Simulation of lithium-ion concentration profiles in separator and cathode of lithium-ion battery using theta formulation under finite difference method / Md Jauharul Haqaiq Harun - Md Jauharul Haqaiq, Harun (2012)
This research focuses on the material balance equation governing the lithium-ion concentration in an electrolyte/solution phase of a lithium-ion battery. The main objective of this research is to obtain the solution for this governing equation in order to simulate the concentration profile of a lithium-ion battery during discharge process. The second objective of this research is to study the behavior of these lithium-ion concentrations in the electrolyte/solution phase of a lithium-ion battery under various conditions. In order to achieve the second objective of this study, various simulations of lithium-ion concentrations in the electrolyte/solution phase of a lithium-ion battery were performed. Several difference parameter values of discharge current (I), electrode porosity (ε), discharge time (τ) and combination of separator/cathode thicknesses (Ls/Lc) were used to simulate the behavior of lithium-ion in the battery system. The material balance equation governing the lithium-ion concentration in the electrolyte/solution phase of a lithium-ion battery for separator is defined as These equations are solved using the Theta formulation from Finite Difference Method (FDM) based on the relevant initial and boundary conditions. Three schemes are considered from this Theta formulation, which are explicit scheme (α = 0), implicit scheme (α = 1) and Crank Nicolson scheme (α = 0.5). The coding for all three schemes are done using Wolfram MATHEMATICA 8 software and were solved. The significant t-test is used to prove that the profiles of lithium-ion concentration calculated from this work are in good agreement with the published analytical results within 95% confidence interval. The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are used to evaluate the effectiveness and accuracy of the profiles of lithium-ion concentration calculated from this work compared to the published work. Computational time needed by Wolfram Mathematica 8 software to solve the equation is also recorded to identify the fastest scheme based on the same style of computer coding from Theta formulation.