**1. Introduction**

Digital Twin (DT) is a virtual dynamic model of a system, process, or service, with real-world data interactions that facilitate improved system analysis and comprehensive representation [1]. NASA defined DT as an integrated multi-physics, multi-scale simulation of a system that uses the best available physical models, sensor data, and historical data to mirror the life of its physical twin [2]. The applications of DT are: (1) to simulate the behavior of the physical twin before its usage, where even without the benefit of continuous sensor updates, the DT can study the effects of various parameters, determine the various anomalies and validate the degradation mitigation strategies; (2) to simulate the system behavior during operation, through the continuous update of actual load, temperature, and other environmental factors, as input to the models, enabling continuous predictions for the physical twin; (3) to perform diagnostics in the event of a fault or damage; (4) to serve as a platform where the effects of parameter modifications, not considered during the design phase, can be studied. In practice, DT implementation involves allocating realworld data to the virtual model or platform. Boschert et al. [3] identified that simulation would become the primary tool for decision support once a DT is fully integrated. Likewise, Kunath et al. [4] summarized the three main functions of a DT: Prediction—execution of studies ahead of the system run; Safety—monitoring and control of the system state in terms

**Citation:** Singh, S.; Weeber, M.; Birke, K.P. Implementation of Battery Digital Twin: Approach, Functionalities and Benefits. *Batteries* **2021**, *7*, 78. https://doi.org/10.3390/ batteries7040078

Academic Editors: Carlos Ziebert and Seung-Wan Song

Received: 30 July 2021 Accepted: 15 November 2021 Published: 16 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**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/).

of a continuous prediction during the system run; Diagnosis—analysis of unpredicted disturbances during the system run.

By definition, a **model** is a simplified abstraction of the structure or processes that define a real system. In that sense, models do not aim to replicate the original system in intensive detail [5]. The idea of moving a digital model closer to the real system is in fact a basic rationale for building computer models. Some models are extreme simplifications of the real system, while some are much closer to the real system, through multiscale simulations and interdisciplinary collaborations. The difference between a DT and a simulation model has been discussed previously [1,6], but it is essential to address the features that qualify a model as a DT: (1) model of the product—physical or data-driven; (2) evolving set of real-world data about/related to the product; (3) method of adjusting the model in accordance with the data. According to [7], the DT evaluation framework consists of four metrics, autonomy, intelligence, learning, and fidelity.

Some articles [8,9] describe seemingly similar concepts to DTs, such as digital shadow, virtual model, product avatar and digital thread, but they do not necessarily indicate the complete concept of DT, but rather fragments of overlapping functions. DT implementation is often mapped to IoT (Internet of Things) devices and CPS (Cyber-Physical Systems) [10,11], due to its high dependence on a compatible mode of data acquisition. A DT can have single or multiple stakeholders and may make use of 3D simulations, IoT devices, 4G and 5G networks, blockchain, edge computing, cloud computing, and artificial intelligence. Depending on the complexity, a DT may have access to past and present operational data along with predictive capabilities.

A multitude of literature [12,13] has been published, defining and characterizing the concept of DT in a variety of domains. However, missing from the literature is a consistent view on what the DT is and how the concept is helping to meet the challenges of the many use-cases to which it is being associated as a solution approach [14]. Some articles [15–17] suggest the methodologies, frameworks, and interpretation of DT for specific use cases. While this may help understand the system boundaries, it also leads to inconsistent ideas of the requirements of DT implementation and thus generating the risk of diluting the concept. The potential costs, infrastructure challenges, clarity of return on investments for product/process DT are not transparent. Without substantial effort to describe and quantify the DT benefits, it is challenging even to suggest that the concept itself may be the most appropriate solution to the challenges faced by each particular industry [14].

DT is generally perceived with the core idea that it is a model that can replicate the behavior of an existing system through the acquisition of real system data. This highlights the importance and completeness of the phrase "replicate the behavior". To which extent is the replication satisfactory? DTs at first may appear to be a replica but replicating every behavioral aspect might not necessarily be realistic. For example, in battery DTs, it is unnecessary to digitally replicate each of the molecular, fluid, and structural behavior of each cell component. DTs need not attempt to mirror everything about the original system [5]. Hence, the reality of an exhaustive high-fidelity DT, which replicates every aspect of the physical system and maximizes services while minimizing expense and technical difficulty of implementation, is ambiguous. The level of model fidelity, cost, and effort for implementation is subject to limitations which will vary depending on the use case and its applications. Furthermore, the idea of DTs across the lifecycle is not yet fully understood. The number of DTs required across the entire lifecycle, or the transitions and interactions between the software components of the DT are yet to be explored.

Therefore, the stakeholders in industries or academia looking to invest in or develop a DT face the following challenges:


The hypothesis that DT would be a driver for product lifecycle management and smart manufacturing in the future needs to be tested. This paper is a part of an ongoing study that investigates the DT functionalities and quantifies the DT attributes across the life cycle phases of a battery system. Essentially, the pressing question is whether battery DT is a practical and realistic solution to meeting the growing challenges of the battery industry, such as degradation evaluation, usage optimization, manufacturing inconsistencies, second-life application possibility, etc. Within the scope of this paper, the concept of DT will be explicitly explored for battery cells and the functionalities it can offer during the operation and end-of-life (EoL) phases. Research on battery DT has already gained much popularity, and with this paper, we aim to provide a consistent approach to DT implementation for battery cells. In doing so, we identify the efforts for implementing a battery DT. The contributions of this paper are as follows: (1) literature-analysis of the potential functionalities of a battery DT during operation and EoL; (2) battery DT implementation approach; (3) KPIs (Key Performance Indicators) to quantify the valueadd of battery DTs; (4) testing the main functions of the implementation approach on a DFN model.

This paper is structured as follows: Section 2 reviews past literature followed by a discussion about battery DT functionalities during operation and EoL. Section 3 outlines the approach of battery DT implementation with subsections elaborating each step. Section 4 demonstrates the results of the application of the described approach in Python. Lastly, Sections 5 and 6 is a discussion of the contributions of the paper and its future scope.
