An overview of mathematical modeling of electrochemical supercapacitors/ultracapacitors

Varieties of electrochemical supercapacitors ESs models has been presented in the literature, but most do not capture all necessary parameters to build theoretical basis for calculations and optimization of parameters of various types and designs of ESs with simultaneous account of properties of electrode materials, electrolytes, separators, designs, and values of charge and discharge currents of the ES. This work reviews existing models and discusses the benefits and setbacks of each type and attempt to synergize the existing models to realize more real-life model built on realistic assumptions and with thermal model (temperature distribution) that is useful for thermal management/cooling strategies for supercapacitors cell. Results in literature generally show the basic relationship between supercapacitors components, but hardly any existing model is currently able to take due account of ESs parameters and other factors like internal temperature rise and interfacial electric field in a rigorous manner, hence the discrepancy between results of theoretical and experimental measurements of parameters of real-life supercapacitors. In order to build supercapacitors with improved key parameters and optimal design, account of thickness, strong dependence of capacitance of polarizable electrodes on their potential, temperature distributions, specific mechanisms or combination of different mechanisms of self-discharge, type and value of conductivity of electrodes material and conductivity of electrolyte in its pores must be considered. (C) 2014 Elsevier B.V. All rights reserved.