對鋰電池模(mo)(mo)(mo)(mo)型的(de)(de)(de)(de)建(jian)模(mo)(mo)(mo)(mo)有(you)(you)兩種途徑，一(yi)種是對(dui)(dui)電(dian)池(chi)進(jin)行(xing)大(da)量的(de)(de)(de)(de)實驗，積累實驗數據(ju)，對(dui)(dui)采集到(dao)的(de)(de)(de)(de)數據(ju)進(jin)行(xing)模(mo)(mo)(mo)(mo)擬，總結得(de)出鋰離子電(dian)池(chi)的(de)(de)(de)(de)變化規律；另一(yi)種是對(dui)(dui)鋰離子電(dian)池(chi)的(de)(de)(de)(de)微觀行(xing)為進(jin)行(xing)研究，通(tong)過對(dui)(dui)微觀行(xing)為的(de)(de)(de)(de)描述，借助計算機手段，建(jian)立具有(you)(you)理(li)論基礎的(de)(de)(de)(de)模(mo)(mo)(mo)(mo)型。常用的(de)(de)(de)(de)鋰電(dian)池(chi)模(mo)(mo)(mo)(mo)型主要有(you)(you)內阻模(mo)(mo)(mo)(mo)型，等效電(dian)路模(mo)(mo)(mo)(mo)型，遺(yi)傳算法(fa)模(mo)(mo)(mo)(mo)型，神經(jing)網(wang)絡模(mo)(mo)(mo)(mo)型以及電(dian)化學模(mo)(mo)(mo)(mo)型。

1、鋰電(dian)池模(mo)型(xing)的(de)內(nei)阻模(mo)型(xing)

內(nei)(nei)(nei)(nei)(nei)阻(zu)(zu)模(mo)型(xing)是(shi)最簡單的(de)(de)(de)電(dian)池(chi)(chi)(chi)模(mo)型(xing)，通常用來(lai)預測(ce)電(dian)池(chi)(chi)(chi)的(de)(de)(de)容(rong)量(liang)[]。一般說(shuo)來(lai)，電(dian)池(chi)(chi)(chi)容(rong)量(liang)隨著電(dian)壓和內(nei)(nei)(nei)(nei)(nei)阻(zu)(zu)變(bian)(bian)化(hua)。由于電(dian)壓在(zai)(zai)不同(tong)放電(dian)電(dian)流(liu)下(xia)會(hui)有(you)不同(tong)的(de)(de)(de)變(bian)(bian)化(hua)，研究(jiu)者們就試圖建立內(nei)(nei)(nei)(nei)(nei)阻(zu)(zu)與容(rong)量(liang)之(zhi)間的(de)(de)(de)關系。然而內(nei)(nei)(nei)(nei)(nei)阻(zu)(zu)并非一個本征的(de)(de)(de)數(shu)值，內(nei)(nei)(nei)(nei)(nei)阻(zu)(zu)模(mo)型(xing)需要(yao)大量(liang)的(de)(de)(de)實驗(yan)數(shu)據(ju)。例如(ru)電(dian)池(chi)(chi)(chi)的(de)(de)(de)最大容(rong)量(liang)在(zai)(zai)不同(tong)溫度下(xia)的(de)(de)(de)變(bian)(bian)化(hua)規(gui)律，電(dian)池(chi)(chi)(chi)輸出端電(dian)壓在(zai)(zai)不同(tong)電(dian)流(liu)倍率下(xia)的(de)(de)(de)變(bian)(bian)化(hua)規(gui)律，電(dian)池(chi)(chi)(chi)內(nei)(nei)(nei)(nei)(nei)阻(zu)(zu)在(zai)(zai)不同(tong)溫度下(xia)的(de)(de)(de)變(bian)(bian)化(hua)規(gui)律。根據(ju)實驗(yan)得到的(de)(de)(de)數(shu)據(ju)，根據(ju)電(dian)池(chi)(chi)(chi)使用環境的(de)(de)(de)不同(tong)，依靠電(dian)池(chi)(chi)(chi)內(nei)(nei)(nei)(nei)(nei)阻(zu)(zu)來(lai)判定(ding)電(dian)池(chi)(chi)(chi)的(de)(de)(de)容(rong)量(liang)，因此該模(mo)型(xing)更(geng)接(jie)近于一個數(shu)據(ju)庫(ku)。

2、鋰電池模(mo)型的等效(xiao)電路模(mo)型

由于電(dian)(dian)(dian)池(chi)(chi)在電(dian)(dian)(dian)流的(de)(de)(de)(de)作用下(xia)會(hui)體現電(dian)(dian)(dian)阻(zu)(zu)以及電(dian)(dian)(dian)容的(de)(de)(de)(de)部分特征，v.Johsonl6.]等(deng)(deng)人提出(chu)可(ke)以用等(deng)(deng)效電(dian)(dian)(dian)路(lu)(lu)(lu)來建立電(dian)(dian)(dian)池(chi)(chi)模型(xing)，模擬電(dian)(dian)(dian)池(chi)(chi)的(de)(de)(de)(de)動態與靜態性(xing)能。基本(ben)的(de)(de)(de)(de)鋰離子電(dian)(dian)(dian)池(chi)(chi)等(deng)(deng)效電(dian)(dian)(dian)路(lu)(lu)(lu)，其(qi)中V以和V分別(bie)代表電(dian)(dian)(dian)池(chi)(chi)的(de)(de)(de)(de)開路(lu)(lu)(lu)電(dian)(dian)(dian)壓(ya)和輸出(chu)電(dian)(dian)(dian)壓(ya)，R為(wei)電(dian)(dian)(dian)池(chi)(chi)內阻(zu)(zu)，RG并聯電(dian)(dian)(dian)路(lu)(lu)(lu)模擬電(dian)(dian)(dian)池(chi)(chi)的(de)(de)(de)(de)外特性(xing)。

3、鋰電池模型(xing)的遺(yi)傳(chuan)算法(fa)模型(xing)

基于(yu)遺(yi)傳算(suan)(suan)法的(de)鋰離子(zi)電(dian)池(chi)模(mo)(mo)型，一般(ban)情況下可以分析實驗(yan)數(shu)據(ju)，求解(jie)方程等方法建(jian)立模(mo)(mo)型，模(mo)(mo)擬電(dian)池(chi)的(de)特性。但是由于(yu)電(dian)池(chi)內部的(de)化學反(fan)應非常復雜，很(hen)難找到合(he)適的(de)函(han)數(shu)來(lai)(lai)描述電(dian)池(chi)模(mo)(mo)型。遺(yi)傳算(suan)(suan)法計算(suan)(suan)方便，輸出函(han)數(shu)形式(shi)十(shi)分靈活，可以用來(lai)(lai)建(jian)立鋰離子(zi)電(dian)池(chi)的(de)模(mo)(mo)型。

4、鋰(li)電池模型的神經網絡模型

研(yan)究使用神(shen)經網(wang)絡算法建(jian)立電(dian)(dian)池(chi)模型(xing)的(de)可行性(xing)，建(jian)立了鋰離子(zi)電(dian)(dian)池(chi)的(de)模型(xing)，并且成功(gong)地預(yu)測電(dian)(dian)動(dong)汽車中(zhong)電(dian)(dian)池(chi)的(de)剩余電(dian)(dian)量。

將(jiang)神經網絡算(suan)法(fa)與模糊算(suan)法(fa)聯(lian)合使用(yong)(yong)，取(qu)長補短，彌補兩個(ge)算(suan)法(fa)各自的不足，用(yong)(yong)來(lai)估計鋰離子電(dian)池(chi)的剩(sheng)余容量，提高了單一算(suan)法(fa)的估計精度。

5、鋰電(dian)池模型(xing)的電(dian)化學模型(xing)

電(dian)(dian)化(hua)學(xue)模(mo)型(xing)(xing)(xing)是(shi)根(gen)據電(dian)(dian)池(chi)(chi)基本化(hua)學(xue)原理(li)建(jian)(jian)立的(de)(de)模(mo)型(xing)(xing)(xing)，鋰離子電(dian)(dian)池(chi)(chi)原理(li)性(xing)(xing)(xing)模(mo)型(xing)(xing)(xing)是(shi)從1982年west的(de)(de)研究基礎(chu)上(shang)逐步建(jian)(jian)立起來的(de)(de)。West 在研究纖(xian)維(wei)(wei)狀(zhuang)活(huo)性(xing)(xing)(xing)物質(zhi)顆(ke)粒(li)所組成的(de)(de)多(duo)孔(kong)電(dian)(dian)極(ji)(ji)時，建(jian)(jian)立了一(yi)個(ge)準(zhun)二維(wei)(wei)的(de)(de)多(duo)孔(kong)電(dian)(dian)極(ji)(ji)模(mo)型(xing)(xing)(xing)，假定電(dian)(dian)池(chi)(chi)中(zhong)(zhong)的(de)(de)溶液相為(wei)二元溶液體(ti)系，將擴散系數默認為(wei)常數，固相擴散過程為(wei)控(kong)制步驟，電(dian)(dian)化(hua)學(xue)過程忽(hu)略(lve)不(bu)(bu)計。由(you)于(yu)(yu)鋰電(dian)(dian)池(chi)(chi)也是(shi)多(duo)孔(kong)電(dian)(dian)極(ji)(ji)體(ti)系，在研究Li:LiClO4:TIS2電(dian)(dian)池(chi)(chi)模(mo)型(xing)(xing)(xing)時，采用了相似的(de)(de)處(chu)理(li)方式，考慮到電(dian)(dian)池(chi)(chi)的(de)(de)構(gou)造(zao)，模(mo)型(xing)(xing)(xing)中(zhong)(zhong)引入了隔(ge)膜這(zhe)一(yi)結(jie)構(gou)。Mao等人的(de)(de)研究結(jie)果表明，隔(ge)膜越薄，電(dian)(dian)池(chi)(chi)能夠釋放(fang)出更多(duo)地電(dian)(dian)量。但是(shi)由(you)于(yu)(yu)該模(mo)型(xing)(xing)(xing)不(bu)(bu)是(shi)真正的(de)(de)電(dian)(dian)池(chi)(chi)模(mo)型(xing)(xing)(xing)，僅(jin)僅(jin)對單個(ge)電(dian)(dian)極(ji)(ji)的(de)(de)原理(li)進行(xing)研究，沒有將電(dian)(dian)池(chi)(chi)看成一(yi)個(ge)整體(ti)進行(xing)建(jian)(jian)模(mo)，因(yin)此模(mo)型(xing)(xing)(xing)并(bing)不(bu)(bu)能完全模(mo)擬電(dian)(dian)池(chi)(chi)的(de)(de)化(hua)學(xue)特性(xing)(xing)(xing)。在上(shang)述模(mo)型(xing)(xing)(xing)中(zhong)(zhong)，都假設鋰離子嵌入過程無限快，因(yin)此在電(dian)(dian)極(ji)(ji)/電(dian)(dian)解液界面是(shi)存(cun)在電(dian)(dian)化(hua)學(xue)平衡(heng)體(ti)系的(de)(de)。也就是(shi)說，電(dian)(dian)池(chi)(chi)的(de)(de)OCP（Open Circuit Potential顆(ke)粒(li)表面濃度和附近(jin)電(dian)(dian)解液濃度相關。

Doyle在(zai)研(yan)(yan)究(jiu)(jiu)Li:PEO3LiCF3SO3：TiS2電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)時(shi)，根據多孔電(dian)(dian)(dian)(dian)(dian)極(ji)模(mo)(mo)(mo)型(xing)建(jian)立(li)真正(zheng)意義上的(de)(de)電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)模(mo)(mo)(mo)型(xing)。采(cai)用巴(ba)特(te)勒-沃(wo)爾默方程來(lai)描(miao)(miao)述(shu)(shu)每個(ge)電(dian)(dian)(dian)(dian)(dian)極(ji)上發生(sheng)的(de)(de)電(dian)(dian)(dian)(dian)(dian)化(hua)(hua)學(xue)(xue)反(fan)應(ying)，用Fick定律來(lai)描(miao)(miao)述(shu)(shu)電(dian)(dian)(dian)(dian)(dian)極(ji)內(nei)部鋰(li)顆粒的(de)(de)擴(kuo)(kuo)散(san)現象，并默認擴(kuo)(kuo)散(san)系(xi)數為(wei)(wei)常數，在(zai)發生(sheng)化(hua)(hua)學(xue)(xue)反(fan)應(ying)時(shi)，電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)體(ti)積的(de)(de)變(bian)化(hua)(hua)被忽略(lve)不(bu)(bu)計，在(zai)電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)的(de)(de)隔(ge)膜(mo)處，鋰(li)離子(zi)經過隔(ge)膜(mo)形成一(yi)層(ceng)SEI膜(mo)，將這(zhe)層(ceng)膜(mo)簡(jian)化(hua)(hua)成為(wei)(wei)一(yi)個(ge)膜(mo)電(dian)(dian)(dian)(dian)(dian)阻，該電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)模(mo)(mo)(mo)型(xing)不(bu)(bu)考慮副反(fan)應(ying)的(de)(de)發生(sheng)。在(zai)[1]的(de)(de)基礎上，Fuller[1]等(deng)建(jian)立(li)了(le)在(zai)稀溶液理論下描(miao)(miao)述(shu)(shu)鋰(li)離子(zi)電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)化(hua)(hua)學(xue)(xue)特(te)性(xing)的(de)(de)方程，建(jian)立(li)了(le)通用的(de)(de)鋰(li)離子(zi)電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)模(mo)(mo)(mo)型(xing)。Fuller等(deng)人的(de)(de)研(yan)(yan)究(jiu)(jiu)解(jie)釋了(le)電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)的(de)(de)開路電(dian)(dian)(dian)(dian)(dian)位ocP和SOC之間的(de)(de)聯系(xi)，這(zhe)項工作(zuo)具有十(shi)分重要的(de)(de)意義。該研(yan)(yan)究(jiu)(jiu)表明OCP與(yu)SOc曲(qu)線(xian)的(de)(de)關系(xi)是非線(xian)性(xing)的(de)(de)，電(dian)(dian)(dian)(dian)(dian)流密(mi)度與(yu)該曲(qu)線(xian)的(de)(de)關系(xi)十(shi)分緊密(mi)，OCP與(yu)soc曲(qu)線(xian)的(de)(de)變(bian)化(hua)(hua)率(lv)越大，電(dian)(dian)(dian)(dian)(dian)流密(mi)度的(de)(de)分布越均(jun)勻。隨(sui)后Nalin和Giacomo等(deng)在(zai)前人的(de)(de)基礎之上采(cai)用有限(xian)元的(de)(de)方法對鋰(li)離子(zi)電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)的(de)(de)化(hua)(hua)學(xue)(xue)模(mo)(mo)(mo)型(xing)進行(xing)求(qiu)解(jie)，并將所求(qiu)解(jie)的(de)(de)模(mo)(mo)(mo)型(xing)與(yu)實際的(de)(de)電(dian)(dian)(dian)(dian)(dian)池(chi)(chi)放電(dian)(dian)(dian)(dian)(dian)特(te)性(xing)進行(xing)比較。