Nassim A. Samad 1 Mem. ASME Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail: nassimab@umich.edu Boyun Wang Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail: bywang@umich.edu Jason B. Siegel Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail: siegeljb@umich.edu Anna G. Stefanopoulou Professor Fellow ASME William Clay Ford Professor of Manufacturing Mechanical Engineering, Automotive Research Center, University of Michigan, Ann Arbor, MI 48109 e-mail: annastef@umich.edu Parameterization of Battery Electrothermal Models Coupled With Finite Element Flow Models for Cooling Developing and parameterizing models that accurately predict the battery voltage and temperature in a vehicle battery pack are challenging due to the complex geometries of the airflow that influence the convective heat transfer. This paper addresses the difficulty in parameterizing low-order models which rely on coupling with finite element simula- tions. First, we propose a methodology to couple the parameterization of an equivalent circuit model (ECM) for both the electrical and thermal battery behavior with a finite element model (FEM) for the parameterization of the convective cooling of the airflow. In air-cooled battery packs with complex geometries and cooling channels, an FEM can provide the physics basis for the parameterization of the ECM that might have different convective coefficients between the cells depending on the airflow patterns. The second major contribution of this work includes validation of the ECM against the data collected from a three-cell fixture that emulates a segment of the pack with relevant cooling condi- tions for a hybrid vehicle. The validation is performed using an array of thin film temper- ature sensors covering the surface of the cell. Experiments with pulsing currents and drive cycles are used for validation over a wide range of operating conditions (ambient temperature, state of charge, current amplitude, and pulse width). [DOI: 10.1115/1.4035742] 1 Introduction Growing use and acceptance of lithium-ion batteries in automo- tive and high-power applications are the result of lowered battery cost and increased system safety. Accurate mathematical battery models are necessary to define the safe operating limits, both ther- mal and electrochemical. Without accurate models, battery per- formance is sacrificed due to the overlying conservative bounds. The battery temperature must be regulated during high power operation due to internal heating of the cell. If the cell temperature rises above the breakdown temperature of the electrolyte or solid–electrolyte interface, thermal runaway could occur [1]. Researchers have focused on analyzing and understanding the behavior of lithium-ion cells as a means to overcome these obstacles. Bernardi et al. [2] proposed a general energy balance for batteries to predict the temperature. Successive researchers have attempted different approaches to modeling the thermal and electrical behavior of lithium-ion batteries. Physics-based models [3–5], which solve the governing equations of lithium-ion trans- port in the cell, can predict microscopic level behavior and per- formance, but require large computational power to solve the associated differential equations. Other models, which are more adequate for control-oriented purposes such as in the battery man- agement system (BMS) of a vehicle, employ electrical circuit ele- ments [6–15] to model the physical responses of the battery. These equivalent circuit models (ECMs) models are relatively easy to parameterize and are sufficiently accurate which justifies their use in a BMS. Equivalent circuit models have been applied to cylindrical and prismatic cells. In cylindrical cells, ECM models that predict internal cell temperatures can be used to limit power [16] and reg- ulate battery states. Gao at al. [11] formulated a single RC equiva- lent circuit model with temperature and state of discharge (SOD) dependent open circuit voltage (OCV), coupled with a “bulk” thermal model that characterizes the whole battery as one uniform temperature. Perez et al. [12] expanded on Gao’s model to include a two-state thermal model (surface and core) coupled with a dou- ble RC equivalent circuit model with temperature and state of charge-dependent parameters. Smith et al. [14] used finite-volume methods to model the temperature distributions along with a representative equivalent circuit model. Prismatic cells can be physically packaged more efficiently than cylindrical cells. These cells are usually used in consumer electronics, like phones and laptops, and in hybrid electric vehicles such as the Ford Fusion Hybrid and the Toyota Prius Hybrid. However, they are harder to model than cylindrical cells due to their slightly more complex geometry. Many techniques were proposed in the literature for modeling the thermal behavior of prismatic cells [7,13,15,17–21]. Wang and coworkers [17] con- sidered different thermal models and studied the computational effi- ciency and accuracy of these models. Inui et al. [18] considered the effect of the cross-sectional area of a prismatic battery on the tem- perature distributions within that battery. Gualous and coworkers [19] developed a new thermal parameter estimation tool using a first-order Cauer thermal model, and investigated the behavior of a battery under abuse conditions. Other more recent models have presented coupled electrothermal models that can predict temper- ature distributions in a prismatic cell [7,13,20]. In particular, coupled electrothermal models with distributed equivalent circuits [7,13] have been able to capture the local dynamics of prismatic cells and observe the local variations in temperature, current, and SOC. 1 Corresponding author. Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS,MEASUREMENT, AND CONTROL. Manuscript received October 6, 2015; final manuscript received December 19, 2016; published online May 9, 2017. Assoc. Editor: Beshah Ayalew. Journal of Dynamic Systems, Measurement, and Control JULY 2017, Vol. 139 / 071003-1 Copyright V C 2017 by ASME Downloaded From: https://dynamicsystems.asmedigitalcollection.asme.org/ on 10/30/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use