State of charge estimation for electric vehicle batteries using unscented kalman filtering Wei He, Nicholas Williard, Chaochao Chen, Michael Pecht ⇑ Center for Advanced Life Cycle Engineering, University of Maryland, College Park, MD 20742, USA article info Article history: Received 16 June 2012 Received in revised form 1 October 2012 Accepted 22 November 2012 Available online 16 January 2013 abstract Due to the increasing concern over global warming and fossil fuel depletion, it is expected that electric vehicles powered by lithium batteries will become more common over the next decade. However, there are still some unresolved challenges, the most notable being state of charge estimation, which alerts driv- ers of their vehicle’s range capability. We developed a model to simulate battery terminal voltage as a function of state of charge under dynamic loading conditions. The parameters of the model were tailored on-line in order to estimate uncertainty arising from unit-to-unit variations and loading condition changes. We used an unscented Kalman filtering-based method to self-adjust the model parameters and provide state of charge estimation. The performance of the method was demonstrated using data col- lected from LiFePO 4 batteries cycled according to the federal driving schedule and dynamic stress testing. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction With increasing concerns about global warming and fossil fuel depletion, the automobile industry is facing a transition from inter- nal combustion engines (ICEs) to electric vehicles (EVs). The major industrialized nations have outlined their plans for EV develop- ment and production. For example, the US government set a goal of having one million EVs on the road by 2015 [1], and the Chinese government plans to have five million EVs on the road by 2020 [2]. Although EVs will inevitably permeate the market, challenges still exist. One challenge is the ‘‘range anxiety’’ problem, which re- fers to the driver’s fear of running out of battery power on the road [3]. As of 2011, the driving range of an EV was only 40–100 miles, which is 3–4 times less than ICE vehicles. Adding to the problem is the current lack of battery charging infrastructure. Therefore, to prevent EVs from running out of charge on the road and leaving passengers stranded, the ability to predict their residual range is needed. The first step in residual range prediction is to know how much capacity remains in the battery, also known as its state of charge (SOC). The most common method for SOC estimation is Coulomb counting [4,5], in which the remaining charge is calculated by inte- grating the current entering or leaving the battery over time. Cou- lomb counting is simple and easy to implement in on-board applications. However, it requires knowledge of the starting SOC. In addition, Coulomb counting is an open-loop method, and mea- surement noise and battery aging can cause drift. Another popular method for SOC estimation is the voltage-based method, which in- fers SOC by an open circuit voltage (OCV)-SOC look-up table [6]. However, OCV measurement requires a long period of rest before the terminal voltage converges to the actual OCV. With the use of a battery model, it is possible to infer the battery’s OCV from its terminal voltage, but this approach can generate large errors if the model employed is not accurate. A ±0.01 V modeling error in the OCV could produce a 10% error in SOC estimation for LiFePO 4 batteries. Other work has been conducted using computational intelligence algorithms, such as fuzzy-logic [7], artificial neural networks (NNs) [8–12], and support vector machines (SVMs) [13–15], which do not require detailed expert knowledge of bat- tery systems. A typical example is the SVM-based SOC estimator for a large-scale lithium–ion polymer battery pack developed by Hansen and Wang [13]. The SVM estimator was tested with US06 dynamic operational data from the US Department of Energy’s Hy- brid Electric Vehicle program, and the root-mean-square (RMS) er- ror of the SOC estimation was within 6%. Computational intelligence methods can be accurate if the training data are suffi- cient to cover the loading conditions of the battery. However, col- lecting training data that provide good coverage of all the loading conditions can be time consuming. Recently, effort has been focused on developing model-based filtering methods [16–24] aimed at establishing closed-loop esti- mation. The equivalent circuit model and electrochemical model are used to establish a battery state-space model, where the cur- rent is used as the input, the terminal voltage is the output, and the SOC is set as the hidden state. Then, a filtering method, such as the extended Kalman filter (EKF) or particle filter (PF) is utilized to estimate the hidden state. Plett [16–18] developed an EKF framework for SOC estimation of LiFePO 4 batteries, which is closed-loop in nature. At each time point, the filter proposes a 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.11.010 ⇑ Corresponding author. E-mail address: pecht@calce.umd.edu (M. Pecht). Microelectronics Reliability 53 (2013) 840–847 Contents lists available at SciVerse ScienceDirect Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel