Adaptive PDE Observer for Battery SOC/SOH Estimation

This paper develops an adaptive PDE observer for battery state-of-charge (SOC) and state-of-health (SOH) estimation. Real-time state and parameter information enables opera-tion near physical limits without compromising durability, thereby unlocking the full potential of battery energy stor-age. SOC/SOH estimation is technically challenging because battery dynamics are governed by electrochemical princi-ples, mathematically modeled by partial differential equations (PDEs). We cast this problem as a simultaneous state (SOC) and parameter (SOH) estimation design for a linear PDE with a nonlinear output mapping. Several new theoretical ideas are developed, integrated together, and tested. These include a backstepping PDE state estimator, a Padé-based parameter identifier, nonlinear parameter sensitivity analysis, and adaptive inversion of nonlinear output functions. The key novelty of this design is a combined SOC/SOH battery estimation algorithm that identifies physical system variables, from measurements of voltage and current only. Nomenclature A Cell cross sectional area [m2] a j Specific interfacial surface area [m2/m3] c0e Li concentration in electrolyte phase [mol/m 3] c js Li concentration in solid phase [mol/m3] c jss Li concentration at particle surface [mol/m3] c js,max Max Li concentration in solid phase [mol/m3] D js Diffusion coefficent in solid phase [m2/sec3] F Faraday’s constant [C/mol] I Input current [A] i j0 Exchange current density [V] j Positive (+) or negative (-) electrode k j Reaction rate [A·mol1.5/m5.5] L j Electrode thickness [m] nLi Total number of Li ions [mol] q Boundary input coefficient parameter R Universal gas constant [J/mol-K] R f Lumped current collector resistance [Ω] R js Particle radius [m] r Radial coordinate [m] or [m/m