**4. Results and Discussion**

#### *4.1. Spatial Temperature Estimation of TECM and ANN*

In order to compare the temperature estimation of the real-time thermal models to the target results of the reference system in Section 3.1, an independent dataset of the reference system based on the ADAC electric vehicle cycle is chosen. The corresponding 2000 s current profile is repeated until the lower cut-off voltage of 3 V is reached. For adequate comparison, a homogeneous constant temperature of 25 °C is defined for the starting and cooling condition. To emulate realistic application conditions, the target data for the observer contain a normally distributed noise with a mean value of 0 K and a standard deviation of 0.2 K. Figure 6 displays the estimated transient temperatures of the core, the electronics and a terminal, as well as the related temperature deviation Δ*T* of the real-time models. The need for spatial resolution modeling is clearly illustrated by the differences between the local measurement points. At the point of the maximum temperature, differences of up to 4 K are detected. However, there are differences for the modeling approaches and the positions. At high thermal loads, the TECM slightly overestimates the core temperature and underestimates the terminal temperature. For the temperature estimation at the electronics, the dynamic changes in the electronics heat generation in combination with the three representative thermal masses lead to a maximum deviation of 2.7 K for the TECM. The deviation of the electronics results from the lumped representation. Thereby, thermal masses and resistances are based on the initial geometries and material properties. Thus, parameter deviations and contact resistances lead to differences. Corresponding model deviations can be reduced by simple optimization procedures, which is a step towards data-driven models. Overall, the TECM model reveals a good temperature estimation with the highest mean deviation of 0.15 K at the electronics.

The ANN shows in total very small deviations with a maximum difference of −0.67 K at the electronics temperature. The low noise on the deviation also shows that the dynamics of the specific location is represented accordingly. The advantage of the ANN compared to the TECM is due to the training with comparable datasets, which contain the dynamic behavior. For all locations, the mean deviation is below 0.05 K without any static offset or time-dependent drift of the estimation results. Other comparison differences are summarized in Table 3. The overall estimation accuracy of both models is very good within a RMSE of 0.23 K for the TECM and 0.08 K for the ANN. Regarding the computation of the results, the total solving time with the same commercial laptop is 30 s for the ANN model and 60 s for a maximum timestep of 1 s. Thus, both approaches are adequate for real-time estimation with calculation times of 20 ms and 10 ms per timestep. However, the computation time will differ for realistic BEV hardware, which needs to be the focus of future work.

**Figure 6.** Transient temperature profiles of the TECM and the ANN and the related estimation deviation in comparison to the target data of the reference system. The locations of (**a**) the cell core, (**b**) the electronics and (**c**) the terminal.

**Table 3.** Comparison of the TECM and the ANN model for the estimation scenario of Figure 6.


<sup>1</sup> On a commercial laptop with Intel i5 CPU.

In general, physics-based or data-driven approaches can be used for estimation and prediction applications, as outlined in the introduction. Both have proven high accuracy for the challenging task of a large format prismatic cell with electronics. Nevertheless, the general concept of the models offers certain advantages and disadvantages for use. The present ANN is more accurate and provides at least small benefits related to the computation time. However, adequate training datasets must exist for training and parametrization. Additionally, changes in the hardware and materials that have not been part of the training data would generate discrepancies in the estimated results. With the physics-based TECM model hardware changes can be implemented easier or the area of application can be extended. The parametrization does not need multiple datasets for different behavior, but a detailed analysis of corresponding geometries and materials. For example, using the model for thermal runaway investigations can be provided by implementing the corresponding Arrhenius-based heat generation equations above the normal temperature range of 60 °C, as proposed, e.g., in [68]. Since the lumped approach does not represent all physical phenomena, estimation deviations arise with the present model. However, these can be reduced by suitable optimization processes. The use of both models is discussed in the second part of this paper, which describes the implementation of new BTMS functionalities.
