Computers and Chemical Engineering 64 (2014) 114–123 Contents lists available at ScienceDirect Computers and Chemical Engineering j our na l ho me pa g e: www.elsevier.com/locate/compchemeng Adaptive gain sliding mode observer for state of charge estimation based on combined battery equivalent circuit model Xiaopeng Chen, Weixiang Shen ∗ , Zhenwei Cao, Ajay Kapoor Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia a r t i c l e i n f o Article history: Received 3 February 2013 Received in revised form 8 February 2014 Accepted 16 February 2014 Available online 22 February 2014 Keywords: Adaptive gain sliding mode observer Battery management system Combined battery equivalent circuit model Electric vehicle Lithium-polymer battery State of charge a b s t r a c t An adaptive gain sliding mode observer (AGSMO) for battery state of charge (SOC) estimation based on a combined battery equivalent circuit model (CBECM) is presented. The error convergence of the AGSMO for the SOC estimation is proved by Lyapunov stability theory. Comparing with conventional sliding mode observers for the SOC estimation, the AGSMO can minimise chattering levels and improve the accuracy by adaptively adjusting switching gains to compensate modelling errors. To design the AGSMO for the SOC estimation, the state equations of the CBECM are derived to capture dynamics of a battery. A lithium-polymer battery (LiPB) is used to conduct experiments for extracting parameters of the CBECM and verifying the effectiveness of the proposed AGSMO for the SOC estimation. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction In recent decades, the progressive increase of petrol costs and air pollution of the exhaust fumes from petrol-driven vehicles has stimulated a surge of research and innovation in electric vehi- cle (EV) technologies. Lithium-ion or lithium-polymer batteries (LiPBs) have been adopted as primary power sources in EVs due to their merits in high power and energy densities, high operating voltages, extremely low self-discharge rate and long cycle life in the comparison with other types of batteries such as lead-acid or nickel-metal hydride batteries. For the application of the batter- ies in EVs, the state of charge (SOC) is one of the key parameters which corresponds to the amount of residual available capacity, its accurate indication is crucial for optimising battery energy utilisa- tion, informing drivers the reliable EV travelling range, preventing batteries from over-charging or over-discharging and extend- ing battery life cycles. Unfortunately, the SOC cannot be directly measured by a sensor as it involves in complex electrochemical processes of a battery. An advanced algorithm is required to esti- mate the SOC with the aids of measurable parameters of a battery such as terminal voltage and current. A variety of the SOC estimation techniques has been reviewed by Piller, Perrin, and Jossen (2001) and each method has its own ∗ Corresponding author. Tel.: +61 3 9214 5886; fax: +61 3 9214 8264. E-mail addresses: xchen@swin.edu.au (X. Chen), wshen@swin.edu.au (W. Shen). advantages in certain aspects. The ampere-hour (Ah) counting is the most applicable approach for the SOC indication in many commer- cial battery management systems (BMSs). It simply integrates the battery charge and discharge currents over time and accumulates errors caused by the embedded noises in current measurements. Furthermore, this non-model and open-loop based method has difficulty in determining the initial SOC value. An improved ver- sion of the Ah counting has exhibited better SOC estimation results by on-line evaluating charge and discharge efficiencies with the recalibration of the cell capacity (Ng, Moo, Chen, & Hsieh, 2009). Battery impedance measurement technique is also used for the SOC estimation through injecting small ac signals with a wide range of frequencies into a battery to detect the variation of battery internal impedances (Rodrigues, Munichandraiah, & Shukla, 2000). However, the measured impedances cannot completely model the dynamics of batteries in the case of large discharge current in EVs. Furthermore, the application of impedance spectroscopy has to be carried out in temperature-controlled environment that requires bulky and costly auxiliary equipment since the temperature signif- icantly affects impedance curves. Another category of the SOC estimation methods is based on “black-box” established on machine learning strategies, which includes artificial neural networks (ANNs) (Shen, 2007; Shen, Chan, Lo, & Chau, 2002), fuzzy neural networks (Li, Wang, Su, & Lee, 2007), adaptive fuzzy neural networks (Chau, Wu, Chan, & Shen, 2003) and support vector machine (Hansen & Wang, 2005). These data- oriented approaches can accurately estimate the SOC without its http://dx.doi.org/10.1016/j.compchemeng.2014.02.015 0098-1354/© 2014 Elsevier Ltd. All rights reserved.