【《锂离子电池分数阶等效电路模型分析》1600字】

锂离子电池分数阶等效电路模型分析锂离子电池等效电路模型通常可分为整数阶模型与分数阶模型ADDINEN.CITE<EndNote><Cite><Author>Hidalgo-Reyes</Author><Year>2019</Year><RecNum>52</RecNum><DisplayText>[17]</DisplayText><record><rec-number>52</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615621387">52</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hidalgo-Reyes,J.I.</author><author>Gómez-Aguilar,J.F.</author><author>Escobar-Jiménez,R.F.</author><author>Alvarado-Martínez,V.M.</author><author>López-López,M.G.</author></authors></contributors><titles><title>Classicalandfractional-ordermodelingofequivalentelectricalcircuitsforsupercapacitorsandbatteries,energymanagementstrategiesforhybridsystemsandmethodsforthestateofchargeestimation:Astateoftheartreview</title><secondary-title>MicroelectronicsJournal</secondary-title></titles><periodical><full-title>MicroelectronicsJournal</full-title></periodical><pages>109-128</pages><volume>85</volume><section>109</section><dates><year>2019</year></dates><isbn>00262692</isbn><urls></urls><electronic-resource-num>10.1016/j.mejo.2019.02.006</electronic-resource-num></record></Cite></EndNote>[17]。美国爱达荷国家实验室设计提出了最早的等效电路模型，即Rint模型，模型包括一个理想电压源和一个串联欧姆内阻。Rint模型可描述动力电池内阻特性与开路特性，无法实现动态特性模拟。此后，研究人员在Rint模型基础上构建了Thevenin模型，通过串接一个RC环节描述其在电流激励下的电压驰豫特性，虽然该模型解决了动态特性模拟问题，但其在高倍率循环、使用边缘区间内工作特性较差。在此基础上，二阶等效电路模型（DP模型）通过额外串接1个RC环节，模拟在电流激励作用下锂离子电池不同时间尺度上的极化特性，具有较好的模拟效果ADDINEN.CITE<EndNote><Cite><Author>Lai</Author><Year>2021</Year><RecNum>58</RecNum><DisplayText>[18]</DisplayText><record><rec-number>58</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615621427">58</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Lai,Xin</author><author>Meng,Zheng</author><author>Wang,Shuyu</author><author>Han,Xuebing</author><author>Zhou,Long</author><author>Sun,Tao</author><author>Li,Xiangjun</author><author>Wang,Xiangjin</author><author>Ma,Yuhan</author><author>Zheng,Yuejiu</author></authors></contributors><titles><title>GlobalparametricsensitivityanalysisofequivalentcircuitmodelbasedonSobol’methodforlithium-ionbatteriesinelectricvehicles</title><secondary-title>JournalofCleanerProduction</secondary-title></titles><periodical><full-title>JournalofCleanerProduction</full-title></periodical><volume>294</volume><section>126246</section><dates><year>2021</year></dates><isbn>09596526</isbn><urls></urls><electronic-resource-num>10.1016/j.jclepro.2021.126246</electronic-resource-num></record></Cite></EndNote>[18]。2001年，美国《PNGV电池试验手册》阐述了PNGV模型构建方法，在原有模型基础上额外串联一个电容模拟在持续电流激励下产生的开路电压飘移过程。整数阶模型通过提高串联的RC环节数、增添额外的电阻特性等提高模型精度，然而高阶等效电路模型产生的额外参数，通过提高RC并联支路数来提高模型精度，但高阶模型必然导致参数增加及运算复杂度增大，同时也增加了模型参数辨识的难度ADDINEN.CITE<EndNote><Cite><Author>Hua</Author><Year>2021</Year><RecNum>56</RecNum><DisplayText>[19,20]</DisplayText><record><rec-number>56</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615621414">56</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hua,Xiao</author><author>Zhang,Cheng</author><author>Offer,Gregory</author></authors></contributors><titles><title>Findingabetterfitforlithiumionbatteries:Asimple,novel,loaddependent,modifiedequivalentcircuitmodelandparameterizationmethod</title><secondary-title>JournalofPowerSources</secondary-title></titles><periodical><full-title>JournalofPowerSources</full-title></periodical><volume>484</volume><section>229117</section><dates><year>2021</year></dates><isbn>03787753</isbn><urls></urls><electronic-resource-num>10.1016/j.jpowsour.2020.229117</electronic-resource-num></record></Cite><Cite><Author>Shi</Author><Year>2020</Year><RecNum>50</RecNum><record><rec-number>50</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615621374">50</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Shi,Meihua</author><author>Yuan,Jingchao</author><author>Dong,Li</author><author>Zhang,Dan</author><author>Li,Aijun</author><author>Zhang,Jiujun</author></authors></contributors><titles><title>Combiningphysicochemicalmodelwiththeequivalentcircuitmodelforperformancepredictionandoptimizationoflead-acidbatteries</title><secondary-title>ElectrochimicaActa</secondary-title></titles><periodical><full-title>ElectrochimicaActa</full-title></periodical><volume>353</volume><section>136567</section><dates><year>2020</year></dates><isbn>00134686</isbn><urls></urls><electronic-resource-num>10.1016/j.electacta.2020.136567</electronic-resource-num></record></Cite></EndNote>[19,20]。随着对分数阶方程研究深入，基于分数阶方程简化得到的分数阶等效电路模型是目前基于等效电路提出的较好的模型解决方案ADDINEN.CITE<EndNote><Cite><Author>Xu</Author><Year>2013</Year><RecNum>48</RecNum><DisplayText>[21]</DisplayText><record><rec-number>48</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615613823">48</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Xu,Jun</author><author>Mi,ChuntingChris</author><author>Cao,Binggang</author><author>Cao,Junyi</author></authors></contributors><titles><title>Anewmethodtoestimatethestateofchargeoflithium-ionbatteriesbasedonthebatteryimpedancemodel</title><secondary-title>JournalofPowerSources</secondary-title></titles><periodical><full-title>JournalofPowerSources</full-title></periodical><pages>277-284</pages><volume>233</volume><section>277</section><dates><year>2013</year></dates><isbn>03787753</isbn><urls></urls><electronic-resource-num>10.1016/j.jpowsour.2013.01.094</electronic-resource-num></record></Cite></EndNote>[21]，其结构相对简单，模型精度好、参数辨识难度低，但计算复杂度较高ADDINEN.CITE<EndNote><Cite><Author>Hu</Author><Year>2018</Year><RecNum>115</RecNum><DisplayText>[22]</DisplayText><record><rec-number>115</rec-number><foreign-keys><keyapp="EN"db-id="09dexz9w59adeced09q5adw1azzt2azarfta"timestamp="1619831689">115</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hu,Minghui</author><author>Li,Yunxiao</author><author>Li,Shuxian</author><author>Fu,Chunyun</author><author>Qin,Datong</author><author>Li,Zonghua</author></authors></contributors><titles><title>Lithium-ionbatterymodelingandparameteridentificationbasedonfractionaltheory</title><secondary-title>Energy</secondary-title></titles><periodical><full-title>Energy</full-title></periodical><pages>153-163</pages><volume>165</volume><section>153</section><dates><year>2018</year></dates><isbn>03605442</isbn><urls></urls><electronic-resource-num>10.1016/j.energy.2018.09.101</electronic-resource-num></record></Cite></EndNote>[22]。分数阶模型最早起源于电化学阻抗谱测试结果，使用常相位元件（CPE）来模拟电化学阻抗谱中双电层电容弥散效应，以实现迟滞特性的模拟ADDINEN.CITE<EndNote><Cite><Author>Xu</Author><Year>2013</Year><RecNum>48</RecNum><DisplayText>[21]</DisplayText><record><rec-number>48</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615613823">48</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Xu,Jun</author><author>Mi,ChuntingChris</author><author>Cao,Binggang</author><author>Cao,Junyi</author></authors></contributors><titles><title>Anewmethodtoestimatethestateofchargeoflithium-ionbatteriesbasedonthebatteryimpedancemodel</title><secondary-title>JournalofPowerSources</secondary-title></titles><periodical><full-title>JournalofPowerSources</full-title></periodical><pages>277-284</pages><volume>233</volume><section>277</section><dates><year>2013</year></dates><isbn>03787753</isbn><urls></urls><electronic-resource-num>10.1016/j.jpowsour.2013.01.094</electronic-resource-num></record></Cite></EndNote>[21]。与整数阶模型中的RC环节相似，分数阶模型中并联支路称之为ZARC元件，由CPE元件和电阻并联而成ADDINEN.CITE<EndNote><Cite><Author>Vyroubal</Author><Year>2018</Year><RecNum>60</RecNum><DisplayText>[23]</DisplayText><record><rec-number>60</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615621439">60</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Vyroubal,Petr</author><author>Kazda,Tomáš</author></authors></contributors><titles><title>Equivalentcircuitmodelparametersextractionforlithiumionbatteriesusingelectrochemicalimpedancespectroscopy</title><secondary-title>JournalofEnergyStorage</secondary-title></titles><periodical><full-title>JournalofEnergyStorage</full-title></periodical><pages>23-31</pages><volume>15</volume><section>23</section><dates><year>2018</year></dates><isbn>2352152X</isbn><urls></urls><electronic-resource-num>10.1016/j.est.2017.10.019</electronic-resource-num></record></Cite></EndNote>[23]。REF_Ref70713596\h图7系统分析并对比了目前应用的等效电路模型的计算复杂度与模型准确度。较为常用的分数阶等效电路模型简图如REF_Ref70713571\h图8所示。图SEQ图\*ARABIC7现有等效电路模型计算复杂度与精度对比分析a)R(RQ)分数阶模型b)R(RQ)W分数阶模型c)R(RWQ)分数阶模型d)R(RQ)(RQ)分数阶模型图SEQ图\*ARABIC8分数阶等效电路模型的常见结构考虑本文的SOC估计结果需应用于主动均衡系统，需满足车载嵌入式系统的计算需求，因此模型结果复杂度、参数数量与辨识难度、计算量与数据存储量等均需综合考虑。本文采用二阶等效电路模型为基础，耦合分数阶元件实现分数阶等效电路模型构建，通过使用ZARC元件代替二阶等效电路模型中的RC环节，从而实现模型的基本结构构建。CPE元件的阻抗与频率存在关系如式REF_Ref70714653\h(2.2)：(2.SEQ(2.\*ARABIC2)其中Q和α为常相位元件的参数，j为虚数单位，f对应频率。当α=0时，常相位元件退化成电阻，当α=1时，CPE退化成电容。但实际应用过程中虚实数间计算较为不便，因此将分数阶等效电路模型简化到实数域是解决分数阶模型建模的研究重点。在实际使用过程中建立系统状态方程和状态空间方程时，可将系统在复数域内建模，从而得到CPE元件的简便表达方法依据分数阶偏微分方程原理，结合基尔霍夫电压定律，可得到如公式REF_Ref70714685\h(2.3)分数阶电路方程：(2.SEQ(2.\*ARABIC3)式中的Dα是在微分符号，表征该函数的α阶倒数。Dα表达式如式所示：(2.SEQ(2.\*ARABIC4)在不考虑分数阶模型的计算过程下，对上述方程组进行离散化，得到离散空间内的系统状态空间模型：(2.SEQ(2.\*ARABIC5)该离散模型中仍包含极化电压的分数阶倒数，因此简化该导数至实数阶是目前的研究重点。Grunward-Letnekov等人ADDINEN.CITE<EndNote><Cite><Author>Zhang</Author><Year>2020</Year><RecNum>51</RecNum><DisplayText>[24]</DisplayText><record><rec-number>51</rec-number><foreign-keys><keyapp="EN"db-id="txevr25dadtxrzea2wdpzts8wprwvtdd5vsz"timestamp="1615621380">51</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Zhang,Q.</author><author>Shang,Y.</author><author>Li,Y.</author><author>Cui,N.</author><author>Duan,B.</author><author>Zhang,C.</author></authors></contributors><auth-address>SchoolofControlScienceandEngineering,ShandongUniversity,Jinan250061,China. SchoolofControlScienceandEngineering,ShandongUniversity,Jinan250061,China.Electronicaddress:zchui@.</auth-address><titles><title>Anovelfractionalvariable-orderequivalentcircuitmodelandparameteridentificationofelectricvehicleLi-ionbatteries</title><secondary-title>ISATrans</secondary-title></titles><periodical><full-title>ISATrans</full-title></periodical><pages>448-457</pages><volume>97</volume><edition>2019/10/28</edition><keywords><key