Simplified exponential equivalent circuit models for prediction of printed supercapacitor's discharge behavior - Simulations and experiments

Although supercapacitors (SCs) are promising devices for energy storage systems due to their high-power density and long lifecycle, they suffer from high leakage current and self-discharge. In this work, a simple and practical exponential equivalent circuit model (ECM) and three sub-ECMs based on electrical parameters and self-discharge profile of 12 printed flexible SCs are proposed to account for non-linear leakage and self-discharge phenomena in SCs. The capacitance and equivalent series resistance (ESR) of SCs are determined from the experiments. Besides, rather than modelling different self-discharge mechanisms within a SC cell, an exponential current/voltage function is employed for each SC in this study as a variable leakage resistance (VLR). The proposed ECMs are based on empirical parameters, without considering the physical mechanisms. Using the ECMs and only knowing two to four parameters for each SC cell, the discharge behaviors of SCs, electrochemical double-layer capacitors (EDLCs) type may be predicted with a high degree of accuracy over the long term (maximum simulation error in 31 days: less than 4%). Accordingly, the proposed ECMs, in contrast to those published in the literature, have the potential to be used in practical applications in the long-term as a result of their simplicity and high accuracy.