Elsevier

Journal of Power Sources

Volume 134, Issue 2, 12 August 2004, Pages 252-261
Journal of Power Sources

Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 1. Background

https://doi.org/10.1016/j.jpowsour.2004.02.031Get rights and content

Abstract

Battery management systems (BMS) in hybrid-electric-vehicle (HEV) battery packs must estimate values descriptive of the pack’s present operating condition. These include: battery state of charge, power fade, capacity fade, and instantaneous available power. The estimation mechanism must adapt to changing cell characteristics as cells age and therefore provide accurate estimates over the lifetime of the pack.

In a series of three papers, we propose a method, based on extended Kalman filtering (EKF), that is able to accomplish these goals on a lithium-ion polymer battery pack. We expect that it will also work well on other battery chemistries. These papers cover the required mathematical background, cell modeling and system identification requirements, and the final solution, together with results.

This first paper investigates the estimation requirements for HEV BMS in some detail, in parallel to the requirements for other battery-powered applications. The comparison leads us to understand that the HEV environment is very challenging on batteries and the BMS, and that precise estimation of some parameters will improve performance and robustness, and will ultimately lengthen the useful lifetime of the pack. This conclusion motivates the use of more complex algorithms than might be used in other applications. Our premise is that EKF then becomes a very attractive approach. This paper introduces the basic method, gives some intuitive feel to the necessary computational steps, and concludes by presenting an illustrative example as to the type of results that may be obtained using EKF.

Introduction

This paper is the first in a series of three that describe advanced algorithms for a battery management system (BMS) for hybrid-electric-vehicle (HEV) application. This BMS is able to estimate battery state of charge (SOC), instantaneous available power, and parameters indicative of the battery state of health (SOH) such as power fade and capacity fade, and is able to adapt to changing cell characteristics over time as the cells in the battery pack age. The algorithms have been successfully implemented on a lithium-ion polymer battery (LiPB) pack, and we also expect them to work well for other battery chemistries.

A hybrid-electric-vehicle is one with both a gasoline (or diesel) engine and an electric motor. Both may be coupled directly to the power train—resulting in a “parallel hybrid” configuration—where the motor provides boost energy to supplement the engine and acts as a generator when coasting, braking, or when the engine can supply extra power to charge the battery pack. Alternately, the engine may be used exclusively to drive a generator that charges the battery pack; the motor is then coupled directly to the power train—resulting in a “series hybrid” configuration. The series configuration promises greater potential efficiency, at the cost of a larger required battery pack. At the time of the writing of this paper, the only HEVs on the market in the US are parallel hybrid systems and require a battery pack of fairly modest size. Even so, and because of the demanding requirements on a pack of limited capacity, advanced methods must be used to estimate SOC, SOH, and instantaneous power in order to safely, efficiently and aggressively exploit the pack capabilities.

The method we use to estimate these parameters is based on Kalman filter theory. Kalman filters are an intelligent—and sometimes optimal—means for estimating the present value of the time-varying “state” of a dynamic system. By modeling our battery system to include the wanted unknown quantities in its state description, we may use a Kalman filter to estimate their values. An additional benefit of the Kalman filter is that it automatically provides dynamic estimation error bounds on these estimates as well. We exploit this fact to give aggressive performance from our battery pack, without fear of causing damage by over-charge or over-discharge. Note that there have been other reported methods for SOC estimation that use Kalman filtering [1], [2], but the method in this series of papers expands on these results and also differs in some important respects, as will be outlined later [3].

This first paper is an introduction to the problem. It describes the HEV environment and the algorithmic requirement specifications for a BMS. The remainder of the paper is a brief tutorial on the Kalman filter theory necessary to grasp the content of the remaining papers; additionally, a nonlinear extension called the “extended Kalman filter” (EKF) is discussed.

The second paper [3] describes some mathematical cell models that may be used with this method. It also gives an overview of other modeling methods in the literature and shows how an EKF may be used to adaptively identify unknown parameters in a cell model, in real time, given cell input–output data.

The third paper [4] covers the parameter estimation problem; namely, how to dynamically estimate SOC, power fade, capacity fade and so forth. An EKF is used in conjunction with the cell model. The cell model may be fixed, or may itself have adaptable parameters so that the model tracks cell aging effects. Details for a practical implementation are discussed.

We now proceed by discussing requirements for a BMS in the HEV environment, and comparing them to requirements for other battery-powered systems. The additional requirements of HEV justify the use of advanced algorithms. We then review essential Kalman filter theory with the aim being to demystify the steps involved. An example of linear Kalman filtering is given to illustrate the presentation.

Section snippets

HEV versus portable electronics BMS environments

In principle, the results of these papers could be applied to manage the performance of any battery-based system, including, for example, hybrid electric vehicles, battery electric vehicles (BEVs) and consumer portable electronics (PE). The HEV environment, however, is particularly harsh—imposing many difficult requirements on the battery cells and BMS—and motivates the use of advanced techniques. In our experience, battery management algorithms developed for portable electronic applications,

Linear Kalman filtering

Many of the algorithm requirements just described prescribe estimating parameters of a battery pack that may not be directly measured. We find that Kalman filtering provides an elegant and powerful solution. Kalman filtering is an established technology for dynamic system state estimation that is in common use in many fields including: target tracking, global positioning, dynamic systems control, navigation, and communication, but is not widely known in the battery field. The Kalman filter

Extended Kalman filtering

The Kalman filter is the optimum state estimator for a linear system with the assumptions as described. If the system is nonlinear, then we may use a linearization process at every time step to approximate the nonlinear system with a linear time varying (LTV) system. This LTV system is then used in the Kalman filter, resulting in an extended Kalman filter (EKF) on the true nonlinear system. Note that although EKF is not necessarily optimal, it often works very well.

We model the nonlinear system

Example of Kalman filtering

In order to illustrate some of the concepts outlined in this paper, we present a simple example of linear Kalman filtering. We consider the system defined by the linear circuit in Fig. 5. We find the continuous-time state-space model of this circuit to be: vc(t)=−1R2Cvc(t)−1Ci(t)+1Cw(t),vt(t)=vc(t)−R1i(t)+v(t),where vc(t) is the capacitor voltage as a function of time, i(t) the current exciting the circuit, and vt(t) the terminal voltage, as indicated in the diagram. This circuit is a crude

Conclusions

In this paper we have described the algorithmic requirements of the BMS and its operating environment in the HEV scenario. The particular demands of HEV justify the use of advanced algorithms. We have also reviewed the Kalman filter and extended Kalman filter methods, explaining the motive of each computational step. We presented an example to clarify the discussion. In the following two papers, we will combine this information in such a way that we are able to meet the algorithmic requirements

Acknowledgements

This work was supported in part by Compact Power Inc. (CPI). The use of company facilities, and many enlightening discussions with Drs. Mohamed Alamgir and Dan Rivers and others are gratefully acknowledged.

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The author is also consultant to Compact Power Inc., Monument, CO 80132, USA. Tel.: +1-719-488-1600; fax: +1-719-487-9485.

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