On State of Charge Estimation Accuracy for Battery Cells Connected in Series

Open Access
Safi, Jariullah
Graduate Program:
Mechanical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 30, 2015
Committee Members:
  • Hosam Kadry Fathy, Thesis Advisor
  • Sean N Brennan, Thesis Advisor
  • batteries
  • extended kalman filter
  • fisher information
  • cramer rao lower bound
  • bias
  • collective
  • estimation
  • state of charge
  • SOC
This thesis studies the joint estimation of state of charge (SOC) and current sensor bias in a series string of battery cells. Specifically we present - for the first time - a rigorous analysis of the benefits of estimating the SOC of multiple cells in a series string together along with supporting simulation evidence and discuss the role and benefits of SOC heterogeneity in a string of identical cells. While our approach applies generally to most battery chemistries, this thesis focuses on Lithium-Ion cells. We show through derivation of a Fisher information (FI) matrix using a linear first order integrator model of a cell that estimate variance decreases as a larger number of series connected cells is modeled together. The same derivation concludes that the presence of cells with a higher open-circuit voltage vs SOC slope can improve estimate variance even in small strings. We then test the results of the derivation in simulation for both an initial condition estimation problem and a state estimation problem representative of online estimation in battery management systems. This process introduces a modified dual polarization type equivalent circuit model of Lithium Ion batteries. This model maps a combination of the diffusion states and the state of charge to the output voltage: a nuance inspired by the output equation of a physics-based battery model. A discussion of model identification and the design of an extended Kalman filter (EKF) for a string composed of an arbitrary number of cells follows. For these purposes the initial conditions of all cells are unknown and the string current measurement is assumed to be biased. We then study the performance of the filter as a function of the number of modeled cells, the voltage vs SOC slope of individual cells (achieved by using different initial conditions for some cells), and the statistics of the current sensor. Monte Carlo simulations against a high fidelity physics based model of a Lithium-Iron-Phosphate string of cells show that increasing the number of modeled cells and heterogeneity in cell initial conditions can improve estimator performance in the presence of current noise: a result that extends earlier analyses of the impact of current bias. The thesis concludes with a discussion of the results as well as some pack design recommendations.