TY - JOUR
T1 - Control oriented 1D electrochemical model of lithium ion battery
AU - Smith, Kandler A.
AU - Rahn, Christopher D.
AU - Wang, Chao Yang
N1 - Funding Information:
This work was performed at the Pennsylvania State University Electrochemical Engine Center. The authors gratefully acknowledge funding provided by the U.S. Department of Energy Graduate Automotive Technology Education (G.A.T.E.) program through the Pennsylvania Transportation Institute.
PY - 2007/9
Y1 - 2007/9
N2 - Lithium ion (Li-ion) batteries provide high energy and power density energy storage for diverse applications ranging from cell phones to hybrid electric vehicles (HEVs). For efficient and reliable systems integration, low order dynamic battery models are needed. This paper introduces a general method to generate numerically a fully observable/controllable state variable model from electrochemical kinetic, species and charge partial differential equations that govern the discharge/charge behavior of a Li-ion battery. Validated against a 313th order nonlinear CFD model of a 6 Ah HEV cell, a 12th order state variable model predicts terminal voltage to within 1% for pulse and constant current profiles at rates up to 50 C. The state equation is constructed in modal form with constant negative real eigenvalues distributed in frequency space from 0 to 10 Hz. Open circuit potential, electrode surface concentration/reaction distribution coupling and electrolyte concentration/ionic conductivity nonlinearities are explicitly approximated in the model output equation on a local, electrode-averaged and distributed basis, respectively. The balanced realization controllability/observability gramian indicates that the fast electrode surface concentration dynamics are more observable/controllable than the electrode bulk concentration dynamics (i.e. state of charge).
AB - Lithium ion (Li-ion) batteries provide high energy and power density energy storage for diverse applications ranging from cell phones to hybrid electric vehicles (HEVs). For efficient and reliable systems integration, low order dynamic battery models are needed. This paper introduces a general method to generate numerically a fully observable/controllable state variable model from electrochemical kinetic, species and charge partial differential equations that govern the discharge/charge behavior of a Li-ion battery. Validated against a 313th order nonlinear CFD model of a 6 Ah HEV cell, a 12th order state variable model predicts terminal voltage to within 1% for pulse and constant current profiles at rates up to 50 C. The state equation is constructed in modal form with constant negative real eigenvalues distributed in frequency space from 0 to 10 Hz. Open circuit potential, electrode surface concentration/reaction distribution coupling and electrolyte concentration/ionic conductivity nonlinearities are explicitly approximated in the model output equation on a local, electrode-averaged and distributed basis, respectively. The balanced realization controllability/observability gramian indicates that the fast electrode surface concentration dynamics are more observable/controllable than the electrode bulk concentration dynamics (i.e. state of charge).
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U2 - 10.1016/j.enconman.2007.03.015
DO - 10.1016/j.enconman.2007.03.015
M3 - Article
AN - SCOPUS:34547133470
SN - 0196-8904
VL - 48
SP - 2565
EP - 2578
JO - Energy Conversion and Management
JF - Energy Conversion and Management
IS - 9
ER -
