### Abstract

The accuracy of identifying the parameters of models describing lithium ion batteries (LIBs) in typical battery management system (BMS) applications is critical to the estimation of key states such as the state of charge (SoC) and state of health (SoH). In applications such as electric vehicles (EVs) where LIBs are subjected to highly demanding cycles of operation and varying environmental conditions leading to non-trivial interactions of ageing stress factors, this identification is more challenging. This paper proposes an algorithm that directly estimates the parameters of a nonlinear battery model from measured input and output data in the continuous time-domain. The simplified refined instrumental variable method is extended to estimate the parameters of a Wiener model where there is no requirement for the nonlinear function to be invertible. To account for nonlinear battery dynamics, in this paper, the typical linear equivalent circuit model (ECM) is enhanced by a block-oriented Wiener configuration where the nonlinear memoryless block following the typical ECM is defined to be a sigmoid static nonlinearity. The nonlinear Weiner model is reformulated in the form of a multi-input, single-output linear model. This linear form allows the parameters of the nonlinear model to be estimated using any linear estimator such as the well-established least squares (LS) algorithm. In this paper, the recursive least square (RLS) method is adopted for online parameter estimation. The approach was validated on experimental data measured from an 18650-type Graphite/Lithium-Nickel-Cobalt-Aluminium-Oxide (C_{6}/LiNiCoAlO_{2}) lithium-ion cell. A comparison between the results obtained by the proposed method and by nonparametric frequency-based approaches for obtaining the model parameters is presented. It is shown that although both approaches give similar estimates, the advantages of the proposed method are (i) the simplicity by which the algorithm can be employed on-line for updating nonlinear equivalent circuit model (NL-ECM) parameters and (ii) the improved convergence efficiency of the on-line estimation.

Original language | English |
---|---|

Pages (from-to) | 497-508 |

Number of pages | 12 |

Journal | Applied Energy |

Volume | 204 |

Early online date | 25 Jul 2017 |

DOIs | |

Publication status | Published - 15 Oct 2017 |

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### Bibliographical note

Under a Creative Commons license### Keywords

- Continuous time wiener model
- Lithium ion battery
- Nonlinear equivalent circuit model
- Online parameter estimation
- Simplified refined instrumental variable method

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Energy(all)

### Cite this

*Applied Energy*,

*204*, 497-508. https://doi.org/10.1016/j.apenergy.2017.07.030

**On-line scheme for parameter estimation of nonlinear lithium ion battery equivalent circuit models using the simplified refined instrumental variable method for a modified Wiener continuous-time model.** / Allafi, Walid; Uddin, Kotub; Zhang, Cheng; Mazuir Raja Ahsan Sha, Raja; Marco, James.

Research output: Contribution to journal › Article

*Applied Energy*, vol. 204, pp. 497-508. https://doi.org/10.1016/j.apenergy.2017.07.030

}

TY - JOUR

T1 - On-line scheme for parameter estimation of nonlinear lithium ion battery equivalent circuit models using the simplified refined instrumental variable method for a modified Wiener continuous-time model

AU - Allafi, Walid

AU - Uddin, Kotub

AU - Zhang, Cheng

AU - Mazuir Raja Ahsan Sha, Raja

AU - Marco, James

N1 - Under a Creative Commons license

PY - 2017/10/15

Y1 - 2017/10/15

N2 - The accuracy of identifying the parameters of models describing lithium ion batteries (LIBs) in typical battery management system (BMS) applications is critical to the estimation of key states such as the state of charge (SoC) and state of health (SoH). In applications such as electric vehicles (EVs) where LIBs are subjected to highly demanding cycles of operation and varying environmental conditions leading to non-trivial interactions of ageing stress factors, this identification is more challenging. This paper proposes an algorithm that directly estimates the parameters of a nonlinear battery model from measured input and output data in the continuous time-domain. The simplified refined instrumental variable method is extended to estimate the parameters of a Wiener model where there is no requirement for the nonlinear function to be invertible. To account for nonlinear battery dynamics, in this paper, the typical linear equivalent circuit model (ECM) is enhanced by a block-oriented Wiener configuration where the nonlinear memoryless block following the typical ECM is defined to be a sigmoid static nonlinearity. The nonlinear Weiner model is reformulated in the form of a multi-input, single-output linear model. This linear form allows the parameters of the nonlinear model to be estimated using any linear estimator such as the well-established least squares (LS) algorithm. In this paper, the recursive least square (RLS) method is adopted for online parameter estimation. The approach was validated on experimental data measured from an 18650-type Graphite/Lithium-Nickel-Cobalt-Aluminium-Oxide (C6/LiNiCoAlO2) lithium-ion cell. A comparison between the results obtained by the proposed method and by nonparametric frequency-based approaches for obtaining the model parameters is presented. It is shown that although both approaches give similar estimates, the advantages of the proposed method are (i) the simplicity by which the algorithm can be employed on-line for updating nonlinear equivalent circuit model (NL-ECM) parameters and (ii) the improved convergence efficiency of the on-line estimation.

AB - The accuracy of identifying the parameters of models describing lithium ion batteries (LIBs) in typical battery management system (BMS) applications is critical to the estimation of key states such as the state of charge (SoC) and state of health (SoH). In applications such as electric vehicles (EVs) where LIBs are subjected to highly demanding cycles of operation and varying environmental conditions leading to non-trivial interactions of ageing stress factors, this identification is more challenging. This paper proposes an algorithm that directly estimates the parameters of a nonlinear battery model from measured input and output data in the continuous time-domain. The simplified refined instrumental variable method is extended to estimate the parameters of a Wiener model where there is no requirement for the nonlinear function to be invertible. To account for nonlinear battery dynamics, in this paper, the typical linear equivalent circuit model (ECM) is enhanced by a block-oriented Wiener configuration where the nonlinear memoryless block following the typical ECM is defined to be a sigmoid static nonlinearity. The nonlinear Weiner model is reformulated in the form of a multi-input, single-output linear model. This linear form allows the parameters of the nonlinear model to be estimated using any linear estimator such as the well-established least squares (LS) algorithm. In this paper, the recursive least square (RLS) method is adopted for online parameter estimation. The approach was validated on experimental data measured from an 18650-type Graphite/Lithium-Nickel-Cobalt-Aluminium-Oxide (C6/LiNiCoAlO2) lithium-ion cell. A comparison between the results obtained by the proposed method and by nonparametric frequency-based approaches for obtaining the model parameters is presented. It is shown that although both approaches give similar estimates, the advantages of the proposed method are (i) the simplicity by which the algorithm can be employed on-line for updating nonlinear equivalent circuit model (NL-ECM) parameters and (ii) the improved convergence efficiency of the on-line estimation.

KW - Continuous time wiener model

KW - Lithium ion battery

KW - Nonlinear equivalent circuit model

KW - Online parameter estimation

KW - Simplified refined instrumental variable method

UR - http://www.scopus.com/inward/record.url?scp=85025595123&partnerID=8YFLogxK

U2 - 10.1016/j.apenergy.2017.07.030

DO - 10.1016/j.apenergy.2017.07.030

M3 - Article

VL - 204

SP - 497

EP - 508

JO - Applied Energy

JF - Applied Energy

SN - 0306-2619

ER -