現今許多的鋰電池電路模型中，部份過於簡陋，無法模擬出電池老化與溫度的問題，而功能完善的模型，卻只能模擬放電行為，缺乏充放電皆可的電路模型，此外，現階段的電路模型，皆只能針對特定製造商的電池型號，模擬其行為與特性。
此篇論文提出一個非線性鋰電池充放電之電路模型。只要根據電池製造商的電極與電解液的阻抗數據資料，作為推導模型內重要組成元件參數，即可得到與實際電池相似的表現。此研究實驗使用磷酸鋰鐵離子電池作為對照，結果表明，其測量結果與模擬結果的兩者誤差，在放電實驗下，當電池電壓值達到截止電壓2.5V，時間為6480秒，其兩者電壓值誤差為3.12%，其兩條曲線在穩態時，最大電壓誤差則為16mV，誤差百分比為0.501%；在充電實驗下，當電池電壓達到預定的額定電壓3.65V，時間為2880秒，其兩者電壓值誤差為0.712%，最大電壓誤差則為37mV，誤差百分比為1.072%。因此，所提出的電路模型可適用於鋰電池的模擬工作上，除了降低電池實驗的風險外，也減少電池製造商的生產成本，並且希望能預測出電池使用的極限區塊，防止電池汽化或爆炸等危險。

Nowadays, lithium battery circuit models, some are too simple, can not simulate the cycle time and temperature effects. One with fully functioning model can only simulate discharging behavior, not charging. In addition, at this stage, circuit models are only for specific manufacturer, not an universal solution.
This paper presents the circuit model for both battery charging and discharging. Based on the manufacturer’s data sheet, the model parameters are extracted to derive the coefficients of the expressions of the major components in the circuit model. This experiment used Lithium iron phosphate ion battery for a comparison. Results show that, at the battery discharging and charging conditions, the errors between the measurement results and the simulated results. In discharging condition, when the battery voltage reaches cut-off voltage 2.5V, the time is 6480 seconds, the error is 3.12%. And the maximum error voltage is 16mV, in 0.501%. In charging condition, when the battery voltage reaches a predetermined nomial voltage 3.65V, the time is 2880 seconds, the error is 0.712%. And the maximum error voltage is 37mV, in 1.072%. Thus, the proposed circuit model can be used for battery simulation. It not only diminishes the risk of experimental safety but also decreases the cost from battery manufacturer.

[1]B. Schweighofer, K. M. Raab, and G. Brasseur, “Modeling of high power automotive batteries by the use of an automated test system,” IEEE Trans. Instrum. Meas., vol. 52, no. 4, pp. 1087-1091, Aug. 2003.
[2]Z. M. Salameh, M. A. Casacca, andW. A. Lynch, “A mathematical model for lead-acid batteries,” IEEE Trans. Energy Convers., vol. 7, no. 1, pp. 93-98, Mar. 1992.
[3]S. Gold, “A pspice macro model for lithium-ion batteries,” in Proc. 12th Annu. Battery Conf. Applications and Advances, pp. 215-222, 1997.
[4]M. Chen, A. Rinc’on-Mora , “Accurate electrical battery model capable of predicting runtime and I–V performance,” IEEE Trans.Energy Convers., vol. 21, no. 2, pp. 504-511, Jun. 2006.
[5]M. Valvo, F. E. Wicks, D. Robertson, and S. Rudin, “Development and application of an improved equivalent circuit model of a lead acid battery,” in Proc. Energy Convers. Eng. Conf., vol. 2, pp. 1159-1163, Aug. 1996.
[6]M. C. Glass, “Battery electrochemical nonlinear/dynamic SPICE model,” in Proc. Energy Convers. Eng. Conf., vol. 1, pp. 292-297, 1996.
[7]L. Gao, S. Liu, and R. A. Dougal, “Dynamic lithium-ion battery model for system simulation,” IEEE Trans. Compon. Packag. Technol., vol. 25,no. 3, pp. 495-505, Sep. 2002.
[8]洪裕桓，”智慧型鋰電池管理系統之研製”，國立中山大學電機工程系 碩士論文，民國94年6月。