Temperature Interval Estimation Approach for Lithium-ion Battery Packs: A Continuous-Discrete Correction Strategy
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摘要: 针对复杂非线性、域内扰动、测量噪声、环境温度变化及初始条件等不确定因素影响下的锂离子电池组, 提出一种基于偏微分方程模型的区间观测器来以上下界的形式反映电池组内部温度. 首先, 将电池组视为一个温度由内向外呈放射状分布的圆柱形结构电池, 基于其轴对称结构以及径向为主导的热传导行为, 建立描述其热行为的一维径向偏微分方程模型. 然后, 采用空间点测量与时间非周期离散测量相结合的方式获取电池组表面温度数据, 并基于各类未知不确定参数的已知上下界, 设计基于连续-离散混合系统的区间观测器, 引入一个辅助计时器变量以驱动连续系统与离散系统之间的切换, 确保在测量时刻及时校正估计误差, 有效缩小估计区间宽度. 进一步, 构造包含函数时间导数与负部分函数的方程, 通过分析负函数部分为零和非负离散时间系统理论证明了估计误差的非负性, 在此基础上建立包含计时器的Lyapunov函数, 结合递推归纳法得到估计误差有界的充分条件. 最后, 以3并3串锂电池组为例, 仿真验证本文所提区间观测器的有效性和优越性.Abstract: For lithium-ion battery packs influenced by uncertainties such as complex nonlinearity, in-domain disturbances, measurement noise, ambient temperature variations, and initial conditions, an interval observer based on partial differential equation models is proposed to reflect the internal temperature of the battery packs in the form of upper and lower bounds. First, the battery packs are conceptualized as a cylindrical structure with radial temperature distribution from the core outward. Based on its axisymmetric structure and radial-dominated heat transfer behavior, a one-dimensional radial partial differential equation model is established to describe its thermal behavior. Then, surface temperature data of the battery packs are acquired by combining point measurements in space and non-periodic discrete measurements in time. Based on known upper and lower bounds for various unknown uncertain parameters, an interval observer with continuous-discrete hybrid systems is designed. An auxiliary timer variable is introduced to drive the switching between the continuous and discrete systems, ensuring timely correction of estimation errors at measurement moments and effectively narrowing the width of the estimation interval. Furthermore, an equation incorporating the time derivative of the function and its negative part is constructed, and the non-negativity of the estimation error is proven by analyzing the negative part to be zero and using the non-negative discrete-time system theory. Based on this, a Lyapunov function including the timer is established, and combined with mathematical induction, sufficient conditions for the boundedness of the estimation errors are obtained. Finally, simulations using a three-series-three-parallel lithium battery pack validate the effectiveness and superiority of the proposed interval observer.
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图 1 热电偶传感器植入电池内部示意图
Fig. 1 Schematic diagram of thermocouple sensor implanted inside battery
图 3 3并3串电池组的平面布局示意图
Fig. 3 Schematic diagram of the planar layout of 3-parallel-3-series battery packs
图 4 电池组温度$T$以及区间观测器的动态演化轮廓
Fig. 4 The dynamic evolution profiles of battery packs temperature $T$ and interval observer
图 5 电池组温度$T$以及区间观测器在不同空间位置下的动态演化轮廓
Fig. 5 The dynamic evolution profiles of battery packs temperature $T$ and interval observer at different spatial locations
图 6 不同观测器下不同空间位置的观测结果
Fig. 6 Estimation results for different spatial locations under different observers
表 1
18650 圆柱形电池的模型参数Table 1 Model parameters for the
18650 cylindrical battery符号 参数值 单位 $T_{ref}$ 295.150 K $T_{\infty}$ $298.150-\cos(\pi t)$ K $E_{a}$ 33.800 KJ/mol $R_{g}$ 8.314 J/(mol K) $k_{p}$ 0.980 W/(m K) $\rho_{p}$ 2118 $\text{kg/m}^3$ $C_{p}$ 711 J/(kg K) $h_{p}$ 69.890 $\text{W/(m}^2{\text{ K)}}$ 
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