# Enhancing Supercapacitor Simulation Accuracy Through a Novel Hybrid Modeling Approach
## 5 Conclusions  
In this study, a new hybrid modeling method called the Hybrid Modeling Approach for Supercapacitors--HyMASC--was proposed for modeling of the supercapacitors. The new method combines the well-established Zubieta and Bonert techniques with the MATLAB Parameter Estimator application. The aim was to capitalize on the strengths of each approach while mitigating their respective limitations. Through the utilization of values obtained from the Zubieta and Bonert methods as input conditions for the parameter estimator, as well as successive iterative optimization processes driven by experimental data, the simulation results showed better performance using the optimized parameter values. The proposed method offers better insights by fine-tuning the parameters of the equivalent model so that it closely reproduces the SC dynamics. Another advantage of using the HyMASC method is the ability to compensate for the eventual deviations in calculating the parameters using Zubieta methods due to experimental data limitations (DAQ accuracy, signal noise, etc.).  
An additional advantage of the HyMASC method is its scalability and adaptability to various supercapacitor types and configurations, making it suitable for a wide range of applications beyond those traditionally addressed in the literature. Therefore, the HyMASC method can be seamlessly integrated into design workflows for hybrid energy storage systems. This adaptability is particularly valuable for industries aiming to accelerate the development of electric vehicles and renewable energy systems, where iterative prototyping and rapid validation are of the utmost importance. Furthermore, the ability to reduce experimental error impacts makes the method a viable candidate for digital twin implementations, enabling real-time monitoring and predictive maintenance of energy storage systems.  
The investigation showcased the efficacy of this integrated approach through validation against experimental data collected from two GreenCap electric double-layer supercapacitors. The developed experiments focused on modeling and comparing the obtained results with other methods proposed in the literature. It was observed that for the same experimental data, by implementing the HyMASC method, the MRE was reduced from 2.52 to 0.47 in the case of 300 SC and from 2.17 to 0.85 for the 400 SC. The MAE was reduced from 0.0492 V to 0.004 V (300 SC) and from 0.0744 to 0.0108 (400 SC) in comparison with the Zubieta method. In comparison, with other modeling methods from the literature, improvements in the modeling performance were observed.  
It can be concluded that the outcomes of the presented research offer positive implications for the field of supercapacitor modeling within hybrid energy storage systems. The improvements in parameter estimation accuracy showcased the potential of the HyMASC method. Using this method, reliable and accurate supercapacitor models that closely emulate real-world behavior can be developed. The presented approach addresses existing challenges and also offers a systematic framework for improving parameter estimation accuracy.  
Conceptualization, D.L., C.L. and F.I.B.; methodology, D.L., C.L. and F.I.B.; software, D.L. and C.L.; validation, D.L. and C.L.; formal analysis, D.L. and C.L.; investigation, D.L. and C.L.; resources, D.L. and C.L.; data curation, D.L.; simulation data, D.L.; writing--original draft preparation, D.L., C.L. and F.I.B.; writing--review and editing, D.L., C.L. and F.I.B.; visualization, C.L. and D.L.; supervision, C.L.; funding acquisition, C.L. and D.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors express their thanks for the support offered by the Intelligent Mechatronic Systems Laboratory at the Technical University of Cluj-Napoca in developing the research presented in the paper.  
The authors declare no conflicts of interest.