A systematical evaluation of polynomial based equivalent circuit model for charge redistribution dominated self-discharge process in supercapacitors

• Investigate the effects of initial voltage and temperature on charge redistribution dominated self-discharge.
• Establish a polynomial based equivalent circuit model.
• Systematically evaluate the effect of polynomial order on model performance.
• Investigate the impacts of initial voltage and temperature on model performance.
• Compare the prediction performance between polynomial and interpolation methods.

Accurate modeling of the charge redistribution dominated self-discharge process plays a significant role in power management systems for supercapacitors. Although equivalent circuit models (ECMs) are widely used to describe the nonlinear behaviors of the self-discharge process, they are usually separately established at different initial voltages, which might result in poor prediction performances at other unseen initial voltages. In this study, a three-branch model with a leakage resistance is used to describe the nonlinear dynamic behavior of the supercapacitor self-discharge dominated by charge redistribution and the circuit parameters in ECMs are explicitly modeled as a function of the initial voltage. Polynomial functions with different orders are systematically evaluated by means of fitting and prediction accuracy. The impacts of initial voltage and temperature on the charge redistribution dominated self-discharge process are experimentally investigated with a 3000 F commercial supercapacitor. The modeling results show that a 5th-order polynomial function is sufficient high enough to characterize the nonlinear effect of initial voltage on the charge redistribution dominated self-discharge in terms of prediction accuracy. Moreover, the prediction accuracy of polynomial function based ECMs are significantly better than that of interpolation based ECMs, which further validates the effectiveness of the proposed model.