Adaptive Partial Differential Equation Observer for Battery State of Charge/State of Health Estimation Via an Electrochemical Model

Abstract

This paper develops an adaptive partial differential equation (PDE) observer for battery stateofcharge (SOC) and stateofhealth (SOH) estimation. Realtime state and parameter information enables operation near physical limits without compromising durability, thereby unlocking the full potential of battery energy storage. SOC/SOH estimation is technically challenging because battery dynamics are governed by electrochemical principles, mathematically modeled by 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 Padأ©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.