Modeling and simulation of PEM fuel cell – power converter system M. Petrinić and Ž. Jakopović Department of electric machines, drives and automation Faculty of Electrical Engineering and Computing Unska 3, Zagreb, Croatia Telephone: +385 1 6129 804, Fax: +385 1 6129 705 E-mail: miroslav.petrinic@fer.hr; zeljko.jakopovic@fer.hr Abstract – Parasitic capacitances of Proton Exchange Membrane (PEM) fuel cell are causing electrical effects resulting with change of dynamic behavior of fuel cell stack output voltage. This paper shows PEM fuel cell dynamic model with capability of easy integration of humidity, temperature and pressures dynamics, as well as their control. Fuel cell stack dynamic model was linked with boost converter averaged dynamic model, obtained using state space method, containing controller that keeps converter output voltage constant. A variety of step load changes was simulated on this structure, resulting effects were observed on stack current, stack voltage and converter output voltage responses. Obtained results are showing difference between corresponding responses of this model and the one which neglects effects of parasitic capacitances of PEM fuel cell. I. INTRODUCTION Direct electrochemical transformation with efficiency of up to 45 %, high energy density out of small dimensions (up to 2 W/cm 2 ), silent operation and zero gas emissions are attributes that cause large interest in PEM fuel cells and are reasons that application of this technology is considered in transport, static production of electric energy and power supply for wireless electrical devices. But for designing a good power source based on this technology, fuel cell behavior, its characteristics, connected power converter and its control, their interaction, as well as mathematical models used to describe and simulate different operation modes, have to be well known. Only then, satisfactory system behavior and energy quality can be achieved. Today a large number of mathematical PEM fuel cell models exists, whose purpose spreads from fuel cell designing, across describing static and dynamic behavior, up to operation analysis in complex systems, where fuel cells have to meet specific work conditions. Most of dynamic models are dealing with temperature and fluid pressures, because these variables are known to have time constants that can last even few seconds, while influence of pararasitic capacitances on output cell voltage is often neglected. Models that take into account this effect [4] usually use highly evolved fuel cell equivalent electrical circuits composed of resistance- capacitance parallels connected in series. These complex structures are describing high frequency electric effects very precisely, but determination of their capacitance values demands additional electric measurement on a real fuel cell, and presents severe problem. That is the reason why simplified model, that has only one time constant, was used in this case, to describe electric dynamic of PEM. In this model, all parasitic capacitances are represented with one connected in parallel with activation and concentration resistances of fuel cell. As far as power converters are concerned, papers can be found that focus on power converters whose characteristics and regulation techniques have been customized to suit PEM fuel cells. Some of them deal with designs that allow cheap production [5], while others, based on good knowledge of PEM characteristics, describe complex structures resulting with high energy quality, by using hybrid PEM-battery power source [6]. As these models are often customized for certain purpose (for instance automotive applications), they are not suitable for studying of fuel cell operation effects on power converter operation, neither for analyzing effects caused by different controllers. For those reasons, appropriate boost power converter dynamic model is used here, that when connected to a fuel cell model, gives stack current, stack voltage and converter output voltage responses in short simulation execution time. In that way, a system suitable for interaction between PEM fuel cell and power converter was obtained. II. FUEL CELL MODEL PEM fuel cell electrochemical process starts on the anode side (Fig 1.) where H 2 molecules are brought by flow plate channels. Anode catalyst divides hydrogen on protons H + that travel to cathode through membrane and electrons e - that travel to cathode over external electrical circuit. At the cathode hydrogen protons H + and electrons e - combine with oxygen O 2 by use of catalyst, to form water H 2 O and heat. Described reactions can be expressed using equations: − + + → e H H 2 2 2 (Anode), (1) 0 2 2 2 1 2 2 H e H O → + + − + (Cathode). (2) Amount of chemical energy released in these reactions depends on hydrogen pressure, oxygen pressure and fuel cell temperature. Using change in Gibbs free energy, this amount can be expressed as: ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − Δ = Δ ) ln( 2 1 ) ln( 2 2 0 O H fc f f p p RT g g , (3)