中文摘要：

锂离子电池内部结构是一种复杂的分布参数系统,如果为了降低计算难度而使用常微分方程描述锂离子电池,可能会引入系统误差,降低系统模型的可信度,需要使用偏微分方程建立分布参数系统的精确模型.本文提出了一种基于单粒子模型和抛物型偏微分方程的锂离子电池系统建模与故障监测系统设计方法,当锂离子浓度实测值与理想值的残差大于预设门槛时判定分布参数系统处于故障状态.通过一个仿真实例进行了锂离子电池系统建模和故障诊断实验,实验证明基于单粒子模型和偏微分方程的锂离子电池故障监测系统具有更高的精确度和可信度.

英文摘要：

Li-ion battery is a complicated distributed parameter system that can be described precisely by field theory and partial differential equations. In order to reduce the calculation amount and the solution difficulty, a distributed param- eter system is often described by ordinary differential equation model during the design and the analysis. As a result, systemic error is caused, and the reliability of the system model is reduced. The rechargeable Li-ion batteries are widely used in many fields because of their excellent properties. The research on the modeling and failure monitor of Li-ion battery can evaluate its working state, and improve the security during its servicing. Li-ion battery system is regarded as a distributed parameter system in this paper. Single particle model is a simplification of a Li-ion battery under a few assumptions. According to the measured data, single particle model can be used for estimating the parameter at a fast simulation speed. Li-ion battery model based on partial difference equations and single particle model is proposed to detect the failure and evaluate the working state of Li-ion battery system. Lithium ion concentration is an unmea- surable distributed variable in the anode of Li-ion battery. The failure monitor system can track the real-time Li ion concentration in the anode of Li-ion battery, calculate the residual which is the difference between the measured value and the ideM value. A failure can be judged when the residual is beyond a predefined failure threshold. A simulation example verifies that the accuracy and the effectiveness of Li-ion battery failure monitor system based on parabolic partial difference equations and single particle model is reliable.