Theoretical Analysis of Battery SOC Estimation Errors Under Sensor Bias and Variance

This paper provides a theoretic and systematic analysis on the battery state of charge (SOC) estimation errors caused by sensor noises. The considered noises include the bias and the variance of both current and voltage sensors. Specifically, the bias and the variance of the SOC estimation error are derived as explicit functions of sensor noises, battery parameters, and observer tuning parameters. The derivation is performed for the Kalman filter, which is the most commonly used method for SOC estimation, and the least squares method. It is found that the observer parameter tuning is subject to a tradeoff between suppressing the estimation bias and variance. Either one of these two errors becomes dominant under different observer parameter ranges. The fundamental estimation error that cannot be mitigated through observer tuning has also been identified. The results have been validated by both simulation and experiment. The obtained theoretical findings are of great practical significance as they could be used to guide sensor selection and observer design, as well as enable online uncertainty management.