Fractional-order models of supercapacitors, batteries and fuel cells: a survey

This paper surveys fractional-order electric circuit models that have been reported in the literature to best fit experimentally collected impedance data from energy storage and generation elements, including super-capacitors, batteries, and fuel cells. In all surveyed models, the employment of fractional-order capacitors, also known as constant phase elements, is imperative not only to the accuracy of the model but to reflect the physical electrochemical properties of the device.

[1]  O. Briat,et al.  Influence of relaxation process on supercapacitor time response , 2009, 2009 13th European Conference on Power Electronics and Applications.

[2]  Mehmet Önder Efe,et al.  Fractional Order Systems in Industrial Automation—A Survey , 2011, IEEE Transactions on Industrial Informatics.

[3]  M. Nakagawa,et al.  Basic Characteristics of a Fractance Device , 1992 .

[4]  Ahmed S. Elwakil,et al.  Guest Editorial Fractional-Order Circuits and Systems , 2013, IEEE J. Emerg. Sel. Topics Circuits Syst..

[5]  A. Emadi,et al.  A New Battery/UltraCapacitor Hybrid Energy Storage System for Electric, Hybrid, and Plug-In Hybrid Electric Vehicles , 2012, IEEE Transactions on Power Electronics.

[6]  Alireza Khaligh,et al.  Battery, Ultracapacitor, Fuel Cell, and Hybrid Energy Storage Systems for Electric, Hybrid Electric, Fuel Cell, and Plug-In Hybrid Electric Vehicles: State of the Art , 2010, IEEE Transactions on Vehicular Technology.

[7]  Jean-Michel Vinassa,et al.  Fractional non-linear modelling of ultracapacitors , 2010 .

[8]  Pritpal Singh,et al.  Equivalent circuit parameters of nickel/metal hydride batteries from sparse impedance measurements , 2004 .

[9]  D. Mahinda Vilathgamuwa,et al.  Flying Supercapacitors as Power Smoothing Elements in Wind Generation , 2013, IEEE Transactions on Industrial Electronics.

[10]  G. Joos,et al.  Supercapacitor Energy Storage for Wind Energy Applications , 2007, IEEE Transactions on Industry Applications.

[11]  Ahmed S. Elwakil,et al.  Measurement of Supercapacitor Fractional-Order Model Parameters From Voltage-Excited Step Response , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[12]  Dirk Uwe Sauer,et al.  Application-specific parameterization of reduced order equivalent circuit battery models for improved accuracy at dynamic load , 2013 .

[13]  D. Cahela,et al.  Impedance modeling of nickel fiber/carbon fiber composite electrodes for electrochemical capacitors , 1997, Proceedings of the IECON'97 23rd International Conference on Industrial Electronics, Control, and Instrumentation (Cat. No.97CH36066).

[14]  Dae-Keun Kang,et al.  Investigation on cell impedance for high-power lithium-ion batteries , 2007 .

[15]  Oriol Gomis-Bellmunt,et al.  A Power Smoothing System Based on Supercapacitors for Renewable Distributed Generation , 2015, IEEE Transactions on Industrial Electronics.

[16]  J. J. Quintana,et al.  IDENTIFICATION OF THE FRACTIONAL IMPEDANCE OF ULTRACAPACITORS , 2006 .

[17]  Peter J. Mahon,et al.  Measurement and modelling of the high-power performance of carbon-based supercapacitors , 2000 .

[18]  Manuel Duarte Ortigueira,et al.  Fractional Calculus for Scientists and Engineers , 2011, Lecture Notes in Electrical Engineering.

[19]  Dominik Sierociuk,et al.  Ultracapacitor modelling and control using discrete fractional order state-space models and Fractional Kalman Filters , 2007, 2007 European Control Conference (ECC).

[20]  Alain Oustaloup,et al.  A fractional order model for lead-acid battery crankability estimation , 2010 .

[21]  Dominik Sierociuk,et al.  Comparison and validation of integer and fractional order ultracapacitor models , 2011 .

[22]  Pragasen Pillay,et al.  PEMFC Fault Diagnosis, Modeling, and Mitigation , 2008, 2008 IEEE Industry Applications Society Annual Meeting.

[23]  Belkacem Ould-Bouamama,et al.  Model based PEM fuel cell state-of-health monitoring via ac impedance measurements , 2006 .

[24]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

[25]  A. K. Shukla,et al.  AC impedance and state-of-charge analysis of alkaline zinc/manganese dioxide primary cells , 2000 .

[26]  R. Kötz,et al.  Principles and applications of electrochemical capacitors , 2000 .

[27]  Aiguo Patrick Hu,et al.  Integration of supercapacitors into wirelessly charged biomedical sensors , 2011, 2011 6th IEEE Conference on Industrial Electronics and Applications.

[28]  Alain Oustaloup,et al.  On Lead-Acid-Battery Resistance and Cranking-Capability Estimation , 2010, IEEE Transactions on Industrial Electronics.

[29]  S. Westerlund,et al.  Capacitor theory , 1994 .

[30]  Lijun Gao,et al.  Electrochemical study on lithium iron phosphate/hard carbon lithium-ion batteries , 2012, Journal of Solid State Electrochemistry.

[31]  Pritpal Singh,et al.  Extracting equivalent circuit parameters of lead-acid cells from sparse impedance measurements , 2002 .

[32]  Wei Jiang,et al.  Active Current Sharing and Source Management in Fuel Cell–Battery Hybrid Power System , 2010, IEEE Transactions on Industrial Electronics.

[33]  Sehwan Kim,et al.  Design and Performance Analysis of Supercapacitor Charging Circuits for Wireless Sensor Nodes , 2011, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[34]  Ahmed S Elwakil,et al.  Fractional-order circuits and systems: An emerging interdisciplinary research area , 2010, IEEE Circuits and Systems Magazine.

[35]  Dirk Uwe Sauer,et al.  Adaptive estimation of the electromotive force of the lithium-ion battery after current interruption for an accurate state-of-charge and capacity determination , 2013 .

[36]  Boris Tartakovsky,et al.  Electrochemical characterization of anodic biofilm development in a microbial fuel cell , 2013, Journal of Applied Electrochemistry.

[37]  R. Martin,et al.  Modeling electrochemical double layer capacitor, from classical to fractional impedance , 2008, MELECON 2008 - The 14th IEEE Mediterranean Electrotechnical Conference.

[38]  Ning-Yih Hsu,et al.  Impedance studies and modeling of direct methanol fuel cell anode with interface and porous structure perspectives , 2006 .

[39]  Dominik Sierociuk,et al.  Time domain validation of ultracapacitor fractional order model , 2010, 49th IEEE Conference on Decision and Control (CDC).

[40]  Yang Wang,et al.  Modeling Ultracapacitors as Fractional-Order Systems , 2010 .

[41]  Xi Li,et al.  Generalized predictive control for fractional order dynamic model of solid oxide fuel cell output power , 2010 .

[42]  S. Rodrigues,et al.  AC impedance and state-of-charge analysis of a sealed lithium-ion rechargeable battery , 1999 .

[43]  Jean-Michel Vinassa,et al.  Embedded Fractional Nonlinear Supercapacitor Model and Its Parametric Estimation Method , 2010, IEEE Transactions on Industrial Electronics.

[44]  Vicente Feliu,et al.  Analysis of the Fractional Dynamics of an Ultracapacitor and Its Application to a Buck-Boost Converter , 2010 .

[45]  Valeriy Martynyuk,et al.  Fractional model of an electrochemical capacitor , 2015, Signal Process..

[46]  V. V. Viswanathan,et al.  Effect of state of charge on impedance spectrum of sealed cells Part I: Ni-Cd cells , 1995 .

[47]  Jennifer Bauman,et al.  A Comparative Study of Fuel-Cell–Battery, Fuel-Cell–Ultracapacitor, and Fuel-Cell–Battery–Ultracapacitor Vehicles , 2008, IEEE Transactions on Vehicular Technology.

[48]  Jun Xu,et al.  A new method to estimate the state of charge of lithium-ion batteries based on the battery impedance model , 2013 .