Improved Modulation Strategy Based on Minimum Energy Storage Principle for Electrolytic-Capacitor-Less Six-Switch Converter

Round 1

Reviewer 1 Report

Dear authors, the theme is interesting and actual. The references are actual, however can be improved. In general, you need to revise the figures legends and you need to put the end punctuation in equations. You also need to uniformize the call figures in the paper. I think you do not use the recent template because the number of lines appears on the left side instead of the right side.

I will describe some mistakes that I detect in the paper:

- In line 1, you do not identify the type of paper;

- In line 11, you have “six-switch AC-AC converter” but in line 22 you have “six-switch AC-DC-AC converter”. You need to uniformize;

- In line 26, I suggest change “AC/DC/AC” to “AC-DC-AC”;

- In line 27, you need to put space between aircraft and [1];

- In line 50, you introduce the acronymous “PF” but you do not use it during the paper;

- In line 82, you need to put space between the chapter number and text;

- In line 85, I suggest change “AC/DC/AC” to “AC-DC-AC”;

- In line 105, I suggest identifying the generated references;

- In line 132, change the legend to “Four working states of six-switch converter: (a) rectification state; (b) inversion state; (c) freewheeling state; (d) both-way state.”;

- In line 136, put “Figure 5” in the same line;

- In line 137, change “Fig. 5(a)” to “Figure 5 (a)”. You need to uniformize the ;

- In line 140, change the legend to “Schematic diagram of the switching state: (a) state A; (b) state B.”;

- In line 141, I suggest change “have been defined in the previous paper” to “were previously defined on paper”;

- In lines 146, 147, 149, you do need to introduce again the acronymous because you do that before;

- In line 155, you need to rewrite the text “Rectification state (or inversion state) and rectification state (or inversion state)”;

- In lines 165, 166, you do need to introduce again the acronymous because you do that before;

- In line 167, the obtained results are in a steady state? Because the waveform of VDC increase;

- In line 168, you do not put the end punctuation in legend;

- In line 181, you do not identify the “KCL”;

- In line 228, I suggest change “ac” to “AC”;

- In line 249, the call “ic” is correct?;

- In line 270, in Table 2 change “10KHz” to “10kHz”;

- In line 278, in Figure 8 the vd is in a steady state?;

- In line 287, in Figure 9 the vd is in a steady state? Because the phase angle between waveforms change during the time;

- In line 308, you do not put the end punctuation in legend;

- In line 315, you do not put the end punctuation in legend;

- In line 319, change the legend to “Control signal of ST1, ST2, ST3: (a) traditional modulation strategy; (b) improved modulation strategy.”;

- In line 323, change the legend to “Output waveforms: (a) traditional modulation strategy; (b) improved modulation strategy.”;

- In line 334, change the legend to “FFT Analysis of uc: (a) traditional modulation strategy; (b) improved modulation strategy.”;

- In line 356, change the legend to “Capacitor voltage waveforms in line frequency cycle when φ=0°: (a) traditional modulation strategy; (b) improved modulation strategy.”;

- In line 358, change the legend to “The capacitance voltage waveforms when the voltage ripples are about 2%: (a) traditional modulation strategy; (b) improved modulation strategy.”.

Author Response

Reviewer: 1 
Specific and Thorough Comments to the Author 

Q1.In line 1, you do not identify the type of paper;

R: Thanks for your comments, the type of paper “Article” is identified.

Q2. In line 11, you have “six-switch AC-AC converter” but in line 22 you have “six-switch AC-DC-AC converter”. You need to uniformize;

R: Thanks for your comments, they are unified as the “six-switch AC-AC converter”

Q3. In line 26, I suggest change “AC/DC/AC” to “AC-DC-AC”;

R: Thanks for your comments, the “AC/DC/AC” is changed to “AC-DC-AC”.

Q4. In line 27, you need to put space between aircraft and [1];

R: Thanks for your comments, a space is added between aircraft and [1].

Q5. In line 50, you introduce the acronymous “PF” but you do not use it during the paper;

R: Thanks for your comments, the “PF” is rewritten to “power factor”.

Q6. In line 82, you need to put space between the chapter number and text;

R: Thanks for your comments, a space is added between the chapter number and text.

Q7. In line 85, I suggest change “AC/DC/AC” to “AC-DC-AC”;

R: Thanks for your comments, the “AC/DC/AC” is changed to “AC-DC-AC”.

Q8. In line 105, I suggest identifying the generated references;

R: Thanks for your comments, S_T1, S_T2, and S_T3 are marked in the Figure 2.

Q9. In line 132, change the legend to “Four working states of six-switch converter: (a) rectification state; (b) inversion state; (c) freewheeling state; (d) both-way state.”;

R: Thanks for your comments, the legend is changed as suggested.

Q10. In line 136, put “Figure 5” in the same line;

R: Thanks for your comments, “Figure 5” is put in the same line.

Q11. In line 137, change “Fig. 5(a)” to “Figure 5 (a)”. You need to uniformize the ;

R: Thanks for your comments, “Fig. 5(a)” is unified as “Figure 5 (a)”.

Q12. In line 140, change the legend to “Schematic diagram of the switching state: (a) state A; (b) state B.”;

R: Thanks for your comments, the legend is changed as suggested.

Q13. In line 141, I suggest change “have been defined in the previous paper” to “were previously defined on paper”;

R: Thanks for your comments, “ have been defined in the previous paper” is changed to “were previously defined on paper”.

 

Q14. In lines 146, 147, 149, you do need to introduce again the acronymous because you do that before;

R: Thanks for your comments, the acronymous are introduced again.

Q15. In line 155, you need to rewrite the text “Rectification state (or inversion state) and rectification state (or inversion state)”;

R: Thanks for your comments, the text is rewrriten as “Two RS (or IS) are too close”.

Q16. In lines 165, 166, you do need to introduce again the acronymous because you do that before;

R: Thanks for your comments, the acronymous are introduced again.

Q17. In line 167, the obtained results are in a steady state? Because the waveform of VDC increase;

R: Thanks for your comments, the obtained results are in a steady state and Figure 6 shows the enlarged view of v_d which the voltage fluctuation value is much less than the steady- state value. It is just a schematic of v_d’s behavior in a switching cycle.

Q18. In line 168, you do not put the end punctuation in legend;

R: Thanks for your comments, the end punctuation is put in legend.

Q19. In line 181, you do not identify the “KCL”;

R: Thanks for your comments, “KCL” is Kirchhoff’s Current Law, which is usually abbreviated.  

Q20. In line 228, I suggest change “ac” to “AC”;

R: Thanks for your comments, “ac” is changed to “AC”.

Q21. In line 249, the call “ic” is correct?;

R: Thanks for your comments, it’s correct. Amplitude of current i_c is I_c.

Q22. In line 270, in Table 2 change “10KHz” to “10kHz”;

R: Thanks for your comments. “10KHz” is changed to ”10kHz”.

Q23. In line 278, in Figure 8 the vd is in a steady state?;

R: Thanks for your comments. Yes. As can be seen from the vertical coordinates, the fluctuation is far less than the steady-state value.

Q24. In line 287, in Figure 9 the vd is in a steady state? Because the phase angle between waveforms change during the time;

R: Thanks for your comments. v_d is in a steady state. The phase angle between two waveforms does change during the time, but it is also cyclical.

Q25. In line 308, you do not put the end punctuation in legend;

R: Thanks for your comments, the end punctuation is put in legend.

Q26. In line 315, you do not put the end punctuation in legend;

R: Thanks for your comments, the end punctuation is put in legend.

Q27. In line 319, change the legend to “Control signal of ST1, ST2, ST3: (a) traditional modulation strategy; (b) improved modulation strategy.”;

R: Thanks for your comments, the legend is changed as suggested.

Q28. In line 323, change the legend to “Output waveforms: (a) traditional modulation strategy; (b) improved modulation strategy.”;

R: Thanks for your comments, the legend is changed as suggested.

Q29. In line 334, change the legend to “FFT Analysis of uc: (a) traditional modulation strategy; (b) improved modulation strategy.”;

R: Thanks for your comments, the legend is changed as suggested.

Q30. In line 356, change the legend to “Capacitor voltage waveforms in line frequency cycle when φ=0°: (a) traditional modulation strategy; (b) improved modulation strategy.”;

R: Thanks for your comments, the legend is changed as suggested.

Q31. In line 358, change the legend to “The capacitance voltage waveforms when the voltage ripples are about 2%: (a) traditional modulation strategy; (b) improved modulation strategy.”.

R: Thanks for your comments, the legend is changed as suggested.

Author Response File: Author Response.doc

Reviewer 2 Report

The paper presents a study on “Improved Modulation Strategy Based on Minimum Energy Storage Principle for Electrolytic-Capacitor-Less Six-Switch Converter”. The main idea is related to a suitable modulation strategy to overcome the issue arising from the presence of twice the grid frequency at the dc-link of single-phase converter, so reducing the need of a large capacitance. This translates in the possibility of avoiding the use of an electrolytic capacitor so improving system power density and life-time.

Some critical comments about the work are reported below.

 

• 2: It could be useful to report the y-axis labels for the sub-plots related to the switching signals and the time unit of measure in ms.
• 4 is cited in the text prior to Fig.3.
• Page 5, line 141: the authors wrote “vcw, vrA, and vrX have been defined in the previous paper,…”, which is the previous paper?
• Page 5, line 155: “Rectification state” is repeated two times.
• Page 5, line 165: liner is linear.
• (2): why there is the minus sign at the second member? Probably, the minus sign is due to the fact that theta1 is defined in eq.(8) as the phase angle of rectifier modulation reference, while formally in eq.(2) should appear the difference between the grid voltage/current phase angle and the rectifier modulation reference phase angle. The former is equal to zero by considering grid voltage and current in phase (i.e., unity power factor) as the authors stated in eq.(15). The authors should clearly define the angle theta1 when it is introduced for the first time in eq.(2).
• (8) and (9) introduce the modulation references with no explanation.
• The phase angle phi is reported in lower case in equations, while in upper case in the text. Please check this issue throughout the paper.
• Section 3: to derive the minimum value of I’c for the improved modulation (eqs. 19-25) the authors use phase angle phi as in the case of traditional modulation (eqs.(9-17)), but the values for minimizing the current are different ((theta0-theta1)/2 for traditional modulation; theta0-theta1 for improved modulation). In fact , in table 2, the authors introduce the phase angle phi’ (which is twice of phi) for the improved modulation. In addition, at line 228, the authors wrote: “Therefore, phi is equal to (theta0-theta1)/2 in this paper…”. Please, clarify this point which is misleading.
• 7 and 8: please try to improve their readability. Moreover, the output inverter voltage is previously named Vc (see also Fig.1), while now is reported as Uc, also in the text (lines 274, 278). This happens also in the following part of the paper (Table 3, Table 4, Fig.13 and so on).
• Table 3, 4: it could be better to report the units of measure in square brackets. Then, if you define the ripple coefficient in percent (in the header row), you can avoid to use for each value in the corresponding column.
• From tables 3 and 4 and Fig.10 the ripple does not show a monotonically decreasing trend. Could you better explain this behavior?
• Line 313: Please define the acronyms RCP and FPGA.
• 12: It could be useful to establish a relation between the switching pattern in Fig.12 and the operating sequences reported at the beginning of section 3 with the aim of better highlighting the difference between the traditional and proposed modulation. For example by considering a single switching cycle to verify the fast charging and discharging of the proposed modulation in a complete switching cycle.
• Page 12, line:338: the authors wrote: “…which proves that the proposed modulation strategy can not only reduce the DC side voltage ripple coefficient under the line frequency, but also improve the output voltage waveform.” The better output voltage THD is a consequence of the reduced ripple.
• Page 12, line:338: the authors wrote: “The stable operation of the system can be strictly ensured when the ripple coefficient is less than 2%.”. Could you better clarify this statement?

The experimental results shown in Fig.16 seem to be in disagreement with the simulated performance reported in Table3,4 and Fig.10. From these latter, it appears that the condition of a ripple coefficient less than 2% could be reached with a capacitance value lower than 100uF for the improved modulation and with a value of about 600uF for the traditional one. You should add a comment on this issue.

Author Response

Reviewer: 2 
The following comments should be considered. 

 

Q1.2: It could be useful to report the y-axis labels for the sub-plots related to the switching signals and the time unit of measure in ms.

R: Thanks for your comments. The time unit of measurement is changed to ms. It is usually unnecessary to specify the y-axis labels of switching signals. ‘1’ means high level and ‘0’ means low level.

Q2.4 is cited in the text prior to Fig.3.

R: Thanks for your comments. 4 is not cited in the text prior to Fig.3.

Q3.Page 5, line 141: the authors wrote “vcw, vrA, and vrX have been defined in the previous paper,…”, which is the previous paper?

R: Thanks for your comments. Page 3, line107, “v_cw is the common triangular carrier, v_rA and v_rX are the upper and the lower modulation references, respectively.”

Q4.Page 5, line 155: “Rectification state” is repeated two times.

R: Thanks for your comments, the original sentence is rewritten as “Two RS (or IS) are too close, and there is only one FS between them...”

Q5.Page 5, line 165: liner is linear.

R: Thanks for your comments. “liner” is modified to “linear”.

Q6. (2): why there is the minus sign at the second member? Probably, the minus sign is due to the fact that theta1 is defined in eq.(8) as the phase angle of rectifier modulation reference, while formally in eq.(2) should appear the difference between the grid voltage/current phase angle and the rectifier modulation reference phase angle. The former is equal to zero by considering grid voltage and current in phase (i.e., unity power factor) as the authors stated in eq.(15). The authors should clearly define the angle theta1 when it is introduced for the first time in eq.(2).

R: Thanks for your comments, the sentence “Ɵ₁ represents the phase angle of rectification modulation reference and Ɵ_o is the power factor angle of inverter load ” is added in Page 6, line 170.

Q7. (8)and (9) introduce the modulation references with no explanation.

R: Thanks for your comments, the explanation  “v_cw is the common triangular carrier, v_rA and v_rX are the upper and the lower modulation references, respectively” is introduced in page 3, line107.

Q8.The phase angle phi is reported in lower case in equations, while in upper case in the text. Please check this issue throughout the paper.

R: Thanks for your comments. Phi is unified into ‘φ’

Q9.Section 3: to derive the minimum value of I’c for the improved modulation (eqs. 19-25) the authors use phase angle phi as in the case of traditional modulation (eqs.(9-17)), but the values for minimizing the current are different ((theta0-theta1)/2 for traditional modulation; theta0-theta1 for improved modulation). In fact , in table 2, the authors introduce the phase angle phi’ (which is twice of phi) for the improved modulation. In addition, at line 228, the authors wrote: “Therefore, phi is equal to (theta0-theta1)/2 in this paper…”. Please, clarify this point which is misleading.

R: Thanks for your comments. If the load is known, Ɵ_o is determined. The radio of X₁/X₂ is about 0.2, so Ɵ₁ can be determined according to formula (2). Therefore, both Ɵ_o and Ɵ₁ have been determined and values in table 2 are available. According to the derivation of this paper, the current is minimal when φ is (Ɵ_o-Ɵ₁)/2 for traditional modulation and Ɵ_o-Ɵ₁ for improved modulation. In this paper, it is proved by theory that the improved modulation strategy (directly reflected in the change in the φ value) can make the fluctuation smaller when the circuit parameters (like R,L,C,etc) are the same.

Q10.7 and 8: please try to improve their readability. Moreover, the output inverter voltage is previously named Vc (see also Fig.1), while now is reported as Uc, also in the text (lines 274, 278). This happens also in the following part of the paper (Table 3, Table 4, Fig.13 and so on).

R: Thanks for your comments. All ‘U’ are unified into ‘V’ throughout the paper and some figures’ readability are improved. 

Q11.Table 3, 4: it could be better to report the units of measure in square brackets. Then, if you define the ripple coefficient in percent (in the header row), you can avoid to use for each value in the corresponding column.

R: Thanks for your comments. The units are reported in square brackets. The column of ripple coefficient is modified.

Q12.From tables 3 and 4 and Fig.10 the ripple does not show a monotonically decreasing trend. Could you better explain this behavior?

R: Thanks for your comments. As Cd increases, the DC-link voltage fluctuation should reduce. However, when the capacitor is small, DC-link voltage waveform under the line frequency cycle is mainly caused by the oscillation under the switching cycle. In fact, the magnitude of voltage fluctuation under the switching cycle still shows a decline trend.

For example, Cd of the yellow one is 100u where Cd of the blue one is 200u. Obviously, DC-link voltage waveform under the line frequency cycle of this time is mainly affected by the oscillation under the switching cycle (It is directly reflected in the thick envelope of the yellow waveform).

Q13.Line 313: Please define the acronyms RCP and FPGA.

R: Thanks for your comments. RCP is configuration-based software and it is equivalent to the role of DSP in this experiment, used to output control signal. It is not the core of the experiment and is usually abbreviated. Line 313 outlines what it does.

FPGA means ‘Field Programmable Gate Array’. It usually does not expand the explanation, generally using abbreviation form in the paper.

Q14.12: It could be useful to establish a relation between the switching pattern in Fig.12 and the operating sequences reported at the beginning of section 3 with the aim of better highlighting the difference between the traditional and proposed modulation. For example by considering a single switching cycle to verify the fast charging and discharging of the proposed modulation in a complete switching cycle.

R: Thanks for your comments. First, Fig.12 shows the specific switching action. According to this scheme, the results described at the beginning of section 3 can be realized respectively. Figure 6 already shows the difference between the traditional and proposed modulation, and verifies the fast charging and discharging of the proposed modulation in a complete switching cycle.

Q15.Page 12, line:338: the authors wrote: “…which proves that the proposed modulation strategy can not only reduce the DC side voltage ripple coefficient under the line frequency, but also improve the output voltage waveform.” The better output voltage THD is a consequence of the reduced ripple.

R: Thanks for your comments. Rewrite the original sentence as “...which proves that the proposed modulation strategy can reduce the DC side voltage ripple coefficient under the line frequency, thereby improving the output voltage waveform.”