*3.1. Reference System*

The cell under investigation is a prismatic 25 Ah cell from SANYO/Panasonic with a Nickel-Mangan-Cobalt-Oxide (NMC) cathode and graphite anode material. The dimensions of the cell are 14.8 cm, 2.65 cm and 9.1 cm.

In our previous work [19], the cell was combined with electronics to form an intelligent cell prototype. A schematic representation of this setup is shown in Figure 2a. For the prismatic cell equipped with electronics, a detailed electro-thermal 3D CFD model was implemented to investigate the specific influences of the electronics to the cell. The shown cell with electronics is utilized for parametrization of the models of the cell and the electronics in this work. The dataset of the previous investigation is used as target data for

both simplified real-time modeling approaches. Considering that no measurement data of the jelly roll core temperature are available, the neural network is trained using the highly resolved and already experimentally validated CFD model. This teacher approach, using a detailed model for the training of a simplified real-time model, is similarly done for other applications, e.g., by Fang et al. [54]. In addition, the neural network uses independent datasets for training and validation. For this purpose, datasets for the temperature range of 15–45 °C are available, which contain many different static and dynamic load profiles, as well as the information about local heat generation and temperatures. Figure 2b shows, as an example, a part of the data for a reference temperature of 25 °C.

(**a**) Cell prototype and schematic geometry for detailed 3D CFD model in [19].

(**b**) Example investigation results used as training or target data.

**Figure 2.** Reference system based on our previous investigation [19]: (**a**) Cell prototype with electronics and corresponding schematic geometry for the detailed 3D spatially dependent electro-thermal CFD model. (**b**) Example results for the temperature and heat generation behavior of the prototype cell for 25 °C starting temperature. Various comparable datasets in the range of 15–45 °C are used as a training or target profile.

For a meaningful scenario, BEV boundary conditions are considered [21]. The cell is assumed to be adiabatic in all directions with the exception of the connection to the cooling system at the bottom with the temperature *T*cool. For the investigation on a system level, cells are additionally thermally coupled via the casing and the busbars, which are described in Section 3.4. For a realistic cooling system behavior, a simplified model is introduced that is comparable to [55–57]. Thereby, the cooling system is regulated stepwise and rule-based which is an extension of the thermostat controller [58,59]. The maximum heat flow per cell *Q*˙ max, that can be dissipated by the cooling system, is controlled in three steps as shown

in Figure 3. Starting with a deactivated cooling system for an optimal cell temperature below 30 °C in step 0, the cooling system performance rises stepwise to a maximum of 9 W at 38 °C for step 3. A hysteresis of 0.3 K , visualized by the marked line, is used for the regulation of the cooling power [60]. Excessive heat production of the cell, exceeding the cooling power limit, leads to an increase in the cooling system temperature.

**Figure 3.** Overview of stepwise cooling system regulation with a hysteresis of 0.3 K for decreasing and increasing temperatures.

#### *3.2. Physics-Based Thermal Equivalent Circuit Model*

A commonly used physics-based modeling approach for conventional cells is a lumped thermal model, also called TECM. The basic structure of TECMs is symbolized in the left-hand section of the thermal submodel in Figure 1. In general, in a TECM, the component to be observed is discretized by small volumes. Each volume is represented by a thermal node, which contains the thermal capacity and parameters of the volume respectively. The thermal capacity of one volume *i* is calculated using Equation (4).

$$\mathbf{C}\_{\text{th},i} = \rho\_{i} \cdot V\_{i} \cdot \mathbf{c}\_{\text{p},i} \tag{4}$$

where *ρ<sup>i</sup>* and *c*p,*<sup>i</sup>* are the averaged density and specific heat capacity of the volume *i*, and *Vi* is its geometric volume. Thermal capacities, therefore, describe the heat accumulation analogously to electrical capacitances [24]. In each thermal node, the volumetric fraction of the total heat generation is used as a heat source, which is analogous to a current source in electrical models. The thermal nodes are connected by thermal resistances defining the heat transfer between them [24]:

$$R\_{\text{th,cond}} = \frac{L}{\lambda \cdot A} \tag{5}$$

*L* is the distance between two thermal nodes, *λ* is the heat conduction coefficient of the respective material and *A* is the cross-sectional area of the heat transfer path between two nodes.

The total TECM for the cell and the detailed electronics model is shown in the left-hand section of Figure 4. Significant temperature gradients can result in large format prismatic battery cells [21]. Therefore, the cell-internal structure is included in the TECM to model a more realistic temperature distribution through a physics-based model in comparison to other implemented lumped thermal models [28]. For that purpose, 3 × 3 × 3 nodes standing for volumes of the same size are arranged in the mid of the jelly roll. In order to model the complex curved geometry of the jelly roll, three nodes are added below and above the 3 × 3 × 3 cuboid, respectively, resulting to a total number of 33 nodes inside the jelly roll. In the same manner, the case is discretized by each of the nine nodes on the *x*-*y*-side, three nodes on the *y*-*z*-side and two nodes for cell top and one for the bottom. Additional nodes are added for the current collectors and the cell terminals. Computer tomography scans have shown that electrolyte is remaining at the bottom of the case [21].

Therefore, the connection between the jelly roll and the bottom case is considered via heat conduction through the electrolyte.

**Figure 4.** Real-time thermal models for a intelligent cell in a BEV battery system: (**a**) Overview of the TECM and the ANN modeling details. (**b**) Bottom view of the electronics hardware geometry and the related TECM model.

The electronics can have significant influence on the jelly roll temperature [19]. Therefore, the thermal influences of the specific electronics are considered by a lumped electronics model of the real hardware. In Figure 4a the general positioning and thermal connection of the electronics is revealed. Additionally, Figure 4b depicts a detailed view of the electronics components and the modeling scheme. An one-dimensional heat conduction and temperature distribution along the current path in *x*-direction is considered. Three thermal nodes are integrated representing the thermal masses of the current conducting copper inlays. Temperature and current dependent heat generation is located in all current carrying parts. The information of the current and the SOC are provided by the framework emulating a BMS, but they are not further used in the present implementation. The TECM calculates the temperature at the thermal nodes and also at the positions where thermistors are integrated on the hardware prototype. Using this presented structure of the TECM makes it possible to estimate the temperature in multiple positions and dimensions of the cell which is advantageous for the later system level implementation described in Section 3.4. The TECM is implemented in MATLAB/Simulink Version 2020a using Simscape.

Thermal masses and thermal resistances are determined analytically on the basis of material parameters, dimensions and manufacturers data of the investigated prismatic cell and electronics. The initial material parameters used are listed in Table 1.



<sup>1</sup> [61], <sup>2</sup> Cell manufacturer data sheet (25 °C), <sup>3</sup> [21], <sup>4</sup> manufacturer data sheet.
