标题： 使用动力学和随机电池模型模拟放电状态下的电池单元 显示英文标题

标题： Modeling battery cells under discharge using kinetic and stochastic battery models

摘要： 本文我们回顾了几种简单电池单元的数学建模方法，并进一步发展了这些思想，重点放在电荷回收和电池对外部负载的响应行为上。 我们关注那些使用少量参数和基本电池数据的模型，而不是特定电池化学反应和材料特性的详细特性，从动力学电池模型的耦合常微分方程线性动态开始。 我们证明了一个相关的偏微分方程组（具有罗宾边界条件）出现在空间动力学电池模型的极限情况下，并提供了该解的新概率表示，即有限区间上带有漂移的布朗运动，在区间的两边边界处反射。 为了比较动力学和随机电池模型中的线性和非线性动态，我们研究了状态代表电池可用容量和剩余容量的马尔可夫链。 一个自然的尺度限制导致一类非线性常微分方程，可以显式求解并与线性模型获得的容量进行比较。 为了表明建模的潜在用途，我们简要讨论了放电曲线的比较和对电池性能的影响。 显示英文摘要

摘要： In this paper we review several approaches to mathematical modeling of simple battery cells and develop these ideas further with emphasis on charge recovery and the response behavior of batteries to given external load. We focus on models which use few parameters and basic battery data, rather than detailed reaction and material characteristics of a specific battery cell chemistry, starting with the coupled ODE linear dynamics of the kinetic battery model. We show that a related system of PDE with Robin type boundary conditions arises in the limiting regime of a spatial kinetic battery model, and provide a new probabilistic representation of the solution in terms of Brownian motion with drift reflected at the boundaries on both sides of a finite interval. To compare linear and nonlinear dynamics in kinetic and stochastic battery models we study Markov chains with states representing available and remaining capacities of the battery. A natural scaling limit leads to a class of nonlinear ODE, which can be solved explicitly and compared with the capacities obtained for the linear models. To indicate the potential use of the modeling we discuss briefly comparison of discharge profiles and effects on battery performance.