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. 2025 Jul 17;20(7):e0325645.
doi: 10.1371/journal.pone.0325645. eCollection 2025.

Genetic algorithm for parameter optimization of supercapacitor model

Filipe Menezes  1 , Sérgio Cunha  1 , William Assis  1 , Allan Manito  1 , Reinaldo Leite  1 , Thiago Soares  1 , Hugo Lott  2
Affiliations

Genetic algorithm for parameter optimization of supercapacitor model

Filipe Menezes et al. PLoS One. .

Abstract

Electric energy storage systems have advanced significantly in recent years, driven by the growing expansion of renewable energy sources, the rise of electromobility, and other emerging configurations within the current electrical energy system. Among the various energy storage technologies, supercapacitors have gained considerable attention. Due to their ability to deliver large amounts of power over short periods, supercapacitors can be highly effective in hybrid storage systems, for example, enhancing overall system performance. Therefore, detailed studies on supercapacitors and their electrical circuit models have been developed with the aim of representing them as close as possible to actual physical behavior for numerous applications, such as in the context of Digital Twin (DT), an application that will support the monitoring of the operation and health of the supercapacitor throughout its useful life. The present work aims to estimate optimally some parameters of an electrical circuit model of a supercapacitor, in such a way as to obtain responses with very low errors and, thus, be able to use this computational electrical modeling for the development of a Digital Twin system. For the optimal adjustment of the electrical circuit model parameters, a Genetic Algorithm (GA) is used. The response of the electrical circuit, adjusted by the Genetic Algorithm (GA), is then compared to the response obtained through computer simulation of a supercapacitor using PSIM software, which is a software well validated in such studies. The results demonstrated strong alignment between the response using GA and the response using PSIM. Specifically, the charge and discharge curves of the supercapacitor, obtained through GA adjustment and PSIM simulation, were very similar, showing an error of just 2.2%. Thus, the supercapacitor model adjusted via GA demonstrates a good response to the physical phenomenon in question and can be used to develop a Digital Twin (DT) system, aiding in the operational and health monitoring of the supercapacitor.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Flowchart of the proposed methodology.
Fig 2
Fig 2. Equivalent electrical model of SC.
Source: adapted from [13].
Fig 3
Fig 3. Typical CCCD graph for SCs with steady-state voltage drop: Complete cycle of charge, self-discharge, and discharge.
Fig 4
Fig 4. Typical CCCD graph for SCs with steady-state voltage drop: slight voltage drop immediately after charging ended.
The data obtained from the charge and discharge curve are crucial for determining the capacitance (Csc) and equivalent series resistance (Resr). The data extracted from Figs 3 and 4 are applied to the following Eqs (1) and (2).
Fig 5
Fig 5. Genetic Algorithm Flowchart.
Fig 6
Fig 6. Initial population example.
Fig 7
Fig 7. Example of accumulated skills distribution per individual and individual selection probability.
Fig 8
Fig 8. Crossing mechanism.
Fig 9
Fig 9. Circuit for a complete SC cycle (SC reference).
Fig 10
Fig 10. Charging curve of the target SC: Complete charging cycle, with key points for calculating Csc.
Fig 11
Fig 11. Charging curve of the target SC: Immediate voltage drop at the transition from charging to self-discharge, with key points for calculating Resr.
Fig 12
Fig 12. Charging curve modeled by the settings determined by the GA compared with the target charging curve.
Fig 13
Fig 13. Circuit for a complete SC cycle (SC modeled).
Fig 14
Fig 14. Comparison between the target voltage curve and the modeled voltage curve with GA.
See this image and copyright information in PMC

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