Dimensionless Tuning Procedure of the Kalman Filter for State-Of-Charge Estimators

This paper presents a solution to the challenging problem of estimating the state of charge (SOC) of batteries using a Kalman filter algorithm. The algorithm requires knowledge of the dynamical model and its parameters, along with the covariance matrices associated with measurement noise, process noise, and initial estimation error. However, determining the values for the process noise and initial estimation error matrices is often difficult. To address this issue, we propose a novel method to tune these matrices based on a new tuning parameter, the measurement noise variance, and the expected slope of the open circuit voltage vs. state of charge curve. We demonstrate the effectiveness of the proposed approach through extensive simulations involving various batteries and operating conditions in an electrical driving scenario. We assess the performance of the Kalman filter estimation under noisy environments, wrong initial conditions, and modeling errors, obtaining dimensionless performance indices that quantify its behavior. By analyzing the simulation results, we establish a general design procedure for the process covariance matrix, where the user only needs to set the desired limits for the state of charge error in noisy environments and the convergence time under wrong initializations. This design procedure is applicable to batteries of any type, sampling period, or measurement noise level, providing a practical and efficient solution for accurate state of charge estimation