**1. Introduction**

In the past few decades, the transport mobility sector, and especially the automotive industry, has experienced considerable changes. In order to address the climate change problems and particularly, to reduce CO2 emissions, among other technologies, Electric Vehicles (EVs) are becoming increasingly important [1]. Due to their high energy and power density, lithium-ion (li-ion) batteries are the most preferred battery type for EV applications [2]. Nevertheless, the challenges and limitations related to costs, safety and aging need to be addressed and are part of current research [3]. One important factor influencing performance, safety and life time of the battery pack, is temperature [2,4,5]. Low temperatures lead to less available power and capacity and can result in irreversible battery degradation when reaching subzero values. High temperatures outside the optimal range of 15–35 °C [4] lead to accelerated aging and may result in a thermal runaway when exceeding the safety limit of 60 °C [4,5]. Monitoring battery cell temperatures is, therefore, necessary, which is a task of the Battery Thermal Management System (BTMS) as part of the Battery Management System (BMS) [4]. The basic approach in commercial vehicles is to measure the temperature at a few discrete points at the surface or tab of li-ion cells in the system [6]. In large format battery cells this temperature may greatly differ from the temperature reached in the battery cell core [7–9], which is the critical temperature in terms of performance and safety. Therefore, the temperature estimation by using thermal models

**Citation:** Kleiner, J.;

Stuckenberger, M.; Komsiyska, L.; Endisch, C. Advanced Monitoring and Prediction of the Thermal State of Intelligent Battery Cells in Electric Vehicles by Physics-Based and Data-Driven Modeling. *Batteries* **2021**, *7*, 31. https://doi.org/10.3390/ batteries7020031

Academic Editor: Kai Peter Birke

Received: 5 March 2021 Accepted: 7 May 2021 Published: 11 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

is a first step and a necessary part to enable precise thermal state monitoring. In addition, predictive thermal management with several advantages, such as the core temperature information, can be utilized [10–13].

The development of next generation intelligent battery systems takes this into account by advanced monitoring of the individual cell states [14,15]. Sensors are integrated in cell-level electronics and intelligent algorithms determine the cell state, detect faults or perform bad-block management [16–18]. In our previous work [19], a prismatic cell was equipped with electronics for single cell data acquisition and system reconfiguration. The use of sensors integrated in mass-produced electronics in combination with thermal models enables the core temperature of the battery cells to be monitored. This avoids the need to integrate additional temperature sensors into the cell, as proposed by [5,7], which would lead to increased production costs and safety issues [8]. However, for thermal state monitoring, the internal cell behavior needs to be modeled and the developed models have to be integrated in the vehicle architecture. Cell-level modeling is necessary, since cooling system gradients and cell-to-cell variations lead to different thermal conditions for cells in a system [20]. A substantial thermal gradient also arises due to the thermal coupling between cells. Therefore, the thermal states of multiple cells differ and need to be monitored individually.

Many different approaches for thermal models for conventional battery cells can be found in the literature. The modeling approaches can generally be separated into physicsbased and data-driven models. Another common designation is white-box and black-box modeling depending on the way the results are derived from the inputs. In general, the prediction of a white-box model is physically and geometrically motivated and can be understood more intuitively compared to black-box models which are solely data-driven. There are detailed physical-based electrochemical-thermal models that are coupled, e.g., with geometries modeled by Computational Fluid Dynamics (CFD) or Finite Element Method (FEM) approaches [21,22] or even in combination with mechanical models [23]. Those models are useful for battery design but their main drawback is their low computational speed, which does not allow using them for online temperature estimation in a BTMS [24,25]. Lumped thermal models consider the relevant physical phenomena and simplify the differential equation system by concentrating the important cell characteristics on a few points [24,25]. The model parameters can be derived analytically for known material parameters [24,26,27] or fitted to experimental measurements [25,28]. The latter are a first step towards data-driven models and, therefore, one representative of the so called gray-box approaches. Completely data-driven models do not represent the cell internal physical and geometrical properties and model the output behavior implicitly. Thereby, mostly with the help of machine learning methods mathematical relations between inputs and outputs are trained [29]. Examples are models using Support Vector Machines [30] and Artificial Neural Networks (ANNs) [9,29,31]. The latter are a novel topic of research in the field of thermal battery modeling and have proven to have advantages in modeling non-linear dynamic relations as they can be found in batteries [9]. Nevertheless, the ANN approaches found in the literature are mainly simple network architectures, such as Feedforward (FF) [29,31], and none of them considers integrating the ANN as thermal model in a total model system. Data-driven time-series prediction, implemented, for example, as Nonlinear AutoregRessive with eXogeneous input (NARX) architecture, is particularly reported in the literature to be adequate as thermal parameter forecasting in energy systems [32,33] or surface temperature predictions of cylindrical cells [34]. However, there are currently no models that use NARX networks for core temperature modeling of large format cells, neither for conventional, nor for intelligent batteries.

Since both approaches, physical-based and data-driven modeling, seem to be adequate as thermal battery models, it is important to compare the modeling approaches related to the application in Battery Electric Vehicles (BEVs). Thereby, the latest developments in terms of hardware and structure of intelligent cells are taken into account in this work. Currently, there are neither physical-based nor data-driven models that consider the hardware influences within intelligent cells on the battery's temperature.

The application of cell individual temperature monitoring by using a thermal model in a real BEV system creates an additional opportunity to estimate the core temperature, and also the new possibility to predict the temperature for future events and to utilize corresponding operation strategies. Only a few approaches exist for using battery temperature prediction in BEV scenarios [10,12,35,36]. The results are promising with thermal models that can be used to improve the prediction of the driving range [35], control the regulation of an air- and liquid-dual cooling system [10], or predict the future available battery power [36]. However, there are certainly more applications in which real-time thermal modeling can lead to advances in the specific prediction scenario. In this work, the cases of State-Of-Power (SOP) prediction and advanced cooling system regulation are proposed.

Prediction functionalities, such as SOP prediction, are important for the BEV application as a means of knowing the available power in situations such as user acceleration requirement or long-term performance availability without fear of overcharging or overdischarging [37]. Current publications focus on the calculation of the available SOP based on current, voltage and State-Of-Charge (SOC) limitations of the cells [37–43]. For low SOCs, the discharge current is the limiting factor, while for high SOCs, the charging current is taken accordingly. At the same time, the maximum permissible load and the voltage limits of the cell restrict the maximum power output. However, in reality, the SOP is also limited by the rising temperatures during maximum performance. For that purpose, temperature estimation for an adequate SOP prediction is necessary, as performed in this work.

Another investigated use case of temperature prediction is related to the cooling system regulation. Amini et al. [44] argue that temperature prediction achieves a planning horizon to activate or deactivate the cooling system which is necessary as the cooling system contains high thermal masses. By reducing the initial phase for a battery thermal management system, the power necessary for cooling can be reduced in general [45]. Additionally, the goal of the cooling system is always to keep all cells in the optimal thermal range. However, there are applications discussed in the literature that prefer increased temperatures. For example, heating the battery to 40 °C instead of cooling it to 25 °C is known to reduce the stress and degradation caused by the intercalation and deintercalation processes and, therefore, aging [46]. Another application is the thermally challenging fast charging of EVs. Yang et al. [47–49] reveal slow preheating as favorable for fast charging procedures, leading to much less heat generation during the fast charging and, therefore, to less energy demand for the cooling. Collin et al. [50] mention, in their work on advanced fast charging technologies, the first approaches in commercial BEVs that perform defined pre-conditioning to improve fast charging.

In this work, the focus is on developing a thermal model for an intelligent prismatic 25 Ah cell prototype, including electronics for a BEV application. The aim is to represent the thermal interactions within the large format cell and the actual influence of the electronics. For the first time, the existing approaches for conventional battery cells, e.g., a physicsbased and a data-driven model using the example of a Thermal Equivalent Circuit Model (TECM) and an ANN respectively, are implemented and compared. The two thermal modeling methods are parametrized and implemented for an existing intelligent cell hardware published in our former work [19] and integrated in a total framework for a BEV application. The models are used for the cell-level temperature estimation of different local temperatures and are compared in terms of parametrization, accuracy and computation time. Using intelligent cells and the thermal models for advanced thermal management, novel temperature prediction applications in a realistic BEV scenario are presented. Improvements for SOP prediction are then presented by considering the thermal cell state. In a second application, an predictive cooling system regulation is presented that enables pre-conditioning for fast charging.
