Peukert方程的适用性分析及基于二阶段放电法的Peukert模型修正

仝猛^*,a,b, 卢兰光^b,欧阳明高^b,邵静玥^b,李哲^b,王瑛^b,王斌^b,林庆峰^c,赵伟^a

a长安大学工程机械学院/汽车学院b清华大学汽车工程系

c北京航空航天大学交通科学与工程学院

摘要：安时积分法是一种估计电池可用电量、剩余电量及SOC的实用方法，但电流倍率对其存在不可忽视的影响。基于铅酸电池试验的Peukert方程提供了一个修正电流倍率影响的经验模型。通过对该模型机理及应用的重新审视，发现这个模型的修正或使用并非总是合理有效。如对于锂离子等高性能、高效率的电池或动态工况下工作的电池适用性降低。

问题根源在于依据传统的单个阶段的恒流放电方法所建立的Peukert模型，忽视了电流倍率对于剩余电量的影响，在Peukert模型的试验及应用中，将不同倍率下的可用电量等同于电池容量，导致了对于剩余电量的忽视，如此就会将放电过程中的电荷损失及剩余电量的影响混淆在一起。那么，通过Peukert方程折算，大倍率电流放电的对于电池的等效放电量将被高估，电池荷电状态将被低估。

基于上述分析，本文提出一种二阶段放电试验方法来建立修正了的Peukert模型，即：对于每种倍率分别进行二个阶段的恒流放电，特定倍率放电到截至电压—静置—标准倍率放电到截至电压（CC-OC-CC）。依据二个阶段放电的总电量（第二阶段放电中电荷损耗为二阶小量，为了简化，认为其损耗比例（库伦效率）等同于第一阶段），而非可用电量即第一阶段的电量，去建立Peukert方程（其Peukert系数不同于原始Peukert模型的系数，具有更明确的物理意义）。如此以来不同倍率放电电池可达到相同的状态，故所建立的Peukert方程将反映的是倍率与电池最大可用电量之间的关系模型，该容量等于最大可用电化学容量减去电荷损耗，故也间接反映了倍率与电荷损耗（库伦效率）之间的关系。电荷损失与剩余电量在方程中的影响被分离。另外磷酸铁锂电池试验表明剩余电量与电流倍率的关系规律性更强，更符合Peukert形式的方程，与铅酸电池Peukert模型的机理一致，均为取决于电池中的扩散过程，故剩余电量的估计也可直接据此估计。

关键词：Peukert模型 二阶段放电 安时积分法 放电倍率修正 剩余电量 荷电状态

中图分类号：

Analysis of Rationality/Usability of Peukert Equation and amendment Based on Two Stage Discharge Method in Capacity Estimation

Tong Meng^*,a,b,Languang Lu ^b, Minggao Ouyang ^b, Jingyue Shao ^b, Zhe Li ^b, Ying Wang ^b, Bin Wang ^b, Qingfeng Lin ^c, Wei Zhao ^a

a. Department of Construction Mechanical, Chang An University, Xi’an, China; b. Department of Automotive Engineering, Tsinghua University, Beijing, China; c. School of Transportation Science & Engineering, BeiHang University

Abstract: Peukert Equation is wildly accepted as a c-rate compensation method for the state of charge or reminding capacity calculation in battery management for hybrid vehicle or electric vehicle. But Peukert Equation’s are found to be not accurate or applicable in many cases, such as high performance or high coulombic efficiency batteries or batteries working under dynamic load. Based on the previous efforts in [6], the Peukert Equation is reviewed again, and the reasons are thoroughly analyzed. Their root and main source are considered to be confusion or mixed usage of remaining capacity and the coulombic loss in the Peukert Equation.

A two stage “Constant Charge – Open Circuit - Constant Charge” discharge regime is presented to avoid such confusion. According to the total discharged capacity of the two stages, other than the single stage discharged capacity of various rate currents, a new Peukert Equation with a different Peukert coefficient is established, which reveals the correlation of maximum available capacity (omitting (the 2^nd order small) capacity loss errors at the second stage accounting to adopt the second stage standard C-rate discharge) or coulombic loss with the C-rate. The new model should be more applicable to dynamic load because minimizing the effect of different C-rate on remaining capacity. Anyway, for the diffusion process are considered for the governing principle, which are in agreement to the experiment of Lithium Iron Phosphate battery, the remaining capacity could be estimated directly with a similar form equation, correlating with the C-rate.

Keywords: Peukert Equation   two stage discharge   Coulombic counting   C-rate  Remaining capacity   State of Charge (SOC)

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