J. Cent. South Univ. Technol. (2007)05−0690−06
DOI: 10.1007/s11771−007−0132−y
Estimation of equivalent internal-resistance of PEM fuel cell
using artificial neural networks
LI Wei(李 炜), ZHU Xin-jian(朱新坚), MO Zhi-jun(莫志军)
(Department of Automation, Fuel Cell Research Institute, Shanghai Jiaotong University, Shanghai 200030, China)
Abstract：A practical method of estimation for the internal-resistance of polymer electrolyte membrane fuel cell (PEMFC) stack was
adopted based on radial basis function (RBF) neural networks. In the training process, k-means clustering algorithm was applied to
select the network centers of the input training data. Furthermore, an equivalent electrical-circuit model with this internal-resistance
was developed for investigation on the stack. Finally using the neural networks model of the equivalent resistance in the PEMFC
stack, the simulation results of the estimation of equivalent internal-resistance of PEMFC were presented. The results show that this
electrical PEMFC model is effective and is suitable for the study of control scheme, fault detection and the engineering analysis of
electrical circuits.
Key words: polymer electrolyte membrane fuel cell(PEMFC); equivalent internal-resistance; radial basis function; neural networks
1 Introduction
Fuel cells have become one of the major areas of
research in academia and the industry with the numerous
advantages better than the batteries and especially than
the other small-scale sources of electricity, including the
photovoltaic and solar cells
[1]
. The main factors to
increase the interest in PEMFC are as follows: 1) low
operating temperature that permits short start-up and
shut-down periods and rapid response to load variations;
2) low pressure that allows safety; 3) the by-product
waste is water; 4) low emission and high efficiency; 5)
modularity; 6) potential cost reduction due to a scale
economy.
It is necessary to use an estimated method for an
equivalent resistance of an electrical PEMFC model. It is
difficult to model the PEMFC theoretically based on
mechanistic approaches because various crucial variables
should be considered in the modeling procedure. Though
assumptions and approximations have to be made for the
purpose of developing the mechanistic models, these
PEMFC models are still complex and hard to be
operated.
In order to avoid having to acquire a good
knowledge of physicochemical phenomena and the
process parameters, “black-box” models are used to
achieve behavioral modeling of PEMFC
[2]
. These models
just make mappings for the relationships between the
inputs and outputs with the experimental data, and do not
reflect the inner states of PEMFC during the operation.
Although the electrical PEMFC model described in this
paper is established through RBF neural networks and
belongs to “black-box” model, it is not complex and the
parameter (nonlinear internal resistance) has an explicit
mechanistic explanation that is also helpful to analyze
the actual PEMFC inner-performance.
In this paper, a brief description of the physical
structure and the operating principles of a PEMFC were
presented. Moreover, a set of equations was used to
represent an electrical PEMFC model and the definition
of the internal-resistance was described in detail. The
framework of RBF neural networks and the algorithm for
the parameter compensation of the internal-resistance
were illustrated and the on-line electrical PEMFC model
was established.
2 Physical structure and electrical model of
PEMFC
A typical PEMFC is shown in Fig.1. It consists of
an anode and a cathode electrode with a
proton-conducting membrane as the electrolyte
sandwiched in between
[3]
. H
2
obtained from methanol
(CH
3
OH), petroleum products or natural gas acts as
fuel. It is fed through a narrow channel from one end
of the plate (Anode,
negative electrode). Similarly, O
2
enters the fuel cell from the other end of the plate
Foundation item: Project (2003AA517020) supported by the National High-Tech Research and Development Program of China
Received date: 2006−10−20; Accepted date: 2006−12−23
Corresponding author: LI Wei, PhD; Tel: +86-21-34201547; E-mail: li_wei@sjtu.edu.cn