State of charge estimation of lithium-ion batteries using optimized Levenberg-Marquardt wavelet neural network

State of charge (SOC) is one of the most critical parameters for indication of the remaining energy which is vital important for the safety and reliability of power system. In this paper, Levenberg-Marquardt (L-M) algorithm optimized multi-hidden-layer wavelet neural network (WNN) model and a series of novel intelligent SOC estimation methods using L-M based WNN are proposed. Particle swarm optimization (PSO) algorithm is used to optimize L-M based three-layer WNN (LMWNN) for SOC estimation problem. Furthermore, it is validated that L-M based multi-hidden-layer WNN (LMMWNN) has better performance than LMWNN. Basing the specific characteristic of SOC estimation, the LMMWNN method is optimized by combining piecewise-network method (PLMMWNN) and seven-point linear smoothing method (smoothed PLMMWNN). Under single driving cycle, such as the New European Driving Cycle(NEDC), the mean absolute error of PLMMWNN can be decreased to 0.6% and the maximum absolute error 5%. A comparison study of the series of WNN-based methods with BP neural network (BPNN) and extend Kalman filter (EKF) is conducted. The robustness evaluation, which is based on untrained driving cycles test, measurement noise test and piecewise training and batteries test, indicates the good performance on estimation accuracy, applicability and robustness of the proposed methods.