An improved exponential model for charge and discharge behavior of printed supercapacitor modules under varying load conditions

We report an improved and simple exponential model for the charging and discharging behavior of series-
connected modules of supercapacitors under varying load conditions and over extended periods of time. In
this work, only a single variable leakage resistance (VLR) with exponential current/voltage profile is used to
model the effects of different self-discharge mechanisms of a supercapacitor. Due to the simplicity and accuracy
of the simulations, the proposed model can be implemented in practical applications, both short-term and long-
term, unlike the two-, three-branch, and exponential models with voltage/time profile reported in the literature.
We have modeled four different energy modules using the electrical parameters of 12 printed supercapacitors in
order to study and compare the series connected supercapacitors’ behavior in each energy module. The key
parameters such as capacitance and equivalent series resistance (ESR) of supercapacitors were based on
experimental results. The numerical exponential method reported here enables modelling of the nonlinear
behavior of self-discharge and leakage current over a wide range of load conditions and time periods.
Furthermore, we have modified the linear model reported in the literature for leakage and self-discharge and
compared the results with our nonlinear model.