# An enhanced neural network algorithm and its applications for numerical optimization and parameter extraction of photovoltaic models

**Authors:** Aining Chi, Seyedali Mirjalili, Yiying Zhang

PMC · DOI: 10.1038/s41598-026-37918-9 · 2026-02-04

## TL;DR

This paper introduces an enhanced neural network algorithm for optimizing photovoltaic models and shows it outperforms existing methods in parameter extraction.

## Contribution

The novel ENNA algorithm uses a new transfer operator with three learning strategies for improved optimization performance.

## Key findings

- ENNA achieved root mean square errors of 0.00098602, 0.000982485, and 0.00242507 for three PV models.
- ENNA outperformed 10 metaheuristic algorithms in numerical comparisons and convergence performance.
- The algorithm was tested on 52 benchmark functions and showed strong optimization capabilities.

## Abstract

Solar energy is a clean energy source with great application prospects. Photovoltaic (PV) system plays a very important role in converting solar energy into electricity. Optimizing, controlling, and simulating the PV system is of great significance for improving the conversion efficiency of solar energy. The key lies in how to extract the unknown parameters of the PV model. To address this issue, this paper proposes an enhanced neural network algorithm (ENNA). In ENNA, a new transfer operator with three learning strategies based on the defined perturbation operator and elite operator is designed, which makes full use of the obtained population information, including the optimal position of the population, the mean position of the population, and the historical population. To verify the performance of ENNA, ENNA is first used to solve 52 complex benchmark functions. Then, ENNA is employed to extract the unknown parameters of three PV models, i.e., single diode model (SDM), double diode model (DDM), and PV module model (PVM). The optimal root mean square errors obtained by ENNA in SDM, DDM, and PVM are 0.00098602, 0.000982485, and 0.00242507, respectively. ENNA is compared with 10 powerful metaheuristics in terms of numerical comparison, average ranking and convergence performance, and its optimal solutions are compared with the reported optimal solutions of 10 metaheuristic algorithms. The experimental results have demonstrated the excellent performance of ENNA in PV model parameter estimation. The source code of ENNA can be obtained by https://ww2.mathworks.cn/matlabcentral/fileexchange/182977-enna.

## Full-text entities

- **Diseases:** TSA (MESH:D012513), SDM (MESH:D012640), DDM (MESH:D004195), WOA (MESH:D007859)
- **Chemicals:** oxygen (MESH:D010100), GaAs (MESH:C043055), DE (-), silicon (MESH:D012825), CEC (MESH:C051731)
- **Species:** Homo sapiens (human, species) [taxon 9606], Bacillus sp. SA (species) [taxon 1168094]

## Figures

22 figures with captions in the complete paper: https://tomesphere.com/paper/PMC12923673/full.md

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Source: https://tomesphere.com/paper/PMC12923673