# Estimate e-Golf Battery State Using Diagnostic Data and a Digital Twin

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions. A regulation by the European Parliament and Council in 2019 reduced the limit for CO

_{2}emissions by a vehicle fleet to 95 g/km [1], and this trend will go on. To comply with legislation, it is even more important for original equipment manufacturers (OEM) to produce emission-free or low-emission vehicles, such as battery electric vehicle (BEV) or hybrid electric vehicle (HEV).

## 2. Technical Background

#### 2.1. Methods of Battery State Estimation

#### 2.1.1. State of Charge

#### 2.1.2. State of Health

#### 2.1.3. Assess Methods for This Work

#### 2.2. OBD-II Interface

#### 2.3. Digital Twin System

#### 2.4. Battery System of the VW e-Golf

## 3. Goal and Innovation of This Work

- Digital battery twin: Working towards a digital battery twin, the use case of automotive battery pack online parameter estimation is of crucial importance. Therefore, we want to build on the digital twin paradigm in this work and define an architecture that shapes a modular, cloud-based digital twin. To date, no detailed reference architecture for a digital battery twin in this use case can be found in literature, however, online estimation methods have already been developed, for example, in Karger et al. [28] or Baumann et al. [23].
- State estimation using OBD data: Using battery state estimation as a use case, we want to achieve a cell-individual assessment of the battery system. Being able to apply this method to electric vehicles in use, we want to rely on diagnostic data, which come with certain limitations concerning sample rate and availability. Only limited edge processing can be done in the vehicle, such as decoding the diagnostic data. The novel approach presented here utilizes only standard uds-diagnostic queries to gather data from the whole battery system. Coping with the limited data quality, the most suitable state estimation methods are chosen to be implemented and tested.
- Holistic implementation: Using real driving cycles, we implement and test the chosen methods integrated into the twin system. We develop a pipeline from the car to the cloud, and finally to the user display.

## 4. Method

#### 4.1. Diagnostic Interface: Reverse Engineering

#### 4.2. Diagnostic Interface: Data Acquisition

#### 4.2.1. Test Kit

#### 4.2.2. Rotation System

#### 4.2.3. Data Logger

#### 4.2.4. Transfer to Cloud

#### 4.3. Analysis

#### 4.3.1. Estimating Capacity

_{c}) can be determined as Shen et al. [30] proposes in Equation (3).

#### 4.3.2. Estimating Resistance

_{r}), we use a three-step method. First, we estimate the up-to-date internal resistance at specific environmental conditions. Second, from a set of internal resistances at varying environmental conditions, we generate one model for the ${R}_{i}$ per cell. Third, we evaluate this model and use the result to determine the SOH

_{r}using Equation (4).

## 5. Results

#### 5.1. Data Collected

#### 5.2. Reverse Engineering and Data Logging

#### 5.3. On the Capacity

_{c}of 93.7%. This method is also applicable to the individual cells. To estimate the SOC of the cells, their OCV characteristics need to be known. For this work, we use a lithium nickel manganese cobald oxid (NMC) OCV characteristic of similar-sized cells because we do not have access to the actual characteristics of the built-in cells.

_{c}of 96.4%) and for cell 7750 we get 70 Ah (SOH

_{c}of 93.3%).

#### 5.4. On the Internal Resistance

_{r}from the resistances, the samples for each cell are fitted again over the temperature and SOC range of their instant of recording. Figure 12 shows fits for cell 7744 and 7750, scoring a RMSE of $0.19$ m$\mathrm{\Omega}$ and $0.23$ m$\mathrm{\Omega}$ respectively. The ${R}_{i,ref}$ at the reference point of cell 7744 is $2.1$ m$\mathrm{\Omega}$ with a confidence bandwidth of 2.0m$\mathrm{\Omega}$–2.2m$\mathrm{\Omega}$. Cell 7750 exhibits a ${R}_{i,ref}$ of $3.3$ m$\mathrm{\Omega}$ with a confidence band of 3.1m$\mathrm{\Omega}$–3.4m$\mathrm{\Omega}$. The orange, x-shaped data points in the upper part of Figure 11 refer to the evaluation of this curve fit at the reference point of 18 ${}^{\circ}\mathrm{C}$ and an SOC of 60 %. This reference point was chosen because most data points were recorded in this area, which gives the highest validity. Figure 13 shows the distribution of data points of cell 7744. We can see that most data are available around the chosen reference point.

_{r}based on the internal resistance can now be calculated. The lower part of Figure 11 shows the SOH

_{r}for all cells. Negative values or values close to zero SOH

_{r}occur because we set the ${R}_{eol}$ at 60% increase of ${R}_{bol}$. Other sources allow for a 200% increase [37], which would increase all SOH

_{r}. The average SOH

_{r}calculated from the cells is 64.3%. This result cannot be compared to the SOH

_{c}value, since there is no relationship between the chosen boundary resistances ${R}_{eol}$, ${R}_{bol}$ and the capacity. The right side of Figure 11 shows the kde of both the resistance and the SOH

_{r}. Because SOH

_{r}results from the resistances, the densities follow the same shape. The average SOH

_{r}is 60.7% at a standard deviation of 29.8%.

#### 5.5. Architecture of the Digital Twin Used

_{s}) and access the database directly.

_{r}and SOH

_{c}and places these characteristics back in the twins database.

_{c}and SOH

_{r}are listed as well as capacity and the current temperature. The lower half of the front end shows the cell-individual SOH

_{c}and SOH

_{r}. By grouping all the cells into modules, and coloring them according to their SOH, the status can be evaluated and interpreted by humans at first glance.

## 6. Discussion

#### 6.1. State Estimation Using Diagnostic Data

_{r}, an initial ${R}_{i,initial}$ has to be known. For the test case given, we do not have this kind of ${R}_{i,initial}$ for every cell, since we only started observing the car in the middle of its life. This makes it hard to calculate a meaningful SOH

_{r}for the individual cells. Still, one could estimate a relative change in SOH

_{r}from this point on. Using the average values of the battery packs from the INL tests and scaling them to cell level, we neglect the cell-individual ${R}_{i,initial}$. In the future, when digital twins of battery systems are widely established, one could use end-of-line tests of manufacturing lines to estimate a meaningful initial state of the battery system and its cells. Also, a complete state estimation from the first moment on could close this gap.

_{r}and SOH

_{c}for both, cell 7750 appears worse than cell 7744 in both metrics. Other cells show non-coherent behavior; one explanation for this may be the lack of data, especially when it comes to different environmental conditions or load profiles. When only one third the number of data points is used, the confidence interval width rises from $0.2$ m$\mathrm{\Omega}$ to $0.3$ m$\mathrm{\Omega}$ for cell 7744 and from $0.3$ m$\mathrm{\Omega}$ to $0.5$ m$\mathrm{\Omega}$ for cell 7750.

#### 6.2. Digital Twin Architecture

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SOH_{r} | State of health (Resistance) |

SOH_{c} | State of health (Capacity) |

SOH | State of Health |

SAAS | Software as a service |

IAAS | Infrastructure as a service |

paas | Platform as a service |

API | Application programming interface |

API | Application programming interfaces |

dod | Depth of discharge |

INL | Idaho National Laboratory |

uds | Unified diagnostic services |

OCV | Open circuit voltage |

ECM | Equivalent circuit model |

AWS | Amazon Web Services |

OBD | On-board diagnosis |

SOC | State of charge |

EOL | End of life |

BOL | Begin of life |

RMSE | Root mean squared error |

isotp | ISO 15765-2 Transport protocol for automotive bus systems |

gnss | Global navigation satellite system |

MQTT | Message queuing telemetry transport |

iot | Internet of things |

kde | Kernel density estimation |

OEM | Original equipment manufacturers |

BEV | Battery electric vehicle |

HEV | Hybrid electric vehicle |

bms | Battery management system |

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**Figure 1.**Setup for data acquisition (green: test kit, black OBD logger) and reverse engineering wiring (blue).

**Figure 2.**The measurement cycle for one cell is made up of three phases. One-shot measurements enclose the time series of one specific cell voltage and current measurement.

**Figure 3.**Toolchain to acquire and process the OBD data in a cloud-based digital twin and display on a web front end.

**Figure 4.**Used ECM containing two RC elements and a SOC-dependant OCV. All parameters in the schema are estimated using least-squares method. ${V}_{k}$ and the current serve as reference for the fit.

**Figure 5.**Charging measurement of all cells in the vehicle. Due to cell rotation, we record each cell once every 250 s. We can see that in the lower SOC region deviations are highest.

**Figure 6.**(

**Left side**): All e-Golf cells with their start and end voltage of the charging process, sorted by the start voltage. (

**Right side**): Histogram of the start voltages. The distribution is skewed to the right, indicating a surplus of cells with lower depth of discharge (dod).

**Figure 8.**The inferred resistances of all cells as indicated by the color, plotted over the environmental variables SOC and temperature.

**Figure 9.**Example fitting result of one 30 s cycle measurement. A RMSE of $1.23$ mV indicates a good model fit with the original data. Positive currents correspond to a discharge of the battery.

**Figure 10.**Internal resistance for cell 7744 and 7750 over the temperature. As expected, lower temperatures yield to higher impedance.

**Figure 11.**(

**Top**): Internal resistance of all cells. The raw values are the average values of all samples passed through the ECM. The model data are the results of the ECM fitted over SOC and temperature, and evaluated at 18 ${}^{\circ}\mathrm{C}$ and a SOC of 60%. (

**Bottom**): SOH

_{r}of the cells. The SOH

_{r}cannot be compared to the SOH

_{c}. Reference for SOH

_{r}: $SO{H}_{r}=0$ at 60% increase of ${R}_{bol}$. On the right side, we show the kernel density estimation (kde) of the internal resistance and the resulting SOH

_{r}.

**Figure 12.**Curve fit of all samples of cell 7744 and 7750 over temperature and SOC. The SOC-axis is modeled by a polynomial and the temperature axis is modeled by an exponential relationship as Equation (2) shows. The reference point ${R}_{i}$ is marked in yellow.

**Figure 14.**Architecture of the digital twin system. For this work, the system was hosted in the AWS cloud. Individual twins share the same resources as models, aggregators and APIs. In the upper part, the front end shows the results to the user. In total, 88 cell-blocks consisting of three parallelly connected cells can be observed.

**Table 1.**Suitability of the methods for determining the state of health via the on board diagnosis (OBD) interface during real operation.

Method | Used | Comment |
---|---|---|

State of charge | ||

Circuit principle methods | Yes | Using OCV in reverse discharge test |

Filter methods | Yes | No parametrized model. Fit-model-corrected OCV-method used |

Data-driven methods | No | Not enough data for learning |

State of health | ||

Discharge test | Yes | Ampere counting used for capacity estimation |

Measurement of quiescent voltage characteristic | No | No measurement of quiescent charac. possible |

Internal resistance method | Yes | Estimate ${R}_{i}$ using ECM fit |

Impedance spectroscopy | No | No online suitability |

Chemical analysis | No | Can’t destroy cells |

Model-based methods | No | Neither model of stress factors nor data available |

Measurement of intracellular pressure | No | No online suitability |

**Table 2.**UDS IDs for the used labels and factors to convert raw measurements ot physically meaningful values. These IDs can be queried from the battery management controller.

Signal | UDS ID | Calculation | Description |
---|---|---|---|

HV current | 0x1E3D | value$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}0.25$ | Current through the battery pack |

HV voltage | 0x1E3B | value$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}0.25$ | Voltage of the battery pack |

HV temperature | 0x2A0B | value$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\frac{1}{64}$ | Temperature of the battery pack |

SOC | 0x028C | value$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\frac{1}{2.5}$ | SOC of the battery pack |

Voltage cell 1 | 0x1E40 | value$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}0.25$ | This is the base address for the cell voltages. Increment for following cells. |

Any tuple can be recorded at an approx. 5 Hz to 9 Hz rate. |

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## Share and Cite

**MDPI and ACS Style**

Merkle, L.; Pöthig, M.; Schmid, F.
Estimate e-Golf Battery State Using Diagnostic Data and a Digital Twin. *Batteries* **2021**, *7*, 15.
https://doi.org/10.3390/batteries7010015

**AMA Style**

Merkle L, Pöthig M, Schmid F.
Estimate e-Golf Battery State Using Diagnostic Data and a Digital Twin. *Batteries*. 2021; 7(1):15.
https://doi.org/10.3390/batteries7010015

**Chicago/Turabian Style**

Merkle, Lukas, Michael Pöthig, and Florian Schmid.
2021. "Estimate e-Golf Battery State Using Diagnostic Data and a Digital Twin" *Batteries* 7, no. 1: 15.
https://doi.org/10.3390/batteries7010015