Review Reports

1

The conclusions to the article are very poor. They should be developed, the more so as the authors have a lot of interesting results.

Reply:

Many thanks for the Reviewer’s valuable suggestion. The conclusion has been revised and strengthened.

2

Why do simulation studies for SPWM and modified SPWM have a higher THD value than in experimental studies? The authors concluded: "The modified SPWM control decreased the THD from 10.95% to 4.55% in simulations, from 7% to 4.34% in actual measurements instead of other complex control."

Usually, the simulation model does not take into account many elements that in the real system affect the worse result? Usually the simulation results give the better result.

Reply:

Many thanks for the Reviewer’s reminding. Previously, we got all the parameters of the components from their datasheet. We analyzed the simulation results and the actual measurements, where the improvement trend using modified SPWM in the proposed inverter could be verified. However, the simulation result was worse than the actual measurement. Through the Reviewer's reminding, we checked the simulation and found that we did not take into account the equivalent series of the inductors L₁, L₂ (0.2 Ω) and the capacitors C₁ and C₂ (0.02 Ω), which are measured by the LCR meter (WK3255B). Due to the characteristic of the SSDBI, the equivalent series resistance of the inductor L₁ and L₂ affects the THD a lot while the equivalent series resistance of the capacitors C₁ and C₂ have little influence of the THD. After the improvement of the simulation, the simulation results are more realistic like the actual measurement. The description and the results have been revised in Line 236-237, Page 11, Table 2, and Page 18-24.

3

Not all abbreviations that were used for the first time were explained, eg the summary uses the acronym AC, SPWM, THD, which are explained later in the text. However, the abbreviation SSDBI or BESS were explained on the first use.

Reply:

Many thanks to the Reviewer’s reminding. The explanations of the abbreviations AC, SPWM, THD have been added in the Abstract.

4

What type of load has been used in the simulation and tests? What was its value?

Reply:

Many thanks for the Reviewer’s reminding. The descriptions of the load are added in Line 245-246, Page 11.

5

In chapter 2.1. Steady-state analysis of the SSDBI has been thoroughly described only mode 1 and 2, mod 3 and 4 have not been described.

Reply:

Many thanks for the Reviewer’s reminding. Both Converter 1 and Converter 2 have opposite but similar operation modes in the positive (Mode 1 and Mode 2) and negative (Mode 3 and Mode 4) half periods, respectively. So the previous steady-state analysis only took the positive half period (Mode 1 and Mode 2) as an example. All the complete descriptions have been added in Line 146-149, Page 5.

6

Why are V_{control (spwm)} and V_{control (modified_spwm)} voltage different in Figure 8a? The introduced modification should rather be visible only in the voltage V_{AC (spwm)} and AC (modified_spwm), which are the result of the circuit and the modified algorithm.

Reply:

Many thanks for the Reviewer’s reminding. The traditional SPWM and other control methods are usually designed around sinusoidal waveform and triangle waveform. However, most of these control methods are designed for bridge-type inverters, which have a simple and constant voltage gain. In this study, the voltage gain of the proposed inverters can be obtained in the paper, which is more complicated than other inverters. So, the modified SPWM proposed in this study change the V_control waveform to adjust the proper duty ratio of the inverter so that a better V_ac can be visible. The related descriptions have been added in Line 198-205, Page 8-9.

7

What is the point of modifying the SPWM, since the VAC voltage shown in Figure 9 can be reduced to a sinusoidal shape by using a filter? So maybe using a filter would be a better elaboration than complicating SPWM modulation.

Reply:

Many thanks for the Reviewer’s valuable suggestion. Most of the V_ac distortion phenomenon happens because of the ripple, while the V_ac shown in Figure 9 is caused by the SSDBI’s voltage gain (Equation (12)), which can’t be reduced to the sinusoidal shape by using a filter. And also, the LC filter for 50 or 60 Hz is large and heavy. Thus, in this study, the modified SPWM control proposed can improve the V_ac without applying the LC filter to have a better result.

1

A modification of the SPWM method has been proposed, but it is well known that this method is not used in real circuits, due to the poor utilisation of the DC link voltage. Why did the authors not compare their method with the SPWM method with an additional third harmonic or the space vector method (SVPWM)? For an article to present real value it must be done and the results presented.

Reply:

Many thanks for the Reviewer’s valuable suggestion. The SVPWM control and the SPWM control with an additional third harmonic are algorithms for inverters creating AC waveforms. As aforementioned, the SVPWM control and the SPWM control with an additional third harmonic have better utilization of the DC link. And these brilliant controls are usually used in three-phase buck inverters driving three-phase motors. These controls regard the inverter and the motor as a whole to control the motor’s RPM by adjusting voltage and frequency but constant flux. The SPWM controls are not used in real circuits when the load is a motor. However, the SSDBI proposed in this study is a single-phase inverter without a specified type of load, which has been described by the Reviewer’s reminder (Suggestion 4 and 5). In addition, the SPWM controls are commonly used in real applications, which have a constant frequency, such as telecommunication base stations or uninterrupted power supplies. What’s more, the contribution and the improvement of the modified SPWM control are based on the characteristics of the SSDBI. If the proposed SSDBI applies the SPWM control with an additional third harmonic, the distortion, the voltage peak of V_ac and the THD will not be overcome because these problems are caused by the special voltage gain of the SSDBI. The related description has been added in Line 111-117, Page 4. Nevertheless, the Reviewer’s valuable suggestion is very important for our follow-up research. The SSDBI architecture has the potential to extend to three-phase applications, such as driving a three-phase motor. By applying the brilliant control, such as the SVPWM and the SPWM control with an additional third harmonic, the extended architecture may show its advantage compared with the traditional three-phase inverter.

2

The authors describe the operation of the converter in great detail, the SPWM method, but it is not clear where equation 20 comes from. Please derive this relation and describe the idea it contains.

Reply:

Many thanks for the Reviewer’s reminding. Equation (20) is modified from equation (12), and the related descriptions have been added in Line 209, Page 9.

3

Equation 21 should be shown in full not simplified form.

Reply:

Many thanks for the Reviewer's valuable suggestion. Equation (21) has been changed to full form.

4

I have not found anywhere what AC load parameters were used in the simulation and experiment (resistance, inductance)?

Reply:

Many thanks for the Reviewer’s reminding. The related descriptions of the load are added in Line 245-246, Page 11.

5

In order for the results of experiments and simulations to be valuable, they should be performed for several load levels, not just one as the authors have done.

Reply:

Many thanks for the Reviewer’s valuable suggestion. The results of the experiments and the simulations have been added for additional load conditions (25% and 50% load). The related descriptions have been also added in Line 257-259, Page 12. The results (figures and description) have been highlighted and can be obtained from Page 13 to 23.

6

The discussion of the results, especially in comparison with the long theoretical description, is not detailed enough; similarly, the summary should also contain more content, especially concerning the authors' own contribution.

Reply:

Many thanks for the Reviewer’s valuable suggestion. The conclusion has been revised and strengthened.

1

I am glad that I could help you improve the article. Thanks for the replies and the corrections.

Reply:

Thanks to the reviewer for providing many valuable comments, which made the quality of this paper significantly improved. Thanks again for the reviewer's contribution.

1

After adding additional results of simulations and research, please compare them briefly in the form of a table and additionally comment them.
The authors still haven't responded to the last sentence in my last comment, namely they haven't included the information about authors' own contribution. It is not clear to the reviewer if the proposed method was come from the literature or if it is the authors own study, if so, please highlight this in the text.

Reply:

Many thanks for the Reviewer’s valuable suggestion. The SSDBI topology has been raised and discussed in recent years. The voltage distortion of the AC side will occur when the SSDBI using traditional SPWM control is operating in high voltage gain [17]. This study certified the phenomenon with the simulation and hardware experiment. To overcome the problem, this study analyzed the characteristics of the SSDBI and inferred an appropriate duty’s mathematical model according to the relationship between V_AC and V_DC (Equation (11)-(12)). Since the derived duty’s mathematical model modified the traditional SPWM control, the SSDBI using the modified SPWM control improved the voltage distortion of the AC side and the THD. The SSDBI were tested under three different loads (25%, 50%, and 100%) to verify the theoretical prediction with both simulation and hardware experiments, respectively. After collating the above results, the improvement of the voltage distortion of the AC side can be obtained from Figure 15 to Figure 20, and the THD comparison of the simulation results and hardware experiment results can be obtained in Table 3, where the THD in the simulation is closed to the hardware experiment, the modified SPWM control has better performance than the traditional SPWM control. All the descriptions have been added in Line 352-366, Page 23-24.