本研究利用鯨群演算法結合電化學熱流模型對鋰離子電池進行溫度及電壓之多目標最佳化參數辨識，研究的主要目標是希望透過鯨群演算法的搜尋能力在不進行量測下得到具有物理意義的電池參數。得到辨識的參數後，進行其他工作條件如5C高電流充放電、WLTP (Worldwide Harmonized Light-duty Vehicles Test Procedure)車輛路況動態負載之充放電預測。另外將此最佳化之參數作為基準，對電化學熱流模型中的35個參數分成四類別包括動力學參數、幾何參數、濃度參數及熱力學參數進行一次一因子法(One factor at a time, OFAT)的敏感度分析。
研究流程主要可分成實驗部分與模擬部分:實驗部分先針對鋰離子電池實際進行充放電測試，得到的數據除了得以驗證之後模型的正確性外，還需用在演算法適應值的計算上。模擬部分首先要建立正確的電化學熱流模型與建立鯨群演算法的程式，並將其連結，使其能進行即時的資料傳輸功能，如此才能透過演算法的搜尋能力進行模型的參數辨識。
根據目前實驗與模擬結果有以下結論:透過鯨群演算法辨識出來的參數與文獻參數相比較，足以證明使用鯨群演算法對電化學熱流模型進行參數辨識是可行的方法。且透過鯨群演算法得到的模型充放電表現相當接近實驗值，在5C定電流充電的情況下電壓均方根誤差(Root Mean Square Error, RMSE)僅24.33mV，溫度RMSE僅0.96˚C，SOC (State of Charge)的RMSE僅0.07%。在WLTP車輛路況動態負載下RMSE僅19.04mV，溫度僅0.19˚C，SOC僅0.17%。依照本研究建立的流程能在不進行任何實驗量測下得到鋰離子電池相關之電化學參數，若將其應用至電池管理系統將得到準確的模擬結果。在敏感度分析的結果中可以發現幾何相關參數敏感度較大。此敏感度分析可作為未來模型簡化或是電池材料開發的參考依據。

This thesis employs the WOA (Whale Optimization Algorithm) to identify the unknown 35 parameters of the electrochemical thermal model for the lithium-ion battery. The main goal of the research is to use the searching ability of the WOA to obtain physical parameters without measurement or disassembly. After getting the optimized parameters, using them to other operating conditions such as high C-Rate charge and discharge conditions and WLTP (Worldwide Harmonized Light-duty Vehicles Test Procedure) dynamic vehicle load to validate the model. In addition, the optimized parameters are used as the baseline to conduct the sensitivity analysis by OFAT (One factor at a time method) to identify the influence of all parameters on the electrochemical thermal model.
The model validation results show that the performance obtained through the WOA is quite close to the experiment. Under WLTP dynamic vehicle load, the RMSE (Root Mean Square Error) is 19.04mV, the temperature RMSE is 0.19˚C, and the SOC (State of Charge) is 0.17%. Under 5C charge condition, the RMSE is 24.33mV, the temperature RMSE is 0.96˚C, and the SOC is 0.07%. In the sensitivity analysis, the results reveal that geometric parameters, such as porosity and particle radius of the electrode, have a significant influence on the performance of lithium-ion batteries. The sensitive result can be used as a reference for future model simplification or battery material development. In summary, the accurate parameter identification and the sensitivity provide a future methodology from an electrochemical view to design a proper control model for the battery management system.

摘要 I
Abstract II
誌謝 III
第一章 緒論 1
1.1 前言 1
1.2 研究動機 7
1.3 研究目標 8
第二章 研究理論 10
2.1 電化學熱模型 10
2.1.1 鋰離子濃度平衡 12
2.1.2 電子電荷平衡 14
2.1.3 電化學動力學 17
2.1.4能量平衡 18
2.1.5 Arrhenius方程式 19
2.1.6 荷電狀態 (State-of-charge) 19
2.2 元啟發式演算法 20
2.2.1 鯨群演算法簡介 21
2.2.2收縮環繞機制 (Shrinking encircling mechanism) 21
2.2.3螺旋更新位置 (Spiral updating position) 23
2.2.4水泡網獵捕法 (Bubble-net attacking method) 24
第三章 實驗方法及模擬 25
3.1 充放電實驗 26
3.1.1 實驗材料與設備 27
3.1.2 實驗流程 28
3.2 建立鋰電池模型 28
3.2.1 幾何模型與求解器 29
3.2.2 參數設定 30
3.2.3 開路電位 31
3.3 鯨群演算法 33
3.3.1 辨識區間 34
3.3.2 目標函數 (Objective function) 35
3.3.3 演算法參數設定 36
3.4 行車型態 36
3.4.1 WLTP行車型態 37
3.5 敏感度分析 38
3.5.1 一次一因子法 (One factor at a time method) 38
第四章 結果與討論 40
4.1 最佳化結果 40
4.1.1 參數辨識結果 42
4.2 模型驗證結果 43
4.2.1 1C充放電模型驗證 44
4.2.2 其他定電流充放電模型驗證 45
4.2.3 WLTP行車型態驗證 49
4.2.4 電池溫度分布 50
4.3 敏感度分析結果 51
第五章 結論與未來研究方向 53
5.1 結論 53
5.2 未來研究方向 54
參考文獻 55
附錄一 文獻之參數值分類 60

[1] ROBECO Company(https://www.robeco.com/en/insights/2018/11/electric-vehicles-coming-of-age.html)
[2] Y. Miao, P. Hynan, A. von Jouanne, and A. Yokochi, "Current Li-ion battery technologies in electric vehicles and opportunities for advancements," Energies, vol. 12, no. 6, p. 1074, 2019.
[3] A. El Kharbachi, O. Zavorotynska, M. Latroche, F. Cuevas, V. Yartys, and M. Fichtner, "Exploits, advances and challenges benefiting beyond Li-ion battery technologies," Journal of Alloys and Compounds, vol. 817, p. 153261, 2020.
[4] A. Jokar, B. Rajabloo, M. Désilets, and M. Lacroix, "Review of simplified Pseudo-two-Dimensional models of lithium-ion batteries," Journal of Power Sources, vol. 327, pp. 44-55, 2016.
[5] X. Hu, S. Li, and H. Peng, "A comparative study of equivalent circuit models for Li-ion batteries," Journal of Power Sources, vol. 198, pp. 359-367, 2012.
[6] H. Lipu, M. Hannan, A. Hussain, A. Ayob, M. H. Saad, and K. M. Muttaqi, "State of charge estimation in lithium-ion batteries: A neural network optimization approach," Electronics, vol. 9, no. 9, p. 1546, 2020.
[7] J. Newman and W. Tiedemann, "Porous‐electrode theory with battery applications," AIChE Journal, vol. 21, no. 1, pp. 25-41, 1975.
[8] M. Doyle, T. F. Fuller, and 1. Newman, "Modeling of galvanostatic charge and discharge of the Iithium/polymerlinsertion cell," Journal of the Electrochemical Society, vol. 140, no. 6, pp. 1526-1533, 1993.
[9] M. Doyle, J. Newman, A. S. Gozdz, C. N. Schmutz, and J. M. Tarascon, "Comparison of modeling predictions with experimental data from plastic lithium ion cells," Journal of the Electrochemical Society, vol. 143, no. 6, p. 1890, 1996.
[10] D. Zhang, B. N. Popov, and R. E. White, "Modeling lithium intercalation of a single spinel particle under potentiodynamic control," Journal of the Electrochemical Society, vol. 147, no. 3, p. 831, 2000.
[11] W. Gu and C. Wang, "Thermal‐electrochemical modeling of battery systems," Journal of The Electrochemical Society, vol. 147, no. 8, p. 2910, 2000.
[12] P. M. Gomadam, R. E. White, and J. W. Weidner, "Modeling heat conduction in spiral geometries," Journal of the Electrochemical Society, vol. 150, no. 10, p. A1339, 2003.
[13] L. Cai and R. E. White, "Mathematical modeling of a lithium ion battery with thermal effects in COMSOL Inc. Multiphysics (MP) software," Journal of Power Sources, vol. 196, no. 14, pp. 5985-5989, 2011.
[14] S. Mirjalili and A. Lewis, "The whale optimization algorithm," Advances in engineering software, vol. 95, pp. 51-67, 2016.
[15] J. Nasiri and F. M. Khiyabani, "A whale optimization algorithm (WOA) approach for clustering," Cogent Mathematics & Statistics, vol. 5, no. 1, p. 1483565, 2018.
[16] X. Lai et al., "A comparative study of global optimization methods for parameter identification of different equivalent circuit models for Li-ion batteries," Electrochimica Acta, vol. 295, pp. 1057-1066, 2019.
[17] L. A. Wong, V. K. Ramachandaramurthy, S. L. Walker, P. Taylor, and M. J. Sanjari, "Optimal placement and sizing of battery energy storage system for losses reduction using whale optimization algorithm," Journal of Energy Storage, vol. 26, p. 100892, 2019.
[18] L. Oca et al., "Physico-chemical parameter measurement and model response evaluation for a pseudo-two-dimensional model of a commercial lithium-ion battery," Electrochimica Acta, vol. 382, p. 138287, 2021.
[19] B. Sundén, Hydrogen, Batteries and Fuel Cells. Academic Press, 2019.
[20] ANR26650m1 manual(https://www.batteryspace.com/prod-specs/6610.pdf)
[21] H. Liu, Z. Wei, W. He, and J. Zhao, "Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: A review," Energy conversion and management, vol. 150, pp. 304-330, 2017.
[22] J. Chiew, C. Chin, W. Toh, Z. Gao, J. Jia, and C. Zhang, "A pseudo three-dimensional electrochemical-thermal model of a cylindrical LiFePO4/graphite battery," Applied Thermal Engineering, vol. 147, pp. 450-463, 2019.
[23] C. Lee, Y. Hong, M. Hayrapetyan, X. Yang, and Z. Xi, "Derivation and tuning of a solvable and compact differential–algebraic equations model for LiFePO 4–graphite Li–ion batteries," Journal of Applied Electrochemistry, vol. 48, no. 3, pp. 365-377, 2018.
[24] E. Prada, D. Di Domenico, Y. Creff, J. Bernard, V. Sauvant-Moynot, and F. Huet, "Simplified electrochemical and thermal model of LiFePO4-graphite Li-ion batteries for fast charge applications," Journal of The Electrochemical Society, vol. 159, no. 9, p. A1508, 2012.
[25] M. G. Hennessy and I. R. Moyles, "Asymptotic reduction and homogenization of a thermo-electrochemical model for a lithium-ion battery," Applied Mathematical Modelling, vol. 80, pp. 724-754, 2020.
[26] S. V. Erhard, P. J. Osswald, J. Wilhelm, A. Rheinfeld, S. Kosch, and A. Jossen, "Simulation and measurement of local potentials of modified commercial cylindrical cells," Journal of The Electrochemical Society, vol. 162, no. 14, p. A2707, 2015.
[27] P. J. Osswald, S. V. Erhard, J. Wilhelm, H. E. Hoster, and A. Jossen, "Simulation and measurement of local potentials of modified commercial cylindrical cells: I. Cell preparation and measurements," Journal of The Electrochemical Society, vol. 162, no. 10, p. A2099, 2015.
[28] M. Safari and C. Delacourt, "Modeling of a commercial graphite/LiFePO4 cell," Journal of The Electrochemical Society, vol. 158, no. 5, p. A562, 2011.
[29] Y. Ye, Y. Shi, and A. A. Tay, "Electro-thermal cycle life model for lithium iron phosphate battery," Journal of Power Sources, vol. 217, pp. 509-518, 2012.
[30] X. Bei, Q. Liu, J. Cong, X. Liu, J. Yu, and H. Yang, "Simulation of electrochemical-thermal behavior for a 26650 lithium iron phosphate/graphite cell," Ionics, vol. 25, no. 8, pp. 3715-3726, 2019.
[31] L. Zhang, L. Wang, G. Hinds, C. Lyu, J. Zheng, and J. Li, "Multi-objective optimization of lithium-ion battery model using genetic algorithm approach," Journal of Power Sources, vol. 270, pp. 367-378, 2014.
[32] L. Zhang et al., "Parameter sensitivity analysis of cylindrical LiFePO4 battery performance using multi-physics modeling," Journal of The Electrochemical Society, vol. 161, no. 5, p. A762, 2014.
[33] W. Dreyer, J. Jamnik, C. Guhlke, R. Huth, J. Moškon, and M. Gaberšček, "The thermodynamic origin of hysteresis in insertion batteries," Nature materials, vol. 9, no. 5, pp. 448-453, 2010.
[34] P. Albertus, J. Couts, V. Srinivasan, and J. Newman, "II. A combined model for determining capacity usage and battery size for hybrid and plug-in hybrid electric vehicles," Journal of Power Sources, vol. 183, no. 2, pp. 771-782, 2008.
[35] T. Sasaki, Y. Ukyo, and P. Novák, "Memory effect in a lithium-ion battery," Nature materials, vol. 12, no. 6, pp. 569-575, 2013.
[36] K. Chew, C. Koay, and Y. Yong, "ADVISOR Simulation of Electric Vehicle Performance On Various Driving Cycles," Int. J. Innovative Science, Engineering & Technology, vol. 1, pp. 70-76, 2014.