Lithium-Battery-SOC.rar_蓄电池_电池状态估计_单片机开发_嵌入式/单片机/硬件编程下载-pudn.com

<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/622bacea3d2fbb0007c6b411/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/622bacea3d2fbb0007c6b411/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1 </div><div class="t m0 x2 h3 y2 ff2 fs0 fc0 sc0 ls0 ws0">978-1-4673-1561-6/12/$31.00 ©2012 IEEE </div><div class="t m0 x3 h4 y3 ff3 fs1 fc0 sc0 ls0 ws0">High Fidelity Electrical Model with Thermal </div><div class="t m0 x4 h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">Dependence for Characterization and Simula-</div><div class="t m0 x5 h4 y5 ff3 fs1 fc0 sc0 ls0 ws0">tion of High Power Lithium Battery Cells</div><div class="t m0 x6 h5 y6 ff3 fs0 fc0 sc0 ls0 ws0">Tarun Huria, Massimo Ceraolo </div><div class="t m0 x7 h6 y7 ff3 fs2 fc0 sc0 ls0 ws0">Department of Energy and Systems Engineering </div><div class="t m0 x8 h6 y8 ff3 fs2 fc0 sc0 ls0 ws0">University of Pisa </div><div class="t m0 x9 h6 y9 ff3 fs2 fc0 sc0 ls0 ws0">Largo Lazzarino, Pisa 56122 Italy </div><div class="t m0 xa h6 ya ff3 fs2 fc0 sc0 ls0 ws0">m.ceraolo@ing.unipi.it </div><div class="t m0 xb h5 y6 ff3 fs0 fc0 sc0 ls0 ws0">Javier Gazzarri, Robyn Jackey </div><div class="t m0 xc h6 y7 ff3 fs2 fc0 sc0 ls0 ws0">MathWorks </div><div class="t m0 xd h6 y8 ff3 fs2 fc0 sc0 ls0 ws0">39555 Orchard Hill Place, Suite 280 </div><div class="t m0 xe h6 y9 ff3 fs2 fc0 sc0 ls0 ws0">Novi, MI 48375 USA </div><div class="t m0 xf h6 ya ff3 fs2 fc0 sc0 ls0 ws0">robyn.jackey@mathworks.com </div><div class="t m0 x10 h6 yb ff3 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h7 yc ff4 fs3 fc0 sc0 ls0 ws0">Abstract— The growing need for accurate simulation of </div><div class="t m0 x2 h7 yd ff3 fs3 fc0 sc0 ls0 ws0">advanced lithium cells for powertrain electrification de-</div><div class="t m0 x2 h7 ye ff3 fs3 fc0 sc0 ls0 ws0">mands fast and accurate modeling schemes. Additionally, </div><div class="t m0 x2 h7 yf ff3 fs3 fc0 sc0 ls0 ws0">battery models must account for thermal effects because of </div><div class="t m0 x2 h7 y10 ff3 fs3 fc0 sc0 ls0 ws0">the paramount importance of temperature in kinetic and </div><div class="t m0 x2 h7 y11 ff3 fs3 fc0 sc0 ls0 ws0">transport phenomena of electrochemical systems. This pa-</div><div class="t m0 x2 h7 y12 ff3 fs3 fc0 sc0 ls0 ws0">per presents an effective method for developing a multi-</div><div class="t m0 x2 h7 y13 ff3 fs3 fc0 sc0 ls0 ws0">temperature lithium cell simulation model with thermal de-</div><div class="t m0 x2 h7 y14 ff3 fs3 fc0 sc0 ls0 ws0">pendence. An equivalent circuit model with one voltage </div><div class="t m0 x2 h7 y15 ff3 fs3 fc0 sc0 ls0 ws0">source, one series resistor, and a single RC block was able </div><div class="t m0 x2 h7 y16 ff3 fs3 fc0 sc0 ls0 ws0">to account for the discharge dynamics observed in the ex-</div><div class="t m0 x2 h7 y17 ff3 fs3 fc0 sc0 ls0 ws0">periment. A parameter estimation numerical scheme using </div><div class="t m0 x2 h7 y18 ff3 fs3 fc0 sc0 ls0 ws0">pulse current discharge tests on high power lithium (LiNi-</div><div class="t m0 x2 h7 y19 ff3 fs3 fc0 sc0 ls0 ws0">CoMnO</div><div class="t m0 x11 h8 y1a ff3 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12 h7 y19 ff3 fs3 fc0 sc0 ls0 ws0"> cathode and graphite-based anode) cells under </div><div class="t m0 x2 h7 y1b ff3 fs3 fc0 sc0 ls0 ws0">different operating conditions revealed dependences of the </div><div class="t m0 x2 h7 y1c ff3 fs3 fc0 sc0 ls0 ws0">equivalent circuit elements on state of charge, average cur-</div><div class="t m0 x2 h7 y1d ff3 fs3 fc0 sc0 ls0 ws0">rent, and temperature. The process is useful for creating a </div><div class="t m0 x2 h7 y1e ff3 fs3 fc0 sc0 ls0 ws0">high fidelity model capable of predicting electrical cur-</div><div class="t m0 x2 h7 y1f ff3 fs3 fc0 sc0 ls0 ws0">rent/voltage performance and estimating run-time state of </div><div class="t m0 x2 h7 y20 ff3 fs3 fc0 sc0 ls0 ws0">charge. The model was validated for a lithium cell with an </div><div class="t m0 x2 h7 y21 ff3 fs3 fc0 sc0 ls0 ws0">independent drive cycle showing voltage accuracy within </div><div class="t m0 x2 h7 y22 ff3 fs3 fc0 sc0 ls0 ws0">2%. The model was also used to simulate thermal buildup </div><div class="t m0 x2 h7 y23 ff3 fs3 fc0 sc0 ls0 ws0">for a constant current discharge scenario. </div><div class="t m0 x4 h9 y24 ff4 fs3 fc0 sc0 ls0 ws0">Keywords- high-power lithium cell; thermal model, </div><div class="t m0 x2 h9 y25 ff4 fs3 fc0 sc0 ls0 ws0">electrical equivalent lithium cell model. state of charge, </div><div class="t m0 x2 h9 y26 ff4 fs3 fc0 sc0 ls0 ws0">pulse discharge test, energy storage; electric vehicle, hy-</div><div class="t m0 x2 h9 y27 ff4 fs3 fc0 sc0 ls0 ws0">brid electric vehicle </div><div class="t m0 x13 ha y28 ff3 fs2 fc0 sc0 ls0 ws0">I. NOMENCLATURE </div><div class="c x2 y29 w2 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">BMS</div></div><div class="c x14 y29 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y29 w4 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">battery management system</div></div><div class="c x16 y29 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y2b w5 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">C</div></div><div class="c x17 y2c w6 hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">n</div></div><div class="c x18 y2b w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y2b w7 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">capacitor </div></div><div class="c x19 y2b w8 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">n</div></div><div class="c x1a y2b w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">, </div></div><div class="c x1b y2b w9 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">where </div></div><div class="c x1c y2b w8 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">n</div></div><div class="c x1d y2b wa hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x1e y2b wb hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">is a natural number </div></div><div class="c x1f y2b w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y2e w5 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">C</div></div><div class="c x17 y2f wc hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">Q</div></div><div class="c x7 y2e w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y2e wd hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">cell capacity (Ah)</div></div><div class="c x20 y2e w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y30 w5 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">C</div></div><div class="c x17 y31 we hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">T</div></div><div class="c x18 y30 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y30 wf hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">heat capacitance (J m</div></div><div class="c x21 y32 w10 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">-</div></div><div class="c x22 y32 w6 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">3</div></div><div class="c x23 y30 w11 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x24 y30 w12 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">K</div></div><div class="c x25 y32 w10 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">-</div></div><div class="c x26 y32 w13 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">1</div></div><div class="c x27 y30 w6 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">)</div></div><div class="c x28 y30 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y34 w14 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">E</div></div><div class="c x17 y35 wc hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">m</div></div><div class="c x7 y34 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y34 w15 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">electromotive force of main branch</div></div><div class="c x29 y34 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y36 w14 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">E</div></div><div class="c x2a y37 w13 hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">p</div></div><div class="c x18 y36 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y36 w16 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">electromotive force of parasitic branch</div></div><div class="c x2b y36 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y38 w17 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">ECM</div></div><div class="c x2c y38 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y38 w18 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">equivalent circuit model</div></div><div class="c x2d y38 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y39 w19 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">EKF</div></div><div class="c x3 y39 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x15 y39 w1a hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">extended Kalman filter</div></div><div class="c x2e y39 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y3a w1b hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">I</div></div><div class="c x2f y3b wc hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">m</div></div><div class="c x30 y3a w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x5 y3a w1c hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">current in main branch (A)</div></div><div class="c x28 y3a w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y3c w1b hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">I</div></div><div class="t m0 x2f he y3d ff4 fs6 fc0 sc0 ls0 ws0">n</div><div class="c x2a y3c w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x5 y3c w1d hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">current in branch </div></div><div class="c x31 y3c w8 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">n</div></div><div class="c x32 y3c w1e hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">, </div></div><div class="c x33 y3c w1f hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">where </div></div><div class="c x34 y3c w8 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">n</div></div><div class="c x35 y3c w20 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x36 y3c w21 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">is a natural </div></div><div class="t m0 x5 h6 y3e ff3 fs2 fc0 sc0 ls0 ws0">number (A) </div><div class="c x2 y3f w1b hb"><div class="t m0 x0 hc y40 ff4 fs2 fc0 sc0 ls0 ws0">I</div></div><div class="c x2f y41 w13 hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">p</div></div><div class="c x2a y3f w3 hb"><div class="t m0 x0 hc y40 ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x5 y3f w22 hb"><div class="t m0 x0 h6 y40 ff3 fs2 fc0 sc0 ls0 ws0">current in parasitic branch (A)</div></div><div class="c x37 y3f w3 hb"><div class="t m0 x0 h6 y40 ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x2 y42 w23 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">NMC</div></div><div class="c x38 y42 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x5 y42 w20 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">n</div></div><div class="c x39 y42 w24 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">ickel</div></div><div class="c x3a y42 w6 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">-</div></div><div class="c x3b y42 w25 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">manganese</div></div><div class="c x3c y42 w13 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">-</div></div><div class="c x3d y42 w26 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">cobalt</div></div><div class="c x26 y42 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y43 w27 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">OCV</div></div><div class="c x3f y43 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y43 w28 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">open circuit voltage (V)</div></div><div class="c x41 y43 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y44 w29 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">P</div></div><div class="c x42 y45 w11 hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">s</div></div><div class="c x43 y44 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y44 w2a hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">power dissipated inside </div></div><div class="c x44 y44 w2b hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">the cell (W)</div></div><div class="c x45 y44 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y46 w12 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">Q</div></div><div class="c x46 y47 w2c hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">e</div></div><div class="c x47 y46 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y46 w2d hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">extracted charge from cell (Ah)</div></div><div class="c x48 y46 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y48 w14 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">R</div></div><div class="t m0 x42 he y49 ff4 fs6 fc0 sc0 ls0 ws0">n</div><div class="c x49 y48 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x40 h6 y4a ff3 fs2 fc0 sc0 ls0 ws0">resistor n, where n is a natural number (</div><div class="c x4a y4b w1e h11"><div class="t m0 x0 h12 y4c ff7 fs2 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x4b h6 y4a ff3 fs2 fc0 sc0 ls0 ws0">) </div><div class="c x3e y4d w14 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">R</div></div><div class="c x42 y4e we hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">T</div></div><div class="c x49 y4d w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y4d w2e hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">convection resistance </div></div><div class="c x4c y4d w2f hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">(W</div></div><div class="c x4d y4f w13 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">1</div></div><div class="c x4e y4d wa hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x4f y4d w1e hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">m</div></div><div class="c x50 y4f w10 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">-</div></div><div class="c x51 y4f w6 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">2</div></div><div class="c x52 y4d w11 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x53 y4d w12 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">K</div></div><div class="c x54 y4f w10 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">-</div></div><div class="c x55 y4f w13 hf"><div class="t m0 x0 h10 y33 ff3 fs6 fc0 sc0 ls0 ws0">1</div></div><div class="c x56 y4d w6 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">)</div></div><div class="c x57 y4d w6 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">)</div></div><div class="c x58 y4d w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y50 w30 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">s</div></div><div class="c x59 y50 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y50 w31 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">Laplace transform variable</div></div><div class="c x5a y50 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y51 w24 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">SOC</div></div><div class="c x5b y51 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y51 w32 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">state of charge</div></div><div class="c x5c y51 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y52 w29 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">T</div></div><div class="c x42 y52 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y52 w33 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">inner cell temperature (ºC)</div></div><div class="c x4f y52 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y53 w29 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">T</div></div><div class="c x42 y54 w6 hd"><div class="t m0 x0 he y2d ff4 fs6 fc0 sc0 ls0 ws0">a</div></div><div class="c x43 y53 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y53 w34 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">ambient temperature (ºC)</div></div><div class="c x4d y53 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y55 w12 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0">V</div></div><div class="c x42 y55 w3 hb"><div class="t m0 x0 hc y2a ff4 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x40 y55 w35 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">voltage (V)</div></div><div class="c x5d y55 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="c x3e y56 w36 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0">Z</div></div><div class="t m0 x42 h10 y57 ff3 fs6 fc0 sc0 ls0 ws0">p</div><div class="c x49 y56 w3 hb"><div class="t m0 x0 h6 y2a ff3 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x40 h6 y58 ff3 fs2 fc0 sc0 ls0 ws0">impedance of parasitic branch (</div><div class="c x48 y59 w37 h11"><div class="t m0 x0 h12 y4c ff7 fs2 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x5e h6 y58 ff3 fs2 fc0 sc0 ls0 ws0">) </div><div class="t m0 xe ha y5a ff3 fs2 fc0 sc0 ls0 ws0">II. INTRODUCTION </div><div class="t m0 x5f h6 y5b ff3 fs2 fc0 sc0 ls0 ws0">An accurate forecast of the remaining driving range </div><div class="t m0 x3e h6 y5c ff3 fs2 fc0 sc0 ls0 ws0">of an electric vehicle (EV) is crucial to avoid range anx-</div><div class="t m0 x3e h6 y5d ff3 fs2 fc0 sc0 ls0 ws0">iety. Drivers need to know how much further they </div><div class="t m0 x3e h6 y5e ff3 fs2 fc0 sc0 ls0 ws0">would travel before their vehicle batteries require a re-</div><div class="t m0 x3e h6 y5f ff3 fs2 fc0 sc0 ls0 ws0">charge. In addition, the battery management system </div><div class="t m0 x3e h6 y60 ff3 fs2 fc0 sc0 ls0 ws0">should predict when batteries need replacement. The </div><div class="t m0 x3e h6 y22 ff3 fs2 fc0 sc0 ls0 ws0">remaining charge calculation must be precise to utilize </div><div class="t m0 x3e h6 y61 ff3 fs2 fc0 sc0 ls0 ws0">the battery’s full capability. The state of charge (SOC) </div><div class="t m0 x3e h6 y62 ff3 fs2 fc0 sc0 ls0 ws0">of a battery or pack of batteries is analogous to a fuel </div><div class="t m0 x3e h6 y63 ff3 fs2 fc0 sc0 ls0 ws0">gauge of a conventional vehicle. </div><div class="t m0 x5f h6 y64 ff3 fs2 fc0 sc0 ls0 ws0">Accurate run-time SOC estimation techniques are al-</div><div class="t m0 x3e h6 y65 ff3 fs2 fc0 sc0 ls0 ws0">so needed by the battery management system (BMS) for </div><div class="t m0 x3e h6 y66 ff3 fs2 fc0 sc0 ls0 ws0">cell balancing of battery packs in vehicles with electri-</div><div class="t m0 x3e h6 y67 ff3 fs2 fc0 sc0 ls0 ws0">fied powertrains. The SOC estimation must be accurate </div><div class="t m0 x3e h6 y68 ff3 fs2 fc0 sc0 ls0 ws0">under all vehicle operating conditions, and account for </div><div class="t m0 x3e h6 y69 ff3 fs2 fc0 sc0 ls0 ws0">changes in temperature, different rates of current, and </div><div class="t m0 x3e h6 y6a ff3 fs2 fc0 sc0 ls0 ws0">cell aging. High temperatures, broad SOC operation </div><div class="t m0 x3e h6 y6b ff3 fs2 fc0 sc0 ls0 ws0">ranges, and strenuous load profiles accelerate cell aging. </div><div class="t m0 x3e h6 y6c ff3 fs2 fc0 sc0 ls0 ws0">Coulomb counting (i.e. integration of the current) is a </div><div class="t m0 x3e h6 y6d ff3 fs2 fc0 sc0 ls0 ws0">simple technique for estimating the SOC by integrating </div><div class="t m0 x3e h6 y6e ff3 fs2 fc0 sc0 ls0 ws0">the measured current with time. However, coulomb </div><div class="t m0 x3e h6 y6f ff3 fs2 fc0 sc0 ls0 ws0">counting has several drawbacks. Coulomb counting de-</div><div class="t m0 x3e h6 y70 ff3 fs2 fc0 sc0 ls0 ws0">pends on the current flowing from the cell into external </div><div class="t m0 x3e h6 y71 ff3 fs2 fc0 sc0 ls0 ws0">circuits and does not account for self-discharge currents </div><div class="t m0 x3e h6 y72 ff3 fs2 fc0 sc0 ls0 ws0">or parasitic reactions in the cell. Current measurement </div><div class="t m0 x3e h6 y73 ff3 fs2 fc0 sc0 ls0 ws0">errors accumulate with time, and should be corrected by </div><div class="t m0 x3e h6 y74 ff3 fs2 fc0 sc0 ls0 ws0">periodic recalibration. The maximum charge capacity of </div><div class="t m0 x3e h6 y75 ff3 fs2 fc0 sc0 ls0 ws0">the cell depends on a number of factors, such as average </div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bacea3d2fbb0007c6b411/bg2.jpg"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">2 </div><div class="t m0 x2 h6 y76 ff3 fs2 fc0 sc0 ls0 ws0">discharge current, discharge time, inner cell tempera-</div><div class="t m0 x2 h6 y77 ff3 fs2 fc0 sc0 ls0 ws0">ture, storage time (self-discharge), and cycle-age [1]. </div><div class="t m0 x4 h6 y78 ff3 fs2 fc0 sc0 ls0 ws0">Equivalent circuit modeling (ECM) is the most </div><div class="t m0 x2 h6 y79 ff3 fs2 fc0 sc0 ls0 ws0">common approach for battery numerical analysis. For </div><div class="t m0 x2 h6 y7a ff3 fs2 fc0 sc0 ls0 ws0">lithium cells, a one or two RC block model with no </div><div class="t m0 x2 h6 y7b ff3 fs2 fc0 sc0 ls0 ws0">parasitic branch is a common choice [1-3]. It has the </div><div class="t m0 x2 h6 y7c ff3 fs2 fc0 sc0 ls0 ws0">advantage of being computationally simple and is eas-</div><div class="t m0 x2 h6 y7d ff3 fs2 fc0 sc0 ls0 ws0">ily combined with other methods such as coulomb </div><div class="t m0 x2 h6 y7e ff3 fs2 fc0 sc0 ls0 ws0">counting with an OCV / SOC correlation for periodic </div><div class="t m0 x2 h6 y7f ff3 fs2 fc0 sc0 ls0 ws0">recalibration during rest. The model also lends itself </div><div class="t m0 x2 h6 y80 ff3 fs2 fc0 sc0 ls0 ws0">to the use of adaptive methods, such as extended </div><div class="t m0 x2 h6 y81 ff3 fs2 fc0 sc0 ls0 ws0">Kalman filter (EKF) [3-5]. </div><div class="t m0 x4 h6 y82 ff3 fs2 fc0 sc0 ls0 ws0">This paper presents a new and intuitive method for </div><div class="t m0 x2 h6 y83 ff3 fs2 fc0 sc0 ls0 ws0">developing a non-isothermal lithium cell model. Re-</div><div class="t m0 x2 h6 y84 ff3 fs2 fc0 sc0 ls0 ws0">ducing the general ECM with n RC blocks to an ECM </div><div class="t m0 x2 h6 y85 ff3 fs2 fc0 sc0 ls0 ws0">with just a single RC block was sufficient to account </div><div class="t m0 x2 h6 y86 ff3 fs2 fc0 sc0 ls0 ws0">for all dynamic characteristics of the cell, including </div><div class="t m0 x2 h6 y87 ff3 fs2 fc0 sc0 ls0 ws0">nonlinear open-circuit voltage, average discharge cur-</div><div class="t m0 x2 h6 y88 ff3 fs2 fc0 sc0 ls0 ws0">rent and inner cell temperature. A numerical parame-</div><div class="t m0 x2 h6 y89 ff3 fs2 fc0 sc0 ls0 ws0">ter estimation scheme using pulse current discharge </div><div class="t m0 x2 h6 y8a ff3 fs2 fc0 sc0 ls0 ws0">tests on high power lithium nickel-manganese-cobalt </div><div class="t m0 x2 h6 y8b ff3 fs2 fc0 sc0 ls0 ws0">oxide (NMC) cells under different operating condi-</div><div class="t m0 x2 h6 y8c ff3 fs2 fc0 sc0 ls0 ws0">tions was implemented using MATLAB</div><div class="t m0 x36 h10 y8d ff3 fs6 fc0 sc0 ls0 ws0">®</div><div class="t m0 x60 h6 y8c ff3 fs2 fc0 sc0 ls0 ws0">, Simulink</div><div class="t m0 x61 h10 y8d ff3 fs6 fc0 sc0 ls0 ws0">®</div><div class="t m0 x62 h6 y8c ff3 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h6 y8e ff3 fs2 fc0 sc0 ls0 ws0">and Simscape</div><div class="t m0 x63 h10 y8f ff3 fs6 fc0 sc0 ls0 ws0">TM</div><div class="t m0 x64 h6 y8e ff3 fs2 fc0 sc0 ls0 ws0">. The parameter estimation procedure </div><div class="t m0 x2 h6 y90 ff3 fs2 fc0 sc0 ls0 ws0">revealed dependencies of the equivalent circuit ele-</div><div class="t m0 x2 h6 y91 ff3 fs2 fc0 sc0 ls0 ws0">ments on SOC and temperature, which were subse-</div><div class="t m0 x2 h6 y92 ff3 fs2 fc0 sc0 ls0 ws0">quently implemented as lookup tables that defined the </div><div class="t m0 x2 h6 y93 ff3 fs2 fc0 sc0 ls0 ws0">values of the equivalent circuit elements. The model </div><div class="t m0 x2 h6 y94 ff3 fs2 fc0 sc0 ls0 ws0">was validated using independent experimental data, </div><div class="t m0 x2 h6 y95 ff3 fs2 fc0 sc0 ls0 ws0">and then used for general simulation purposes. This </div><div class="t m0 x2 h6 y96 ff3 fs2 fc0 sc0 ls0 ws0">process can be used for runtime SOC estimation. </div><div class="t m0 x4 h6 y97 ff3 fs2 fc0 sc0 ls0 ws0">The paper is organized as follows: Section III de-</div><div class="t m0 x2 h6 y98 ff3 fs2 fc0 sc0 ls0 ws0">scribes the background and model formulation, while </div><div class="t m0 x2 h6 y99 ff3 fs2 fc0 sc0 ls0 ws0">Section IV deals with the experimental setup. The re-</div><div class="t m0 x2 h6 y9a ff3 fs2 fc0 sc0 ls0 ws0">sults of the experimental tests on the cells are com-</div><div class="t m0 x2 h6 y9b ff3 fs2 fc0 sc0 ls0 ws0">pared with the modeling results in Section V. Section </div><div class="t m0 x2 h6 y9c ff3 fs2 fc0 sc0 ls0 ws0">VI summarizes the work and states suggestions for </div><div class="t m0 x2 h6 y9d ff3 fs2 fc0 sc0 ls0 ws0">future work. </div><div class="t m0 x65 ha y9e ff3 fs2 fc0 sc0 ls0 ws0">III. BACKGROUND AND MODEL FORMULATION </div><div class="t m0 x4 h6 y9f ff3 fs2 fc0 sc0 ls0 ws0">A number of models have been developed in the </div><div class="t m0 x2 h6 ya0 ff3 fs2 fc0 sc0 ls0 ws0">past to characterize and simulate lithium cells. De-</div><div class="t m0 x2 h6 ya1 ff3 fs2 fc0 sc0 ls0 ws0">tailed electrochemical models that simulate the inter-</div><div class="t m0 x2 h6 ya2 ff3 fs2 fc0 sc0 ls0 ws0">nal dynamics of the lithium cells [6-9] are computa-</div><div class="t m0 x2 h6 ya3 ff3 fs2 fc0 sc0 ls0 ws0">tionally-intensive, time-consuming, inflexible and un-</div><div class="t m0 x2 h6 ya4 ff3 fs2 fc0 sc0 ls0 ws0">suitable for system-level modeling or run-time appli-</div><div class="t m0 x2 h6 ya5 ff3 fs2 fc0 sc0 ls0 ws0">cations. An alternative approach is to use equivalent </div><div class="t m0 x2 h6 ya6 ff3 fs2 fc0 sc0 ls0 ws0">circuit models (ECM) [1-3]. In this case, the goal is to </div><div class="t m0 x2 h6 ya7 ff3 fs2 fc0 sc0 ls0 ws0">establish a direct correlation between electrochemical </div><div class="t m0 x2 h6 ya8 ff3 fs2 fc0 sc0 ls0 ws0">phenomena inside the cell and the circuit elements. </div><div class="t m0 x2 h6 ya9 ff3 fs2 fc0 sc0 ls0 ws0">Their level of complexity is decided as a trade-off be-</div><div class="t m0 x2 h6 yaa ff3 fs2 fc0 sc0 ls0 ws0">tween the fidelity and computational effort. These </div><div class="t m0 x2 h6 yab ff3 fs2 fc0 sc0 ls0 ws0">models can capture nonlinear electrochemical phe-</div><div class="t m0 x2 h6 yac ff3 fs2 fc0 sc0 ls0 ws0">nomena, and yet avoid lengthy electrochemical pro-</div><div class="t m0 x2 h6 yad ff3 fs2 fc0 sc0 ls0 ws0">cess calculations. They are especially suitable for sys-</div><div class="t m0 x2 h6 yae ff3 fs2 fc0 sc0 ls0 ws0">tem-level modeling (e.g. powertrain electrification). </div><div class="t m0 x5f h6 y76 ff3 fs2 fc0 sc0 ls0 ws0">Most models in the current literature do not account </div><div class="t m0 x3e h6 y77 ff3 fs2 fc0 sc0 ls0 ws0">for thermal effects. This work overcomes this limitation </div><div class="t m0 x3e h6 yaf ff3 fs2 fc0 sc0 ls0 ws0">by including temperature as an independent variable in </div><div class="t m0 x3e h6 yb0 ff3 fs2 fc0 sc0 ls0 ws0">the look-up tables that define the circuit elements. </div><div class="t m0 x66 h13 yb1 ff3 fs5 fc0 sc0 ls0 ws0">Figure 1. A general equivalent circuit model [1, 10-11] of an electro-</div><div class="t m0 x67 h13 yb2 ff3 fs5 fc0 sc0 ls0 ws0">chemical cell. The number of equivalent circuit elements results in a </div><div class="t m0 x68 h13 yb3 ff3 fs5 fc0 sc0 ls0 ws0">trade-off between fidelity and complexity. The parasitic branch can </div><div class="t m0 x69 h13 yb4 ff3 fs5 fc0 sc0 ls0 ws0">be neglected for cells with high coulombic efficiencies. </div><div class="t m0 x5f h6 yb5 ff3 fs2 fc0 sc0 ls0 ws0">Fig.1 shows the generalized ECM presented in [10-</div><div class="t m0 x3e h6 y89 ff3 fs2 fc0 sc0 ls0 ws0">11] for lead-acid batteries, but which can be used to de-</div><div class="t m0 x3e h6 yb6 ff3 fs2 fc0 sc0 ls0 ws0">pict an electrochemical cell of any chemistry. </div><div class="t m0 x5f h6 yb7 ff3 fs2 fc0 sc0 ls0 ws0">The choice of the model structure responds to a </div><div class="t m0 x3e h6 yb8 ff3 fs2 fc0 sc0 ls0 ws0">trade-off between the ability to fit experimental data and </div><div class="t m0 x3e h6 yb9 ff3 fs2 fc0 sc0 ls0 ws0">equivalent circuit complexity (and computational re-</div><div class="t m0 x3e h6 y54 ff3 fs2 fc0 sc0 ls0 ws0">sources). An extremely complex equivalent circuit </div><div class="t m0 x3e h6 yba ff3 fs2 fc0 sc0 ls0 ws0">would fit experimental data sets well, but would be </div><div class="t m0 x3e h6 y57 ff3 fs2 fc0 sc0 ls0 ws0">computationally expensive, making it unsuitable for </div><div class="t m0 x3e h6 ybb ff3 fs2 fc0 sc0 ls0 ws0">embedded control applications. In general, the level of </div><div class="t m0 x3e h6 ybc ff3 fs2 fc0 sc0 ls0 ws0">complexity should be limited by the computational re-</div><div class="t m0 x3e h6 ybd ff3 fs2 fc0 sc0 ls0 ws0">sources available and the possibility of correlating each </div><div class="t m0 x3e h6 ybe ff3 fs2 fc0 sc0 ls0 ws0">circuit component with an electrochemical phenomenon </div><div class="t m0 x3e h6 y97 ff3 fs2 fc0 sc0 ls0 ws0">inside the cell. A model of adequate fidelity is useful for </div><div class="t m0 x3e h6 y98 ff3 fs2 fc0 sc0 ls0 ws0">diagnosis purposes, since variation of its elements can </div><div class="t m0 x3e h6 ybf ff3 fs2 fc0 sc0 ls0 ws0">be linked directly to a physical or electrochemical pro-</div><div class="t m0 x3e h6 y9a ff3 fs2 fc0 sc0 ls0 ws0">cess, such as charge, capacity, or health. </div><div class="t m0 x5f h6 yc0 ff3 fs2 fc0 sc0 ls0 ws0">Depending on the characteristics of the problem to </div><div class="t m0 x3e h6 yc1 ff3 fs2 fc0 sc0 ls0 ws0">be analyzed, the number of RC blocks typically ranges </div><div class="t m0 x3e h6 yc2 ff3 fs2 fc0 sc0 ls0 ws0">from one to two, since larger numbers increase compu-</div><div class="t m0 x3e h6 yc3 ff3 fs2 fc0 sc0 ls0 ws0">tational effort without significantly improving model </div><div class="t m0 x3e h6 yc4 ff3 fs2 fc0 sc0 ls0 ws0">accuracy. </div><div class="t m0 x6a h14 yc5 ff5 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x6b h13 yc6 ff3 fs5 fc0 sc0 ls0 ws0">Figure 2: The model used for the paper, with n=1. </div><div class="t m0 x5f h6 yc7 ff3 fs2 fc0 sc0 ls0 ws0">A single RC block model (Figure 2) is adequate for </div><div class="t m0 x3e h6 yc8 ff3 fs2 fc0 sc0 ls0 ws0">many problems of industrial relevance, and has been </div><div class="t m0 x3e h6 yc9 ff3 fs2 fc0 sc0 ls0 ws0">adopted in this work. The estimation techniques present-</div><div class="t m1 x3f h15 yca ff4 fs7 fc0 sc0 ls0 ws0">E </div><div class="t m1 x6c h15 ycb ff3 fs7 fc0 sc0 ls0 ws0">+ </div><div class="t m1 xb h15 ycc ff4 fs7 fc0 sc0 ls0 ws0">I </div><div class="t m1 x6d h15 ycd ff4 fs7 fc0 sc0 ls0 ws0">I </div><div class="t m1 x6e h15 yce ff4 fs7 fc0 sc0 ls0 ws0">C </div><div class="t m1 x6f h15 ycf ff4 fs8 fc0 sc0 ls0 ws0">1 </div><div class="t m1 x70 h15 yd0 ff4 fs7 fc0 sc0 ls0 ws0">C </div><div class="t m1 x52 h15 yd1 ff4 fs8 fc0 sc0 ls0 ws0">n </div><div class="t m1 x71 h15 yd2 ff4 fs7 fc0 sc0 ls0 ws0">R </div><div class="t m1 x72 h15 yd3 ff4 fs8 fc0 sc0 ls0 ws0">n </div><div class="t m1 x44 h15 yd4 ff4 fs8 fc0 sc0 ls0 ws0">n </div><div class="t m1 x73 h15 yd5 ff4 fs8 fc0 sc0 ls0 ws0">1 </div><div class="t m1 x74 h15 yd3 ff4 fs7 fc0 sc0 ls0 ws0">R </div><div class="t m1 x75 h15 yd4 ff4 fs8 fc0 sc0 ls0 ws0">1 </div><div class="t m1 x76 h15 yd6 ff4 fs7 fc0 sc0 ls0 ws0">V </div><div class="t m1 x4a h15 yd7 ff4 fs7 fc0 sc0 ls0 ws0">R </div><div class="t m1 x77 h15 yd8 ff4 fs8 fc0 sc0 ls0 ws0">0 </div><div class="t m1 x78 h15 yd9 ff4 fs8 fc0 sc0 ls0 ws0">m </div><div class="t m1 x79 h15 yda ff4 fs7 fc0 sc0 ls0 ws0">I </div><div class="t m1 x69 h15 ydb ff4 fs8 fc0 sc0 ls0 ws0">m </div><div class="t m1 x7a h16 ydc ff8 fs7 fc0 sc0 ls0 ws0">+ </div><div class="t m1 x4a h16 ydd ff6 fs7 fc0 sc0 ls0 ws0"> </div><div class="t m1 x7b h17 yde ff4 fs7 fc0 sc0 ls0 ws0">I</div><div class="t m1 x7c h18 ydf ff4 fs9 fc0 sc0 ls0 ws0">p</div><div class="t m1 x7a h16 yde ff6 fs7 fc0 sc0 ls0 ws0"> </div><div class="t m1 x7c h16 ye0 ff6 fs7 fc0 sc0 ls0 ws0"> </div><div class="t m1 x54 h17 ye1 ff4 fs7 fc0 sc0 ls0 ws0">E</div><div class="t m1 x7d h18 ye2 ff4 fs9 fc0 sc0 ls0 ws0">p</div><div class="t m1 x57 h16 ye1 ff8 fs7 fc0 sc0 ls0 ws0"> </div><div class="t m1 x56 h16 ye3 ff6 fs7 fc0 sc0 ls0 ws0"> </div><div class="t m1 x7e h17 ye4 ff4 fs7 fc0 sc0 ls0 ws0">Z</div><div class="t m1 x7d h18 ye5 ff4 fs9 fc0 sc0 ls0 ws0">p</div><div class="t m1 x57 h16 ye4 ff8 fs7 fc0 sc0 ls0 ws0"> </div><div class="t m1 x56 h16 ye6 ff6 fs7 fc0 sc0 ls0 ws0"> </div><div class="t m2 x7f h19 ye7 ff3 fsa fc0 sc0 ls0 ws0">+ </div><div class="t m2 x44 h1a ye8 ff4 fsa fc0 sc0 ls0 ws0">R</div><div class="t m2 x4d h1b y66 ff3 fsb fc0 sc0 ls0 ws0">0</div><div class="t m2 x4e h19 ye8 ff3 fsa fc0 sc0 ls0 ws0">(SOC,</div><div class="t m3 x48 h1c ye8 ff9 fsc fc0 sc0 ls0 ws0"></div><div class="t m2 x7e h19 ye8 ff3 fsa fc0 sc0 ls0 ws0">) </div><div class="t m2 x80 h1d ye7 ff4 fsd fc0 sc0 ls0 ws0">V </div><div class="t m2 x45 h1a ye9 ff4 fsa fc0 sc0 ls0 ws0">+ </div><div class="t m2 x81 h1a yea ff4 fsa fc0 sc0 ls0 ws0">- </div><div class="t m2 x82 h1a ye8 ff4 fsa fc0 sc0 ls0 ws0">C</div><div class="t m2 x83 h1b y66 ff3 fsb fc0 sc0 ls0 ws0">1</div><div class="t m2 x84 h19 ye8 ff4 fsa fc0 sc0 ls0 ws0">(SOC,</div><div class="t m3 x85 h1c ye8 ff9 fsc fc0 sc0 ls0 ws0"></div><div class="t m2 x86 h1a ye8 ff4 fsa fc0 sc0 ls0 ws0">) </div><div class="t m2 x5d h1a yeb ff4 fsa fc0 sc0 ls0 ws0">R</div><div class="t m2 x87 h1b yec ff3 fsb fc0 sc0 ls0 ws0">1</div><div class="t m2 x88 h19 yeb ff4 fsa fc0 sc0 ls0 ws0">(SOC,</div><div class="t m3 x89 h1c yeb ff9 fsc fc0 sc0 ls0 ws0"></div><div class="t m2 x8a h1a yeb ff4 fsa fc0 sc0 ls0 ws0">) </div><div class="t m2 x8b h1a yed ff4 fsa fc0 sc0 ls0 ws0">I</div><div class="t m2 x8c h1b yee ff3 fsb fc0 sc0 ls0 ws0">1</div><div class="t m2 x5c h1a yed ff4 fsa fc0 sc0 ls0 ws0"> </div><div class="t m2 x8d h1a y67 ff4 fsa fc0 sc0 ls0 ws0">I</div><div class="t m2 x8e h1b yef ff3 fsb fc0 sc0 ls0 ws0">m</div><div class="t m2 x8f h1a y67 ff4 fsa fc0 sc0 ls0 ws0"> </div><div class="t m2 x90 h1a yf0 ff4 fsa fc0 sc0 ls0 ws0">E</div><div class="t m2 x8e h1b yf1 ff3 fsb fc0 sc0 ls0 ws0">m</div><div class="t m2 x8f h19 yf0 ff4 fsa fc0 sc0 ls0 ws0">(SOC,</div><div class="t m3 x8b h1c yf0 ff9 fsc fc0 sc0 ls0 ws0"></div><div class="t m2 x84 h1a yf0 ff4 fsa fc0 sc0 ls0 ws0">) </div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div>