##
413
Experimental Parameter Identification of a LiFePO4 Thermal Battery Model through Identifiability Maximization Using Input Trajectory Optimization

Previous research studies in depth the estimation of entropy coefficients^{1–5}, other thermo-electrochemical parameters,^{6,7} and the identifiability of electrochemical systems using Fisher information^{8}. The identification of entropy coefficients is done using calorimetric and potentiometric measurements ^{2,9–11}. These research studies use battery cycler and environmental chambers as actuators in combination with sensors ranging from simple thermocouples on one end to sophisticated calorimeters on the other end of the spectrum. This work, in contrast, answers for the first time these two questions: (i) What is the quantified identifiability, using Fisher information, of the experimentally obtained thermal parameters? (ii) How does the identifiability change with the choice of experimental thermal cycles? The first part of this paper comprises a Fisher information-based analysis of the identifiability of the model to determine which input dynamics affect the parameter estimation accuracy the most. The second part of the paper involves optimizing a set of noninvasive dynamic experiments that account for the hardware operational constraints. The third part involves experimentally identifying and validating the thermal parameters as accurately as possible.

The most valuable contribution of this work is not necessarily the identified model of battery thermal dynamics, but rather the layout of a rigorous procedure to measure the accuracy of its parameters and a sense of how one can improve the reliability through more sophisticated and extensive experimentation.

**Figure 1: **Open circuit voltage and ambient temperature profile as a function of time for a LiFePO4 battery at 30% SOC.

**Reference**

1. K. E. Thomas, C. Bogatu, and J. Newman, *J. Electrochem. Soc.*, **148**, A570 (2001).

2. K. Jalkanen, T. Aho, and K. Vuorilehto, *J. Power Sources*, **243**, 354–360 (2013).

3. J. Hong, H. Maleki, S. Al Hallaj, L. Redey, and J. R. Selman, *J. Electrochem. Soc.*, **145, **1489-1501 (1998).

4. R. E. Williford, V. V. Viswanathan, and J.-G. Zhang, *J. Power Sources*, **189**, 101–107 (2009).

5. C. Forgez, D. Vinh Do, G. Friedrich, M. Morcrette, and C. Delacourt, *J. Power Sources*, **195**, 2961–2968 (2010).

6. Y. Hu, B. J. Yurkovich, S. Yurkovich, and Y. Guezennec, *ASME 2009 Dyn. Syst. Control Conf. Vol. 2*, 233–240 (2009).

7. L. Zhang, C. Lyu, L. Wang, W. Luo, and K. Ma., "Thermal-Electrochemical Modeling and Parameter Sensitivity Analysis of Lithium-ion Battery",* Chemical Engineering Transactions*, **33**, 943–948 (2013).

8. J. C. Forman, S. J. Moura, J. L. Stein, and H. K. Fathy, *J. Power Sources*, **210**, 263–275 (2012)

9. Takano, K., Y. Saito, K., Kanari, K., Nozaki, K., Kato, A., Negishi, A., and Kato, T., 2002. “Entropy change in lithium ion cells on charge and discharge”. *Journal of Applied Electrochemestry*,** 32**, 251–258 (2002).

10. K. Onda, H. Kameyama, T. Hanamoto, and K. Ito, *J. Electrochem. Soc.*, **150**, A285 (2003).

11. S. J. Bazinski and X. Wang, *J. Electrochem. Soc.*, **161**, A168–A175 (2013).