736 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012 A Method for Online Capacity Estimation of Lithium Ion Battery Cells Using the State of Charge and the Transferred Charge Markus Einhorn, Member, IEEE, Fiorentino Valerio Conte, Christian Kral, Senior Member, IEEE, and Juergen Fleig Abstract—In this paper, a method to estimate the capacity of individual lithium ion battery cells during operation is presented. When having two different states of charge of a battery cell as well as the transferred charge between these two states, the capacity of the battery cell can be estimated. The method is described in detail and validated on a battery cell with a current pulse test cycle. It is then applied to a real-life cycle; the accuracy is analyzed and discussed. Index Terms—Battery management, capacity estimation, lithium ion (Li-ion) battery, state of charge. I. I NTRODUCTION T HE ESTIMATION of the remaining as well as the total capacity of a battery cell is an important issue both for mobile and stationary battery applications. The capacity of a battery cell is changing over its lifetime due to aging, and thus a method to estimate its capacity is necessary [1], [2]. The capacity of a battery cell can be estimated by fully discharg- ing it and integrating the measured current (charge counting) [3], [4]. When lithium ion (Li-ion) battery cells are serially connected to a battery stack, the discharging process has to stop as soon as one cell is completely discharged [5]. The cell with the lowest capacity is usually the first one which is completely discharged and therefore limits the capacity of the whole battery. Though the capacity of this cell could be estimated by measuring and integrating the cell current, the capacities of the other cells cannot be determined with charge counting. However, a battery stack is usually not completely dis- charged. For example the battery package of an electric vehicle is typically charged before it is completely empty. Hence, a Manuscript received August 17, 2011; accepted November 16, 2011. Date of publication December 26, 2011; date of current version March 21, 2012. Paper 2011-ESC-448, presented at the 2010 IEEE International Conference on Sustainable Energy Technologies (ICSET), Kandy, Sri Lanka, December 6–9, and approved for publication in the IEEE TRANSACTIONS ON I NDUSTRY APPLICATIONS by the Energy Systems Committee of the IEEE Industry Applications Society. This work was supported by the Austrian Research Promotion Agency (Oesterreichische Forschungsfoerderungsgesellschaft mbH, Klimaund Energiefonds, Neue Energien 2020) under Research Project 825484, Energy Management for Batteries (e-manager). M. Einhorn, F. V. Conte, and C. Kral are with the Mobility Department, Electric Drive Technologies, Austrian Institute of Technology (AIT), 1210 Vienna, Austria (e-mail: markus.einhorn@ait.ac.at; valerio.conte@ait.ac.at; christian.kral@ait.ac.at). J. Fleig is with the Institute of Chemical Technologies and Analytics, Vienna University of Technology, 1060 Vienna, Austria (e-mail: j.fleig@tuwien.ac.at). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2011.2180689 Fig. 1. Equivalent circuit of a battery cell. battery cell is either charged or discharging stops, before it is completely discharged. In this paper, a method which allows estimating the capacity of any battery cell is presented. With this method, the cell does not have to be completely discharged. The method is explained in detail and validated by using a current pulse test cycle as well as a real-life cycle. II. CELL CAPACITY ESTIMATION METHOD In this section, the proposed method for the online capacity estimation of a single battery cell is presented. The stored charge Q in a battery cell referred to the total capacity C is defined as the state of charge SOC = Q C . (1) Therefore, SOC =1 when the battery cell is fully charged and SOC =0 when the battery cell is completely discharged. During charging/discharging, between time t α and t β , the stored charge is altered from Q α to Q β = Q α - ΔQ α,β = Q α - t β  t α I cell (t)dt. (2) I cell is positive during discharging as shown in a Fig. 1 as a typical equivalent circuit of a battery cell. In the same manner as Q α changes to Q β , the SOC changes from SOC α = SOC(t α ) to SOC β = SOC(t β ). By using (1) for t α as well as for t β and (2), the total capacity of the battery cell can be calculated with C = C α,β = Q α - Q β SOC α - SOC β = t β  t α I cell (t)dt SOC(t α ) - SOC(t β ) . (3) 0093-9994/$26.00 © 2011 IEEE