An Improved Preisach Model for Magnetic Hysteresis of Grain-Oriented Silicon Steel under PWM Excitation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I suggest rejecting this manuscript. It can be resubmitted later but after substantial modifications to its body.

Introduction section refers to an error that the Preisach model gives. No discussion of the origins of this error, nor example of this error, no proper reference to such error are mentioned. There are two references [6] by Im in 2022 and [7] by Farrokh in 2022. Reference [6] does not talk about errors at all (it just an application of the classical Preisach model). Reference [7] mentions error of the classical Preisach model but says nothing related to PWM or power transformers. 

What is E&S model? Is it Energy-surface model? Reference to original publication is needed. As well as original references to other models named in the introduction are needed.

Section 2 is written in a very unclear way. Usage of unusual for magnetics community terminology is observed. Could that be a translation issue? Starting with Normal Preisach Model, that is known as the CLASSICAL Preisach model. What is the term "limiting magnetic hysteresis loop"? It is not defined. Is that just  a minor hysteresis loop (that could be symmetric or asymmetric)?

Lines 111-117 present an equation with an explanation but it would help (a lot) to have a more detailed explanation where these definitions of T(alpha, beta) and F(alpha) are coming from (maybe in Appendix). What will be T(-H1,H1), i.e. symmetrical minor loop? Was there a specific form assumed for the Preisach function?

Figure 4 has no meaning in this paper. Remove it.

Do I understand correctly that Eq.(6) and Eq.(7) describe modification to the classical Preisach model and now the Preisach function is assumed to be a NON-CONSTANT (since gamma1, gamma2 and gamma3 are varying)? Do I understand correctly that gamma1, gamma2 and gamma3 depend on Hn1 and Hn2 in Eq.(9)? Does it mean that since you used 30 harmonics (lines 400-401), you should identify gamma1, gamma2 and gamma3 for all these 30 harmonics? Or, since you used only three asymmetrical minor loops (e.g., in Figure 14), you should identify gamma1, gamma2 and gamma3 only for three turning points?

Section 3 is unnecessarily long and, when discussing the system and PWM, it is mostly common knowledge that can be covered with references.

Section 4 with results (should be Results and Discussion) : This section needs also a discussion on the dependence of gamma1, gamma2 and gamma3 on H. It also needs  comparison of gamma1, gamma2 and gamma3 for different cases of K. Also, are gamma1, gamma2 and gamma3 for different cases of K, i.e. should those sets of values of gamma1, gamma2 and gamma3 be identified again in case a new PWM is used?

List of references should be updated together with the Introduction.

References from 13 to 19 are copy-paste references from the template for IEEE Transactions on Magnetics. They are not relevant at all to this manuscript.

Summary of main issues:

- (Section 1, 2 pages long) Absence of good Introduction to the subject of the research.

- (Section 2, 5 pages long) Clarification of some parts of the text in Section 2 is needed. One figure should be removed. Deeper discussion should be added. Better/standard terminology should be used.

- (Section 3, 8 pages long) This section should be reduced significantly. Some parts are common knowledge and should be added to the body of the manuscript.

- (Section 4, 3 pages long) This section needs also a discussion on the dependence of gamma1, gamma2 and gamma3 on H. It also needs  comparison of gamma1, gamma2 and gamma3 for different cases of K.

- (Section 5) Remove future work from Conclusions. Put it to Section 4, which should be Results and Discussion section.

- (References) Inadequate. References from 13 to 19 are copy-paste references from the template for IEEE Transactions on Magnetics. They are not relevant at all to this manuscript. Choice of other references is questionable.

Comments on the Quality of English Language

Minor typos can be seen here and there. Occasional rephrasing of some parts of the text is also needed. But overall, the quality of English is good.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

General comments:

It is clear that the writers have put a considerate effort into creating an experimental setup and also connective the valuable links between theory, simulation and measurement.

However those links are not presented or proven in a manner strong enough to support the application of the presented improved method. What is more, the discretisation of this model "e.g. with hysterons" is not clearly shown, and a lot of important steps connecting the results with the theory and the method are not elaborated. E.g. construction parameters of the device under test and tolerances. It is normal that not everything can be documented about a self-made device, but some parameters must be stated; especially since those were included in the assumptions that create the mathematical model. E.g. dimensions of the device under test. E.g. on Figure 4, some dimensions are shown and the values for them but the cross sectional geometry of the sheets is not stated. Finally, the errors are a fundamental way of supporting the improvement of the model but curves or equations regarding those are not stated.

In all graphs it is preferable to avoid writing properties and units as "t/s" which can be confused with a ratio, but instead use "t in s" or "Time (s)" to avoid confusion.

Finally, and most importantly, this work and modelling needs to be numerically compared with or at least mention references with comparisons between other state-of-the-art theoretical models that are shown in table 1.

 

Content comments:

1. On line 70 "However, when most magnetic hysteresis models and the improved models are used  for PWM excitation, the error will be amplified"

Please provide an example or a more elaborate explanation of the reason why "the error will be amplified". Which error and why will be amplified?

2. On line 75 you are mentioning the "wiping-out property". Since it is the 1st time you mention this property in the text, better to move the explanation from line 162 to line 75 or at least mention that this is further explained on line 162.

3. On line 78 you mention "ring-sample test method". Please enter a reference for this method.

4. On equation (1) you have the γ property as only a function of H. If it is indeed independent of α and β, better to move it outside the integral. If it is dependent, also include the α and β as its variables.

5. On line 123 you use the term "complex" signal. Better to describe it as non-sinusoidal. The tern complex signal might be confused with a complex-valued signal.

6. How was Figure 3 calculate? With what software and which formula exactly? Also it would help to provide an Short-time Fourier transform in order to show how the frequency components change within the period or at least present an FFT of the presented signals in order to show the relation of frequency components.

7. Since they are a part of the measurement process, the response of the power amplifier and the isolation amplifier (magnitude, phase) should be stated to show that the results are not altered significantly by them.

This can be from the manuals (e.g. linear response in what range with that latency) or from an individual measurement. It is also better to perform this at least on 2 signal  levels is order to verify the linearity, e.g. 1V frequency sweep and 2V sweep.

8. On line 333 elaborate on the meaning of  "the attenuation coefficient can be set to within 0.3 as needed. "

9. On line 341 separate the sentences with . or ;. "wave, this"

10. Figure 13 needs to have a thinner blue line or a wider horizontal axis, or at least a magnified window in order to show the oscillations details.

 

 

 

Comments on the Quality of English Language

Structural/phrasing comments:

1. On lines 71 & 127 replace the phrase  "the error will be amplified" with "the absolute value of the error of (property of which the error is evaluated) will be increased"

2. On line 74 replace the phrase "improving the mathematical relationship equation" with "improving the approximation formula".

3. On line 158 replace the phrase "Up to now, all equations of the improved Preisach model have been given" with "the improved Preisach model is described by equations (give numbers)".

4. On line 159 replace the word "device" with the word "setup" and refer to the explanation of that setup in the text/section where it is explained.

5. On line 182 replace "to solve the problems in the above analysis" with "to resolve the aforementioned problems

6. On line 186 replace "array" with "arrays"

7. On lines 220 and 221, remove the phrase " and strong universality". If it means something different that "wide application range" then elaborate.

8. On line 229 replace the word "current" with present or other synomym. The word current might be confused with the property of current.

9. On line 231 replace the phrase "have wiping-out property" with "possess a wiping-out property".

10. The sentences on lines 235-237 need rewriting. Some phrases seem not correct and self-devised. E.g. "hotspot of domestic and foreign scholars", " key point of the research", "From the practical needs".

11. On line 245 change "Therefore, this paper only considers one-dimensional" to "Therefore, this paper only considers an one-dimensional"

12. On lines 246-247 replance "Up to now, in the international standard methods are Epstein test method, single sheet test method, ring-sample test method. "

with "Presently, the international standard methods are: The Epstein test method, the single sheet test method and the ring-sample test method. " and also add references.

The article "The" is also missing on various places in the text. e.g. on line 252 "Ring-sample test method" needs to be "The ring-sample test method".

13. Line 262 change "in this paper" to "of this paper".

14. On line 265, separate the sentences, thus replace ", to verify" with ". In order to verify".

15. On line 269  change "The sample to be tested in this article is a oriented silicon steel sample (B27R085) Its structure diagram " to "The sample tested in this article is a oriented silicon steel sample (B27R085). Its structure diagram".

16. In line 273 change " we selected 10 turns" to "10 turns were selected". It is best in general to use passive voice and mainly a single tense (e.g. only past or only present tense) in order to be consistent.

E.g. line 276 "were selected" but line 278 "is selected" is confusing for the reader about the sequential order of the processes.

17. On line 352 replace " fixed carrier ratio of 20. " with "uses a  fixed carrier ratio of 20. "

18. Lines 372, 384 and 404 probably need to be in bold font or at least separated from the rest of the text.

19. On line 373 replace "Ampere's Loop Law" with "Ampère's circuital law".

20. In line 385, remove "In the measurement, "

21. On lines 407-408 the phrase "The waveform of magnetic induction strength B is the waveform of magnetic induction strength B" seems redundant.

22. Further elaborate on how from the voltage and current signals, the curves on Figures 14-17 are calculated. E.g. what integration interval etc. Also add points A, B, C, .... in order to show the evolution of that signal; otherwise it is not clear where each cycle starts and ends. Also describe the physical aspect of the device under test. E.g. wrapped sheets of that material, with that material as insulation, with that spacing etc as these were taken into account in order to get the B-H curves form the V-I measurements.

Also add these points on Figure 3, or a Figure like Figure 3, in order to show which points in time correspond to which in the B/H curves.

23. Add figures of the errors and their respective equations, e.g. with time as the horizontal axis, in order to show measurement vs simulation.

24. On line 482 change "adopted" into "presented.

 

 

Typos/Syntax:

1. At line 228 after ; a lower case letter must follow.

2. On line 183 replace "we needs to propose an improved Preisach mode" with "an improved Preisach mode is proposed"

3. The sentence in lines 345-348 needs to be rewritten as its meaning is not consistent.

 

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors, 

I think the manuscript is interesting and displays what appears to be a meticulous investigation of a Preisach model for Silicon steel under PWM excitations, which is improved by an auto-consistent process that uses a set of experimentally fitted-like parameters in order to account for several regions of the hysteresis loops of the magnetizable-material that are not well described by Previous implementations of the model, at least from a minimalist approximation for the material's properties and magnetism origin.

The manuscript is long but well focused, pertinent and it dares to look for those small differences that from a correct scope might made the difference required to systematically improved upon our actual thresholds for energy-saving purposes. The manuscript presents a bit of ingenuity from the state-of-the-art of this area viewpoint i.e., modeling of magnetism and conceptualization, some parts of the manuscript lack the rigor of the proper lenguaje and understanding of the generally of the hysteresis phenomena, but if taken just within the scope of the application itself it works properly. 

Nevertheless, some aspects require to be addressed before a possible publication: I have attached an annotated pdf of the manuscript with minor suggestions and corrections. Also, I have plotted the final data of the authors to launch to them a question that is a little bit more than curious and that to my extend needs to be responded before publication, and of course, briefly discussed in the conclusions.

I therefore would suggest publication of this manuscript if those comments are properly addressed. 

 

 

 

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The manuscript requires the corrections of few typos still. Some sentences are not clearly written and are too long. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It seems to me that the manuscript was rushed with corrections and not thoroughly checked before the next round of revision. There are still issues unanswered. I list them below together with some suggestions on how to improve this manuscript. 

 

Introduction has been improved but more work is needed.

1) Normal Preisach Model or Traditional Preisach Model should be changed into CLASSICAL Preisach model. If needed, the abbreviation can be introduced, but everywhere throughout the text, the term Classical Preisach model should be used when referring to the model/results before the improvement. 

2) "oriented silicon steel" - what is oriented for this steel? Please update the terminology here.

3) lines 35-36, check/rewrite/clarify the sentence.

4) sentence starting with "According to the theory described in ferromagnetism" on the line 39, it is too long and rewrite the beginning.

5) Throughout the text I found [Error! Reference source not found]. Why is that?

6) lines 67-68: "a series of improvements and improvements" - change that

7) line 69 - "above four common". Though you listed 5 models: including "hybrid model". 

8) What does E&S model stand for? Decipher E&S in the text of the manuscript the same way you did for S-W or J-A models.

9) line 73- "the relative value of the error will be increased." - the second mentioning of the error. But not still not sure the error between/in what?    

10) line 53 - comma vs. dot

 

Section 2:

1) Eq(1) should not be written for B - Ignoring normalization issues with probability distribution function, magnetic field and areas of integration - If square operators are used, you will reach saturation for B in case huge magnetic field is applied with your Eq.(1). This is not correct, so check Eq.(1)

2) Figure 1, the label "-1" is misplaced for gamma_{alpha,beta}

3)  line 133 " lead to significant errors" - Again, the reader has not been informed about the issue yet: what are those errors you are taking about? I see gaps in the logic of the manuscript: Figure 3(b) shows H(t) for two signals: SIN and PWM. Well, one can (and should) take both H(t) and feed them into Eq(1) and see the outcomes. The outcomes will be Figure 3(a). I do not see any errors here - two different inputs result in two different outputs.

4) line 155-156, "external excitation is non-sinusoidal (such as PWM excitation), the normal Preisach model will produce large model errors" - Again the question is why?

5) line 174, "The improved Preisach model is described by equations (give numbers)." - who are you talking to? The reader?

6) line 175-177 - the sentence should be rewritten.

 

Section 3:

1) Line 357 - What is 0.3? Attenuation coefficient of what?

 

Section 4:

1) Line 481, Table 5, Figure 19. Write and introduce not error1 and error2 (or err1 and err2) but eBr and eBm - it will be much more informative and the reader will know right away which error belongs to which quantity.

2) Could the eBm, i.e. the error for Bm (saturated Magnetic Flux) be higher for the classical Preisach model due to the fact mentioned for Eq.(1)? The magnetic fields are small in your Figures 15-18 (60A/m max) but that should be commented on.

3) My previous comment is still unanswered: This section needs also a discussion on the dependence of gamma1, gamma2 and gamma3 on H. It also needs comparison of gamma1, gamma2 and gamma3 for different cases of K. Doing so, you will show whether gamma1, gamma2 and gamma3 identified once is enough.  

 

Comments on the Quality of English Language

The whole text of the manuscript needs checking. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

See file

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

I am afraid that some of my comments are still unanswered. So, I suggest Major Revision one more time.

- line 14 abstract. "error" - we are coming again and again to the "error" - in the abstract AND in the manuscript, there is lack of a clear definition that "error" is error of comparison between experiment and theoretical models. This clear explanation is missing for the reader. In the abstract, there is a need to specify WHAT ERROR the authors are talking about.

- line 40. "According to ferromagnetism"... This beginning should be rewritten. Choice of words here is not correct.

- line 44. "domain wall ... moves continuously". Only when magnetic field is changing.

- lines 47-49. there are plenty of reports where not only sinusoidal excitation is proposed for the measurements. Please rewrite this sentence (stating, e.g., standard methods or more popular methods or something like that).

- line 70. five is stated. Table 1 lists only 4. What are the properties of hybrod model [14]? Why are these advantages and disadvantages not listed?

- Decipher what is E&S model. S-W model stands for Stoner-Wohlfarth. You name E&S model but you do not tell why is it named E&S. Earlier, you stated that this is Energy surface model... Is that true? If yes, decipher that in the text of your manuscript.

- line 74. error of what. see comment above. You should state that you compare prediction by the model(s) with the experiment.

- copying from my previous report:

"Eq(1) should not be written for B - Ignoring normalization issues with probability distribution function, magnetic field and areas of integration - If square operators are used, you will reach saturation for B in case huge magnetic field is applied with your Eq.(1). This is not correct, so check Eq.(1)"

Your explanation is wrong. Mathematically, the classical Presiach function connects OUTPUT with INPUT through normalized probability distribution function. From physics point of view, Ms is added in front of the integral. It is not B. Read my comment again and recall the connection between B, M and H. And rewrite this part of the text.

- Once again, copying from my report:

"Figure 3(b) shows H(t) for two signals: SIN and PWM. Well, one can (and should) take both H(t) and feed them into Eq(1) and see the outcomes. The outcomes will be Figure 3(a). I do not see any errors here - two different inputs result in two different outputs."

If one does not compare with the experiment, one cannot say which model is better based on YOUR plots in Figure 3(a) and (b). You are confusing the reader with this statement about the "Figure 3 wants to show the difference between sinusoidal excitation and non-sinusoidal excitation, and the “error” refers to the error of the magnetic hysteresis, i.e., the error of the magnetic field strength in relation to the magnetic induction strength on the sample." There is no error in this case! Different inputs (figure 3(b)) will lead to different outputs (figure 3(a)).

- Figure 15. Thank you for adding that! Units are missing. Also, should it start from H=0 and not from H=50?

- What is expected Ms of the material? Please specify in the table.

- in all figure 16 and further. Change word "normal" to "classical" since I asked you to use the term Classical Presiach model. The way to improve that, label lines as CPM (Classical Presiach model) and IPM (improved Presiach model).

- you used mixed style of references: in some all full name of authors, then only one letter of the first name, which can be in front of the family name or after it, in some cases the first name or the first letter of the first name is missing. In some cases, the last name is split in two...

 

Comments on the Quality of English Language

Minor changes to the manuscript are required.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 4

Reviewer 1 Report

Comments and Suggestions for Authors

I would like thank the authors for their revised version of the manuscript. In my opinion, this version is now closer to the final one but I am requesting at least one more Revision as some of my comments are still unanswered properly.

- Abstract. The phrase ("error" is error of comparison between experiment and theoretical models) is strangely written. Rewrite this with this suggested phrase or its improvements: "(The error here refers to the discrepancy between experimental results and theoretical model predictions.")

- line 67-69: rewrite your sentence in the following form: "In terms of magnetic hysteresis modeling, the classical magnetic hysteresis models mainly include the Preisach model [AddReference], the Jiles-Atherton (J-A) model [11], the Stoner-Wohlfarth (S-W) model [12], the Enokizono-Soda (E&S) model [13], the hybrid magnetic hysteresis model [14], etc."

- line 76-77: The sentence in the brackets "(The "error" when ...)" should be rewritten. A copy of the proposed by me sentence from the abstract can be used: (Here, as in the abstract, the error refers to the discrepancy between experimental results and theoretical model predictions.)

- Eq.(1) - the equation written in [18] is also wrong, so here you have an obligation to use the correct one. You can easily update your existing text without much effort: (step 1) line 102: Write: "According to the classical Preisach model, the magnetization M ..." instead of "The flux density B ..." ; (step 2) rewrite equation (1) with M instead of B; (step 3) Somewhere later, line 113 for example, add a statement that for this manuscript, since the measurements are in B=mju0*(H+M), and since M is much greater than H for the range of magnetic fields used in this work, one can rewrite eq.(1) with B.

- Figure caption for Figure 16: add this text: Here and in the following figures, 'CPM' stands for the classical Preciach model and 'IPM' for the improved Preciach model.

- you used mixed style of references: in some all full name of authors, then only one letter of the first name, which can be in front of the family name or after it, in some cases the first name or the first letter of the first name is missing. In some cases, the last name is split in two... Here are few examples: (example 1) Ref.13 - Prof. Enokizono has initial M.;  (example 2) Ref. 15,16, 22 - initial stands after the family name; (example 3) the style of references is different (volume, pages, issues, journal abbreviation, italic font, etc.) - compare Ref. 19 with Ref. 21 or Ref. 22;  (example 4) Ref. 24 - Prof. E. Della Torre - (not Delia) there is a typo on IEEE Trans. Magnetics webpage. (example 5) Ref. 25 - in addition to the order of first initial and last name, what is the source of this reference? (example 6) Ref. 28 - the second author last name is "Mount" and "Mo unt"

Comments on the Quality of English Language

N/A

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 5

Reviewer 1 Report

Comments and Suggestions for Authors

Few minor points left:

 

You did not correct the sentence on the lines 67-69 as it was suggested:

Comments 2: - line 67-69: rewrite your sentence in the following form: "In terms of magnetic hysteresis modeling, the classical magnetic hysteresis models mainly include the Preisach model [AddReference], the Jiles-Atherton (J-A) model [11], the Stoner-Wohlfarth (S-W) model [12], the Enokizono-Soda (E&S) model [13], the hybrid magnetic hysteresis model [14], etc."

Response 2: Thank you for pointing this out. I've rewritten this sentence. The position in the article is page 2, paragraph 2, and line 67-69.

You have to include (J-A), (S-W) and Enokizono-Soda (E&S). You are using these abbreviations J-A, S-W and E&S but do not say what are they stand for. Hence, You have to include (J-A), (S-W) and Enokizono-Soda (E&S)  

 

lines 492-493. This sentence

Figure 16-Figure 20, 'CPM' stands for the classical Preisach model and 'IPM' for the 492 improved Preisach model

should be positioned IN the figure caption of the Figure 16.

 

Comments on the Quality of English Language

N/A  

Author Response

Please see the attachment.

Author Response File: Author Response.pdf