# A Comparative Study on the Parameter Identification of an Equivalent Circuit Model for an Li-ion Battery Based on Different Discharge Tests

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## Abstract

**:**

## 1. Introduction

## 2. Experiment

## 3. Battery Model and Parameter Identification

_{oc}), internal resistance (R

_{s}) and two RC loop circuits. The OCV is considered as the voltage source, the internal resistance represents the ohmic resistance, and the polarization resistance (R

_{1}, R

_{2}) and polarization capacitance (C

_{1}, C

_{2}) in the RC circuits describe the dynamic characteristic of the Li-ion battery. The voltages V

_{s}, V

_{1}, V

_{2}are the voltages across R

_{s}, C

_{1}, C

_{2}, respectively.

_{L}is the load current with a negative value for charging and positive value for discharge.

_{s}, R

_{1}, R

_{2}, C

_{1}, C

_{2}) for the second-order RC equivalent circuit using MLR, ECF, SDOT estimators. Different parameter estimators have different strengths, varying in complexity and accuracy. Therefore, we chose these three methods because each of them has a different strength: (i) MLR is the statistical method, which is widely used to find the variable relationship; (ii) ECF has a simple algorithm compared to the others; and (iii) SDOT offers high accuracy, but requires a heavy computation burden. The details for each estimator are explained in the following subsection.

#### 3.1. Multiple Linear Regression (MLR)

_{i}) and one dependent variable (y). The equation for multiple linear regression with n observations has the following form:

_{oc}, was estimated from the voltage before each discharge cycle and the internal resistance, R

_{s}

_{,}was calculated (see Figure 3)

_{10}, V

_{20}are the unknown parameters related to the model parameters R

_{1}, R

_{2}, C

_{1}, C

_{2}by

_{10}, V

_{20}from the MLR method, the model parameters can be determined.

#### 3.2. Exponential Curve Fitting (ECF)

_{oc}− R

_{s}I

_{L}, b = I

_{L}R

_{1}, c = R

_{1}C

_{1}, d = I

_{L}R

_{2}and e = R

_{2}C

_{2}. Similar to the MLR method, the open-circuit voltage, V

_{oc}, and the internal resistance, R

_{s}, can be defined from the voltage response of the pulse test. The coefficients a, b, c, d and e were calculated by using the curve fitting tool in Matlab.

#### 3.3. Simulink Design Optimization Tool (SDOT)

_{s}, R

_{1}, R

_{2}, C

_{1}, C

_{2}) were tuned until the estimated voltage was in good agreement with the measured voltage. The optimization method used here was the nonlinear least square function presented as the following equation:

## 4. Results and Discussion

#### 4.1. Pulse Discharge Test

#### 4.1.1. Pulse Discharge Test

#### 4.1.2. Constant Current Discharge Test

#### 4.1.3. Dynamic Discharge Tests for EVs

#### 4.2. Identify the Model Parameters

_{s}, R

_{1}, R

_{2}, C

_{1}, C

_{2}) parameters for ECM, the OCV for each SOC is calculated based on the pulse test experiment. The estimated model parameters obtained from MLR, ECF and SDOT are shown in Figure 9. The internal resistance, R

_{s}, parameter of MLR and ECF are exactly the same, because both are calculated using the voltage response from the pulse test data, but SDOT has a different scheme. This is the reason why the estimated parameters from SDOT are different. The resistance, R

_{s}and R

_{1}, tends to increase at low SOC (0–30%). For the polarization parameters, the large increase in the polarization resistance (R

_{i}) observed in SDOT can be compensated by the decrease in the polarization capacitance (C

_{i}) and vice versa. For example, the large value of R

_{2}at 80% SOC or the significant decrease in ${R}_{1}$ at 10% SOC are compensated by a small value of C

_{2}or a large capacitance, C

_{1}, respectively. One interesting point is that all the parameters are nearly constant in between 30–60% SOC, but a dramatic change is observed at 0–30% SOC and 70–100% SOC when the nonlinearity behavior is dominated in the OCV–SOC relationship. The estimated terminal voltage of the battery for the pulse test and its relative error are demonstrated in Figure 10. The relative error is a difference between the simulation and experiment. It is found that the predictions fit very well with the experimental data, especially in the case of SDOT. The relative error is almost zero; a large error is observed only at a low SOC (less than 10% SOC).

#### 4.3. Simulated Terminal Voltage for the Dynamic Discharge Tests

_{i}is the measured voltage and ${\widehat{V}}_{i}$ is the estimated voltage.

- For the pulse test, the MAE (RMSE) of the predicted voltage is 12.8 (31.5), 12.2 (27.9) and 4.2 (10.1) mV for MLR, ECF and SDOT, respectively. The errors of SDOT are around three times less than the other two methods, but it took a longer time to calculate.
- For the CC test, the MAEs of the three methods are comparable (19.1 mV(MLR) 20.2 mV(ECF) 21.9 mV(SDOT)), but the RMSE value of SDOT is obviously higher than the others (34.2 mV(MLR) 35.3 mV(ECF) 47.8 mV(SDOT)). This excess RMSE of SDOT is caused by a large error between the calculated and measured voltages at a low SOC when the nonlinearity is dominated (see Figure 10).
- The results under the dynamic ISO and WLTP discharge tests have a similar tendency. The SDOT is the best method providing the smallest error, followed by the MLR and ECF estimations, respectively. As can be seen in the figure, MLR and SDOT produce a comparable error, for example, the MAE for ISO is 6.1 mV (4.5 mV) and WLTP is 11.4 mV (10.2 mV) for MLR (SDOT).

## 5. Conclusions

_{s}, R

_{1}, R

_{2}, C

_{1}, C

_{2}). SDOT provides the best fit in the battery voltage of the pulse test. Using the estimated parameters, the CC discharge test, ISO and WLTP profiles were simulated and compared to the experimental response. For the CC discharge test, the simulation fits very well with the experiment, except at a low SOC when the OCV–SOC relationship exhibits the nonlinear characteristic. Additionally, it is found that the MAE of three estimators under the CC discharge test is comparable. This means that under the constant current usage, such as electronic device application, the identification is not the important key. The MLR and ECF are less complicated than SDOT, but can provide the same accuracy as SDOT. The situation is different in EV discharge tests (ISO and WLTP), in which the SDOT offers the best fit with a small margin of error compared to MLR and ECF. The MAE and RSME of ECF are twice as high as SDOT, in the case of the ISO procedure. However, the higher the accuracy, the heavier the computation burden. Calculations using SDOT took a long time, so it is probably not suitable for EV application. In contrast, MLR calculation is faster and is not complicated. Although the accuracy of MLR is lower than that of SDOT, it can be improved by increasing the rest time between pulses or reducing the SOC step, as these two parameters can affect the OCV approximation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Böttiger, M.; Paulitschke, M.; Bocklisch, T. Systematic Experimental Pulse Test Investigation for Parameter Identification of an Equivalent Based Lithium-Ion Battery Model. Energy Procedia
**2017**, 135, 337–346. [Google Scholar] [CrossRef] - Masoudinejad, M. Open-Loop Dynamic Modeling of Low-Budget Batteries with Low-Power Loads. Batteries
**2020**, 6, 50. [Google Scholar] [CrossRef] - Yong, J.Y.; Ramachandaramurthy, V.K.; Tan, K.M.; Mithulananthan, N. A Review on the State-of-the-Art Technologies of Electric Vehicle, Its Impacts and Prospects. Renew. Sustain. Energy Rev.
**2015**, 49, 365–385. [Google Scholar] [CrossRef] - Cuma, M.U.; Koroglu, T. A Comprehensive Review on Estimation Strategies Used in Hybrid and Battery Electric Vehicles. Renew. Sustain. Energy Rev.
**2015**, 42, 517–531. [Google Scholar] [CrossRef] - Mayer, B.; Schier, M.; Friedrich, H.E. Stand-Alone Battery Thermal Management for Fast Charging of Electric Two Wheelers—Integrated Busbar Cooling. World Electr. Veh. J.
**2019**, 10, 37. [Google Scholar] [CrossRef] [Green Version] - Wei, P.; Fan, M.Q.; Chen, H.C.; Yang, X.R.; Wu, H.M.; Chen, J.; Li, T.; Zeng, L.W.; Li, C.M.; Ju, Q.J.; et al. Enhanced Cycle Performance of Hollow Polyaniline Sphere/Sulfur Composite in Comparison with Pure Sulfur for Lithium–Sulfur Batteries. Renew. Energy
**2016**, 86, 148–153. [Google Scholar] [CrossRef] - Ruiz, V.; Pfrang, A.; Kriston, A.; Omar, N.; Van den Bossche, P.; Boon-Brett, L. A Review of International Abuse Testing Standards and Regulations for Lithium Ion Batteries in Electric and Hybrid Electric Vehicles. Renew. Sustain. Energy Rev.
**2018**, 81, 1427–1452. [Google Scholar] [CrossRef] - Madani, S.; Schaltz, E.; Knudsen Kær, S. An Electrical Equivalent Circuit Model of a Lithium Titanate Oxide Battery. Batteries
**2019**, 5, 31. [Google Scholar] [CrossRef] [Green Version] - Baczyńska, A.; Niewiadomski, W.; Gonçalves, A.; Almeida, P.; Luís, R. Li-NMC Batteries Model Evaluation with Experimental Data for Electric Vehicle Application. Batteries
**2018**, 4, 11. [Google Scholar] [CrossRef] [Green Version] - Meng, J.; Stroe, D.-I.; Ricco, M.; Luo, G.; Teodorescu, R. A Simplified Model-Based State-of-Charge Estimation Approach for Lithium-Ion Battery with Dynamic Linear Model. IEEE Trans. Ind. Electron.
**2019**, 66, 7717–7727. [Google Scholar] [CrossRef] [Green Version] - Jiang, J.; Liang, Y.; Ju, Q.; Zhang, L.; Zhang, W.; Zhang, C. An Equivalent Circuit Model for Lithium-Sulfur Batteries. Energy Procedia
**2017**, 105, 3533–3538. [Google Scholar] [CrossRef] - Lu, L.; Han, X.; Li, J.; Hua, J.; Ouyang, M. A Review on the Key Issues for Lithium-Ion Battery Management in Electric Vehicles. J. Power Sources
**2013**, 226, 272–288. [Google Scholar] [CrossRef] - Technologies in Battery Management System—A Review. Available online: http://www.ijstr.org/final-print/feb2020/Technologies-In-Battery-Management-System-a-Review.pdf (accessed on 6 February 2022).
- Li, X.; Li, J.; Xu, L.; Ouyang, M.; Han, X.; Lu, L.; Lin, C. Online Management of Lithium-Ion Battery Based on Time-Triggered Controller Area Network for Fuel-Cell Hybrid Vehicle Applications. J. Power Sources
**2010**, 195, 3338–3343. [Google Scholar] [CrossRef] - Yang, N.; Zhang, X.; Li, G. State of Charge Estimation for Pulse Discharge of a LiFePO4 Battery by a Revised Ah Counting. Electrochim. Acta
**2015**, 151, 63–71. [Google Scholar] [CrossRef] - How, D.N.T.; Hannan, M.A.; Hossain Lipu, M.S.; Ker, P.J. State of Charge Estimation for Lithium-Ion Batteries Using Model-Based and Data-Driven Methods: A Review. IEEE Access
**2019**, 7, 136116. [Google Scholar] [CrossRef] - Yang, F.; Li, W.; Li, C.; Miao, Q. State-of-Charge Estimation of Lithium-Ion Batteries Based on Gated Recurrent Neural Network. Energy
**2019**, 175, 66–75. [Google Scholar] [CrossRef] - Chen, L.; Wang, Z.; Lu, Z.; Li, J.; Ji, B.; Wei, H.; Pan, H. A Novel State-of-Charge Estimation Method of Lithium-Ion Batteries Combining the Grey Model and Genetic Algorithms. IEEE Trans. Power Electron.
**2018**, 33, 8797–8807. [Google Scholar] [CrossRef] [Green Version] - Chandran, V.; Patil, C.K.; Karthick, A.; Ganeshaperumal, D.; Rahim, R.; Ghosh, A. State of Charge Estimation of Lithium-Ion Battery for Electric Vehicles Using Machine Learning Algorithms. World Electr. Veh. J.
**2021**, 12, 38. [Google Scholar] [CrossRef] - Klein, R.; Chaturvedi, N.A.; Christensen, J.; Ahmed, J.; Findeisen, R.; Kojic, A. Electrochemical Model Based Observer Design for a Lithium-Ion Battery. IEEE Trans. Control Syst. Technol.
**2013**, 21, 289–301. [Google Scholar] [CrossRef] - Zhang, X.; Lu, J.; Yuan, S.; Yang, J.; Zhou, X. A Novel Method for Identification of Lithium-Ion Battery Equivalent Circuit Model Parameters Considering Electrochemical Properties. J. Power Sources
**2017**, 345, 21–29. [Google Scholar] [CrossRef] - Zhou, Y.; Huang, M. On-Board Capacity Estimation of Lithium-Ion Batteries Based on Charge Phase. J. Electr. Eng. Technol.
**2018**, 13, 733–741. [Google Scholar] - Uddin, K.; Perera, S.; Widanage, W.; Marco, J. Characterising Li-Ion Battery Degradation through the Identification of Perturbations in Electrochemical Battery Models. World Electr. Veh. J.
**2015**, 7, 76–84. [Google Scholar] [CrossRef] [Green Version] - Wang, J.; Zhang, L.; Xu, D.; Zhang, P.; Zhang, G. A Simplified Fractional Order Equivalent Circuit Model and Adaptive Online Parameter Identification Method for Lithium-Ion Batteries. Math. Probl. Eng.
**2019**, 2019, 6019236. [Google Scholar] [CrossRef] - Zhang, Q.; Shang, Y.; Li, Y.; Cui, N.; Duan, B.; Zhang, C. A Novel Fractional Variable-Order Equivalent Circuit Model and Parameter Identification of Electric Vehicle Li-Ion Batteries. ISA Trans.
**2020**, 97, 448–457. [Google Scholar] [CrossRef] - He, H.; Xiong, R.; Guo, H.; Li, S. Comparison Study on the Battery Models Used for the Energy Management of Batteries in Electric Vehicles. Energy Convers. Manag.
**2012**, 64, 113–121. [Google Scholar] [CrossRef] - Zhang, J.; Wang, P.; Liu, Y.; Cheng, Z. Variable-Order Equivalent Circuit Modeling and State of Charge Estimation of Lithium-Ion Battery Based on Electrochemical Impedance Spectroscopy. Energies
**2021**, 14, 769. [Google Scholar] [CrossRef] - De Sutter, L.; Nikolian, A.; Timmermans, J.-M.; Omar, N.; Van Mierlo, J. Online Multi Chemistry SoC Estimation Technique Using Data Driven Battery Model Parameter Estimation. World Electr. Veh. J.
**2018**, 9, 16. [Google Scholar] [CrossRef] [Green Version] - Vilsen, S.B.; Stroe, D.-I. Battery State-of-Health Modelling by Multiple Linear Regression. J. Clean. Prod.
**2021**, 290, 125700. [Google Scholar] [CrossRef] - Zhang, R.; Xia, B.; Li, B.; Cao, L.; Lai, Y.; Zheng, W.; Wang, H.; Wang, W.; Wang, M. A Study on the Open Circuit Voltage and State of Charge Characterization of High Capacity Lithium-Ion Battery under Different Temperature. Energies
**2018**, 11, 2408. [Google Scholar] [CrossRef] [Green Version] - Tudoroiu, R.-E.; Zaheeruddin, M.; Tudoroiu, N.; Radu, S.-M. SOC Estimation of a Rechargeable Li-Ion Battery Used in Fuel Cell Hybrid Electric Vehicles—Comparative Study of Accuracy and Robustness Performance Based on Statistical Criteria. Part II: SOC Estimators. Batteries
**2020**, 6, 41. [Google Scholar] [CrossRef] - Wen, F.; Duan, B.; Zhang, C.; Zhu, R.; Shang, Y.; Zhang, J. High-Accuracy Parameter Identification Method for Equivalent-Circuit Models of Lithium-Ion Batteries Based on the Stochastic Theory Response Reconstruction. Electronics
**2019**, 8, 834. [Google Scholar] [CrossRef] [Green Version] - Chen, Z.; Mi, C.C.; Fu, Y.; Xu, J.; Gong, X. Online Battery State of Health Estimation Based on Genetic Algorithm for Electric and Hybrid Vehicle Applications. J. Power Sources
**2013**, 240, 184–192. [Google Scholar] [CrossRef] - Xia, B.; Lao, Z.; Zhang, R.; Tian, Y.; Chen, G.; Sun, Z.; Wang, W.; Sun, W.; Lai, Y.; Wang, M.; et al. Online Parameter Identification and State of Charge Estimation of Lithium-Ion Batteries Based on Forgetting Factor Recursive Least Squares and Nonlinear Kalman Filter. Energies
**2017**, 11, 3. [Google Scholar] [CrossRef] [Green Version] - Sun, X.; Ji, J.; Ren, B.; Xie, C.; Yan, D. Adaptive Forgetting Factor Recursive Least Square Algorithm for Online Identification of Equivalent Circuit Model Parameters of a Lithium-Ion Battery. Energies
**2019**, 12, 2242. [Google Scholar] [CrossRef] [Green Version] - BSI Standard Publication. Electrically Propelled Road Vehicles—Test Specification for Lithium-Ion Traction Battery Packs and Systems—Part 2: High-Energy Applications; BSI Standards Limited 2012: London, UK, 2012. [Google Scholar]
- United Nations. Addendum 15: Global Technical Regulation No. 15—Worldwide Harmonized Light Vehicles Test Procedure; UNECE: Geneva, Switzerland, 2014. [Google Scholar]

**Figure 9.**The estimated parameters of the second-order RC ECM for MLR (solid), ECF (dashed) and SDOT (dotted). The symbols represent the experimental data and the lines are the linear interpolation of the experimental data.

**Figure 10.**The battery terminal voltage of the pulse discharge test and the relative error for three estimations.

**Figure 11.**The battery terminal voltage of the CC discharge test and the relative error for the three estimations.

**Figure 12.**The battery terminal voltage of the ISO dynamic test and the relative error for the three estimations.

**Figure 13.**The battery terminal voltage of the WLTP dynamic test and the relative error for the three estimations.

**Figure 14.**The mean absolute error (MAE) and root mean square error (RMSE) obtained from the three parameter estimators.

Item | Specification |
---|---|

Capacity | Nominal 3200 mAh/Minimum 3100 mAh |

Nominal voltage | 3.67 V |

Maximum charge voltage | 4.2 ± 0.05 V |

Maximum charge current | 1.0C (3100 mA) |

Maximum discharge current | 10 A |

Standard charge | CC 0.5C (1550 mA)/CV 4.2 V/Cut-off 50 mA |

Standard discharge | CC 0.2C (620 mA)/Cut-off 2.5 V |

Operating temperature | Charge 0–45 °C/Discharge −20–60 °C |

No. of Testing | 1 | 2 | 3 | 4 | 5 | Average |
---|---|---|---|---|---|---|

Capacity (mAh) | 2969 | 2943 | 2946 | 2952 | 2954 | 2951 |

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**MDPI and ACS Style**

Poopanya, P.; Sivalertporn, K.; Phophongviwat, T.
A Comparative Study on the Parameter Identification of an Equivalent Circuit Model for an Li-ion Battery Based on Different Discharge Tests. *World Electr. Veh. J.* **2022**, *13*, 50.
https://doi.org/10.3390/wevj13030050

**AMA Style**

Poopanya P, Sivalertporn K, Phophongviwat T.
A Comparative Study on the Parameter Identification of an Equivalent Circuit Model for an Li-ion Battery Based on Different Discharge Tests. *World Electric Vehicle Journal*. 2022; 13(3):50.
https://doi.org/10.3390/wevj13030050

**Chicago/Turabian Style**

Poopanya, Piyawong, Kanchana Sivalertporn, and Teeraphon Phophongviwat.
2022. "A Comparative Study on the Parameter Identification of an Equivalent Circuit Model for an Li-ion Battery Based on Different Discharge Tests" *World Electric Vehicle Journal* 13, no. 3: 50.
https://doi.org/10.3390/wevj13030050