Analytic Derivation of Battery SOC Estimation Error under Sensor Noises

It is well recognized that voltage and current sensor noises are one of the major sources of battery state of charge (SOC) estimation errors. However, quantitative relationship between the estimation error and sensing noises remains to be established systematically. This paper is devoted to filling this critical gap by deriving the analytic expression of the SOC estimation error under sensing noises. The considered sensing noises include both bias and variance. The derivation is based on a Kalman filter and an equivalent circuit battery model. The obtained analytic expressions can be conveniently used to evaluate the robustness and reliability of SOC estimation as well as guide observer design.