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Research Papers

Battery State of Health Monitoring by Estimation of Side Reaction Current Density Via Retrospective-Cost Subsystem Identification

[+] Author and Article Information
Xin Zhou

Department of Mechanical Engineering,
University of Michigan,
G029 Walter E. Lay Automotive Laboratory,
1231 Beal Avenue,
Ann Arbor, MI 48109
e-mail: zhouxin@umich.edu

Dennis S. Bernstein

Professor
Department of Aerospace Engineering,
University of Michigan,
3020 FXB Building,
1320 Beal Avenue,
Ann Arbor, MI 48109
e-mail: dsbaero@umich.edu

Jeffrey L. Stein

Professor
Mem. ASME
Department of Mechanical Engineering,
University of Michigan,
2480 GG Brown Laboratories,
2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: stein@umich.edu

Tulga Ersal

Mem. ASME
Department or Mechanical Engineering,
University of Michigan,
G029 Walter E. Lay Automotive Laboratory,
1231 Beal Avenue,
Ann Arbor, MI 48109
e-mail: tersal@umich.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 30, 2016; final manuscript received January 8, 2017; published online June 5, 2017. Assoc. Editor: Beshah Ayalew.

J. Dyn. Sys., Meas., Control 139(9), 091007 (Jun 05, 2017) (15 pages) Paper No: DS-16-1163; doi: 10.1115/1.4036030 History: Received March 30, 2016; Revised January 08, 2017

This paper introduces a new method to monitor battery state of health (SOH). In particular, the side reaction current density is estimated as a direct SOH indicator for the first time and its estimation is formulated as an inaccessible subsystem identification problem, where the battery health subsystem is treated as an inaccessible subsystem with the side reaction current density as the output. Inaccessibility in this context refers to the fact that the inputs and outputs of the subsystem are not measurable in situ. This subsystem is identified using retrospective-cost subsystem identification (RCSI) algorithm, and the output of the identified battery health subsystem provides an estimate for the side reaction current density. Using an example parameter set for a LiFePO4 battery, simulations are performed to obtain estimates under various current profiles. These simulations show promising results in identifying the battery health subsystem and estimating the side reaction current density with RCSI under ideal conditions. Robustness of the algorithm under nonideal conditions is analyzed. Estimation of the side reaction current density using RCSI is shown to be sensitive to nonideal conditions that cause errors in the measurement or estimation of the battery voltage. A method for quantitatively assessing the impact of nonideal conditions on the side reaction current estimation accuracy is provided. The proposed estimation technique, including the method for estimating the side reaction current density using RCSI and the framework analyzing its robustness, can also be applied to other parameter sets and other battery chemistries to monitor the SOH change resulting from any electrochemical-based degradation mechanism that consumes cyclable Li-ions.

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Figures

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Fig. 1

The schematic of the electrochemical model of a LiFePO4 battery

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Fig. 2

The architectures of (a) the battery model and (b) retrospective-cost subsystem identification for estimation of the side reaction current density. Note that the output of the SOH model in (a) is the side reaction current density Jsd.

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Fig. 3

The estimates and relative estimation errors ε of the subsystem parameter θ and the side reaction current density Jsd under ideal conditions with three input currents: (a) a 1 C CCCD cycle, (b) a 10 C CCCD cycle, and (c) a simulated current profile generated by an electric vehicle following an UDDS

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Fig. 4

The voltage difference ΔV of the DFN50 model caused by the current perturbation ΔI during the 1 C CCC mode

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Fig. 5

The estimates and relative estimation errors ε of the subsystem parameter θ and the side reaction current density Jsd under the presence of (a) input and (b) output measurement noise. The bounds of the relative estimation errors are on the order of 10% as required.

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Fig. 6

(a) The relative estimation errors ε of the subsystem parameter θ and the side reaction current density Jsd and (b) the voltage difference under the presence of a 1% SOC error. The bound of the relative estimation errors in (a) is on the same order as expected from the voltage difference in (b).

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Fig. 7

The relative estimation errors ε of the subsystem parameter θ and the side reaction current density Jsd under the 1 C CCC mode with DFN50 as the true main system and (a) DFN30, (b) DFN10, and (c) SPM as the main system model. The differences in the voltage responses during 1 C CCC mode between DFN50 and (d) DFN30, (e) DFN10, and (f) SPM. The bounds of the relative estimation errors in (a), (b), and (c) are on the same orders as expected from the voltage differences in (d), (e), and (f), respectively.

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Fig. 8

The estimates of (a) the subsystem parameter θ and (b) the side reaction current density Jsd, and (c) relative estimation errors ε under parametric errors in Rfilm and Ds,n. (d) presents the voltage difference between the DFN50 model with values of Rfilm and Ds,n in fresh and degraded batteries during 1 C CCC mode.

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Fig. 9

The relative estimation errors ε of the subsystem parameter θ and the side reaction current density Jsd under (a) the 1 C CCC mode and (b) the UDDS cycle under the presence of form discrepancy between the subsystem and the subsystem model. (c) presents the relative estimation errors under the same UDDS cycle as in (b), but with the estimation algorithm shut down whenever discharge current is above 5 C. Note that shutting down the estimation algorithm during high C-rate discharge reduces estimation errors.

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