Dynamic Prediction of Power Storage and Delivery by Data-Based Fractional Differential Models of a Lithium Iron Phosphate Battery

A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF) method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs), where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 ) in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system.

[1]  Ehsan Samadani,et al.  Three-dimensional Multi-Particle Electrochemical Model of LiFePO4 Cells based on a Resistor Network Methodology , 2016 .

[2]  Xin Zhao,et al.  Data-based modeling of a lithium iron phosphate battery as an energy storage and delivery system , 2013, 2013 American Control Conference.

[3]  Roger A. Dougal,et al.  Dynamic lithium-ion battery model for system simulation , 2002 .

[4]  Ralph E. White,et al.  Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries , 2006 .

[5]  Canbing Li,et al.  Aggregator-Based Interactive Charging Management System for Electric Vehicle Charging , 2016 .

[6]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[7]  Osama A. Mohammed,et al.  Advanced Battery Management and Diagnostic System for Smart Grid Infrastructure , 2016, IEEE Transactions on Smart Grid.

[8]  Ralph E. White,et al.  Modeling Lithium Intercalation of a Single Spinel Particle under Potentiodynamic Control , 2000 .

[9]  Simone Orcioni,et al.  Battery management system simulation using SystemC , 2015, 2015 12th International Workshop on Intelligent Solutions in Embedded Systems (WISES).

[10]  Hugues Garnier,et al.  An optimal instrumental variable method for continuous-time fractional model identification , 2008 .

[11]  Marion Gilson,et al.  The CONTSID Toolbox: A Software Support for Data-based Continuous-time Modelling , 2008 .

[12]  Li Kexue,et al.  Laplace transform and fractional differential equations , 2011 .

[13]  Afshin Izadian,et al.  Adaptive Nonlinear Model-Based Fault Diagnosis of Li-Ion Batteries , 2015, IEEE Transactions on Industrial Electronics.

[14]  Longyun Kang,et al.  Joint Estimation of the Electric Vehicle Power Battery State of Charge Based on the Least Squares Method and the Kalman Filter Algorithm , 2016 .

[15]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[16]  Haiqing Wang,et al.  A New Method for State of Charge Estimation of Lithium-Ion Battery Based on Strong Tracking Cubature Kalman Filter , 2015 .

[17]  Binggang Cao,et al.  Evaluation of Model Based State of Charge Estimation Methods for Lithium-Ion Batteries , 2014 .

[18]  Guy Marlair,et al.  Safety focused modeling of lithium-ion batteries: A review , 2016 .

[19]  Jasim Ahmed,et al.  Algorithms for Advanced Battery-Management Systems , 2010, IEEE Control Systems.

[20]  Hongjie Wu,et al.  Stability Analysis for Li-Ion Battery Model Parameters and State of Charge Estimation by Measurement Uncertainty Consideration , 2015 .

[21]  Jaw-Kuen Shiau,et al.  Li-Ion Battery Charging with a Buck-Boost Power Converter for a Solar Powered Battery Management System , 2013 .

[22]  Huazhen Fang,et al.  Improved adaptive state-of-charge estimation for batteries using a multi-model approach , 2014 .

[23]  Yuang-Shung Lee,et al.  Intelligent control battery equalization for series connected lithium-ion battery strings , 2005, IEEE Trans. Ind. Electron..

[24]  Leon R. Roose,et al.  Extended Kalman Filter with a Fuzzy Method for Accurate Battery Pack State of Charge Estimation , 2015 .

[25]  Eduard Petlenkov,et al.  FOMCON: Fractional-order modeling and control toolbox for MATLAB , 2011, Proceedings of the 18th International Conference Mixed Design of Integrated Circuits and Systems - MIXDES 2011.

[26]  Bruno Francois,et al.  Energy Management and Operational Planning of a Microgrid With a PV-Based Active Generator for Smart Grid Applications , 2011, IEEE Transactions on Industrial Electronics.

[27]  James Marco,et al.  Analysis of a Battery Management System (BMS) Control Strategy for Vibration Aged Nickel Manganese Cobalt Oxide (NMC) Lithium-Ion 18650 Battery Cells , 2016 .

[28]  T. Kaczorek,et al.  Fractional Linear Systems and Electrical Circuits , 2014 .

[29]  Hongwen He,et al.  Evaluation of Lithium-Ion Battery Equivalent Circuit Models for State of Charge Estimation by an Experimental Approach , 2011 .

[30]  Peter C. Young,et al.  Direct Identification of Continuous-time Models from Sampled Data: Issues, Basic Solutions and Relevance , 2008 .

[31]  Sören Hohmann,et al.  Fractional algebraic identification of the distribution of relaxation times of battery cells , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[32]  A. Oustaloup,et al.  Fractional state variable filter for system identification by fractional model , 2001, 2001 European Control Conference (ECC).

[33]  Rolf Findeisen,et al.  Electrochemical Model Based Observer Design for a Lithium-Ion Battery , 2013, IEEE Transactions on Control Systems Technology.

[34]  Igor Podlubny,et al.  The Laplace Transform Method for Linear Differential Equations of the Fractional Order , 1997, funct-an/9710005.

[35]  Helmuth Biechl,et al.  Modelling of Li-ion batteries using equivalent circuit diagrams , 2012 .

[36]  Joo-Ho Choi,et al.  Metamodel for Efficient Estimation of Capacity-Fade Uncertainty in Li-Ion Batteries for Electric Vehicles , 2015 .

[37]  Mariesa L. Crow,et al.  Battery Energy Storage System (BESS) and Battery Management System (BMS) for Grid-Scale Applications , 2014, Proceedings of the IEEE.

[38]  S. Moura,et al.  Enhanced Performance of Li-Ion Batteries via Modified Reference Governors and Electrochemical Models , 2015, IEEE/ASME Transactions on Mechatronics.

[39]  Miroslav Krstic,et al.  PDE estimation techniques for advanced battery management systems — Part II: SOH identification , 2012, 2012 American Control Conference (ACC).

[40]  Min Xu,et al.  Estimation of State of Charge for Two Types of Lithium-Ion Batteries by Nonlinear Predictive Filter for Electric Vehicles , 2015 .

[41]  Miroslav Krstic,et al.  PDE estimation techniques for advanced battery management systems — Part I: SOC estimation , 2012, 2012 American Control Conference (ACC).

[42]  Alain Oustaloup,et al.  Instrumental variable method with optimal fractional differentiation order for continuous-time system identification , 2009 .

[43]  Michael Pecht,et al.  Battery Management Systems in Electric and Hybrid Vehicles , 2011 .