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Research Papers

Reduced Order Impedance Models of Lithium Ion Batteries

[+] Author and Article Information
Githin K. Prasad

Research Assistant
Department of Mechanical and
Nuclear Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: gkp104@psu.edu

Christopher D. Rahn

Professor
Department of Mechanical and
Nuclear Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: cdrahn@psu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 24, 2012; final manuscript received January 28, 2014; published online April 8, 2014. Assoc. Editor: Evangelos Papadopoulos.

J. Dyn. Sys., Meas., Control 136(4), 041012 (Apr 08, 2014) (8 pages) Paper No: DS-12-1317; doi: 10.1115/1.4026652 History: Received September 24, 2012; Revised January 28, 2014

This paper develops reduced order, linear models of lithium ion batteries that can be used for model-based power train simulation, design, estimation, and controlling in hybrid and electric vehicles (HEV). First, a reduced order model is derived from the fundamental governing electrochemical charge and Li+ conservation equations that are linearized at the operating state of charge and low current density. The equations are solved using analytical and numerical techniques to produce the transcendental impedance or transfer function from input current to output voltage. This model is then reduced to a low order state space model using a system identification technique based on least squares optimization. Given the prescribed current, the model predicts voltage and other variables such as electrolyte and electrode surface concentration distributions. The second model is developed by neglecting electrolyte diffusion and modeling each electrode with a single active material particle. The transcendental particle transfer functions are discretized using a Padé Approximation. The explicit form of the single particle model impedance can be realized by an equivalent circuit with resistances and capacitances related to the cell parameters. Both models are then tuned to match experimental electrochemical impedance spectroscopy (EIS) and pulse current-voltage data.

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Figures

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Fig. 1

1D schematic of a lithium ion battery

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Fig. 2

Impedance frequency response at 60% SOC: transcendental transfer function (dotted), reduced order model (dash-dotted), padé approximated single particle model (dashed), and experimental EIS (solid)

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Fig. 3

Electrolyte concentration distribution, cex,t, time response: 5C discharge from 60% SOC at various times

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Fig. 4

Solid phase surface concentration distribution, cs,e(x,t), time response: 5C discharge from 60% SOC at various times

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Fig. 5

Current density distribution, j(x,t), time response: 5C discharge from 60% SOC at various times

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Fig. 6

Experimental (solid), single particle model (dashed) and reduced order model (dashed) pulse charge/discharge time response at 60% SOC

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Fig. 7

Equivalent circuit model of Padé approximated single particle model

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