{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
Please cite us if you use the software
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Padulles-Hauer Dynamic Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Version 1.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n",
"The Padulles dynamic model can predict the transient response of cell voltage, temperature of the cell, hydrogen/oxygen out flow rates and cathode and anode channel temperatures/pressures under sudden change in load current. Hence, a dynamic fuel cell simulation is developed in this model, which incorporates the dynamics of flow and pressure in the anode and cathode channels and mass/ heat transfer transient features in the fuel cell body.\n",
"
This model is based on several assumptions: \n",
"
\n", "Padulles-Hauer Dynamic Model is a dynamic electrochemical simulation model of a grid independent proton exchange membrane (PEM) fuel cell. This model includes a methanol reformer to generate hydrogen from methanol and the PEM stack. The model is used to predict the output voltage and power of a PEMFC. It has to be noted that the reformer model is a second order transfer function. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fig1. Padulles-Hauer Dynamic Model Block Diagram
\n", " \n", "$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "
$$V_0$$ | \n", "Intercept of the curve obtained by linear approximation | \n", "$$V$$ | \n", "
$$k$$ | \n", "Slope of the curve obtained by linear approximation | \n", "$$A^{-1}$$ | \n", "
$$P_{max}$$ | \n", "Maximum power obtained by linear approximation | \n", "$$W$$ | \n", "
$$V_{FC}|P_{max}$$ | \n", "Cell voltage at maximum power obtained by linear approximation | \n", "$$V$$ | \n", "
$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "
$$\\eta|P_{Max}$$ | \n", "Cell efficiency at maximum power | \n", "$$--$$ | \n", "
$$P_{Max}$$ | \n", "Maximum power | \n", "$$W$$ | \n", "
$$P_{Elec} $$ | \n", "Total electrical power | \n", "$$W$$ | \n", "
$$P_{Thermal} $$ | \n", "Total thermal power | \n", "$$W$$ | \n", "
$$V_{FC}|P_{Max}$$ | \n", "Cell voltage at maximum power | \n", "$$V$$ | \n", "
$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "$$Value$$ | \n", "
$$T$$ | \n", "Fuel cell temperature | \n", "$$K$$ | \n", "$$User$$ | \n", "
$$N_0$$ | \n", "Number of cells | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$E_0$$ | \n", "No load voltage | \n", "$$V$$ | \n", "$$User$$ | \n", "
$$K_{H_2}$$ | \n", "Hydrogen valve constant | \n", "$$kmol.s^{-1}.atm^{-1}$$ | \n", "$$User$$ | \n", "
$$K_{H_2O}$$ | \n", "Water valve constant | \n", "$$kmol.s^{-1}.atm^{-1}$$ | \n", "$$User$$ | \n", "
$$K_{O_2}$$ | \n", "Oxygen valve constant | \n", "$$kmol.s^{-1}.atm^{-1}$$ | \n", "$$User$$ | \n", "
$$\\tau_{H_2}^{(s)}$$ | \n", "Hydrogen time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$\\tau_{H_2O}^{(s)}$$ | \n", "Water time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$\\tau_{O_2}^{(s)}$$ | \n", "Oxygen time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$\\tau_{1}^{(s)}$$ | \n", "Reformer time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$\\tau_{2}^{(s)}$$ | \n", "Reformer time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$CV$$ | \n", "Conversion factor | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$B$$ | \n", "Activation voltage constant | \n", "$$V$$ | \n", "$$User$$ | \n", "
$$C$$ | \n", "Activation constant parameter | \n", "$$A^{-1}$$ | \n", "$$User$$ | \n", "
$$R^{int}$$ | \n", "Fuel cell internal resistance | \n", "$$\\Omega$$ | \n", "$$User$$ | \n", "
$$r_{h-o}$$ | \n", "Hydrogen-Oxygen flow ratio | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$q_{methanol}$$ | \n", "Molar flow of methanol | \n", "$$kmol.s^{-1}$$ | \n", "$$User$$ | \n", "
$$i_{start}$$ | \n", "Cell operating current start point | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_{step}$$ | \n", "Cell operating current step | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_{stop}$$ | \n", "Cell operating current end point | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$P_{H_2}$$ | \n", "Hydrogen partial pressure | \n", "$$atm$$ | \n", "$$System$$ | \n", "
$$P_{H_2O}$$ | \n", "Water partial pressure | \n", "$$atm$$ | \n", "$$System$$ | \n", "
$$P_{O_2}$$ | \n", "Oxygen partial pressure | \n", "$$atm$$ | \n", "$$System$$ | \n", "
$$K_r$$ | \n", "Modeling constant | \n", "$$kmol.s^{-1}.A^{-1}$$ | \n", "$$System$$ | \n", "
$$q_{O_2}^{(inlet)}$$ | \n", "Molar flow of oxygen | \n", "$$kmol.s^{-1}$$ | \n", "$$System$$ | \n", "
$$q_{H_2O}^{(inlet)}$$ | \n", "Molar flow of water | \n", "$$kmol.s^{-1}$$ | \n", "$$System$$ | \n", "
$$q_{H_2}^{(inlet)}$$ | \n", "Molar flow of hydrogen | \n", "$$kmol.s^{-1}$$ | \n", "$$System$$ | \n", "
$$\\mu_F$$ | \n", "The fuel utilization | \n", "$$--$$ | \n", "$$0.95$$ | \n", "
$$HHV$$ | \n", "Higher heating value potential | \n", "$$V$$ | \n", "$$1.482$$ | \n", "
$$R$$ | \n", "Universal gas constant | \n", "$$J.kmol^{-1}.K^{-1}$$ | \n", "$$8314.47$$ | \n", "
$$F$$ | \n", "Faraday’s constant | \n", "$$C.kmol^{-1}$$ | \n", "$$96484600$$ | \n", "
$$E_{th}$$ | \n", "Theoretical potential | \n", "$$V$$ | \n", "$$1.23$$ | \n", "
\n", "1- J. Padulles, G.W. Ault, J.R. McDonald. 2000. \"An integrated SOFC plant dynamic model for power systems\n", "simulation.\" Journal of Power Sources (Elsevier) 86 (1-2): 495-500. doi:10.1016/S0378-7753(99)00430-9\n", "\n", "
\n", "2- Hauer, K.-H. 2001. \"Analysis tool for fuel cell vehicle hardware and software (controls) with an application\n", "to fuel economy comparisons of alternative system designs.\" Ph.D. dissertation, Transportation Technology\n", "and Policy, University of California Davis.\n", "" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }