Parallel Operation Strategy of Inverters Based on an Improved Adaptive Droop Control and Equivalent Input Disturbance Approach

Response to Reviewer 1 Comments

1. Summary

First of all, we would like to express our sincere thanks to the Editor-in-Chief and the reviewers for their helpful comments and suggestions concerning our manuscript. The explanation of the modifications as well as corrections made in this revision are shown below and they are arranged by comment numbers following by the reply. The changes being made to the revised manuscript are marked in red words.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Thank you for your evaluation. We have added introductions to the paper.

Are all the cited references relevant to the research?

Can be improved

Thank you for your evaluation.

Is the research design appropriate?

Can be improved

Thank you for your evaluation.

Are the methods adequately described?

Can be improved

Thank you for your evaluation. We have added a description of the method in the paper. Please see the attachment.

Are the results clearly presented?

Can be improved

Thank you for your evaluation. We have modified the simulation experiment. Please see the attachment.

Are the conclusions supported by the results?

Can be improved

Thank you for your evaluation.

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: Please explain the drawbacks of the conventional droop controls for parallel inverters in a separate section first and then justify going for an adaptive droop with EID and virtual impedance.

Response 1: Thank you for pointing this out. This is indeed a good suggestion. We have modified the Introduction. In paragraph 6 of the Introduction, we describe the shortcomings of conventional droop control and then explain the rationale for using the EID method and improved adaptive droop control based on virtual impedance.

... In the parallel inverter system, the traditional droop control cannot solve the power sharing problem caused by the difference between the inverter equivalent output impedance and the line impedance. Therefore, an adaptive virtual impedance method is added to the traditional droop control to improve the power allocation accuracy of the traditional droop control. However, the traditional droop control still has the problem of voltage drop, which is improved by adding a link to compensate the voltage drop in the droop control to improve the energy efficiency. For the disturbance of the system caused by the fluctuation of the load side, the disturbance of the voltage tracking link is suppressed by combining with the EID method to reduce the circulating current fluctuation, which further improves the power sharing accuracy and system stability....

Comments 2: please improve the quality of Figure 3.

Response 2: Thank you very much for your suggestion. We have modified figure 3 to emphasize this point. Please see lines 166.

Comments 3: if you have carried out these studies with simulation, do not use words like experiment shows as in lines 378, 401, and 408.

Response 3: Thank you very much for your suggestion. We have amended the word "experiments" in the paper to "simulation experiments". See lines 383, 391 and 403 of the paper.

…Comparative active and reactive power simulation experiments are performed by…

…Simulation experiments show that the improved droop controller based …

…is proposed. Simulation experiments experimentally…

Comments 4: Please correct the typos in the following lines: line 96, line 139, line 264 and line 357.

Response 4: Thank you very much for your suggestion.

For 96 lines of questioning: In paragraph 6 of the Introduction. Taking into account the suggestions of other reviewers, we have revised this paragraph. Look specifically at paragraph 6 of the paper.

....

In the parallel inverter system, the traditional droop control cannot solve the power sharing problem caused by the difference between the inverter equivalent output impedance and the line impedance. Therefore, an adaptive virtual impedance method is added to the traditional droop control to improve the power allocation accuracy of the traditional droop control. However, the traditional droop control still has the problem of voltage drop, which is improved by adding a link to compensate the voltage drop in the droop control to improve the energy efficiency. For the disturbance of the system caused by the fluctuation of the load side, the disturbance of the voltage tracking link is suppressed by combining with the EID method to reduce the circulating current fluctuation, which further improves the power sharing accuracy and system stability.   ....

For 139 lines of questioning: we have revised this paragraph. Please see lines 136.

.... In medium or high voltage microgrids, the inductive impedance in the line plays a major role [27, 28, 29]. There exists  in the feeder impedance. In practical applications the system power angle  is generally very small. At this point there is  and . The active and reactive power output from the inverter can be simplified a  ....

For 264 lines of questioning: Please see lines 262.

…

Compared with the traditional droop control strategy, the strategy proposed in this paper introduces a proportional term and voltage dips compensation in the droop control equation to form a new power outer loop. A virtual …

For 357 lines of questioning: Please see lines 354.

 The public bus initially carries a certain load and increases the load at 0.2s. The initial public bus load is 10kW active power and 4kVar reactive power. The public bus added loads of 4kW active power and 2kVar reactive power.

Comments 5: please explain what is Pn and Qn in equation 2.

Response 5: Thank you for pointing this out. This is indeed a good suggestion. We explain Pn and Qn in equation 2 in line 146.

....  Pn and Qn are the rated frequency and rated voltage of the parallel operation system of inverters; ....

Comments 6: Consider providing additional simulation case study scenarios and results that better describe the circulating current fluctuations and stability improvements.

Response 6: Thank you for pointing this out. This is indeed a good suggestion. We have modified the simulation experiment. We add a description of the suppression of circulation fluctuations in the simulation experiments. Please see the attachment.

4. Response to Comments on the Quality of English Language

Point 1: Minor editing of English language.

Response 1: Thank you very much for your suggestion. We've tweaked the paper in part.  The changes being made to the revised manuscript are marked in red words. We have also changed the font of some formulas in the papert. Please see the attachment.

5. Additional clarifications

Response to Reviewer 2 Comments

1. Summary

First of all, we would like to express our sincere thanks to the Editor-in-Chief and the reviewers for their helpful comments and suggestions concerning our manuscript. The explanation of the modifications as well as corrections made in this revision are shown below and they are arranged by comment numbers following by the reply. The changes being made to the revised manuscript are marked in red words.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

Thank you for your evaluation.

Are all the cited references relevant to the research?

Yes

Thank you for your evaluation.

Is the research design appropriate?

Yes

Thank you for your evaluation.

Are the methods adequately described?

Can be improved

Thank you for your evaluation. We have added a description of the method in the paper. Please see the attachment.

Are the results clearly presented?

Can be improved

Thank you for your evaluation. We have modified the simulation experiment. Please see the attachment.

Are the conclusions supported by the results?

Yes

Thank you for your evaluation.

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: You may add a short explanation about the available methods for estimating and updating the complex virtual impedance.

Response 1: Thank you for pointing this out. This is indeed a good suggestion. We mentioned in the paper that the phase angle of the system impedance  after the introduction of virtual impedance. So that the inverter satisfies the condition of power approximate decoupling. Please see line 227.

....The method of adaptive virtual complex impedance that we adopt when dividing the virtual complex impedance into two parts: the reference value and the adaptive value, and the adaptive part is transformed by the ratio of active and reactive power to voltage magnitude, respectively [34]. When there is a difference in feeder impedance, the size of the virtual complex impedance is adjusted by setting the adaptive scaling factor to satisfy Equation 6, so as to reduce the power sharing error.....

Comments 2: Explain the assumption of R/X ratio on lines 140 and 198 and is it valid on

Response 2: Thank you for pointing this out. This is indeed a good suggestion. In medium- and high-voltage grids there exists X>>R, and the relationship between the power and droop equations is based on this. Please see line 136

… In medium or high voltage microgrids, the inductive impedance in the line plays a major role [27, 28, 29]. There exists  in the feeder impedance. In practical applications the system power angle  is generally very small. At this point there is  and . The active and reactive power output from the inverter can be simplified as …

However, in low voltage microgrids there is R>>X. In order to use droop control in low voltage microgrids, therefore virtual impedance is introduced to change the total output impedance of the system. This is the reason why the virtual impedance method is used in this paper. See line 197 for this explanation

… According to the line impedance parameters under different voltage levels [30]. And set the resistance-inductance ratio condition as  that is, the phase angle of the system impedance . This design can make the inverter meet the condition of approximate power decoupling. …

Comments 3: Explain stability testing of the proposed control.

Response 3: Thank you for pointing this out. The following will briefly explain the stability judgement of the method proposed in this paper. Our proposed control method can be simplified as generating a reference signal and then tracking this reference signal. The stability of the system depends on the stability of the EID controller.

The stability judgement method used in this paper can be seen through the literature [26], and the parameter calculation method of [26] is taken in the simulation experiments, using LQR to find the gain , , . Therefore, it is not repeated in the paper.

Please see line 341

Comments 4: In Fig. 1, explain the connection of output current "Io" in the feedback loop.

Response 4: Thank you for pointing this out. In the method proposed in this paper, the input to the EID controller is a reference signal on the dq-axis, and unlike conventional double-loop control, the EID controller does not require an output current "Io" as feedback. We have redrawn Figure 1, and thanks again for pointing this out.

 Please see lines 111.

Comments 5: Explain the new proposed blocks in Fig. 5 relative to Fig. 1 the following paper:

Li, M.; She, J.; Liu, Z.-T.; Wu, M.; Ohyama, Y. An Improved Equivalent-Input-Disturbance Method for Uncertain Networked Control Systems with Packet Losses and Exogenous Disturbances. Actuators 2021, 10, 263. https://doi.org/10.3390/act10100263

Response 5: Thank you for pointing this out. This is indeed a good suggestion. We have redrawn Fig. 5. Compared to the above literature, firstly, the EID controller proposed in this paper is based on voltage tracking and disturbance suppression in the context of parallel connection of inverters. Secondly, the input to the EID controller in this paper is a reference signal on the rotating dq coordinate system, so that both ucd and ucq signals exist on the input channel. And the controlled object is a three-phase ac system. The signals are transferred as constant values in the two-phase IEID control system and as three-phase AC electrical signals in the three-phase controlled system.

 Please see lines 332.

Comments 6: Improve the representation of figures 9 and 10 by adding grids and zoom the overshooting with original reference in the background.

Response 6: Thank you very much for your suggestion. We have modified figures 9 and 10 to emphasize this point. We increased the power output under more operating conditions. Please see the attachment

4. Response to Comments on the Quality of English Language

Point 1:

5. Additional clarifications

Response to Reviewer 3 Comments

1. Summary

First of all, we would like to express our sincere thanks to the Editor-in-Chief and the reviewers for their helpful comments and suggestions concerning our manuscript. The explanation of the modifications as well as corrections made in this revision are shown below and they are arranged by comment numbers following by the reply. The changes being made to the revised manuscript are marked in red words.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

Thank you for your evaluation.

Are all the cited references relevant to the research?

Yes

Thank you for your evaluation.

Is the research design appropriate?

Can be improved

Thank you for your evaluation. We have modified the description of the design control methodology. Please see the attachment.

Are the methods adequately described?

Yes

Thank you for your evaluation.

Are the results clearly presented?

Can be improved

Thank you for your evaluation. We have modified the simulation experiment. Please see the attachment.

Are the conclusions supported by the results?

Yes

Thank you for your evaluation.

3. Point-by-point response to Comments and Suggestions for Authors

The discussion on control design started stating that medium and high voltage lines are more inductive than resistive (X >> R). What about microgrids in low voltage grids? What difference must the control strategy deal with? Morevover, the example in section 5 uses a low voltage grid.

Response: Thank you for pointing this out. This is indeed a good suggestion. In medium- and high-voltage grids there exists X>>R, and the relationship between the power and droop equations is based on this. Please see line 136

… In medium or high voltage microgrids, the inductive impedance in the line plays a major role [27, 28, 29]. There exists  in the feeder impedance. In practical applications the system power angle  is generally very small. At this point there is  and . The active and reactive power output from the inverter can be simplified as …

However, in low voltage microgrids there is R>>X. In order to use droop control in low voltage microgrids, therefore virtual impedance is introduced to change the total output impedance of the system. This is the reason why the virtual impedance method is used in this paper. See line 197 for this explanation

… According to the line impedance parameters under different voltage levels [30]. And set the resistance-inductance ratio condition as  that is, the phase angle of the system impedance . This design can make the inverter meet the condition of approximate power decoupling. …

Therefore, the simulation part of this paper is also verified using a low-voltage microgrid.

Comments 1:  line 93 - define, in the first appearance, the acronym EID (Equivalent input disturbance)

Response 1:  Thank you for pointing this out. We agree with this comment. Therefore, We have made changes to the abbreviations. Specifically, see line 87 of the paper.

... current. The Equivalent Input Disturbance (EID) method is a perturbation suppression control method [25,26]. The loop …

Comments 2: Variables are in a different font from the text. Try to correct it to facilitate the reading.

Response 2: Thank you for pointing this out. We have changed the font of the variable

Comments 3: fig. 3 - increase this figure.

Response 3: Thank you very much for your suggestion. We have modified figure 3 to emphasize this point. Please see lines 166.

Comments 4: line 356 - K, in capital letters, stands for Kelvin. It should be k (lower case) of kilo. Revise it throughout the text.

Response 4: Thank you for pointing this out. We have corrected the unit of power.

Please see lines 354.

 The public bus initially carries a certain load and increases the load at 0.2s. The initial public bus load is 10kW active power and 4kVar reactive power. The public bus added loads of 4kW active power and 2kVar reactive power.

4. Response to Comments on the Quality of English Language

Point 1: line 100 - classical droop control. "so" as to achieve - comma instead of final point between control and so

Response 1: Thank you for pointing this out. Taking into account the suggestions of other reviewers, we have revised this paragraph.

... In the parallel inverter system, the traditional droop control cannot solve the power sharing problem caused by the difference between the inverter equivalent output impedance and the line impedance. Therefore, an adaptive virtual impedance method is added to the traditional droop control to improve the power allocation accuracy of the traditional droop control. However, the traditional droop control still has the problem of voltage drop, which is improved by adding a link to compensate the voltage drop in the droop control to improve the energy efficiency. For the disturbance of the system caused by the fluctuation of the load side, the disturbance of the voltage tracking link is suppressed by combining with the EID method to reduce the circulating current fluctuation, which further improves the power sharing accuracy and system stability. ...

Point 2:  line 170 - system is uc1. the state - t of the should be in capital letter.

Response 1: Thank you for pointing this out. We've made changes to line 169.

.... system is . The state and output equations of the inverter system can be obtained. ...

5. Additional clarifications