State-of-Charge estimation from a thermal–electrochemical model of lithium-ion batteries

Shu Xia Tang, Leobardo Camacho-Solorio, Yebin Wang, Miroslav Krstic

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


A thermal–electrochemical model of lithium-ion batteries is presented and a Luenberger observer is derived for State-of-Charge (SoC) estimation by recovering the lithium concentration in the electrodes. This first-principles based model is a coupled system of partial and ordinary differential equations, which is a reduced version of the Doyle–Fuller–Newman model. More precisely, the subsystem of Partial Differential Equations (PDEs) is the Single Particle Model (SPM) while the Ordinary Differential Equation (ODE) is a model for the average temperature in the battery. The observer is designed following the PDE backstepping method. Since some coefficients in the coupled ODE–PDE system are time-varying, this results in the time dependency of some coefficients in the kernel function system of the backstepping transformation and it is non-trivial to show well-posedness of the latter system. Adding thermal dynamics to the SPM serves a two-fold purpose: improving the accuracy of SoC estimation and keeping track of the average temperature which is a critical variable for safety management in lithium-ion batteries. Effectiveness of the estimation scheme is validated via numerical simulations.

Original languageEnglish
Pages (from-to)206-219
Number of pages14
StatePublished - Sep 2017


  • Battery management systems
  • Infinite dimensional systems
  • Lithium-ion batteries
  • PDE backstepping


Dive into the research topics of 'State-of-Charge estimation from a thermal–electrochemical model of lithium-ion batteries'. Together they form a unique fingerprint.

Cite this