Analytical and Stochastic Modelling of Battery Cell Dynamics

Abstract

Abstract. In this work we present and discuss a modelling framework for the basic discharge process which occurs in simple electrochemical battery cells. The main purpose is to provide a setting for analyzing delivered capacity, battery life expectancy and other measures of performance. This includes a number of deterministic and stochastic variations of kinetic battery models. The primary tool is a novel phase plane analysis of the balance of nominal and theoretical capacity. In particular, we study spatial versions of such models which lead to a linear diffusion equation with Robin type boundary conditions under scaling. Explicit solutions are obtained by considering reflected Brownian motion.

Markov Modeling of Battery Cell Behavior Taking into Account Pulsed Discharge Recovery

“…We derived results on the delivered and gained capacities. These quantities where studied in [8] for the kinetic battery models. Moreover, we investigated the mean and variance of the number of pulses.…”

“…The theoretical capacity of the battery is a measure of the maximal charge which in principle could be obtained where the battery discharged arbitrarily slow, restricted only by the total amount of electrochemical material contained in the cell. Over the years, many battery models have been developed for different application areas (see for instance [1,3,[5][6][7][8][9][10][11][12] and references therein). Chiasserini and Rao in [3] have introduced a battery model with recovery effect.…”

“…Chiasserini and Rao in [3] have introduced a battery model with recovery effect. Kaj and Konané, in [8] have studied the so-called kinetic battery model, KIBAM with some extensions like the spatial diffusion KiBAM and diffusive model KiDiBAM. Chen and al, in [1] have studied an electric model of the battery capable of capturing the runtime of the battery.…”

“…Clearly, the path can not visit the shadowed area in the lower right corner. In some natural models, like the kinetic battery model (see [8]) the path x(v), 0 ≤ v ≤ T , can not cross the line x = cv, where c = N/T is the initial ratio of nominal to theoretical capacity.…”

Modeling battery cells under discharge using kinetic and stochastic battery models

“…Charge recovery in this framework consists in the continuous transition of bound charge to available charge. As observed in [5] and further investigated in [6], more general spatial versions of these models are related to the diffusion model of Rakhmatov and Vrudhula [13,15], and leads to a class of second order diffusion equations with Robin type boundary conditions. Quoting [12], the linear dynamics of the kinetic battery model is useful in getting an intuitive idea of how and why the recovery occurs but it needs a number of additions to be useful for the types of batteries used in mobile computing.…”