Li-ion storage models for energy system optimization: the accuracy-tractability tradeoff

ABSTRACT

There is a need for accurate analytical models that describe how a Lithium-ion battery's state of charge evolves as a result of a charging or discharging operation and that can be used in optimization problems. Although 'white box' models that take into account the details of electro-chemical processes can be highly accurate, they are not typically suitable for optimization problems. We propose two models that represent different tradeoffs between accuracy and tractability. We validate the accuracy of these models with data traces obtained from extensive experiments using two different commercially-available cells based on two distinct Li-ion technologies. We find that one of our models can be easily adopted for use in a mathematical optimization problem, while significantly increasing the range of C-rates over which it is accurate (<5% error) compared to the models that are currently being used.

References

1. A123 Systems. High Power Lithium Ion APR18650M1A, 2009. LiFePO4 cell specifications.
2. K. M. Chandy, S. H. Low, U. Topcu, and H. Xu. A simple optimal power flow model with energy storage. In Decision and Control (CDC), 2010 49th IEEE Conference on, pages 1051--1057. IEEE, 2010.
3. D. Doerffel and S. A. Sharkh. A critical review of using the Peukert equation for determining the remaining capacity of Lead-acid and Lithium-ion batteries. Journal of Power Sources, 155(2): 395--400, 2006.
4. N. Gast, J.-Y. Le Boudec, A. Proutière, and D.-C. Tomozei. Impact of storage on the efficiency and prices in real-time electricity markets. In Proceedings of the fourth international conference on Future energy systems, pages 15--26. ACM, 2013.
5. Y. Ghiassi-Farrokhfal, F. Kazhamiaka, C. Rosenberg, and S. Keshav. Optimal design of solar PV farms with storage. Sustainable Energy, IEEE Transactions on, 6(4): 1586--1593, 2015.
6. Y. Ghiassi-Farrokhfal, S. Keshav, and C. Rosenberg. Toward a realistic performance analysis of storage systems in smart grids. Smart Grid, IEEE Transactions on, 6(1): 402--410, 2015.
7. H. He, R. Xiong, and J. Fan. Evaluation of Lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach. Energies, 4(4): 582--598, 2011.
8. X. Hu, S. Li, and H. Peng. A comparative study of equivalent circuit models for Li-ion batteries. Journal of Power Sources, 198: 359--367, 2012.
9. R. Huang, S. H. Low, U. Topcu, K. M. Chandy, and C. R. Clarke. Optimal design of hybrid energy system with PV/wind turbine/storage: A case study. In Smart Grid Communications (SmartGridComm), 2011 IEEE International Conference on, pages 511--516. IEEE, 2011.
10. F. Kazhamiaka, C. Rosenberg, and S. Keshav. Practical strategies for storage operation in energy systems: design and evaluation. Accepted to IEEE Transactions on Sustainable Energy, 2016.
11. Leclanché. LecCell 30Ah High Energy, 02 2014. Lithium-Titanate cell specifications.
12. A. Mishra, R. Sitaraman, D. Irwin, T. Zhu, P. Shenoy, B. Dalvi, and S. Lee. Integrating energy storage in electricity distribution networks. In Proceedings of the 2015 ACM Sixth International Conference on Future Energy Systems, pages 37--46. ACM, 2015.
13. B. Nykvist and M. Nilsson. Rapidly falling costs of battery packs for electric vehicles. Nature Climate Change, 5(4): 329--332, 2015.
14. N. Omar, P. V. d. Bossche, T. Coosemans, and J. V. Mierlo. Peukert revisited -- critical appraisal and need for modification for Lithium-ion batteries. Energies, 6(11): 5625--5641, 2013.
15. J. Qin, Y. Chow, J. Yang, and R. Rajagopal. Modeling and online control of generalized energy storage networks. In Proceedings of the 5th international conference on Future energy systems, pages 27--38. ACM, 2014.
16. P. Ramadass, B. Haran, P. M. Gomadam, R. White, and B. N. Popov. Development of first principles capacity fade model for Li-ion cells. Journal of The Electrochemical Society, 151(2): A196--A203, 2004.
17. K. A. Smith, C. D. Rahn, and C.-Y. Wang. Control oriented 1d electrochemical model of Lithium ion battery. Energy Conversion and Management, 48(9): 2565--2578, 2007.
18. M. Swierczynski, D.-I. Stroe, A.-I. Stan, R. Teodorescu, and S. K. Kaer. Investigation on the self-discharge of the lifepo4/c nanophosphate battery chemistry at different conditions. In Transportation Electrification Asia-Pacific (ITEC Asia-Pacific), 2014 IEEE Conference and Expo, pages 1--6. IEEE, 2014.
19. J. Vetter, P. Novák, M. Wagner, C. Veit, K.-C. Möller, J. Besenhard, M. Winter, M. Wohlfahrt-Mehrens, C. Vogler, and A. Hammouche. Ageing mechanisms in Lithium-ion batteries. Journal of power sources, 147(1): 269--281, 2005.
20. S. S. Zhang. The effect of the charging protocol on the cycle life of a Li-ion battery. Journal of power sources, 161(2): 1385--1391, 2006.
21. A. H. Zimmerman. Self-discharge losses in lithium-ion cells. Aerospace and Electronic Systems Magazine, IEEE, 19(2): 19--24, 2004.

Index Terms

• Hardware

  • Power and energy

    • Energy generation and storage

      • Batteries

• Mathematics of computing

  • Mathematical analysis

    • Mathematical optimization

      • Continuous optimization

        • Convex optimization