A high-gain adaptive observer for detecting Li-ion battery terminal voltage collapse

doi:10.1016/j.automatica.2013.12.011

Automatica

Volume 50, Issue 3, March 2014, Pages 896-902

https://doi.org/10.1016/j.automatica.2013.12.011 Get rights and content

Abstract

We use a high-gain adaptive observer and a trend filtering algorithm to detect early stages that lead to terminal voltage collapses in Li-ion batteries. This approach allows accurate detection without having sophisticated battery models. Theoretical analysis proves that the physical Li-ion battery becomes unstable when the estimated states of the observer enter instability. The trend filtering algorithm is able to detect such instability under large perturbations from the discharge current. Extensive simulation and experimental results demonstrate the effectiveness of the algorithms and its robustness under realistic perturbations.

Introduction

Low self-discharge rate, no memory effect, and high energy density are some of the characteristics (Linden & Reddy, 2002) that make Li-ion batteries viable as power sources for a broad range of applications. The terminal voltage of a battery drops sharply from its operating value when it is in a low state of charge (SoC) (Hatzell, Sharma, & Fathy, 2012). Hence early detection is crucial to avoid system failure.

A constant threshold voltage can be used to determine that a particular battery is discharged (Kim & Shin, 2009). This method is inaccurate since the terminal voltage of a battery depends on the discharge current it supplies. Using a constant voltage threshold can lead to false alarms in the presence of noise or large spikes in the discharge current. Another strategy is to use a threshold on the SoC. This strategy is affected by load demand, number of charge–discharge cycles and temperature. Determining the SoC involves a method named “coulomb counting”, which introduces errors as the measured input current is integrated in the presence of measurement errors (Pop, Bergveld, Danilov, & Regtien, 2008).

Incorporating battery models improves the accuracy of detecting an impending terminal voltage collapse. Various types of battery models (Chen and Mora, 2006, Knauff et al., 2007, Rao et al., 2003) and associated identification techniques exist (Abu-Sharkh and Doerffel, 2004, Liu, 2011, Schweighofer et al., 2003, Wang et al., 2012). Dynamic battery models along with adaptive thresholds (Zhang, Shi, & Mukhopadhyay, 2013) can overcome some problems with constant thresholds. Filtering algorithms (Plett, 2004, Wang and Cassandras, 2012) for state estimation and fault detection strategies like residual generation can also be used. All the above methods require detailed battery models. Substantial time and effort (Coleman et al., 2008, Sitterly et al., 2011) is needed to obtain such models. Battery characteristics may differ from the model used; resulting in voltage collapse before a particular algorithm detects it. Existing results are either dependent on a particular testing methodology or on a particular type of model (Coleman et al., 2008, Plett, 2004). This paper presents an approach that aims at reducing such dependence without sacrificing the ability to detect voltage collapses.

The contributions of this paper are as follows. We present a general method for detecting Li-ion battery voltage collapses without the requirement of a detailed model. Inspired by universal adaptive stabilization (UAS) (Ilchmann, 1993, Mukhopadhyay et al., 2008) we develop a high-gain adaptive observer which allows us to detect changes in the trend of the transient states of a Li-ion battery. The change in trend helps us decide whether the terminal voltage of a battery is about to collapse. To the best of our knowledge, we are not aware of previous results in the literature that follow a similar approach. This method only requires the measurement of the terminal voltage of a battery and works in the presence of measurement noise or voltage spikes due to non-smooth current discharges. It is not necessary to measure the discharge current nor to use coulomb counting techniques. Thus the cost of accurate current measurement and associated errors are eliminated. This method does not estimate the SoC of a battery and does not set a static threshold on the SoC or terminal voltage, hence it is considerably robust to variations in the SoC and the terminal voltage.

This paper is organized as follows. Section 2 introduces battery models and earlier stability results. Section 3 presents the formulation of the voltage collapse detection problem. The high-gain adaptive observer and a proof of convergence is provided in Section 4. A trend detection algorithm is introduced in Section 5 for detecting terminal voltage collapse. Simulations and experimental results are presented in Sections 6 Simulation, 7 Experiments respectively. A few preliminary results have appeared in our previous paper (Mukhopadhyay & Zhang, 2012). This paper contains improved proofs and experimental results.

Section snippets

Battery model and stability

Chen and Mora’s (CM) model (Chen & Mora, 2006), shown in Fig. 1, is an equivalent circuit representation of a Li-ion battery showing two coupled circuits. The left half models the variation of the SoC $ρ$ (commonly known as the capacity remaining) and the right half models the variation of battery output voltage $y$ as a function of the charge/discharge current $i (t)$ . Knauff et al. (2007) derived the following state space realization for the CM model $\dot{ρ} = - \frac{1}{C_{c}} i$ ${\dot{x}}_{1} = - \frac{x_{1}}{R_{t s} C_{t s}} + \frac{i}{C_{t s}}$ ${\dot{x}}_{2} = - \frac{x_{2}}{R_{t l} C_{t l}} + \frac{i}{C_{t l}}$ $y = E_{o} - x$

Problem formulation

As a battery is gradually discharged, the value of its SoC $ρ$ will decrease until the terminal voltage collapses. Our goal is to detect when a Li-ion battery makes a transition from its stable region of operation (i.e. $ρ \in (δ_{2}, 1]$ ) to the unstable region (i.e. $ρ \in (0, δ_{1})$ ) based on the measurements of its terminal voltage $y$ . On the other hand a temporary drop in terminal voltage does not imply that the battery is unstable. And therefore such temporary drops in terminal voltage make it difficult to

The high-gain adaptive observer

Fig. 2 shows the high-gain adaptive observer we propose for detecting the terminal voltage collapse of a Li-ion battery. It consists of three main blocks. The first block on the left with input $i$ and output $y$ represents the real Li-ion battery, which we assume can be represented by a CM model that is unknown to the observer. The block shown using a dashed rectangle is a high gain observer, it consists of a low pass filtering block which is described in Section 4.1. The block in the middle

Terminal voltage collapse detection

We now propose an algorithm to detect terminal voltage collapses for Li-ion batteries by monitoring trends in the states ${\hat{x}}_{1}, {\hat{x}}_{2}$ . Inspired by the Razumikhin theorem (Zhang & Chen, 1998) and its use in Wu and Zhang (2012) we propose Algorithm 1.

In Algorithm 1 the user picks any value for $j$ from the set ${1, 2}$ . For monitoring both states two copies of the algorithm must be run in parallel with $j = 1, 2$ respectively for each copy. Let ${\hat{x}}_{j_{\min}} = {min}_{τ \in [0, t]} ({\hat{x}}_{j} (τ))$ i.e. the running minimum for state ${\hat{x}}_{j}$ .

Simulation

To investigate the performance of the high-gain adaptive observer and the trend detection algorithm in real-life, we perform the following simulations and experiments.

Experiments

Fig. 6 shows a schematic of the setup used to test Algorithm 1 on a Li-ion battery. Algorithm 1 runs on a computer running Matlab and Simulink. The battery tester board discharges the battery according to commands received from the computer. The Quanser Q2-USB AD/DA board interfaces the computer with the battery tester board. The tester board consists of a Li-ion battery ‘B’ connected in series with a relay unit ‘R’, a light-emitting diode (LED) ‘L’, one of the resistors $R_{1}, \dots, R_{4}$ depending upon

Conclusion

We propose a high-gain adaptive observer and a trend filter to detect changes in trend in the states of a physical Li-ion battery. The method is based on classical techniques, is theoretically justified and also verified by simulations and experiments. This method only requires measurements of the terminal voltage, and does not require measurements of the discharge current. The method is less susceptible to false alarms which are a concern to static threshold based systems. Since the method

Acknowledgment

The authors also wish to acknowledge Phillip Cheng for developing the battery tester board.

Shayok Mukhopadhyay is currently a Ph.D. candidate in electrical engineering at the Georgia Institute of Technology, GA, USA. He received his B.E. in electrical engineering from the College of engineering Pune (C.O.E.P), University of Pune, India in 2006. He received his M.Sc. in electrical engineering from Utah State University, Logan, UT, USA in 2009. His research interests include nonlinear systems and computational methods in general. He also likes computer programming.

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Fumin Zhang received the B.S. and M.S. degrees from Tsinghua University, Beijing, China, in 1995 and 1998, respectively, and the Ph.D. degree from the Department of Electrical and Computer Engineering, University of Maryland, College Park, in 2004. He joined the School of ECE, Georgia Institute of Technology in 2007, where he is an Associate Professor. He was a Lecturer and Postdoctoral Research Associate in the Mechanical and Aerospace Engineering Department, Princeton University from 2004 to 2007. His research interests include marine autonomy, mobile sensor networks, and theoretical foundations for battery supported cyber–physical systems. He received the NSF CAREER Award in 2009, and the ONR YIP Award in 2010.

^☆: This research was partially supported by the ONR grants N00014-09-1-1074 and N00014-10-10712 (YIP), and NSF grants ECCS-0841195 (CAREER), CNS-0931576, OCE-1032285, and IIS-1319874. The material in this paper was partially presented at the 51st IEEE International Conference on Decision and Control (CDC), December 10–13, 2012, Maui, Hawaii, USA. This paper was recommended for publication in revised form by Associate Editor Kyung-Soo Kim under the direction of Editor Toshiharu Sugie.

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Brief paperA high-gain adaptive observer for detecting Li-ion battery terminal voltage collapse☆

Abstract

Introduction

Section snippets

Battery model and stability

Problem formulation

The high-gain adaptive observer

Terminal voltage collapse detection

Simulation

Experiments

Conclusion

Acknowledgment

Journal of Power Sources

Automatica

Journal of Power Sources

Automatica

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Adaptive nonlinear output feedback tracking with a partial high-gain observer and backstepping

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Brief paper
A high-gain adaptive observer for detecting Li-ion battery terminal voltage collapse☆