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电池状态估计:一种基于电压和电流测量的简化电化学电池模型的状态估计方法
Battery_State_Estimation.rar
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内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/6250a1e374bc5c01056d2748/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6250a1e374bc5c01056d2748/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE<span class="_ _0"> </span>TRANSACTIONS<span class="_ _0"> </span>ON<span class="_ _0"> </span>CONTR<span class="_ _1"></span>OL<span class="_ _0"> </span>SYS<span class="_ _1"></span>TEMS<span class="_ _0"> </span>T<span class="_ _2"></span>ECHNOLOGY<span class="_ _3"></span>,<span class="_ _0"> </span>V<span class="_ _1"></span>OL.<span class="_ _0"> </span>25,<span class="_ _0"> </span>NO.<span class="_ _0"> </span>2,<span class="_ _0"> </span>MARCH<span class="_ _0"> </span>2017<span class="_ _4"> </span>453</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws0">Battery<span class="_ _5"> </span>State<span class="_ _5"> </span>Estimation<span class="_ _5"> </span>for<span class="_ _6"> </span>a<span class="_ _5"> </span>Single<span class="_ _6"> </span>Particle</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls2 ws0">Model<span class="_ _6"> </span>W<span class="_ _3"></span>ith<span class="_ _6"> </span>Electrolyte<span class="_ _5"> </span>Dynamics</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls3 ws0">Scott<span class="_ _7"> </span>J.<span class="_ _8"> </span>Moura,<span class="_ _7"> </span><span class="ff2 ls4">Member<span class="_ _9"></span>,<span class="_ _7"> </span>IEEE<span class="_ _a"></span><span class="ff1 ls5">,<span class="_ _7"> </span>Federico<span class="_ _7"> </span>Bribiesca<span class="_ _7"> </span>Ar<span class="_ _1"></span>gomedo,<span class="_ _7"> </span>Reinhardt<span class="_ _7"> </span>Klein,</span></span></div><div class="t m0 x5 h4 y5 ff1 fs2 fc0 sc0 ls6 ws0">Anahita<span class="_ _8"> </span>Mirta<span class="_ _2"></span>bata<span class="_ _2"></span>bae<span class="_ _2"></span>i,<span class="_ _8"> </span>and<span class="_ _8"> </span>Miros<span class="_ _2"></span>lav<span class="_ _8"> </span>Krstic,<span class="_ _8"> </span><span class="ff2 ls4">F<span class="_ _3"></span>ellow<span class="_ _3"></span>,<span class="_ _7"> </span>IEEE</span></div><div class="t m0 x6 h5 y6 ff3 fs3 fc0 sc0 ls7 ws0">Abstract<span class="_ _2"></span><span class="ff4 ls8">&#8212;<span class="_ _b"></span>This<span class="_ _7"> </span>paper<span class="_ _7"> </span>studies<span class="_ _7"> </span>a<span class="_ _c"> </span>state<span class="_ _c"> </span>estimation<span class="_ _7"> </span>scheme<span class="_ _7"> </span>for<span class="_ _c"> </span>a</span></div><div class="t m0 x1 h5 y7 ff4 fs3 fc0 sc0 ls9 ws0">reduced<span class="_ _d"> </span>electrochemical<span class="_ _d"> </span>b<span class="_ _2"></span>attery<span class="_ _d"> </span>model,<span class="_ _d"> </span>u<span class="_ _2"></span>sing<span class="_ _d"> </span>voltage<span class="_ _d"> </span>and<span class="_ _d"> </span>cu<span class="_ _2"></span>r<span class="_ _1"></span>-</div><div class="t m0 x1 h5 y8 ff4 fs3 fc0 sc0 lsa ws0">rent<span class="_ _c"> </span>measu<span class="_ _2"></span>rements.<span class="_ _c"> </span>Real<span class="_ _2"></span>-time<span class="_ _7"> </span>electrochemical<span class="_ _7"> </span>state<span class="_ _7"> </span>information</div><div class="t m0 x1 h5 y9 ff4 fs3 fc0 sc0 lsb ws0">enables<span class="_"> </span>high-&#64257;delity<span class="_"> </span>monitoring<span class="_"> </span>and<span class="_ _0"> </span>high-perf<span class="_ _1"></span>ormanc<span class="_ _1"></span>e<span class="_ _e"> </span>opera<span class="_ _1"></span>tion</div><div class="t m0 x1 h5 ya ff4 fs3 fc0 sc0 lsc ws0">in<span class="_ _c"> </span>adv<span class="_ _1"></span>anced<span class="_ _c"> </span>battery<span class="_ _c"> </span>mana<span class="_ _1"></span>gement<span class="_ _c"> </span>syst<span class="_ _1"></span>ems,<span class="_ _c"> </span>fo<span class="_ _1"></span>r<span class="_ _c"> </span>applications<span class="_ _c"> </span>s<span class="_ _1"></span>uch</div><div class="t m0 x1 h5 yb ff4 fs3 fc0 sc0 lsd ws0">as<span class="_ _f"> </span>consumer<span class="_ _f"> </span>electronics,<span class="_ _f"> </span>el<span class="_ _2"></span>ectri&#64257;ed<span class="_ _f"> </span>vehicles,<span class="_ _f"> </span>and<span class="_ _f"> </span>grid<span class="_ _f"> </span>energy</div><div class="t m0 x1 h5 yc ff4 fs3 fc0 sc0 lse ws0">stora<span class="_ _1"></span>ge.<span class="_ _10"> </span>This<span class="_ _10"> </span>paper<span class="_ _11"> </span>deri<span class="_ _1"></span>ves<span class="_ _11"> </span>a<span class="_ _10"> </span>single<span class="_ _10"> </span>partic<span class="_ _1"></span>le<span class="_ _10"> </span>model<span class="_ _11"> </span>(SPM)</div><div class="t m0 x1 h5 yd ff4 fs3 fc0 sc0 lsf ws0">with<span class="_ _12"> </span>electrolyte<span class="_ _12"> </span>that<span class="_ _12"> </span>achieves<span class="_ _12"> </span>higher<span class="_ _12"> </span>predictive<span class="_ _12"> </span>accuracy<span class="_ _12"> </span>than</div><div class="t m0 x1 h5 ye ff4 fs3 fc0 sc0 ls10 ws0">the<span class="_ _13"> </span>SPM.<span class="_ _13"> </span>Next,<span class="_ _13"> </span>we<span class="_ _13"> </span>p<span class="_ _2"></span>ropose<span class="_ _12"> </span>an<span class="_ _13"> </span>esti<span class="_ _2"></span>mation<span class="_ _13"> </span>scheme<span class="_ _13"> </span>and<span class="_ _13"> </span>p<span class="_ _2"></span>rov<span class="_ _1"></span>e</div><div class="t m0 x1 h5 yf ff4 fs3 fc0 sc0 ls11 ws0">estimatio<span class="_ _1"></span>n<span class="_ _e"> </span>error<span class="_ _e"> </span>system<span class="_ _e"> </span>stability<span class="_ _3"></span>,<span class="_ _c"> </span>a<span class="_ _1"></span>ssuming<span class="_ _e"> </span>that<span class="_ _e"> </span>the<span class="_ _e"> </span>total<span class="_ _e"> </span>amount</div><div class="t m0 x1 h5 y10 ff4 fs3 fc0 sc0 ls12 ws0">of<span class="_ _12"> </span>lithium<span class="_ _12"> </span>in<span class="_ _12"> </span>the<span class="_ _13"> </span>cell<span class="_ _12"> </span>is<span class="_ _12"> </span>known.<span class="_ _12"> </span>The<span class="_ _12"> </span>state<span class="_ _12"> </span>estimatio<span class="_ _1"></span>n<span class="_ _13"> </span>scheme</div><div class="t m0 x1 h5 y11 ff4 fs3 fc0 sc0 ls13 ws0">exploits<span class="_ _14"> </span>the<span class="_"> </span>dynam<span class="_ _1"></span>ical<span class="_"> </span>pro<span class="_ _1"></span>perties,<span class="_"> </span>such<span class="_ _14"> </span>as<span class="_"> </span>mar<span class="_ _1"></span>ginal<span class="_"> </span>stability<span class="_ _3"></span>,<span class="_"> </span>loc<span class="_ _1"></span>al</div><div class="t m0 x1 h5 y12 ff4 fs3 fc0 sc0 ls14 ws0">in<span class="_ _1"></span>ver<span class="_ _1"></span>tibility<span class="_ _3"></span>,<span class="_ _13"> </span>and<span class="_ _12"> </span>conserv<span class="_ _1"></span>ation<span class="_ _12"> </span>of<span class="_ _13"> </span>lithium.<span class="_ _12"> </span>Simulations<span class="_ _12"> </span>demo<span class="_ _1"></span>n-</div><div class="t m0 x1 h5 y13 ff4 fs3 fc0 sc0 ls15 ws0">strate<span class="_ _c"> </span>the<span class="_ _c"> </span>algo<span class="_ _1"></span>rithm&#8217;<span class="_ _1"></span>s<span class="_ _c"> </span>perfo<span class="_ _1"></span>rmance<span class="_ _c"> </span>and<span class="_ _c"> </span>limitatio<span class="_ _1"></span>ns.</div><div class="t m0 x6 h5 y14 ff3 fs3 fc0 sc0 ls16 ws0">Index<span class="_ _13"> </span>T<span class="_ _3"></span>erms<span class="ff4 lsa">&#8212;<span class="_ _b"></span>Batteries,<span class="_ _12"> </span>b<span class="_ _2"></span>attery<span class="_ _12"> </span>managemen<span class="_ _2"></span>t<span class="_ _13"> </span>systems,<span class="_ _13"> </span>elec-</span></div><div class="t m0 x1 h5 y15 ff4 fs3 fc0 sc0 ls17 ws0">trochemical<span class="_ _5"> </span>devices,<span class="_ _6"> </span>n<span class="_ _2"></span>onlin<span class="_ _2"></span>ear<span class="_ _6"> </span>dyn<span class="_ _2"></span>amical<span class="_ _5"> </span>systems,<span class="_ _5"> </span>partial</div><div class="t m0 x1 h5 y16 ff4 fs3 fc0 sc0 ls18 ws0">differe<span class="_ _1"></span>ntial<span class="_ _c"> </span>equations,<span class="_ _c"> </span>stability<span class="_ _15"> </span>analysis,<span class="_ _15"> </span>state<span class="_ _c"> </span>estimation.</div><div class="t m0 x7 h6 y17 ff1 fs4 fc0 sc0 ls19 ws0">I.<span class="_ _12"> </span>I<span class="fs5 ls1a">NT<span class="_ _2"></span>R<span class="_ _1"></span>ODUCTION</span></div><div class="t m0 x1 h7 y18 ff4 fs6 fc0 sc0 ls1b ws0">T</div><div class="t m0 x8 h6 y19 ff1 fs4 fc0 sc0 ls1c ws0">HIS<span class="_ _d"> </span>P<span class="_ _3"></span>APER<span class="_ _d"> </span>stud<span class="_ _2"></span>ies<span class="_ _d"> </span>a<span class="_ _12"> </span>state<span class="_ _d"> </span>estimation<span class="_ _12"> </span>algorithm<span class="_ _d"> </span>b<span class="_ _2"></span>ased</div><div class="t m0 x8 h6 y1a ff1 fs4 fc0 sc0 ls1d ws0">upon<span class="_ _8"> </span>the<span class="_ _8"> </span>single<span class="_ _d"> </span>particl<span class="_ _1"></span>e<span class="_ _d"> </span>model<span class="_ _8"> </span>with<span class="_ _8"> </span>electrolyte<span class="_ _8"> </span>(SPMe)</div><div class="t m0 x1 h6 y1b ff1 fs4 fc0 sc0 ls1e ws0">dynamics&#8212;an<span class="_ _8"> </span>electrochemical<span class="_ _7"> </span>battery<span class="_ _8"> </span>model.<span class="_ _d"> </span>The<span class="_ _8"> </span>algorithm</div><div class="t m0 x1 h6 y1c ff1 fs4 fc0 sc0 ls1f ws0">features<span class="_ _16"> </span>proper<span class="_ _2"></span>ties<span class="_ _10"> </span>such<span class="_ _16"> </span>as<span class="_ _16"> </span>stability<span class="_ _16"> </span>and<span class="_ _16"> </span>con<span class="_ _2"></span>servation<span class="_ _10"> </span>o<span class="_ _2"></span>f</div><div class="t m0 x1 h6 y1d ff1 fs4 fc0 sc0 ls20 ws0">lithium.</div><div class="t m0 x1 h8 y1e ff2 fs4 fc0 sc0 ls21 ws0">A.<span class="_ _c"> </span>Backgr<span class="_ _3"></span>ound<span class="_ _c"> </span>and<span class="_ _c"> </span>Motivati<span class="_ _1"></span>on</div><div class="t m0 x6 h6 y1f ff1 fs4 fc0 sc0 ls22 ws0">Batteries<span class="_"> </span>are<span class="_ _15"> </span>ubiquitous.<span class="_"> </span>They<span class="_"> </span>po<span class="_ _1"></span>wer<span class="_"> </span>a<span class="_ _15"> </span>spectrum<span class="_"> </span>of<span class="_"> </span>d<span class="_ _2"></span>evices<span class="_ _1"></span>,</div><div class="t m0 x1 h6 y20 ff1 fs4 fc0 sc0 ls1e ws0">including<span class="_"> </span>consumer<span class="_"> </span>electronics,<span class="_"> </span>e<span class="ls23">lectri&#64257;ed<span class="_ _15"> </span>vehicles,<span class="_"> </span>and<span class="_ _15"> </span>smart</span></div><div class="t m0 x1 h6 y21 ff1 fs4 fc0 sc0 ls24 ws0">grid<span class="_ _8"> </span>systems.<span class="_ _8"> </span>Control<span class="_ _8"> </span>system<span class="_ _d"> </span>technologies<span class="_ _7"> </span>that<span class="_ _d"> </span>enhance<span class="_ _8"> </span>bat-</div><div class="t m0 x1 h6 y22 ff1 fs4 fc0 sc0 ls25 ws0">tery<span class="_ _d"> </span>performance<span class="_ _7"> </span>are<span class="_ _8"> </span>of<span class="_ _d"> </span>extreme<span class="_ _8"> </span>interest.<span class="_ _8"> </span>In<span class="_ _d"> </span>particular,<span class="_ _7"> </span>elec-</div><div class="t m0 x1 h6 y23 ff1 fs4 fc0 sc0 ls26 ws0">trochem<span class="_ _2"></span>ical<span class="_ _f"> </span>model-<span class="_ _2"></span>based<span class="_ _f"> </span>contro<span class="_ _2"></span>l<span class="_ _f"> </span>systems<span class="_ _f"> </span>p<span class="_ _2"></span>rovide<span class="_ _f"> </span>v<span class="_ _2"></span>isibility</div><div class="t m0 x1 h6 y24 ff1 fs4 fc0 sc0 ls27 ws0">into<span class="_ _17"> </span>operating<span class="_ _f"> </span>regimes<span class="_ _f"> </span>that<span class="_ _17"> </span>induce<span class="_ _17"> </span>degradation.<span class="_ _13"> </span>This<span class="_ _11"> </span>visi<span class="_ _1"></span>-</div><div class="t m0 x1 h6 y25 ff1 fs4 fc0 sc0 ls1f ws0">bility<span class="_ _13"> </span>enables<span class="_ _13"> </span>a<span class="_ _13"> </span>larger<span class="_ _12"> </span>o<span class="_ _2"></span>perational<span class="_ _12"> </span>e<span class="_ _2"></span>n<span class="_ _1"></span>velope<span class="_ _12"> </span>to<span class="_ _13"> </span>incr<span class="_ _2"></span>ease<span class="_ _13"> </span>the</div><div class="t m0 x9 h9 y26 ff1 fs5 fc0 sc0 ls28 ws0">Manuscript<span class="_ _d"> </span>received<span class="_ _d"> </span>July<span class="_ _d"> </span>28,<span class="_ _d"> </span>2015;<span class="_ _d"> </span>re<span class="_ _1"></span>vised<span class="_ _d"> </span>February<span class="_ _d"> </span>7,<span class="_ _d"> </span>2016;<span class="_ _d"> </span>accepted</div><div class="t m0 x1 h9 y27 ff1 fs5 fc0 sc0 ls29 ws0">May<span class="_ _8"> </span>7,<span class="_ _8"> </span>2016.<span class="_ _d"> </span>Date<span class="_ _8"> </span>of<span class="_ _d"> </span>publication<span class="_ _d"> </span>June<span class="_ _8"> </span>10,<span class="_ _d"> </span>2016;<span class="_ _8"> </span>date<span class="_ _d"> </span>of<span class="_ _8"> </span>current<span class="_ _d"> </span>version</div><div class="t m0 x1 h9 y28 ff1 fs5 fc0 sc0 ls29 ws0">February<span class="_ _0"> </span>8,<span class="_ _0"> </span>2017.<span class="_ _0"> </span>Manuscript<span class="_ _0"> </span>recei<span class="_ _1"></span>ved<span class="_ _0"> </span>in<span class="_ _0"> </span>&#64257;nal<span class="_ _0"> </span>form<span class="_ _0"> </span>May<span class="_ _0"> </span>17,<span class="_"> </span>2016.<span class="_ _0"> </span>T<span class="_ _2"></span>his<span class="_ _0"> </span>work</div><div class="t m0 x1 h9 y29 ff1 fs5 fc0 sc0 ls2a ws0">was<span class="_ _0"> </span>supported<span class="_ _0"> </span>in<span class="_ _0"> </span>part<span class="_ _0"> </span>by<span class="_ _0"> </span>the<span class="_ _0"> </span>National<span class="_ _e"> </span>Science<span class="_ _e"> </span>Foundation<span class="_ _0"> </span>within<span class="_ _e"> </span>the<span class="_ _0"> </span>Division</div><div class="t m0 x1 h9 y2a ff1 fs5 fc0 sc0 ls2b ws0">of<span class="_ _e"> </span>Electrical,<span class="_ _c"> </span>Communications<span class="_ _c"> </span>an<span class="ls29">d<span class="_ _e"> </span>Cyber<span class="_ _15"> </span>Systems<span class="_ _15"> </span>under<span class="_ _e"> </span>Grant<span class="_ _15"> </span>1408107<span class="_ _e"> </span>and</span></div><div class="t m0 x1 h9 y2b ff1 fs5 fc0 sc0 ls2c ws0">in<span class="_ _c"> </span>part<span class="_ _8"> </span>by<span class="_ _c"> </span>the<span class="_ _7"> </span>U.<span class="_ _2"></span>S.<span class="_ _c"> </span>D<span class="_ _2"></span>epartment<span class="_ _8"> </span>of<span class="_ _c"> </span>E<span class="_ _2"></span>nergy<span class="_ _c"> </span>through<span class="_ _7"> </span>the<span class="_ _8"> </span>Advanced<span class="_ _7"> </span>Research</div><div class="t m0 x1 h9 y2c ff1 fs5 fc0 sc0 ls2d ws0">Projects<span class="_ _13"> </span>Agency-Energy<span class="_ _13"> </span>under<span class="_ _f"> </span>G<span class="ls1">rant<span class="_ _12"> </span>DE<span class="_ _2"></span>-AR0000278.<span class="_ _13"> </span>Recommended<span class="_ _f"> </span>by</span></div><div class="t m0 x1 h9 y2d ff1 fs5 fc0 sc0 ls2c ws0">Associate<span class="_ _15"> </span>Editor<span class="_ _15"> </span>S<span class="_ _2"></span>.<span class="_ _e"> </span>V<span class="_ _3"></span>arigonda.</div><div class="t m0 x9 h9 y2e ff1 fs5 fc0 sc0 ls2e ws0">S.<span class="_"> </span>J<span class="_ _2"></span>.<span class="_"> </span>Moura<span class="_ _0"> </span>is<span class="_"> </span>with<span class="_ _0"> </span>the<span class="_ _0"> </span>Department<span class="_ _0"> </span>of<span class="_ _0"> </span>Ci<span class="_ _1"></span>vil<span class="_ _0"> </span>and<span class="_"> </span>Environmental<span class="_ _0"> </span>Engineering,</div><div class="t m0 x1 h9 y2f ff1 fs5 fc0 sc0 ls2f ws0">Uni<span class="_ _1"></span>versity<span class="_ _12"> </span>of<span class="_ _12"> </span>California<span class="_ _13"> </span>at<span class="_ _12"> </span>Berkeley<span class="_ _3"></span>,<span class="_ _12"> </span>Berkeley<span class="_ _3"></span>,<span class="_ _f"> </span>CA<span class="_ _12"> </span>94720<span class="_ _d"> </span>USA<span class="_ _12"> </span>(e-mail:</div><div class="t m0 x1 h9 y30 ff1 fs5 fc0 sc0 ls30 ws0">smoura@berkeley<span class="_ _3"></span>.edu).</div><div class="t m0 x9 h9 y31 ff1 fs5 fc0 sc0 ls31 ws0">F<span class="_ _3"></span>.<span class="_ _c"> </span>Bribies<span class="_ _2"></span>ca<span class="_ _7"> </span>Argomedo<span class="_ _7"> </span>is<span class="_ _7"> </span>with<span class="_ _7"> </span>the<span class="_ _7"> </span>Laboratoir<span class="_ _2"></span>e<span class="_ _7"> </span>Am<span class="_ _2"></span>p&#232;re,<span class="_ _7"> </span>Institut<span class="_ _7"> </span>N<span class="_ _2"></span>ational</div><div class="t m0 x1 h9 y32 ff1 fs5 fc0 sc0 ls32 ws0">des<span class="_ _c"> </span>Sciences<span class="_ _7"> </span>Appliqu&#233;es<span class="_ _7"> </span>de<span class="_ _c"> </span>L<span class="_ _1"></span>yon,<span class="_ _15"> </span>U<span class="_ _2"></span>niv<span class="_ _1"></span>ersit&#233;<span class="_ _7"> </span>de<span class="_ _c"> </span>L<span class="_ _1"></span>yon,<span class="_ _c"> </span>V<span class="_ _1"></span>illeurbanne<span class="_ _7"> </span>69621,</div><div class="t m0 x1 h9 y33 ff1 fs5 fc0 sc0 ls33 ws0">France<span class="_ _e"> </span>(e-mail:<span class="_ _15"> </span>federico.bribiesc<span class="_ _1"></span>a@insa-lyon.fr).</div><div class="t m0 x9 h9 y34 ff1 fs5 fc0 sc0 ls34 ws0">R.<span class="_ _f"> </span>Klein<span class="_ _17"> </span>and<span class="_ _f"> </span>A.<span class="_ _f"> </span>Mirtabatabaei<span class="_ _11"> </span>are<span class="_ _17"> </span>with<span class="_ _f"> </span>the<span class="_ _17"> </span>Research<span class="_ _11"> </span>and<span class="_ _f"> </span>T<span class="_ _3"></span>echnol-</div><div class="t m0 x1 h9 y35 ff1 fs5 fc0 sc0 ls28 ws0">ogy<span class="_ _17"> </span>Center<span class="_ _1"></span>,<span class="_ _11"> </span>Robert<span class="_ _17"> </span>Bosch<span class="_ _17"> </span>LL<span class="_ _2"></span>C,<span class="_ _f"> </span>Palo<span class="_ _17"> </span>A<span class="_ _2"></span>lto,<span class="_ _17"> </span>CA<span class="_ _17"> </span>94304<span class="_ _17"> </span>USA<span class="_ _17"> </span>(e-m<span class="_ _2"></span>ail:</div><div class="t m0 x1 h9 y36 ff1 fs5 fc0 sc0 ls28 ws0">reinhardt.klein@us.bos<span class="_ _2"></span>ch.com;<span class="_ _7"> </span>ana<span class="ls35">hita.mirtabatabaei<span class="_ _2"></span>@us.bos<span class="_ _2"></span>ch.com<span class="_ _2"></span>).</span></div><div class="t m0 x9 h9 y37 ff1 fs5 fc0 sc0 ls36 ws0">M.<span class="_"> </span>Krstic<span class="_ _0"> </span>is<span class="_"> </span>with<span class="_"> </span>the<span class="_ _0"> </span>Department<span class="_"> </span>of<span class="_"> </span>M<span class="_ _2"></span>ech<span class="ls35">anical<span class="_ _0"> </span>and<span class="_"> </span>Aer<span class="_ _2"></span>ospace<span class="_ _0"> </span>Engineering,</span></div><div class="t m0 x1 h9 y38 ff1 fs5 fc0 sc0 ls37 ws0">Uni<span class="_ _1"></span>versity<span class="_ _0"> </span>of<span class="_ _0"> </span>California<span class="_ _0"> </span>at<span class="_ _0"> </span>San<span class="_"> </span>Diego,<span class="_ _0"> </span>La<span class="_"> </span>J<span class="_ _2"></span>olla,<span class="_ _0"> </span>CA<span class="_"> </span>92093-0411<span class="_ _0"> </span>USA<span class="_ _0"> </span>(e-mail:</div><div class="t m0 x1 h9 y39 ff1 fs5 fc0 sc0 ls2f ws0">krstic@ucsd.edu).</div><div class="t m0 x9 h9 y3a ff1 fs5 fc0 sc0 ls2f ws0">Color<span class="_ _7"> </span>versions<span class="_ _8"> </span>of<span class="_ _8"> </span>one<span class="_ _7"> </span>or<span class="_ _8"> </span>more<span class="_ _7"> </span>of<span class="_ _8"> </span>the<span class="_ _8"> </span>&#64257;gures<span class="_ _7"> </span>in<span class="_ _8"> </span>this<span class="_ _8"> </span>paper<span class="_ _8"> </span>are<span class="_ _7"> </span>available</div><div class="t m0 x1 h9 y3b ff1 fs5 fc0 sc0 ls35 ws0">online<span class="_ _15"> </span>at<span class="_ _e"> </span>http://ieeexplore.<span class="_ _2"></span>ieee.org.</div><div class="t m0 x9 h9 y3c ff1 fs5 fc0 sc0 ls38 ws0">Digital<span class="_ _15"> </span>Object<span class="_ _15"> </span>Identi&#64257;er<span class="_ _15"> </span>10.<span class="_ _2"></span>1109/TCST<span class="_ _1"></span>.2016.2571663</div><div class="t m0 xa h6 y6 ff1 fs4 fc0 sc0 ls39 ws0">performance<span class="_ _15"> </span>with<span class="_ _7"> </span>respect<span class="_ _7"> </span>to<span class="_ _7"> </span>en<span class="_ _2"></span><span class="ls3a">ergy<span class="_ _c"> </span>capacity<span class="_ _3"></span>,<span class="_ _7"> </span>power<span class="_ _c"> </span>capacity<span class="_ _1"></span>,</span></div><div class="t m0 xa h6 y3d ff1 fs4 fc0 sc0 ls25 ws0">and<span class="_ _8"> </span>fast<span class="_ _d"> </span>charge<span class="_ _8"> </span>rates<span class="_ _8"> </span>[1].<span class="_ _d"> </span>Electrochemical<span class="_ _8"> </span>model-based<span class="_ _8"> </span>state</div><div class="t m0 xa h6 y3e ff1 fs4 fc0 sc0 ls1f ws0">estimation<span class="_ _17"> </span>is<span class="_ _11"> </span>p<span class="_ _2"></span>articularly<span class="_ _17"> </span>cha<span class="ls25">llenging<span class="_ _17"> </span>for<span class="_ _11"> </span>se<span class="_ _1"></span>veral<span class="_ _17"> </span>technical</span></div><div class="t m0 xa h6 y3f ff1 fs4 fc0 sc0 ls3b ws0">reasons.<span class="_"> </span>First,<span class="_ _e"> </span>the<span class="_ _15"> </span>dynamics<span class="_"> </span>are<span class="_ _15"> </span>governed<span class="_"> </span>by<span class="_"> </span>a<span class="_ _15"> </span>system<span class="_ _15"> </span>of<span class="_ _e"> </span>non-</div><div class="t m0 xa h6 y40 ff1 fs4 fc0 sc0 ls27 ws0">linear<span class="_ _c"> </span>partial<span class="_ _15"> </span>different<span class="_ _1"></span>ial<span class="_ _15"> </span>algebraic<span class="_ _c"> </span>equations<span class="_ _15"> </span>[2],<span class="_ _c"> </span>[3].<span class="_ _c"> </span>Second,</div><div class="t m0 xa h6 y41 ff1 fs4 fc0 sc0 ls1c ws0">local<span class="_ _15"> </span>state<span class="_ _7"> </span>observability<span class="_ _15"> </span>does<span class="_ _c"> </span>not<span class="_ _c"> </span>hold<span class="_ _c"> </span>globally<span class="_ _c"> </span>[4].<span class="_ _c"> </span>Third,<span class="_ _15"> </span>th<span class="_ _2"></span>e</div><div class="t m0 xa h6 y42 ff1 fs4 fc0 sc0 ls22 ws0">model<span class="_ _15"> </span>parameters<span class="_ _15"> </span>vary<span class="_ _15"> </span>widely<span class="_ _15"> </span>w<span class="ls3a">ith<span class="_ _c"> </span>electrode<span class="_ _c"> </span>chemistry<span class="_ _3"></span>,<span class="_ _c"> </span>elec-</span></div><div class="t m0 xa h6 y43 ff1 fs4 fc0 sc0 ls3c ws0">trolyte,<span class="_ _e"> </span>packag<span class="_ _2"></span>ing,<span class="_"> </span>an<span class="_ _2"></span>d<span class="_ _e"> </span>time.<span class="_ _15"> </span>Finally<span class="_ _1"></span>,<span class="_"> </span>the<span class="_ _15"> </span>cells<span class="_ _15"> </span>in<span class="_"> </span>b<span class="_ _2"></span>attery<span class="_ _e"> </span>p<span class="_ _2"></span>acks</div><div class="t m0 xa h6 y44 ff1 fs4 fc0 sc0 ls1d ws0">are<span class="_ _7"> </span>generally<span class="_ _c"> </span>heterogeneous<span class="_ _c"> </span>w<span class="ls3d">ith<span class="_ _8"> </span>respect<span class="_ _7"> </span>to<span class="_ _8"> </span>their<span class="_ _7"> </span>parameters,</span></div><div class="t m0 xa h6 y45 ff1 fs4 fc0 sc0 ls3e ws0">temperature,<span class="_ _12"> </span>and<span class="_ _12"> </span>state<span class="_ _13"> </span>of<span class="_ _13"> </span>char<span class="ls1c">ge<span class="_ _12"> </span>(SOC).<span class="_ _13"> </span>Th<span class="_ _2"></span>is<span class="_ _12"> </span>m<span class="_ _2"></span>otiv<span class="_ _1"></span>ates<span class="_ _12"> </span>an</span></div><div class="t m0 xa h6 y46 ff1 fs4 fc0 sc0 ls27 ws0">intimate<span class="_ _d"> </span>understanding<span class="_ _d"> </span>of<span class="_ _12"> </span>the<span class="_ _12"> </span>mathemat<span class="_ _1"></span>ical<span class="_ _d"> </span>model<span class="_ _12"> </span>structure</div><div class="t m0 xa h6 y47 ff1 fs4 fc0 sc0 ls3f ws0">for<span class="_ _15"> </span>an<span class="_ _c"> </span>observer<span class="_ _e"> </span>design.<span class="_ _c"> </span>In<span class="_ _15"> </span>this<span class="_ _c"> </span>paper<span class="_ _1"></span>,<span class="_ _15"> </span>we<span class="_ _c"> </span>address<span class="_ _15"> </span>the<span class="_ _15"> </span>&#64257;rst<span class="_ _c"> </span>two</div><div class="t m0 xa h6 y48 ff1 fs4 fc0 sc0 ls40 ws0">technical<span class="_ _c"> </span>challenges.</div><div class="t m0 xa h8 y49 ff2 fs4 fc0 sc0 ls41 ws0">B.<span class="_ _c"> </span>Relevant<span class="_ _7"> </span>Literatur<span class="_ _1"></span>e</div><div class="t m0 xb h6 y4a ff1 fs4 fc0 sc0 ls42 ws0">Over<span class="_ _7"> </span>the<span class="_ _8"> </span>past<span class="_ _7"> </span>decad<span class="_ _2"></span>e,<span class="_ _7"> </span>the<span class="_ _7"> </span>en<span class="_ _2"></span>gineering<span class="_ _7"> </span>literature<span class="_ _7"> </span>o<span class="_ _2"></span>n<span class="_ _7"> </span>battery</div><div class="t m0 xa h6 y4b ff1 fs4 fc0 sc0 ls43 ws0">estimation<span class="_ _f"> </span>has<span class="_ _f"> </span>grown<span class="_ _13"> </span>c<span class="_ _2"></span>onsiderably<span class="_ _f"> </span>rich<span class="_ _f"> </span>with<span class="_ _f"> </span>various<span class="_ _13"> </span>alg<span class="_ _2"></span>o-</div><div class="t m0 xa h6 y4c ff1 fs4 fc0 sc0 ls3b ws0">rithms,<span class="_ _13"> </span>models,<span class="_ _13"> </span>and<span class="_ _f"> </span>applications.<span class="_ _13"> </span>One<span class="_ _f"> </span>may<span class="_ _f"> </span>categorize<span class="_ _13"> </span>this</div><div class="t m0 xa h6 y4d ff1 fs4 fc0 sc0 ls44 ws0">literature<span class="_ _c"> </span>by<span class="_ _7"> </span>the<span class="_ _7"> </span>battery<span class="_ _7"> </span>models<span class="_ _7"> </span>that<span class="_ _c"> </span>each<span class="_ _7"> </span>alg<span class="_ _2"></span>orithm<span class="_ _7"> </span>employs.</div><div class="t m0 xa h6 y4e ff1 fs4 fc0 sc0 ls45 ws0">Note<span class="_"> </span>that<span class="_ _15"> </span>these<span class="_"> </span>studies<span class="_"> </span>inherently<span class="_"> </span>assume<span class="_"> </span>the<span class="_ _15"> </span>pack<span class="_"> </span>or<span class="_ _15"> </span>modules</div><div class="t m0 xa h6 y4f ff1 fs4 fc0 sc0 ls46 ws0">can<span class="_"> </span>be<span class="_ _e"> </span>conceptualized<span class="_"> </span>as<span class="_"> </span>an<span class="_ _e"> </span>aggregate<span class="_"> </span>single<span class="_"> </span>cell.<span class="_"> </span>This<span class="_ _e"> </span>is<span class="_ _e"> </span>valid</div><div class="t m0 xa h6 y50 ff1 fs4 fc0 sc0 ls1e ws0">when<span class="_ _12"> </span>cell<span class="_ _d"> </span>balancing,<span class="_ _12"> </span>binni<span class="_ _1"></span>ng,<span class="_ _d"> </span>and<span class="_ _12"> </span>temperature<span class="_ _12"> </span>management</div><div class="t m0 xa h6 y51 ff1 fs4 fc0 sc0 ls3f ws0">maintain<span class="_ _15"> </span>homogeneity<span class="_ _15"> </span>across<span class="_ _c"> </span>the<span class="_ _c"> </span>pack<span class="_ _7"> </span>or<span class="_ _c"> </span>module.</div><div class="t m0 xb h6 y52 ff1 fs4 fc0 sc0 ls43 ws0">The<span class="_"> </span>&#64257;rst<span class="_"> </span>category<span class="_"> </span>utilizes<span class="_ _14"> </span>eq<span class="_ _2"></span>uiv<span class="_ _1"></span>alent<span class="_"> </span>circuit<span class="_"> </span>models<span class="_"> </span>(ECMs).</div><div class="t m0 xa h6 y53 ff1 fs4 fc0 sc0 ls47 ws0">These<span class="_ _15"> </span>models<span class="_ _c"> </span>use<span class="_ _7"> </span>circuit<span class="_ _15"> </span>elements<span class="_ _c"> </span>to<span class="_ _7"> </span>mimic<span class="_ _c"> </span>the<span class="_ _c"> </span>input&#8211;output</div><div class="t m0 xa h6 y54 ff1 fs4 fc0 sc0 ls24 ws0">beha<span class="_ _1"></span>vior<span class="_ _c"> </span>of<span class="_ _7"> </span>batteries<span class="_ _c"> </span>[5].<span class="_ _7"> </span>The<span class="_ _7"> </span>seminal<span class="_ _c"> </span>paper<span class="_ _7"> </span>by<span class="_ _7"> </span>Plett<span class="_ _7"> </span>[6]<span class="_ _c"> </span>was</div><div class="t m0 xa h6 y55 ff1 fs4 fc0 sc0 ls48 ws0">one<span class="_ _7"> </span>of<span class="_ _8"> </span>the<span class="_ _8"> </span>&#64257;rst<span class="_ _7"> </span>to<span class="_ _8"> </span>apply<span class="_ _7"> </span>extended<span class="_ _7"> </span>Kalman<span class="_ _7"> </span>&#64257;ltering<span class="_ _7"> </span>(EKF)<span class="_ _7"> </span>to</div><div class="t m0 xa h6 y56 ff1 fs4 fc0 sc0 ls1d ws0">ECMs<span class="_ _c"> </span>for<span class="_ _7"> </span>simultaneous<span class="_ _15"> </span>state<span class="_ _7"> </span>and<span class="_ _c"> </span>parameter<span class="_ _c"> </span>estimation.<span class="_ _c"> </span>Over</div><div class="t m0 xa h6 y57 ff1 fs4 fc0 sc0 ls49 ws0">the<span class="_"> </span>past<span class="_ _e"> </span>decade,<span class="_ _e"> </span>a<span class="_ _e"> </span>variety<span class="_"> </span>of<span class="_ _e"> </span>ECM-based<span class="_"> </span>algorithms<span class="_"> </span>hav<span class="_ _1"></span>e<span class="_"> </span>been</div><div class="t m0 xa h6 y58 ff1 fs4 fc0 sc0 ls3 ws0">de<span class="_ _1"></span>veloped,<span class="_ _7"> </span>including<span class="_ _8"> </span>linear<span class="_ _d"> </span>parameter<span class="_ _8"> </span>varying<span class="_ _8"> </span>observers<span class="_ _7"> </span>[7],</div><div class="t m0 xa h6 y59 ff1 fs4 fc0 sc0 ls4a ws0">sliding-mode<span class="_"> </span>observers<span class="_ _15"> </span>[8],<span class="_ _15"> </span>polynomial<span class="_ _15"> </span>chaos<span class="_ _15"> </span>[9],<span class="_ _c"> </span>neural<span class="_ _c"> </span>net-</div><div class="t m0 xa h6 y5a ff1 fs4 fc0 sc0 ls3b ws0">works<span class="_ _13"> </span>[10],<span class="_ _f"> </span>unscented<span class="_ _13"> </span>Kalman<span class="_ _f"> </span>&#64257;lters<span class="_ _f"> </span>(KFs<span class="_ _1"></span>)<span class="_ _f"> </span>[11],<span class="_ _f"> </span>adapti<span class="_ _1"></span>ve</div><div class="t m0 xa h6 y5b ff1 fs4 fc0 sc0 ls4b ws0">KFs<span class="_ _c"> </span>[12],<span class="_ _15"> </span>and<span class="_ _7"> </span>particle<span class="_ _15"> </span>&#64257;lters<span class="_ _c"> </span>[13].</div><div class="t m0 xb h6 y5c ff1 fs4 fc0 sc0 ls4c ws0">The<span class="_ _17"> </span>second<span class="_ _f"> </span>categor<span class="_ _2"></span>y<span class="_ _f"> </span>of<span class="_ _17"> </span>the<span class="_ _17"> </span>literatu<span class="_ _2"></span>re<span class="_ _f"> </span>con<span class="_ _2"></span>siders<span class="_ _f"> </span>electro-</div><div class="t m0 xa h6 y5d ff1 fs4 fc0 sc0 ls1d ws0">chemical<span class="_ _8"> </span>models,<span class="_ _8"> </span>which<span class="_ _8"> </span>account<span class="_ _8"> </span>for<span class="_ _d"> </span>the<span class="_ _8"> </span>diffusi<span class="_ _1"></span>on,<span class="_ _7"> </span>intercala-</div><div class="t m0 xa h6 y5e ff1 fs4 fc0 sc0 ls45 ws0">tion,<span class="_"> </span>and<span class="_ _c"> </span>electrochemical<span class="_"> </span>kinetics.<span class="_"> </span>Although<span class="_ _e"> </span>these<span class="_ _15"> </span>models<span class="_ _e"> </span>can</div><div class="t m0 xa h6 y5f ff1 fs4 fc0 sc0 ls4d ws0">accurately<span class="_ _7"> </span>predict<span class="_ _8"> </span>internal<span class="_ _7"> </span>state<span class="_ _d"> </span><span class="ls3a">variables<span class="_ _1"></span>,<span class="_ _8"> </span>their<span class="_ _8"> </span>mathematical</span></div><div class="t m0 xa h6 y60 ff1 fs4 fc0 sc0 ls3b ws0">structure<span class="_ _7"> </span>renders<span class="_ _d"> </span>observer<span class="_ _7"> </span>design<span class="_ _d"> </span>challenging.<span class="_ _7"> </span>Consequently<span class="_ _3"></span>,</div><div class="t m0 xa h6 y61 ff1 fs4 fc0 sc0 ls4e ws0">most<span class="_ _17"> </span>approaches<span class="_ _f"> </span>develop<span class="_ _f"> </span>estim<span class="ls4f">ators<span class="_ _11"> </span>for<span class="_ _17"> </span>the<span class="_ _17"> </span>reduced-order</span></div><div class="t m0 xa h6 y62 ff1 fs4 fc0 sc0 ls24 ws0">models.<span class="_ _e"> </span>The<span class="_ _15"> </span>model<span class="_ _15"> </span>reduction<span class="_ _e"> </span>and<span class="_ _15"> </span>the<span class="_ _15"> </span>observer<span class="_ _e"> </span>design<span class="_ _15"> </span>process</div><div class="t m0 xa h6 y63 ff1 fs4 fc0 sc0 ls1c ws0">are<span class="_ _7"> </span>intimately<span class="_ _7"> </span>intertwined,<span class="_ _7"> </span>as<span class="_ _7"> </span>simpler<span class="_ _7"> </span>mod<span class="_ _2"></span>els<span class="_ _c"> </span>ease<span class="_ _7"> </span>estim<span class="_ _2"></span>ation</div><div class="t m0 xa h6 y64 ff1 fs4 fc0 sc0 ls1c ws0">design<span class="_ _8"> </span>at<span class="_ _7"> </span>the<span class="_ _8"> </span>expense<span class="_ _7"> </span>o<span class="_ _2"></span>f<span class="_ _7"> </span>&#64257;delity<span class="_ _1"></span>.<span class="_ _7"> </span>Ideally<span class="_ _1"></span>,<span class="_ _7"> </span>one<span class="_ _8"> </span>seeks<span class="_ _8"> </span>to<span class="_ _7"> </span>d<span class="_ _2"></span>eriv<span class="_ _1"></span>e</div><div class="t m0 xa h6 y65 ff1 fs4 fc0 sc0 ls50 ws0">a<span class="_ _13"> </span>provably<span class="_ _12"> </span>stable<span class="_ _13"> </span>estimato<span class="_ _2"></span>r<span class="_ _13"> </span>for<span class="_ _13"> </span>the<span class="_ _f"> </span>highest<span class="_ _12"> </span>&#64257;d<span class="_ _2"></span>elity<span class="_ _13"> </span>electro-</div><div class="t m0 xa h6 y66 ff1 fs4 fc0 sc0 ls1d ws0">chemical<span class="_ _12"> </span>battery<span class="_ _12"> </span>model<span class="_ _12"> </span>possible.<span class="_ _12"> </span>The<span class="_ _12"> </span>&#64257;rst<span class="_ _13"> </span>wa<span class="_ _1"></span>ve<span class="_ _12"> </span>of<span class="_ _13"> </span>studies</div><div class="t m0 xa h6 y67 ff1 fs4 fc0 sc0 ls51 ws0">utilize<span class="_ _d"> </span>th<span class="_ _2"></span>e<span class="_ _d"> </span>SPM<span class="_ _12"> </span>for<span class="_ _12"> </span>an<span class="_ _d"> </span>estimator<span class="_ _d"> </span>d<span class="_ _2"></span>esign<span class="_ _12"> </span>[4],<span class="_ _d"> </span>[14<span class="_ _2"></span>]&#8211;[1<span class="_ _2"></span>7].<span class="_ _d"> </span>The</div><div class="t m0 xa h6 y68 ff1 fs4 fc0 sc0 ls52 ws0">SPM<span class="_ _f"> </span>idealizes<span class="_ _13"> </span>each<span class="_ _f"> </span>electrode<span class="_ _13"> </span><span class="ls53">as<span class="_ _f"> </span>a<span class="_ _f"> </span>single<span class="_ _13"> </span>spherical<span class="_ _13"> </span>porous</span></div><div class="t m0 xa h6 y69 ff1 fs4 fc0 sc0 ls24 ws0">particle<span class="_ _e"> </span>by<span class="_ _c"> </span>neglect<span class="_ _1"></span>ing<span class="_ _15"> </span>the<span class="_ _15"> </span>electrolyte<span class="_ _e"> </span>dynamics.<span class="_ _15"> </span>This<span class="_ _15"> </span>model<span class="_ _15"> </span>is</div><div class="t m0 xa h6 y6a ff1 fs4 fc0 sc0 ls54 ws0">suitable<span class="_"> </span>for<span class="_"> </span>low<span class="_"> </span><span class="ff2 ls1b">C<span class="_ _18"></span></span><span class="ls55">-rates,<span class="_"> </span>but<span class="_"> </span>loses<span class="_"> </span>&#64257;delity<span class="_"> </span>at<span class="_"> </span><span class="ff2 ls1b">C<span class="_ _18"></span></span><span class="ls27">-rates<span class="_"> </span>abov<span class="_ _1"></span>e<span class="_"> </span><span class="ff2 ls1b">C<span class="_ _a"></span></span><span class="ls20">/2</span></span></span></div><div class="t m0 xc h9 y6b ff1 fs5 fc0 sc0 ls56 ws0">1063-6536<span class="_ _15"> </span>&#169;<span class="_ _e"> </span>2016<span class="_ _15"> </span>I<span class="ls57">EEE.<span class="_ _0"> </span>Personal<span class="_ _15"> </span>u<span class="ls58">se<span class="_ _e"> </span>is<span class="_ _15"> </span>perm<span class="ls2b">itted,<span class="_ _15"> </span>but<span class="_ _e"> </span>republication/redis<span class="_ _2"></span>tri<span class="ls38">bution<span class="_ _7"> </span>requires<span class="_ _15"> </span>IE<span class="_ _2"></span>EE<span class="_ _e"> </span>permis<span class="_ _2"></span>sion.</span></span></span></span></div><div class="t m0 xd h9 y6c ff1 fs5 fc0 sc0 ls28 ws0">See<span class="_ _e"> </span>http://w<span class="_ _2"></span>ww<span class="_ _1"></span>.ieee.org/publications_s<span class="_ _2"></span>tandards<span class="_ _2"></span>/publica<span class="_ _2"></span>tions/<span class="_ _2"></span>rights/i<span class="_ _2"></span>ndex.html<span class="_ _7"> </span>for<span class="_ _15"> </span>more<span class="_ _15"> </span>information.</div><div class="t m0 xe ha y6d ff5 fs7 fc0 sc0 ls1b ws0">Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on January 19,2022 at 04:38:28 UTC from IEEE Xplore. Restrictions apply. </div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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