ABSTRACT

Introduction ......................................................................................................... 988 Model Reformulation ......................................................................................... 991

Reformulation for the Finite Difference Method ............................... 991 Reformulation for Polynomial Representation .................................. 993

Parameter Estimation for Capacity Fade Prediction ...................................... 997 Optimal Design of Lithium-ion Batteries ..................................................... 1001 Conclusions ........................................................................................................ 1003 Acknowledgments ............................................................................................ 1003 References ........................................................................................................... 1004

Several issues arise in the operation of lithium-ion batteries-capacity fade, underutilization, abuse caused by overcharging, and thermal runaway caused by operation outside the safe window (Newman et al, 2003). For example, the batteries used in hybrid cars operate at 50% state of charge to enhance life while compromising on utilization (energy efciency). The capability to accurately predict capacity and internal state variables is highly desired as it can help extend the life of the battery and provide for better operational strategies. Three different approaches have been used in the literature for modeling lithium-ion batteries: (1) empirical models (Plett, 2004), (2) transport phenomena models (Doyle et al, 1993), and (3) stochastic models (Darling and Newman, 1999). Although parameter estimation, design calculations, and dynamic optimization are easiest to apply to empirical models due to their low computational cost, these models fail at many operating conditions and cannot predict the future behavior or current capacity accurately. Several recent studies have tried to understand micro-and nanoscale phenomena in batteries using stochastic methods. These models would need to be coupled with transport phenomena models to predict process behavior of batteries at the system level.