Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs

Abstract

Battery management systems in hybrid electric vehicle 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.

In order to use EKF to estimate the desired quantities, we first require a mathematical model that can accurately capture the dynamics of a cell. In this paper we “evolve” a suitable model from one that is very primitive to one that is more advanced and works well in practice. The final model includes terms that describe the dynamic contributions due to open-circuit voltage, ohmic loss, polarization time constants, electro-chemical hysteresis, and the effects of temperature. We also give a means, based on EKF, whereby the constant model parameters may be determined from cell test data. Results are presented that demonstrate it is possible to achieve root-mean-squared modeling error smaller than the level of quantization error expected in an implementation.

Introduction

This paper is the second 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), power fade, capacity fade and instantaneous available power, and is able to adapt to changing cell characteristics over time as the cells in the battery pack age. The algorithms have been implemented on a lithium-ion polymer battery (LiPB) pack, but we expect them to work well for other battery chemistries.

The method that we use to estimate these parameters is based on Kalman filter theory. (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.) Kalman filters are an intelligent—and sometimes optimal—means for estimating the state of a dynamic system. By modeling our battery system to include the wanted unknown quantities in the “state”, we may use the Kalman filter to estimate their values. An additional benefit of the Kalman filter is that it automatically provides dynamic 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 overcharge or overdischarge.

The first paper [3] is an introduction to the problem. It describes the HEV environment and the 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.

This second paper describes some mathematical cell models that may be used with this method. The HEV application is a very harsh environment, with rate requirements up to and exceeding ±20C and very dynamic rate profiles. This is in contrast to relatively benign portable-electronic applications with constant power output and fractional C rates. Methods for estimating SOC that work well in portable-electronic devices may not work well in the HEV application. If precise SOC estimation is required by the HEV, then a very accurate cell model is necessary.

Results of lab tests on physical cells are presented and compared with model prediction. The best modeling results obtained to date are so precise that the root-mean-squared (RMS) estimation error is less than the quantization noise floor expected in our battery management system design. More importantly, the model allows very precise SOC estimation, therefore allowing the vehicle controller to confidently use the battery pack’s full operating range without fear of over- or under-charging cells. This paper 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 test data.

The third paper [4] covers the real-time parameter estimation problem; namely, how to dynamically estimate SOC, power fade, capacity fade, available power 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 briefly reviewing cell models in the literature that have been proposed for SOC estimation. We explain why these do not meet the requirements presented in [3]. Several models from Refs. [5], [6] do meet the requirements, and they are described in detail here, together with some new models and results. A method for identifying model parameters using an extended Kalman filter is presented, followed by conclusions.