Computationally efficient modeling of the dynamic behavior of a portable PEM fuel cell stack

A numerically efficient mathematical model of a proton exchange membrane fuel cell (PEMFC) stack is presented. The aim of this model is to study the dynamic response of a PEMFC stack subjected to load changes under the restriction of short computing time. This restriction was imposed in order for the model to be applicable for nonlinear model predictive control (NMPC). The dynamic, non-isothermal model is based on mass and energy balance equations, which are reduced to ordinary differential equations in time. The reduced equations are solved for a single cell and the results are upscaled to describe the fuel cell stack. This approach makes our calculations computationally efficient. We study the feasibility of capturing water balance effects with such a reduced model. Mass balance equations for water vapor and liquid water including the phase change as well as a steady-state membrane model accounting for the electro-osmotic drag and diffusion of water through the membrane are included. Based on this approach the model is successfully used to predict critical operating conditions by monitoring the amount of liquid water in the stack and the stack impedance. The model and the overall calculation method are validated using two different load profiles on realistic time scales of up to 30 min. The simulation results are used to clarify the measured characteristics of the stack temperature and the stack voltage, which has rarely been done on such long time scales. In addition, a discussion of the influence of flooding and dry-out on the stack voltage is included. The modeling approach proves to be computationally efficient: an operating time of 0.5 h is simulated in less than 1 s, while still showing sufficient accuracy.

[1]  Sirivatch Shimpalee,et al.  Predicting the transient response of a serpentine flow-field PEMFC: I. Excess to normal fuel and air , 2006 .

[2]  P. R. Pathapati,et al.  A new dynamic model for predicting transient phenomena in a PEM fuel cell system , 2005 .

[3]  Chao-Yang Wang,et al.  Dynamics of polymer electrolyte fuel cells undergoing load changes , 2006 .

[4]  Shanhai Ge,et al.  A mathematical model for PEMFC in different flow modes , 2003 .

[5]  Biao Zhou,et al.  Water and thermal management for Ballard PEM fuel cell stack , 2005 .

[6]  Xianguo Li,et al.  Numerical analysis of dynamic processes in fully humidified PEM fuel cells , 2007 .

[7]  H. Toghiani,et al.  Steady state and dynamic performance of proton exchange membrane fuel cells (PEMFCs) under various operating conditions and load changes , 2006 .

[8]  Anzhong Gu,et al.  Three dimensional, two phase flow mathematical model for PEM fuel cell: Part I. Model development , 2004 .

[9]  T. Springer,et al.  Modeling and Experimental Diagnostics in Polymer Electrolyte Fuel Cells , 1993 .

[10]  Massimo Ceraolo,et al.  Modelling static and dynamic behaviour of proton exchange membrane fuel cells on the basis of electro-chemical description , 2003 .

[11]  Chao-Yang Wang,et al.  A Nonisothermal, Two-Phase Model for Polymer Electrolyte Fuel Cells , 2006 .

[12]  Chao-Yang Wang,et al.  Transient analysis of polymer electrolyte fuel cells , 2005 .

[13]  Paul M. Frank,et al.  Advances in control : highlights of ECC '99 , 1999 .

[14]  Akeel A. Shah,et al.  A transient PEMFC model with CO poisoning and mitigation by O2 bleeding and Ru-containing catalyst , 2007 .

[15]  Guilin Hu,et al.  Transient computation fluid dynamics modeling of a single proton exchange membrane fuel cell with serpentine channel , 2007 .

[16]  J. H. Lee,et al.  Modeling fuel cell stack systems , 1998 .

[17]  Daniel R. Lewin,et al.  Model-based Control of Fuel Cells: (1) Regulatory Control , 2004 .

[18]  Ralph E. White,et al.  A water and heat management model for proton-exchange-membrane fuel cells , 1993 .

[19]  G. Lindbergh,et al.  Mathematical model of the PEMFC , 2000 .

[20]  Markku J. Lampinen,et al.  Analysis of Free Energy and Entropy Changes for Half‐Cell Reactions , 1993 .

[21]  Adam Z. Weber,et al.  Transport in Polymer-Electrolyte Membranes III. Model Validation in a Simple Fuel-Cell Model , 2004 .

[22]  Jürgen Schumacher,et al.  Two-Phase Dynamic Modeling of PEMFCs and Simulation of Cyclo-Voltammograms , 2005 .

[23]  T. Springer,et al.  Polymer Electrolyte Fuel Cell Model , 1991 .

[24]  Brant A. Peppley,et al.  A Review of Mathematical Models for Hydrogen and Direct Methanol Polymer Electrolyte Membrane Fuel Cells , 2004 .

[25]  Chao-Yang Wang,et al.  Computational Fluid Dynamics Modeling of Proton Exchange Membrane Fuel Cells , 2000 .

[26]  Ned Djilali,et al.  A 3D, Multiphase, Multicomponent Model of the Cathode and Anode of a PEM Fuel Cell , 2003 .

[27]  J. C. Amphlett,et al.  A model predicting transient responses of proton exchange membrane fuel cells , 1996 .

[28]  T. Fuller,et al.  Water and Thermal Management in Solid‐Polymer‐Electrolyte Fuel Cells , 1993 .

[29]  T. Nguyen,et al.  An Along‐the‐Channel Model for Proton Exchange Membrane Fuel Cells , 1998 .

[30]  Akeel A. Shah,et al.  Transient non-isothermal model of a polymer electrolyte fuel cell , 2007 .

[31]  Sirivatch Shimpalee,et al.  Predicting the transient response of a serpentine flow-field PEMFC: II: Normal to minimal fuel and AIR , 2006 .

[32]  Ned Djilali,et al.  Computational model of a PEM fuel cell with serpentine gas flow channels , 2004 .

[33]  S. Maharudrayya,et al.  Pressure losses in laminar flow through serpentine channels in fuel cell stacks , 2004 .

[34]  Song-Yul Choe,et al.  A high dynamic PEM fuel cell model with temperature effects , 2005 .

[35]  Chao-Yang Wang,et al.  Fundamental models for fuel cell engineering. , 2004, Chemical reviews.