Comparative Studies of Solutions of Homogeneous Electrochemical Capacitors Models

Abstract

The models of symmetric ECs with self-discharges term have been studied using a combination of various self-discharge mechanisms in devices’ conservation equations (mass transfer and charge) under charge and discharge processes. The models were solved both analytically and numerically for comparative study purpose, three numerical methods (Crank-Nicolson numerical method, fully implicit numerical method, and fully explicit numerical method) were employed via central finite differences for spatial derivatives.The profiles of capacitors with or without self-discharges using Crank-Nicolson numerical solution, fully implicit numerical and fully explicit numerical solution methods were 95%, 80% and 70% respectively in agreement with similar capacitors using analytical solution.Devices without self-discharges were charged from 0.00V to the expected voltage of 1.20V within expected charging time when analytical solution and Crank-Nicolson numerical method were employed, and from 0.00V to 1.15V and 0.00V to 1.00V (which are less than the target voltage) within target charging time by using fully implicit numerical and fully explicit numerical methods, respectively. The energy density of capacitors with electrode and electrolytes effective conductivities of 0.05S/cm without self-discharges using analytical solution, Crank-Nicolson numerical solution, fully implicit numerical and fully explicit numerical solution methods were 35.957Wh/kg, 35.757Wh/kg, 34.282Wh/kg and 24.953Wh/kg, respectively. The first cycle energy efficiency of devices using analytical solution, Crank-Nicolson numerical, fully implicit numerical and fully explicit numerical solution methods for capacitors with electrode and electrolytes effective conductivities of 0.05S/cm without self-discharges Vs were 84.24%, 84.04%, 72.33% and 38.13%, respectively. Simulation results obtained from Crank-Nicolson numerical solution method for certain device is more accurate than those from fully implicit numerical solution and fully explicit numerical solution methods. Thus, the Crank-Nicolson numerical solution method which employs the average of the fully implicit and fully explicit schemes is more realistic than the fully explicit numerical and fully implicit numerical solution methods.