State of charge estimation for Li-ion battery based on model from extreme learning machine $ Jiani Du a , Zhitao Liu b,n , Youyi Wang a a School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore b TUM CREATE,1 CREATE Way, CREATE Tower, Singapore 138602, Singapore article info Article history: Received 20 May 2013 Accepted 23 December 2013 Available online 31 January 2014 Keywords: State of charge (SOC) estimation Battery modeling Extreme learning machine (ELM) Adaptive unscented Kalman filter (AUKF) abstract Lithium-ion (Li-ion) battery state of charge (SOC) estimation is important for electric vehicles (EVs). The model-based state estimation method using the Kalman filter (KF) variants is studied and improved in this paper. To establish an accurate discrete model for Li-ion battery, the extreme learning machine (ELM) algorithm is proposed to train the model using experimental data. The estimation of SOC is then compared using four algorithms: extended Kalman filter (EKF), unscented Kalman filter (UKF), adaptive extended Kalman filter (AEKF) and adaptive unscented Kalman filter (AUKF). The comparison of the experimental results shows that AEKF and AUKF have better convergence rate, and AUKF has the best accuracy. The comparison from the radial basis function neural network (RBF NN) model also verifies that the ELM model has lighter computation load and smaller estimation error in SOC estimation process. In general, the performance of Li-ion battery SOC estimation is improved by the AUKF algorithm applied on the ELM model. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Electric vehicles (EVs) have the advantages of no pollution, high efficiency and comfortable driving environment compared with traditional fossil-fuel vehicles (Ehsani, Gao, & Emadi, 2009). Lithium-ion (Li-ion) batteries are commonly used as the power source for EVs since a Li-ion battery has high efficiency, high charging and discharging rate, low self-discharge, and no memory effect (Faa-Jeng, Ming-Shi, Po-Yi, Han-Chang, & Chi-Hsuan, 2012; Chaturvedi, Klein, Christensen, Ahmed, & AKojic, 2010). However to increase battery life and to ensure safe operation (Jossen, Späth, Döring, & Garche, 1999), a battery management system (BMS) is required to supervise the battery 0 s status and control the battery 0 s energy flow. State of charge (SOC) is an important variable describing the status of a Li-ion battery. SOC is defined as the ratio of the battery 0 s remaining capacity to the nominal capacity (Plett, 2004a). Since over-charging and over-discharging bring inevitable damage to a Li-ion battery, accurate SOC estimation should be provided by the BMS (Plett, 2004b). Piller, Perrin, and Jossen (2001) summarizes different SOC estimation methods. The most widely used technique for SOC estimation is Coulomb counting (Lee, Nam, & Cho, 2007). The principle of Coulomb counting is to take the battery as a capacitor and obtain its storage energy by current integration. Nevertheless, estimation error may be accumulated for this open-loop algorithm, resulting in the estimate drifting away from the true value. Any initial SOC error also causes a bias in the estimation. Another commonly used technique is the open-circuit-voltage (OCV) method. This method obtains SOC from the battery 0 s OCV-SOC relationship (Coleman, Chi Kwan, Chunbo, & Hurley, 2007). However, accurate OCV measurement requires the battery to be in equilibrium state, while the batteries in EVs are at work during driving. Therefore, the OCV method is not suitable for real-time SOC estimation (Piller et al., 2001). The impedance spectroscopy technique measures the battery 0 s impedance by testing the voltage response with a small AC current applied to the battery (Ehsani et al. 2009). A spectroscopy is composed of the impedance data extracted from different fre- quency currents. In (Zenati, Desprez, & Razik, 2010), the intelligent method of fuzzy logic is combined with impedance spectroscopy to achieve better SOC estimation result. This method provides accurate SOC, but it needs specific experiments (Plett, 2004a) so it is not suitable for applications in EVs. Kalman filter (KF) is a mathematical technique that provides an efficient recursive means for estimating the states of a process by minimizing the mean of the squared error (Simon, 2006; Lerro & Bar-Shalom, 1993). Li-ion battery SOC has a nonlinear relationship with other variables (He, Xiong, & Guo, 2012). Therefore, the nonlinear version of KF, extended Kalman filter (EKF), is widely applied to estimate SOC online (Barbarisi, Vasca, & Glielmo, 2006). The essence of EKF is to linearize the system at each time step to Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice 0967-0661/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conengprac.2013.12.014 ☆ This work was financially supported by the Singapore National Research Foundation under its Campus for Research Excellence And Technological Enterprise (CREATE) programme. n Corresponding author. Tel.: þ65 6601 4031; fax: þ65 6694 0062. E-mail address: zhitao.liu@tum-create.edu.sg (Z. Liu). Control Engineering Practice 26 (2014) 11–19