Derivation and experimental analysis of Peukert’s equation in terms of fractional equivalent circuits

Abstract

Using an equivalent circuit model (ECM) of a battery that involves fractional elements we analytically derive Peukert’s empirical equation along with generalisations of the equation for the increasing capacity of the battery as the charge and discharge currents are reduced. The derived generalised Peukert’s Equations are dimensionally consistent and all parameters (including Peukert’s coefficient and the so-called ‘capacity constant’) can be calculated from the parameters of the ECM and operating voltage range of the battery. Experiments are conducted on ten batteries to demonstrate that the resistor fractional-capacitor series ECM fit to discharge times predicts well the impedance spectrum found by electrochemical impedance spectroscopy (EIS), and vice versa, on Li-CO/NCA/NMC and Na-ion batteries. This agreement is not observed on the tested LiFePO and LiTO batteries because the impedance spectrum exhibits behaviour not captured by the ECM. Peukert’s Equation predicts ever increasing capacity as both the charge and discharge currents are reduced. The experimental results confirm this behaviour for all batteries down to the lowest current measured (C/256).