Document Type
Article
Publication Date
2026
DOI
10.1016/j.egyr.2026.109159
Publication Title
Energy Reports
Volume
15
Pages
109159
Abstract
The modeling of photovoltaic (PV) cells through equivalent circuits forms a central element in the analysis, simulation, and optimization of solar energy systems. Traditional approaches often depend on iterative numerical methods to solve the implicit current–voltage (I–V) equations. In contrast, the Lambert W function has emerged as an effective mathematical tool that enables closed-form or semi-analytical expressions for a wide range of PV models. This paper presents a Lambert W-centered review of analytical and semi-analytical formulations for PV equivalent-circuit models, covering classical single-diode and multi-diode structures and modern variants incorporating additional elements, voltage-dependent parameters, and topology rearrangements. The models are organized by circuit complexity and solution type, and their Lambert W-based derivations are summarized within a unified framework. A consistent comparison of 31 models using the RTC France reference cell under standard test conditions (STC) reveals that the best-performing formulation achieves a minimum root-mean-square error (RMSE) of 5.6135 × 10⁻⁴, improving upon the classic single-diode model (7.7465 ×10⁻⁴) by approximately 27.5%. The presented synthesis supports fast and accurate PV modeling for applications such as real-time estimation, MPPT, and embedded implementation.
Rights
© 2026 The Authors.
This is an open access article under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) License.
Data Availability
Article states: "No data was used for the research described in the article."
Original Publication Citation
El-Shahat, A., Ćalasan, M., Vujoševic, S., & Abdel Aleem, S. H. E. (2026). Analytical and semi-analytical modeling of solar cells using the Lambert W function: A comprehensive review of equivalent circuits. Energy Reports, 15, Article 109159. https://doi.org/10.1016/j.egyr.2026.109159
ORCID
0000-0003-0148-5014 (El-Shahat)
Repository Citation
El-Shahat, Adel; Ćalasan, Martin; Vujoševic, Snežana; and Abdel Aleem, Shady H. E., "Analytical and Semi-Analytical Modeling of Solar Cells Using the Lambert W Function: A Comprehensive Review of Equivalent Circuits" (2026). Engineering Technology Faculty Publications. 275.
https://digitalcommons.odu.edu/engtech_fac_pubs/275
Included in
Energy Policy Commons, Power and Energy Commons, VLSI and Circuits, Embedded and Hardware Systems Commons