鋰離子電池具有相較其他種類的電池較高的能量密度、耐溫範圍寬可耐熱耐冷、使用壽命長、安全性佳、環境友善、無記憶效應、體積小重量輕等優勢，需求也日益增長，舉凡大至電網儲能系統的調節，在推廣再生能源時，風力與太陽能雖不需使用燃料且是乾淨能源，但會受天氣影響使得發電量變動起伏，有了電池儲能調節就可以改善電力穩定度；中至將電動汽機車與油電混和車的普遍化增加可行性，是因鋰離子電池的高續航力及壽命，促使交通工具也能減少燃料使用及碳排量；小至隨處可見的電子產品，如智慧型手機、手錶、筆記型電腦等也有鋰離子電池的蹤跡。
在模擬應用中，需要獲得在不同的運轉負載下的鋰離子電池精確動態特性，助於準確的診斷動態電池模型狀態。常用的三種鋰離子電池模型為，電化學模型(Electrochemical Models, EM)、等效電路模型(Equivalent Circuit Models, EchM)和分數階模型 (Fractional Order Models, FOM)，因為EchM的計算效率較EM高，能在電池模擬實驗中常見EchM的使用。若要更精準的預測電池暫態變化及考量非理想因素，可由許多文獻中得到FOM優於EchM的結論，進而在電池管理系統中使用FOM準確地監測電池狀態。FOM特徵是以非電氣特性的恆相位元件及特定指數階的華寶元件替代EchM中的理想電容電感，本文將提出五種較常見的FOM，推導其在含有分數階恆相位元件的模型中的時域電池端電壓與充放電電流之關係式，獲得更為精確的電氣特性結果；並以此五種模型架構代入實驗數據中比較誤差量，最後使用五種最佳化演算法對此最佳模型找出最貼近電池特性的參數組合。

Compared with other kinds of batteries, lithium-ion batteries have the advantages of high energy density, wide temperature range, long cycle life, being eco-friendly, small and light and no memory effect, etc.. Thus, lithium-ion batteries are used in a wide range of applications nowadays. For example, improving power stability of grid energy storage systems, increasing the feasibility of the generalization of electric vehicles and hybrid vehicles by their high endurance and cycle life, and a variety of electronic products powered by lithium-ion batteries.
It is necessary to obtain precise dynamic characteristics of lithium-ion batteries under different operating states to model its status. The three commonly used lithium-ion battery models are electrochemical model (EM), equivalent circuit model (ECM) and fractional order model (FOM). Because the calculation efficiency of ECM is higher than that of EM, ECM is widely used in battery simulation experiments. To predict battery transient response and non-ideal factors better, lots of literatures derived the conclusion that FOM is more precise than ECM.
The characteristic of FOM is to replace capacitance and inductance in ECM with the non-electric constant phase element. This paper will deduce the relationship between the battery terminal voltage and the charging and discharging current of the five common FOMs. Then the results will be substituted into the experimental data to compare the error amount and verify whether the second-order FOM performs better. Finally, using five algorithms to find out which parameter set performs is closest to the battery characteristics.

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