Electrochemical Modeling, Estimation and Control of Lithium Ion Batteries

Open Access
Smith, Kandler A.
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
October 05, 2006
Committee Members:
  • Chao Yang Wang, Committee Chair
  • Christopher Rahn, Committee Chair
  • Qian Wang, Committee Member
  • Joseph Paul Cusumano, Committee Member
  • Karen Ann Thole, Committee Member
  • lithium ion
  • battery
  • hybrid electric vehicle
  • model order reduction
  • diffusion systems
  • state of charge estimation
Batteries directly contribute to the advancement of technologies ranging from portable electronics to fuel-efficient vehicles. In high power applications such as hybrid electric vehicles (HEVs), monitoring algorithms use current and voltage measurements to estimate battery state of charge (SOC) and available power. Despite increased cost, these systems commonly employ conservative, oversized batteries due to poor prediction of current/voltage dynamics and imprecise real-time estimation. This dissertation introduces a general, electrochemical model-based approach for safe and efficient integration of Li-ion batteries into transient, pulse power-type systems. A transient solid-state diffusion model is incorporated into a previously developed 1D electrochemical model. The nonlinear model, solving 4 coupled partial differential equations by a computational fluid dynamics (CFD) technique, is validated against low rate constant current, pulse power, and transient driving cycle data sets from a 6 Ah Li-ion HEV battery. Solid-state Li transport (diffusion) significantly limits high rate performance, and end of discharge at the 2.7 V minimum limit is caused by depleted/saturated active material surface concentrations in the negative/positive electrodes for pulses lasting longer than around 10 seconds. The 3.9 V maximum limit, meant to protect the negative electrode from side reactions such as lithium plating, is overly conservative for pulse charging. Increased power capability may be realized by using a real-time electrochemical model to estimate internal states and control the battery within appropriate limits. Development of a fast, stable, and accurate model is difficult however, given the infinite-dimensional, distributed nonlinear processes governing battery dynamics. Here, an impedance model is derived from the electrochemical kinetic, species and charge transport equations and, using a model order reduction technique developed herein, the high order transfer functions/matrices are numerically reduced to an observable/controllable state variable model in modal form. Open circuit potential and electrode surface concentration nonlinearities are explicitly approximated in the model output equation on a local and electrode-averaged basis, respectively. Validated against the 313th order CFD model, a 12th order state variable model with 0-10 Hz bandwidth predicts terminal voltage to within 25 mV (<1%) for pulse and constant current profiles at rates up to 50C. The modeling methodology is valid for all types of porous electrode Li-ion batteries not operating under severe electrolyte transport limitations. A linear Kalman filter is designed for real-time estimation of internal potentials, concentration gradients, and SOC. A reference current governor predicts operating margin with respect to electrode side reactions and surface depletion/saturation conditions responsible for damage and sudden loss of power. Estimates are compared with the nonlinear CFD model. The linear filter gives to within ~2% performance in the 30-70% SOC range except in the case of severe current pulses that drive electrode surface concentrations near saturation and depletion, although the estimates recover as concentration gradients relax. With 4 to 7 states, the filter has low order comparable to equivalent circuit methods presently employed for battery management but, unlike those empirical methods, enables pulse charging/discharging beyond conservative voltage limits. For the 6 Ah HEV battery, the method increases power density by 22% and streamlines the systems integration process for families of battery/vehicle designs.