# State of Charge Estimation in Lithium-Ion Batteries: A Neural Network Optimization Approach

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## Abstract

**:**

_{2}) and lithium nickel cobalt aluminum oxide (LiNiCoAlO

_{2}) toward SOC estimation under two experimental test conditions: the static discharge test (SDT) and hybrid pulse power characterization (HPPC) test. Also, the accuracy of the proposed method is evaluated under different EV drive cycles and temperature settings. The results show that iFA-based TDNN achieves precise SOC estimation results with a root mean square error (RMSE) below 1%. Besides, the effectiveness and robustness of the proposed approach are validated against uncertainties including noise impacts and aging influences.

## 1. Introduction

#### 1.1. Related Works

#### 1.2. Major Contributions

- The data pre-processing of the proposed iFA-based TDNN algorithm is simple and has easy execution which only requires sensors to monitor the battery variables including voltage, current, and temperature, thereby avoiding the need for an added filter.
- The TDNN has a self-learning algorithm that updates the learning parameters and employs input layer information in the previous time steps to estimate SOC in the future stage. In contrast, the model-based SOC estimation techniques require depth information and knowledge about battery internal characteristics as well as experience and time to develop a battery model and estimate related parameters accurately.
- The traditional TDNN algorithm examines SOC with a trial and error approach to determine the suitable values of input time delay (UTD) and hidden neurons (HNs) [26]. However, the trial and error method has some drawbacks such as inefficiency, data under-fitted, and over-fitted issues. Therefore, the TDNN algorithm is integrated with iFA to avoid the trial and error method and achieve accurate SOC estimation solutions.
- The generalization capability of the iFA-based TDNN algorithm is tested with two dissimilar types of lithium-ion batteries. Moreover, two suitable experimental tests are carried out to validate the proposed algorithm.
- Apart from the experiments, the accuracy of the proposed method is examined using three EV drive cycles such as the dynamic stress test (DST), federal urban drive schedule (FUDS), and US06. Accordingly, the variation of SOC estimation is monitored at three different temperature conditions.
- The influence of electromagnetic interference and low sensor precision might lead to inaccuracy in measured current and voltage values. Thus, this paper considers uncertainty issues such as noise impacts and aging profiles while estimating SOC. The robustness and effectiveness of the iFA-based TDNN method are verified against both bias noise and random noise. The performance of lithium-ion batteries deteriorates after the battery is repeatedly charged and discharged a hundred times. Therefore, the adaptability of the proposed method is assessed under 50, 100, 150, and 200 aging cycles.

## 2. Theoretical Framework of SOC Algorithm

#### 2.1. SOC Modeling with Time Delay Network Algorithm

#### 2.2. Improved Firefly Algorithm

Algorithm 1 Improved Firefly Algorithm (iFA) |

StartDefine the fitness function$f\left(x\right),x={\left({x}_{1},\dots ,{x}_{d}\right)}^{T}$ Create initial population of fireflies$i=1,2,\dots ,Siz{e}_{population}$ |

Assign$\gamma $$\alpha {\beta}_{0}$${L}_{mod}{\sigma}_{1}and{\sigma}_{2}$ |

Assess fitness function of individual fireflies$f\left(x\right),i=1,2,\dots ,Siz{e}_{population}$ |

While$t<Ma{x}_{genertion}$ |

Assess${\mathsf{\xi}}_{seed}$with Equation (14) |

if${\mathsf{\xi}}_{seed}\ge rand$ |

Assess${\beta}_{0}{}^{Proposed}$with Equation (12) |

else |

Assess${\beta}_{0}{}^{Proposed}$with Equation (13) |

end if |

for $i=1:Siz{e}_{population}$for $j=1:Siz{e}_{population}$if $f\left({x}_{j}\right)>f\left({x}_{i}\right)$Move firefly i toward j End ifUpdate the attractiveness of fireflies ($\beta )$ with Equation (10) Assess new solutions and update light intensity with Equation (15) |

end for j |

end for i |

Rank the fireflies and find the current best population |

t = t + 1 |

end while |

## 3. Lithium-Ion Battery Experiments and Data Preparation

#### 3.1. Lithium-Ion Battery Cell

_{2}(LiNCA) and LiNiMnCoO

_{2}(LiNMC), respectively, while the graphite is used as a negative electrode in both batteries. LiNMC is popular due to its extended lifespan, while LiNCA offers a high level of specific energy. Table 1 provides the information and specifications of the two lithium-ion batteries [6].

#### 3.2. Battery Experimental Setup

#### 3.3. Battery Experimental Tests

- (1)
- SDTSDT uses the constant discharge current of the lithium-ion battery to evaluate SOC. The operation of SDT is explained using the steps mentioned below.
- Firstly, a constant current (CC) of 1.3 A (0.5 C) is applied to charge the battery fully until the charge voltage increases to the maximum threshold of 4.2 V.
- Then, a constant voltage (CV) of 4.2 V is applied until a drop in the charge current to 0.13 A (0.05 C) is achieved.
- The battery being tested is kept idle for 1 h.
- A discharge current of 2.6 A (1 C) is applied until the voltage is reduced to 2.75 V.
- The test ends if the battery voltage reaches the minimum threshold of 2.75 V; otherwise, step ii will continue.

- (2)
- HPPC testThe HPPC test consists of the array of charge and discharge current pulses arranged in an orderly manner. The following steps are used to describe the operation of HPPC.
- The CC-CV method is employed to charge the battery completely until the battery current decreases to 0.13 A (0.05 C).
- The battery being tested is kept idle for 1 h.
- A discharge current of 1.3 A (0.5 C) is applied for 10 s.
- The battery being tested is kept idle for 3 min.
- A charge current of 1.3 A (0.5 C) is applied for 10 s.
- The battery is kept idle for 3 min.
- A discharge current of 0.65 A (0.25 C) is applied for 24 min to decrease the SOC capacity of the battery by 10%.
- The experiment ends if the battery voltage reaches the lower cut off voltage; otherwise, step iii will start again.

- (3)
- Noise test

- (4)
- Aging cycle test

- Firstly, the complete charge operation is executed based on the CC-CV method with a constant charge current of 1.3 A (0.5 C) until the battery voltage reaches 4.2 V. After, the charge voltage of 4.2 V is kept constant until the charging current declines to 0.13 A (0.05 C).
- The idle operation of the battery is performed for 15 min.
- A constant discharge current of 2.6 A (1 C) is applied until the battery voltage decreases to 2.75 V.
- The lowest point of the discharge voltage (2.75 V) of the battery is checked. The one aging schedule is completed when the battery reaches a cut-off voltage of 2.75 V; otherwise, step iii will begin again.
- After the completion of one aging cycle, the battery is kept in an idle operation stage for one hour.
- Step i starts again to perform the second aging cycle test. The process continues until the defined cycles are achieved.

#### 3.4. Dataset Training and Testing

#### 3.5. Measurement of SOC Effectiveness

## 4. Design and Implementation of iFA Based TDNN Algorithm for SOC Estimation

#### 4.1. Input Information

#### 4.2. Fitness Function

#### 4.3. Optimization Constraints

#### 4.4. Execution Process of iFA Based TDNN Algorithm

## 5. SOC Experimental Results and Validation

#### 5.1. Assessment of Fitness Function and Optimal Parameter

#### 5.2. Experimental Verification Results

- (1)
- SOC Estimation in LiNCA Battery

- (2)
- SOC Estimation in LiNMC Battery

#### 5.3. SOC Estimation under EV Drive Cycles and Temperatures

#### 5.4. SOC Robustness Validation against Noise Effects

#### 5.5. SOC Robustness Validation against Aging Impacts

#### 5.6. Comparative Validation with the Existing Methods

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The time-delay neural network (TDNN) configuration for state-of-charge (SOC) estimation of the lithium-ion battery.

**Figure 5.**The relationship between SOC and voltage for (

**a**) the LiNCA battery and (

**b**) the LiNMC battery.

**Figure 7.**The response curve for optimization in the SDT load profile of (

**a**) the LiNCA battery and (

**b**) the LiNMC battery.

**Figure 8.**The response curve for optimization in the HPPC load profile of (

**a**) the LiNCA battery and (

**b**) the LiNMC battery.

**Figure 15.**SOC error analysis at 0.01 V/0.1 A bias noise and 0.01 V/ 0.1 A random noise: (

**a**) SDT for the LiNCA battery; (

**b**) SDT for the LiNMC battery; (

**c**) HPPC for the LiNCA battery; and (

**d**) HPPC for the LiNMC battery.

**Figure 17.**Aging performance for the LiNCA battery: (

**a**) SOC estimation under 50 cycles, (

**b**) SOC estimation under 100 cycles, (

**c**) SOC estimation under 150 cycles, and (

**d**) SOC estimation under 200 cycles; (

**e**) SOC error under 50 cycles, (

**f**) SOC error under 100 cycles, (

**g**) SOC error under 150 cycles, and (

**h**) SOC error under 200 cycles.

**Figure 18.**Aging performance for the LiNMC battery: (

**a**) SOC estimation under 50 cycles, (

**b**) SOC estimation under 100 cycles, (

**c**) SOC estimation under 150 cycles, and (

**d**) SOC estimation under 200 cycles; (

**e**) SOC error under 50 cycles, (

**f**) SOC error under 100 cycles, (

**g**) SOC error under 150 cycles, and (

**h**) SOC error under 200 cycles.

Parameters | LiNiCoAlO_{2} | LiNiMnCoO_{2} |
---|---|---|

Nominal capacity (Ah) | 3.2 Ah | 2.6 Ah |

Nominal Voltage (V) | 3.6 | 3.7 |

Min/Max voltage (V) | 2.5/4.2 | 2.75/4.2 |

Charging method | CC-CV | CC-CV |

Charging time (hours) | 4 | 3 |

Charging current (mA) | 1625 | 1300 |

Specific Energy (Wh/kg) | 200–260 | 150–220 |

Weight (g) | 48.5 | 47.0 |

Lifespan (cycles) | 500 | 1000–2000 |

Thermal runaway (temperature) | 150 °C | 210 °C |

Battery Test | Optimal Hyperparameters | LiNCA Battery | LiNMC Battery |
---|---|---|---|

SDT | UTD | 2 | 3 |

HNs | 12 | 15 | |

HPPC | UTD | 4 | 5 |

HNs | 10 | 18 |

SOC Method | BPNN-iFA | RBFNN-iFA | ENN-iFA | TDNN-iFA | ||||
---|---|---|---|---|---|---|---|---|

Load Profile | SDT | HPPC | SDT | HPPC | SDT | HPPC | SDT | HPPC |

RMSE (%) | 0.8620 | 1.4124 | 1.2961 | 2.5155 | 0.7215 | 1.6524 | 0.5844 | 0.8512 |

MSE (%) | 0.0074 | 0.0199 | 0.0168 | 0.0633 | 0.0052 | 0.0273 | 0.0034 | 0.0072 |

MAE (%) | 0.6059 | 0.6659 | 1.1145 | 1.997 | 0.5479 | 1.2294 | 0.2374 | 0.4652 |

MAPE (%) | 3.6939 | 6.2650 | 5.6405 | 10.4826 | 4.2235 | 7.5826 | 2.5864 | 3.5624 |

SD (%) | 0.8610 | 1.1685 | 1.2815 | 2.4878 | 0.6876 | 1.4869 | 0.5841 | 0.8505 |

SOC error bound (%) | [−5.19, 6.45] | [−5.45, 9.98] | [−4.36, 8.89] | [−15.28, 12.32] | [−3.32, 2.26] | [−5.09, 7.17] | [−2.58, 2.05] | [−4.31, 4.73] |

SOC Method | BPNN-iFA | RBFNN-iFA | ENN-iFA | TDNN-iFA | ||||
---|---|---|---|---|---|---|---|---|

Load Profile | SDT | HPPC | SDT | HPPC | SDT | HPPC | SDT | HPPC |

RMSE (%) | 0.7775 | 1.2989 | 1.0576 | 2.1121 | 0.6137 | 1.0272 | 0.3084 | 0.7937 |

MSE (%) | 0.0065 | 0.0169 | 0.0112 | 0.0446 | 0.0038 | 0.0106 | 0.0009 | 0.0063 |

MAE (%) | 0.6091 | 0.4222 | 0.9242 | 1.6669 | 0.4620 | 0.7265 | 0.1452 | 0.3283 |

MAPE (%) | 3.7937 | 7.7595 | 7.1818 | 14.3527 | 4.2617 | 7.2337 | 2.1826 | 5.5247 |

SD (%) | 0.7770 | 1.2982 | 1.0556 | 2.1115 | 0.6123 | 0.9818 | 0.3041 | 0.7940 |

SOC error bound (%) | [−2.94, 3.31] | [−5.47, 15.87] | [−2.97, 5.44] | [−10.87, 6.04] | [−1.62, 3.02] | [−5.24, 8.04] | [−1.18, 1.38] | [−3.32, 4.23] |

Test | Battery | 0.01 V/0.1 A Bias Noise and 0.01 V/0.1 A Random Noise | ||
---|---|---|---|---|

RMSE (%) | MAE (%) | SOC Error (%) | ||

SDT | LiNCA | 0.765 | 0.482 | [−3.9, 4] |

LiNMC | 0.558 | 0.386 | [−2.9, 3.5] | |

HPPC | LiNCA | 1.287 | 0.852 | [−5.2, 6.3] |

LiNMC | 1.112 | 0.728 | [−5.1, 5.8] |

Aging Cycles | Battery | Discharge Capacity (mAh) | Cycle Life (%) |
---|---|---|---|

50 | LiNCA | 3052 | 95.107 |

LiNMC | 2515 | 97.889 | |

100 | LiNCA | 2951 | 91.282 |

LiNMC | 2477 | 97.231 | |

150 | LiNCA | 2850 | 88.629 |

LiNMC | 2460 | 96.931 | |

200 | LiNCA | 2763 | 85.923 |

LiNMC | 2425 | 95.756 |

Aging Cycles | Battery | RMSE (%) | MAE (%) | SOC Error (%) |
---|---|---|---|---|

50 | LiNCA | 0.933 | 0.717 | [−3.4, 6.7] |

LiNMC | 0.821 | 0.623 | [−5.5, 5.7] | |

100 | LiNCA | 1.525 | 0.923 | [−3.6, 7.6] |

LiNMC | 0.864 | 0.685 | [−5.8, 6] | |

150 | LiNCA | 1.878 | 1.338 | [−6.8, 8.8] |

LiNMC | 0.927 | 0.742 | [−6.5, 6.2] | |

200 | LiNCA | 2.614 | 1.785 | [−7.8, 9.9] |

LiNMC | 1.046 | 0.825 | [−6.7, 6.4] |

Ref. | Method | Battery Chemistry | Temperature | Experimental Validation Profile | Error Rate |
---|---|---|---|---|---|

[38] | OCV | 1.1 Ah LiFePO_{4} | 0 °C to 50 °C at an interval of 10 °C | DST, FUDS | RMSE 5% |

[39] | CC | 2.3 Ah Lithium-ion cell | Room temperature | C-rates Charging-discharging current | MAE 1.905% |

[40] | UKF | 24 Ah LiNMC | Room temperature at 25 °C ± 2 °C | 1 C SDT | MAE 2.56% Max SOC error 5.36% |

[41] | H∞ Filter | 2.4 Ah Lithium-ion cell | Constant temperature | 1 C SDT | MAE 3.96% |

[42] | UPF | 10 Ah LiFePO_{4} | −20 °C~50 °C | EV operation condition | RMSE 2.05% |

[43] | RLS | 90 Ah LiFePO_{4} | −10 °C~50 °C | Urban EV drive cycle | RMSE 2.3% MAE 1.8% |

[44] | SMO | 5 Ah Lithium polymer battery | Room temperature | 1 C SDT | RMSE 1.8% |

[45] | PIO | 90 Ah Lithium-ion cells | 0 °C, 25 °C, 40 °C | DST | RMSE 1.2% |

Proposed Method | 3.2 Ah LiNCA | Room Temperature | 1 C SDT, HPPC | MAE 0.2374% (SDT) MAE 0.4612% (HPPC) | |

2.6 Ah LiNMC | MAE 0.1452% (SDT) MAE 0.3283% (HPPC) | ||||

2.0 Ah LiNCA | 0 °C, 25 °C, 45 °C | DST, FUDS, US06 | RMSE < 1% MAE < 0.8% |

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Hossain Lipu, M.S.; Hannan, M.A.; Hussain, A.; Ayob, A.; Saad, M.H.M.; Muttaqi, K.M.
State of Charge Estimation in Lithium-Ion Batteries: A Neural Network Optimization Approach. *Electronics* **2020**, *9*, 1546.
https://doi.org/10.3390/electronics9091546

**AMA Style**

Hossain Lipu MS, Hannan MA, Hussain A, Ayob A, Saad MHM, Muttaqi KM.
State of Charge Estimation in Lithium-Ion Batteries: A Neural Network Optimization Approach. *Electronics*. 2020; 9(9):1546.
https://doi.org/10.3390/electronics9091546

**Chicago/Turabian Style**

Hossain Lipu, M. S., M. A. Hannan, Aini Hussain, Afida Ayob, Mohamad H. M. Saad, and Kashem M. Muttaqi.
2020. "State of Charge Estimation in Lithium-Ion Batteries: A Neural Network Optimization Approach" *Electronics* 9, no. 9: 1546.
https://doi.org/10.3390/electronics9091546