Supercapacitors with carbon electrodes. Energy efficiency: modeling and experimental verification

In the paper, charging–discharging processes in symmetric electrochemical supercapacitors with activated carbon electrodes were studied. Mathematical modeling and experimental verification of these processes were performed. Such factors as the charging of the electric double layer, diffusion–migration transport of species in pores of the electrodes and separator, quasi-reversible Faraday redox reactions of surface groups, kinetics of which is related to the Butler–Volmer type, and porous structure of the electrodes with hydrophobic–hydrophilic characteristics were taken into consideration. The dependencies of energy efficiency on time of charging and discharging, current, and thickness of the electrodes have been calculated. These relations are very important when supercapacitors are applied to smoothing of peak load of electrical networks. The dependence of the efficiency on current is characterized by a maximum and a minimum. The optimal operating modes for the supercapacitors have been found to depend on device parameters. It is important to note that the efficiency value is close to 100 % for supercapacitors under certain conditions, but this magnitude is unattainable for batteries.