• The 4^th section and 4.1. subheading are conceptually correct but mathematically weak comparing to its importance in the proposed strategy. Although the paper introduces MPC as the mechanism used to generate the adjustment factor k, the derivation remains largely descriptive and lacks an accurate mathematical formulation of the predictive control problem. In its current form, the section sounds much more like a general summary of MPC principles than a particular derivation for zero-sequence circulating current cancellation. The analytical connection between the system model, the optimization objective, and the computed adjustment factor is not sufficiently transparent.
• The integration between MPC and the modified 3D-SVPWM is one of core contributions, yet this coordination is described slightly indirectly. Although the adjustment factor is mathematically shown to influence the zero-sequence duty cycle and voltage difference, the dynamic interaction between the MPC output and the PWM stage is not fully clarified. Including a short discussion on how the PWM dynamics and switching delay are accommodated or neglected in the MPC model would improve technical contribution.
• The simulation results demonstrate the effectiveness of the proposed strategy, but the presentation and analysis of these results require further enhancement. While time-domain waveforms of ZSCC and load voltages are shown, the evaluation remains largely qualitative.
• Some performance metrics such as RMS ZSCC values, settling time, overshoot, or total harmonic distortion rates have not been reported in the paper. Besides it is not easy to compare PI-based and MPC-based suppression.
• The reported percentage improvements (e.g., 25% and 30%) are not clearly defined in terms of calculation method or reference values, which reduces their impact. Furthermore, the simulation scenarios are limited to steady-state conditions with parameter mismatch and unbalanced loads. However, the transient conditions such as load steps, DC-bus voltage variations, or inverter synchronization errors are not explored. Including such cases would better demonstrate the claimed robustness and adaptability of the MPC approach.
• The simulation setup lacks sufficient detail regarding controller tuning and computational burden of MPC control algorithm. The parameters such as sampling frequency, MPC computation time, and solver configuration have not been provided that leave open questions about real-time implementability of proposed method.
• Since one of the claimed advantages of the proposed method is reduced complexity and improved adaptability, a brief comparison of computational effort between PI-based and MPC-based approaches would significantly strengthen the argument.
• The experimental validation is absent which could be a drawback for such a study while this may be acceptable for a simulation-focused proposal. The paper should more clearly acknowledge this limitation and outline how the proposed method could be extended to hardware implementation.

 

Author Response

Thank you for your valuable suggestions. I have made certain improvements to the paper based on your advice. For a detailed response, please see the attachment.

                             

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear author,

I have the following suggestions for paper improvement:

1. Please clarify the aim and novelty of your paper.
2. As given in Line 26, the suggested topology is supposed to “enhances system efficiency”. However, the improved efficiency could be better depicted.
3. The modulation method is well described in Section 4. However, the application of the presented equations (1-20) could be better illustrated in Section 5 – Simulation Results. In this format, the two main sections appear completely disconnected.
4. The results in Figs. 10 and 11 require better explanation.
5. The research could be supported by experimental verification to reach the level of a journal with an impact factor.

Thank you for the interesting paper.

Author Response

Thank you for your valuable suggestions. I have made certain improvements to the paper based on your advice. For a detailed response, please see the attachment.

                             

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No more comments all my concerns has been addressed 

Reviewer 3 Report

Comments and Suggestions for Authors

The paper has been significantly improved.

Thank you for your effort.