**2. Battery DT Functionalities during Operation and End-of-Life**

The number of literature specific to DTs has increased drastically in the last decade [8,18]. The topic is explored in various domains, such as product optimization, production planning/control, layout planning, maintenance, or product lifecycle. However, a microscopic look into the implementation of product DT, i.e., battery DTs has become prevalent since the past decade with increased utilization of IoT devices, CPS, and cloud-based services. Sometimes battery model implementation learns from real-time operational data to evaluate the battery states but is not necessarily defined as a battery DT [19]. So, is it crucial to even understand if a model is, in fact, a DT? Generally, at the initial stage of product development, it is not an essential requirement. However, at the business level i.e., in order to draw profits and innovation in the existing business model, a DT can facilitate effective R&D.

In the context of battery systems, it is uncertain whether battery DT insinuates a single cell DT, module-level DT, or pack-level DT. Currently, DTs are the result of custom technical solutions that are difficult to scale [20]. The scalability of battery DTs depends on the extrapolation of cell behavior through physical, physics-based, or data-driven battery models. For this purpose, the term battery DT referred to in this paper implies the DT of a battery cell. However, module and pack-level battery DTs are worth pursuing in the later stages.

The literature review in this paper takes only those published literature into account, which consists of practical implementations of battery DTs with defined DT-functionalities and implementation methods. The focus is on reviewing the latest literature on DTs concerning applications in the battery industry, published in the past 5 years (starting from 2016 to 2021). With Google Scholar as the research literature database and the following logical expression of keywords: ("digital twin") AND ("battery") AND ("lithium-ion"), updates until July 2021, the total number of resulting articles were 392 (39 google scholar pages), among which several articles had to be excluded due to the following reasons:


However, in combination with advanced search for the keywords ("battery digital twin") or ("digital twin" AND "battery") in the title, the literature was filtered down to 9 articles. As a result, Table 1 elaborates the available literature, their reported method of DT implementation, and the corresponding DT functionality.


**Table 1.** Literature review of DT-implementations relevant for battery system.

<sup>1</sup> HI—Health Indicator; LSTM—Long Short-Term Memory; BMS—Battery Management System; AEHF—adaptive extended H-infinity filter; PSO—Particle Swarm Optimization; SOC—State of Charge; SOH—State of Health; OCV—Open Circuit Voltage; ECM—Equivalent Circuit Model; EKF—Extended Kalman Filter; SVM—Support Vector Machines.

While some of the references identified in Table 1 are pioneering attempts to map real-time battery data to the battery models through cloud services, the others have yet again used simulated driving cycle data to validate the state estimation algorithms. This procedure of using drive cycle simulations such as WLTP (Worldwide Harmonized Light Duty Vehicles Test Procedure) or UDDS (Urban Dynamometer Driving Schedule) for validation of battery state estimation algorithms is a state of the art state estimation approach [30]. Nevertheless, this is not ideal for designing battery DT because simulated driving cycles can only validate the algorithm accuracy of static models while battery DTs are dynamic. Additionally, a common observation among all the DT functionalities in Table 1 is that they all have approximately the same output, i.e., SOC, SOH, internal resistance, or capacity. Evaluation of the battery state through these output variables has already been an established requirement from electrical models, electric-thermal models, electrochemical models, and until recently, data-driven (or NN) battery models. In this context, it is worth noting the conundrums that this raises regarding the argument about the need for a battery DT only for performing state estimations. Other than the fact that if implemented correctly, a battery DT should deliver those output variables to the users, developers or testers in real-time, there are no significant utilities that only a battery DT can implement. So, what additional value-add does a battery DT contribute? In an attempt to answer this, the following 2 aspects are now elaborated:


To achieve competitiveness with the internal combustion engine, the key requirement for battery development is high driving ranges, low-charging times, and low battery pack cost. The performance indicators of batteries during **usage** are characterized by cost, specific energy (Wh kg<sup>−</sup>1), energy density (Wh L−1), specific power (W kg−1), and power density (W L−1), and charging time (=fast charging ability) [31]. While a DT cannot take the responsibility of improving the energy density or specific power of a battery, it can significantly aid the design optimization process and EoL assessment process. Sensing the battery data and uploading that to a storage server gives the opportunity to easily access the battery data and create learning models, which directly guide the **product design, and optimization process** [27]. The battery data storage platform stores the design and usage history, which supports **behavioral integration in consequent life cycle phases** and simplifies the **prediction of the remaining useful life** (RUL) during operation and also at EoL for second life assessment [32].

The **Battery Management System (BMS)** is the central element for protecting, monitoring, and controlling the battery-powered system by ensuring safety, efficiency, and reliability [33]. BMS measurements are performed for cell voltages, pack current, pack voltage, and pack temperature and it usually uses these measurements to estimate SOC, SOH, DOD (Depth of Discharge) [34]. Battery DT requires the onboard-BMS to work together with the battery data storage platform.

The potential functionalities of a battery DT in combination with an onboard-BMS are identified in the literature. Identifying the stress factors from the time-series measurement data and calculating its effect on the model parameters facilitates **evaluating battery aging indicators** during operation [25]. Besides, the model update integrated with the charging data enables a battery DT to maximize the optimization objective and select the best parameters for an **optimal charging strategy** such as multi-stage constant current charging, pulse charging, multi-stage constant heat charging and AC charging [35]. Similarly, **thermal management** based on battery DT relies on prediction of aging effect of temperature distribution across the battery pack using thermal models. Detection and traceability of sensor faults, electrical faults, and thermal runaway in a battery DT can allow integration of **fault diagnosis** procedure of the BMS with the battery DT functionalities [32].

In order to identify the functionalities and potentially the value add of a battery DT, the above discussion is encapsulated in Figure 1. The **black circle** lists the functionalities of a BMS, taken from the datasheets of two commercial BMSs found in [36,37]. The extended **blue block** lists the battery DT outputs taken from Table 1. These are the applied battery DT functionalities. Lastly, the **green block** lists the potential DT functionalities identified from the literature (as highlighted above). Thus, Figure 1 compares the **existing BMS functionalities with the applied battery DT functionalities and the potential battery DT functionalities.**

The BMS functionalities taken from the referenced datasheets are to monitor the current and temperature sensors. It uses programmed settings to control the current flow into and out of the battery pack by broadcasting the charge and discharge current limits, cell balancing, and monitoring each cell tap to ensure that cell voltages are not too high or too low. Using the programmed values in the battery pack profile, the BMS calculates the pack and individual cell's internal resistance (SOH) and OCV. Current sensor data is used to calculate the battery pack's SOC (via coulomb counting CC).

**Figure 1.** Comparison of BMS functionalities with the applied battery DT and the potential battery DT functionalities.

The SOC estimation method in the studied BMSs is CC. Literature shows alternative methods with higher estimation accuracy, such as adaptive EKF, impedance method, fuzzy logics, SVM, hybrid method (EKF combined with ANN) [38–40]. Here a DT can complement the current BMS functionalities by applying estimation algorithms with higher accuracy. Moreover, the main functionality of the BMS is to ensure that the battery stays with its specified limits. It takes immediate measurements to analyze the voltage and temperature of the cell to estimate the SOC. It does not consider the degradation effect of the charge/discharge cycles on the battery from an electrochemical perspective. The immediate battery user may not be interested in understanding the degradation effects of the battery, such as loss of lithium, diffusivity of electrolyte or SEI resistivity at the anode. However, for deeper knowledge and future innovations by the battery designers, this would serve as a stepping-stone towards ensuring that the battery lasts until its maximum possible capacity and optimal performance. Hence, a DT can complement the functionalities of a BMS by taking the load for large computation requirements. BMS diagnostics over a long period can be enhanced and even simplified by using a DT.

To sum up, the added value that battery DTs can offer is improved representation, performance estimation, behavioral predictions, optimization strategies, and integration of battery life cycle attributes to the remaining DT functions.

## **3. Approach**

In this section, an approach for implementing a battery DT is introduced. The purpose is to define a functional procedure to move from battery model to battery DT systematically. Figure 2 illustrates the 5-step approach, and each step is then further elaborated. By piecing together the existing methodologies of battery modeling, model parameter estimation, battery state prediction, the efforts needed for implementing a battery DT will be investigated.

**Figure 2.** Approach for battery DT implementation.

*3.1. Step 1: Lightweight or Heavyweight Battery Model Development*

The first step to implement a battery DT is inevitably the development of a reliable battery model. Battery models have become an essential tool in battery-powered applications, which are safety and performance-critical. Depending on how the model inputs and outputs are related, battery models can be classified as empirical, semi-empirical, physical and, data-driven [41,42], while the different types of battery models are:


Fast and accurate identification of the BMS model parameters is a vision for battery developers and engineers. With the outlook of computational expense, the battery model types can be differentiated as either lightweight battery models or heavyweight battery models. Based on [43], the factors which differentiate between the two are as follows:


We limit discussion to only electrochemical and electrical models for this paper. As a lightweight model, ECM of a battery is relatively easy to scale to the module or pack level and is widely used in BMS algorithms. They are derived from the empirical measurements of external characteristics of the cell [44]. However, by observing only the external behavior of the battery, the internal electrochemical dynamics cannot be entirely represented, and it is challenging to provide insights into electrochemical or life-reduction phenomena occurring inside the battery. Additionally, ECMs are developed based on data obtained from specific operating conditions of the target batteries, and their accuracy abruptly decreases while performing calculations on other operating conditions or if the battery is replaced [45].

As heavyweight models, the electrochemical models mainly fall into two categories, single particle model or pseudo two-dimensional (P2D) model (also known as the Doyle-Fuller-Newman—DFN model). DFN model for lithium-ion batteries use the combination of the porous electrode theory and the concentrated solution theory [46]. Compared to ECM, which has less physically relevant parameters, a DFN model contains a large number of parameters with a physical meaning. It calculates electrical, chemical, and electrochemical phenomena occurring inside the battery to predict its performance and lifespan Hence, DFN models provide the opportunity for a deep understanding of lithium-ion batteries' aging mechanisms, accurately predicting battery performance by considering the material characteristics and the electrode design.
