Article(id=1154038492721041498, tenantId=1146029695717560320, journalId=1146031654075715584, issueId=1154038481564197598, articleNumber=null, orderNo=null, doi=10.13234/j.issn.2095-2805.2024.2.183, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1619193600000, receivedDateStr=2021-04-24, revisedDate=1625673600000, revisedDateStr=2021-07-08, acceptedDate=1626105600000, acceptedDateStr=2021-07-13, onlineDate=1753073817662, onlineDateStr=2025-07-21, pubDate=1711728000000, pubDateStr=2024-03-30, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1753073817662, onlineIssueDateStr=2025-07-21, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1753073817662, creator=13701087609, updateTime=1753073817662, updator=13701087609, issue=Issue{id=1154038481564197598, tenantId=1146029695717560320, journalId=1146031654075715584, year='2024', volume='22', issue='2', pageStart='1', pageEnd='455', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1753073815003, creator=13701087609, updateTime=1753780998609, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1157004624629683026, tenantId=1146029695717560320, journalId=1146031654075715584, issueId=1154038481564197598, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1157004624629683027, tenantId=1146029695717560320, journalId=1146031654075715584, issueId=1154038481564197598, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=183, endPage=196, ext={EN=ArticleExt(id=1154038493555707998, articleId=1154038492721041498, tenantId=1146029695717560320, journalId=1146031654075715584, language=EN, title=Overview of Key Reliability Technologies for Power Lithium-ion Batteries Used in Electric Vehicles, columnId=1152281491788100462, journalTitle=Journal of Power Supply, columnName=Battery and Energy Storage, runingTitle=null, highlight=null, articleAbstract=

As power lithium-ion batteries play a key role in the electric vehicle industry, ensuring their working reliability has become a research hotspot at present. In this paper, the materials and manufacturing processes of lithium-ion batteries are reviewed. The battery state estimation and remaining useful life prediction methods are summarized in detail, and the advantages and disadvantages of these methods are discussed. From the perspective of battery management system, the relevant knowledges of equalization management system and thermal management system are sorted out in turn. From the perspective of electric vehicle hybrid energy storage system, the performance degradation mechanism under actual working conditions and the relevant technologies are elaborated upon. Finally, the status quo of key technologies related to the reliability of power lithium-ion batteries used in electric vehicles is summarized from four aspects, and the development possibilities in the future are forecasted.

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随着动力锂离子电池在电动汽车行业发挥关键性作用,保证其工作可靠性已成为当下研究热点。文中综述锂离子电池材料和制造工艺;详细归纳总结电池状态估算方法以及剩余寿命预测方法,并讨论各种方法的优缺点;从电池管理系统层面,先后梳理均衡管理系统和热管理系统相关知识;从电动汽车混合储能系统层面阐述实际工况下性能退化机理及相关技术。最后总结电动汽车动力锂离子电池与可靠性相关的四个方面关键技术的现状,并展望未来发展可能。

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何文轩(1996-),男,中国电源学会会员,硕士研究生。研究方向:锂离子电池安全性与可靠性。E-mail:18328073876@163.com。

耿磊(1991-),男,硕士,工程师。研究方向:混合动力汽车换流器。E-mail:geng.lei@jibei.sgcc.com.cn。

姚芳(1972-),女,通信作者,博士,教授。研究方向:电器可靠性及检测技术。E-mail: yaofang@hebut.edu.cn。

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何文轩(1996-),男,中国电源学会会员,硕士研究生。研究方向:锂离子电池安全性与可靠性。E-mail:18328073876@163.com。

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耿磊(1991-),男,硕士,工程师。研究方向:混合动力汽车换流器。E-mail:geng.lei@jibei.sgcc.com.cn。

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耿磊(1991-),男,硕士,工程师。研究方向:混合动力汽车换流器。E-mail:geng.lei@jibei.sgcc.com.cn。

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姚芳(1972-),女,通信作者,博士,教授。研究方向:电器可靠性及检测技术。E-mail: yaofang@hebut.edu.cn。

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journalId=1146031654075715584, articleId=1154038492721041498, language=CN, label=图9, caption=混合储能系统示意, figureFileSmall=AQ90UJjtPFaVxhI1Q2bxPA==, figureFileBig=4Vk2bIIb05rwJCMeRnuv5A==, tableContent=null), ArticleFig(id=1154038629321134537, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=EN, label=Tab. 1, caption=Comparison among different types of lithium-ion batteries, figureFileSmall=null, figureFileBig=null, tableContent=
锂电池 比能/ 工作 特点
类型 $\left({\mathrm{{Wh}}\cdot {\mathrm{{kg}}}^{-1}}\right)$ 温度/℃
NCM 200 $-{20}\sim {60}$ 能量密度高
LTO 50~90 $-{30}\sim {55}$ 寿命较长、大电流充电
LFP 150 $-{30}\sim {60}$ 电解质易制取、安全性高
), ArticleFig(id=1154038629392437707, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=CN, label=表1, caption=不同类型锂离子电池比较, figureFileSmall=null, figureFileBig=null, tableContent=
锂电池 比能/ 工作 特点
类型 $\left({\mathrm{{Wh}}\cdot {\mathrm{{kg}}}^{-1}}\right)$ 温度/℃
NCM 200 $-{20}\sim {60}$ 能量密度高
LTO 50~90 $-{30}\sim {55}$ 寿命较长、大电流充电
LFP 150 $-{30}\sim {60}$ 电解质易制取、安全性高
), ArticleFig(id=1154038629463740878, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=EN, label=Tab. 2, caption=Comparison among SOC estimation methods for lithium-ion batteries, figureFileSmall=null, figureFileBig=null, tableContent=
估算方法 优点 缺点
放电实验法 可靠性高 需要中断工作,实用性不强
安时积分法 运算简单 估算过程开环, 误差会累积
开路电压法 操作简单、精度高 需要静置电池,不适合在线
卡尔曼滤波 闭环、初始值要求低 需要精确的建模
粒子滤波 非线性、非高斯适用 需要大量样本
滑模观测器 精确稳定 设计复杂
神经网络 非线性适用、硬件要求低 输出结果不稳定
支持向量机 收敛较快 需要大量数据训练
模糊逻辑 不依赖建模精度 规则库需要大量数据
), ArticleFig(id=1154038629518266833, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=CN, label=表2, caption=锂离子电池 SOC 估算方法比较, figureFileSmall=null, figureFileBig=null, tableContent=
估算方法 优点 缺点
放电实验法 可靠性高 需要中断工作,实用性不强
安时积分法 运算简单 估算过程开环, 误差会累积
开路电压法 操作简单、精度高 需要静置电池,不适合在线
卡尔曼滤波 闭环、初始值要求低 需要精确的建模
粒子滤波 非线性、非高斯适用 需要大量样本
滑模观测器 精确稳定 设计复杂
神经网络 非线性适用、硬件要求低 输出结果不稳定
支持向量机 收敛较快 需要大量数据训练
模糊逻辑 不依赖建模精度 规则库需要大量数据
), ArticleFig(id=1154038629568598484, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=EN, label=Tab. 3, caption=Comparison among SOH estimation methods for lithium-ion batteries, figureFileSmall=null, figureFileBig=null, tableContent=
估算方法 优点 缺点
内阻分析法 简单,成本低 精度不高
电化学阻抗谱分析法 阻抗谱曲线信息丰富 测量复杂且需要专业仪器
微分分析法 能与微观电化学机制联系 较为复杂
最小二乘法 计算量小 难以实时获取参数
高斯过程回归 不需实际模型 参数调整复杂、计算量大
灰色理论 所需信息少、小样本适用 适用于中短期预测
自回归模型 简单、实时性好 置信区间大、依赖数据
), ArticleFig(id=1154038629660873175, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=CN, label=表3, caption=锂离子电池 $\mathrm{{SOH}}$ 估算方法比较, figureFileSmall=null, figureFileBig=null, tableContent=
估算方法 优点 缺点
内阻分析法 简单,成本低 精度不高
电化学阻抗谱分析法 阻抗谱曲线信息丰富 测量复杂且需要专业仪器
微分分析法 能与微观电化学机制联系 较为复杂
最小二乘法 计算量小 难以实时获取参数
高斯过程回归 不需实际模型 参数调整复杂、计算量大
灰色理论 所需信息少、小样本适用 适用于中短期预测
自回归模型 简单、实时性好 置信区间大、依赖数据
), ArticleFig(id=1154038629707010522, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=EN, label=Tab. 4, caption=Comparison among RUL prediction methods for lithium-ion batteries, figureFileSmall=null, figureFileBig=null, tableContent=
预测方法 优点 缺点
退化机理模型 直接反映内部机理,精度高 建模难度大, 不适合在线
等效电路模型 简单易实现 模型精度不高
退化经验模型 建模和计算简单 缺少理论支撑和实用性
人工智能 适用于非线性建模 需要大量数据训练
随机过程 符合电池的退化过程 依赖样本历史信息
统计技术 建模简单 精度依赖大量观测数据
), ArticleFig(id=1154038629769925083, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=CN, label=表4, caption=锂离子电池 RUL 预测方法比较, figureFileSmall=null, figureFileBig=null, tableContent=
预测方法 优点 缺点
退化机理模型 直接反映内部机理,精度高 建模难度大, 不适合在线
等效电路模型 简单易实现 模型精度不高
退化经验模型 建模和计算简单 缺少理论支撑和实用性
人工智能 适用于非线性建模 需要大量数据训练
随机过程 符合电池的退化过程 依赖样本历史信息
统计技术 建模简单 精度依赖大量观测数据
), ArticleFig(id=1154038629828645341, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=EN, label=Tab. 5, caption=Equalization circuit classification and characteristics of lithium-ion battery pack, figureFileSmall=null, figureFileBig=null, tableContent=
均衡类型 均衡电路 优点 缺点
能耗型 电阻型 结构简单易控制、成本低、体积小 产热、均衡速度慢、效率低
非能耗型 电容型 控制简单、易扩展 开关数量多、损耗大
电感型 均衡速度较快、效率较高 控制复杂、电压应力大
变压器型 均衡速度和效率适中、电流应力小 难实现、控制复杂
变换器型 均衡速度快、损耗较低 成本较高、控制复杂
电池型 结构简单、成本低 均衡速度一般
), ArticleFig(id=1154038629946085856, tenantId=1146029695717560320, journalId=1146031654075715584, articleId=1154038492721041498, language=CN, label=表5, caption=锂电池组均衡电路分类及特点, figureFileSmall=null, figureFileBig=null, tableContent=
均衡类型 均衡电路 优点 缺点
能耗型 电阻型 结构简单易控制、成本低、体积小 产热、均衡速度慢、效率低
非能耗型 电容型 控制简单、易扩展 开关数量多、损耗大
电感型 均衡速度较快、效率较高 控制复杂、电压应力大
变压器型 均衡速度和效率适中、电流应力小 难实现、控制复杂
变换器型 均衡速度快、损耗较低 成本较高、控制复杂
电池型 结构简单、成本低 均衡速度一般
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电动汽车动力锂离子电池可靠性关键技术综述
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何文轩 1, 2 , 耿磊 3 , 姚芳 1, 2
电源学报 | 电池与储能 2024,22(2): 183-196
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电源学报 | 电池与储能 2024, 22(2): 183-196
电动汽车动力锂离子电池可靠性关键技术综述
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何文轩1, 2 , 耿磊3 , 姚芳1, 2
作者信息
  • 国网冀北张家口供电公司 张家口 075700
  • 何文轩(1996-),男,中国电源学会会员,硕士研究生。研究方向:锂离子电池安全性与可靠性。E-mail:18328073876@163.com。

    耿磊(1991-),男,硕士,工程师。研究方向:混合动力汽车换流器。E-mail:geng.lei@jibei.sgcc.com.cn。

    姚芳(1972-),女,通信作者,博士,教授。研究方向:电器可靠性及检测技术。E-mail: yaofang@hebut.edu.cn。

Overview of Key Reliability Technologies for Power Lithium-ion Batteries Used in Electric Vehicles
Wenxuan HE1, 2 , Lei GENG3 , Fang YAO1, 2
Affiliations
  • State Grid Jibei Zhangjiakou Power Supply Company Zhangjiakou 075700 China
出版时间: 2024-03-30 doi: 10.13234/j.issn.2095-2805.2024.2.183
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随着动力锂离子电池在电动汽车行业发挥关键性作用,保证其工作可靠性已成为当下研究热点。文中综述锂离子电池材料和制造工艺;详细归纳总结电池状态估算方法以及剩余寿命预测方法,并讨论各种方法的优缺点;从电池管理系统层面,先后梳理均衡管理系统和热管理系统相关知识;从电动汽车混合储能系统层面阐述实际工况下性能退化机理及相关技术。最后总结电动汽车动力锂离子电池与可靠性相关的四个方面关键技术的现状,并展望未来发展可能。

锂离子电池  /  状态估算  /  剩余寿命预测  /  均衡管理  /  热管理  /  混合储能

As power lithium-ion batteries play a key role in the electric vehicle industry, ensuring their working reliability has become a research hotspot at present. In this paper, the materials and manufacturing processes of lithium-ion batteries are reviewed. The battery state estimation and remaining useful life prediction methods are summarized in detail, and the advantages and disadvantages of these methods are discussed. From the perspective of battery management system, the relevant knowledges of equalization management system and thermal management system are sorted out in turn. From the perspective of electric vehicle hybrid energy storage system, the performance degradation mechanism under actual working conditions and the relevant technologies are elaborated upon. Finally, the status quo of key technologies related to the reliability of power lithium-ion batteries used in electric vehicles is summarized from four aspects, and the development possibilities in the future are forecasted.

Lithium-ion battery  /  state estimation  /  remaining useful life prediction  /  equalization management  /  thermal management  /  hybrid energy storage
何文轩, 耿磊, 姚芳. 电动汽车动力锂离子电池可靠性关键技术综述. 电源学报, 2024 , 22 (2) : 183 -196 . DOI: 10.13234/j.issn.2095-2805.2024.2.183
Wenxuan HE, Lei GENG, Fang YAO. Overview of Key Reliability Technologies for Power Lithium-ion Batteries Used in Electric Vehicles[J]. Journal of Power Supply, 2024 , 22 (2) : 183 -196 . DOI: 10.13234/j.issn.2095-2805.2024.2.183
近年来, 锂离子电池在电动汽车、便携电子产品以及航空航天等领域凭借其无污染、质量轻、能量密度高、无记忆效应、自放电率低和生命周期长等显著优势, 发挥了重要作用。可靠性通常指产品在规定条件和规定时间下完成规定功能的能力, 包含耐久性、可维修性、设计可靠性三大要素。锂离子电池是一个动态的非线性系统, 具有复杂电化学特性, 对其可靠性关键技术的研究直接关系到电动汽车等产品的整体性能和质量。本文所提及的锂离子电池材料和制造工艺、故障预测与健康管理 PHM (prognostics health management)、电池管理系统 BMS (battery management system) 以及电动汽车混合储能系统等均是与可靠性相关的关键技术, 其发展对锂离子电池在续航、故障预测及维修和安全等方面都具有重要意义。
目前国内外尚缺乏对上述可靠性关键技术的系统整理。因此, 本文首先以电动汽车动力锂离子电池单体为研究对象, 综述锂离子电池材料和制造工艺, 总结故障预测与健康管理中状态估算和寿命预测的各种算法; 然后以电池组为研究对象, 从电池管理系统层面, 归纳均衡管理系统中拓扑和控制策略的设计,以及热管理系统中冷却和加热方案的优化;最后从电动汽车混合储能系统层面出发,阐述实际工况下影响电池性能的机理和功率分配技术。本文讨论各种在用方法和技术的优缺点并展望未来可能的发展方向, 为相关领域研究人员提供一定程度的参考作用。
锂离子电池材料和制造工艺是影响性能的核心所在,也是提升可靠性的根本。电池材料与能量密度、续航、低温特性等息息相关,制造工艺还对电池一致性有直接影响。
锂离子电池主要由正极、负极、电解质、隔膜和电池外壳等部分构成, 通过锂离子在正负极之间反复脱出和嵌入实现充放电功能。目前常见的有三元 (NCM)锂电池、钛酸锂(LTO)电池和磷酸铁锂(LFP) 电池[1],不同锂离子电池的参数和特点如表1 所示。
当下, 锂离子电池中常用的正极材料有层状结构的钴酸锂$\left({{\mathrm{{LiCoO}}}_{2}\text{)和镍钴锰酸锂}\left({{\mathrm{{LiCo}}}_{\mathrm{x}}{\mathrm{{Ni}}}_{\mathrm{y}}{\mathrm{{Mn}}}_{\mathrm{z}}{\mathrm{O}}_{2}}\right)}\right)$ 、 尖晶石型的锰酸锂$\left({{\mathrm{{LiMn}}}_{2}{\mathrm{O}}_{4}}\right)$ 以及不同聚阴离子型的正极材料$\left({{\mathrm{{LiMPO}}}_{4},\mathrm{M}= \mathrm{{Ti}},\mathrm{{Ge}},\mathrm{{Zr}},\mathrm{{Hf}}}\right)$。作为动力电池正极材料, 在保证安全性的基础上, 其未来发展主要倾向于研发能量密度高、清洁环保和成本低廉的电极材料。
而对锂离子电池的负极材料而言,金属锂本是比较理想的材料, 但由于在循环过程中锂枝晶的生长无法保证电池的安全性。经过长时间技术更迭, 当下商用锂离子电池中应用最多的负极材料是石墨类碳材料, 在保证电池高电压优势的情况下也提高了安全性和循环寿命。氮化物、聚硫酸铝(PAS)、锡合金以及其他的金属间化合物等正处于探索阶段。
电解质的作用是运送离子和传导电流, 对电池的性能影响较大。传统电池采用的水系电解质理论分解电压只有${1.23}\mathrm{\;V}$,如果使用该电解质则电压达不到锂离子电池$3 \sim 4\mathrm{\;V}$ 电压的要求,因此对耐高压的有机溶剂和电解质的研究是未来的发展方向之一。目前常用的电解质有环状碳酸酯、环状醚与链状醚等有机液体电解质,咪唑阳离子类、链状季铵阳离子类离子液体电解质, PEO 基、PVC 基等聚合物电解质[2]
隔膜的作用是将正、负极隔开但允许锂离子通过, 应选用热关闭性能好的隔膜, 即温度升高隔膜融化前孔隙发生关闭,内阻极速上升从而使内部反应停止。
锂离子电池主要生产流程有隔膜和极片制造、 电芯制作、装配封装、化成分容等工序, 具体如图1 所示。
制造过程中水分和粉尘的控制是影响电池性能的两个重要因素, 良好的水分控制会大大降低电池鼓胀率并提高性能; 而及时清理车间的灰尘和制造工艺脱落的粉尘等微小颗粒,会降低产生电池内部微短路的可能性。
锂离子电池的荷电状态$\mathrm{{SOC}}$ (state of charge)、 健康状态$\mathrm{{SOH}}$ (state of health) 估计以及剩余寿命 RUL(remaining useful life)预测是目前 PHM 领域的研究热点[3]。准确估算电池$\mathrm{{SOC}}\text{、}\mathrm{{SOH}}$ 和预测电池 RUL 能使电池管理系统更精确地把控电池当前的运行状态并执行相应功能, 对电池的安全、性能提升以及及时维修更换具有指导意义。
SOC 是用来表征锂电池剩余电量的重要参数, 不能直接获取, 如果估算不准确可能会导致锂电池产生过充、过放和过热等问题,进而影响到电池的使用寿命和系统的安全管理。目前, SOC 较为统一的定义是从电量的角度出发, 如美国先进电池联合会 USABC(united states advanced battery consortium) 在其电动汽车实验手册中将 SOC 定义为在一定的放电条件下, 电池剩余电量与相同条件下实际容量的比值, 数学表达式
$\mathrm{{SOC}}= {Q}_{t}/{Q}_{0}$
式中:${Q}_{t}$ 为电池在$t$ 时刻的剩余电量;${Q}_{0}$ 为电池在相同放电条件下的实际容量。
本文将目前国内外对锂电池的 SOC 估算方法总结归纳后大致分为以下三类:常规法、基于电池模型的方法和数据驱动法, 如图2 所示。
常规法算法比较简单, 包括放电实验法、安时积分法、开路电压法等, 适用于 SOC 估算精度要求不高的应用场景。
放电实验法将锂电池放电到截止电压, 通过放电容量反推放电前电池的 SOC。该方法简单可靠, 但耗时长、实用性不强。安时积分法利用一段时间内电流有效值与时间积分来计算容量变化量。该方法运算简单, 可在线估算, 但 SOC 初值无法确定, 且估算误差会不断积累[4]。开路电压法需先长时间静置锂电池使端电压稳定为开路电压, 然后通过开路电压与 SOC 的关系进行估算。该方法简单但电压波动会影响精度, 且由于静置时间较长不适用于电动汽车在线检测。
综上, 常规 SOC 估算方法实现容易, 但精度也较低,故目前应用较少。
基于电池模型的方法通常采用卡尔曼滤波 KF (kalman filtering)、粒子滤波 PF (particle filtering)、 滑模观测器 SMO(sliding mode observer)等进行 SOC 估算。
KF 根据前一时刻估计值及当前测量值, 结合噪声进行闭环迭代修正, 形成最优估计。该方法对初始 SOC 精度要求低、无需大量数据训练,但需精确电池模型和噪声统计特性。例如, 文献[5]通过一种近似的低阶电化学模型,设计了基于扩展$\mathrm{{KF}}$ 的自适应观测器, 在 UDDS 工况下仿真得到该观测器的 SOC 估计误差最大值为 1%。
$\mathrm{{PF}}$ 基于贝叶斯估计和蒙特卡罗方法,利用粒子集表示概率、根据测量值不断更新粒子权重和位置, 当前时刻状态只与上一时刻有关。该方法适用于能用状态空间模型描述的非线性系统, 精度较高、对噪声没有要求。例如, 文献[6]推导了标准伪二维模型的状态空间表达式, 提出一种束缚粒子滤波法, 通过大量仿真验证可行性。
SMO 是利用实测输入输出值估计内部状态值的动态系统。该方法抗干扰能力强,适用于观测反映复杂电化学特性的锂电池内部状态量, 且可不考虑初始 SOC 值, 精度高、稳定性好, 但设计难度大。 例如,文献[7]基于改进 SMO,引入带噪声的滑动平均模型和预报误差法, 用 sigmoid 函数代替符号函数且模型参数随 SOC 实时更新。
综上, 基于电池模型的 SOC 估算方法研究文献丰富。对于电池模型, 由于电化学模型太过复杂, 一般选择等效电路模型, 模型精度也会直接影响 SOC 估算效果。
数据驱动法通过对大量实验数据分析处理进行 SOC 估算, 常用的方法有神经网络 NN(neural network)、支持向量机 SVM(support vector machine) 和模糊逻辑$\mathrm{{FL}}$ (fuzzy logic)等。
$\mathrm{{NN}}$ 模拟人脑机制的信息处理系统,利用样本数据建立输入层和输出层的映射关系。该方法对硬件精度要求不高, 但计算量大, 忽略电池历史状态, 并未考虑时序因素。例如, 文献[8]提出一种负载分类 NN,利用电池静置、充电和放电的数据同时训练 3 个神经网络, 有效降低估计误差。
SVM 是建立在 Vapnik-Chervonenkis 维空间理论和结构风险最小化理论的基础上一种非线性算法。该方法收敛较快, 适用于小样本情况, 但需大量样本数据。例如, 文献[9]以电压、电流和温度作为输入, 利用 SVM 实现快速 SOC 估算, 对硬件要求较低。
FL 是将知识和经验描述为机器可理解的控制规则, 从而用计算机模拟实现对系统的控制。该方法不依赖于系统的精确模型, 但建立规则库需大量数据。例如,文献[10]基于FL,采用交流阻抗和电压恢复值作为输入, 实现不同循环寿命和温度下的 SOC 估算。
综上, 基于数据驱动的 SOC 估算方法不依赖电池模型, 适用于非线性系统, 是目前的热点研究方向。
归纳总结常用 SOC 估算方法的优缺点, 列之于表2
$\mathrm{{SOH}}$ 用来评估锂电池当下的健康状态,准确的$\mathrm{{SOH}}$ 估算有助于规划锂电池的未来运行,为电池可靠运行提供保证。SOH 基于容量的定义是指当前最大可用容量占电池额定容量的百分比, 数学表达式
$\mathrm{{SOH}}= {Q}_{\mathrm{a}}/{Q}_{\mathrm{R}}$
而基于内阻变化定义的数学表达式[11]
$\mathrm{{SOH}}= \left({{R}_{\mathrm{e}}- R}\right)/\left({{R}_{\mathrm{e}}- {R}_{\text{new }}}\right)$
式中:${Q}_{\mathrm{a}}$ 为使用后电池实际最大可用容量;${Q}_{\mathrm{R}}$ 为电池的额定容量;${R}_{\mathrm{e}}$ 为寿命结束时的电池内阻;${R}_{\text{new }}$ 为新电池的内阻;$R$ 为目前的电池内阻。
$\mathrm{{SOH}}$ 估算方法的分类标准有很多,许多$\mathrm{{SOC}}$ 的估算方法同样适用于$\mathrm{{SOH}}$ 估算,这一部分内容不再详细描述。
本文将其他常用的$\mathrm{{SOH}}$ 估算方法分为三大类:特征法、自适应滤波法和数据驱动法[12],如图3 所示。
特征法以电池在性能衰退过程中的某些特征量变化为依据, 通过各种算法建立该特征量与电池$\mathrm{{SOH}}$ 的关系,如内阻分析法、电化学阻抗谱$\mathrm{{EIS}}$ (electrochemical impedance spectroscopy)法、微分分析法等。
内阻分析法以电池内阻作为性能退化特征量, 建立与$\mathrm{{SOH}}$ 的对应关系。该方法简单且成本低,但是精确度不高,普适性不强。例如, 文献[13]基于等效电路模型提出一种混合动力汽车的内阻辨识方法用于$\mathrm{{SOH}}$ 估算,并考虑了温度对估算精度的影响。
EIS 法将电池在不同衰退阶段的阻抗谱曲线与电路模型参数相联系,再根据模型参数与$\mathrm{{SOH}}$ 对应。该方法阻抗谱曲线信息丰富, 但测量复杂且需要专业仪器,一般仅用于离线状态。例如,文献[14] 利用 EIS 构建等效电路模型, 采用自动光谱处理, 得到了基于多元数学分析的$\mathrm{{SOH}}$ 预测算法。
微分分析法基于电池不同老化状态下的微分容量或电压特性曲线, 与电池微观机制相联系, 提取电池老化特征实现$\mathrm{{SOH}}$ 估算。例如,文献[15]基于容量增量提出一种高斯滤波方法, 在获得平滑微分曲线的同时保留老化相关的重要特征, 在小倍率电流下能有效估算$\mathrm{{SOH}}$
目前许多研究致力于发掘能表征电池退化的新特征量估算$\mathrm{{SOH}}$,如恒压充电电流时间常数、充电平均温度等。
自适应滤波法能辨识并根据滤波增益不断更新电池模型参数, 以提高 SOH 估算精度, 常用方法如上文提到的 KF、PF 及最小二乘法 LS (least square)等。
LS 利用线性回归分析求解未知数据并使之与实际数据的误差平方和最小, 实现简单且计算量小,广泛应用于参数辨识,但难以实时获取参数。如文献[16]提出一种多遗忘因子递推 LS 并结合无迹 KF, 利用粒子群算法确定最优遗忘因子, 在温度变化的 NEDC 工况下, 所提方法的平均 SOC 估算误差降至 0.29%。
基于自适应滤波的$\mathrm{{SOH}}$ 估算方法能实现在线估计,因此在工业中应用广泛且精度较高。
数据驱动法基于电池实验数据发掘性能退化规律并用于$\mathrm{{SOH}}$ 估算,如高斯过程回归$\mathrm{{GPR}}$ (gaussian process regression)模型、灰色理论 GF(grey theory) 和自回归 AR(auto regressive)模型等。
GPR 模型是一种能实现基于贝叶斯框架下状态预测的非参数模型, 通常被用于低维和小样本的回归问题。例如,文献[17]选择复合核函数的GPR 模型进行$\mathrm{{SOH}}$ 预测,使用多输出模型充分利用多个电池的数据,提高预测性能。
GF 是指通过少量、不完全的信息建立数学模型并做出预测,应用广泛,尤其是处理小样本问题。 例如,文献[18]建立以欧姆内阻和极化内阻增量、极化电容减少量为输入, 容量为输出的灰色神经网络模型,精度高于传统模型。
$\mathrm{{AR}}$ 模型是一种时间序列分析方法,它基于系统历史状态获取适用于当前的模型阶次和参数, 建立包含数据特征的模型进行估计, AR 模型计算量小、复杂度低。例如, 文献[19]以特定采样率区间的充电电压数据为健康因子,建立了非线性自回归模型, 结果表明在不同循环条件下均方根误差最大 0.46。
综上, 基于数据驱动的 SOH 估算方法不需要了解电池的工作原理和电池模型, 只与收集的老化数据有关,预测精度较高且具有普适性。
总结归纳常用锂离子电池$\mathrm{{SOH}}$ 估算方法的优缺点,列之于表3
$\mathrm{{SOC}}$$\mathrm{{SOH}}$ 单独估算通常忽略两个状态量的耦合关系, 造成估算结果失真。因此, SOC 和 SOH 联合估算将两个状态量相互迭代更新, 随锂离子电池状态变化自适应更新[20]。如文献[21]利用带遗忘因子的 RLS 在线识别与$\mathrm{{SOH}}$ 相关的电池参数并以此估算其容量和最大可用输出功率,对不同老化水平的电池,$\mathrm{{SOH}}$ 估算精度为${0.5}\%;\mathrm{{SOC}}$ 估算由基于 EKF 的二阶等效电路模型来实现,并通过$\mathrm{{SOH}}$ 估算的容量更新, SOC 估算结果显著提高到 1.1%。
动力锂离子电池的寿命通常指循环寿命(cycle life), 即电池的性能指标达到规定的失效阈值前能够完成的循环次数, 影响其寿命的主要因素有温度、充放电倍率和充放电截止电压等。
电池的剩余寿命预测是指通过相对较短时间的电池实验数据, 预测电池初次衰退到失效阈值所需要的时间,利用可靠的寿命预测方法可以节约测试时间和成本。锂电池 RUL 的预测方法有很多, 本文大致上分为以下三类:基于模型的方法、基于数据驱动的方法和基于融合的方法, 如图4 所示。
基于模型的 RUL 预测方法可分为以下三类: 退化机理模型、等效电路模型和经验退化模型。
退化机理模型是基于电池内部电化学机理建立的老化模型。该方法可直接反映内部相关电化学过程, 但参数较多且求解困难, 不适合在线使用。例如, 文献[22]探讨了容量退化和锂盐溶解之间的关系。
等效电路模型是基于电池外部电特性, 利用电气元件搭建电路模型反映内部化学特性。该方法实现简单, 但会忽略部分电化学隐含关系。例如, 文献 [23]将等效电路模型应用于粒子滤波框架中,对不同阶段的锂电池进行 RUL 预测, 若结合放电速率、 温度和放电深度等因素,精度可进一步提高。
经验退化模型是基于统计分析, 建立反映输入输出关联规律的模型, 常用指数函数和幂函数模型,并结合$\mathrm{{KF}}$$\mathrm{{PF}}$ 等更新模型参数。该方法忽略内部的复杂特性, 简化了建模和计算, 但缺少足够的理论支撑。如文献[24]提出了一种基于指数模型和粒子滤波的 RUL 预测方法, 参数自适应更新, 并用外推法得到 RUL 预测均值和概率分布图。
综上, 基于模型的 RUL 预测方法中, 由于退化机理模型太过复杂且普适性较差, 实际应用较少; 等效电路模型和经验退化模型应用较广泛。
基于数据驱动的方法通过研究实验数据中的历史信息发掘退化规律,外推实现剩余寿命预测。 常用基于人工智能的方法、基于随机过程的方法和基于统计技术的方法等。
基于人工智能的方法利用其强大的非线性建模能力, 建立表征电池性能退化特征量与剩余寿命关系的模型, 包括神经网络、支持向量机和相关向量机等[25]。例如,文献[26]基于 NASA 数据集利用深度神经网络进行 RUL 预测,并与 SVM、NN 和线性回归等方法比较验优。
锂电池退化过程本质是一个随机过程, 因此使用基于随机过程的算法在理论上具有优势, 常用的有维纳过程、高斯过程等。例如,文献[27]提出了一种考虑弛豫效应的线性维纳过程 RUL 预测方法, 将锂电池运行分为消除弛豫效应的退化过程和弛豫效应引起的恢复过程, 利用最大似然估计求解先验参数并在贝叶斯框架下在线更新。
基于统计技术的方法按时间序列分析电池退化特征的变化, 并建立统计学模型, 常用自回归统计模型、基于趋势评估等。例如,文献[28]建立统计回归模型并用粒子群算法优化模型参数, 可以在电池早期较准确地预测 RUL。
综上, 基于数据驱动的方法避开了对电池内部失效机理的探究和复杂模型的建立, 成为近年来的研究热点, 该方法的局限在于依赖样本数据包含的历史信息。
为了弥补基于模型和基于数据驱动两种方法的不足, 采用基于融合的方法提高预测精度和鲁棒性。目前,基于融合的方法成为了一大研究热点, 主要包括基于模型和数据驱动方法的融合、数据驱动方法之间的融合[29]。如文献[30]以粒子滤波算法为核心、双指数模型作为状态方程及人工神经网络作为观测方程, 经重采样得到贝叶斯模型的后验参数, 从而得到电池的退化曲线。结果表明该方法预测效果良好, 精度随循环次数增加逐渐提高, 但需减少神经网络带来的误差以及考虑更复杂的环境因素。
总结归纳常用锂离子电池 RUL 预测方法的优缺点,列之于表4
BMS 是电动汽车的核心,它负责监控电池性能, 并调整系统使之与使用条件和环境相匹配, 具体包括数据采集、状态估计、热管理、均衡管理、数据通信和故障诊断等功能,如图5 所示,对维持动力锂离子电池组长寿命、高效率的可靠运行具有实际意义。
均衡管理系统是 BMS 中的核心组件之一。在实际应用中, 单个锂离子电池往往无法满足电动汽车的电压、功率和续航等需求, 所以通常将多个电池串并联成组来提供动力。而由于材料配比和制作工艺等难以避免的问题, 每一块电池出厂时的性能和参数都可能存在或多或少的差异,并且电压、 SOC 和内阻等的差异会随着使用逐渐增大, 电池组不一致性示意如图6 所示。不一致性会导致电池出现过充或过放的现象, 进而内部出现电解质分解和锂枝晶的形成,因此电池寿命和安全性大大降低。
为解决在使用过程中愈渐增大的不一致性问题,必须对电池组进行均衡管理,而对均衡电路的设计是其中的关键之一, 根据均衡过程是否消耗能量可以将均衡电路分为能耗型和非能耗型两大类[31]
能耗型均衡是利用在电池两端并联电阻和开关, 直接将多余电量转化为热能进行消耗, 从而平衡电池间的不一致性。这种方式通常拓扑结构简单、控制容易且成本低,但缺点是能耗严重、均衡速度慢且存在产热过高的问题, 若没有良好的散热系统会影响电池组的性能甚至产生安全隐患。常见的电动汽车目前大多采用该种方法实现均衡功能,如特斯拉、比亚迪等。
非能耗型的均衡电路结构则非常灵活多样, 因为其高效、低能耗的特点, 成为了目前均衡电路的主要研究方向。非能耗型均衡是利用储能元件作为中介, 不直接消耗能量而是通过能量转移的方式实现单体电池间的均衡, 降低不一致性。该方法缺点在于电路结构通常比较复杂、体积和成本难以控制且开关损耗也不容忽视, 目前非能耗型均衡技术也在小范围内推广应用。本文根据均衡中介的不同将均衡电路进一步分为以下几类, 并总结各均衡电路的优缺点, 如表5 所示。
例如,文献[32]提出一种基于冗余电池的主动均衡方法, 根据串联电池的 SOC 调整其与冗余电池并联, 实现能量在电池间的传递, 并且冗余电池在充放电过程中还能充当电源。该方法均衡电路简单, 但需要串联电池容量差值之和小于冗余电池容量。
文献[33]提出一种自动开关耦合电容均衡器, 可以实现串联电池组中任意单体电池间的均衡, 每个单体电池只需要两个开关和一个电容器, 所有 MOSFETs 都由一对互补的 PWM 信号控制。该方法体积较小、成本低、均衡速度较高。上述两种方法的均衡拓扑结构如图7 所示。
对电池组进行均衡管理前首先需要选定一个合适的均衡变量, 然后建立起不一致性的判定标准, 通过衡量电池间均衡变量的差值是否超过预设的标准来判断是否执行均衡管理, 从而使电池组的一致性保持在允许范围内。
常用的均衡变量有工作电压、开路电压和 SOC 等, 它们作为均衡变量各有优劣, 最近也有文献使用多变量融合。①工作电压易于测量、计算效率高、 可防止电池过充放; 但是工作电压易受内部参数和外部环境影响, 在工况下稳定性较差, 可能导致重复均衡。②开路电压能准确反映电池的内部状态;但是需要电池静置测量不易获取。③SOC 直接表征了电池的剩余电量, 是电池最本质和理想的均衡变量, 并且可以忽略电池总容量的差异; 但是在实际工况下实现实时高精度的 SOC 估算较为困难且计算能力要求较高, 目前难以应用于车辆。④多变量融合能结合多个变量的优点、均衡速度快、精度高;但是变量估算困难,控制策略也会更加复杂。例如, 文献[34]先对电池按电压降序排列,过充的先放电, 然后按单体 SOC 和平均 SOC 的差异实现均衡, 均衡速度和一致性表现良好,但控制复杂。
均衡策略主要是为了确保均衡过程的快速、准确和稳定, 根据均衡目标不同可将均衡策略分为阈值合理化、电池容量最大化、均衡时间最小化和均衡能耗最小化。而合适的均衡算法能避免重复均衡, 缩短均衡时间, 提高均衡效率, 目前常用的均衡算法有基于数据驱动的算法和基于的控制算法等。 例如,文献[35]以电压为均衡变量, 优先对串联电池组中电压最低的电池实现均衡, 以此完成对电池组的均衡。文献[36]提出变论域双模糊控制器策略, 在输出论域中引入伸缩因子$a$,自适应调节均衡电流幅值, 在需要较大均衡电流时增大其幅值, 在充放电末期减小其幅值,有效提高均衡速度。
温度是影响动力锂离子电池工作性能和寿命的重要因素。温度过低时,$\mathrm{{Li}}+$ 容易以金属锂的形式在电池负极析出, 并且内阻和极化电压的增加使得放电能力下降, 电池实际可用容量减小; 而温度过高时, 电池内部会出现副反应和元件失效, 导致充放电效率降低, 循环寿命急剧下降, 甚至引发安全问题。为了保证电池安全性和提高性能, 其工作温度的最值和局部温差必须保持在适当的范围内。因此热管理系统作为 BMS 中另一个核心组件显得十分重要, 它能对电池温度进行监控并通过热管理技术及时作出对应调整。
BMS 热管理常见的冷却方案按照传质的不同可以主要可分为空气冷却、液体冷却和相变材料 PCM(phase change material) 冷却, 还有其他冷却方式如空调制冷、热管冷却、热电制冷、泡沫金属冷却和冷板冷却等。
空气冷却是利用空气流动来降低温度, 根据冷却系统是否安装风扇可分为自然冷却和强制风冷。 自然冷却是通过电池箱体内部的空气与发热元件之间的热对流实现冷却的目的, 该方案简单易行但冷却效果有限;而强制风冷一般从空气的流量、电池布局和流道设计等方面研究[37]。Tao 等[38] 发现在考虑冷却效果和成本的前提下, 强制风冷最理想结构是立方排列, Tong 等[39] 发现通过将电池单体进行交错排列可以有效降低电池模块的最大温度变化。
液体冷却已经成为工业中最有效和普遍的冷却技术, 它通过液体把电池组产生的热量与外界空气进行热交换。通常将电池直接沉浸在非导电液体中;或用冷却板(散热器)、管和夹套来分离工作介质和电池, 热量从电池传到冷却板然后被冷却剂带走。液体冷却的优点在于导热率较高, 但是必须要求有良好的密封设计, 因为一旦液体泄漏会造成严重的后果。液体冷却剂在恒压的沸腾过程中温度不会改变,因此选择一种沸点在锂离子电池最佳工作温度范围内的冷却剂, 如 3M 公司生产的氢氟醚冷却液 NOVEC 7000, 不仅可以降低电池组的整体温度,而且可以有效地保持电池组的温度均匀性[40]
PCM 具有熔点低、潜热高的优点。PCM 冷却正是利用相变材料的融化 (凝固) 潜热来吸收电池产生的热量, 电池组工作产生热量时, PCM 将热量以相变热的形式储存, 在较冷的环境工作时再释放出来。该方法适用于寒冷的条件下, 而且成本低, 冷却效果好, 具有一定的发展潜力。文献[41]设计了一种基于四种纯相变材料 (癸酸、二十烷、十水碳酸钠和十八烷)的电池热管理方案, 三层相变材料时效果最佳, 其中导热率较高的相变材料放置在更靠近电池的位置, 导热率较低的相变材料放置在外壁。
综上, 空气冷却简单易实现, 能在较低充放电倍率下实现有效冷却;液体冷却方案中通道的数量和冷却剂流量起着主导作用;PCM 材料导热系数较差限制了其适用性, 可通过添加剂改善性能。
BMS 热管理系统的加热方案按热量来源可分为内部加热和外部加热两大类。
内部加热可以获得更快的温升速率,并且不受电池形状的影响; 但是控制机制复杂并且安全性难以得到很好的保证。Wang 等[42] 提出一种自发热锂离子电池结构, 如图8 所示。将一个有两接头的镍箔嵌入电池内,当表面温度低于设定值时,开关连通镍箔使电流通过产生欧姆热,直至电池温度达到预设值停止加热恢复正常电池状态工作。
外部加热方案按传热介质又可细分为以下几类:空气加热、电加热膜加热、正温度系数 PTC (positive temperature coefficient) 材料加热和液体加热。①空气加热一般是将空气由加热装置加热后通过风扇预热电池,其结构简单、成本低廉,在电动汽车中被广泛采用。②电加热膜一般由电阻丝、绝缘层、导线和接插件组成, 通常采用恒功率加热, 单体电池的温差控制在${8}^{\circ }\mathrm{C}$ 左右,安装位置在模组侧边、模组底部和电池间隙。③PTC 材料加热是利用材料电阻随温度升高而增加的特性,一般由 PTC 元件、导热金属板和引出导线组成, 通常采用自控温加热,单体电池的温差控制在${10}^{\circ }\mathrm{C}$ 左右。文献[43] 中通过仿真对比,电池在${50}^{\circ }\mathrm{C}$ 的初始温度下, PTC 材料加热的温升速率是相同环境温度下空气加热的 6.4 倍, 并且随着 PTC 材料导热系数的增加, 温差减小。④液热系统主要由加热器、热交换器、泵和循环管组成, 可以通过在液冷系统的冷却回路中并入一个加热回路实现对系统加热, 温升速率较高, 单体电池间的温差控制在${5}^{\circ }\mathrm{C}$ 以下[44]
综上, 由于电池类型、充放电倍率等外部条件的差异, 很难对各种加热方案的性能得出明确结论。由于空气加热和液体加热技术复杂性较低, 已经广泛应用于电动汽车;电加热膜的安全性和可靠性还需严格验证; PCM 材料热性能退化和缓慢的相变过程还需实验室条件下进一步的研究。
电动汽车的电气传动系统(如 DC/DC 变换器和电机变频驱动器)通常由高频电力电子器件构成, 电机无功功率消耗以及电力电子器件高频开关动作都会对汽车直流高压母线产生大量高频谐波[45]。 电动汽车混合储能系统能有效抑制高频电流振荡和纹波对电池系统产生的扰动负载, 减轻电池性能所受的负面影响。
电动汽车工况下,动力电池承载的电流具有纹波、高频、快放充等特性,这些特性均会影响电池性能退化。
早期动力铅酸电池实验研究表明, 交流纹波可能导致电池经历浅放电循环, 进而可能导致气体、栅极腐蚀和内热的产生[50]。对于动力锂电池而言,交流纹波对其性能退化有长期影响, 并与电流频率有潜在因果关系,但具体关系还未得知[47]。动力锂电池为高频负载供电时, 由于锂离子没有足够时间脱嵌, 部分以金属锂的形式析出[48]。在实际工况下,电动汽车在加速和刹车时, 大电流反复地快速输出和流入电池组,这样可能会损害电解质,缩短电池寿命[46]。此外,文献 [48]采用$\mathrm{X}$ 射线光电子能谱技术研究锂电池性能的退化机理, 结果表明 SEI 表面膜的形成依赖于耦合交流扰动的频率,进而影响电池退化。
锂电池和超级电容组成的混合储能系统能弥补单一储能系统特性的不足, 其基本拓扑如图9 所示[49]。其中,锂电池用于响应幅值低、波动慢的低频功率分量, 超级电容用于响应幅值高、波动快的高频功率分量。
有研究表明, 对混合储能系统中低频分量和高频分量进行合理分配, 能有效抑制功率波动, 并可通过储存减速时产生的制动能量来提高电动汽车效率。例如,文献[45]提出了基于小波变换的功率分流方法, 将模拟高速公路经济性测试工况数据中的高频、混沌分量进行分离并重构后分配, 将锂电池高频功率需求降低至$1/{16},{50}$ 次充放电循环后锂电池$\mathrm{{SOH}}$ 提高了${0.8}\%$。又如,文献[49]提出了一种基于小波变换的负荷功频域分配方法和量化储能介质频率特性的方法, 建立了储能介质频率特性和小波变化分解层数的关系。
本文对电动汽车动力锂离子电池可靠性关键技术进行综述, 综述锂离子电池的材料和制造工艺现状;分析比较各种 SOC、SOH 估算方法和剩余寿命预测方法的原理、优缺点和适用情况;从 BMS 层面梳理均衡管理系统和热管理系统相关理论和技术;从电动汽车混合储能系统层面梳理实际工况下影响锂电池性能的机理和相关技术。笔者对电动汽车动力锂离子电池可靠性研究展望如下。
(1)锂离子电池电极材料应朝着安全性强、能量密度高、清洁便宜的方向发展,电解质和隔膜应具有良好的热稳定性和热关闭性,除此之外还有阻燃剂、黏结剂等也会影响到电池的性能; 电池制造工艺可以进一步提高自动化程度并且严格把控产品的一致性问题。
(2)在状态估计和寿命预测方面,一是继续通过算法的改进和融合以达到更高的精度;二是需要基于实验室研究成果, 面向实际工况下开展研究; 三是研究对象不仅是锂电池单体,应该向电池模组和电池包推进; 四是可借助充电大数据, 研究数据驱动的电池包状态估计和寿命预测技术。
(3)为提升效率和降低体积, 均衡管理需进一步开展非能耗型均衡拓扑和均衡策略的研究;为降低成本、提高锂电池安全性和稳定性, 热管理研究应更多考虑实际情况下复杂多变的环境因素,建立更加精确的电池产热模型, 并提升加热和冷却系统的工艺和质量。
(4)在电动汽车混合储能系统方面,一是改进和优化储能系统拓扑, 减少损耗和电压畸变等问题;二是研究如何降低放电峰值电流以保证电池工作效率和使用寿命;三是要有效发挥超级电容在大电流快速充放的特性, 提升再生制动能量的回收效率; 四是合理分配该系统中的高频和低频分量, 并根据工况调整控制策略。
  • 河北省自然科学基金资助项目(E2019202481)
  • 河北省自然科学基金资助项目(E2017202284)
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doi: 10.13234/j.issn.2095-2805.2024.2.183
  • 接收时间:2021-04-24
  • 首发时间:2025-07-21
  • 出版时间:2024-03-30
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  • 收稿日期:2021-04-24
  • 修回日期:2021-07-08
  • 录用日期:2021-07-13
基金
Natural Science Foundation of Hebei Province(E2019202481)
河北省自然科学基金资助项目(E2019202481)
Natural Science Foundation of Hebei Province(E2017202284)
河北省自然科学基金资助项目(E2017202284)
作者信息
    国网冀北张家口供电公司 张家口 075700
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2种不同金属材料的力学参数

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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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