# Implementation of Battery Digital Twin: Approach, Functionalities and Benefits

^{1}

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## Abstract

**:**

## 1. Introduction

**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.

- Limited use cases and implementation results available to learn from others;
- No clear guidance on how much to budget;
- Difficult to know where to start to get value quickly;
- Initiatives that are misleadingly branded as “Digital Twin”;
- Limited know-how.

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

- Some articles only mentioned battery DTs as a possible application
- Some of them did not explain the architecture to support battery DTs
- Others were only theoretical articles.

- Battery DT influence on life cycle phases;
- Current BMS functionalities.

**usage**are characterized by cost, specific energy (Wh kg

^{−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].

**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.

**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].

**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.**

## 3. Approach

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

- Electrical model (ECM);
- Electrochemical model (P2D);
- Thermal model;
- Mechanical model;
- Interdisciplinary combined model.

- Battery dynamics represented by the model
- Number of parameters
- Computation time
- Accuracy
- Ease of understanding and complexity for implementation.

#### Experimental Parameter Identification Techniques

**parameter**refers to the characteristic of the battery, including chemical (solid-phase conductivity, diffusion coefficients, etc.) and electric quantities (internal resistance, capacitance, etc.), while the term

**state**refers to the variables which illustrate the behavior of the battery such as SOC and SOH.

_{exp}and V

_{sim}are the experimental and simulated cell output voltage with the same input current, N is the total number of input current data samples, and i is the time index, L is a representation of the RMS error.

#### 3.2. Step 2: Impact Analysis of Real-World Charge/Discharge Cycles on Battery Model Parameter

_{age}), cycle number (N), temperature, SOC, DOD, cycle bandwidth (ΔSOC), charge voltage, C-rate, cycle frequency. Expected parameter changes reviewed in the reference paper and further published literature is depicted in Table 2. Knowing the factors that affect the battery life during cycling is essential to design a DT model that evolves along with the degradation of the actual battery. Hence, the model parameters which are directly and most largely affected by the cycling of the battery system are identified.

#### 3.3. Step 3: Model Parameter-Update Estimation

- Calculate the model parameters at the end of N cycles, and repeat the update process iteratively. Identify the reduced set of parameters (such as in Table 1) directly influenced by the number of cycles and operating conditions. The initial conditions (from the governing equations) of the model are certainly updated. Thus, new parameters set and initial conditions are available to the model for its next simulation (N cycles). For DFN, the mathematical estimations of parameters mainly involves revaluating the governing equations which employs Fick’s law of diffusion, charge and mass conservation, concentrated solution theory and Butler-Volmer electrochemical kinetic expression.
- Calculate the rate of degradation physics caused by lithium plating and SEI growth through the reaction equations and rate expressions [62]. Lithium-plating passive film layers formed by consuming of cyclable Li-ions is influenced by the charge transfer mechanism. The rate of SEI formation reaction is affected by mass transport within the anode and by surface kinetics. Effects of degradation physics are integrated in the model after every N cycles.
- Utilize the fast minimization algorithms such as Gauss-Newton method, prediction error minimization by estimating the parameter-update through synthetic experimental data [63]. Synthetic experimental data can be obtained using simulated battery output with computer-generated randomness. However, this method has an unjustified validation scheme because the input would also be simulated; hence this approach is mainly beneficial for initial testing purposes of the battery DT.
- Apply data-driven parameter identification methods estimation which employs the terminal voltage and load current for parameter update (partially applied in [64]). A comprehensive literature survey of the data-driven parameter identification methods is not conducted. Therefore, this paper does not attempt to review the data-driven parameter identification methods thoroughly. Instead, we choose to review if data-driven approaches can support the parameter-update step. There is no doubt that a large amount of training data (collected at the beginning of life) is a requirement for data-driven parameter-update during usage. Nonetheless, the cost and computation time of the data-driven algorithms [65,66] for application in battery DT need to be compared.

**parameter**estimation algorithms, the gaps between the currently used battery models and the proposed battery DT are as follows; (1) Availability of cycling data to the battery model; (2) Model parameter-update method that does not entirely rely on experimental inputs, but instead on the charge/discharge characteristics and environmental data. Nevertheless, the

**state**estimation algorithms would inherently remain the same in both battery model and DT.

#### 3.4. Step 4: Adaptive Model Update

#### 3.5. Step 5: Battery DT KPI Quantification

- Investment
- ◦
- Effect on optimization cost due to battery DT functionalities.
- ◦
- Cost to establish data acquisition from BMS to the battery model. Here, we assume the preexisting cost of sensors installed on the BMS and the cells.
- ◦
- Cost of data storage method, i.e., cloud server, memory drive, etc.
- ◦
- Computational cost of simulating the algorithms of the battery DT.

- Time
- ◦
- Time needed for the state estimation algorithms, optimization algorithms and other battery DT functionalities
- ◦
- Time to retrieve battery data from its application and assign it to the DT
- ◦
- Speed of battery DT alignment with actual battery, i.e., total time for executing the parameter-update step.

- Accuracy
- ◦
- Accuracy of parameter identification.
- ◦
- Accuracy of parameter-update estimation parameter identification.
- ◦
- Accuracy of state estimation

- Functionalities
- ◦
- DT functionalities that support the battery designers (battery design optimization)
- ◦
- DT functionalities that support the battery users
- ◦
- DT functionalities that support the battery EoL handler (RUL assessment)

## 4. Results

^{−1}], current collector density [kg m

^{−3}], current collector specific heat capacity [J· kg

^{−1}K

^{−1}], current collector thermal conductivity [W m

^{−1}K

^{−1}], nominal cell capacity [A.h], current function [A], electrode properties, and interfacial reactions.

## 5. Discussion

- Level of fidelity expected from a battery DT—A model that captures the electrical, thermal, electrochemical, mechanical and aging aspects of a battery is deemed a high fidelity model. The reality and practicality of such a model are not clear. The cost and time needed for an exhaustive high-fidelity battery DT are high, and the estimate of accuracy improvement is also missing;
- Number of DTs across the battery lifecycle—The idea of a DT across the lifecycle of a product is not entirely understood. This is due to the uncertainty of the number of DTs needed in such cases. Either there is one DT with a large capacity, or there are many small-sized DTs coupled together. For battery DT, the coupling of process and product DT is a possible use case during manufacturing;
- Scaling the battery DT to module and pack-level DT—Achieving battery DTs at scale will require a reduction in technical barriers for their adoption. This implies that for a pack-level battery DT, the number of sensors and the amount of data retrieved will drastically increase. Hence, the data acquisition and storage needs to be seamless;
- Accuracy of behavioral prediction using battery DT—For commercial utilization of battery DTs, it is necessary to compare and quantify the accuracy of existing BMS predictions vs. the prediction of battery DT. Quantification and comparison of percentage error in DT estimations should be the primary focus in future works.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

DFN Model | Derived through | Governing Equations ^{1} |
---|---|---|

Solid phase mass transport equation—Li^{+} concentration in electrodes and separator | Fick’s law of diffusion | $\frac{\partial {c}_{s}\left(x,r,t\right)}{\partial t}=\frac{{D}_{s}}{{r}^{2}}\frac{\partial}{\partial r}\left({r}^{2}\frac{\partial {c}_{s}\left(x,r,t\right)}{\partial r}\right)$ |

Liquid phase mass transport equation—Li^{+} concentration in electrolyte | Conservation of Li+ ions (Conservation of mass) | ${\epsilon}_{e}\frac{\partial {c}_{e}\left(x,t\right)}{\partial t}=\frac{\partial}{\partial x}\left({D}_{e}^{eff}\frac{\partial {c}_{e}\left(x,t\right)}{\partial x}\right)+\left(1-{t}_{+}^{0}\right){A}_{s}j\left(x,t\right)$ |

Solid phase charge transport equation—Potential in electrode | Ohm’s law (Conservation of charge) | $\frac{\partial}{\partial x}\left({\sigma}^{eff}\frac{\partial {\varphi}_{s}\left(x,t\right)}{\partial x}\right)-{A}_{s}Fj\left(x,t\right)=0$ |

Liquid phase charge transport equation—Potential in electrolyte | Ohm’s law and Kirchhoff’s law (Concentrated solution theory, conservation of charge) | $\frac{\partial}{\partial x}\left({\kappa}^{eff}\frac{\partial {\varphi}_{e}\left(x,t\right)}{\partial x}\right)+\frac{\partial}{\partial x}\left({\kappa}_{D}^{eff}\frac{\partial \mathrm{ln}\left({c}_{e}\left(x,t\right)\right)}{\partial x}\right)+{A}_{s}Fj\left(x,t\right)=0$ |

Flux density between solid and liquid phase | Butler-Volmer Equation | $j={k}_{0}{c}_{e}^{1-\alpha}{\left({c}_{s,max}-{c}_{s,e}\right)}^{1-\alpha}{\text{}c}_{s,e}^{\alpha}\left(\mathrm{exp}\left(\frac{\left(1-\alpha )F\right)}{RT}\eta \right)-\mathrm{exp}\left(-\frac{\alpha F}{RT}\eta \right)\right)$ |

^{1}Concentration of lithium in the solid phase ${c}_{s}$(x, r, t) and electrolyte ${c}_{e}$(x,t). Electric potential in the solid phase ϕ

_{s}(x,t) and electrolyte ϕ

_{e}(x,t). Flux density between solid phase and electrolyte j(x,t). Remaining symbols are described in Table 1.

**Table A2.**Equations of ECM model in the time domain for pulse current [72].

ECM Model Equations | Variables |
---|---|

p_{i} = f_{i}(SOC, SOH, T, I)p _{1} = {V_{OCV}, R_{1}, C_{1}, R_{S}} | i is the i-th parameter of the model. R_{1} and C_{1} are the polarization resistance and capacitance and R_{S} is the ohmic resistance. V_{OCV} is the open circuit voltage |

V_{t} = V_{OCV} − V_{1} − V_{Rs}; V_{Rs} = I * R_{S} | where V_{Rs} refers to the voltage reduction from R_{s} and V_{t} is the terminal voltage |

SOC = SOC_{0} − ${{\displaystyle \int}}_{0}^{t}\frac{{I}_{b}}{C}dt$ | SOC calculation using CC, where C is capacity, I_{b} is current, and SOC_{0} is the initial SOC |

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

**Figure 4.**DFN model discharge results with different preconditions. Fully charged—code statement (2). Complete discharge and slow charge—code statement (3).

Reference | Implementation Method ^{1} | DT Functionality |
---|---|---|

[21] | HI and LSTM algorithm | Estimation of battery’s actual discharge capacity |

[22] | Cloud BMS with AEHF-based SOC estimation algorithm and PSO-based SOH estimation algorithm | Estimation of SOC, SOH, capacity fade, power fade |

[23] | On-board diagnosis to cloud environment; ECM model parameter fitting, curve fitting and SOC-OCV curve | SOC, capacity, internal resistance, SOH-R, SOH-C |

[24] | Visual software in LabVIEW; ECM with SVM and filter algorithms | DT platform for spacecraft lithium-ion battery pack degradation assessment; SOC estimation |

[25] | Cloud connected BMS; electric-thermal model and empirical ageing model | Cell voltage and temperature |

[26] | ECM and EFK algorithm | SOC estimation |

[27] | Review paper on battery DT | Battery DT framework and its cyber-physical elements |

[28] | Offline—Regression model using sparse-Proper Generalized Decomposition (s-PGD); Online—Dynamic Mode Decomposition technique | Cell voltage, anode/cathode bulk SOC, anode/cathode surface SOC |

[29] | Linking reduced order model with ECM in Ansys Twin Builder | Real-time temperature of the battery pack at different locations; What-if scenarios for root cause analysis |

^{1}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.

**Table 2.**Impact analysis of model parameters vs. battery degradation factors based on [48,54,55]. Legend for the table:

**x**—impact identified in the reference article, but the impact level is not specified;

**C**—Constants;

**Text**—impact level identified by the reference article;

**Blank (-)**—No direct information found on the sensitivity or dependency for this parameter.

Parameters | Symbol (Unit) ^{1} | High Cycle Number | High C-Rate |
---|---|---|---|

DFN | |||

Thickness | L_{p}, L_{n}, L_{s} (µm) | x [55] | Moderate [55] |

Surface area | A_{p}, A_{n}, A_{s}, (m^{2}) | x [48] | Moderate [55] |

Particle radius | R_{p}^{+}, R_{p}^{−} (µm) | x [54] | x [54] |

Active/Inactive material volume fraction | ε_{s}^{p}, ε_{s}^{n} | x [55] | Moderate [55] |

Electrolyte phase volume fraction | ε_{e}^{p}; ε_{e}^{n} | - | - |

Maximum Li^{+} concentration | c_{s}^{p,n,se} (mol cm^{−3}) | x [48] | Moderate [55] |

Average electrolyte concentration | c_{e} (mol cm^{−3}) | - | x [48] |

Stoichiometry of n, p at 0% and 100% SOC | x_{p,n}^{0,100} | - | - |

Diffusion coefficient in solid and liquid phase | D_{s}^{p}, D_{s}^{n}, D_{e} (m^{2} s^{−1}) | x [54] | - |

Solid phase conductivity | σ_{s}^{p}, σ_{s}^{n} (µm) | x [48] | x [48] |

Li transference number | t_{+}^{0} | Not sensitive [54] | Not sensitive [54] |

Resistivity of film layers (including SEI) | R_{f} (Ω) | Not significant [54] | x [48] |

Negative electrode potential, U− coefficients | - | x [48] | - |

Positive electrode potential, U+, coefficients | - | x [48] | - |

Open circuit potential | V | x [48] | - |

Overpotential | η | Not significant [55] | - |

Reaction flux at the solid particle surface | j (mol cm^{−1} s^{−1}) | - | - |

Exchange (electrolyte and solid) current density | i_{e} (A cm^{−2}) | - | - |

Electrolyte activity coefficient | ±f | C | C |

Bruggeman porosity exponent | p | C | C |

Anodic/Cathodic charge transfer coefficient | α_{a}, α_{c} | C | C |

Intercalation/deintercalation reaction-rate coefficient | k_{n,p} (A cm^{2.5} mol^{−1.5}) | C | C |

Universal gas constant | R | C | C |

Absolute temperature | T | C | C |

Faraday’s constant | F | C | C |

ECM | |||

Internal ohmic resistance | R_{O} (Ω) | Sensitive [56] | Sensitive [56] |

OCV | V_{OCV} (V) | ||

Polarization Resistances | R_{1}, R_{2}… (Ω) | ||

Polarization Capacitances | C_{1}, C_{2}… (F) | ||

Coulomb efficiency | η | Almost constant [57] | Sensitive [57] |

Hysteresis voltage, hysteresis decaying factor | H (V), k | Not significant [58] | Impact of overvoltage [59] |

^{1}n = Negative electrode; p = Positive electrode; se = Separator; s = Solid phase; e = liquid phase.

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**MDPI and ACS Style**

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

**AMA Style**

Singh S, Weeber M, Birke KP.
Implementation of Battery Digital Twin: Approach, Functionalities and Benefits. *Batteries*. 2021; 7(4):78.
https://doi.org/10.3390/batteries7040078

**Chicago/Turabian Style**

Singh, Soumya, Max Weeber, and Kai Peter Birke.
2021. "Implementation of Battery Digital Twin: Approach, Functionalities and Benefits" *Batteries* 7, no. 4: 78.
https://doi.org/10.3390/batteries7040078