Analysis of Generalized Peukert’s Equations for Capacity Calculation of Lithium-Ion Cells

Abstract

In this paper, the possibility of using generalized Peukert’s equations C  = C m /(1  +  ( i / i 0 ) n ), C  = 0.522 C m tanh(( i / i 0 ) n /0.522)/( i / i 0 ) n , and C  =  C m erfc(( i / i k  − 1)/(1/ n ))/erfc( −n ) for the calculation of lithium-ion cells’ released capacity at different discharge currents is analyzed. It is proven that these equations correspond well to the experimental data over the entire change range of the discharge currents. Furthermore, it is demonstrated that the parameter n depends on neither cell capacity nor its format or manufacturer; however, it grows with an increase of the ratio i 0 / С m (or i k / С m ), which depends on an electrode’s effective thickness and the electrochemical system of the lithium-ion cells. Additionally, it is possible to consider the dependence of a lithium-ion cell’s released capacity on a discharge current value as the statistical phase transition subjected to the normal distribution law. The proposed statistical mechanism explains the changes of the parameters n and i 0 ( i k ) based on the type of battery studied.