Control of Fuel Cells

This thesis deals with control of fuel cells, focusing on high-temperature proton-exchange-membrane fuel cells. Fuel cells are devices that convert the chemical energy of hydrogen, methanol or other chemical compounds directly into electricity, without combustion or thermal cycles. They are efficient, scalable and silent devices that can provide power to a wide variety of utilities, from portable electronics to vehicles, to nation-wide electric grids. Whereas studies about the design of fuel cell systems and the electrochemical properties of their components abound in the open literature, there has been only a minor interest, albeit growing, in dynamics and control of fuel cells. In the relatively small body of available literature, there are some apparently contradictory statements: sometimes the slow dynamics of fuel cells is claimed to present a control problem, whereas in other articles fuel cells are claimed to be easy to control and able to follow references that change very rapidly. These contradictions are mainly caused by differences in the sets of phenomena and dynamics that the authors decided to investigate, and also by how they formulated the control problem. For instance, there is little doubt that the temperature dynamics of a fuel cell can be slow, but users are not concerned with the cell’s temperature: power output is a much more important measure of performance. Fuel cells are very multidisciplinary systems, where electrical engineering, electrochemistry, chemical engineering and materials science are all involved at various levels; it is therefore unsurprising that few researchers can master all of these branches, and that most of them will neglect or misinterpret phenomena they are unfamiliar with. The ambition of this thesis is to consider the main phenomena influencing the dynamics of fuel cells, to properly define the control problem and suggest possible approaches and solutions to it. This thesis will focus on a particular type of fuel cell, a variation of proton-exchange-membrane fuel cells with a membrane of polybenzimidazole instead of the usual, commercially available Nafion. The advantages of this particular type of fuel cells for control are particularly interesting, and stem from their operation at temperatures higher than those typical of Nafion-based cells: these new cells do not have any water-management issues, can remove more heat with their exhaust gases, and have better tolerance to poisons such as carbon monoxide. The first part of this thesis will be concerned with defining and modelling the dynamic phenomena of interest. Indeed, a common mistake is to assume that fuel cells have a single dynamics: instead, many phenomena with radically different time scales concur to define a fuel-cell stack’s overall behaviour. The dynamics of interest are those of chemical engineering (heat and mass balances), of electrochemistry (diffusion in electrodes, electrochemical catalysis) and of electrical engineering (converters, inverters and electric motors). The first part of the thesis will first present some experimental results of importance for the electrochemical transient, and will then develop the equations required to model the four dynamic modes chosen to represent a fuel-cell system running on hydrogen and air at atmospheric pressure: cathodic overvoltage, hydrogen pressure in the anode, oxygen fraction in the cathode and stack temperature. The second part will explore some of the possible approaches to control the power output from a fuel-cell stack. It has been attempted to produce a modularised set of controllers, one for each dynamics to control. It is a major point of the thesis, however, that the task of controlling a fuel cell is to be judged exclusively by its final result, that is power delivery: all other control loops, however independent, will have to be designed bearing that goal in mind. The overvoltage, which corresponds nonlinearly to the rate of reaction, is controlled by operating a buck-boost DC/DC converter, which in turn is modelled and controlled with switching rules. Hydrogen pressure, being described by an unstable dynamic equation, requires feedback to be controlled. A controller with PI feedback and a feedforward part to improve performance is suggested. The oxygen fraction in the cathodic stream cannot be easily measured with a satisfactory bandwidth, but its dynamics is stable and disturbances can be measured quite precisely: it is therefore suggested to use a feedforward controller. Contrary to the most common approach for Nafion-based fuel cells, temperature is not controlled with a separate cooling loop: instead, the air flow is used to cool the fuel-cell stack. This significantly simplifies the stack design, operation and production cost. To control temperature, it is suggested to use a P controller, possibly with a feedforward component. Simulations show that this approach to stack cooling is feasible and poses no or few additional requirements on the air flow actuator that is necessary to control air composition in the cathode