Journal of Green Energy Research and Innovation
Quarterly

Maximum Power Point Tracking of Solar Arrays under Partial Shading Condition Using a New Quadratic-Spline Method

Document Type : Research article

Authors

Behrooz Shaban
AbdolHossein Saleh

Department of Electrical Engineering, Faculty of Engineering, Malayer University, Malayer, Iran.‎

10.61882/jgeri.3.1.64
Abstract
Photovoltaic (PV) systems have become indispensable in the renewable energy landscape, harnessing the sun’s abundant and clean potential. However, their efficiency is often compromised by low conversion rates, particularly under partial shading conditions (PSC). This study introduces a novel quadratic spline-based maximum power point tracking (QS-MPPT) technique to optimize PV array performance under both uniform irradiance and PSC. Unlike conventional methods such as Perturb and Observe (P&O) or Incremental Conductance (INC), which struggle to pinpoint the global maximum power point (GMPP) amid the multi-peak power-voltage (P-V) curves typical of PSC, QS-MPPT employs a straightforward quadratic interpolation approach. By leveraging a minimal set of sampled points, this method rapidly and accurately locates the GMPP, ensuring stability without oscillations around the operating point. Simplicity of the proposed method also makes it ideal for implementation on cost-effective microcontrollers, broadening its practical appeal for real-world PV applications. The efficiency of the proposed method is shown by the time domain simulation in the MATLAB/SIMULINK environment and implementation in the form of a processor-in-the-loop (PIL). Through MATLAB simulations, QS-MPPT performance is evaluated and compared with MPPT techniques like P&O, Particle Swarm Optimization (PSO), and Flower Pollination Algorithm (FPA) in three- and four-peak PSC scenarios, where the proposed method shows higher accuracy and faster convergence‎.‎

Graphical Abstract

Maximum Power Point Tracking of Solar Arrays under Partial Shading Condition Using a New Quadratic-Spline Method

Highlights

❖ A novel quadratic spline-based MPPT (QS-MPPT) technique accurately tracks the global maximum power point under partial shading.
❖ The method uses simple interpolation to achieve rapid, oscillation-free convergence, outperforming standard algorithms like P&O and PSO.
❖ Its low complexity enables easy implementation on cost-effective microcontrollers for real-world applications.
❖ Simulations confirm superior accuracy and speed in complex multi-peak shading scenarios compared to existing methods. 

Keywords

Photovoltaic Array
Maximum Power Point Tracking (MPPT)
Partial Shading Conditions
Multi-Peak P-V Characteristics
Quadratic Spline

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, redundancy, have been completely observed by the authors.

Credit Authorship Contribution Statement

Behrooz Shaban: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Roles/Writing - original draft. Abdolhossein Saleh: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Roles/Writing-original draft, Writing-review & editing.

Bibliography

Behrooz Shaban  was born in Brujerd, Lorestan, Iran. He received the Msc. degree in electrical engineering from Malayer University, Hamedan. He is currently Phd candidate at Tafresh University, Tafresh, Markazi. His research interests include switching power converters, distributed generation, and control.

Abdolhossein Saleh was born in Nahavand, Hamedan, Iran, in December, 1987. He received the Ph.D. degree in electrical engineering from Bu-Ali Sina University, Hamedan, in 2019. He is currently an Assistant Professor with Malayer University, Malayer, Hamedan. His research interests include power quality, switching power converters, distributed generation, and microgrids and their control.

Citation
B. Shaban, and A. Saleh, "Maximum Power Point Tracking of Solar Arrays under Partial Shading Condition Using a New Quadratic-Spline Method," Journal of Green Energy Research and Innovation, vol. 3, no. 1, pp. 64-76, 2026.

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Journal of Green Energy Research and Innovation
Volume 3, Issue 1
Spring 2026
Pages 64-76

  • Receive Date 01 September 2025
  • Revise Date 07 October 2025
  • Accept Date 25 October 2025
  • Publish Date 01 April 2026

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