Linearized State Space Modeling of PEMFC for Control Applications
Engr. M. Abbas Abbasi
1
, Engr. M. Bilal Shahid
2
1,2
The Islamia University of Bahawalpur, Pakistan
Abstract: This paper focuses on the linearization study of the non-linear dynamic models of Polymer
Electrolyte Membrane Fuel Cells (PEMFC). Matlab and Control Systems Toolbox have been employed to
study the model. The FC stack voltage is dependent upon the current drawn from the cell, the change in partial
pressures and the change in the amount of inlet flow of water vapor, hydrogen and air. A sudden change in the
state space model inputs is applied to the developed model and the system’s step response is studied. The
partial pressures of H2, O2 and H2O are selected as the state variables of the system.
Keywords: Fuel Cell, Modeling, Matlab, Control, PEMFC, State Space, Linearization
1. Introduction
Fuel cells convert chemical energy to electrical energy based on various operating principles without
producing the byproducts typically associated with conventional power generation methods. They are
environment friendly and have a great potential for higher efficiencies. There are numerous types of fuel cells
including Proton Exchange/Polymer Electrolyte Membrane Fuel Cells (PEMFC), Alkaline Fuel Cells (AFC),
Direct Methanol Fuel Cells (DMFC) etc. differing from one another by the type of fuel they use and the
operating temperature [1].
PEMFC use hydrogen as fuel and operate at low temperatures. The energy conversion phenomenon
associated with fuel cells is very complex and needs thermodynamic as well as chemical reaction equations to
be expressed exactly.
Extensive work is being done in this field to model the fuel cells in different perspectives and under
different operating conditions. Although numerous state space and other PEMFC models are available,
however they are too complex to be understood and be utilized for effective control applications. The fuel cell
dynamics are nonlinear in nature and a large signal state space model is very difficult to establish. However it
is very easy to linearize these models for small changes in the state variables [2]. Such approach has been
adopted and a small signal linearized model is developed for a general PEMFC. Later this model is converted
to time domain by taking the inverse Laplace transform of the General State Space Matrix G(s).The model is
attractive from the control point of view and can easily be extended for other applications.
1. System description and model development
1.1. PEMFC Operation
Fig. 1 shows a simplified schematic of the operation of PEMFC. The figure shows that pressurized
hydrogen (fuel tank) and oxygen taken from the air are fed to the fuel cell from anode and cathode sides
respectively. Reformed methane and other fuels like natural gas can also be fed instead of hydrogen. The
partial pressures of both hydrogen and oxygen need to be regulated. The quality of fuel as well as air is also of
crucial importance. Higher stack voltage can be produced by connecting the various cells in series. In the
presence of the electrolyte catalyst, chemical reaction takes place between hydrogen and oxygen and as a result
water and electricity is produced which can be summarized as [3]:
2011 International Conference on Modeling, Simulation and Control
IPCSIT vol.10 (2011) © (2011) IACSIT Press, Singapore
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