Introducing the Adaptive Nonlinear Input Impedance Control Approach for MPPT of Renewable Generators

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The provided manuscript has pretty good formatting. The analysis, basis of current MPPT model, the modelling and results are provided clear and in informative form.
But it it possible to consider following.
1. It is proposed to use full form of Input Impedance Control in the title because this abbreviation is not generally accepted for Input Impedance Control. At the same time I2C (or IIC) is well recognizable and widespread abbreviation for two wires communication interface. The same for Keywords (I2C approach). Leaving the current title and abbreviation will confuse readers. The possible form of abbreviation is InIC.

2. The Introduction section begins with general statements about applicability of solar panels. This part of Introduction can be appended by few paragraphs with highlighting of cases of application for autonomous power supply in places without centralized electricity. This part of application area analysis should be supported by relevant references in addition to the analysis of the details of drawbacks of existing MPPT strategies. It will help to improve your references list that is too short for this type of articles.

3. The following analysis of MPPT implementations (page 2) is good enough. It remains only to add the structure of all sections in the article after the last paragraph at the end of Introduction section to help readers.

4. Section 2 provides complete and relevant basis for next section with main results. It is possible to use word Model instead of Approach in title of section and subsection 2.2 (this is the model in pure form).

5. Current version of Conclusions section looks like a brief draft. Please extend Conclusions section with highlighting all results of the work. The Discussion section can be also added before the Conclusions. It is reasonable to provide here the summarized drawbacks of known convertors and MPPT strategies. It will help readers to understand the place of your work (in theoretical studies).

Please also consider following recommendations.
- Please improve formatting of table 1 according to requirements of MDPI template.
- The first reference for Figure 4 is in section 4 while the figure itself is in section 2.
- The italic style of figures referencing in the text not fits the MDPI template (Fig.2 - Fig.13 in the text). The same for ordinary text (lines 110-111, 480-481).
- It is reasonable to add a), b), c), and d) labels for elements of Figure 8. The same for Figures 7, 9, and 10.
- Please improve alignment of formulas (26), (39), (41), (42). Update numeration of formulas to avoid of the use (30) twice. Probably, add lines 360 and 361 as the formulas.
- Please ensure the explanation for all abbreviations before the first use (PI in abstract, DSP, DC-DC). It should be done once, there are repeated definitions in the text (MPPT).

Author Response

Response to First Reviewer:

The provided manuscript has pretty good formatting. The analysis, basis of current MPPT model, the modelling and results are provided clear and in informative form.
But it is possible to consider following.

Comment 1: It is proposed to use full form of Input Impedance Control in the title because this abbreviation is not generally accepted for Input Impedance Control. At the same time I²C (or IIC) is well recognizable and widespread abbreviation for two wires communication interface. The same for Keywords (I²C approach). Leaving the current title and abbreviation will confuse readers. The possible form of abbreviation is I²C.

Response 1: Thank you for your valuable feedback. As suggested, the abbreviation “I²C” has been replaced with the full form “Input Impedance Control” in the title and keywords to avoid confusion with the I²C communication protocol.

 

Comment 2: The Introduction section begins with general statements about applicability of solar panels. This part of Introduction can be appended by few paragraphs with highlighting of cases of application for autonomous power supply in places without centralized electricity. This part of application area analysis should be supported by relevant references in addition to the analysis of the details of drawbacks of existing MPPT strategies. It will help to improve your references list that is too short for this type of articles.

Response 2: The author appreciates the reviewer’s constructive feedback. The author has expanded the Introduction section by adding a dedicated paragraphs on the applications of renewable energy systems, particularly in off-grid and remote areas lacking centralised electricity. Additionally, the author has included more references comparing conventional MPPT methods with the proposed adaptive nonlinear I²C-MPPT approach, emphasising its advantages in robustness and dynamic performance as follows.

 

“Renewable energy systems, particularly solar photovoltaic (PV) systems, are increasingly deployed in off-grid and remote regions where centralised electricity infrastructure is unavailable or unreliable. These systems are vital for rural electrification [R1], powering telecommunication towers [R2], and supporting disaster relief operations [R3]. In such applications, energy autonomy is critical, and even minor inefficiencies in power extraction can significantly impact system reliability. For example, in remote healthcare facilities, stable power supply from PV systems ensures the operation of medical equipment, while in agricultural IoT (Internet of Thing) networks, consistent energy harvesting enables real-time monitoring of crop conditions [R4]. The effectiveness of these systems heavily depends on the ability to maximise energy extraction under rapidly changing environmental conditions, which remains a key challenge for conventional MPPT techniques.

MPPT techniques are not limited to PV systems but are also critical for optimising energy extraction from thermoelectric generators (TEGs) [R5], wind turbines [R6], piezoelectric harvesters [R7], and wave energy converters [R8]. Each of these applications requires tailored MPPT strategies due to their distinct electrical characteristics—for instance, TEGs exhibit low-voltage, high-current outputs, while wind turbines face variable torque-speed relationships. Conventional MPPT methods typically rely on voltage or current control which may fail to adapt to dynamic source impedances. However, from a fundamental perspective, MPPT aligns with the maximum power transfer theorem, where optimal energy extraction occurs when the load impedance matches the source impedance. This paper proposes a paradigm shift: instead of tracking voltage or current setpoints, the I²C-MPPT directly regulates the converter’s equivalent input impedance to match the source impedance. By treating MPPT as an impedance control problem, this approach offers a unified, physics-based solution adaptable to diverse renewable generators, overcoming the limitations of heuristic or application-specific voltage/current control methods.”

[R1] Mosetlhe, T.; Yusuff, A.; Ayodele, T.; Ogunjuyigbe, A. Sustainable Rural Electrification through Micro-Grids in Developing Nations—A Review of Recent Development. Energy Rep. 2025, 13, 1171–1177.

[R2] Kaplani, E. Design and Performance Considerations in Standalone PV Powered Telecommunication Systems. IEEE Lat. Am. Trans. 2012, 10, 1723–1729.

[R3] Saxena, A.; Aishwarya, B.; Badhoutiya, A.; Raj, V.H.; Gupta, M.; Khayoon, A.T. Designing a Resilient Microgrid for Disaster-Prone Areas Using Renewable Energy Sources. In Proceedings of the 2024 International Conference on Trends in Quantum Computing and Emerging Business Technologies; Pune, India, 2024; pp. 1–6.

[R4] Rehman, A.U.; Alamoudi, Y.; Khalid, H.M.; Morchid, A.; Muyeen, S.M.; Abdelaziz, A.Y. Smart Agriculture Technology: An Integrated Framework of Renewable Energy Resources, IoT-Based Energy Management, and Precision Robotics. Clean. Energy Syst. 2024, 9.

[R5] Yang, O.; Xie, R.; Duan, J.; Wang, J. State-of-the-Art Review of MPPT Techniques for Hybrid PV-TEG Systems: Modeling, Methodologies, and Perspectives. Glob. Energy Interconnect. 2023, 6, 567–591.

[R6] Zhang, X.; Jia, J.; Zheng, L.; Yi, W.; Zhang, Z. Maximum Power Point Tracking Algorithms for Wind Power Generation System: Review, Comparison and Analysis. Energy Sci. Eng. 2023, 11, 430–444.

[R7] Shen, J.; Xia, Y.; Xia, H. ReL-SSHI Rectifier-Based Piezoelectric Energy Harvesting Circuit with MPPT Control Technique. Microelectron. J. 2022, 121, 105379.

[R8] Zhong, W.; Zhang, M.; Zhang, J.; Liu, J.; Yu, H. Constrained MPPT Strategy for Sustainable Wave Energy Converters with Magnetic Lead Screw. Sustainability 2024, 16, 4847.

 

Comment 3: The following analysis of MPPT implementations (page 2) is good enough. It remains only to add the structure of all sections in the article after the last paragraph at the end of Introduction section to help readers.

Response 3: Thank you for the suggestion. A summary of the paper’s structure has been added at the end of the Introduction section as follows to guide the reader through the contents of the manuscript.

 

“The remainder of this paper is structured as follows: Section II introduces the Input Impedance Control model and explains its integration with renewable energy sources. Section III presents modelling and controller design, including both linear and adaptive nonlinear approaches. Section IV discusses simulation and experimental validation of the proposed method. Finally, Section V concludes the paper by summarising key findings and highlighting future research directions.”

 

Comment 4: Section 2 provides complete and relevant basis for next section with main results. It is possible to use word Model instead of Approach in title of section and subsection 2.2 (this is the model in pure form).

Response 4: We appreciate this insightful observation. The word “Approach” has been replaced with “Model” in Section II and Subsection 2.2 to more accurately reflect the content.

 

Comment 5: Current version of Conclusions section looks like a brief draft. Please extend Conclusions section with highlighting all results of the work. The Discussion section can be also added before the Conclusions. It is reasonable to provide here the summarized drawbacks of known convertors and MPPT strategies. It will help readers to understand the place of your work (in theoretical studies).

Response 5: Thank you for your recommendation. The Conclusion section has been expanded to comprehensively highlight the findings. Additionally, a section has been added to provide context on how this work compares to existing MPPT strategies and converters as follows:

 

“This paper presents a transformative approach to Maximum Power Point Tracking (MPPT) in renewable energy systems by introducing an adaptive nonlinear Input Impedance Control (I²C) strategy. Unlike conventional voltage- or current-based MPPT methods, the proposed approach formulates MPPT as an impedance matching problem based on the Maximum Power Transfer theorem. By dynamically regulating the converter’s input impedance to match the internal impedance of the source, the I²C framework establishes a fundamental shift in control strategy, applicable to a wide range of renewable generators, including photovoltaic (PV) arrays, thermoelectric generators, and wind turbines.

A key innovation of this work lies in the development of a Lyapunov-based adaptive nonlinear controller that guarantees asymptotic stability while accounting for significant system uncertainties. The proposed controller eliminates the need for heuristic tuning or offline training, distinguishing it from traditional PI and AI-based MPPT methods. Simulation and experimental validation confirm the controller’s robustness and superior performance: it achieves transient response times below 1ms and maintains zero steady-state error across varying conditions. The approach successfully withstands extreme operating scenarios, such as 33% step changes in open-circuit voltage and 25% deviations in internal resistance, without compromising tracking accuracy.

Comparative analysis with conventional PI controllers highlights the advantages of the adaptive nonlinear I²C strategy in terms of faster rise time, improved settling time, and resilience to parameter fluctuations. The experimental results, obtained from a DSP-controlled prototype, further validate the real-time feasibility and practical applicability of the proposed control strategy.

In addition to its theoretical rigor and practical robustness, the I²C framework provides a unified control paradigm that simplifies implementation while enhancing reliability. The physical grounding of the method in impedance matching principles enables broad applicability and consistent performance across diverse renewable energy applications. Future research will explore the integration of the proposed I²C strategy into hybrid and grid-forming power systems, expanding its potential to support next-generation distributed energy architectures.”

 

Please also consider following recommendations.
Comment 6: Please improve formatting of table 1 according to requirements of MDPI template.

Response 6: Thank you for pointing this out. The formatting of Table I has been updated in accordance with the MDPI template guidelines as follows:

Table I: Nominal parameter values of the simulated system and experimental setup

Parameter	Symbol	Value
Open-Circuit Voltage	VS	10V
Internal Resistance	RS	1Ω
Load Voltage	VB	24V
Converter Inductance	L	1mH
Switching Frequency	fS	100kHz

 

Comment 7: The first reference for Figure 4 is in section 4 while the figure itself is in section 2.

Response 7: Thank you for your observation. The author confirms that in the revised manuscript, Figure 4 is initially referenced and explained in Section 2 as follows:

 

“Fig.4 illustrates the Thevenin equivalent circuit representation of the input voltage source, which is used to model the renewable energy generator. In this configuration, the open-circuit voltage () and internal resistance () are considered uncertain parameters, reflecting the practical variability of real-world energy sources such as PV and thermoelectric generators. This abstraction enables the use of an equivalent input impedance matching approach, as the MPPT problem is reframed through aligning the converter’s input impedance () with the source’s internal impedance to achieve maximum power transfer.”

 

Comment 8: The italic style of figures referencing in the text not fits the MDPI template (Fig.2 - Fig.13 in the text). The same for ordinary text (lines 110-111, 480-481).

Response 8: Thank you for highlighting the formatting inconsistencies. All figure references have been revised to follow the MDPI template guidelines, using the standard format “Fig. X” instead of the italicised “Fig. X.” Additionally, the italicised text noted in lines 110–111 and 480–481 (in the previous submission) has been corrected to a normal text style in accordance with the MDPI formatting requirements.

 

Comment 9: It is reasonable to add a), b), c), and d) labels for elements of Figure 8. The same for Figures 7, 9, and 10.

Response 9: Thank you for your suggestion regarding the use of labels (a), (b), (c), etc., in multi-part figures. In the current version, each figure is accompanied by a clear legend that distinguishes the plotted curves, and the vertical axes are labelled with their titles to support understanding. As such, the author believes that adding subplot labels would not provide additional clarity and might introduce unnecessary repetition. The figures have been designed to be self-explanatory, and their current structure effectively communicates the intended results. The author appreciates your feedback and respectfully believe the current format better serves the clarity and readability of the presented data.

 

Comment 10: Please improve alignment of formulas (26), (39), (41), (42). Update numeration of formulas to avoid of the use (30) twice. Probably, add lines 360 and 361 as the formulas.

Response 10: Thank you for your detailed comments. The sequence and numbering of all equations have been thoroughly reviewed and corrected in the revised manuscript to avoid duplication, particularly the repeated use of equation number (30). Regarding the alignment of equations (26), (39), (41), and (42), I have carefully rechecked these expressions in the source document and found them to be properly aligned. Although I believe the misalignment was due to the MDPI template conversion, I have verified that all equations are now correctly aligned in the revised manuscript.

 

Comment 11: Please ensure the explanation for all abbreviations before the first use (PI in abstract, DSP, DC-DC). It should be done once, there are repeated definitions in the text (MPPT).

Response 11: Thank you for your careful review. All abbreviations have been checked and explained at their first appearance. Repeated definitions have been removed to improve clarity.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This article proposes a new maximum power point tracking (MPPT) strategy that combines input impedance control (I²C) and adaptive nonlinear controller. It can achieve stable, fast and efficient maximum power extraction under system parameter changes by dynamically matching the impedance between the converter and the power supply, significantly improving the operating efficiency and reliability of renewable energy systems. This is a topic of interest to researchers in related fields, but some improvements are still needed at this stage. My detailed comments are as follows:

1. There are many formatting issues in this article, including but not limited to, the formulas are not centered and some formula numbers are repeated or missing. Please have the author review and make revisions.
2. The experimental part introduces the devices used to implement the controller, but does not provide a graphical summary of the overall system topology, circuit parameters, sensor wiring, etc. It is recommended to add a complete system wiring topology diagram (System block diagram) so that readers can more intuitively understand the experimental platform structure.
3. The reference impedance value is derived by using the improved open-circuit voltage and short-circuit current ratio method, but the applicability of this method under strong shadow or multi-peak conditions has not been verified. It is recommended to add a short discussion or explanation of the applicable boundaries and possible improvement directions of this method.
4. It is recommended to further introduce the risk description mechanism of uncertain factors such as wind energy, photovoltaic output and load changes, and combine certain risk measurement tools (such as CVaR) to expand the robustness analysis of MPPT strategy in uncertain environments. For more comprehensive details, refer to the article at: DOI: 10.1016/j.apenergy.2025.125271.
5. The author can consider extending the MPPT strategy from the perspective of "device-level control" to the "system-level optimization", considering its overall operating efficiency in building complexes and multi-source load coordination systems, and clarifying its coupling relationship with the system optimization goal. For more comprehensive details, refer to the article at: DOI:10.1109/TCE.2024.3412803.

Author Response

Comment: This article proposes a new maximum power point tracking (MPPT) strategy that combines input impedance control (I²C) and adaptive nonlinear controller. It can achieve stable, fast and efficient maximum power extraction under system parameter changes by dynamically matching the impedance between the converter and the power supply, significantly improving the operating efficiency and reliability of renewable energy systems. This is a topic of interest to researchers in related fields, but some improvements are still needed at this stage. My detailed comments are as follows.

Response: The author sincerely thanks the reviewer for their insightful and constructive comments, which have greatly contributed to improving the clarity, depth, and impact of this manuscript. Below are our point-by-point responses:

 

Comment 1: There are many formatting issues in this article, including but not limited to, the formulas are not centred and some formula numbers are repeated or missing. Please have the author review and make revisions.

Response1: Thank you for bringing this to my attention. I have carefully reviewed the manuscript and corrected all formatting inconsistencies related to equations. Specifically, we ensured that:

• All formulas are now properly centered as per MDPI formatting requirements.
• The numbering of equations has been verified and updated to eliminate any duplication or missing references. The earlier repetition of equation (30) has been corrected, and equations have been correctly numbered.

It is worth noting that some of the observed misalignments were likely introduced during the conversion of the manuscript to the MDPI template, which is beyond the author’s direct control. Nevertheless, I have ensured that all equations are now properly formatted and aligned in the revised manuscript, fully in line with MDPI requirements.

 

Comment 2: The experimental part introduces the devices used to implement the controller, but does not provide a graphical summary of the overall system topology, circuit parameters, sensor wiring, etc. It is recommended to add a complete system wiring topology diagram (System block diagram) so that readers can more intuitively understand the experimental platform structure.

Response 2: Many thanks to the respected reviewer for this insightful comment. In response, the author has revised the block diagram of the practical setup (shown in Figure 12 of the revised manuscript) to provide a clearer and more comprehensive overview of the experimental platform. It should be noted that all parameters used in the practical circuit are consistent with those used in the simulation, as listed in Table I. However, all practical values, including the converter inductance, have been clearly labelled in the revised Fig. 12-a.

Regarding the switching devices, the practical setup uses the IRL540NPBF as the main power MOSFET. Additionally, the internal antiparallel diode of this MOSFET is employed as the boost converter’s diode. To ensure this functionality, the gate and source terminals of the mentioned switch (diode-connected MOSFET) are short-circuited; so the device remains off, allowing only the internal diode to conduct as required.

To address the reviewer’s concern about sensing circuits, the voltage sensor board used to monitor the converter’s input voltage is now detailed in Fig. 12-b. This sensing circuit is based on the IL300 optocoupler, configured for unity gain operation. The voltage divider network consisting of R₁ and R₂ determines the input voltage scaling. In this work, the input voltage is assumed to be limited to a maximum of 24 V. Considering the DSP board’s analogue input range limitation of 3 V, the resistors are selected as R₂=7R₁, ensuring proper voltage scaling. Further technical details of the voltage monitoring board are available in [RR1]. In terms of current sensing, a measurement resistor R_m=100 Ω is used, as described in [RR2]. This configuration provides accurate current feedback to the controller while maintaining compatibility with the DSP’s analogue input. These additions ensure that the practical system architecture, sensing design, and experimental configuration are now thoroughly and intuitively presented for the reader’s understanding.

 

Comment 3: The reference impedance value is derived by using the improved open-circuit voltage and short-circuit current ratio method, but the applicability of this method under strong shadow or multi-peak conditions has not been verified. It is recommended to add a short discussion or explanation of the applicable boundaries and possible improvement directions of this method.

Response 3: Thank you for highlighting this important limitation of the open-circuit voltage and short-circuit current ratio method used for reference estimation in this work. The MPPT structure proposed in this paper consists of two distinct components:

1. A closed-loop controller, which generates the switching signal to ensure the converter accurately tracks the reference operating point.
2. A reference calculation unit, which estimates the optimal operating point—typically based on voltage or current in conventional methods.

In contrast to existing voltage- or current-tracking controllers, this paper introduces an impedance-based controller, where the objective is to regulate the converter’s input impedance to match the source impedance. For simplicity and to maintain focus on the controller design, a basic estimation method—based on the fractional open-circuit voltage or short-circuit current ratio—was adopted for calculating the reference input impedance.

The author acknowledges that the V_OC/I_SC method, in its basic form, may not be accurate in the presence of partial shading or multi-peak power-voltage (P-V) characteristics. However, recent advancements in fractional open-circuit voltage techniques [RR3] have enhanced their ability to track the global maximum power point (GMPP), even in the presence of local peaks.

As the primary contribution of this paper lies in the development of a novel adaptive impedance-based controller, an in-depth investigation of GMPP estimation techniques falls beyond the scope of the current study.

 

Comment 4: It is recommended to further introduce the risk description mechanism of uncertain factors such as wind energy, photovoltaic output and load changes, and combine certain risk measurement tools (such as CVaR) to expand the robustness analysis of MPPT strategy in uncertain environments. For more comprehensive details, refer to the article at: DOI: 10.1016/j.apenergy.2025.125271.

Response 4: The author sincerely thanks the reviewer for this valuable suggestion. I fully agree that uncertainty due to environmental and operational variations is a critical aspect of real-world renewable energy systems. In response, the author has included a paragraph in the revised manuscript, highlighting the importance of risk-aware MPPT strategies and the potential application of Conditional Value-at-Risk (CVaR) [RR4] as a robustness assessment tool. While this topic lies beyond the immediate scope of the current study, I have proposed it as an important direction for future research. The suggested reference [RR4] has also been cited to guide interested readers toward more detailed insights.

 

Comment 5: The author can consider extending the MPPT strategy from the perspective of "device-level control" to the "system-level optimization", considering its overall operating efficiency in building complexes and multi-source load coordination systems, and clarifying its coupling relationship with the system optimization goal. For more comprehensive details, refer to the article at: DOI:10.1109/TCE.2024.3412803.

Response 5: Thank you for this valuable perspective. The author agrees that extending MPPT strategies from the converter level to system-level optimisation in larger energy systems is a critical research direction. In the revised manuscript, I have added a discussion on the potential integration of the proposed control strategy within multi-source systems and building-level energy management frameworks. This includes coupling the MPPT controller’s local objectives with higher-level system optimisation goals such as cost minimisation, load coordination, and energy sharing. I have cited the recommended article [RR5] as a relevant example of this broader context.

 

References:

[RR1] Vishay Intertechnology. IL300 Linear Optocoupler—High Gain Stability, Wide Bandwidth. Available online: https://www.vishay.com (accessed on 22 April 2025).

[RR2] LEM International. LA 100-P Current Transducer Datasheet. Available online: https://www.lem.com (accessed on 22 April 2025).

[RR3] Hassan, A.; Bass, O.; Masoum, M.A.S. An Improved Genetic Algorithm Based Fractional Open Circuit Voltage MPPT for Solar PV Systems. Energy Rep. 2023, 9, 1535–1548.

[RR4] Zhai, X.; Li, Z.; Li, Z.; Xue, Y.; Chang, X.; Su, J.; Jin, X.; Wang, P.; Sun, H. Risk-Averse Energy Management for Integrated Electricity and Heat Systems Considering Building Heating Vertical Imbalance: An Asynchronous Decentralized Approach. Appl. Energy 2025, 383, 125271.

[RR5] Zhang, H.; Liu, Y.; Wu, C.; Tan, Y.; Li, Z.; Zhang, D. A Stochastic Bi-Level Optimal Allocation Approach of Intelligent Buildings Considering Energy Storage Sharing Services. IEEE Trans. Consum. Electron. 2024, 70, 5142–5153.

Author Response File: Author Response.pdf