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MODELING FOR CONTROL

Lithium-Ion Battery State of Charge and Critical Surface Charge Estimation Using an Electrochemical Model-Based Extended Kalman Filter

[+] Author and Article Information
Domenico Di Domenico

 Institut Français du Pétrole (IFP), IFP Energies Nouvelles, Rond-Point de l’échangeur de Solaize, B.P. 3, 69360 Solaize, Lyon, Francedidomend@ifp.fr

Anna Stefanopoulou

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2121annastef@umich.edu

Giovanni Fiengo

Dipartimento di Ingegneria, Università degli Studi del Sannio, Piazza Roma 21, 82100 Benevento, Italygifiengo@unisannio.it

J. Dyn. Sys., Meas., Control 132(6), 061302 (Oct 29, 2010) (11 pages) doi:10.1115/1.4002475 History: Received September 29, 2008; Revised March 22, 2010; Published October 29, 2010; Online October 29, 2010

This paper presents a numerical calculation of the evolution of the spatially resolved solid concentration in the two electrodes of a lithium-ion cell. The microscopic solid concentration is driven by the macroscopic Butler–Volmer current density distribution, which is consequently driven by the applied current through the boundary conditions. The resulting, mostly causal, implementation of the algebraic differential equations that describe the battery electrochemical principles, even after assuming fixed electrolyte concentration, is of high order and complexity and is denoted as the full order model. The full order model is compared with the results in the works of Smith and Wang (2006, “Solid-State Diffusion Limitations on Pulse Operation of a Lithium-Ion Cell for Hybrid Electric Vehicles,” J. Power Sources, 161, pp. 628–639) and Wang (2007 “Control oriented 1D Electrochemical Model of Lithium Ion Battery,” Energy Convers. Manage., 48, pp. 2565–2578) and creates our baseline model, which will be further simplified for charge estimation. We then propose a low order extended Kalman filter for the estimation of the average-electrode charge similarly to the single-particle charge estimation in the work of White and Santhanagopalan (2006, “Online Estimation of the State of Charge of a Lithium Ion Cell,” J. Power Sources, 161, pp. 1346–1355) with the following two substantial enhancements. First, we estimate the average-electrode, or single-particle, solid-electrolyte surface concentration, called critical surface charge in addition to the more traditional bulk concentration called state of charge. Moreover, we avoid the weakly observable conditions associated with estimating both electrode concentrations by recognizing that the measured cell voltage depends on the difference, and not the absolute value, of the two electrode open circuit voltages. The estimation results of the reduced, single, averaged electrode model are compared with the full order model simulation.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic macroscopic (x-direction) cell model with coupled microscopic (r-direction) solid diffusion model. The electrodes nomenclature refers to the battery discharge (reproduced from 11 and 12).

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Figure 2

Schematic representation of the set of equations and of the boundary conditions for the potentials and solid concentration. The current I is assumed to be positive (battery discharge) and provide boundary condition (boxes with dotted line) and the nonlocal constraints (boxes with solid line) governing the Butler–Volmer current density.

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Figure 3

Battery voltage prediction. SOC initial conditions used in the model vary from 30% to 70% of the total charge.

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Figure 4

Numerical solution during discharge referring to a battery current I=30 A after 2 s (i.e., after 4 s of the FreedomCAR test). The solid concentration critical point for electrodes depletion/saturation is highlighted with a circle.

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Figure 5

Numerical solution during charge referring to a current I=−25 A after 3 s (i.e., after 55 s of the FreedomCAR test). The solid concentration critical point for electrodes depletion/saturation is highlighted with a circle.

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Figure 6

Voltage response of average versus full order model for different constant current from 10 A to 300 A

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Figure 7

Average versus full order model

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Figure 8

Average versus full order battery model: negative and positive electrode solid material concentration. The different lines represent the concentration values along the x-direction.

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Figure 9

Average versus full order battery model: error between the average solid concentration and the solid concentration at the electrodes-separator interface

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Figure 10

Average versus full order battery model: spatial distribution of electrode solid surface concentration at various time (0.1 s, 1 s, 5 s, and 15 s) during a 30 A discharge and its error with respect to the average model prediction

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Figure 11

Spatial distribution of electrode solid surface concentration during pulse operation at various time (0.1 s, 0.3 s, and 0.5 s) during a 180 A discharge and its error with respect to the average model prediction

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Figure 12

Kalman filter: solid concentration estimation

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Figure 13

Kalman filter: error between the average solid concentration estimation and full order model prediction at the electrolytes-separator interface. The transient in the EKF estimation is not shown.

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Figure 14

Kalman filter: CSC and SOC estimations compared with the coulomb counting SOC

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Figure 15

Kalman filter: open circuit voltage estimation

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Figure 16

Kalman filter: solid concentration estimation when noise is added to the measurements

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Figure 17

Kalman filter: cell voltage estimation when noise is added to the measurements

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