Modeling of Supercapacitor Behavior With an Improved Two-Branch Equivalent Circuit

Abstract

In this paper, an improved two-branch equivalent circuit model with a controlled current source is proposed to describe the real-time charge/discharge and self-discharge operating characteristics of a supercapacitor (SC). First, the self-discharge mechanism of the SC is investigated based on the two-branch model and experimental analyses at the different charge and discharge stages. Furthermore, the controlled current source is introduced into the two-branch model to reflect the self-discharge effect of the SC. On this basis, the recursive least square method is adapted to identify the model parameters. To improve the accuracy of the proposed model, the iterative optimization algorithm is also adapted to optimize the dynamic parameters of the controlled current source. Finally, the improved two-branch equivalent circuit model with the controlled current source is simulated. The simulation results are basically in accordance with the experimental results. The relative error of the proposed model is less than 0.7%. Compared with the conventional two-branch model, the proposed model can not only reflect the SC dynamic behavior during the charge/discharge phase but also better reflect the self-discharge effect of the SC. INDEX TERMS Supercapacitor, equivalent circuit model, self-discharge effect, controlled current source, parameters identification.

Experimental design for an enhanced parametric modeling of supercapacitor equivalent circuit model

“…Moreover [10] in their study the self-discharge rate was improved in their model but still there are long and complex method of the identification process of internal parameters by using filters and However in this study, the self-discharge rate during rest was relatively low and better than line transmission (Matlab) model with small variation error, so that it is not modelled as main parameters in this paper. In addition [28] stated in their study that it is difficult to have a unified standard to compare the self-discharge rates due to the different systems (including electrode materials, electrolytes, separators, and initial cell voltages) employed by researchers for self-discharge tests.…”

“…Also another study done by [6] too many hardware tools used and their maximum relative error of terminal voltage was 0.25 V. Besdies, the study done by [10] introduced the modeling of supercapacitor with improved two-branch circuit model by adding current controlled source to improve self-discharge rate of supercapacitor voltage. In this study they used neware testing device but the maximum relative errors ranged from 0.19 and up to 2.35% for similar experiments test profiles applied in this work.…”

“…Fundamentally, SCs store electrical energy through the development of the double layer capacitor structure at the interface between the anodes and the electrolyte [9]. The uses of supercapacitor can be varied between electric vehicles (EVs), solar/wind power applications remote sensor nodes and hybrid electrical vehicles [10]. Supercapacitors have an essentially lower energy density and higher power density when compared with traditional batteries [11].…”

Modeling, Simulation, and Characterization of a Supercapacitor in Automotive Applications

“…A Nonlinear Least Squares Method (NLSM) is employed. Its mathematical formulation is provided in (15) minF (p) subject to…”

The different approach for supercapacitor modelling in the perspective of self-discharge study

“…The parameter identifications also need helps from the experimental data and some researcher uses a more complex calculation approach that needs helps from tools such as the least square method algorithm. The two branch ECM in Figure 3 has been used for characterization and behavior study for the supercapacitor in [37]- [40] while Figure 4 also shows the two branch ECM that has been used in [33], [36], [41] for modelling the supercapacitor behavior. The high self-discharge rate of a SC also can happen due to overcharged since the electrolyte might be decomposed into a gaseous state or solid product [42].…”