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Additional Research Papers

Impedance Spectroscopy Study and System Identification of a Solid-Oxide Fuel Cell Stack With Hammerstein–Wiener Model

[+] Author and Article Information
M. Y. Abdollahzadeh Jamalabadi

Department of Mechanical, Robotics and
Energy Engineering,
Dongguk University,
Seoul 04620, Korea

Manuscript received January 1, 2017; final manuscript received February 19, 2017; published online May 9, 2017. Assoc. Editor: Kevin Huang.

J. Electrochem. En. Conv. Stor. 14(2), 021002 (May 09, 2017) (12 pages) Paper No: JEECS-17-1001; doi: 10.1115/1.4036278 History: Received January 01, 2017; Revised February 19, 2017

In this paper, the electrochemical impedance spectroscopy (EIS) method is applied through a transient in solid oxide fuel cell (SOFC) to obtain the dynamic modeling. Instead of measuring the current response of a fuel cell to a small sinusoidal perturbation in voltage at each frequency, the Hammerstein–Wiener model identification method is applied through a one transient who leads to the significant decrease of computational costs. Dynamic responses are determined as the solutions of coupled partial differential equations derived from conservation laws of charges, mass, momentum, and energy with electrochemical kinetics by using Butler–Volmer model and gas diffusion on the extended Maxwell-Stefan species equations or dusty gas model (DGM). Because the system consisted of electrical and mechanical components, the behavior of the system was nonlinear. The obtained results are in good qualitative agreement with experimental data published in literatures shown the effectiveness of the propose model. Finally, a parametric study based on the obtained model is performed to study the effects of channel length, inlet H2 concentration, inlet velocity, and cell temperature in Nyquist plots and the voltage responses to step changes in the fuel concentration and load current. The model can be useful as a benchmark for illustrating different designs and control schemes.

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References

Jamalabadi, M. Y. A. , 2013, “ Electrochemical and Exergetic Modeling of a CHP System Using Tubular Solid Oxide Fuel Cell and Mini Gas Turbine,” ASME J. Fuel Cell Sci. Technol., 10(5), p. 051007. [CrossRef]
Jamalabadi, M. Y. A. , 2014, “ Economic and Environmental Modelling of a MGT-SOFC Hybrid Combined Heat and Power System for Ship Applications,” Middle-East J. Sci. Res., 22(4), pp. 561–574.
Jamalabadi, M. Y. A. , Park, J. H. , and Lee, C. Y. , 2014, “ Economic and Environmental Modelling of a Micro Gas Turbine and Solid Oxide Fuel Cell Hybrid Combined Heat and Power System,” Int. J. Appl. Environ. Sci., 9(4), pp. 1769–1781.
Jelavic, M. , Peric, N. , and Petrovic, I. , 2006, “ Identification of Wind Turbine Model for Controller Design,” 12th International Conference on Power Electronics and Motion Control (EPE-PEMC 2006), Portorož, Slovenia, Aug. 30–Sept. 1, pp. 1608–1613.
Koveos, Y. , and Tzes, A. , 2009, “ Modelling and Identification of Resonance Fluid Actuator,” Third IEEE Multi-Conference on Systems and Control (MSC 2009), St. Petersburg, Russia, July 8–10, pp. 560–565.
Laghrouche, S. , Ahmed, F. S. , El Baghdouri, M. , Wack, M. , Gaber, J. , and Becherif, M. , 2010, “ Modelling and Identification of a Mechatronics Exhaust Gas Recirculation Actuator of an Internal Combustion Engine,” American Control Conference (ACC), Baltimore, MD, June 30–July 2, pp. 2242–2247.
Ljung, L. , 1999, System Identification: Theory for the User, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ.
Nelles, O. , 2001, Nonlinear System Identification: From Classical Approaches to Neural Network and Fuzzy Models, Springer, Berlin.
Singhal, S. C. , and Kendall, K. , 2003, High-Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Application, Elsevier Science, Oxford, UK.
Achenbach, E. , 1994, “ Three-Dimensional and Time-Dependent Simulation of a Planar Solid Oxide Fuel Cell Stack,” J. Power Sources, 49(1–3), pp. 333–348. [CrossRef]
Achenbach, E. , 1995, “ Response of a Solid Oxide Fuel Cell to Load Change,” J. Power Sources, 57(1–2), pp. 105–109. [CrossRef]
Sedghisigarchi, K. , and Feliachi, A. , 2004, “ Dynamic and Transient Analysis of Power Distribution Systems With Fuel Cells—Part I: Fuel-Cell Dynamic Model,” IEEE Trans. Energy Convers., 19(2), pp. 423–428. [CrossRef]
Xue, X. , Tang, J. , Sammes, N. , and Du, Y. , 2005, “ Dynamic Modeling of Single Tubular SOFC Combining Heat/Mass Transfer and Electrochemical Reaction Effects,” J. Power Sources, 142(1–2), pp. 211–222. [CrossRef]
Macdonald, J. R. , 2005, Impedance Spectroscopy—Theory Experiment and Application, Wiley, New York.
Verkerk, M. J. , and Burggraaf, A. J. , 1983, “ Oxygen Transfer on Substituted ZrO2, Bi2O3, and CeO2 Electrolytes With Platinum Electrodes,” J. Electrochem. Soc., 130(1), pp. 78–84. [CrossRef]
Jamalabadi, M. Y. A. , 2014, “ Simulation of Electrochemical Impedance Spectroscopy of a Solid Oxide Fuel Cell Anodes,” World Appl. Sci. J., 32(4), pp. 667–671.
Jamalabadi, M. Y. A. , Park, J. H. , and Lee, C. Y. , 2015, “ Optimal Design of MHD Mixed Convection Flow in a Vertical Channel With Slip Boundary Conditions and Thermal Radiation Effects by Using Entropy Generation Minimization Method,” Entropy, 17(2), pp. 866–881. [CrossRef]
Jamalabadi, M. Y. A. , and Park, J. H. , 2014, “ Thermal Radiation, Joule Heating, and Viscous Dissipation Effects on MHD Forced Convection Flow With Uniform Surface Temperature,” Open J. Fluid Dyn., 4(2), pp. 125–132. [CrossRef]
Jamalabadi, M. Y. A. , 2014, “ Experimental Investigation of Thermal Loading of a Horizontal Thin Plate Using Infrared Camera,” J. King Saud Univ.—Eng. Sci., 26(2), pp. 159–167. [CrossRef]
Jamalabadi, M. Y. A. , Ghasemi, M. , and Hamedi, M. H. , 2013, “ Numerical Investigation of Thermal Radiation Effects on Open Cavity With Discrete Heat Sources,” Int. J. Numer. Methods Heat Fluid Flow, 23(4), pp. 649–661. [CrossRef]
Jamalabadi, M. Y. A. , Ghasemi, M. , and Hamedi, M. H. , 2012, “ Two-Dimensional Simulation of Thermal Loading With Horizontal Heat Sources,” Proc. Inst. Mech. Eng., Part C, 226(5), pp. 1302–1308. [CrossRef]
Jamalabadi, M. Y. A. , 2015, “ Numerical Investigation of Thermal Radiation Effects on Electrochemical Impedance Spectroscopy of a Solid Oxide Fuel Cell Anode,” Mater. Perform. Charact., 4(1), pp. 1–28.
VanderSteen, J. D. J. , and Pharoah, J. G. , 2006, “ Modeling Radiation Heat Transfer With Participating Media in Solid Oxide Fuel Cells,” ASME J. Fuel Cell Sci. Technol., 3(1), pp. 62–67. [CrossRef]
Tanaka, T. , Inui, Y. , Urata, A. , and Kanno, T. , 2007, “ Three Dimensional Analysis of Planar Solid Oxide Fuel Cell Stack Considering Radiation,” Energy Convers. Manage., 48(5), pp. 1491–1498. [CrossRef]
Murthy, S. , and Fedorov, A. G. , 2003, “ Radiation Heat Transfer Analysis of the Monolith Type Solid Oxide Fuel Cell,” J. Power Sources, 124(2), pp. 453–458. [CrossRef]
Daun, K. J. , Beale, S. B. , Liu, F. , and Smallwood, G. J. , 2006, “ Radiation Heat Transfer in Planar SOFC Electrolytes,” J. Power Sources, 157(1), pp. 302–310. [CrossRef]
Damm, D. L. , and Fedorov, A. G. , 2005, “ Spectral Radiative Heat Transfer Analysis of the Planar SOFC,” ASME J. Fuel Cell Sci. Technol., 2(4), pp. 258–262. [CrossRef]
Yakabe, H. , Ogiwara, T. , Hishinuma, M. , and Yasuda, I. , 2001, “ 3D Model Calculation for Planar SOFC,” J. Power Sources, 102(1–2), pp. 144–154.
Primdahl, S. , and Mogensen, M. , 1998, “ Gas Conversion Impedance: A Test Geometry Effect in Characterization of Solid Oxide Fuel Cell Anodes,” J. Electrochem. Soc., 145(7), p. 2431. [CrossRef]
Primdahl, S. , and Mogensen, M. , 1999, “ Gas Diffusion Impedance in Characterization of Solid Oxide Fuel Cell Anodes,” J. Electrochem. Soc., 146(8), p. 2827. [CrossRef]
Bieberle, A. , and Gauckler, L. , 2002, “ State-Space Modeling of the Anodic SOFC System Ni, H2–H2OYSZ,” Solid State Ionics, 146(1–2), pp. 23–41. [CrossRef]
Bessler, W. , 2005, “ A New Computational Approach for SOFC Impedance Based on Detailed Electrochemical Reaction-Diffusion Models,” Solid State Ionics, 176(11–12), pp. 997–1011. [CrossRef]
Bessler, W. , 2006, “ Gas Concentration Impedance of Solid Oxide Fuel Cell Anodes. I: Stagnation Point Flow Geometry,” J. Electrochem. Soc., 153(8), pp. A1492–A1504. [CrossRef]
Bessler, W. G. , and Gewies, S. , 2007, “ Gas Concentration Impedance of Solid Oxide Fuel Cell Anodes. II: Channel Geometry,” J. Electrochem. Soc., 154(6), pp. B548–B559. [CrossRef]
Kato, T. , Nozaki, K. , Negishi, A. , Kato, K. , Momma, A. , Kaga, Y. , Nagata, S. , Takano, K. , Inagaki, T. , Yoshida, H. , Hosoi, K., Hoshino, K., Akbay, T., and Akikusa, J., 2004, “ Impedance Analysis of a Disk-Type SOFC Using Doped Lanthanum Gallate Under Power Generation,” J. Power Sources, 133(2), pp. 169–174. [CrossRef]
Takano, K. , Nagata, S. , Nozaki, K. , Momma, A. , Kato, T. , Kaga, Y. , Negishi, A. , Kato, K. , Inagaki, T. , Yoshida, H. , Hosoi, K., Hoshino, K., Akbay, T., and Akikusa, J., 2004, “ Numerical Simulation of a Disk-Type SOFC for Impedance Analysis Under Power Generation,” J. Power Sources, 132(1–2), pp. 42–51. [CrossRef]
Dahleh, M. A. , 2009, System Identification (Lecture Notes), MIT, Cambridge, MA.
Soderstrom, T. , and Stoica, P. , 1989, System Identification, Prenntice-Hall, Upper Saddle River, NJ.
Pelckmans, K. , 2012, “ Lecture Notes for a Course on System Identification,” Uppsala University, Uppsala, Sweden.
Kamen, E. W. , and Su, J. K. , 1999, Introduction to Optimal Estimation, Springer, London.
Bove, R. , and Ubertini, S. , 2008, Modeling Solid Oxide Fuel Cells, Springer, Dordrecht, The Netherlands.
Sergey, V. , and Francesco, B. , 2014, “ Solving Linear and Quadratic Programs With an Analog Circuit,” Comput. Chem. Eng., 70, pp. 160–171. [CrossRef]
Orazem, M. E. , and Tribollet, B. , 2008, Electrochemical Impedance Spectroscopy, Wiley, Hoboken, NJ.
Llibre, J. , and Valls, C. , 2007, “ Global Analytic First Integrals for the Real Planar Lotka–Volterra System,” J. Math. Phys., 48(3), p. 033507. [CrossRef]
Keegan, K. , Khaleel, M. , Chick, L. , Recknagle, K. , Simner, S. , and Deibler, J. , 2002, “ Analysis of a Planar Solid Oxide Fuel Cell Based Automotive Auxiliary Power Unit,” SAE Technical Paper No. 2002-01-0413.
Ferreira, J. A. , Barbeiro, S. , Mary, G. P. , and Wheeler, F. , 2013, Modelling and Simulation in Fluid Dynamics in Porous Media, Springer, New York, pp. 55–66.
Civan, F. , 2002, “ Implications of Alternative Macroscopic Descriptions Illustrated by General Balance and Continuity Equations,” J. Porous Media, 5(4), pp. 271–282. [CrossRef]
Kolditz, O. , Shao, H. , Wang, W. , and Bauer, S. , 2015, Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: Modelling and Benchmarking, Springer, Cham, Switzerland.
Cengel, Y. , and Boles, M. A. , 2015, Thermodynamics: An Engineering Approach, 8th ed., McGraw-Hill, Seattle, WA.
Ichikawa, Y. , and Selvadurai, A. P. S. , 2012, Transport Phenomena in Porous Media: Aspects of Micro/Macro Behaviour, Springer-Verlag, Berlin.
Whitaker, S. , 1986, “ Flow in Porous Media I: A Theoretical Derivation of Darcy's Law,” Transp. Porous Media, 1(1), pp. 3–25. [CrossRef]
Bear, J. , 1972, Dynamics of Fluids in Porous Media, Dover Publications, Mineola, NY.
Wilke, C. R. , 1950, “ A Viscosity Equation for Gas Mixtures,” J. Chem. Phys., 18(4), pp. 517–519.
Gambill, W. R. , 1959, “ How to Estimate Mixtures Viscosities,” Chem. Eng., 66, pp. 151–152.
Chapman, S. , and Cowling, T. G. , 1999, The Mathematical Theory of Non-Uniform Gases an Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, Cambridge University Press, Cambridge, UK.
Touloukian, S. , Saxena, S. C. , and Hestermans, P. , 1975, Viscosity (Thermophysical Properties of Matter, Vol. 11), IFI/Plenum, New York.
Buddenberg, J. W. , and Wilke, C. R. , 1949, “ Calculation of Gas Mixture Viscosities,” Ind. Eng. Chem., 41(7), pp. 1345–1347. [CrossRef]
Bird, R. , Stewart, W. , and Lightfoot, E. , 1960, Transport Phenomena, Wiley, New York.
Neufeld, P. D. , Jansen, A. R. , and Aziz, R. A. , 1972, “Empirical Equations to Calculate 16 of the Transport Collision Integrals Ω(l, s)* for the Lennard–Jones (12–6) Potential,” J. Chem. Phys., 57(3), pp. 1100–1102. [CrossRef]
Bao, C. , Cai, N. , and Croiset, E. , 2011, “ An Analytical Model of View Factors for Radiation Heat Transfer in Planar and Tubular Solid Oxide Fuel Cells,” J. Power Sources, 196(6), pp. 3223–3232. [CrossRef]
Damm, D. L. , and Fedorov, A. G. , 2005, “ Radiation Heat Transfer in SOFC Materials and Components,” J. Power Sources, 143(1–2), pp. 158–165. [CrossRef]
Damm, D. L. , and Fedorov, A. G. , 2004, “ Spectral Radiative Heat Transfer Analysis of the Planar SOFC,” ASME Paper No. IMECE2004-60142.
Modest, M. F. , 2003, Radiative Heat Transfer, 2nd ed., Academic Press, New York.
Mahcene, H. , Meddour, N. , Bechki, D. , Bouguettaia, H. , and Moussa, H. B. , 2014, “ Radiation Phenomenon in Electrodes/Electrolyte Interface of Solid Oxide Fuel Cells,” Energy Proc., 50(2014), pp. 229–236. [CrossRef]
Ferguson, J. , Fiard, J. , and Herbin, R. , 1996, “ Three-Dimensional Numerical Simulation for Various Geometries of Solid Oxide Fuel Cells,” J. Power Sources, 58(2), pp. 109–222. [CrossRef]
Zhu, H. , and Kee, R. , 2003, “ A General Mathematical Model for Analyzing the Performance of Fuel-Cell Membrane-Electrode Assemblies,” J. Power Sources, 117(1–2), pp. 61–74. [CrossRef]
Chan, S. , Chen, X. , and Khor, K. , 2004, “ Cathode Micromodel of Solid Oxide Fuel Cell,” J. Electrochem. Soc., 151(1), pp. A164–A172. [CrossRef]
Ackmann, T. , de Haart, L. , Lehnert, W. , and Stolten, D. , 2003, “ Modeling of Mass and Heat Transport in Planar Substrate Type SOFCs,” J. Electrochem. Soc., 150(6), pp. A783–A789. [CrossRef]
Li, P.-W. , Schaefer, L. , and Chyu, M. K. , 2005, “ Multiple Transport Processes in Solid Oxide Fuel Cells,” Transport Phenomena in Fuel Cells, B. Sundén , and M. Faghri , eds., WIT Press, Billerica, MA, pp. 1–41.
Okimoto, Y. , Katsufuji, T. , Ishikawa, T. , Urushibara, A. , Arima, T. , and Tokura, Y. , 1995, “ Anomalous Variation of Optical Spectra With Spin Polarization in Double-Exchange Ferromagnet: La1−xSrxMnO3,” Phys. Rev. Lett., 75(1), pp. 109–112. [CrossRef] [PubMed]
Kakaç, S. , Pramuanjaroenkij, A. , and Zhoub, X. , 2007, “ A Review of Numerical Modeling of Solid Oxide Fuel Cells,” Int. J. Hydrogen Energy, 32(7), pp. 761–786. [CrossRef]
Costamagna, P. , and Honegger, K. , 1998, “ Modeling of Solid Oxide Heat Exchanger Integrated Stacks and Simulation at High Fuel Utilization,” J. Electrochem. Soc., 145(11), pp. 3995–4007. [CrossRef]
Lee, S. , Kim, G. , Vohs, J. M. , and Gorte, R. J. , 2008, “ SOFC Anodes Based on Infiltration of La0.3Sr0.7TiO3,” J. Electrochem. Soc., 155(11), pp. B1179–B1183. [CrossRef]
Küngas, R. , Yu, A. S. , Levine, J. , Vohs, J. M. , and Gorte, R. J. , 2013, “ An Investigation of Oxygen Reduction Kinetics in LSF Electrodes,” J. Electrochem. Soc., 160(2), pp. F205–F211. [CrossRef]
Bessler, W. G. , Warnatz, J. , and Goodwin, D. G. , 2007, “ The Influence of Equilibrium Potential on the Hydrogen Oxidation Kinetics of SOFC Anodes,” Solid State Ionics, 177(39–40), pp. 3371–3383. [CrossRef]
Chaisantikulwat, A. , Diaz-Goano, C. , and Meadows, E. , 2008, “ Dynamic Modelling and Control of Planar Anode-Supported Solid Oxide Fuel Cell,” Comput. Chem. Eng., 32(10), p. 2365. [CrossRef]
Jamalabadi, M. Y. A., 2013, “ Simulation of Electrochemical Impedance Spectroscopy of a Solid Oxide Fuel Cell Anodes,” 5th European Fuel Cell Piero Lunghi Conference (EFC13), Rome, Italy, Dec. 11–13, pp. 395–396.
Revankar, S. T. , and Majumdar, P. , 2014, Fuel Cells Principles, Design, and Analysis, CRC Press, Boca Raton, FL.
Loveday, D. , Peterson, P. , and Rodgers, B. , 2004, “ Evaluation of Organic Coatings With Electrochemical Impedance Spectroscopy. Part 1: Fundamentals of Electrochemical Impedance Spectroscopy,” JCT CoatingsTech, 1(8), pp. 46–52.
Barsoukov, E. , and Macdonald, J. R. , 2005, Impedance Spectroscopy; Theory, Experiment, and Applications, 2nd ed., Wiley Interscience Publications, Hoboken, NJ.
Gabrielle, C. , 1980, “ Identification of Electrochemical Processes by Frequency Response Analysis,” Solartron Instrumentation Group, Leicester, UK, Technical Report No. 004/83.
Mansfeld, F. , 1990, “ Electrochemical Impedance Spectroscopy (EIS) as a New Tool for Investigation Methods of Corrosion Protection,” Electrochim. Acta, 35(10), p. 1533. [CrossRef]
Boukamp, B. A. , 1993, “ Practical Application of the Kramers-Kronig Transformation on Impedance Measurements in Solid State Electrochemistry,” Solid State Ionics, 62(1–2), pp. 131–141. [CrossRef]
Huang, B. , Qi, Y. , and Murshed, A. , 2013, Dynamic Modelling and Predictive Control in Solid Oxide Fuel Cells: First Principle and Data-Based Approaches, Wiley, Hoboken, NJ.
Gemmen, R. S. , and Johnson, C. D. , 2005, “ Effect of Load Transients on SOFC Operation—Current Reversal on Loss of Load,” J. Power Sources, 114(1), pp. 152–164. [CrossRef]

Figures

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Fig. 1

Schematic of the planar SOFC

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Fig. 2

Cross section view of the planar SOFC

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Fig. 3

Longitudinal view of the planar SOFC

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Fig. 4

Configuration for diffuse interchange in planar SOFC [60]

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Fig. 5

Radiative properties of electrolyte, anode, and cathode bulk materials

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Fig. 6

Comparison of numerical and experimental cell polarization at 750 °C, 3.8 cm2 active area, 300 sccm air flow rate, 200 sccm fuel flow rate, fuel composed of ∼3% H2O, specified %H2, and balance N2

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Fig. 7

Pressure and density contours at various time-steps

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Fig. 8

u—velocity contours at various sections at t = 0.1 s

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Fig. 9

Developed velocity contour at t = 0.1 s

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Fig. 10

H2O mass fraction contours in t = 0.1 s

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Fig. 11

H2O mass fraction contours at various locations in t = 0.1 s

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Fig. 12

H2, O2, and N2 mass fraction and mean molar mass contours at t = 0.1 s

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Fig. 13

Temperature distribution at t = 0.1 s

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Fig. 14

Voltage distributions and heat generated contours in the midplane (x = 9.5 mm)

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Fig. 15

Transient output voltages with respect to the step input in the inlet hydrogen feeding

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Fig. 16

Transient output voltages with respect to the step input in the load current density

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Fig. 17

Transient maximum temperature of solid part with respect to the step input in the inlet hydrogen feeding

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Fig. 19

Comparison of various control model in hydrogen voltage relation

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Fig. 20

Comparison of various control model in current voltage relation

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