Mathematical Modeling and Synthesis of an Electrical Equivalent Circuit of an Electrochemical Device

Abstract

The given research is aimed at the mathematical modeling and synthesis of the electrical equivalent circuit of an electrochemical device as an element of an electrical circuit. Mathematical modeling is completed in the result of a systematic study of the concentration and electric fields in a two-electrode electrochemical system. The object of study is considered to be linear with constant parameters. The object sizes are considered to be insignificant that’s why the electric current density on the electrodes surface is assumed to be equally distributed. Diffusion in the electrolyte becomes the limiting stage of electrode processes in the system with a finite mass transfer rate. The Laplace operator method is used as a research method, it is used to calculate the voltage at the electrodes of an electrochemical device. The mathematical model of an electrochemical device has been developed in the run of the system study and an electrical equivalent circuit has been synthesized, which contains infinite number of parallel branches including active and reactive elements. Besides, analytical formulas have been obtained that can be used in the process of calculation individual discrete parameters on these branches. In case of engineering calculations, the number of branches in the electrical equivalent circuit can be limited with the finite number, specified by accuracy of the calculations. It should be also mentioned that as a result of the study, it has become possible to synthesize all kinds of particular characteristics of an electrochemical device as well as the opportunity to study the dynamics of various transition processes in it.