mathematical model for lead-acid batteries.zip

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这篇文章主要介绍了如何建立一个等效电路铅酸电池模型
mathematical model for lead-acid batteries.zip
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<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/625aae7492dc900e62f11cec/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/625aae7492dc900e62f11cec/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE </div><div class="t m1 x2 h3 y1 ff2 fs1 fc0 sc0 ls1 ws0">Transactions </div><div class="t m2 x3 h4 y1 ff2 fs2 fc0 sc0 ls2 ws0">on </div><div class="t m3 x4 h5 y1 ff2 fs3 fc0 sc0 ls3 ws0">Energy </div><div class="t m4 x5 h3 y1 ff2 fs1 fc0 sc0 ls4 ws0">Conversion, </div><div class="t m5 x6 h6 y1 ff2 fs0 fc0 sc0 ls5 ws0">Vol. </div><div class="t m4 x7 h3 y1 ff2 fs1 fc0 sc0 ls5 ws0">7, </div><div class="t m6 x8 h7 y1 ff2 fs4 fc0 sc0 ls6 ws0">No.1, </div><div class="t m7 x9 h6 y1 ff2 fs0 fc0 sc0 ls7 ws0">March </div><div class="t m6 xa h7 y1 ff2 fs4 fc0 sc0 ls8 ws0">1992 </div><div class="t m8 xb h8 y2 ff2 fs5 fc0 sc0 ls9 ws0">A <span class="_ _0"></span><span class="lsa">Mathematical <span class="_ _1"></span>Model <span class="_ _0"></span>for <span class="_ _0"></span>Lead-Acid <span class="_ _1"></span>Batteries </span></div><div class="t m0 x4 h9 y3 ff1 fs6 fc0 sc0 lsb ws0">Ziyad <span class="_ _2"></span><span class="lsc">M. <span class="_ _1"> </span></span>Salameh </div><div class="t m0 xc h9 y4 ff1 fs6 fc0 sc0 lsd ws0">Margaret </div><div class="t m9 xd ha y5 ff1 fs7 fc0 sc0 lse ws0">A. </div><div class="t m0 xe h9 y5 ff1 fs6 fc0 sc0 lsb ws0">Casacca <span class="_ _3"> </span><span class="lsf">William </span></div><div class="t ma xf hb y5 ff1 fs8 fc0 sc0 ls10 ws0">A. </div><div class="t m0 x10 h9 y5 ff1 fs6 fc0 sc0 lsf ws0">Lynch </div><div class="t m0 x11 h9 y6 ff1 fs6 fc0 sc0 ls11 ws0">Senior <span class="lsb">Member, <span class="_ _4"></span><span class="ls12">IEEE <span class="_ _5"> </span><span class="ls13">Student Member, </span>IEEE <span class="_ _5"> </span></span></span>Student <span class="_ _2"></span><span class="lsb">Member, <span class="_ _4"></span><span class="ls12">IEEE </span></span></div><div class="t m0 x12 h9 y7 ff1 fs6 fc0 sc0 ls13 ws0">Department </div><div class="t mb x13 hc y8 ff1 fs9 fc0 sc0 ls14 ws0">of </div><div class="t m0 x14 h9 y8 ff1 fs6 fc0 sc0 ls11 ws0">Electrical <span class="_ _4"></span>Engineering </div><div class="t m0 x15 h9 y9 ff1 fs6 fc0 sc0 ls11 ws0">University </div><div class="t mc x16 h9 ya ff1 fs6 fc0 sc0 ls15 ws0">of </div><div class="t m0 x17 h9 ya ff1 fs6 fc0 sc0 lsf ws0">Lowell </div><div class="t m0 x18 h9 yb ff1 fs6 fc0 sc0 ls11 ws0">Lowell, <span class="_"> </span><span class="ls13">Massachusetts </span></div><div class="t m0 x19 hd yc ff3 fs8 fc0 sc0 ls16 ws0">01854 </div><div class="t md x1a he yd ff4 fsa fc0 sc0 ls17 ws0">Abstract </div><div class="t me x1b hf ye ff3 fsb fc0 sc0 ls5 ws0">A </div><div class="t m0 x1c h9 ye ff1 fs6 fc0 sc0 ls18 ws0">mathematical model of <span class="_ _2"></span>a lead-acid <span class="_ _2"></span>battery <span class="_ _2"></span><span class="ls5">is <span class="_ _6"></span><span class="ls18">presented <span class="_ _2"></span><span class="ls5">in </span></span></span></div><div class="t m0 x1a h9 yf ff1 fs6 fc0 sc0 ls18 ws0">this <span class="_ _7"></span>paper. <span class="_ _8"> </span><span class="ls5">This <span class="_ _2"></span></span>model <span class="_ _7"></span>takes <span class="_ _7"></span><span class="ls5">into <span class="_ _2"></span>account </span>self-discharge, <span class="_ _1"> </span>battery </div><div class="t m0 x1a h9 y10 ff1 fs6 fc0 sc0 ls18 ws0">storage capacity, <span class="_ _9"></span>internal resistance, overvoltage and environmental </div><div class="t m0 x1a h9 y11 ff1 fs6 fc0 sc0 ls5 ws0">temperature. <span class="_ _a"> </span><span class="lsc">Nonlinear <span class="_"> </span>components <span class="_"> </span><span class="lsf">are <span class="_ _7"></span><span class="ls18">used <span class="_ _b"> </span><span class="ls11">to <span class="_ _2"></span></span></span></span></span>represent <span class="_ _1"> </span>the </div><div class="t m0 x1a h9 y12 ff1 fs6 fc0 sc0 ls18 ws0">behavior <span class="ls5">of <span class="_ _9"></span><span class="ls18">the different <span class="_ _2"></span>battery parameters thereby simplifying <span class="_ _2"></span>the </span></span></div><div class="t m0 x1a h9 y13 ff1 fs6 fc0 sc0 lsb ws0">model <span class="_ _c"> </span><span class="lsf">design. <span class="_ _a"> </span><span class="ls12">The <span class="_ _d"> </span></span></span>model <span class="_ _c"> </span>components <span class="_ _8"> </span><span class="lsf">are <span class="_ _8"> </span><span class="ls13">found <span class="_ _d"> </span><span class="ls11">using </span></span></span></div><div class="t m0 x1a h9 y14 ff1 fs6 fc0 sc0 ls18 ws0">manufacturers specifications and experimental <span class="lsc">tests. <span class="_ _1"> </span><span class="ls19">A </span></span>comparison </div><div class="t m0 x1a h9 y15 ff1 fs6 fc0 sc0 ls18 ws0">between <span class="_ _9"></span><span class="ls5">the </span></div><div class="t mf x1d h10 y16 ff1 fsc fc0 sc0 ls1a ws0">model </div><div class="t m0 x1e h9 y16 ff1 fs6 fc0 sc0 ls18 ws0">and <span class="_ _9"></span>experimental results obtained <span class="lsc">from <span class="_ _9"></span><span class="ls18">a <span class="_ _9"></span>battery </span></span></div><div class="t m0 x1a h9 y17 ff1 fs6 fc0 sc0 ls18 ws0">evaluation </div><div class="t m10 x1f h11 y18 ff3 fs3 fc0 sc0 ls1b ws0">test </div><div class="t m0 x20 h9 y18 ff1 fs6 fc0 sc0 ls18 ws0">system <span class="_ _9"></span><span class="lsc">was </span></div><div class="t m11 x21 h10 y18 ff1 fsc fc0 sc0 ls1c ws0">used </div><div class="t m0 x22 h9 y18 ff1 fs6 fc0 sc0 ls5 ws0">for <span class="_ _9"></span><span class="ls18">verification. <span class="_"> </span>This </span></div><div class="t m12 x13 h10 y18 ff1 fsc fc0 sc0 ls1d ws0">model </div><div class="t m0 x23 h9 y18 ff1 fs6 fc0 sc0 ls5 ws0">can <span class="_ _9"></span><span class="ls15">be </span></div><div class="t m0 x1a h9 y19 ff1 fs6 fc0 sc0 ls15 ws0">used </div><div class="t m13 x24 hb y1a ff1 fs8 fc0 sc0 ls1e ws0">to </div><div class="t m14 x1b h12 y1a ff5 fsc fc0 sc0 ls1f ws0">accurately </div><div class="t m0 x25 h9 y1a ff1 fs6 fc0 sc0 ls18 ws0">evaluate <span class="_ _9"></span><span class="ls19">battery <span class="ls18">performance </span></span></div><div class="t m15 x26 h9 y1a ff1 fs6 fc0 sc0 ls18 ws0">in </div><div class="t m0 x15 h9 y1a ff1 fs6 fc0 sc0 ls18 ws0">electrical <span class="_ _9"></span>systems. </div><div class="t m0 x1b h9 y1b ff1 fs6 fc0 sc0 ls18 ws0">Lead-acid <span class="_ _7"></span>batteries <span class="_ _1"> </span><span class="ls19">lire <span class="_ _7"></span></span>used <span class="_ _7"></span>in <span class="_ _2"></span><span class="ls19">many <span class="_ _4"></span></span>electrical <span class="_"> </span>systems <span class="_ _7"></span><span class="ls5">to </span></div><div class="t m0 x1a h9 y1c ff1 fs6 fc0 sc0 ls5 ws0">store <span class="_ _7"></span><span class="ls13">or </span>deliver <span class="_ _2"></span>energy. <span class="_ _a"> </span><span class="ls13">To <span class="_ _2"></span><span class="ls18">use <span class="_ _1"> </span></span></span>batteries <span class="_ _7"></span><span class="lsc">more <span class="_ _4"></span></span>efficiently <span class="_ _7"></span>it <span class="_ _4"></span><span class="ls11">is </span></div><div class="t m0 x1a h9 y1d ff1 fs6 fc0 sc0 ls5 ws0">important <span class="_ _2"></span>that <span class="_ _7"></span>their <span class="_ _2"></span>response <span class="_ _4"></span>to <span class="_ _4"></span>various <span class="_ _2"></span>operating <span class="_ _7"></span>conditions <span class="_ _2"></span><span class="ls11">is </span></div><div class="t m0 x1a h9 y1e ff1 fs6 fc0 sc0 ls18 ws0">understood. </div><div class="t m0 x1b h9 y1f ff1 fs6 fc0 sc0 lsf ws0">The <span class="_ _6"></span><span class="lsc">energy <span class="ls18">stored <span class="_ _2"></span><span class="ls5">in </span>a lead-acid <span class="_ _2"></span>battery <span class="_ _2"></span><span class="ls5">is chemical <span class="_ _6"></span><span class="ls18">energy </span></span></span></span></div><div class="t m0 x1a h9 y20 ff1 fs6 fc0 sc0 ls18 ws0">that <span class="_ _1"> </span><span class="ls5">is <span class="_ _7"></span>translated <span class="_ _2"></span><span class="lsf">into </span>electrical <span class="_ _2"></span>energy. <span class="_ _c"> </span>Lead-acid <span class="_ _7"></span></span>batteries </div><div class="t m16 x27 h13 y21 ff5 fsd fc0 sc0 ls20 ws0">are. </div><div class="t m0 x1a h9 y22 ff1 fs6 fc0 sc0 ls18 ws0">rechargeable <span class="_ _6"></span>and <span class="_ _9"></span>have <span class="_ _9"></span><span class="ls19">the <span class="ls18">following <span class="_ _e"></span>reversible <span class="_ _6"></span>reaction: </span></span></div><div class="t m17 x28 h14 y22 ff6 fs2 fc0 sc0 ls5 ws0">[ </div><div class="t m0 x29 h9 y22 ff1 fs6 fc0 sc0 ls21 ws0">11 </div><div class="t m0 x2a h9 y23 ff1 fs6 fc0 sc0 lsb ws0">Pb </div><div class="t m18 x2b h15 y24 ff6 fse fc0 sc0 ls5 ws0">+ </div><div class="t m19 x2c h16 y24 ff5 fsf fc0 sc0 ls22 ws0">Pboz </div><div class="t m1a x2d h17 y24 ff6 fs10 fc0 sc0 ls5 ws0">+ </div><div class="t m0 x2e h9 y24 ff1 fs6 fc0 sc0 lsc ws0">2HzS04 </div><div class="t m1b x2f h18 y25 ff6 fs4 fc0 sc0 ls23 ws0">f--+ </div><div class="t m0 x30 h9 y25 ff1 fs6 fc0 sc0 lsf ws0">2PbS04 </div><div class="t m1c x9 h19 y25 ff6 fs11 fc0 sc0 ls5 ws0">+ </div><div class="t m0 x31 h9 y25 ff1 fs6 fc0 sc0 lsb ws0">2H20 </div><div class="t m0 x32 h9 y26 ff1 fs6 fc0 sc0 ls18 ws0">(1) </div><div class="t m1d x33 h1a y27 ff2 fs12 fc0 sc0 ls24 ws0">93 </div><div class="t m1e x34 h13 y28 ff4 fsd fc0 sc0 ls25 ws0">"cc </div><div class="t m1f x35 h1b y29 ff7 fs13 fc0 sc0 ls5 ws0">0 </div><div class="t m20 x36 h1c y29 ff6 fs14 fc0 sc0 ls26 ws0">'I<span class="fc0 sc0"> </span></div><div class="t m21 x37 h1d y2a ff8 fsc fc0 sc0 ls1c ws0">Figure </div><div class="t m9 x38 h1e y2a ff8 fs7 fc0 sc0 ls27 ws0">1: </div><div class="t m21 x39 h1d y2a ff8 fsc fc0 sc0 ls28 ws0">Thevenin <span class="_ _7"></span>Battery <span class="_ _4"></span>Model </div><div class="t m0 x3a h9 y2b ff1 fs6 fc0 sc0 ls15 ws0">An <span class="_ _f"> </span><span class="lsc">improvement <span class="_ _b"> </span><span class="ls18">upon <span class="_ _b"> </span>the <span class="_"> </span></span>Thevenin <span class="_ _b"> </span>model <span class="_"> </span><span class="ls5">is <span class="_ _0"> </span><span class="ls18">a <span class="_ _1"> </span></span>linear </span></span></div><div class="t m0 x3b h9 y2c ff1 fs6 fc0 sc0 ls5 ws0">electrical <span class="ls18">battery <span class="_ _7"></span>model, <span class="_ _7"></span>shown <span class="_ _2"></span>in <span class="_ _7"></span>Figure </span></div><div class="t m22 x3c ha y2c ff1 fs7 fc0 sc0 ls29 ws0">2. </div><div class="t m0 x3d h9 y2c ff1 fs6 fc0 sc0 ls5 ws0">This <span class="ls18">model </span></div><div class="t m23 x3e h1f y2c ff5 fs15 fc0 sc0 ls2a ws0">[4] </div><div class="t m0 x3f h9 y2c ff1 fs6 fc0 sc0 ls18 ws0">uses </div><div class="t m0 x3b h9 y2d ff1 fs6 fc0 sc0 ls5 ws0">linear <span class="ls18">components <span class="_ _4"></span></span>to <span class="_ _7"></span><span class="ls18">account <span class="_ _7"></span></span>for <span class="_ _2"></span>self-discharge </div><div class="t m24 x40 h20 y2e ff1 fs16 fc0 sc0 ls2b ws0">(Rp) </div><div class="t m0 x41 h9 y2e ff1 fs6 fc0 sc0 lsc ws0">and <span class="_ _2"></span><span class="ls18">various </span></div><div class="t m0 x3b h9 y2f ff1 fs6 fc0 sc0 ls18 ws0">overvoltages <span class="_ _1"> </span><span class="ls19">(nm(t) <span class="_ _9"></span><span class="ls18">network). <span class="_ _10"> </span>Though <span class="_ _2"></span>more <span class="_ _2"></span>accurare, <span class="_ _7"></span>this <span class="_ _2"></span>model </span></span></div><div class="t m0 x3b h9 y30 ff1 fs6 fc0 sc0 ls18 ws0">however <span class="_ _7"></span><span class="ls5">does <span class="_ _2"></span></span>not </div><div class="t m25 x42 h21 y31 ff1 fs4 fc0 sc0 ls2c ws0">take </div><div class="t m0 x43 h9 y31 ff1 fs6 fc0 sc0 lsf ws0">into <span class="_ _2"></span><span class="ls18">account <span class="_ _2"></span><span class="ls5">temperature <span class="_ _9"></span><span class="lsc">dependence <span class="_ _2"></span>and </span></span></span></div><div class="t m0 x44 h9 y32 ff1 fs6 fc0 sc0 ls19 ws0">uses <span class="ls18">different <span class="_ _9"></span>sets </span></div><div class="t mc x45 h9 y33 ff1 fs6 fc0 sc0 ls2d ws0">of </div><div class="t m0 x46 h9 y33 ff1 fs6 fc0 sc0 ls18 ws0">element <span class="_ _9"></span>values <span class="_ _9"></span>to <span class="_ _9"></span>model <span class="_ _9"></span>the <span class="ls19">battery <span class="_ _b"> </span></span>at <span class="_ _9"></span>different </div><div class="t m0 x44 h9 y34 ff1 fs6 fc0 sc0 ls18 ws0">states </div><div class="t mc x47 h9 y35 ff1 fs6 fc0 sc0 ls2e ws0">of </div><div class="t m0 x48 h9 y35 ff1 fs6 fc0 sc0 ls18 ws0">charge. <span class="_ _a"> </span><span class="ls5">Thus, </span>a <span class="_ _7"></span><span class="ls5">continuous <span class="_ _6"></span><span class="ls18">battery <span class="_ _1"> </span>evaluation <span class="_"> </span>becomes </span></span></div><div class="t m0 x44 h9 y36 ff1 fs6 fc0 sc0 ls18 ws0">tedious. </div><div class="t m0 x1a h9 y37 ff1 fs6 fc0 sc0 lsf ws0">The <span class="_ _7"></span><span class="ls5">battery <span class="_ _2"></span>voltage <span class="_ _4"></span><span class="ls11">is <span class="_ _2"></span></span>related <span class="_ _1"> </span>to <span class="_ _4"></span><span class="ls18">the <span class="_"> </span></span></span>sum <span class="_ _2"></span><span class="ls18">of <span class="_"> </span><span class="ls5">the <span class="_ _7"></span>reduction <span class="_ _4"></span></span>and </span></div><div class="t m0 x1a h9 y38 ff1 fs6 fc0 sc0 ls5 ws0">oxidation <span class="_ _1"> </span>potentials. </div><div class="t m0 x49 h9 y39 ff1 fs6 fc0 sc0 ls5 ws0">Electrical <span class="_ _1"> </span><span class="lsf">energy <span class="_ _4"></span><span class="ls11">is <span class="_ _7"></span><span class="lsc">produced <span class="_ _f"> </span><span class="ls18">when <span class="_"> </span></span></span></span></span>the </div><div class="t m0 x1a h9 y3a ff1 fs6 fc0 sc0 ls5 ws0">chemicals <span class="_ _9"></span>in <span class="_ _2"></span>the <span class="_ _2"></span><span class="ls18">battery <span class="_ _1"> </span></span>react <span class="_ _2"></span><span class="ls18">with <span class="_ _7"></span><span class="lsf">one <span class="_ _2"></span></span>another. <span class="_ _a"> </span><span class="lsf">The </span></span>rate <span class="_ _2"></span>of <span class="_ _2"></span>the </div><div class="t m0 x1a h9 y3b ff1 fs6 fc0 sc0 ls18 ws0">chemical <span class="_ _6"></span>reaction <span class="_ _9"></span>varies <span class="_ _9"></span><span class="ls15">with <span class="_ _2"></span><span class="ls18">the <span class="_ _9"></span>following <span class="_ _6"></span>conditions: <span class="_ _9"></span><span class="ls19">[2] </span></span></span></div><div class="t m26 x47 h22 y3c ff3 fsd fc0 sc0 ls2f ws0">"b </div><div class="t m27 x4a h23 y3c ff3 fs17 fc0 sc0 ls30 ws0">Fb </div><div class="t m28 x20 h24 y3d ff3 fs18 fc0 sc0 ls31 ws0">1. </div><div class="t m0 x4b h9 y3d ff1 fs6 fc0 sc0 ls18 ws0">State <span class="_ _9"></span>of <span class="_ _2"></span>charge </div><div class="t m0 x4c h9 y3e ff1 fs6 fc0 sc0 ls19 ws0">2. <span class="_ _2"></span><span class="ls18">Battery <span class="_ _9"></span>storage <span class="_ _6"></span>capacity </span></div><div class="t m29 x4c h10 y3f ff1 fsc fc0 sc0 ls1d ws0">3. </div><div class="t m2a x4b h25 y3f ff5 fs19 fc0 sc0 ls32 ws0">Rate </div><div class="t m0 x4d h9 y3f ff1 fs6 fc0 sc0 ls33 ws0">of <span class="_ _2"></span><span class="ls18">chargeldischarge </span></div><div class="t me x4c hf y40 ff3 fsb fc0 sc0 ls34 ws0">4. </div><div class="t m0 x4b h9 y40 ff1 fs6 fc0 sc0 ls18 ws0">Envimnmental <span class="_ _6"></span>temperature </div><div class="t m2b x4c h26 y41 ff9 fs18 fc0 sc0 ls35 ws0">5. </div><div class="t m0 x4b h9 y41 ff1 fs6 fc0 sc0 ls15 ws0">AgeIShelf <span class="_ _2"></span><span class="lsc">life </span></div><div class="t m0 x1b h9 y42 ff1 fs6 fc0 sc0 lsf ws0">There <span class="_ _4"></span><span class="lsc">have <span class="_ _b"> </span><span class="ls18">been <span class="_ _b"> </span><span class="ls19">many <span class="_ _f"> </span><span class="ls5">proposals <span class="_"> </span></span></span></span></span>for <span class="_ _4"></span><span class="ls5">lead-acid <span class="_"> </span>battery </span></div><div class="t m0 x1a h9 y43 ff1 fs6 fc0 sc0 ls18 ws0">models. <span class="_ _f"> </span><span class="lsf">One <span class="_ _e"></span><span class="ls18">of <span class="_ _7"></span>these <span class="_ _2"></span><span class="ls5">is </span>the <span class="lsc">Thevenin </span>equivalent <span class="_ _2"></span><span class="ls5">circuit, <span class="_ _9"></span><span class="ls18">shown in </span></span></span></span></div><div class="t m0 x1a h9 y44 ff1 fs6 fc0 sc0 ls5 ws0">Figure <span class="_ _2"></span><span class="lsb">1, <span class="_ _e"></span><span class="ls18">which <span class="_ _2"></span><span class="ls11">is <span class="_ _6"></span><span class="ls18">a <span class="_ _7"></span>simple <span class="_ _7"></span><span class="ls15">way <span class="_ _7"></span><span class="ls5">of </span></span>demonstrating <span class="_ _4"> </span>the <span class="_ _7"></span>behavior <span class="_ _2"></span>of </span></span></span></span></div><div class="t m0 x1a h9 y45 ff1 fs6 fc0 sc0 ls18 ws0">battery <span class="_"> </span>voltage </div><div class="t m2c x3 h6 y46 ff2 fs0 fc0 sc0 ls0 ws0">(vb). </div><div class="t m0 x4e h9 y46 ff1 fs6 fc0 sc0 lsb ws0">It <span class="ls5">contains <span class="ls18">the <span class="_ _7"></span>electrical <span class="_"> </span>values <span class="_ _7"></span>of <span class="_ _4"> </span>no-load </span></span></div><div class="t m0 x1a h9 y47 ff1 fs6 fc0 sc0 ls18 ws0">voltage </div><div class="t m2d x4f h27 y48 ff2 fs1a fc0 sc0 ls36 ws0">(VOC), </div><div class="t m0 x50 h9 y48 ff1 fs6 fc0 sc0 ls5 ws0">internal <span class="_ _2"></span>resistance </div><div class="t m2e x51 h28 y48 ff5 fs1b fc0 sc0 ls37 ws0">(RI) </div><div class="t m0 x52 h9 y48 ff1 fs6 fc0 sc0 lsc ws0">and <span class="_ _7"></span><span class="ls5">overvoltage <span class="_ _7"></span>(parallel </span></div><div class="t m0 x1a h9 y49 ff1 fs6 fc0 sc0 ls18 ws0">combination </div><div class="t m2f x53 ha y4a ff1 fs7 fc0 sc0 ls38 ws0">of </div><div class="t m30 x54 hc y4a ff1 fs9 fc0 sc0 ls5 ws0">C </div><div class="t m0 x55 h9 y4a ff1 fs6 fc0 sc0 lsc ws0">and </div><div class="t m31 x56 h29 y4a ff5 fs1 fc0 sc0 ls39 ws0">R2). </div><div class="t m32 x57 h2a y4a ff5 fs1a fc0 sc0 ls3a ws0">[3] </div><div class="t m0 x58 h9 y4a ff1 fs6 fc0 sc0 ls5 ws0">This <span class="ls18">model <span class="_ _9"></span><span class="ls5">is <span class="_ _2"></span><span class="ls18">not </span>accurate <span class="_ _6"></span><span class="ls18">because </span></span></span></div><div class="t m0 x1a h9 y4b ff1 fs6 fc0 sc0 ls18 ws0">these <span class="_ _9"></span>values </div><div class="t m33 x1d h2b y4c ff5 fs1c fc0 sc0 ls3b ws0">are </div><div class="t m0 x54 h9 y4c ff1 fs6 fc0 sc0 ls18 ws0">not <span class="_ _9"></span>constants as modeled <span class="_ _e"></span>but </div><div class="t m34 x59 h9 y4c ff1 fs6 fc0 sc0 ls5 ws0">in </div><div class="t m0 x9 h9 y4c ff1 fs6 fc0 sc0 ls18 ws0">fact </div><div class="t m35 x5a h13 y4c ff5 fsd fc0 sc0 ls3c ws0">are </div><div class="t m0 x5b h9 y4c ff1 fs6 fc0 sc0 ls18 ws0">functions <span class="_ _9"></span>of </div><div class="t m0 x1a h9 y4d ff1 fs6 fc0 sc0 ls18 ws0">the various <span class="_ _6"></span><span class="lsf">bamry <span class="_ _9"></span><span class="ls18">conditions stated <span class="_ _6"></span>above. </span></span></div><div class="t m36 x5c h2c y4e ff6 fs1d fc0 sc0 ls3d ws0">c, </div><div class="t m37 x5d h2d y4f ff3 fs1b fc0 sc0 ls3e ws0">Eo </div><div class="t m21 x5e h1d y50 ff8 fsc fc0 sc0 ls1c ws0">Figure </div><div class="t m38 x5f h2e y50 ff8 fs8 fc0 sc0 ls3f ws0">2: </div><div class="t m21 x60 h1d y50 ff8 fsc fc0 sc0 ls28 ws0">Linear <span class="_ _7"></span><span class="ls1c">Electrical <span class="_ _1"> </span><span class="ls40">Model </span></span></div><div class="t m0 x61 h9 y51 ff1 fs6 fc0 sc0 ls41 ws0">An <span class="_ _2"></span><span class="ls18">equivalent <span class="_ _9"></span>circuit for a Nickel-Cadmium <span class="_ _e"></span>storage <span class="_ _6"></span>cell was </span></div><div class="t m0 x62 h9 y52 ff1 fs6 fc0 sc0 lsc ws0">developed <span class="ls18">using <span class="_ _4"></span>nonlinear <span class="_ _2"></span>elements.[5] <span class="_ _a"> </span></span>The <span class="ls18">mathematical <span class="_ _4"></span>model </span></div><div class="t m0 x62 h9 y53 ff1 fs6 fc0 sc0 ls18 ws0">described <span class="ls33">in <span class="_ _4"></span><span class="ls19">this <span class="_ _2"></span></span></span>paper <span class="_ _2"></span>utilizes <span class="_ _2"></span>a similar <span class="_ _2"></span>technique <span class="ls5">for </span>the lead-acid </div><div class="t m0 x62 h9 y54 ff1 fs6 fc0 sc0 ls19 ws0">battery </div><div class="t ma x61 hb y55 ff1 fs8 fc0 sc0 ls42 ws0">thus </div><div class="t m0 x63 h9 y55 ff1 fs6 fc0 sc0 ls18 ws0">allowing <span class="_ _6"></span>a continuous <span class="_ _6"></span>evaluation <span class="_ _9"></span><span class="ls43">of <span class="_"> </span><span class="ls18">battery <span class="_ _6"></span>performance </span></span></div><div class="t m0 x62 h9 y56 ff1 fs6 fc0 sc0 ls18 ws0">that <span class="_ _2"></span><span class="ls5">is </span>both <span class="_ _2"></span>uncomplicated <span class="_ _7"></span>and <span class="_ _2"></span>accurate. <span class="_ _d"> </span><span class="ls5">This </span>model <span class="_ _2"></span>was <span class="_ _2"></span>verified </div><div class="t m0 x62 h9 y57 ff1 fs6 fc0 sc0 ls18 ws0">experimentally <span class="_ _7"></span>on <span class="_ _2"></span>the <span class="_ _2"></span>University <span class="_ _2"></span>of <span class="_ _2"></span><span class="lsc">Lowell <span class="_ _2"></span></span>battery <span class="_ _2"></span>evaluation <span class="_ _2"></span>test </div><div class="t m0 x64 h9 y58 ff1 fs6 fc0 sc0 ls18 ws0">system. </div><div class="t m39 x1a h2f y59 ff5 fs2 fc0 sc0 ls44 ws0">91 </div><div class="t m3a x65 h30 y59 ff5 fs18 fc0 sc0 ls45 ws0">WM </div><div class="t m3b x1b h31 y59 ff4 fs12 fc0 sc0 ls5 ws0">154-5 </div><div class="t m3c x4c h29 y59 ff5 fs1 fc0 sc0 ls5 ws0">EC </div><div class="t m3d x66 h32 y59 ff3 fs16 fc0 sc0 ls5 ws0">A </div><div class="t m3c x67 h29 y59 ff5 fs1 fc0 sc0 ls46 ws0">Paper <span class="_ _9"></span>recommended <span class="_ _9"></span><span class="ls5">and approved </span></div><div class="t m3c x68 h29 y5a ff5 fs1 fc0 sc0 ls5 ws0">by <span class="_ _7"></span>the <span class="_ _2"></span><span class="ls46">IEEE <span class="_ _6"></span><span class="ls5">Energy <span class="_ _7"></span>Development <span class="_ _1"> </span>and <span class="_ _2"></span>Power <span class="ls46">Generation </span></span></span></div><div class="t m3c x68 h29 y5b ff5 fs1 fc0 sc0 ls5 ws0">Committee </div><div class="t m3e x1d h33 y5c ff5 fs1e fc0 sc0 ls5 ws0">of </div><div class="t m3c x54 h29 y5c ff5 fs1 fc0 sc0 ls5 ws0">the <span class="_ _2"></span><span class="ls46">IEEE <span class="_ _6"></span>Power <span class="ls5">Engineering <span class="_ _4"> </span>Society <span class="_ _7"></span>for </span></span></div><div class="t m3c x68 h29 y5d ff5 fs1 fc0 sc0 ls46 ws0">Presentation <span class="ls5">at the <span class="_ _2"></span>IEEE/PES <span class="_ _7"></span></span>1991 <span class="_ _6"></span><span class="ls5">Winter <span class="_ _2"></span><span class="ls46">Meeting, </span></span></div><div class="t m3c x68 h29 y5e ff5 fs1 fc0 sc0 ls47 ws0">New <span class="_ _e"></span>York, <span class="_ _6"></span>New <span class="_ _6"></span>York, <span class="_ _6"></span><span class="ls5">February </span></div><div class="t m3f x6 h2f y5f ff5 fs2 fc0 sc0 ls48 ws0">3-7, </div><div class="t m3c x8 h29 y5f ff5 fs1 fc0 sc0 ls5 ws0">1991. <span class="_"> </span><span class="ls46">Manuscript </span></div><div class="t m3c x68 h29 y60 ff5 fs1 fc0 sc0 ls46 ws0">submitted <span class="_ _e"></span>August </div><div class="t m40 xb h31 y60 ff5 fs12 fc0 sc0 ls24 ws0">31, </div><div class="t m3c x67 h29 y60 ff5 fs1 fc0 sc0 ls46 ws0">1990; <span class="_ _e"></span><span class="ls5">made <span class="_ _7"></span>available </span></div><div class="t m41 x69 h34 y60 ff5 fs1f fc0 sc0 ls49 ws0">for </div><div class="t m3c x68 h29 y61 ff5 fs1 fc0 sc0 ls46 ws0">printing December </div><div class="t m42 x4d h30 y61 ff5 fs18 fc0 sc0 ls4a ws0">18, </div><div class="t m3c x6a h29 y61 ff5 fs1 fc0 sc0 ls5 ws0">1990. </div><div class="t m0 x61 h9 y62 ff1 fs6 fc0 sc0 ls19 ws0">A battery <span class="ls18">evaluation <span class="_ _6"></span><span class="ls19">test <span class="_ _2"></span><span class="ls18">system <span class="_ _e"></span>was <span class="_ _9"></span>designed <span class="_ _9"></span>and <span class="_ _9"></span>built at <span class="_ _9"></span>the </span></span></span></div><div class="t m0 x64 h9 y63 ff1 fs6 fc0 sc0 ls18 ws0">University <span class="_ _9"></span><span class="ls15">of <span class="_ _2"></span><span class="ls18">Lowell. <span class="_ _4"></span>The <span class="ls19">battery </span>evaluation <span class="ls19">test </span>scheme <span class="_ _6"></span>consists <span class="_ _9"></span><span class="lsf">of </span></span></span></div><div class="t m0 x64 h9 y64 ff1 fs6 fc0 sc0 ls18 ws0">a <span class="_ _2"></span><span class="ls5">data <span class="_ _7"></span></span>acquisition <span class="_"> </span><span class="ls5">system, </span>a <span class="_ _2"></span><span class="ls5">controller <span class="_ _2"></span></span>rack <span class="_ _7"></span>and <span class="_ _4"></span><span class="lsf">two </span>temperature </div><div class="t m0 x64 h9 y65 ff1 fs6 fc0 sc0 ls5 ws0">controlled <span class="ls18">chambers. <span class="_ _a"> </span></span>(See <span class="ls18">Figure </span></div><div class="t m43 x6b h2a y66 ff5 fs1a fc0 sc0 ls4b ws0">3) </div><div class="t m0 x6c h9 y66 ff1 fs6 fc0 sc0 ls18 ws0">Voltage <span class="_ _4"></span><span class="ls5">controlled <span class="lsf">mrrent </span></span></div><div class="t m0 x64 h9 y67 ff1 fs6 fc0 sc0 ls15 ws0">Source <span class="ls18">controllers <span class="_ _2"></span>are used <span class="_ _2"></span><span class="ls19">to <span class="_ _2"></span></span>test the <span class="_ _2"></span>batteries. <span class="_"> </span><span class="lsc">The </span></span></div><div class="t m44 x6d h35 y68 ff1 fs1a fc0 sc0 ls4c ws0">WAC </div><div class="t m0 x6e h9 y68 ff1 fs6 fc0 sc0 ls18 ws0">analog </div><div class="t m0 x64 h9 y69 ff1 fs6 fc0 sc0 ls5 ws0">outputs <span class="_ _7"></span>are <span class="_ _4"></span><span class="ls18">used <span class="_"> </span></span>to <span class="_ _4"></span>supply <span class="_ _7"></span><span class="ls18">the <span class="_ _1"> </span></span>controllers <span class="_ _4"></span><span class="ls18">with <span class="_"> </span></span>the <span class="_ _7"></span>appropriate </div><div class="t m0 x64 h9 y6a ff1 fs6 fc0 sc0 ls18 ws0">analog <span class="_ _2"></span>input <span class="_ _2"></span>voltages. Every <span class="_ _7"></span>two minutes <span class="_ _2"></span>the <span class="_ _2"></span>PMAC measures the </div><div class="t m0 x6f h9 y6b ff1 fs6 fc0 sc0 ls5 ws0">current, <span class="ls18">voltage <span class="_ _1"> </span>and <span class="_ _1"> </span>temperature <span class="_ _1"> </span><span class="lsf">of <span class="_ _2"></span></span>each <span class="_ _1"> </span>batttery <span class="_"> </span>and <span class="_ _7"></span>stores <span class="_ _1"> </span>this </span></div><div class="t m0 x6f h9 y6c ff1 fs6 fc0 sc0 ls18 ws0">information. </div><div class="t m6 x5b h7 y6d ff2 fs4 fc0 sc0 ls23 ws0">0885-8969/9 </div><div class="t m45 x70 h36 y6d ff7 fs20 fc0 sc0 ls5 ws0">2$03.000 </div><div class="t m6 x71 h7 y6d ff2 fs4 fc0 sc0 ls8 ws0">1992 </div><div class="t m46 x72 h2 y6d ff1 fs0 fc0 sc0 ls4d ws0">IEEE </div><div class="t m47 x73 h37 y6e ff3 fs21 fc0 sc0 ls5 ws0">1 </div></div><div class="pi" data-data='{"ctm":[1.550689,0.000000,0.000000,1.550689,0.000000,0.000000]}'></div></div> </body> </html>
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