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Research Papers

Physics-Based Model of a Valve-Regulated Lead-Acid Battery and an Equivalent Circuit

[+] Author and Article Information
Zheng Shen

e-mail: zus120@psu.edu

Christopher D. Rahn

Professor
Fellow ASME
e-mail: cdrahn@psu.edu
Department of Mechanical and Nuclear Engineering,
Mechatronics Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 17, 2012; final manuscript received February 15, 2013; published online May 16, 2013. Assoc. Editor: Luis Alvarez.

J. Dyn. Sys., Meas., Control 135(4), 041011 (May 16, 2013) (7 pages) Paper No: DS-12-1143; doi: 10.1115/1.4023765 History: Received May 17, 2012; Revised February 15, 2013

Lead (Pb)-acid batteries are a low-cost power source for applications ranging from hybrid and electric vehicles (HEVs) to large-scale energy storage. Efficient simulation, design, and management systems require the development of low order but accurate models. In this paper we develop a reduced-order Pb-acid battery model from first principles using linearization and the Ritz discretization method. The model, even with a low-order discretization, accurately predicts the voltage response to a dynamic pulse current input and outputs spatially distributed variables of interest. A dynamic averaged model is developed from the Ritz model and realized by an equivalent circuit. The circuit resistances and capacitances depend on electrochemical parameters, linking the equivalent circuit model to the underlying electrochemistry of the first principles model.

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Figures

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Fig. 1

Schematic diagram of a lead-acid cell

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Fig. 2

Experimental and simulated time response to a pulse charge/discharge current input: (a) voltage output for the switched linear models with N = 8 (blue, solid) and N = 1 (green, dashed), charge model (red, dash-dotted), discharge model (yellow, dotted), and experiment (black, solid). (b) Input current.

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Fig. 3

Spatial distributions in response to current input from Fig. 2(b) at t = 200 s (blue, solid), 300 s (green, dashed), 400 s (yellow, dash-dotted), and 500 s (red, dotted): (a) acid concentration c(x, t), (b) electrolyte potential ϕe (x, t), and (c) solid-phase potential ϕs (x, t)

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Fig. 4

Equivalent circuit model

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