**1. Introduction**

The performance of lithium ion batteries (LIBs) is strongly dependent on the cell temperature, particularly with regard to battery aging and safety issues. With low temperatures there is a risk of lithium plating due to reduced reaction kinetics, which results in decreased lithium availability. However, operating LIBs at a high temperature can cause a rise in undesirable side reactions that cause rapid degradation, including capacity and power loss [1]. Furthermore, there is a risk of material decomposition which can trigger a so-called thermal runaway and may lead to self-ignition and even an explosion [2]. High temperature issues are caused by cell-internal heat generation, and low temperature operation is generated due to environmental temperatures.

There are various temperature indication methods in existence. Raijmakers et al. provided a broad overview on various temperature indication methods for LIBs [3]. The most common approach uses a conventional temperature sensor, such as a thermocouple or thermistor, placed on the housing of the cell. However, the core temperature varies widely from the surface temperature in cases of heavy loading, and the temperature rise can only be detected with a time-shift or requires extensive thermal models [4–6]. Moreover, the accuracy varies with thermal contact and the position of the temperature sensor. In addition, in most cases not every cell is equipped with a sensor, and therefore the pack design needs to be considered to detect feasible hot spots [7]. Thus, a thermal runaway can only be detected stochastically [2]. By placing temperature sensors internally, these

**Citation:** Ströbel, M.; Pross-Brakhage, J.; Kopp, M.; Birke, K.P. Impedance Based Temperature Estimation of Lithium Ion Cells Using Artificial Neural Networks. *Batteries* **2021**, *7*, 85. https://doi.org/10.3390/ batteries7040085

Academic Editor: Catia Arbizzani

Received: 31 July 2021 Accepted: 8 December 2021 Published: 12 December 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/).

problems can be avoided. This might lead to an increase in costs, more complexity for manufacturers and possible negative effects in terms of battery life [1,8].

The impedance based methods have gained substantial interest because of their characteristic of measuring the average internal temperature without using internal or external hardware [9]. Therefore, the method is also known as sensorless temperature measurement. Figure 1 clarifies the temperature's strong dependency on the battery's characteristic impedance response. Additionally, with increased temperature, a significant reduction in impedance response can be observed. Such measurements were conducted by the authors. EIS measurements were performed on Samsung INR18650-15L cells at different temperatures. Details about the experimental process are described in Section 2.1.

**Figure 1.** Nyquist plot for 3 Samsung INR18650-15L1 cells at different temperatures from 0 to 60 ◦C.

The impedance can also be detected in other battery states, such as the state of health with respect to nominal capacity (*C*/*C*N, SoHC) and the state of charge (SoC); therefore, those other states can be crucial input variables for battery management systems [3,10]. In Figure 2 the progression of the impedance for different cycles and three different cells are presented, and it points out the continuous increase in impedance with over the lifecycle. Details about the experimental process are described in Section 2.1. However, it is important to distinguish the various influence factors from each other and find the optimal basis for predictions [11–14].

Srinivasan et al. were the first to find the relation between impedance at a specific frequency and the temperature—more precisely, the phase shift at a frequency that is associated with the solid electrolyte interface [12]. Contrarily, Schmidt et al. made use of the real part of the impedance measurement at higher frequencies, because the time constant has a significantly lower level of correlation with the SoC, which enables improved temperature estimation at unknown SoCs [11]. Similarly, Richardson et al. analyzed the influence of internal thermal gradients on the impedance. It can be shown that this technique estimates the volume-average temperature and is therefore able to detect internal hotspots without any time delays [8].

**Figure 2.** Nyquist plot for 3 Samsung INR18650-15L1 cells after 100, 200, 300, 400, and 500 cycles.

Most publications in this field either show a correlation between a measurable value (e.g., impedance) and the state of interest (e.g., SoC or temperature), or present the state estimation results for a single cell. The state estimation of a number of cells of the same cell type is more complicated due to the existence of variations among individual cells. In this case it is crucial to select the required input parameters. Several studies have raised concerns regarding the question of finding the optimum input variable for determining the temperature. Beelen et al. compared some of these approaches and performed a sensitivity analysis to optimize the prediction accuracy [15]. In the case of an unknown SoC, the achieved average bias was ±0.4 K with an average standard deviation of ±0.7 K. The study highlights the importance of selecting the appropriate input parameters for temperature determination.

This study investigates an approach using ANNs, which are promising for handling multidimensional feature problems. The procedure can be automated and can be easily transferred to other cell chemistries. There are only a few studies available which present data based temperature estimation methods using artificial neural networks. Feng et al. combined the advantages of physical models with artificial neural networks to enhance the performance for estimating the SoC and temperature [16]. Hasan et al. estimated cell temperature based on a nonlinear, autoregressive exogenous artificial neural network and time series data, namely, current and ambient temperature for a battery container [17]. However, there are a number of studies that present ANN based methods for estimating the SoC and SoH [18–21]. Khumprom et al. confirmed ANNs' ability to approximate a nonlinear system by comparing a deep ANN against other machine learning algorithms for SoH prediction; the former could either match or outweigh the other algorithms' performances [22]. Furthermore, some researchers have used impedance data in combination with ANNs. Messing et al. used impedance data for equivalent circuit parameterization and input data for the ANN [23]. However most approaches use methods which require a lot of computational effort due to the need for solving partial differential equations and the fitting of physical models or time series.

For this study, we chose an approach using impedance data from directly measurable indicators (voltage, current, time) as input data and linking impedance based temperature estimation with ANNs. The implied advantage is that error-prone parameterization may be dispensed with. Since it is necessary to monitor the voltage of a lithium ion cell constantly, it should be possible to perform a four-point measurement on each cell by using an AC current source in the battery system to create the EIS spectra. Our main focus

lies in demonstrating the technical feasibility of this concept. In contrast to many other publications, the state estimation was not performed for a single cell but for a number of cells. We show that it is possible to train an ANN with data from a number of cells to estimate the temperatures of other cells of the same cell type. An advantage of the EIS-ANN method is that once the ANN is trained, the temperature estimation is completed within milliseconds since there is no need to solve partial differential equations. In addition, a perspective is given on the possibility of utilizing this method of impedance based state estimation using ANNs to estimate the SoC and the SoHC.

In Section 2, we describe the data acquisition and the architecture of the ANN. In Section 3 we present the results of the temperature, SoC and SoHC estimations and discuss the limitations of the ANN method.
