# Deep Learning in the State of Charge Estimation for Li-Ion Batteries of Electric Vehicles: A Review

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## Abstract

**:**

## 1. Introduction

_{curr}is the real-time battery capacity, and C

_{full}is the fully charged state. When the battery is fully charged, the SOC is 100%, and the SOC is 0% when the battery discharge is completed [3]. In the practical application of BMS in EVs, the mathematical presentation of SOC depends on the method of SOC estimation.

## 2. Process of SOC Estimation Using the Deep Learning Method

_{Min}and X

_{Max}are the minimum and maximum values of the variable. After the maximum–minimum normalization, the values of different unit variables are transformed between 0 and 1. Then, the standardized feature data are randomly divided into the training set, validation set, and test set. The training set is used to train a model related to the lithium battery’s SOC with the feature data, the validation set is used to verify whether the parameters of the training set are reasonable to adjust the model parameters, and the test set is used to test the generalization ability of the trained model and can only be used once. The trained model is trained in the selected neural network with the training set, and the model trained by the training set is verified in the validation set to see if the accuracy reaches the highest accuracy, If the desired accuracy is not achieved, you can choose to adjust the parameters of the neural network, and then model training. If necessary, the neural network can also be re-selected for training. If a satisfactory accuracy is achieved, the trained model is tested in the test set to derive the predicted SOC values. The final step is model evaluation; the predicted SOC values are compared with the actual SOC values in the test set using the root mean square error (RMSE), the mean absolute error (MAE), or the mean square error (MSE) to evaluate the model accuracy, and the root mean square error, mean error, and mean square error are shown in Equation (3),

_{pre}is the predicted SOC value through the model based on the deep learning method, and SOC

_{act}is the actual SOC value in the test set. The smaller the error obtained from the above formula, the higher the model accuracy.

## 3. Li-Ion Battery Dataset

## 4. Deep Learning Neural Network Structure in SOC Estimation

#### 4.1. Single Structure

#### 4.1.1. MLP Type—DNN

#### 4.1.2. Convolutional Type—TCN

#### 4.1.3. Recurrent Type—LSTM

_{t}, V

_{t}, I

_{avg}, V

_{avg}”, and the test result was an RMSE of 0.56% and MAE of 0.46% in US06, which was higher than that using only LSTM and GRU in that paper. Wong et al. [70] used the undisclosed ‘UNIBO Power-tools Dataset’ as a training dataset and dataset [51] as a test dataset in the LSTM structure; the input variables were current, voltage, and temperature, and the MAE was 1.17% at 25 °C. Du et al. [71] tested two LR1865SK Li-ion battery cells at room temperature and used the dataset in [45] as the comparative case to test the model trained by LSTM; the input variables were current, voltage, temperature, cycles, energy, power, and time; the MAE was 0.872% at an average level. YANG et al. [72] used the LSTM to build a model for lithium battery SOC estimation; the data were obtained from the A123 18560 lithium battery under three drive cycles, i.e., DST, US06, and FUDS; the input vectors were current, voltage, and temperature. In addition, the model robustness was tested in the unknown initial state of the lithium battery, with the Unscented Kalman Filter [73] (UKF) method for comparison; the test results showed that the RMS of LSTM was significantly smaller than that of UKF.

#### 4.1.4. Recurrent Type—GRU

#### 4.2. Hybrid Structure

#### 4.2.1. 1D-CNN + LSTM

#### 4.2.2. 1D-CNN + GRU + FC

#### 4.2.3. NN + Filter Algorithm

#### 4.3. Trans Structure

#### 4.3.1. Transfer Learning

#### 4.3.2. Transformer

## 5. Evaluation and Future Development

_{avg}: average current, V

_{avg}: average voltage, MAX: maximum error)

**Data**: Due to the different battery types, battery parameters, and battery manufacturers for different electric vehicles, the SOC of the lithium battery that provides power cannot be generalized by a model. The failure and life cycle testing of lithium batteries take a long time and have a significant time cost. Generally, scientific research institutions or colleges and universities conduct battery parameter tests, so the quantity and quality of data obtained are limited. At present, models trained by deep learning can only achieve high accuracy under certain operating conditions or certain temperatures. For a general model, the amount of data is far from enough, and to maximize the utilization ratio of Li-ion cell data, there are some methods that can be used: (1) Time series data augmentation: the Li-ion data can be further augmented because they are the time series data, and several methods can be found in the paper [91], and in the state of charge for the Li-ion battery estimation problem, adding noise is the simple and effective method, which can be found in the paper [89]. (2) Creation of new variables based on original data, which can be created by some variables such as the derivation of voltage, current, and temperature based on voltage, current, and temperature; in addition, variables should be created according to the science of Li-ions. (3) Transfer of the model from the different Li-ion datasets: to improve the precision of SOC estimation, the model can be frozen or fine-tuned in a neural network layer to accomplish the target learning tasks; furthermore, when the amount of data is sufficient, the pre-trained models such as GPT-3 and BERT can be applied to the Li-ion SOC estimation problem.**Computing power**: Most electric vehicles generally have an in-vehicle computing platform with high-cost performance and low computing power and power consumption as the “brain” of the electronic and electrical equipment due to cost or power consumption reasons. To speed up the training, most of the deep learning is currently based on special processing units, such as graphic processing units and tensor processing units. For accelerated operations, however, these special computing units are designed without considering power consumption and cannot be directly used for onboard computing power platforms for electric vehicles. In addition, at present, all lithium battery SOC estimation based on deep learning is to test the battery separately under simulated driving conditions and to conduct offline training according to the obtained data. On-board training is carried out on the data measured by the sensors in the environment.**Interpretability**: Previously, there was no recognized scientific explanation for machine learning in computer science; nowadays, it is only used as a black box. This feature results in a lack of stability and interpretability compared with traditional methods. There is no fixed solution to the situation that does not meet expectations, so it sometimes takes a long time.

## 6. Conclusions

**High-quality data**: Some public lithium battery data sets may not meet the actual needs due to reasons such as models or unexpected situations. From the actual needs, it may be necessary to re-test the lithium battery. In the next step, the SOC test of the lithium battery should be considered. Establishing a set of accepted testing methods or standards, which may be an efficient way to generate high-quality data at scale, can avoid duplication of testing, reduce testing time, and improve data quality.**Computer science**: Most of the existing deep learning-based lithium battery SOC estimation research uses neural networks that have made breakthroughs in the field of computer science as a method to migrate to this problem. In the future, we can focus on breakthrough research results in the field of computer science, which can be studied by referring to relevant theories and algorithms; the relevant science of battery chemistry can be used as a priori knowledge to construct the characteristics related to the state parameters of lithium batteries.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Convolutional Type: (

**a**) 1D-CNN schematic; (

**b**) Dilated causal convolution and residual connection in TCN.

**Figure 6.**Recurrent Type: (

**a**) Recurrent neural network; (

**b**) Long short-term memory neural network; (

**c**) Gated recurrent unit.

**Figure 8.**A case of the NN + filter algorithm architecture diagram (LSTM + AHIF, reprinted with permission from Ref. [81]. Copyright 2021, Elsevier.).

Dataset | Battery | Data | Ambient Temperature | Number of Battery | Refs |
---|---|---|---|---|---|

NASA-PCoE | 2 Ah 18650 | Voltage, Current, Temperature | 43 °C, 4 °C, 4 °C | 34 | [45] |

CALCE | 1.1 Ah, LiCoO_{2}1.5 Ah, LiCoO _{2}1.35 Ah, LiCoO _{2}2.4 Ah, LiFePO _{4}2.23 Ah, LiFePO _{4}2.3 Ah, LNMC | Current, Voltage Charge Capacity, Discharge Capacity, Charge Energy, Discharge Energy, dV/dt | 50 °C, 45 °C, 40 °C, 30 °C, 25 °C, 20 °C, 0 °C, −5 °C, −10 °C, −40 °C | 144 (1.5 Ah, LiCoO_{2}) | [46] |

Toyota–MIT–Stanford | 1.1 Ah, LiFePO_{4} | Temperature, Current, Voltage, Charge, Discharge Capacity, Per-cycle Measurements of Capacity, Internal Resistance, and Charge Time | 30 °C | 124 | [47] |

224 | [48] | ||||

Panasonic 18650PF | 2.9 Ah, NCA Panasonic 18650PF | Voltage, Current, Capacity, Energy, Temperature | 25 °C, 10 °C, 0 °C, −10 °C, −20 °C | 1 | [49] |

Turnigy Graphene | 5 Ah, Turnigy Graphene | Voltage, Current, Time, Power | 40 °C, 25 °C, 10 °C, 0 °C,−10 °C, −20 °C | 1 | [50] |

LG 18650HG2 | 3 Ah, LG HG2 | Voltage, Current, Power, Battery Case Temperature | 1 | [51] | |

IFP-1865140 | 10 Ah, LiFePO_{4} | Voltage, Current, Capacity | 25 °C | 3 | [52] |

IFP-1665130 | Voltage, Current, Time | 4 | [53] |

Neural Network | Refs | Dataset | Input Variables | Error | |
---|---|---|---|---|---|

Single Structure | DNN | [55] | [49] | $V(t),T(t),{I}_{avg}(t),{V}_{avg}(t)$ | MAE: 0.61%, RMSE: 0.78%, MAX (25 °C): 2.38% |

[56] | Undisclosed | $V(t),I(t),T(t)$ | RMSE: 2.0527, MAE: 0.00421 | ||

[57] | [46] | $V(t),I(t),T(t)$ | RMSE: 3.68%, MAE: 0.13% | ||

[58] | Undisclosed | $V(t),I(t),T(t),Time,Condition$ | MSE: 0.0247% | ||

TCN | [63] | [49] | $V(k),I(k),T(k)$ | (25 °C) RMSE: 0.85, MAE: 0.70, MAX (25 °C): 2.96 (−20~25 °C) RMSE: 2.00, MAE: 1.55, MAX (25 °C): 7.63 | |

LSTM | [66] | Undisclosed | $\begin{array}{l}V(t),V(t-1),V(t-2),\\ I(t),I(t-1),I(t-2),\\ SOC(t),SOC(t-1),SOC(t-2)\end{array}$ | RMSE: 0.4127~0.7012 RMSE: 0.4127~0.5476 | |

[67] | [49] | $V(k),I(k),T(k)$ | RMSE: 0.7%, MAE: 0.6%, MAX (25 °C): 2.6% | ||

[68] | [46] | $V,T,{I}_{avg},{V}_{avg}$ | RMSE: 0.45~1.89%, MAE: 0.37~1.48% | ||

[70] | [51], Undisclosed | $V(k),I(k),T(k)$ | RMSE: 1.57~2.89%, MAE: 1.17~2.22% | ||

[71] | [45], Undisclosed | $\begin{array}{l}V(t),I(t),T(t),\\ Cycles,Energy,Power,Time\end{array}$ | RMSE: 0.731~1.860%, MAE: 0.608~1.165% | ||

[72] | Undisclosed | RMSE: 1.07~1.39%, MAE: 0.94~2.45% | |||

GRU | [74] | Undisclosed | $V(k),I(k),T(k)$ | RMSE < 3.5%, MAE < 2.5% | |

[75] | [46] | $V(k),I(k),T(k)$ | RMSE: 0.65%, MAE: 0.46%; RMSE: 0.75%, MAE: 0.52% | ||

[76] | [46] | $V(t),I(t),T(t)$ | RMSE: 0.84~1.08% | ||

[77] | [46] | $V(k),I(k),T(k)$ | RMSE: 0.55~2.45%, MAE: 0.42~1.77% | ||

[78] | Undisclosed | $V(t),I(t),T(t)$ | RMSE < 1.5%, MAE < 0.6% | ||

Hybrid Structure | 1D-CNN + LSTM | [79] | Undisclosed | $V(t),{I}_{}(t),T(t),{I}_{avg}(t),{V}_{avg}(t)$ | RMSE: 0.54~1.38%, MAE: 0.33~0.87% |

1D-CNN + GRU + FC | [80] | Undisclosed | $V(t),I(t),T(t)$ | RMSE: 0.0098~0.0211, MAE: 0.0078~0.0168 | |

LSTM + UKF | [82] | Undisclosed | $V(t),I(t),T(t)$ | RMSE: 0.93%, MAE: 0.82% | |

LSTM + CKF | [83] | Undisclosed | $V(k-1),I(k),T(k),SOC(k)$ | MAE < 2% | |

LSTM + EKF | [84] | [46,49] | $V,I,T,dV$ | RMSE: 0.48% | |

LSTM + AHIF | [81] | Undisclosed | $V(k),I(k),T(k),SOH$ | RMSE: 0.22~1.09%, MAX: 0.89~2%, MAE: 0.21~1.18% | |

Trans Structure | Transfer learning | [85] | [46,49] | $V(t),I(t),T(t)$ | RMSE: 0.49~1.57%, MAE: 0.39~1.32%RMSE: 0.49~1.57%, MAE: 0.39~1.32% |

[86] | [49,50] | $V(k),I(k),T(k)$ | (25 °C) RMSE: 0.36~1.02%, MAE: 0.26~0.61% | ||

Transformer | [89] | [51] | $V(k),I(k),T(k)$ | RMSE: 0.9056%, MAE: 0.4459% | |

[90] | [46] | $I(t)-T(t),V(t)-T(t)$ | (50 °C) RMSE: 0.54%, MAE: 0.49% |

Neural Network | Advantage | Disadvantage | |
---|---|---|---|

Single | DNN | Unlimited data input dimensions | Prone to overfitting and local optimum problems |

1D-CNN | Extraction of time series data features | Lower precision when this is the only method used | |

TCN | Handling of time series data | Lower robustness | |

LSTM | Longer historical time series data can be linked, can alleviate the problem of gradient disappearance and gradient explosion | Many calculation parameters, large capacity storage, and long training time | |

GRU | Fewer computing parameters | Long training time | |

Hybrid | 1D-CNN + X + Y + … | Combining the advantages of multiple neural networks | Relatively complex model |

NN + Filter Algorithm | Merge the advantages of neural network and filter algorithm | Large capacity storage, long process time, and complex structure | |

Trans | Transferlearning | Transfer feature of source data to target data | Hard to know which part can be used as knowledge for transfer in the target learning task. |

Transformer | Achieve the data feature connection | Higher calculation complexity, computing power requirements, and data demand |

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**MDPI and ACS Style**

Zhang, D.; Zhong, C.; Xu, P.; Tian, Y.
Deep Learning in the State of Charge Estimation for Li-Ion Batteries of Electric Vehicles: A Review. *Machines* **2022**, *10*, 912.
https://doi.org/10.3390/machines10100912

**AMA Style**

Zhang D, Zhong C, Xu P, Tian Y.
Deep Learning in the State of Charge Estimation for Li-Ion Batteries of Electric Vehicles: A Review. *Machines*. 2022; 10(10):912.
https://doi.org/10.3390/machines10100912

**Chicago/Turabian Style**

Zhang, Dawei, Chen Zhong, Peijuan Xu, and Yiyang Tian.
2022. "Deep Learning in the State of Charge Estimation for Li-Ion Batteries of Electric Vehicles: A Review" *Machines* 10, no. 10: 912.
https://doi.org/10.3390/machines10100912