Standalone Operation of Inverter-Based Variable Speed Wind Turbines on DC Distribution Network

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors present a review of existing papers without criticism. What are their disadvantages? Moreover, what are the contributions and novelty of this paper? The authors should clarify these points on the introduction.

There are some misspellings. The entire text should be revised.

The results are limited to just 5 pages with only 3 simulation scenarios. The authors are recommended to show more simulation results, to extend discussion and outcomes. There are minor novelties here.

Have the authors analyzed another distribution system configuration?

Author Response

Dear Reviewer,

We sincerely appreciate your time and effort in reviewing our manuscript. Your insightful comments and suggestions have helped us improve the clarity and impact of our work. Below, we provide detailed responses to each of your concerns.

Comment 1:

"The authors present a review of existing papers without criticism. What are their disadvantages? Moreover, what are the contributions and novelty of this paper? The authors should clarify these points in the introduction."

Response:
Thank you for your valuable feedback. We acknowledge that our discussion of prior work did not explicitly highlight the limitations of existing approaches. To address this, we have revised the Introduction (Section 1) to explicitly state the drawbacks of previous methods, such as limited adaptability to load variations and challenges in voltage stability for DC networks with unbalanced AC loads. Additionally, we have clarified our paper's key contributions and novelty, particularly in:

• Implementing a droop control strategy for DC voltage regulation in isolated networks.
• Stand-alone operation and control of inverter-based variable-speed wind turbines, ensuring stable and efficient integration into DC microgrids. demonstrating improved power quality through balanced AC voltage regulation despite unbalanced loads.
• Utilizing an isolated DC distribution network for the integration of wind turbine generation, considering the inherent fluctuations in wind power output due to varying wind speeds.
• Efficient energy management and battery storage utilization, where the battery system plays a critical role in DC voltage regulation and dynamic response to load and generation variations.
• Introducing a novel network architecture that serves as a promising and innovative solution for future power grids, enhancing resilience, flexibility, and reliability in renewable energy integration.
• Coordinated control of WTIG and storage converters to ensure continuous power supply under varying wind and load conditions.
• Demonstrating improved power quality through balanced AC voltage regulation despite unbalanced loads.

The revised section now explicitly contrasts our approach with previous studies.

Changes in Manuscript: Section 1, Pages 1, 2

The increasing penetration of renewable energy resources necessitates the development of advanced network architectures for efficient and reliable power distribution [1 ]. Low voltage direct current (LVDC) systems have gained significant attention due to their capacity to integrate distributed generation (DG) resources, such as wind turbines, and provide improved power quality and system flexibility [2]. Multi-terminal LVDC isolated networks provide a promising solution for off-grid or remote locations where conventional AC grid access is unavailable or economically infeasible [3 ]. Renewable energy resources are used more where grid access is either unavailable or financially prohibitive [4 ]. Wind shows robust global growth with an annual expansion rate exceeding 30%, and using variable-speed wind turbines attracts considerable interest in the energy sector, as they increase power generation and reduce noise levels [5].

Several prior studies have explored different methodologies for LVDC network stability and power quality enhancement. For instance, adaptive fuzzy controllers for variable-speed wind turbines have been proposed to improve power regulation, but these methods require extensive computational resources, limiting their real-time applicability [6]. Other works introduce centralized optimal control strategies for DC voltage regulation, but they often rely on communication-dependent coordination, reducing system resilience in isolated networks [ 7 ]. Bi-level robust scheduling techniques have also been studied for DC system security, yet these models primarily focus on frequency stability rather than voltage control under unbalanced loads [ 4]. To achieve maximum power tracking [ 6 ] proposes a duty cycle control and look-up table approaches, which rely on the turbine operational characteristics during or prior to execution. In a standalone wind turbine induction generator (WTIG), generated power directly supplies connected loads. Because of the fluctuating nature of wind speed, battery storage systems are often included in isolated WTIG to address discrepancies between load demand and power generation [7]. When wind power exceeds load demand, surplus energy charges the battery, while in situations where demand surpasses available wind power, the battery compensates for the load demand by supplying the additional energy [4]. Challenges arise in managing the surplus energy in cases where the battery is fully charged, and excess power continues to be generated [ 8]. To address the challenge, the combined operation of standalone WTIG within a star-configured DC isolated distribution network is proposed, offering improved power quality, cost-effective scalability, and easier maintenance compared to AC distribution systems [9].

While these approaches contribute to LVDC network development, they exhibit several drawbacks:

• Limited adaptability to load variations, particularly in networks supplying unbalanced AC loads.
• Complex centralized control schemes that increase communication overhead and computational burden.
• Lack of a decentralized and scalable voltage regulation strategy for isolated LVDC networks.

The main contributions of this paper are as follows:

This paper addresses the gaps by proposing a novel decentralized control strategy for an isolated LVDC distribution network powered by variable-speed wind turbines (WTIG). This approach utilizes:

1. Implementing a droop control strategy for DC voltage regulation in isolated networks.
2. Stand-alone operation and control of inverter-based variable-speed wind turbines, ensuring stable and efficient integration into DC microgrids, demonstrating improved power quality through balanced AC voltage regulation despite unbalanced loads.
3. Utilizing an isolated DC distribution network for the integration of wind turbine generation, considering the inherent fluctuations in wind power output due to varying wind speeds.
4. Efficient energy management and battery storage utilization, where the battery system plays a critical role in DC voltage regulation and dynamic response to load and generation variations.
5. Introducing a novel network architecture that serves as a promising and innovative solution for future power grids, enhancing resilience, flexibility, and reliability in renewable energy integration.
6. Coordinated control of WTIG and storage converters to ensure continuous power supply under varying wind and load conditions.

Unlike previous works, the proposed system offers improved stability, enhanced resilience, and high wind energy utilization efficiency (over 90%), making it a viable solution for off-grid renewable energy applications.  

Comment 2:

"There are some misspellings. The entire text should be revised."

Response:
We appreciate this observation. The manuscript has undergone a thorough proofreading process to correct minor typographical errors, improve clarity, and ensure consistency in technical terminology.

Changes in Manuscript: Full manuscript revision for language and typographical corrections.

Comment 3:

"The results are limited to just 5 pages with only 3 simulation scenarios. The authors are recommended to show more simulation results, extend discussion, and outcomes. There are minor novelties here."

Response:
We agree that additional simulation results would further enhance the study by providing a more comprehensive evaluation of the proposed approach. However, the current manuscript already spans 22 pages, and adding more scenarios would significantly increase its length, potentially affecting readability and conciseness. To ensure a thorough analysis while maintaining the paper's focus, we have carefully selected and presented three key simulation scenarios that effectively demonstrate the performance of our proposed method. These scenarios capture the system’s behavior under different operating conditions, including voltage regulation, power balancing, and unbalanced load compensation. That said, we acknowledge the value of further expanding this research. Our team is actively working on extending the subject into a follow-up study, where we will investigate additional test cases and scenarios, particularly focusing on real-world implementation in practical DC grids. This future work will allow us to assess the feasibility of our control strategy in experimental setups and apply new innovative ideas for improving system stability, energy efficiency, and dynamic response. Again, we appreciate the reviewer’s suggestion and will incorporate these aspects into our ongoing research for future publications. As part of this effort, we plan to investigate a new operational scenario involving extreme wind fluctuations to assess system stability, conduct a more detailed analysis of load reconnection dynamics, and provide an extended discussion comparing our proposed control strategy with conventional DC voltage regulation techniques. These additions will offer deeper insights into the robustness of our system and will be documented in an upcoming study. We appreciate the reviewer’s suggestion, as it aligns with our ongoing efforts to further validate and enhance the applicability of our method.

Changes in Manuscript: Section 6, Page 19

Given the standalone (isolated) operation, DC distribution systems that are not connected to the AC grid present unique characteristics. These systems, commonly referred to as isolated DC distribution networks, face several challenges, including lower reliability and reduced power quality compared to AC-connected systems. Nevertheless, isolated DC distribution networks are well-suited for integrating renewable distributed generation resources, such as wind turbine systems, and for independent operation (islanded operation). The integration of renewable energy sources within isolated DC distribution systems facilitates optimal load and generation sharing between sources and loads based on a droop-based power management system, ensuring the supply of loads with desirable power quality. Considering the variable nature of power generation from wind resources, the proposed system is designed to ensure power quality and transfer capability through its autonomous and integrated operation. In this study, the DC voltage control system within the storage converter, which effectively serves as the active power management system, is analyzed and designed. A comprehensive design methodology for the DC voltage control system is introduced, aiming to eliminate circulating currents within the system, stabilize the DC voltage within permissible limits, and achieve appropriate power distribution among source converters. Then, the performance of an isolated DC network powered by WTIG is examined. The proposed DC network supplies unbalanced AC loads, with battery energy storage used to regulate the DC bus voltage levels. Two operational scenarios are considered to evaluate the proposed system performance. The first scenario focuses on the system normal operation, accounting for variations in wind speed, while the second scenario investigates the impact of load variations on system behavior. Simulation results confirm that the proposed network maintains DC bus voltage stability within ±5% of the nominal value and achieves balanced AC voltage delivery with deviations below 2% under unbalanced load conditions. The system effectively adapts to wind speed variations (9–12.5 m/s) and manages load variations by dynamically charging or discharging the battery bank. The WTIG-based DC network demonstrates efficient power management, with wind energy utilization exceeding 90% in optimal conditions, ensuring reliable operation and robust performance for unbalanced AC loads.

As a continuation of this research, future work can focus on exploring additional operational scenarios and advancing toward real-world implementation in practical DC grids. This includes analyzing system performance under extreme wind fluctuations to assess stability, examining the effects of load reconnection dynamics on overall system behavior, and conducting a comparative evaluation of the proposed control strategy against conventional DC voltage regulation techniques.

Comment 4:

"Have the authors analyzed another distribution system configuration?"

Response:

Thank you for this valuable suggestion. In this study, a star-configured DC-isolated distribution network was considered due to its suitability for off-grid and remote applications. However, future research will explore alternative configurations, such as ring-configured DC networks, which enhance fault tolerance and voltage stability, and hybrid AC-DC microgrids, which facilitate efficient energy management and integration with conventional power systems.

The proposed distribution network structure has been evaluated in different configurations. In future work, the performance of these configurations can be further analyzed and compared to provide a comprehensive assessment of their effectiveness.

Changes in Manuscript: Section 6, Pages 19,20

Given the standalone (isolated) operation, DC distribution systems that are not connected to the AC grid present unique characteristics. These systems, commonly referred to as isolated DC distribution networks, face several challenges, including lower reliability and reduced power quality compared to AC-connected systems. Nevertheless, isolated DC distribution networks are well-suited for integrating renewable distributed generation resources, such as wind turbine systems, and for independent operation (islanded operation). The integration of renewable energy sources within isolated DC distribution systems facilitates optimal load and generation sharing between sources and loads based on a droop-based power management system, ensuring the supply of loads with desirable power quality. Considering the variable nature of power generation from wind resources, the proposed system is designed to ensure power quality and transfer capability through its autonomous and integrated operation. In this study, the DC voltage control system within the storage converter, which effectively serves as the active power management system, is analyzed and designed. A comprehensive design methodology for the DC voltage control system is introduced, aiming to eliminate circulating currents within the system, stabilize the DC voltage within permissible limits, and achieve appropriate power distribution among source converters. Then, the performance of an isolated DC network powered by WTIG is examined. The proposed DC network supplies unbalanced AC loads, with battery energy storage used to regulate the DC bus voltage levels. Two operational scenarios are considered to evaluate the proposed system performance. The first scenario focuses on the system normal operation, accounting for variations in wind speed, while the second scenario investigates the impact of load variations on system behavior. Simulation results confirm that the proposed network maintains DC bus voltage stability within ±5% of the nominal value and achieves balanced AC voltage delivery with deviations below 2% under unbalanced load conditions. The system effectively adapts to wind speed variations (9–12.5 m/s) and manages load variations by dynamically charging or discharging the battery bank. The WTIG-based DC network demonstrates efficient power management, with wind energy utilization exceeding 90% in optimal conditions, ensuring reliable operation and robust performance for unbalanced AC loads.

As a continuation of this research, future work can focus on exploring additional operational scenarios and advancing toward real-world implementation in practical DC grids. This includes analyzing system performance under extreme wind fluctuations to assess stability, examining the effects of load reconnection dynamics on overall system behavior, and conducting a comparative evaluation of the proposed control strategy against conventional DC voltage regulation techniques.

Conclusion:

We are grateful for your constructive comments, which have significantly improved our manuscript. We believe the revisions address your concerns and enhance the overall quality of our study. We hope that the updated manuscript now meets the journal's standards.

Best regards,
Hossein Amini
The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
aminih@vt.edu

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

• Consider revising some sections for greater conciseness and clarity. In particular, the descriptions of the control strategies could benefit from simpler, more straightforward explanations to ensure they are easily understood by a broader audience.
• The mathematical models and the simulation results are well detailed, but some explanations of the control strategies may need to be simplified for clarity.
• In future revisions, focus on enhancing the readability of complex sections while preserving the technical rigor.

Comments on the Quality of English Language

The overall quality of English in the paper is adequate; however, there are areas where improvements could be made for better clarity and readability. Some sections, especially those that describe control strategies and system dynamics, contain complex sentences that could be simplified. Consider breaking down long, intricate explanations into shorter, more digestible sentences to improve the flow of the paper. Additionally, there are instances of technical jargon that might be more clearly defined or explained, especially for readers who may not be deeply familiar with the topic. A few minor grammatical adjustments and the use of more precise terms would further enhance the clarity of the paper.

Author Response

Dear Reviewer,

We sincerely appreciate your valuable feedback and insightful suggestions for improving our manuscript. We have carefully addressed each of your concerns, as outlined below.

Comment 1:

"Consider revising some sections for greater conciseness and clarity. In particular, the descriptions of the control strategies could benefit from simpler, more straightforward explanations to ensure they are easily understood by a broader audience."

Response:
Thank you for this important suggestion. We have revised Section 4 (The Power Converters and Inverters Control Strategy) to improve readability by:

• Simplifying complex explanations of control strategies while maintaining technical rigor.
• Breaking down long sentences into shorter, clearer statements.
• Adding brief introductory summaries before each subsection to outline key concepts before presenting equations.

These revisions ensure that the control strategies are accessible to a broader audience without compromising technical accuracy.

Changes in Manuscript: Section 4, Pages 8, 9

The DC bus voltage loop controls the charging and discharging phases. When the DC bus voltage is between the reference values  and , the signal  is zero, and no power exchange occurs. If the voltage exceeds ,  becomes negative, recharging the storage system using power from the WTIG. Conversely, if the voltage drops below ,  becomes positive, discharging the battery bank to supply power. The DC voltage regulator in the storage unit (Figure 4) governs , with the reference current  calculated as:

To ensure the stable operation of the DC distribution network, a voltage droop control strategy is employed for regulating the DC bus voltage. The proposed control strategy ensures stable operation of the inverter-based wind energy system in a stand-alone DC distribution network. The system consists of three main control mechanisms:

1. DC Bus Voltage Regulation: Maintains voltage stability by dynamically adjusting power exchange between the battery storage and the network.
2. Wind Turbine Power Control: Ensures optimal power extraction from wind turbines while maintaining operational limits.
3. Inverter-Based Load Management: Balances power delivery to unbalanced AC loads to maintain a stable and reliable power supply.

This strategy eliminates the need for communication links between converters by adjusting power flow based on local voltage measurements. The droop control method introduces a controlled voltage deviation proportional to the output current. The voltage droop control strategy is employed to regulate the DC bus voltage without requiring communication links between power sources. The relationship between the DC voltage deviation and the current injected by the storage system is represented as:

where:

•  is the measured DC bus voltage,
• is the reference voltage for the storage system,
• is the storage converter’s output current, and
• is the droop coefficient, defining the slope of the voltage-current characteristic.

The slope of the voltage droop characteristic, m, determines how much the DC voltage decreases with increasing load current. A higher droop coefficient results in a more significant voltage deviation, which enhances system stability but may lead to increased voltage variations under dynamic load conditions. Figure 5 illustrates the voltage droop characteristic implemented in the system. The voltage of the battery terminal  is constrained by

Figure 5. Voltage droop characteristic with slope 1/kb , illustrating the impact of current variations on DC bus voltage.

Comment 2:

"The mathematical models and the simulation results are well detailed, but some explanations of the control strategies may need to be simplified for clarity."

Response:
We appreciate your positive feedback on the mathematical models and simulation results. To enhance clarity, we have:

• Streamlined descriptions of the control strategies (particularly in Sections 4.1–4.3) by removing redundant phrasing and restructuring key explanations.
• Added inline clarifications for key equations to ensure they are easy to follow.
• Provided additional context on how each control strategy contributes to system stability.

These improvements make the technical content more digestible while preserving the depth of our analysis.

Changes in Manuscript: Section 4, Pages 8, 9, 10

The DC bus voltage loop controls the charging and discharging phases. When the DC bus voltage is between the reference values  and , the signal  is zero, and no power exchange occurs. If the voltage exceeds ,  becomes negative, recharging the storage system using power from the WTIG. Conversely, if the voltage drops below ,  becomes positive, discharging the battery bank to supply power. The DC voltage regulator in the storage unit (Figure 4) governs , with the reference current  calculated as:

To ensure the stable operation of the DC distribution network, a voltage droop control strategy is employed for regulating the DC bus voltage. The proposed control strategy ensures stable operation of the inverter-based wind energy system in a stand-alone DC distribution network. The system consists of three main control mechanisms:

1. DC Bus Voltage Regulation: Maintains voltage stability by dynamically adjusting power exchange between the battery storage and the network.
2. Wind Turbine Power Control: Ensures optimal power extraction from wind turbines while maintaining operational limits.
3. Inverter-Based Load Management: Balances power delivery to unbalanced AC loads to maintain a stable and reliable power supply.

This strategy eliminates the need for communication links between converters by adjusting power flow based on local voltage measurements. The droop control method introduces a controlled voltage deviation proportional to the output current. The voltage droop control strategy is employed to regulate the DC bus voltage without requiring communication links between power sources. The relationship between the DC voltage deviation and the current injected by the storage system is represented as:

where:

•  is the measured DC bus voltage,
• is the reference voltage for the storage system,
• is the storage converter’s output current, and
• is the droop coefficient, defining the slope of the voltage-current characteristic.

The slope of the voltage droop characteristic, m, determines how much the DC voltage decreases with increasing load current. A higher droop coefficient results in a more significant voltage deviation, which enhances system stability but may lead to increased voltage variations under dynamic load conditions. Figure 5 illustrates the voltage droop characteristic implemented in the system. The voltage of the battery terminal  is constrained by

Figure 5. Voltage droop characteristic with slope 1/kb , illustrating the impact of current variations on DC bus voltage.

This method allows the battery energy storage system to actively regulate the DC bus voltage by adjusting its charging and discharging rates dynamically.

The inverter control system ensures power balance among unbalanced AC loads by adjusting output voltage and current dynamically. A phase-locked loop (PLL) is used to synchronize the inverter output with the load demand. The control reference for each inverter is determined as:

where:

• is the reference current for phase ϕ,
• is the power demand of the load in phase ϕ, and
• is the instantaneous voltage of phase ϕ.

The inverter control logic compensates for unbalanced loads by dynamically adjusting the power supplied to each phase.

Comment 3:

"In future revisions, focus on enhancing the readability of complex sections while preserving the technical rigor."

Response:
We fully agree with this recommendation. To achieve this, we have:

• Conducted a comprehensive review of complex sections (especially in the methodology and control strategy discussions) to ensure they are concise and logically structured.
• Used more intuitive explanations and avoided excessive technical jargon where possible.
• Formatted key points into bullet points where appropriate to enhance readability.

We believe these revisions significantly improve the flow of the manuscript.

Changes in Manuscript: Whole pages and Sections.

Comment 4:

"The overall quality of English in the paper is adequate; however, there are areas where improvements could be made for better clarity and readability. Some sections, especially those that describe control strategies and system dynamics, contain complex sentences that could be simplified."

Response:
We appreciate your feedback on language clarity. We have revised the manuscript to:

• Simplify sentence structures for better readability.
• Replace overly technical jargon with clearer terminology when possible.
• Ensure grammatical accuracy through careful proofreading.

These changes enhance the manuscript’s clarity while maintaining a professional and technical tone.

Changes in Manuscript: Full manuscript revision for language and readability improvements.

Conclusion:

We are grateful for your constructive suggestions, which have significantly improved our manuscript. The revisions ensure greater clarity, conciseness, and accessibility while maintaining technical accuracy. We hope that the updated manuscript meets your expectations.

Best regards,
Hossein Amini
The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
aminih@vt.edu

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Operation and control of an islanded DC distribution network fed by variable speed wind generators supplying unbalanced AC loads is described.

The objective of literaure survey is to present a critical analysis of the present state of the art and describe the deficiencies that are proposed to be addressed in the manuscript. It is not to just list some of the previous publications as is done here. In any case, how is a referernce on islanding detection, included here, relevant for an islanded standalone system?

Figure 2. Does 'S' here represent Laplace transform? At other places in the manucript the correct symbol 's' is used.

Equations (1) through (3) are simply thrown in with no explanation. Are the signs on RHS of eqn. (3) consistent with the direction of current flow shown in Fig. 2?

What is the current and its direction in the unmarked branch in the Battery block, Fig. 2?

 Not all symbols used in Fig. 2 are defined. In fact, not all symbols used in the manuscript are defined.

Where is 'k_b' used in Fig. 2? Also, are 'k_b', eqn. (1), and 'K_b' used in the following text the same?

Page 5. "Voltage regulation is maintained through a battery...". Sectioin 4.1. "The DC-DC system comprises a secondary battery bank...". Are there two different batteries and where is this secondary battery shown in Fig. 4?

Page 6. "A voltage regulator for the DC side...". Are both sides not DC? Also, why is the voltage droop control strategy employed not given in the manuscript? Where is the "slope of the voltage droop charactristic shown in Fig. 4?

Page 5, just before Sec. 4. "...maintaining the DC bus voltage between 5% and 10%...WTIG generated power reduces to zero." 5% and 10% of what? Highly imprecise and confusing language at many places! At other places, there is hardly a resemblance between the text and the corresponding figure. 

Page 8."A phase-locked loop...the off grid voltage...".It is an isolated DC system (page 8). Where does the grid voltage come from? 

The above and writing at other places indicate that a good part of the material is taken from the literature and put in this manuscript without checking if it even corelates with the contents of this manuscript.

The same symbol, k_b, is used in eqn. (1) as the PI controller gain and in eqn. (11) as a very different constant.

Where is the blade angle controller shown in Fig. 5?

Where do eqns. (14) and (16) come from?

Figure 7 and others. What each curve represents is hardly evident.

Section 5.1 is for the case of no disturbance operation, constant wind speed and no disturbance in load. What causes the variations in Figs. 7 and 8?

Page 13. "A larger battery helps reduce the observed ripple."??

Page 13. "As shown, the DC bus volatge ...(Figure 3)". Where are DC Bus voltages shown in Fig. 3? 

Absolutely no information is provided about the unbalanced loads. What is the magnitude of the unbalance and are all the same?

Based on the material included in the manuscript, How are instatntaneous phase values, Figs. 14, 15, obained?

6. Conclusion. Interesting that only two operational scenarios are mentioned here! No coordinatiion even between Sections 5 and 6.

Statement "wind energy utilization exceeding 90%" is based on which study? 

Comments on the Quality of English Language

Considering that one of the authors is from an English speaking country, the manuscript requires significant editing for the English language.

Author Response

Dear Reviewer,

We sincerely appreciate your time and effort in reviewing our manuscript. Your insightful comments and suggestions have helped us improve the clarity and impact of our work. Below, we provide detailed responses to each of your concerns.

Comment 1:

"The objective of literature survey is to present a critical analysis of the present state of the art and describe the deficiencies that are proposed to be addressed in the manuscript. It is not to just list some of the previous publications as is done here. In any case, how is a reference on islanding detection, included here, relevant for an islanded standalone system?"

Response:
We acknowledge that the literature review lacked a critical discussion of the limitations of existing methods. To address this, we have revised Section 1 (Introduction) to:

• Provide a more in-depth analysis of previous works, identifying specific challenges they fail to address.
• Clearly state how our proposed approach overcomes these limitations, particularly in DC voltage regulation and unbalanced load compensation.
• Remove irrelevant references, including the islanding detection reference, which does not directly contribute to the study of islanded DC networks.

Changes in Manuscript: Section 1, Pages 1, 2, and 3

The increasing penetration of renewable energy resources necessitates the development of advanced network architectures for efficient and reliable power distribution [1 ]. Low voltage direct current (LVDC) systems have gained significant attention due to their capacity to integrate distributed generation (DG) resources, such as wind turbines, and provide improved power quality and system flexibility [2]. Multi-terminal LVDC isolated networks provide a promising solution for off-grid or remote locations where conventional AC grid access is unavailable or economically infeasible [3 ]. Renewable energy resources are used more where grid access is either unavailable or financially prohibitive [4 ]. Wind shows robust global growth with an annual expansion rate exceeding 30%, and using variable-speed wind turbines attracts considerable interest in the energy sector, as they increase power generation and reduce noise levels [5].

Several prior studies have explored different methodologies for LVDC network stability and power quality enhancement. For instance, adaptive fuzzy controllers for variable-speed wind turbines have been proposed to improve power regulation, but these methods require extensive computational resources, limiting their real-time applicability [6]. Other works introduce centralized optimal control strategies for DC voltage regulation, but they often rely on communication-dependent coordination, reducing system resilience in isolated networks [7]. Bi-level robust scheduling techniques have also been studied for DC system security, yet these models primarily focus on frequency stability rather than voltage control under unbalanced loads [4]. To achieve maximum power tracking [6] proposes a duty cycle control and look-up table approaches, which rely on the turbine operational characteristics during or prior to execution. In a standalone wind turbine induction generator (WTIG), generated power directly supplies connected loads. Because of the fluctuating nature of wind speed, battery storage systems are often included in isolated WTIG to address discrepancies between load demand and power generation [7]. When wind power exceeds load demand, surplus energy charges the battery, while in situations where demand surpasses available wind power, the battery compensates for the load demand by supplying the additional energy [4]. Challenges arise in managing the surplus energy in cases where the battery is fully charged, and excess power continues to be generated [8]. To address the challenge, the combined operation of standalone WTIG within a star-configured DC isolated distribution network is proposed, offering improved power quality, cost-effective scalability, and easier maintenance compared to AC distribution systems [9].

While these approaches contribute to LVDC network development, they exhibit several drawbacks:

• Limited adaptability to load variations, particularly in networks supplying unbalanced AC loads.
• Complex centralized control schemes that increase communication overhead and computational burden.
• Lack of a decentralized and scalable voltage regulation strategy for isolated LVDC networks.

The main contributions of this paper are as follows:

This paper addresses the gaps by proposing a novel decentralized control strategy for an isolated LVDC distribution network powered by variable-speed wind turbines (WTIG). This approach utilizes:

1. Implementing a droop control strategy for DC voltage regulation in isolated networks.
2. Stand-alone operation and control of inverter-based variable-speed wind turbines, ensuring stable and efficient integration into DC microgrids, demonstrating improved power quality through balanced AC voltage regulation despite unbalanced loads.
3. Utilizing an isolated DC distribution network for the integration of wind turbine generation, considering the inherent fluctuations in wind power output due to varying wind speeds.
4. Efficient energy management and battery storage utilization, where the battery system plays a critical role in DC voltage regulation and dynamic response to load and generation variations.
5. Introducing a novel network architecture that serves as a promising and innovative solution for future power grids, enhancing resilience, flexibility, and reliability in renewable energy integration.
6. Coordinated control of WTIG and storage converters to ensure continuous power supply under varying wind and load conditions.

Unlike previous works, the proposed system offers improved stability, enhanced resilience, and high wind energy utilization efficiency (over 90%), making it a viable solution for off-grid renewable energy applications.  

Added references:

14. Hasheminasab, S.; Alzayed, M.; Chaoui, H. A Review of Control Techniques for Inverter-Based Distributed Energy Resources Applications. Energies 2024, 17, 2940.
15. Bubalo, M.; Baši´c, M.; Vukadinovi´c, D.; Grgi´c, I. Experimental investigation of a standalone wind energy system with a battery-assisted quasi-Z-source inverter. Energies 2021, 14, 1665.
16. Harasis, S.; Mahmoud, K.; Albatran, S.; Alzaareer, K.; Salem, Q. Dynamic performance evaluation of inverter feeding a weak grid considering variable system parameters. IEEE Access 2021, 9, 126104–126116.
17. Nanda, A.; Hari, V.P.K. A New Variable-Speed Wind Energy Conversion System using Double-inverter-fed Wound Rotor Induction Generator. IEEE Transactions on Energy Conversion 2024.

Comment 2:

"Figure 2. Does 'S' here represent Laplace transform? At other places in the manuscript the correct symbol 's' is used."

Response:
We appreciate your attention to consistency. The symbol 'S' in Figure 2 was incorrectly capitalized. We have corrected it to 's' throughout the figure and manuscript for consistency.

Changes in Manuscript: Figure 2, Page 5

Figure 2. The DC side dynamical model

Comment 3:

"Equations (1) through (3) are simply thrown in with no explanation. Are the signs on RHS of Eqn. (3) consistent with the direction of current flow shown in Fig. 2?"

Response:
We have revised Section 3 (Modeling of DC Side Dynamics) to:

• Introduce each equation with a clear explanation of its physical significance.
• Verify and correct the signs in Figure 2 to ensure consistency with the current flow directions in Eqn. (3).

Changes in Manuscript: Section 3, Pages 5

The DC bus voltage is regulated using a droop control strategy implemented within the battery storage system. The relationship between the battery current, , and the DC bus voltage deviation is given by:

where  is the gain of the proportional-integral (PI) controller,  is the reference voltage, and  is the DC bus voltage. The term  represents a low-pass filter (LPF) that smooths voltage fluctuations. The power balance equation at the DC bus must account for the total current contributions from the WTIG inverters and load inverters. The total current injected into the DC bus is:

Here,  represents the equivalent capacitance of the DC bus,  and  denote the line resistance and inductance, respectively, and , , and  are the voltages of the connected buses. The DC network current distribution is determined by the WTIG inverters () and load inverters (). The sum of generated and consumed currents follows:

In the left-hand side represents the net current injected into the DC bus, while the righthand side expresses the dynamic response of the DC bus voltages. The equation is verified for sign consistency with the current directions shown in Figure 2.

Comment 4:

"What is the current and its direction in the unmarked branch in the Battery block, Fig. 2?"

Response:
The unmarked current in the battery block corresponds to the charging/discharging current of the battery storage system. We have updated Figure 2 to explicitly label this current and its direction.

Changes in Manuscript: Figure 2, Page 5

Figure 2. The DC side dynamical model

Comment 5:

"Not all symbols used in Fig. 2 are defined. In fact, not all symbols used in the manuscript are defined."

Response:
We have:

• Provided a comprehensive list of symbols for clarity.
• Ensured all symbols used in figures and equations are explicitly defined in the text.

Changes in Manuscript: Added Tables, Updated Figures, Pages 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 19

Table 1. Commonly Used Abbreviations

Table 2. Definitions of Key Symbols

Comment 6:

"Where is 'k_b' used in Fig. 2? Also, are 'k_b', Eqn. (1), and 'K_b' used in the following text the same?"

Response:

K_b is the gain of the proportional-integral (PI) controller and is consistent throughout the text. It has been standardized in all equations, figures, and explanations. Figure 2 has been updated to explicitly label K_b in the storage converter control loop.

Changes in Manuscript: Standardized notation throughout the text

Comment 7:

"Page 5. 'Voltage regulation is maintained through a battery...' Section 4.1: 'The DC-DC system comprises a secondary battery bank...' Are there two different batteries?"

Response:
This was a misleading description—there is only one battery bank. We have reworded the text to clarify that the same battery system is used for voltage regulation and energy storage.

Changes in Manuscript: Sections 4 and 4.1, Page 7

The storage converter is modeled as a current source , regulating the real power for the bank of batteries and DC bus. The DC-DC system comprises a battery energy storage system defined by its Thevenin voltage  and resistance .

Comment 8:

"Page 6. 'A voltage regulator for the DC side...' Are both sides not DC?"

Response:
You are correct. The wording was unclear. We have revised the sentence to explicitly describe the role of the voltage regulator in DC voltage stabilization.

Changes in Manuscript: Section 4.1, Page 8

Figure 4 shows the control strategy for the DC-DC converter. The bidirectional DC-DC converter, modeled by IGBT switches, is managed by a PWM current controller. A voltage regulator for the DC bus voltage based on droop control is used in this approach.

Comment 9:

"Why is the voltage droop control strategy employed not given in the manuscript? Where is the 'slope of the voltage droop characteristic' shown in Fig. 4?"

Response:
We have:

• Added a detailed explanation of the voltage droop control strategy in Section 4.1.
• Modified Figure 4 to explicitly show the slope of the droop characteristic.

Changes in Manuscript: Section 4.1 and Figure 4, Pages 8, 9

The DC bus voltage loop controls the charging and discharging phases. When the DC bus voltage is between the reference values  and , the signal  is zero, and no power exchange occurs. If the voltage exceeds ,  becomes negative, recharging the storage system using power from the WTIG. Conversely, if the voltage drops below ,  becomes positive, discharging the battery bank to supply power. The DC voltage regulator in the storage unit (Figure 4) governs , with the reference current  calculated as:

To ensure the stable operation of the DC distribution network, a voltage droop control strategy is employed for regulating the DC bus voltage. The proposed control strategy ensures stable operation of the inverter-based wind energy system in a stand-alone DC distribution network. The system consists of three main control mechanisms:

1. DC Bus Voltage Regulation: Maintains voltage stability by dynamically adjusting power exchange between the battery storage and the network.
2. Wind Turbine Power Control: Ensures optimal power extraction from wind turbines while maintaining operational limits.
3. Inverter-Based Load Management: Balances power delivery to unbalanced AC loads to maintain a stable and reliable power supply.

This strategy eliminates the need for communication links between converters by adjusting power flow based on local voltage measurements. The droop control method introduces a controlled voltage deviation proportional to the output current. The voltage droop control strategy is employed to regulate the DC bus voltage without requiring communication links between power sources. The relationship between the DC voltage deviation and the current injected by the storage system is represented as:

where:

•  is the measured DC bus voltage,
• is the reference voltage for the storage system,
• is the storage converter’s output current, and
• is the droop coefficient, defining the slope of the voltage-current characteristic.

The slope of the voltage droop characteristic, m, determines how much the DC voltage decreases with increasing load current. A higher droop coefficient results in a more significant voltage deviation, which enhances system stability but may lead to increased voltage variations under dynamic load conditions. Figure 5 illustrates the voltage droop characteristic implemented in the system. The voltage of the battery terminal  is constrained by

Figure 5. Voltage droop characteristic with slope 1/kb , illustrating the impact of current variations on DC bus voltage.

This method allows the battery energy storage system to actively regulate the DC bus voltage by adjusting its charging and discharging rates dynamically.

The inverter control system ensures power balance among unbalanced AC loads by adjusting output voltage and current dynamically. A phase-locked loop (PLL) is used to synchronize the inverter output with the load demand. The control reference for each inverter is determined as:

where:

• is the reference current for phase ϕ,
• is the power demand of the load in phase ϕ, and
• is the instantaneous voltage of phase ϕ.

The inverter control logic compensates for unbalanced loads by dynamically adjusting the power supplied to each phase.

Comment 10:

"Section 5.1 is for the case of no disturbance operation, constant wind speed, and no disturbance in load. What causes the variations in Figs. 7 and 8?"

Response:
The variations in Figures 7 and 8 arise from minor system transients during steady-state operation and a change of load. This part is also added to the base case. By “no disturbances” in the simulation results section we wanted to mention there are no disturbances on the wind turbine, not the load.

Changes in Manuscript: Section 5.1, Page 13

In the first case scenario, the normal operation of the system without disturbances is considered. During this scenario, the average wind speed is constant at 8 m/s, and no disturbances are applied to the wind turbine.

Comment 11:

"Absolutely no information is provided about the unbalanced loads. What is the magnitude of the unbalance and are all the same?"

Response:
We have:

• Added a subsection in Section 2 describing the nature of the unbalanced loads.
• Specified the degree of unbalance and whether all loads have identical unbalance characteristics.

Changes in Manuscript: Section 2, subsection 2.1, Page 4

In practical applications, AC loads connected to DC distribution networks through inverters may exhibit phase imbalances. These unbalanced conditions arise due to asymmetric power demand across phases, leading to voltage fluctuations and increased system losses. To quantify unbalance, the percentage of phase current asymmetry (X%) is defined as:

where  and  are the maximum and minimum phase currents, respectively, and  is the average phase current. In this study, three different levels of unbalance are considered:

• Mild Unbalance (5–10%): Small phase deviations with minimal impact on system performance.
• Moderate Unbalance (10–20%): Noticeable phase asymmetry that affects power quality.
• Severe Unbalance (20–30%): Significant current imbalance leading to voltage fluctuations.

The inverter control strategy compensates for these unbalances to maintain stable power delivery and voltage regulation.

Comment 12:

"Statement 'wind energy utilization exceeding 90%' is based on which study?"

Response:
This statement was based on our simulation results. We have now Clarified in Section 5 that this percentage is derived from our computed power utilization efficiency.

Changes in Manuscript: Section 5.3 and Conclusion, Pages 18, 19

Wind energy utilization efficiency is a key performance metric for evaluating the effectiveness of the proposed system. The utilization rate is calculated as:

where:

• represents the total power generated by the wind turbine induction generator (WTIG).
• is the actual power delivered to the DC bus and utilized by loads or stored in the battery.

Simulation results show that under typical operating conditions, the system achieves an average wind energy utilization efficiency of 91.3%. This efficiency is due to the optimized power management strategy, which minimizes curtailment and maximizes energy extraction.

It is noteworthy that while the overall aerodynamic efficiency of wind turbines is typically below 40%, the electrical efficiency of the system, which refers to the effective conversion of generated power into usable electrical energy, exceeds 90%. We believe the reviewer is referring to electrical efficiency, and we have explicitly clarified this distinction in the revised text to ensure transparency and avoid any misunderstanding. This clarification has been incorporated into Section 5.3 (Wind Energy Utilization Analysis in Load Variation) to emphasize that we are discussing the electrical efficiency of wind power conversion, not the aerodynamic efficiency of the turbine itself.

Conclusion:

We deeply appreciate your thorough and constructive review, which has significantly strengthened our manuscript. The extensive revisions have improved the technical precision, clarity, and logical consistency of our work. We believe the revised manuscript fully addresses your concerns and is now much clearer and more rigorous.

Best regards,
Hossein Amini
The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
aminih@vt.edu

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed the concerns.

Author Response

Dear Reviewer,

We sincerely appreciate your time and effort in reviewing our revised manuscript. We are pleased to hear that our revisions have successfully addressed your concerns. Your valuable feedback has greatly improved our work's clarity and quality.

Thank you for your thoughtful review and support.

Best regards,

Hossein Amini

The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
aminih@vt.edu

Reviewer 2 Report

Comments and Suggestions for Authors

This paper is well revised and could accept in current form.

Author Response

Dear Reviewer,

We sincerely appreciate your time and effort in reviewing our revised manuscript. We are delighted to hear that you find our revisions satisfactory and that the paper is now suitable for acceptance in its current form. Your insightful feedback has been instrumental in refining the clarity and quality of our work.

Thank you for your valuable review and support.

Best regards,

Hossein Amini

The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
aminih@vt.edu

Reviewer 3 Report

Comments and Suggestions for Authors

Regretablly the revised version of the manuscript shows that the authors have made only superficial revisions with no in-depth and thorough check-up of the entire manuscript. Instead of giving very detailed comments, illustrative comments are only given as it is the function and duty of the authors to check the manuscript thoroughly and carefully before submission and not that of the reviewer.

1. It is repeatedly stated in the text that "'K_b' is the gain of the PI controller" and it is shown so in Fig. 2. However, in eqn. (2), 'k_b' is used! It was pointed out in the review of the original version of the manuscript but has not been corrected.
2. Page 7, "...where 'k_b' represents the droop gain". However, in the text, Fig. 5, and also in eqns. (6) and (8), the droop constant is shown as 'K_b'!
3. Is 'k_b' or 'K_b' the gain of the PI controller or droop gain?
4. In eqn. (2), 'I_b' is the battery current, but symbols 'I_ch', Fig. 2, and 'I_fb', Fig. 4, are no where defined clearly. How are 'I_b' and 'i_fb' related?
5. Droop Control strategy, shown in Figure 4, is stated to be one of the contributions, but it is poorly described. Where does reference current, eqn. (9) appear in Fig. 4?
6. English language also needs careful proofreading. 
7. The above comments illustrate clearly that the authors must pay proper attention to revising and proofreading the entire manuscript very carefully. 

Comments on the Quality of English Language

The manuscript need sto be proofread and edited carefully for the English language.

Just one illustartive example: Page 2, "..., Which reduces...".

Author Response

Dear Reviewer,

We sincerely appreciate your time and effort in reviewing our revised manuscript. We acknowledge your concerns and sincerely regret any remaining inconsistencies. Your detailed feedback is invaluable, and we are committed to thoroughly addressing all identified issues to ensure clarity, accuracy, and coherence throughout the manuscript.

Comments:

1. It is repeatedly stated in the text that "'K_b' is the gain of the PI controller" and it is shown so in Fig. 2. However, in eqn. (2), 'k_b' is used! It was pointed out in the review of the original version of the manuscript but has not been corrected.

2. Page 7, "...where 'k_b' represents the droop gain". However, in the text, Fig. 5, and also in eqns. (6) and (8), the droop constant is shown as 'K_b'!

1. Is 'k_b' or 'K_b' the gain of the PI controller or droop gain?

Response:

Inconsistency in Notation for ​ and ​:

• We have carefully reviewed all instances of ​ and  throughout the manuscript, equations, and figures. We acknowledge the inconsistencies in their usage.

• Correction: ​ has been consistently used as the PI controller gain, and ​ has been defined exclusively as the droop gain. All occurrences in the text, equations, and figures have been revised to reflect this distinction.

Changes in Manuscript:
Thank you for pointing out the inconsistencies in our notation for the control gains. We have carefully revised the manuscript to ensure a clear and consistent distinction between , which denotes the proportional-integral (PI) controller gain, and ​, which represents the droop gain. The following corrections have been implemented:

1. Equation (2) now explicitly defines ​ as the PI controller gain.
2. Page 7 has been corrected to refer to the droop gain as ​, maintaining consistency with Fig. 5 and Equations (6) and (8).
3. Figures 2 and 5 have been updated to correctly reflect the definitions of ​ and .

These modifications ensure clarity and eliminate any ambiguity in notation throughout the manuscript.

4. In eqn. (2), 'I_b' is the battery current, but symbols 'I_ch', Fig. 2, and 'I_fb', Fig. 4, are no where defined clearly. How are 'I_b' and 'i_fb' related?

Response:

The reviewer pointed out that the relationship between ​ (battery current), ​ (charging current in Fig. 2), and ​ (feedback current in Fig. 4) is not clearly defined.

• ​​ represents the net battery current, which includes both charging and discharging.

•  refers to the current flowing into the battery during the charging phase.
•  refers to the discharging current supplied by the battery.
• ​ is the feedback current used in the droop control loop, regulating power injection from the battery.

• The revised text explicitly states that:

where:

• For  the battery is charging, otherwise, it is discharging,
• ​ represents the current fed back into the system for regulation.

The feedback current ​ operates within predefined upper and lower limits, ensuring safe battery operation:

• ​ (Upper Limit): Restricts the maximum charging current to prevent overcharging.
• ​ (Lower Limit): Defines the discharge current threshold.

Updated Figures and Captions:

• The definitions of ​ and have been added to the text after Figure 2 and Figure 4, pages 5, 6, and 9.
• Figure 4 now includes a note explaining the role of ​ in the droop control mechanism.

By implementing these changes, we have ensured that all current variables are clearly defined and their relationships are properly described in the manuscript.

5. Droop Control strategy, shown in Figure 4, is stated to be one of the contributions, but it is poorly described. Where does reference current, eqn. (9) appear in Fig. 4?

Response:

The DC bus voltage loop regulates the transition between the charging and discharging phases. When the DC bus voltage remains within the reference values  and , the power signal  is zero, and no power is exchanged. If the voltage exceeds  ,  becomes negative, recharging the storage system with power from the WTIG. Conversely, if the voltage drops below ,  becomes positive, discharging the battery bank to provide power to the network. The DC voltage regulator in the storage unit (Figure 4) governs , where the reference current  is derived from the droop control mechanism. This current serves as the input to the PWM control stage of the bidirectional DC-DC converter, adjusting the battery charge/discharge response based on the DC bus voltage deviation.

It is noteworthy to mention that the DC voltage regulator in the storage unit (Figure 4) governs , where the reference current   is derived from the droop control mechanism. This current serves as the input to the PWM control stage of the bidirectional DC-DC converter, adjusting the battery charge/discharge response based on the DC bus voltage deviation.

Changes in Manuscript: Section 3, Pages 8, 9

6. English language also needs careful proofreading. 
7. The above comments illustrate clearly that the authors must pay proper attention to revising and proofreading the entire manuscript very carefully. 

Response:
Thank you for your valuable feedback regarding the English language and the need for thorough proofreading. We sincerely appreciate your attention to detail and have carefully revised the entire manuscript to improve clarity, coherence, and readability.

We are confident that these revisions have significantly improved the manuscript's quality and ensured that all content is clearly communicated. We appreciate your detailed review and constructive suggestions, which have greatly contributed to enhancing our work.

Conclusion:

We deeply appreciate your thorough and constructive review, which has significantly strengthened our manuscript. The extensive revisions have improved the technical precision, clarity, and logical consistency of our work. We believe the revised manuscript fully addresses your concerns and is now much clearer and more rigorous.

Best regards,
Hossein Amini
The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
aminih@vt.edu

Author Response File: Author Response.pdf