  In this paper, we consider the problem of state of charge estimation for
rechargeable batteries. Coulomb counting is one of the traditional approaches
to state of charge estimation and it is considered reliable as long as the
battery capacity and initial state of charge are known. However, the Coulomb
counting method is susceptible to errors from several sources and the extent of
these errors are not studied in the literature. In this paper, we formally
derive and quantify the state of charge estimation error during Coulomb
counting due to the following four types of error sources: (i) current
measurement error; (ii) current integration approximation error; (iii) battery
capacity uncertainty; and (iv) the timing oscillator error/drift. It is shown
that the resulting state of charge error can either be of the time-cumulative
or of state-of-charge-proportional type. Time-cumulative errors increase with
time and has the potential to completely invalidate the state of charge
estimation in the long run. State-of-charge-proportional errors increase with
the accumulated state of charge and reach its worst value within one
charge/discharge cycle. Simulation analyses are presented to demonstrate the
extent of these errors under several realistic scenarios and the paper
discusses approaches to reduce the time-cumulative and state of
charge-proportional errors.
