Control Oriented 1D Electrochemical Model of Lithium Ion Battery

Kandler A. Smith, Christopher D. Rahn, Chao Yang Wang

Research output: Contribution to journalArticlepeer-review

378 Scopus Citations


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).

Original languageAmerican English
Pages (from-to)2565-2578
Number of pages14
JournalEnergy Conversion and Management
Issue number9
StatePublished - 2007

NREL Publication Number

  • NREL/JA-540-41778


  • Distributed parameter model order reduction
  • Electrochemical model
  • Hybrid electric vehicle
  • Lithium ion battery
  • State of charge estimation


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