Pareto Frontier of the Arm Energy Ripple and the Conduction Losses of a Modular Multilevel Converter

Round 1

Reviewer 1 Report

Pareto frontier of the arm energy ripple and the conduction losses for different operating conditions. From the set of optimal solutions, the best trade off between energy ripple and power losses can be chosen depending on the application requirements. Therefore, an optimal operating point regarding capacitor voltage ripple and circulating current was found, optimizing efficiency and allowing a reduction of capacitance, hence size and cost. The theoretical analysis and results are validated experimentally on a prototype test-bench.

 

The work is well written, and this article has scientific quality. The article is interesting for the readers, and this work has enough references, in addition, these references are current and of quality.

 

I suggest some improvements:
- Please, you must put in the title the meaning of MMC. In this way, readers will understand its meaning.
- In the text, you must indicate the formula you refer to, (1) or (2). Normally the formulas should be indicated in the writing of the text.


After these minor changes, the article can be published.

Author Response

- Please, you must put in the title the meaning of MMC. In this way, readers will understand its meaning.

Thank you for the hint. MMC has been expanded in the title.

 

- In the text, you must indicate the formula you refer to, (1) or (2). Normally the formulas should be indicated in the writing of the text.

The manuscript has been improved upon your comment: At all relevant places,
there is an explicit reference to the equations of interest.

Reviewer 2 Report

The paper has 36 references. Only 12 are from Journals, none from Energies. Non-Journal references can be difficult to find in the long term. Therefore, I suggest that the Authors should increase the share of Journal references and, in particular, include some from Energies. Otherwise, it would seem that this manuscript is out of the scope of this Journal.

Author Response

"The paper has 36 references. Only 12 are from Journals, none from Energies. Non-Journal references can be difficult to find in the long term. Therefore, I suggest that the Authors should increase the share of Journal references and, in particular, include some from Energies.
Otherwise, it would seem that this manuscript is out of the scope of this Journal."

Thank you for your comment. In view of your suggestion, the manuscript has been updated with 5 Energies references ([4], [9], [10], [12] and [16]). We would like to point out that there are few articles in Energies about modular multilevel converters. Furthermore, there are no articles in Energies that research on capacitor design, semiconductor losses or energy ripple in modular multilevel converters, which limits possible Energies references in our manuscript. Thus, our manuscript would be the first article in Energies on that matter.

On the other hand, we think conference papers should not be difficult to find in the long term, as they are electronically archived in the same databases as journal articles.

Reviewer 3 Report

The paper under review considers the issue of "Pareto Frontier of the Arm Energy Ripple and the Conduction Losses of an MMC"

In the reviewer’s opinion, in general, the paper is quite interesting.
However, there are several important aspects that require authors comments
or possibly improvements:
1) In order to help readers, please provide the final design procedure of the proposed approach step by step
2) From a practical point of view, what are the limitations of the proposed method? Will we always find a global minimum?
3) Comparing with another method and discussing other solutions would be pleasantly weird

Author Response

1) In order to help readers, please provide the final design procedure of the proposed approach step by step

This paper focusses on the exploration of the trade-off between energy ripple and conduction losses. Although it is linked to the capacitor design, we think it cannot be regarded as a fully determinate procedure leading to a specific capacitor value. Instead, our simple modeling allows for a very early assessment of the trade-off between energy ripple and conduction losses by fast calculation of the Pareto frontier with only a few required parameters. This avoids simulations that can take long to set up and to run.

However, in view of your comment, the new section 3.5 has been added to better explain how the Pareto frontier can be used in an MMC desing procedure.

 

2) From a practical point of view, what are the limitations of the proposed method? Will we always find a global minimum?

One of the main challenges in the MMC optimization lies in the fact that the objective function, defined in equation (29) in the manuscript, is non-convex. Therefore, it is not guaranteed that the global minimum will be found. In consequence and for each value of lambda, the minimization algorithm is run for multiple starting points (8 in the case of the numerical results presented in the manuscript), and the solution for the lowest value of objective function F is chosen. One of the starting points corresponds to the model-based case C, while the rest are generated from the uniformly distributed random interval between zero and the output current value for the initial circulating current amplitudes, and between -pi and pi for the initial circulating current angles. Furthermore, it is known that the solutions for the angles are bounded, i.e., they lie in the interval between -pi and pi, while the amplitudes are always greater than zero, reducing the search space.

The first paragraph of section 3.4 has been updated to explain the multiple starting point approach.

3) Comparing with another method and discussing other solutions would be pleasantly weird

In comparison to the MATLAB functions paretosearch(), patternsearch(), and gamultiobj(), the Pareto frontier obtained by fmincon() was superior in all the examples we tried. This information has been added in Section 3.4. We hope this addresses your question.

 

Round 2

Reviewer 3 Report

Responses to my remarks are satisfactory. The article can be published in its present form.