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Nonlinear Temperature-Dependent State Model of Cylindrical LiFePO_{4} Battery for Open-Circuit Voltage, Terminal Voltage and State-of-Charge Estimation with Extended Kalman Filter

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## Abstract

**:**

## 1. Introduction

_{4}) batteries have become popular for renewable energy storage devices, electric vehicles [1,2,3] and smart grids [4,5,6]. However, the batteries are quite vulnerable to temperature variation and unforeseen operating conditions such as being overly charged or discharged, which affects its performance and reduces its lifespan in an electric vehicle. There have been many efforts in recent years to enhance the accuracy of the SOC estimation in a battery management system (BMS) [7]. A detailed literature review can be found in the following references [8,9,10,11]. The common Coulomb counting or Ampere-hour method [12] uses the current reading of the battery over the operating period to calculate SOC values.

## 2. Cell Nonlinear Temperature-Dependent State Model

## 3. Cell SOC-OCV Relationship

_{oc}as follows.

## 4. Cell Temperature Model

^{−1}m

^{−2}K

^{4}, $d{U}_{oc}/d{T}_{cell}$ is the reversible heat term or entropy coefficient and ${R}_{c}$ is the contact resistance in $\mathsf{\Omega}$. The terminal voltage ${U}_{t}$ and open-circuit voltage ${U}_{oc}$ can be seen in (4) and (6), respectively. The values of the parameters related to the battery cell can be found in Table 1.

## 5. Cell Terminal Voltage Model

## 6. SOC Estimation by Extended Kalman Filter Method

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, S.; Luo, Y.; Wang, J.; Wang, X.; Li, K. Predictive Energy Management Strategy for Fully Electric Vehicles Based on Preceding Vehicle Movement. IEEE Trans. Intell. Transp. Syst.
**2017**, 18, 3049–3060. [Google Scholar] [CrossRef] - Alhanouti, M.; Gießler, M.; Blank, T.; Gauterin, F. New Electro-Thermal Battery Pack Model of an Electric Vehicle. Energies
**2016**, 9, 563. [Google Scholar] [CrossRef] - Hussein, A.A. Capacity Fade Estimation in Electric Vehicle Li-Ion Batteries Using Artificial Neural Networks. IEEE Trans. Ind. Appl.
**2015**, 51, 2321–2330. [Google Scholar] [CrossRef] - Tenfen, D.; Finardi, E.C.; Delinchant, B.; Wurtz, F. Lithium-ion battery modeling for the energy management problem of microgrids. IET Gener. Transm. Distrib.
**2016**, 10, 576–584. [Google Scholar] [CrossRef] - Ye, F.; Qian, Y.; Hu, R. Incentive Load Scheduling Schemes for PHEV Battery Exchange Stations in Smart Grid. IEEE Syst. J.
**2015**, 11, 922–930. [Google Scholar] [CrossRef] - Casals, L.C.; Garca, B.A. Communications concerns for reused electric vehicle batteries in smart grids. IEEE Commun. Mag.
**2016**, 54, 120–125. [Google Scholar] [CrossRef][Green Version] - Lelie, M.; Braun, T.; Knips, M.; Nordmann, H.; Ringbeck, F.; Zappen, H.; Sauer, D.U. Battery Management System Hardware Concepts: An Overview. Appl. Sci.
**2018**, 8, 534. [Google Scholar] [CrossRef] - Li, Z.; Huang, J.; Liaw, B.Y.; Zhang, J. On state-of-charge determination for lithium-ion batteries. J. Power Sources
**2017**, 348, 281–301. [Google Scholar] [CrossRef] - Jaguemont, J.; Boulon, L.; Dubé, Y. A comprehensive review of lithium-ion batteries used in hybrid and electric vehicles at cold temperatures. Appl. Energy
**2016**, 164, 99–114. [Google Scholar] [CrossRef] - Marongiu, A.; Nußbaum, F.G.W.; Waag, W.; Garmendi, M.; Sauer, D.U. Comprehensive study of the influence of aging on the hysteresis behavior of a lithium iron phosphate cathode-based lithium ion battery—An experimental investigation of the hysteresis. Appl. Energy
**2016**, 171, 629–645. [Google Scholar] [CrossRef] - Hannan, M.A.; Lipu, M.S.H.; Hussain, A.; Mohamed, A. A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations. Renew. Sustain. Energy Rev.
**2017**, 78, 834–854. [Google Scholar] [CrossRef] - Zhang, C.; Li, K.; Deng, J.; Song, S. Improved Real-time State-of-Charge Estimation of LiFePO
_{4}Battery Based on a Novel Thermoelectric Model. IEEE Trans. Ind. Electron.**2017**, 64, 654–663. [Google Scholar] [CrossRef] - Cacciato, M.; Nobile, G.; Scarcella, G.; Scelba, G. Real-Time Model-Based Estimation of SOC and SOH for Energy Storage Systems. IEEE Trans. Power Electron.
**2017**, 32, 794–803. [Google Scholar] [CrossRef] - Fuller, T.F.; Doyle, M.; Newman, J. Simulation and optimization of the dual lithium ion insertion cell. J. Electrochem. Soc.
**1994**, 141, 1–10. [Google Scholar] [CrossRef] - Santhanagopalan, S.; Guo, Q.; Ramadass, P.; White, R.E. Review of models for predicting the cycling performance of lithium ion batteries. J. Power Sour.
**2006**, 156, 620–628. [Google Scholar] [CrossRef] - Lotfi, N.; Landers, R.G.; Li, J.; Park, J. Reduced-Order Electrochemical Model-Based SOC Observer with Output Model Uncertainty Estimation. IEEE Trans. Control. Syst. Technol.
**2017**, 25, 1217–1230. [Google Scholar] [CrossRef] - Rahimian, S.K.; Rayman, S.; White, R.E. Extension of physics based single particle model for higher charge–discharge rates. J. Power Sources
**2013**, 224, 180–194. [Google Scholar] [CrossRef] - Bartlett, A.; Marcicki, J.; Onori, S.; Rizzoni, G.; Yang, X.G.; Miller, T. Electrochemical Model-Based State of Charge and Capacity Estimation for a Composite Electrode Lithium-Ion Battery. IEEE Trans. Control. Syst. Technol.
**2016**, 24, 384–399. [Google Scholar] [CrossRef] - Chen, Z.; Fu, Y.; Mi, C.C. State of Charge Estimation of Lithium-Ion Batteries in Electric Drive Vehicles Using Extended Kalman Filtering. IEEE Trans. Veh. Technol.
**2013**, 62, 1020–1030. [Google Scholar] [CrossRef] - Kim, J.; Cho, B.H. State-of-Charge Estimation and State-of-Health Prediction of a Li-Ion Degraded Battery Based on an EKF Combined With a Per-Unit System. IEEE Trans. Veh. Technol.
**2011**, 60, 4249–4260. [Google Scholar] [CrossRef] - Ghalkhania, M.; Bahiraeib, F.; Nazric, G.A.; Saifa, M. Electrochemical-Thermal Model of Pouch-type Lithium-ion Batteries. Electrochim. Acta
**2017**, 247, 569–587. [Google Scholar] [CrossRef] - Mendoza, S.; Rothenberger, M.; Liu, J.; Fathy, H.K. Maximizing Parameter Identifiability of a Combined Thermal and Electrochemical Battery Model Via Periodic Current Input Optimization. IFAC PapersOnLine
**2017**, 50, 7314–7320. [Google Scholar] [CrossRef] - Zou, C.; Hu, X.; Wei, Z.; Tang, X. Electrothermal dynamics-conscious lithium-ion battery cell-level charging management via state-monitored predictive control. Energy
**2017**, 141, 250–259. [Google Scholar] [CrossRef] - Hosseinzadeh, E.; Marco, J.; Jennings, P. Electrochemical-Thermal Modelling and Optimisation of Lithium-Ion Battery Design Parameters Using Analysis of Variance. Energies
**2017**, 10, 1278. [Google Scholar] [CrossRef] - Tagade, P.; Hariharan, K.S.; Basu, S.; Verma, M.K.S.; Kolake, S.M.; Song, T.; Oh, D.; Yeo, T.; Doo, S. Bayesian calibration for electrochemical thermal model of lithium-ion cells. J. Power Sources
**2016**, 320, 296–309. [Google Scholar] [CrossRef] - Lai, Y.; Du, S.; Ai, L.; Ai, L.; Cheng, Y.; Tang, Y.; Jia, M. Insight into heat generation of lithium ion batteries based on the electrochemical-thermal model at high discharge rates. Int. J. Hydrogen Energy
**2015**, 40, 13039–13049. [Google Scholar] [CrossRef] - Arunachalam, H.; Onori, S. Temperature-dependent multiscale-dynamics in Lithium-Ion battery electrochemical models. In Proceedings of the 2015 American Control Conference, Chicago, IL, USA, 1–3 July 2015. [Google Scholar]
- Li, J.; Cheng, Y.; Jia, M.; Tang, Y.; Lin, Y.; Zhang, Z.; Liu, Y. An electrochemical thermal model based on dynamic responses for lithium iron phosphate battery. J. Power Sources
**2014**, 255, 130–143. [Google Scholar] [CrossRef] - Saw, L.H.; Ye, Y.; Tay, A.A.O. Electrochemical–thermal analysis of 18,650 Lithium Iron Phosphate cell. Energy Convers. Manag.
**2013**, 75, 162–174. [Google Scholar] [CrossRef] - Zhu, C.; Li, X.; Song, L.; Xiang, L. Development of a theoretically based thermal model for lithium ion battery pack. J. Power Sources
**2013**, 223, 155–164. [Google Scholar] [CrossRef] - Saw, L.H.; Ye, Y.; Tay, A.A.O. Electro-thermal analysis and integration issues of lithium ion battery for electric vehicles. Appl. Energy
**2014**, 131, 97–107. [Google Scholar] [CrossRef] - Hu, Y.; Yurkovich, S.; Guezennec, Y.; Yurkovich, B.J. Electro-thermal battery model identification for automotive applications. J. Power Sources
**2011**, 196, 449–457. [Google Scholar] [CrossRef] - Chen, X.; Shen, W.; Dai, M.; Cao, Z.; Jin, J.; Kapoor, A. Robust Adaptive Sliding-Mode Observer Using RBF Neural Network for Lithium-Ion Battery State of Charge Estimation in Electric Vehicles. IEEE Trans. Veh. Technol.
**2016**, 65, 1936–1947. [Google Scholar] [CrossRef] - Ma, Y.; Li, B.; Li, G.; Zhang, J.; Chen, H. A nonlinear observer approach of SOC estimation based on hysteresis model for lithium-ion battery. IEEE/CAA J. Autom. Sin.
**2017**, 4, 195–204. [Google Scholar] [CrossRef] - Hu, Y.; Yurkovich, S. Battery cell state-of-charge estimation using linear parameter varying system techniques. J. Power Sources
**2012**, 198, 338–350. [Google Scholar] [CrossRef] - Greenleaf, M.; Dalchand, O.; Li, H.; Zheng, J.P. A Temperature-Dependent Study of Sealed Lead-Acid Batteries Using Physical Equivalent Circuit Modeling With Impedance Spectra Derived High Current/Power Correction. IEEE Trans. Sustain. Energy
**2015**, 6, 380–387. [Google Scholar] [CrossRef] - Dvorak, D.; Bäuml, T.; Holzinger, A.; Popp, H. A Comprehensive Algorithm for Estimating Lithium-Ion Battery Parameters From Measurements. IEEE Trans. Sustain. Energy
**2018**, 9, 771–779. [Google Scholar] [CrossRef] - Fotouhi, A.; Auger, D.J.; Propp, K.; Longo, S. Lithium-Sulfur Battery State-of-Charge Observability Analysis and Estimation. IEEE Trans. Power Electron.
**2018**, 33, 5847–5859. [Google Scholar] [CrossRef] - Charkhgard, M.; Farrokhi, M. State-of-Charge Estimation for Lithium-Ion Batteries Using Neural Networks and Ekf. IEEE Trans. Ind. Electron.
**2010**, 57, 4178–4187. [Google Scholar] [CrossRef] - He, W.; Williard, N.; Chen, C.; Pecht, M. State of Charge Estimation for Li-Ion Batteries Using Neural Network Modeling and Unscented Kalman Filter-Based Error Cancellation. Int. J. Electr. Power Energy Syst.
**2014**, 62, 783–791. [Google Scholar] [CrossRef] - Wang, S.C.; Liu, Y.H. A Pso-Based Fuzzy-Controlled Searching for the Optimal Charge Pattern of Li-Ion Batteries. IEEE Trans. Ind. Electron.
**2015**, 62, 2983–2993. [Google Scholar] [CrossRef] - Fekry, H.M.; Hassan, M.A.M.; Aziz, M.M.A.E. The state of charge estimation for rechargeable batteries using Adaptive Neuro Fuzzy Inference System (ANFIS). In Proceedings of the First International Conference on Innovative Engineering Systems, Alexandria, Egypt, 7–9 December 2012; pp. 201–206. [Google Scholar]
- Nuhic, A.; Terzimehic, T.; Soczka-Guth, T.; Buchholz, M.; Dietmayer, K. Health diagnosis and remaining useful life prognostics of lithium-ion batteries using data-driven methods. J. Power Sources
**2013**, 239, 680–688. [Google Scholar] [CrossRef] - Weng, C.; Cui, Y.; Sun, J.; Peng, H. On-board state of health monitoring of lithium-ion batteries using incremental capacity analysis wit support vector regression. J. Power Sources
**2013**, 235, 36–44. [Google Scholar] [CrossRef] - Fang, H.; Wang, Y.; Sahinoglu, Z.; Wada, T.; Hara, S. State of charge estimation for lithium-ion batteries: An adaptive approach. Control Eng. Pract.
**2014**, 25, 45–54. [Google Scholar] [CrossRef] - Du, J.; Liu, Z.; Wang, Y. State of charge estimation for Li-ion battery based on model from extreme learning machine. Control Eng. Pract.
**2014**, 26, 11–19. [Google Scholar] [CrossRef] - Du, J.; Liu, Z.; Chen, C.; Wang, Y. Li-ion battery SOC estimation using EKF based on a model proposed by extreme learning machine. In Proceedings of the 7th IEEE Conference on Industrial Electronics and Applications, Singapore, 18–20 July 2012; pp. 1648–1653. [Google Scholar]
- Densmore, A.; Hanif, M. Modeling the condition of Lithium Ion Batteries using the extreme machine learning. In Proceedings of the IEEE PES Power Africa Conference, Livingstone, Zambia, 28 June–3 July 2016; pp. 184–188. [Google Scholar]
- Far, R.R.; Chakrabarti, S.; Saif, M. Multi-Step Parallel-Strategy for Estimating the Remaining Useful Life of Batteries. In Proceedings of the IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE), Windsor, ON, Canada, 30 April–3 May 2017; pp. 1–4. [Google Scholar]
- Tang, X.; Yao, K.; Liu, B.; Hu, W.; Gao, F. Long-Term Battery Voltage, Power, and Surface Temperature Prediction Using a Model-Based Extreme Learning Machine. Energies
**2018**, 11, 86. [Google Scholar] [CrossRef] - Chin, C.; Gao, Z.C. State-of-Charge Estimation of Battery Pack under Varying Ambient Temperature Using an Adaptive Sequential Extreme Learning Machine. Energies
**2018**, 11, 711. [Google Scholar] [CrossRef] - Remmlinger, J.; Buchholz, M.; Dietmayer, K. Model-based on-board monitoring for lithium-ion batteries. ATZ Autom.
**2014**, 62, 282–295. [Google Scholar] [CrossRef] - Plett, G.L. Extended Kalman filtering for battery management systems of LiPB based HEV battery packs: Part 1. Background. J. Power Sources
**2004**, 134, 252–261. [Google Scholar] [CrossRef] - Plett, G.L. Extended kalman filtering for battery management systems of LIPB based HEV battery packs: Part 2. Modeling and identification. J. Power Sources
**2004**, 134, 262–276. [Google Scholar] [CrossRef] - Plett, G.L. Extended Kalman filtering for battery management systems of LiPBbased hev battery packs: Part 3. State and parameter estimation. J. Power Sources
**2004**, 134, 277–292. [Google Scholar] [CrossRef] - Plett, G.L. Sigma-point Kalman filtering for battery management systems of LIPB-based HEV battery packs: Part 1: Introduction and state estimation. J. Power Sources
**2006**, 161, 1356–1368. [Google Scholar] [CrossRef] - Plett, G.L. Sigma-point kalman filtering for battery management systems of LIPB-based HEV battery packs: Part 2: Simultaneous state and parameter estimation. J. Power Sources
**2006**, 161, 1369–1384. [Google Scholar] [CrossRef] - Zhang, F.; Liu, G.; Fang, L.; Wang, H. Estimation of Battery State of Charge with H∞ Observer: Applied to a Robot for Inspecting Power Transmission Lines. IEEE Trans. Ind. Electron.
**2012**, 59, 1086–1095. [Google Scholar] [CrossRef] - Zhang, F.; Liu, G.; Fang, L. A battery state of charge estimation method using sliding mode observer. In Proceedings of the 7th World Congress on Intelligent Control and Automation Conference, Chongqing, China, 25–27 June 2008. [Google Scholar]
- Zhang, F.; Liu, G.; Fang, L. A battery State of Charge estimation method with extended Kalman filter. In Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Xi’an, China, 2–5 July 2008. [Google Scholar]
- Zhang, F.; Liu, G.; Fang, L. Battery state estimation using Unscented Kalman Filter. In Proceedings of the IEEE International Conference on Robotics and Automation, Kobe, Japan, 12–17 May 2009. [Google Scholar]
- Ali, D.; Mukhopadhyay, S.; Rehman, H. A novel adaptive technique for Li-ion battery model parameters estimation. In Proceedings of the 2016 IEEE National Aerospace and Electronics Conference (NAECON) and Ohio Innovation Summit (OIS), Dayton, OH, USA, 26–29 July 2017. [Google Scholar]
- Wang, Y.; Fang, H.; Zhou, L.; Wang, Y.; Fang, H.; Zhou, L.; Wada, T. Revisiting the State-of-Charge Estimation for Lithium-Ion Batteries: A Methodical Investigation of the Extended Kalman Filter Approach. IEEE Control Syst.
**2017**, 37, 73–96. [Google Scholar] - Jia, J.; Lin, P.; Chin, C.S.; Toh, W.D.; Gao, Z.; Lyu, H.; Cham, Y.T.; Mesbahi, E. Multirate strong tracking extended Kalman filter and its implementation on lithium iron phosphate (LiFePO
_{4}) battery system. In Proceedings of the IEEE 11th International Conference on Power Electronics and Drive Systems, Sydney, Australia, 9–12 June 2015; pp. 640–645. [Google Scholar] - Gao, Z.; Chin, C.S.; Chiew, J.H.K.; Jia, J.B.; Zhang, C.Z. Design and Implementation of Smart Lithium-ion Battery System with Real-time Fault Diagnosis Capability for Electric Vehicles. Energies
**2017**, 10, 1503. [Google Scholar] [CrossRef] - Gao, Z.; Chin, C.S.; Woo, W.L.; Jia, J. Integrated Equivalent Circuit and Thermal Model for Simulation of Temperature-Dependent LiFePO4 Battery in Actual Embedded Application. Energies
**2017**, 10, 85. [Google Scholar] [CrossRef] - Waag, F.W.; Sauer, D.U. Application-specific electrical characterization of high power batteries with lithium titanate anodes for electric vehicles. Energy
**2016**, 112, 294–306. [Google Scholar] - Wijewardana, S.; Vepa, R.; Shaheed, M.H. Dynamic battery cell model and state of charge estimation. J. Power Sources
**2016**, 308, 109–120. [Google Scholar] [CrossRef] - Bernardi, D.; Pawlikowski, E.; Newman, J. A general energy balance for battery systems. J. Electrochem. Soc.
**1985**, 132, 5–12. [Google Scholar] [CrossRef] - Li, Y.; Wang, C.; Gong, J. A combination Kalman filter approach for State of Charge estimation of lithium-ion battery considering model uncertainty. Energy
**2016**, 109, 933–946. [Google Scholar] [CrossRef] - Zhang, R.H.; He, Z.C.; Wang, H.W.; You, F.; Li, K.N. Study on self-tuning tyre friction control for developing main-servo loop integrated chassis control system. IEEE Access
**2017**, 5, 6649–6660. [Google Scholar] [CrossRef] - Xiong, H.; Zhu, X.; Zhang, R. Energy Recovery Strategy Numerical Simulation for Dual Axle Drive Pure Electric Vehicle Based on Motor Loss Model and Big Data Calculation. Complexity
**2018**, 4071743. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Proposed ambient and cell temperature-dependent ECM of battery cell; (

**b**) terminal voltage of 1RC and 2RC as compared to experiment data.

**Figure 7.**(

**a**) proposed OCV-SOC relationship as compared to experimental data (at ambient temperature of 25 °C); (

**b**) block diagram for OCV-SOC relationship at different ambient temperature (

**c**) proposed OCV-SOC relationship to experimental data at different ambient temperature; (

**d**) RMSE of OCV as compared to the proposed method at a different ambient temperature.

**Figure 12.**Thermal image of cell temperature at ambient temperature of 25 °C (for constant 2 A load current).

**Figure 13.**Cell temperature at different ambient temperature (for constant 2 A load current) for 3000 s.

**Figure 21.**SOC and RMSE of SOC as compared to experimental result at ambient temperature of (

**a**) 5 °C; (

**b**) 15 °C; (

**c**) 35 °C; (

**d**) 45 °C.

**Figure 22.**SOC as compared to experimental result at different ambient temperature (5 °C, 15 °C and 25 °C).

**Figure 23.**SOC as compared to experimental result at different ambient temperature (35 °C and 45 °C).

Parameters | Values |
---|---|

Nominal Capacity, C_{n} (Ah) | 2.5 |

Cell density, $\rho $ (kgm^{−3}) | 2700 |

Cell mass, m (kg) | 0.076 |

Surface Area of Heat Exchange, ${A}_{cell}$ (m^{2}) | 0.0175 |

Specific Heat Capacity of the Cell, ${c}_{p}\left(\mathrm{J}/\mathrm{kgK}\right)$ | 825 |

Contact resistance, ${R}_{c}$ (Ω) | 25 µΩ |

Entropy coefficient $\mathrm{d}{U}_{oc}/\mathrm{d}{T}_{cell}$ | 0.00125 [2] |

Convective Heat Transfer Coefficient, $h$ (W/m^{2}/K) | 4 |

Stefan-Boltzmann constant term,$\sigma $ | 5.67 × 10^{−8} J·s^{−1}m^{−2}K^{4} |

The emissivity of heat term, $\epsilon $ | 0.95 |

Hysteresis voltage dynamics time constant, $\beta $ | 2.47 × 10^{−3} [63] |

Ambient Temperature (°C) | RMSE of Terminal Voltage (V) |
---|---|

5 | 0.0663 |

15 | 0.0262 |

25 | 0.0153 |

35 | 0.0533 |

45 | 0.0523 |

**Table 3.**RMSE comparison between the proposed model using EKF for SOC and terminal voltage estimation.

Models | Parameters | RMSE | ||||
---|---|---|---|---|---|---|

5 °C | 15 °C | 25 °C | 35 °C | 45 °C | ||

With temperature | SOC | 0.0166 | 0.1197 | 0.2932 | 0.2919 | 0.1132 |

Without temperature | 0.3002 | 0.2785 | 0.2801 | 0.2788 | 0.2784 | |

Percent improvement | 94.0% | 57.0% | (5.00%) | (5.00%) | 59.0% | |

With temperature | Terminal Voltage | 0.0593 | 0.1186 | 0.138 | 0.1268 | 0.1082 |

Without temperature | 0.1344 | 0.1199 | 0.1352 | 0.1281 | 0.127 | |

Percent improvement | 56.0% | 1.08% | (2.07%) | 1.00% | 15.0% |

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**MDPI and ACS Style**

Chin, C.S.; Gao, Z.; Chiew, J.H.K.; Zhang, C. Nonlinear Temperature-Dependent State Model of Cylindrical LiFePO_{4} Battery for Open-Circuit Voltage, Terminal Voltage and State-of-Charge Estimation with Extended Kalman Filter. *Energies* **2018**, *11*, 2467.
https://doi.org/10.3390/en11092467

**AMA Style**

Chin CS, Gao Z, Chiew JHK, Zhang C. Nonlinear Temperature-Dependent State Model of Cylindrical LiFePO_{4} Battery for Open-Circuit Voltage, Terminal Voltage and State-of-Charge Estimation with Extended Kalman Filter. *Energies*. 2018; 11(9):2467.
https://doi.org/10.3390/en11092467

**Chicago/Turabian Style**

Chin, Cheng Siong, Zuchang Gao, Joel Hay King Chiew, and Caizhi Zhang. 2018. "Nonlinear Temperature-Dependent State Model of Cylindrical LiFePO_{4} Battery for Open-Circuit Voltage, Terminal Voltage and State-of-Charge Estimation with Extended Kalman Filter" *Energies* 11, no. 9: 2467.
https://doi.org/10.3390/en11092467