# Batteries: Modeling and State of Charge Estimation

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## Abstract

In a battery, reduction and oxidation reactions occur at each of the two electrodes, which are separated by an ionically conductive electrolyte. Typically in a battery, several electrochemical cells are connected in series to provide fixed electromotive force or voltage. Unlike a fuel cell, an electrochemical cell used in a battery is one in which one or both of the reactants are permanently contained in the cell and are not continuously supplied from an external source, and the reaction products are not continuously removed.

## Keywords

Kalman Filter Unscented Kalman Filter Battery Model Innovation Sequence Unscented Transformation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

- Appelbaum J, Weiss R (1982) An electrical model of the lead-acid battery. IEEE telecommunications energy conference, INTELEC82, pp 304–307Google Scholar
- Barsali S, Ceraolo M (2002) Dynamical models of lead-acid batteries: implementation issues. IEEE Trans Energy Convers 17(1):16–23CrossRefGoogle Scholar
- Bhangu BS, Bentley P, Stone DA, Bingham CM (2005) Nonlinear observers for predicting state-of-charge and state-of-health of lead-acid batteries for hybrid electric vehicles. IEEE Trans Vehicular Tech 54:783–794CrossRefGoogle Scholar
- Blanchet I, Frankignoul C, Cane MA (1997) A comparison of adaptive Kalman filters for a tropical pacific ocean model. Monthly Weather Rev, Am Meteorol Soc 125(1):40–58CrossRefGoogle Scholar
- Brown RB, Hwang PYC (1997) Introduction to random signals and applied Kalman filtering, 3rd edn. John Wiley, New YorkMATHGoogle Scholar
- Buller S, Thele M, De Doncker RWAA, Karden E (2005) Impedance-based simulation models of super capacitors and li-ion batteries for power electronic applications. IEEE Trans Ind Appl 41(3):742–747CrossRefGoogle Scholar
- Casacca MA, Salameh ZM (1992) Determination of lead-acid battery capacity via mathematical modeling techniques. IEEE Trans on Energy Convers 7(3):442–446CrossRefGoogle Scholar
- Chan HL, Sutanto D (2000) A new battery model for use with battery energy storage systems and electric vehicles power systems. IEEE Power Eng Soc Winter Meeting, 1(IEEE 0-7803-5935-6/00), pp 470–475Google Scholar
- Evensen G (2003) The ensemble Kalman filter: theoretical and practical implementation. J Ocean Dyn, Springer 53:343–367CrossRefGoogle Scholar
- Evensen G (2007) Data assimilation: the ensemble Kalman filter, SpringerGoogle Scholar
- Giglioli R, Cerolo P (1990) Charge and discharge fourth order dynamic model of the lead battery. 10th international electric vehicle symposium, Hong Kong, pp 1–9Google Scholar
- Han J, Kim D, Sunwoo M (2009) State-of-charge estimation of lead-acid batteries using an adaptive extended Kalman filter. J Power Sources 188:606–612CrossRefGoogle Scholar
- Harris CJ (1976) Problems in system identification and control. Bulletin of the IMA 12(5):139–150Google Scholar
- Hussain AA, Batarseh I (2011) An overview of generic battery models, IEEE power and energy society general meeting, pp 1–6Google Scholar
- Janczak A (2005) Identification of nonlinear systems using neural networks and polynomial models. Springer-Verlag, New YorkMATHGoogle Scholar
- Juang JN (1994) Applied system identification. Prentice-Hall, New JerseyMATHGoogle Scholar
- Julier SJ (2002) The scaled unscented transformation. Proc Am Control Conf 6:4555–4559Google Scholar
- Julier SJ, Uhlmann J (2000) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401–422MathSciNetCrossRefGoogle Scholar
- Julier SJ, Uhlmann J, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimator. IEEE Trans on Automat Contr 45(3):477–482MathSciNetCrossRefMATHGoogle Scholar
- Kailath T (1974) A view of three decades of linear filtering theory. Trans IEEE, IT-20, pp 146–181Google Scholar
- Karden E (2001) Using low-frequency impedance spectroscopy for characterization, monitoring, and modeling of industrial batteries, Ph.D. dissertation, ISEA. RWTH Aachen, Aachen, GermanyGoogle Scholar
- Kerschen G, Worden K, Vakakis AF, Golinval JC (2006) Past, present and future of nonlinear system identification in structural dynamics. Mech Syst Sign Process 20:505–592CrossRefGoogle Scholar
- Ljung L (1999) System identification: theory for the user, prentice hall information and system science series, 2nd edn. Prentice Hall, Upper Saddle River, New JerseyGoogle Scholar
- Ljung L (2006) Identification of nonlinear systems. IEEE ICARV, 1–4244–0342–1/06Google Scholar
- Manwell J, McGowan J (1993) Lead acid battery storage model for hybrid energy system. Sol Energ 50:399–405CrossRefGoogle Scholar
- Manwell J, McGowan J (1994) Extension of the kinetic battery model for wind/hybrid power system. Proc 5th Eur Wind Energy Assoc Conf, pp 1182–1187Google Scholar
- Mauracher P, Karden E (1997) Dynamic modelling of lead/acid batteries using impedance spectroscopy for parameter identification. J Power Sources 67:69–84CrossRefGoogle Scholar
- Mehra RK (1970) On the identification of variances and adaptive Kalman filtering. IEEE transactions on automatic control AC-15(2), pp 175–184Google Scholar
- Mehra RK (1972) Approaches to adaptive filtering. IEEE Trans Autom Control 17(5):693–698MathSciNetCrossRefMATHGoogle Scholar
- Mohamed AH, Schwarz KP (1999) Adaptive Kalman filtering for INS/GPS. J Geodesy 73:193–203CrossRefMATHGoogle Scholar
- Myers KA, Tapley BD (1976) Adaptive sequential estimation with unknown noise statistics. IEEE Trans Autom Control 21:520–523CrossRefMATHGoogle Scholar
- Nasar SA, Unnewehr LE (1993) Electromechanics and electric machines, 2nd edn. Wiley, USAGoogle Scholar
- Nelles O (2001) Nonlinear system identification. Springer-Verlag, New YorkCrossRefMATHGoogle Scholar
- Plett G (2004a) Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: part 1. Background J Power Sources 134:252–261CrossRefGoogle Scholar
- Plett G (2004b) Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: part 2. Model Ident J Power Sources 134:262–276CrossRefGoogle Scholar
- Plett G (2004c) Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: part 3, state and parameter estimation. J Power Sources 134:277–292CrossRefGoogle Scholar
- Plett G (2006) Sigma-point Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 1: Introduction and state estimation, J Power Sources 161:1356–368Google Scholar
- Pop V, Bergveld H, Danilov D, Regtien P, Notten P (2008) Battery management systems: accurate state-of-charge indication for battery-powered applications. philips research book series. Springer press, Berlin, GermanGoogle Scholar
- Reddy T (2010) Linden’s handbook of batteries. 4th ed, McGraw-Hill professionalGoogle Scholar
- Robbins T, Hawkins J (1994) Battery model for over current protection simulation of DC distribution systems, Sixteenth IEEE international telecommunications energy conference, INTELEC94, pp 307–314Google Scholar
- Sage AP (1972) System identification-history, methodology, future prospects. In: Pilkey WD, Cohen R (eds) System identification of vibrating structures: mathematical models from test data. ASME, New YorkGoogle Scholar
- Salameh ZM, Casacca MA, Lynch WA (1992) A mathematical model for lead-acid batteries. IEEE Trans Energ Convers 7(1):93–98CrossRefGoogle Scholar
- Shepherd C (1965) Design of primary and secondary cells. J Electrochem Soc 112(7):657–664CrossRefGoogle Scholar
- Song Q, Qi J, Han J (2006) An adaptive UKF algorithm and its application in mobile robot control. ROBIO ‘06, IEEE international conference on robotics and biomimetic, Kunming, China, pp 1117–1122Google Scholar
- Vasebi A, Partovibakhsh M, Mohammad S, Bathaee T (2007) A novel combined battery model for state-of-charge estimation in lead-acid batteries based on extended Kalman filter for hybrid electric vehicle applications. J Power Sources 174:30–40CrossRefGoogle Scholar
- Vepa R, Zhahir A (2011) High-precision kinematic satellite and doppler aided inertial navigation system. Royal Inst Navig J Navig 64(01):91–108Google Scholar

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