Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Title:

1. Please replace ADRC with Active Disturbance Rejection Control

Abstract:

1. Please remove the format bold on " Enhancing"
2. What is an ultra weak grid? please explain this expression ultra weak grid.
3. In the context, please add a transition between the two sentences
4. Please explain the main features of the proposed control strategy:
5. In line 16-17, the authors say:" This paper propose... based virtual inertia method"

This sentence can be reworded to outline the main features (reactive power support and virtual inertia support) of the proposed strategy.

6. What are GFM and ADRC? Please these terms before their first utilization
7. Validation: Please discuss the investigated system: voltage and power rating, converter topology and implemented modulation, operating conditions, etc.
8. What are the relevant outcomes of this work?

Keywords:

1. The terms short-circuit ratio, Linear Extended State Observer, Grid Connected Converter do not appear in the abstract

1.    Introduction

1. Context (line 36 – 37, in P1)
   1. Please explain what is a weak grid?
2. Why do you introduce the limitations of PI controller here? (line 41 – 42, in P1)
   1. These sentences should not be here.
3. What is the link between the first and second paragraphs?
   1. Please add transition between these sentences
4. In line 53-54, the authors said “VSG based methods typically focus on… during fault”
5. please add references for these statements
6. What is the link between paragraph 2 (in line 45-56) and paragraph 3(in line 57-73)
   1. Please add transition between these paragraphs
   2. What is grid following mode? please explain this concept
7. Contributions of this work (line 58 – 73, in P2):
   1. In line 94-95, what conventional methods? Please enumerate at least two of these methods
   2. The contributions (2 and 3) are included in (1):
      1. Why separate them?
   3. This text is unhelpful at this point. For easier reading, the authors could move it to the section “simulation and HIL results.
8. In line 110-113, p3, please move these sentences above table 1.
9. Please add the plan of the paper

2.    Structure of the proposed controller

1. What is BSM? Please define this expression before its first utilization
2. In Figure 1, what is the topology of the investigated voltage source converter?
3. What are symmetrical and asymmetrical fault? Please explain these expressions
4. In this section, why do you need the subsection II-A (sensor data integrity Attacks)
5. Please add references for Figure 3.

2.1.VSG based GFM Control Strategy

1. In Figure 3, how do you obtain the synchronization angle θ?
   1. Please add the PLL block in this figure
2. What is the link between the first (lines 162-169) and second (lines 170-181) paragraphs?
   1. Please add transition between these sentences
3. Equations 1 and 2
   1. Please align these equations
   2. Add references for these equations
   3. How do you compute the coefficients and ? Please provide their expressions or add references showing how to compute them.
4. Please add references for Figure 4.

2.4. Mathematical modelling of Virtual Capacitor based Virtual Inertia Control 

1. Please normalize equations
   1. Equations 5-7 are not aligned
   2. Please check numbering of equation 7
   3. Certain terms are formatted in italic while the others are normal.
2. Section 2.4 appear twice in the document. Please correct it.
   1. Mathematical modelling of Virtual Capacitor based Virtual Inertia Control
   2. Modelling of ESO for DC Bus voltage control

2.4. Modelling of ESO for DC Bus voltage Control 

1. What are ESO, LESO, LSEF and VIC? Please define these expressions before their first utilization
2. Equation 9 is useless. Please remove it
3. In line 253, please remove “&”
4. Equations 10-15, 21-28 are not properly aligned. Please align these equations
5. Equation 16 can be simplified. Please put it into a more usable form
6. Line 307-309 are useless. Please remove them
7. Equations 19 and 20 are exactly the same. Please remove equation 19
8. Equation 27 is not properly aligned. Please check it
9. Table 2 is not properly aligned. Please check it
10. Result and Discussions:
    1. In table 2, what is the short-circuit ratio of the investigated system?
    2. This section is not numbered. Please check it
    3. Investigated system
11. What performance indices have been considered for comparison purposes? Why have you selected these indices?
    1. Figure 10:
       1. Please reduce the simulation time to increase the resolution of the plots
       2. The subplots within this figure are not numbered
       3. The legend in the converter currents do not match Figure 1
       4. During the fault, why the converter output currents are unbalanced? Please explain these results.
       5. Which grid code sets the PCC voltage limit to 1.1pu? please provide reference
    2. Figures 11-13: grid powers or converter output powers?
       1. Please clarify what powers are shown
       2. They are not properly aligned with their respective titles
       3. Please increases the resolution of these plots
          • The y-axis can be scaled in kW, kVAR and kA
       4. Add y-labels on Figure 12-14
       5. Figures 12-13 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents. This will further validate the results shown in Figure 11.
       6. What FRT standards? What are the limits imposed by these standards?
    3. Figures 14-17:
       1. Why do you need background colors in Figure 14? Please remove them for more clarity.
       2. Add y-labels on Figure 12-14
       3. Please increases the resolution of these plots
       4. They are not properly aligned with their respective titles
       5. Figures 16-17 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents. This will further validate the results shown in Figure 15
    4. Figures 18-21:
       1. In Figure 18, why the converters output currents are unbalanced during the fault? Please explain the results.
       2. Add y-labels on Figure 20-21
       3. Please increases the resolution of these plots
       4. They are not properly aligned with their respective titles
       5. Figures 20-21 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents.
    5. Figures 22-26:
       1. Add y-labels on Figure 23-25
       2. Please increases the resolution of these plots
       3. They are not properly aligned with their respective titles
       4. Figures 24-25 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents.
    6. Figures 27 - 28:
       1. Please annotate components in Figure 27

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The manuscript would benefit from improvements in English language quality, especially regarding grammar, paragraph structure within individual sections, and logical transitions between sections.

Author Response

REVIEWER 1 COMMENTS

Comment 1: Title:

1. Please replace ADRC with Active Disturbance Rejection Control

Response 1:

Thank you for your valuable comments and ADRC is replaced with Active Disturbance Rejection Control in title.

This information has been added to the revised manuscript on line 2 of page 1 in yellow highlight.

Comment 2: Abstract:

1. Please remove the format bold on " Enhancing"

Response 2:

Thank you for your valuable comments and bold is removed.

This information has been added to the revised manuscript on line 14 of page 1 in yellow highlight.

Comment 3: What is an ultra-weak grid? please explain this expression ultra weak grid.

Response 3:

Thank you for your valuable comments and ultra weak grid in power system is characterised by extremely low Short Circuit Ratio typically less than 2 and higher grid impedance. The X/R ratio in this paper is considered to be as 1 where the grids ability to maintain voltage and frequency stability is severely compromised posing major challenges for Inverter Based Resources. Ultra weak grids are highly sensitive to disturbances.

This information has been added to the revised manuscript on line (16-21) of page 1 in yellow highlight.

Comment 4. In the context, please add a transition between the two sentences

Response 4:

Thank you for your valuable comments and transition has been added between each sentences in abstract.

This information has been added to the revised manuscript on line (14-30) of page 1 in yellow highlight.

  Comment 5. Please explain the main features of the proposed control strategy:

Response 5:

Thank you for your valuable comments and the proposed approach integrates voltage feedforward reactive power support using ADRC to regulate q axis current and better DC bus voltage support is provided by virtual capacitor based virtual inertia method by regulating the d axis current using ADRC comparing with PI controller during symmetrical and asymmetrical fault and real time validation is done using OP4610.

This information has been added to the revised manuscript on line (24-30) of page 1 in yellow highlight.

Comment 6: In line 16-17, the authors say:" This paper propose... based virtual inertia method"

This sentence can be reworded to outline the main features (reactive power support and virtual inertia support) of the proposed strategy.

Response 6:

Thank you for your valuable comments and the proposed approach integrates voltage feedforward reactive power support and a virtual capacitor-based virtual inertia method to enhance fault ride-through (FRT) capability and DC link voltage stability.

This information has been added to the revised manuscript on line (25-28) of page 1 in yellow highlight.

Comment 7: What are GFM and ADRC? Please these terms before their first utilization

Response 7:

Thank you for your valuable comments and In Grid Forming Mode of operation the converter acts as voltage source and helps to maintain the voltage stability.

This information has been added to the revised manuscript on line (23-24) of page 1 in yellow highlight.

 

Thank you for your valuable comments and Active Disturbance Rejection Control is a robust, model free method used for rapid rejection of disturbances.

This information has been added to the revised manuscript on line (26-27) of page 1 in yellow highlight.

Comment 8: Validation: Please discuss the investigated system: voltage and power rating, converter topology and implemented modulation, operating conditions, etc.

Response 8:

Thank you for your valuable comments and A 415 V, 110 KVA , Three phase two pulse, sinusoidal Pulse Width Modulation and ultra weak grid condition where X/R=1 is the system considered for study. Under normal operating condition converter operates in GFM mode as it remains stable during ultra weak grid condition so GFM mode of operation is preferred during normal operating condition. When symmetrical or asymmetrical fault occurs mode of operation of converter changes to GFL as it controls current during fault for safe operation and after clearance of fault the converter reverts back to GFM mode for normal operation.

This information has been added to the revised manuscript on line (18-21) of page 1 in yellow highlight.

Comment 9: What are the relevant outcomes of this work?

Response 9:

Thank you for your valuable comments and the relevant outcomes of this work is to Enhance fault ride-through (FRT) capability and DC link voltage stability.

This information has been added to the revised manuscript on line (27-28) of page 1 in yellow highlight.

Comment 10: Keywords:

1. The terms short-circuit ratio, Linear Extended State Observer, Grid Connected Converter do not appear in the abstract

Response 10:

 Thank you for your valuable comments and I have included short-circuit ratio, Grid Connected Converter in the abstract and removed  Linear Extended State Observer

This information has been added to the revised manuscript on line (31-33) of page 1 in yellow highlight.

Comment 11: Introduction

1. Context (line 36 – 37, in P1)
1. Please explain what is a weak grid?

Response 11

Thank you for your valuable comment and a weak grid has low short circuit strength and high grid impedance, which makes less stable and more prone to voltage and frequency fluctuations especially during fault or while connected to a power electronic based converters.

This information has been added to the revised manuscript on line (16-17) of page 1 in yellow highlight.

Comment 12: (line 41 – 42, in P1)

1. These sentences should not be here.

Response 12:

Thank you for your valuable comment and I have removed that line

Comment 13: What is the link between the first and second paragraphs?

1. Please add transition between these sentences

Response 13:

Thank you for your valuable comments and added transition between these sentences

This information has been added to the revised manuscript on line (39-40) (45-46) of page 1 in yellow highlight.

Comment 14: In line 53-54, the authors said “VSG based methods typically focus on… during fault”

please add references for these statements

Response 14:

Thank you for your valuable comments and Added references [12-14]

This information has been added to the revised manuscript on line (53- 56) of page 2 in yellow highlight.

Comment 15: What is the link between paragraph 2 (in line 45-56) and paragraph 3(in line 57-73)

Please add transition between these paragraphs

Response 15:

Thank you for your valuable comments and added transition between these paragraphs

In addition to synthetic inertia based approaches like VSG another crucial aspect for improving system resilience under weak grid conditions is effective fault current limitation, particularly through Grid Following Mode operation. In GFL mode, converters synchronize to the grid through Phase Locked Loop (PLL) and regulate d-q axis currents to control active and reactive power outputs rather than directly controlling voltage or frequency. This mode is essential for safely limiting fault currents during grid disturbances especially under weak grid conditions.

This information has been added to the revised manuscript on line (59-65) of page 2 in yellow highlight.

Comment 16: What is grid following mode? please explain this concept

Response 16:

Thank you for your valuable comments and in GFL mode, converters synchronize to the grid through Phase Locked Loop (PLL) and regulate d-q axis currents to control active and reactive power outputs rather than directly controlling voltage or frequency. This mode is essential for safely limiting fault currents during grid disturbances especially under weak grid conditions.

This information has been added to the revised manuscript on line (61-65) of page 2 in yellow highlight.

Comment 17: Contributions of this work (line 58 – 73, in P2):

In line 94-95, what conventional methods? Please enumerate at least two of these methods

Response 17:

Thank you for your valuable comments and other methods such as virtual sequence control, limiters and saturators modify the current response during faults and cap excessive current [27-29] but often provide limited voltage support. Cross-Forming techniques offer quick fault current limitation and grid synchronization but suffers from inherent stability issues under severe faults [30]. These methods, while reducing fault current often introduce additional complexity and frequently neglect DC link voltage regulation. Their inability to sustain voltage recovery during severe faults limits their practical deployment, necessitating improved and coordinated control strategies. Conventional control methods such as Proportional Integral (PI) control and Model Predictive Control (MPC) have been widely used for voltage and current regulation in GCC. PI controllers are easy to implement but suffer from poor dynamic performance under weak grid condition and lack robustness during disturbances. MPC provides improved transient response and predictive control but is computationally intensive making it unsuitable for quick fault mitigation and real time applications in ultra weak grids [34].

This information has been added to the revised manuscript on line (74-87) of page 2 in yellow highlight.

Comment 18: The contributions (2 and 3) are included in (1):

1. Why separate them?

Response 18:

Thank you for your valuable comments and combined as one by removing point numbers

Unlike conventional methods, the proposed system enables the GCC to operate in both GFM and GFL modes under ultra weak grid conditions. During normal operation, the GCC operates in VSG based GFM mode ensuring stable voltage regulation. Upon fault detection, the disturbance detector shifts GCC to GFL mode where the ADRC based reactive power control loop regulates the quadrature axis currents to limit fault currents. Simultaneously, virtual capacitor method using ADRC, facilitates active power transfer stabilizing the DC link voltage through rapid disturbance rejection capabilities. Post-fault, the system seamlessly reverts to GFM mode, improving resilience under varying conditions. ADRC ensures rapid disturbance rejection and robustness. This approach enhances grid reliability, supports weak grid integration, improves FRT capability and ensures consistent operation. It promotes resilient renewable energy adoption and is adaptable to real world scenarios.

 

This information has been added to the revised manuscript on line (107-114) of page 3 in yellow highlight.

Comment 19: This text is unhelpful at this point. For easier reading, the authors could move it to the section “simulation and HIL results.

Response 19: Thank you for your valuable comments and i have removed those sentences.

Comment 20: In line 110-113, p3, please move these sentences above table 1.

Response 20:

Thank you for your valuable comments and moved sentences above table 1.

To further highlight the advantages of the proposed approach, a detailed comparison with existing methods is presented in Table.1. The comparison focuses on various aspects such as DC link voltage stability enhancements, FRT capability improvement, disturbance rejection and control transition handling.

 

This information has been added to the revised manuscript on line (115-118) of page 3 in yellow highlight.

Comment 21: Please add the plan of the paper

Response 21:

Thank you for your valuable comments and added the plan of the paper

The structure of the paper is organized as follows, where, Section 2 describes the system architecture and proposed control strategy, including the mathematical formulation for the ADRC based approach. Section 3 presents the simulation and real time results obtained from RT-LAB which demonstrate the effectiveness of the proposed method under various fault conditions. A detailed comparison with existing methods focusing on aspects such as FRT capability and DC link voltage stability is also provided. Section 4 concludes the paper and outlines the potential areas for future research.

This information has been added to the revised manuscript on line (119-126) of page 3 in yellow highlight.

Comment 22:

2. Structure of the proposed controller

1. What is BSM? Please define this expression before its first utilization

Response 22:

Thank you for your valuable comments and the Battery Management system (BMS) ensures DC link voltage stability at its nominal voltage by managing battery charging and discharging. If the PV power generation is insufficient, BMS discharges battery and if PV power is excessive, the battery charges. The primary direction of power flow in this study is considered to be from DC microgrid to AC grid.

 

This information has been added to the revised manuscript on line (137-140) of page 4 in yellow highlight.

Comment 23: In Figure 1, what is the topology of the investigated voltage source converter?

Response 23:

Thank you for your valuable comments and three phase, two level voltage source converter connected to grid through an LCL filter. The converter uses six IGBT based switches and operates under SPWM.

This information has been added to the revised manuscript on line 130-131 of page 3 in yellow highlight.

Comment 24: What are symmetrical and asymmetrical fault? Please explain these expressions

Response 24:

Thank you for your valuable comments and in contrast asymmetrical L-G fault which is considered for study in this paper affects the faulted phase and causes imbalance to the system. While symmetrical faults are less common but more severe, asymmetrical faults occur more frequently in real world scenarios both causing voltage instability particularly under ultra weak grid conditions.

This information has been added to the revised manuscript on line (163-168) of page 4 in yellow highlight.

Comment 25: In this section, why do you need the subsection II-A (sensor data integrity Attacks)

Response 25:

This question seems irrelevant

Comment 26: Please add references for Figure 3.

Response 26:

Thank you for your valuable comments and added Reference [40][41]

This information has been added to the revised manuscript on line 200 of page 6 in yellow highlight.

Comment 27: VSG based GFM Control Strategy

1. In Figure 3, how do you obtain the synchronization angle θ?

Response 27:

Thank you for your valuable comments and synchronization angle θ is obtained From fig 4

This information has been added to the revised manuscript on line 218 of page 7 in yellow highlight.

Comment 28: Please add the PLL block in this figure

Response 28:

Thank you for your valuable comments and in GFM mode synchronization angle θ is obtained from VSG based active power frequency control equations shown in fig 4. In GFM mode no PLL is involved and the converter acts as voltage and forms the grid regulating system voltage and frequency.

Comment 29: What is the link between the first (lines 162-169) and second (lines 170-181) paragraphs?

1. Please add transition between these sentences

Response 29:

Thank you for your valuable comments and added transition between  sentences

This information has been added to the revised manuscript on line (188-200) of page 6 in yellow highlight.

Comment 30: Equations 1 and 2

Please align these equations

Response 30:

Thank you for your valuable comments and aligned all the equations

Comment 31: Add references for these equations

Response 31:

Thank you for your valuable comments and added reference [40][41]

This information has been added to the revised manuscript on line 200 of page 6 in yellow highlight.

Comment 32: How do you compute the coefficients and ? Please provide their expressions or add references showing how to compute them.

Response 32:

Thank you for your valuable comments and the droop coefficients governing the steady state power sharing and frequency voltage regulation are critical for balancing system stability and coordinated operation. The active power frequency droop coefficient  and reactive power voltage droop coefficient  are typically based on the systems steady state response and stability margins [14,42].

This information has been added to the revised manuscript on line (213-216) of page 3 in yellow highlight.

Comment 33: Please add references for Figure 4.

Response 33:

Thank you for your valuable comments and added Reference [40][41]

This information has been added to the revised manuscript on line 200 of page 6 in yellow highlight.

Comment 34: 2.4 Mathematical modelling of Virtual Capacitor based Virtual Inertia Control 

1. Please normalize equations

Response 34:

Thank you for your valuable comments and normalized all the equations

Comment 35: Equations 5-7 are not aligned

Response 35:

Thank you for your valuable comments and aligned all the equations

Comment 36: Please check numbering of equation 7

Response 36:

Thank you for your valuable comments and changed the numbering of equation

This information has been added to the revised manuscript on page 8 in yellow highlight.

Comment 37: Certain terms are formatted in italic while the others are normal.

Response 37:

Thank you for your valuable comments and normalized all the equations

Comment 38: Section 2.4 appear twice in the document. Please correct it.

1. Mathematical modelling of Virtual Capacitor based Virtual Inertia Control
2. Modelling of ESO for DC Bus voltage control

Response  38:

Thank you for your valuable comments and changed to section

• Mathematical modelling of Virtual Capacitor based Virtual Inertia Control

2.3.2        Modelling of ESO for DC Bus voltage control

 

This information has been added to the revised manuscript on line (232,263) of page 7,8 in yellow highlight.

Comment 39: 2.4. Modelling of ESO for DC Bus voltage Control 

1. What are ESO, LESO, LSEF and VIC? Please define these expressions before their first utilization

Response 39:

Thank you for your valuable comments and ESO is the core component of ADRC which estimates both the actual state variable and total disturbances including internal and external ones in real time and provides excellent disturbance rejection without requiring an accurate system model. 

This information has been added to the revised manuscript on line (339-341) of page 11 in yellow highlight.

Response 39 :

Thank you for your valuable comments and LESO is the simplified linear form of ESO used for accurate estimation of disturbance and state reconstruction using linear observer which offers ease of tuning and computation suitable for practical application.

This information has been added to the revised manuscript on line (385-388) of page 12 in yellow highlight.

Response 39:

Thank you for your valuable comments and Linear State Error Feedback control law in conjunction with LESO generates the control inputs based on estimated state errors aiming to regulate system outputs while compensating for disturbances observed by the observer.

This information has been added to the revised manuscript on line (398-400) of page 12 in yellow highlight.

Response 39:

Thank you for your valuable comments and in DC microgrid there is no rotating rotor or special energy storage system to provide additional transient compensation power during faults which is realized by virtual capacitor virtual inertia strategy to address this challenge by simulating the dynamic behaviour of actual capacitor to absorb sudden power fluctuations. It enhance the DC bus voltage stability by mimicking physical inertia and damping and thereby improves transient performance under disturbances.

This information has been added to the revised manuscript on line (233-236) of page 7 in yellow highlight.

Comment 40: Equation 9 is useless. Please remove it

Response 40

Thank you for your valuable comments and removed that equation

Comment 41: In line 253, please remove “&”

Response 41

Thank you for your valuable comments and removed “&”

Comment 42: Equations 10-15, 21-28 are not properly aligned. Please align these equations

Response 42:

Thank you for your valuable comments and A\aligned all the equations

Comment 43: Equation 16 can be simplified. Please put it into a more usable form

Response 43:

 Thank you for your valuable comments and equation 15 is written in general state space form as . Where X represents the system state vector and A is the system matrix and U is the control or input vector and B is the input matrix.

Comment 44: Line 307-309 are useless. Please remove them

Response 44:

This question seems irrelevant

Comment 45: Equations 19 and 20 are exactly the same. Please remove equation 19

Response 45:

Thank you for your valuable comments and removed those equations

Comment 46: Equation 27 is not properly aligned. Please check it

Response 46:

Thank you for your valuable comments and aligned those equation

Comment 47: Table 2 is not properly aligned. Please check it

Response 47:

Thank you for your valuable comments and aligned the Table 2

Comment 48: Result and Discussions:

1. In table 2, what is the short-circuit ratio of the investigated system?

Response 48:

Thank you for your valuable comments and included the SCR =0.5

This information has been added to the revised manuscript in Table 2 of page 14 in yellow highlight

Comment 49: This section is not numbered. Please check it

Response 49:

Thank you for your valuable comments and numbered as 3. Results and Discussion

This information has been added to the revised manuscript on line 484 of page 14 in yellow highlight

Comment 50: Investigated system

Response 50:

Thank you for your valuable comments and a 415 V, 110 KVA , Three phase two pulse, sinusoidal Pulse Width Modulation and ultra weak grid condition where X/R=1 is the system considered for study.

This information has been already added to the revised manuscript on line 18-19 of page 1 in yellow highlight.

Comment 51:

What performance indices have been considered for comparison purposes? Why have you selected these indices?

Response 51:

Thank you for your valuable comments and Current crest factor reflects the severity of peak currents relative to their RMS value. Excessive current peaks during faults under ultra weak grid condition can over stress the converter switches and filter components. Lower CFC observed in GFL mode shows enhanced current regulation and smoother FRT performance. Mean absolute voltage error quantifies the average deviation of voltage and current from their references directly indicating the controllers steady state accuracy. ADRC consistently achieves lower MAE for current and voltage regulation during GFL operation enhancing system stability and reducing current overshoots compared to PI. ITAE captures both the magnitude and duration of voltage and current deviations providing insights to the transient response and recovery time post fault. Lower ITAE value during GFM to GFL mode switching highlights faster stabilization of system voltage and currents ensuring rapid system recovery. Quantifying internal converter power loss reflects overall operational efficiency. Switching to GFL mode shows reduced power loss indicating higher efficiency. Phase imbalance is a critical power quality metric especially under ultra weak grid condition and faults where, symmetrical operation often deteriorates. ADRC significantly reduces voltage and current imbalances demonstrating enhanced ability to maintain symmetrical operation even during mode transitions. This multidimensional assessment frameworks confirm the superiority of ADRC based control and strategic GFM to GFL switching in enhancing FRT capability, maintaining current limits and preserving voltage symmetry under ultra weak grids and fault conditions.

A set of critical performance indices were selected to rigorously compare the effectiveness of ADRC along with mode transition from GFM to GFL particularly under ultra weak grid and severe symmetrical and asymmetrical fault scenarios. These indices provide a comprehensive evaluation of dynamic performance, power quality and system reliability.

 

This information has been added to the revised manuscript on line(684-701) of page 21 in yellow highlight

Comment 52:

Figure 10:

1.Please reduce the simulation time to increase the resolution of the plots

Response 52:

Thank you for your valuable comments and in GFM mode, i gave disturbance between 0.1-0.3 Sec acting in GFL mode and 0.3-0.5 sec GFM mode, atleast i needed this much run time of simulation to observe the transition. But effort has been made to increase the resolution of figure 10.

Comment 53:

2.The subplots within this figure are not numbered

Response 53:

Thank you for your valuable comments and two input scope is used and both PCC voltage and converter currents are taken as single screen shot output. Hence single numbering and general naming of figure has been done.

Comment 54:

3.The legend in the converter currents do not match Figure 1

Response 54:

Thank you for your valuable comments and corrected the legend in the converter currents.

This information has been added to the revised manuscript in pages 15,17,18,19 from figures 10,13,16,19.

Comment 55:

4. During the fault, why the converter output currents are unbalanced? Please explain these results.

Response 55:

Thank you for your valuable comments and in ultra weak grid conditions, symmetrical faults cause distorted and unbalanced current response due to the converter operation in GFM mode because the converter lacks sufficient grid support to enforce balanced voltage regulation.

This information has been added to the revised manuscript on line (516-519) of page 15 in yellow highlight.

Comment 56:

5.Which grid code sets the PCC voltage limit to 1.1pu? please provide reference

Response 56:

Thank you for your valuable comments and IEEE 1547-2018 specifies PCC voltage limits between 0.9-1.1 p.u for a certain duration of time and mandate the converter current to remain within the safe threshold to avoid hardware damage.

This information has been added to the revised manuscript on line (522-525) of page 15 in yellow highlight.

Comment 57:

6.Figures 11-13: grid powers or converter output powers?

1.Please clarify what powers are shown

Response 57:

Thank you for your valuable comments and Power measured at PCC

This information has been added to the revised manuscript in fig 11 and 14 of page 16 and 17 in yellow highlight

Comment 58:

They are not properly aligned with their respective titles

Response 58:

Thank you for your valuable comments and Corrected and aligned with their respective titles

This information has been added to the revised manuscript in fig 11 and 14 of page 16 and 17 in yellow highlight

Comment 59:

Please increases the resolution of these plots

Response 59:

Thank you for your valuable comments and Increased the resolution of all the plots

This information has been added to the revised manuscript in fig 11.12,13 of page 16 and 17 in yellow highlight

Comment 60:

The y-axis can be scaled in kW, kVAR and kA

Response 60:

Thank you for your valuable comments and scaling has been changed in p.u commonly

This information has been added to the revised manuscript in fig 11.12,13 of page 16 and 17 in yellow highlight

Comment 61:

 

Response 61:

Thank you for your valuable comments and added y-labels on Figure 12-14

This information has been added to the revised manuscript fig 12,13,14 of page 16 and 17 in yellow highlight.

Comment 62:

Figures 12-13 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents. This will further validate the results shown in Figure 11.

Response 62:

Thank you for your valuable comments and d-axis and q-axis currents are shown in a single graph

This information has been added to the revised manuscript in fig 12 and 15 of page 18 in yellow highlight.

Comment 63:

What FRT standards? What are the limits imposed by these standards?

Response 63:

Thank you for your valuable comments and according to FRT standard the converter must remain connected to the system during voltage disturbances for a short duration of time and support grid stability without disconnecting. Most of the grid codes specify, PCC voltage limits to be under 0.9 to 1.1 p.u which is +/-10% of nominal voltage . IEEE 1547-2018 specifies PCC voltage limits between 0.9-1.1 p.u for a certain duration of time.

This information has been added to the revised manuscript on line 551-553 of page 16 in yellow highlight.

Comment 64:

Figures 14-17:

Why do you need background colors in Figure 14? Please remove them for more clarity.

Response 64:

Thank you for your valuable comments and inorder to differentiate between GFM and GFL modes of operation I have used different colours to differentiate as per IEEE reference paper. As per your suggestion I have removed the background colour.

This information has been added to the revised manuscript on fig 13 now in page 17.

Comment 65: Please increases the resolution of these plots

Response 65:

Thank you for your valuable comments and increased the resolution of these plots

This information has been added to the revised manuscript on fig 13-15 of page 17 and 18 in yellow highlight.

Comment 66: They are not properly aligned with their respective titles

Response 66:

Thank you for your valuable comments and properly aligned with their respective titles now

This information has been added to the revised manuscript on on fig 13-15 of page 17 and 18 in yellow highlight.

Comment 67: Figures 16-17 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents. This will further validate the results shown in Figure 15

Response 67:

Thank you for your valuable comments an  d-axis and q-axis currents are shown in a single graph

This information has been added to the revised manuscript in fig 15 of page 17 in yellow highlight.

Comment 68: Figures 18-21:

In Figure 18, why the converters output currents are unbalanced during the fault? Please explain the results.

Response 68:

Thank you for your valuable comments and the unbalanced converter output currents are due to the asymmetrical nature of L-G fault. The ultra weak grid condition combined to GFM operation during such faults limits the ability to maintain symmetrical conditions.

This information has been added to the revised manuscript on line 611-616 of page 18 in yellow highlight.

Comment 69: Add y-labels on Figure 20-21

Response 69:

Thank you for your valuable comments and added y-labels to fig 17 and18 now

This information has been added to the revised manuscript of fig 17 and 18 in page 19 in yellow highlight.

Comment 70: Please increases the resolution of these plots

Response 70:

Thank you for your valuable comments and increased the resolution of these plots

This information has been added to the revised manuscript fig 16,17,18 in page 18,19 in yellow highlight.

Comment 71: They are not properly aligned with their respective titles

Response 71:

Thank you for your valuable comments and properly aligned with their respective titles now

This information has been added to the revised manuscript fig 16,17,18 in page 18,19 in yellow highlight

Comment 72: Figures 20-21 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents.

Response 72:

Thank you for your valuable comments and d-axis and q-axis currents are shown in a single graph

This information has been added to the revised manuscript of fig 18 in page 19 in yellow highlight.

Comment 73: Figures 22-26:

Add y-labels on Figure 23-25

Response 73:

Thank you for your valuable comments and added y-labels to all figures

This information has been added to the revised manuscript of fig 19,20,21 of page 19,20 in yellow highlight.

Comment 74: Please increases the resolution of these plots

  Response 74:

Thank you for your valuable comments and increased the resolution of these plots

This information has been added to the revised manuscript of fig 19,20,21 of page 19,20 in yellow highlight

Comment 75: They are not properly aligned with their respective titles

Response 75:

Thank you for your valuable comments and properly aligned with their respective titles

This information has been added to the revised manuscript of fig 19,20,21 of page 19,20 in yellow highlight.

Comment 76: Figures 24-25 can be grouped within one figure to illustrate the behaviors of the d-axis and q-axis currents.

Response 76:

Thank you for your valuable comments and d-axis and q-axis currents are shown in a single graph in fig 21 now

This information has been added to the revised manuscript on fig 21 of page 20 in yellow highlight.

Comment 77: Figures 27 - 28:

Please annotate components in Figure 27

Response 77:

Thank you for your valuable comments and Figure 30 now is already annotated in the legend describing each components.

This information has been added to the revised manuscript in fig 30 of page 26 in yellow highlight.

Reviewer 2 Report

Comments and Suggestions for Authors

The GFM-GFL mode switching proposed in this paper, combined with ADRC and virtual inertia control strategy, has significant innovation and practical value in fault recovery of ultra weak power grids. At the same time, not only was the performance under symmetric/asymmetric faults verified through MATLAB simulation, but real-time hardware in the loop testing was also conducted using OPAL-RT, resulting in good consistency and improving the credibility of the conclusions. If we can further optimize the depth of theoretical analysis, coverage of experimental conditions, and standardization of expression, it will have greater academic influence and engineering reference value. A few small suggestions:
1) Table 1 compares the strategies proposed in this paper with methods such as VSG and virtual impedance in the literature, highlighting the advantages of ADRC+VCVI in terms of mode switching, current limiting, and DC voltage stability. However, it can further supplement the comparison with emerging control methods in recent years, such as model predictive control and adaptive control.
2) Add comparative experiments under different X/R ratios (such as X/R=5, 10) to verify the adaptability of the strategy in weaker power grids.
3) Test the system response under extreme operating conditions (such as continuous faults, multiple inverters in parallel) and evaluate the robustness of the strategy.

Author Response

REVIEWER 2 COMMENTS

Comment 1: The GFM-GFL mode switching proposed in this paper, combined with ADRC and virtual inertia control strategy, has significant innovation and practical value in fault recovery of ultra weak power grids. At the same time, not only was the performance under symmetric/asymmetric faults verified through MATLAB simulation, but real-time hardware in the loop testing was also conducted using OPAL-RT, resulting in good consistency and improving the credibility of the conclusions. If we can further optimize the depth of theoretical analysis, coverage of experimental conditions, and standardization of expression, it will have greater academic influence and engineering reference value.

 

A few small suggestions:
1) Table 1 compares the strategies proposed in this paper with methods such as VSG and virtual impedance in the literature, highlighting the advantages of ADRC+VCVI in terms of mode switching, current limiting, and DC voltage stability. However, it can further supplement the comparison with emerging control methods in recent years, such as model predictive control and adaptive control.

Response 1:

Thank you for your valuable comments and implementing and benchmarking the additional methods such as MPC and adaptive control technique require substantial redesign and validation efforts which falls beyond the current scope and timeline of this work. So, I have highlighted this aspect as future research work to be carried out. Specifically, I will plan to investigate how the proposed strategy works under MPC and adaptive control interms of FRT, DC bus voltage regulation and dynamic performance under grid disturbances and will compare and contrast the pros and cons of each methods.

This information has been added to the revised manuscript on line 871-873 of page 24 in blue highlight.

Comment 2: Add comparative experiments under different X/R ratios (such as X/R=5, 10) to verify the adaptability of the strategy in weaker power grids.

Response 2:

Thank you for your valuable comments and in this study X/R ratio indicates the ratio of grid reactance to resistance which indicates the grid strength. Normally, X/R ratio=5 indicates weak to moderately strong grids where reactance becomes more dominant but grid stability may still be compromised under large disturbances. According to my analysis in GFM mode (ie) before symmetrical three phase fault under X/R=5 converter produces unbalanced current waveform but during symmetrical fault after 0.1 sec in GFL mode currents are maintained properly to 1 p.u. focussing on current regulation rather than voltage regulation and again after fault in GFM mode the converter currents are unbalanced. The voltage waveform in GFM mode under X/R=5 is slightly distorted and during fault in GFL mode voltage waveform experiences severe dip which is expected under moderately strong grid condition where voltage support cannot be actively provided by the converter.

Fig.1. PCC voltage and converter currents during symmetrical fault between 0.1 to 0.3 sec for X/R=5

Fig.2. PCC voltage and converter currents during symmetrical fault between 0.1 to 0.3 sec for X/R=10

From Fig.2. X/R ratio=10 represents strong grids (ie) more inductive grid. In GFM mode (ie) before symmetrical fault under X/R=10 converter produces unbalanced current waveform but during fault after 0.1 sec in GFL mode currents are maintained properly to 1 p.u. focussing on current regulation rather than voltage regulation and again after fault in GFM mode the converter currents are unbalanced. The voltage waveform in GFM mode under X/R=10 before fault is slightly distorted and during fault in GFL mode voltage waveform experiences severe drop which is expected under strong grid condition where voltage support is not actively provided by the converter in GFL mode. A more comprehensive parametric study across broader X/R ratio and SCR variations are planned as future work to validate the proposed strategy across diverse grid conditions.

Fig.3. PCC voltage and converter currents during asymmetrical (L-G) fault between 0.1 to 0.3 sec for X/R=5

According to my analysis in GFM mode (ie) before L-G fault under X/R=5 converter produces unbalanced current waveform but during fault after 0.1 sec in GFL mode currents are maintained properly to 1 p.u. focussing on current regulation rather than voltage regulation and again after fault in GFM mode the converter currents are unbalanced. The voltage waveform in GFM mode under X/R=5 is slightly distorted and during fault in GFL mode voltage waveform is severely unbalanced which is expected under moderately strong grid condition where voltage support is not actively provided by the converter.

Fig.4. PCC voltage and converter currents during asymmetrical (L-G) fault between 0.1 to 0.3 sec for X/R=10

X/R ratio=10 represents strong grids (ie) more inductive grid which offers improved voltage stability but may introduce higher power oscillations during fault. In GFM mode (ie) before L-G fault under X/R=10 converter produces unbalanced current waveform but during fault after 0.1 sec in GFL mode currents are maintained properly to 1 p.u. focussing on current regulation rather than voltage regulation and again after fault in GFM mode the converter currents are unbalanced. The voltage waveform in GFM mode under X/R=10 is slightly distorted and during fault in GFL mode voltage waveform is severely unbalanced which is expected under strong grid condition where voltage support is not actively provided by the converter.

A more comprehensive parametric study across broader X/R ratio and SCR variations are planned as future work to validate the proposed strategy across diverse grid conditions.

These results confirm that the proposed control strategy ensures effective current limitation to 1 p. u during faults across different X/R ratios, showing its adaptability from weak to strong grids. Despite voltage distortions inherent to strong grids in GFM mode, ADRC based current control reliably maintains current regulation highlighting its robustness and suitability for enhancing FRT performance. 

This information has been added to the revised manuscript on line 765-808 of page 23-25 in blue highlight.

Comment 3: Test the system response under extreme operating conditions (such as continuous faults, multiple inverters in parallel) and evaluate the robustness of the strategy.

Response 3:

Thank you for your valuable comments and the present work has been extended to test the system response under multiple fault events, thereby examining the controller strategies capability to withstand multiple faults under ultra weak grid conditions.

Fig.5. PCC voltage and converter currents during multiple symmetrical faults between 0.1-0.3 sec and 0.5-0.7 sec.

During the time (0.1 to 0.3 sec) and (0.5 to 0.7 sec) three phase symmetrical faults are applied at the PCC. Onset of faults converter shifts to GFL mode where, PCC voltage magnitude drops to near zero. Deep voltage sag exists between (0.1 to 0.3 sec and 0.5 to 0.7 sec) and converter does not inject current beyond its rated capacity protecting the hardware. In healthy intervals, (0 to 0.1 sec,0.3 to 0.5 sec, after 0.7 sec) in GFM mode PCC voltage stabilizes, indicating proper control and also the converter currents are also balanced and sinusoidal indicating the robustness of the proposed control strategy during multiple or prolonged fault events. However, current scope is limited to single converter system and testing with parallel converter system makes the system more complex in terms of synchronization of connected converters, coordination of current control and mode transitions. Therefore, first portion of reviewers suggestion has been addressed and coordinated control with multiple parallel inverters is recognised as a direction for future research.

Fig.6. PCC voltage and converter currents during multiple asymmetrical faults between 0.1-0.3 sec and 0.5-0.7 sec.

During the time (0.1 to 0.3 sec) and (0.5 to 0.7 sec) three phase asymmetrical faults are applied at the PCC. Onset of faults converter shifts to GFL mode where, PCC voltage magnitude unbalances. Unbalanced voltages with sag exists between (0.1 to 0.3 sec and 0.5 to 0.7 sec) and converter does not inject current beyond its rated capacity protecting the hardware. In healthy intervals, (0 to 0.1 sec,0.3 to 0.5 sec, after 0.7 sec) in GFM mode PCC voltage stabilizes, indicating proper control and also the converter currents are also balanced and sinusoidal indicating the robustness of the proposed control strategy during multiple or prolonged fault events. However, current scope is limited to single converter system and testing with parallel converter system makes the system more complex in terms of synchronization of connected converters, coordination of current control and mode transitions. Therefore, first portion of reviewers suggestion has been addressed and coordinated control with multiple parallel inverters is recognised as a direction for future research.

This information has been added to the revised manuscript on line (809-826) (873-875) of page 25,26 and 27 in blue highlight.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Improved Fault Resilience of GFM-GFL converters in ultra weak grids using ADRC and virtual inertia control

Abstract:

1. Validation: Please discuss the investigated system: voltage and power rating, converter topology and implemented modulation, operating conditions, etc.
2. What are the relevant outcomes of this work?

1.     Structure of the proposed controller

1. In this section, why do you need the subsection II-A (sensor data integrity Attacks)
2. Please add references for Figure 3.

2.1.VSG based GFM Control Strategy

1. In Figure 3, how do you obtain the synchronization angle θ?
   1. Please add the PLL block in this figure
2. Equations 1 and 2
   1. Add references for these equations
   2. How do you compute the coefficients and ? Please provide their expressions or add references showing how to compute them.
3. Please add references for Figure 4.

2.3.1. Mathematical modelling of Virtual Capacitor based Virtual Inertia Control 

1. Please normalize equations
   1. Equations 5-7 are not aligned
   2. Please check numbering of equation 7 (see Page 8, lines 255-257)
   3. Certain terms are formatted in italic while the others are normal.

2.4. Modelling of ESO for DC Bus voltage Control 

1. Equations 9-24, are not properly aligned. Please align these equations
2. Please check the equations 25-26
3. Table 2 is not properly aligned. Please check it, (please check it)

Comments for author File: Comments.pdf

Author Response

Submission ID: sustainability-3713504

 

ROUND 2- REVIEWER 1 COMMENTS

Comment 1: Validation: Please discuss the investigated system: voltage and power rating, converter topology and implemented modulation, operating conditions, etc.

Response 1: Thank you for your valuable comments and A 415 V, 110 KVA , Three phase two pulse, sinusoidal Pulse Width Modulation and ultra weak grid condition where X/R=1 is the system considered for study. Under normal operating condition converter operates in GFM mode as it remains stable during ultra weak grid condition so GFM mode of operation is preferred during normal operating condition. When symmetrical or asymmetrical fault occurs mode of operation of converter changes to GFL as it controls current during fault for safe operation and after clearance of fault the converter reverts back to GFM mode for normal operation.

This information has been added to the revised manuscript on line (18-21) of page 1 in yellow highlight.

Comment 2: What are the relevant outcomes of this work?

Response 2: Thank you for your valuable comments and the relevant outcomes of this work is to Enhance Fault Ride-Through (FRT) capability and DC link voltage stability.

This information has been added to the revised manuscript on line (24-27) (29-31) of page 1 in yellow highlight.

Comment 3: Structure of the proposed controller - In this section, why do you need the subsection II-A (sensor data integrity Attacks)

Response 3: This question seems irrelevant as i haven’t used any subsection II-A (sensor data integrity Attacks). I have used only subsections such as 2.1. VSG based GFM Control Strategy, 2.2. ADRC based GFL control strategy, 2.3. Modelling of ADRC , 2.3.1. Mathematical Modelling of Virtual Capacitor based Virtual Inertia Control, 2.3.2. Modelling of ESO for DC Bus voltage control, 2.4 LCL filter model in dq reference frame, 2.4.1 Expanded State Observer for outer reactive power control loop, 2.4.2 Linear State Error Feedback Control, 2.4.3 Parameter Tuning of ADRC Controller. Only these are the subsections I have used in my manuscript under section 2.

 

Comment 4: Please add references for Figure 3.

Response 4: Thank you for your valuable comments and added Reference [40]. In Reference [40], page number 99972 Fig 4(a) is the reference to be mentioned specifically.

This information has been added to the revised manuscript on line 192 of page 6 in yellow highlight.

Comment 5: VSG based GFM Control Strategy-In Figure 3, how do you obtain the synchronization angle θ?

Response 5: Thank you for your valuable comments and synchronization angle θ is obtained From fig 4.The reference for figure 4 is given in [40][41]. In Reference [40], page number 99972 Fig 4(a) is the reference to be mentioned specifically.

This information has been added to the revised manuscript on line 221 of page 7 in yellow highlight.

Comment 6: Please add the PLL block in this figure

Response 6: Thank you for your valuable comments and in GFM mode the converter does not rely on PLL for synchronisation. Instead, synchronisation angle θ is internally generated by integrating the frequency derived from VSG based active power frequency control law equation as shown in fig 4. Since the converter in GFM mode operates as controlled voltage source it establishes and regulates the voltage magnitude and system frequency rather than tracking an external grid signal. Therefore, no PLL block is required and not added in Figure 4.

Comment 7: Equations 1 and 2 Add references for these equations

Response 7: Thank you for your valuable comments and added reference [40]. In Reference [40], page number 99972, Fig 4(a) from that reference Equations 1 and 2 can be written.

This information has been added to the revised manuscript on line 202 of page 6 in yellow highlight.

Comment 8: How do you compute the coefficients ? and ??? Please provide their expressions or add references showing how to compute them.

Response 8:  Thank you for your valuable comments and the droop coefficients governing the steady state power sharing and frequency voltage regulation are critical for balancing system stability and coordinated operation. The active power frequency droop coefficient  and reactive power voltage droop coefficient  are typically based on the systems steady state response and stability margins. They are derived from . Where,  is the maximum allowable frequency deviation,  is the expected power variation,  is permissible voltage deviation,  is rated reactive power capability. The damping coefficient D=  Where, K= and J is virtual inertia, K is system gain,  is damping ratio. These are mentioned in reference [42].

This information has been added to the revised manuscript on line (219) of page 3 in yellow highlight.

Comment 9: Please add references for Figure 4.

Response 9: Thank you for your valuable comments and added Reference [40].

This information has been added to the revised manuscript on line 202 of page 6 in yellow highlight.

Comment 10: Equations 5-7 are not aligned

Response 10: Thank you for your valuable comments and aligned all the equations

Comment 11: Please check numbering of equation 7 (see Page 8, lines 255-257)

Response 11: Thank you for your valuable comments and changed the numbering of equation

This information has been added to the revised manuscript on page 8 in yellow highlight.

Comment 12: Certain terms are formatted in italic while the others are normal.

Response 12: Thank you for your valuable comments and normalized all the equations

Comment 13:  2.4. Modelling of ESO for DC Bus voltage Control -Equations 9-24, are not properly aligned. Please align these equations

Response 13: Thank you for your valuable comments and aligned those equation

• Comment 14: Please check the equations 25-26

Response 14: Thank you for your valuable comments and both equations are correct.

• Comment 15: Table 2 is not properly aligned. Please check it, (please check it)

Response 15: Thank you for your valuable comments and aligned the Table 2

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The author has carefully revised the paper and addressed the questions I previously raised. I believe it is now ready for acceptance. Thank you for the author's work!

Author Response

Comment 1 : The author has carefully revised the paper and addressed the questions I previously raised. I believe it is now ready for acceptance. Thank you for the author's work!

Response 1 : Thank you for your valuable comment.