Modeling the dynamic self-discharge effects of supercapacitors using a controlled current source based ladder equivalent circuit

Modeling the self-discharge effects can be very useful for the energy awareness of supercapacitors. In this paper, the conventional charge redistribution, the residual charge redistribution and the leakage of charge during self discharge of a supercapacitor are investigated by a set of experimental results. A novel controlled current source based ladder equivalent circuit model (ECM) is proposed for depicting the dynamic self-discharge effects of the supercapacitor. The originality of the proposed model is that the controlled current source can reflect the diffusion phenomenon of the supercapacitor residual charge during rest phases. Based on the experimental data, the ladder ECM parameters are identified by the least square and bilinear transformation methods. Furthermore, the controlled current source is designed according to the identified parameters and the estimated voltage error of the ladder ECM. Validation is done based on experimentally observed results and simulation results. The comparative results show that the percent relative error of the proposed model is within 0.8%. In addition, the energy awareness and the estimated energy efficiency of the supercapacitor would also be improved by using the proposed model.