A Critical Review of Using the Peukert Equation and its Generalizations for Lithium-Ion Cells

Abstract

In this paper, the Peukert’s equation was studied experimentally and theoretically at various discharge currents for lithium-ion cells. The classical Peukert’s equation is not applicable at small discharge currents as according to this equation, at the discharge current decrease, the capacity released by the cells tends to infinity. The generalized Peukert’s equation C = C m /(1+(i/i0)n) corresponds well to the experimental data obtained at small and middle discharge currents. However at high discharge currents, the capacity released by the lithium-ion cells drops much faster than it is predicted by the known Peukert’s equation generalizations. In this paper both experimentally and theoretically, it is proved that the reason of the sharp decrease of the cells capacity at high discharge currents is the voltage drop at cells internal resistance. Based on the obtained results, the following equation was proposed: C = C m (1−i/i1)/((1−i/i1)+i n/i0n). This equation corresponds well to the experimental data at any discharge currents, as it takes into consideration the voltage drop, caused by the cell internal resistance.

Range, Endurance, and Optimal Speed Estimates for Multicopters

“…Due to its simplicity, the Peukert Model has since become the standard approach to model the effective capacity under load. It has also been shown to hold for LiPo batteries at medium discharge rates [15], [28]. Generalizations to medium discharge (around 1 C) rates exist as well [29], [15].…”

“…It has also been shown to hold for LiPo batteries at medium discharge rates [15], [28]. Generalizations to medium discharge (around 1 C) rates exist as well [29], [15].…”

“…The above mentioned works either assume that the battery is an ideal energy storage or use the Peukert model [14] to calculate the battery capacity. However, this model is only accurate for the low to medium discharge rates [15] typically encountered in ground vehicles or fixed-wing aircraft but not well-suited for the very high power demand of multicopters.…”

Anisotropic crystallite size distributions in LiFePO4 powders

“…Information on the anisotropy of size-distribution functions can be used to analyze the relations between the battery capacity and the charge-discharge rate. 5,6 The fraction of composite (fused) particles consisting of several crystallites can be used to estimate the ion diffusion length along the block boundaries; the activation energy of such diffusion may differ signicantly from the bulk values. 4,16,27,47 The frequency distribution functions of different particle dimensions L s and L b can be decomposed into the components L [hkl] by careful accounting for the anisotropy of crystallites extracted from XRD measurements.…”

“…[1][2][3][4] A decrease in the particle size shortens the Li diffusion length and the discharge-charge time. 5,6 This time also depends on the mechanism of the new phase nucleation on the particle surface, 7 on the nucleation rate 8 and on the time of the LiFePO 4 / FePO 4 phase boundary motion in the particle. The latter depends on the structural defects in the particles: intrinsic, 9 impurity and isovalent 1 defects, deformations and 3D structuring of the phase boundary, and stress/deformation relationships.…”