鋰電池建模，實作與可變結構控制 阮成南、蔡耀文
E-mail: [email protected]
摘 要
本文利用狀態空間識別理論，建立一個全新的鋰電池模型，依據這個新模型，建立一個以參考模型(reference model)與可變 結構控制器(variable structure control)為基礎的磷酸鋰鐵(LiFePO4)電池充放電管理方法。 經由Matlab/Simulink之模擬，本研 究使用狀態空間方程式來描述磷酸鋰鐵電池的充電與放電過程特性，Matlab的曲線擬合工具(curve-fitting tool)被用來獲得部 分電池參數。 本法之模擬結果接近於實驗結果，電池充放電模組能夠適切地描述鋰電池特性，而且非常適合於現代控制理 論之應用。根據實驗結果顯示，本文所採用的方法，可作為磷酸鋰鐵電池以及其他種類電池之建模參考。本研究之結果除 了有助於新電池的建模和特性研究外，也可以運用於串聯電池組之相關研究。 最後，考慮磷酸鋰鐵電池不確定成分特性的 干擾，本文利用可變結構系統理論，設計一組強健型控制器，電腦模擬結果顯示其效果良好，這也證明了本文提出的全新 鋰電池模型非常適合於現代控制理論之應用。
關鍵詞 : 鋰電池、磷酸鋰鐵(LiFePO4)、電池建模、狀態空間、可變結構控制(VSC) 目錄
Inside Front Cover Signature Page Chinese Abstract...iii English Abstract...iv Acknowledgement...v Table of Contents...vi Table of Figures...ix List of Abbreviations...xii Chapter 1 Introduction...1 1.1 The Li-ion batteries...1 1.2 LiFePO4 batteries’
characteristics...4 1.3 Battery State of Charge...5 1.4 Motivation...6 1.5 Methodology...7 1.6 Thesis outline...9 Chapter 2 Mathematical Modelling of a Battery...10 2.1 General Modelling...10 2.1.1 ADVISOR Models...10 2.1.2 The battery model in MATLAB Help...10 2.1.3 The Rint Model...12 2.1.4 The RC Model...13 2.1.5 The Thevenin Model...14 2.1.6 The DP Model...15 2.2 Conventional Modelling...16 2.2.1 The RC1C2 model...17 2.2.2 The RLC model...23 2.3 Introduction to PWM concept...30 Chapter 3 New battery state-space modelling...33 3.1 New battery modelling...33 3.2 Basic parameters...35 3.2.1 From
manufacturer...35 3.2.2 Calculation...35 3.3 Development of State-Space Equations...38 3.3.1 Discharge model...38 3.3.1.1 Simple discharge circuit for a single battery...38 3.3.1.2 Detailed battery discharging model...40 3.3.2 Charge model...47 3.3.2.1 Simple charge model for a single battery...47 3.3.2.2 Detailed battery charging model...49 3.4 Comparison of simulation and practical results...53 3.4.1 Discharging process...55 3.4.2 Charging process...56 Chapter 4 Variable Structure Controller for single battery...58 4.1 Objectives...58 4.2 Introduction to reference model and the controller...58 4.2.1 Reference model...59 4.2.2 Variable structure control...61 4.3 Derivation of equations...62 4.2.1 Equations for discharging process...63 4.2.2 Equations for charging process...71 4.4 Large-scale batteries with balancing techniques...74 4.4.1 Conventional SOC balancing technique...75 4.4.2 Novel SOC
balancing technique...76 Chapter 5 Conclusion...77 5.1 Contributions...77 5.2 Recommendations...78 References...80 Appendix...85 參考文獻
[1]Cadex Electronics Inc., http://batteryuniversity.com [Accessed June 19, 2012].
[2]Mathworks Help. http://www.mathworks.com/help/toolbox/ [Accessed June 19, 2012].
[3]A123 Systems, Inc. http://www.a123systems.com/ [Accessed June 19, 2012].
[4]A BMS monitors and protects cells in a battery. Available online: http://liionbms.com/php/about_bms.php [Accessed June 19, 2012].
[5]Battery model. MATLAB Help: Simulink Library Browser > Simscape > SimPowerSystems > Blocks > Electrical Sources > Battery. Online at:
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/battery.html [Accessed June 19, 2012].
[6]Model Reference Control. MATLAB Help: Neural Network Toolbox > User’s Guide > Control Systems > Model Reference Control. Or available online at: http://www.mathworks.com/help/toolbox/nnet/ug/bss37c6-1.html [Accessed June 19, 2012].
[7]Jonghoon Kim, Jongwon Shin, Changyoon Jeon, and Bohyung Cho. High Accuracy State-of-Charge Estimation of Li-Ion Battery Pack based on Screening Process. IEEE (2011).
[8]Jonghoon Kim, Jongwon Shin, Changyoon Chun, and Bohyung Cho. Stable Configuration of a Li-Ion Series Battery Pack based on Screening Process for Improved Voltage/SOC Balancing. IPEC, Sapporo, Japan, June 21-24 (2010).
[9]Jong-Hoon Kim, Jong-Won Shin, Chang-Yoon Jeon, and Bo-Hyung Cho. Screening Process of Li-Ion Series Battery Pack for Improved Voltage/SOC Balancing. The 2010 International Power Electronics Conference. IEEE (2010).
[10]T. Markel, A. Brooker, T. Hendricks, V. Johnson, K. Kelly, B. Kramer, M. O’Keefe, S. Sprik, and K. Wipke. ADVISOR: a systems analysis tool for advanced vehicle modelling. Journal of Power Sources 110 255–266 (2002).
[11]Hongwen He, Rui Xiong, and Jinxin Fan. Evaluation of Lithium-Ion Battery Equivalent Circuit Models for State of Charge Estimation by an Experimental Approach. Energies, 4, 582-598; ISSN 1996-1073 (2011) www.mdpi.com/journal/energies [12]Hongwen He, Rui Xiong, Xiaowei Zhang, Fengchun Sun, and JinXin Fan. State-of-Charge Estimation of the Lithium-Ion. IEEE Transactions on Vehicular Technology, Vol. 60, No.
4, May 2011.
[13]Anahita Banaei, Amir Khoobroo, and Babak Fahimi. Online Detection of terminal voltage in Li-ion Batteries via Battery Impulse Response.
IEEE (2009).
[14]Matthias Durr, Andrew Cruden, Sinclair Gair, and J.R. McDonald. Dynamic model of a lead acid battery for use in a domestic fuel cell system. Journal of Power Sources 161, 1400–1411 (2006).
[15]Feng Xuyun and Sun Zechang. A battery model including hysteresis for State-of-Charge estimation in Ni-MH battery. IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, Harbin, China (2008).
[16]Dai Haifeng, Wei Xuezhe, and Sun Zechang. State and Parameter Estimation of a HEV Li-ion Battery Pack Using Adaptive Kalman Filter with a New SOC-OCV Concept. International Conference on Measuring Technology and Mechatronics Automation (2009).
[17]Min Chen and Gabriel A. Rinc’on-Mora. Accurate Electrical Battery Model Capable of Predicting Runtime and I–V Performance. IEEE Transactions on Energy Conversion, Vol. 21, No. 2, June 2006.
[18]Masatoshi Uno and Koji Tanaka. Influence of High-Frequency Charge–Discharge Cycling Induced by Cell Voltage Equalizers on the Life Performance of Lithium-Ion Cells. IEEE Transactions on Vehicular Technology, Vol. 60, No. 4, May 2011.
[19]Sudarshan Rao Nelatury and Pritpal Singh. Equivalent circuit parameters of nickel/metal hydride batteries from sparse impedance measurements. Journal of Power Sources 132, 309–314 (2004).
[20]Liao Chenglin, Tang Zining, and Wang Lifang. SOC Estimation of LiFeO4 Battery Energy Storage System. (2009) [21]Kuo-Kai Shyu, Yao-Wen Tsai, and Chiu-Keng Lai. Sliding mode control for mismatched uncertain systems. Electronics Letters, 26th November 1998 Vol. 34 No.
24 (p.2359-2360). Online No: 19981546, IEEE 1998, 12 October 1998.
[22]Kuo-Kai Shyu, Yao-Wen Tsai, and Chiu-Keng Lai (2001). A dynamic output feedback controllers for mismatched uncertain variable structure systems. Automatica 37 (2001) 775-779.
[23]?ak, S. H., & Hui, S. On variable structure output feedback controllers for uncertain dynamic systems. IEEE Transactions on Automation Control, AC-38, 1509-1512 (1993).
[24]Wei Wang, Kenzo Nonami, and Yuta Ohira. Model Reference Sliding Mode Control of Small Helicopter X.R.B based on Vision.
International Journal of Advanced Robotic Systems, Vol. 5, No. 3. ISSN 1729-8806, pp. 235-242 (2008).
[25]Yang Zhi-jun, Qi Xiao-hui, and Shan Gan-lin. Fault Tolerant Flight Control Law Design with a Model-Following Sliding Mode Controller.
International Conference on Measuring Technology and Mechatronics Automation (2009).
[26]Yang Zhi-jun, Qi Xiao-hui, and Shan Gan-lin. Model-Following Sliding Mode Controller Design for Flight Control Systems with Wind Disturbances. IEEE (2009).
[27]Wen-long Song and Jun Cao. Model Reference Adaptive Sliding Mode Control of Uncertain Systems Subject to Input Nonlinearity. IEEE (2006).
[28]Wen-Jer Chang and Koan-Yuh Chang. H∞ norm and variance constrained controller design for stochastic model reference systems via sliding mode control concept. Proceedings of the American Control Conference San Diego, California, June 1999.
[29]Sarah K Spurgeon, Christopher Edwards, and Neale P Foster. Robust Model Reference Control Using a Sliding Mode Controller/Observe Scheme with application to a Helicopter Problem. IEEE Workshop on Variable Structure Systems (1996).
[30]A. M. Hasanul Basher. Swing-free transport using Variable Structure Model Reference Control. IEEE (2001).
[31]Uma maheswararao.Ch, Y.S.Kishore Babu, and K.Amaresh. Sliding mode speed control of a DC motor. International Conference on Communication Systems and Network Technologies. IEEE (2011).
[32]R. K. Munje, M. R. Roda, and B. E. Kushare. Speed Control of DC Motor Using PI and SMC. IEEE (2010).
[33]Hahnsang Kim and Kang G. Shin. On Dynamic Recon?guration of A Large-Scale Battery System. 15th IEEE Real-Time and Embedded Technology and Applications Symposium (2009).
[34]IBM Research – Almaden, Lithium/Air Battery Project (Battery 500). Available online at:
http://www.almaden.ibm.com/st/smarter_planet/battery/ [Accessed July 03, 2012].
[35]Gang Ning and Branko N. Popov. Cycle Life Modeling of Lithium-Ion Batteries. Journal of The Electrochemical Society, 151 (10) A1584-A1591 (2004).
[36]Yancheng Zhang and Chao-Yang Wang. Cycle-Life Characterization of Automotive Lithium-Ion Batteries with LiNiO2 Cathode. Journal of The Electrochemical Society, 156 (7) A527-A535 (2009).
[37]J. Li, E. Murphy, J. Winnick, and P.A. Kohl. Studies on the cycle life of commercial lithium ion batteries during rapid charge–discharge cycling. Journal of Power Sources 102, 294–301 (2001).
[38]Ogata, K. State Space Analysis of Control Systems. Prentice-Hall, Inc. (1967).
[39]Ogata, K. Modern Control Engineering (4th ed.). Prentice-Hall, Inc. (2002).
[40]Frank L. Lewis. Applied Optimal Control & Estimation. Prentice-Hall, Inc. (1992).
