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Research Papers

A Fast, Memory-Efficient Discrete-Time Realization Algorithm for Reduced-Order Li-Ion Battery Models

[+] Author and Article Information
Krishnakumar Gopalakrishnan

Department of Mechanical Engineering,
Imperial College London,
South Kensington,
London SW7 2AZ, UK
e-mails: krishnakumar@imperial.ac.uk;
krishnak@vt.edu

Teng Zhang

Department of Mechanical Engineering,
Imperial College London,
South Kensington,
London SW7 2AZ, UK
e-mail: t.zhang@imperial.ac.uk

Gregory J. Offer

Department of Mechanical Engineering,
Imperial College London,
South Kensington,
London SW7 2AZ, UK
e-mail: gregory.offer@imperial.ac.uk

1Corresponding author.

Manuscript received April 18, 2016; final manuscript received December 12, 2016; published online February 28, 2017. Assoc. Editor: Jan Van herle.

J. Electrochem. En. Conv. Stor. 14(1), 011001 (Feb 28, 2017) (8 pages) Paper No: JEECS-16-1050; doi: 10.1115/1.4035526 History: Received April 18, 2016; Revised December 12, 2016

Research into reduced-order models (ROM) for Lithium-ion batteries is motivated by the need for a real-time embedded model possessing the accuracy of physics-based models, while retaining computational simplicity comparable to equivalent-circuit models. The discrete-time realization algorithm (DRA) proposed by Lee et al. (2012, “One-Dimensional Physics-Based Reduced-Order Model of Lithium-Ion Dynamics,” J. Power Sources, 220, pp. 430–448) can be used to obtain a physics-based ROM in standard state-space form, the time-domain simulation of which yields the evolution of all the electrochemical variables of the standard pseudo-2D porous-electrode battery model. An unresolved issue with this approach is the high computation requirement associated with the DRA, which needs to be repeated across multiple SoC and temperatures. In this paper, we analyze the computational bottleneck in the existing DRA and propose an improved scheme. Our analysis of the existing DRA reveals that singular value decomposition (SVD) of the large Block–Hankel matrix formed by the system's Markov parameters is a key inefficient step. A streamlined DRA approach that bypasses the redundant Block–Hankel matrix formation is presented as a drop-in replacement. Comparisons with existing DRA scheme highlight the significant reduction in computation time and memory usage brought about by the new method. Improved modeling accuracy afforded by our proposed scheme when deployed in a resource-constrained computing environment is also demonstrated.

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Figures

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Fig. 1

Reduced-order modeling (ROM) workflow using classical DRA. (The shaded blocks represent computational bottlenecks).

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Fig. 3

Reduced-order modeling (ROM) workflow using improved DRA

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Fig. 4

Comparison of singular values computed by the conventional and improved SVD methods

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Fig. 5

Memory usage of classical and improved DRA. Overall, RAM usage as well as RAM used only for SVD computation is illustrated.

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Fig. 6

Computation times for classical and improved DRA schemes

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Fig. 7

Comparison of singular values computed by conventional and improved SVD methods under a practical RAM limit of 10 GB

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Fig. 8

Time-domain simulation depicting solid surface concentrations at the boundary of positive electrode and separator

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