PhD Thesis

Modeling and Control of PEM Fuel Cells

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  • Started: 02/11/2009
  • Finished: 22/09/2017



The internal behavior of a PEM fuel cell (PEMFC) is complex. This makes it often unpredictable, erratic, with a fragile balance. Within a PEMFC different nature phenomena, intimately related, occur: fluid-dynamic phenomena, diffusion, migration, electrochemical reactions, electrical currents, heat transfer, changes of state. All these phenomena makes the modeling of PEM cells a particularly challenging task. On the other hand, it is necessary to model the gas supply subsystem (air compressor, valves, humidifiers, cooling tanks ...), the management system of water and heat, and the conditioning system of electricity generated. The literature has extensively discussed the modeling of PEM cells, but the vast majority of models are stationary. The dynamic models, in general, have a high level of simplification, and often do not integrate all the subsystems that should be monitored.

In addition, there is a great deal of effort in improvement of PEMFC efficiency and durability, since these are factors that affect PEMFC competitiveness. Several variables whose variations affect the performance and durability of PEM fuel cells, such as concentrations of oxygen, water and temperature, have spatial dependence in the direction of the channels of the cathode and anode. To model in detail the variations of these variables, the introduction of partial differential equations in the model (PDE) is required. To perform numerical simulations of such models, it is necessary to discretize the PDE system. The discretization of the model results in a system of differential-algebraic equations (DAE) of high order, which slows down the numerical simulations and makes unfeasible the application of most control techniques. Therefore, model order reduction techniques are required (MOR).

It is expected that obtaining reduced models of PEMFC facilitates the development of efficient nonlinear controllers for them.


The literature contains various proposals for PEMFC controllers. In general, liner controllers are proposed which present some deficiencies. In the first place, nonlinearities cause inadequacy of controllers for certain operating conditions, and likewise, performance optimization is only effective in certain setpoints. Second, temperature and humidity controllers are not integrated and no solutions are given for the expulsion of liquid water from inside the stack. Moreover there are no controllers based on indicators that monitor durability and efficiency. Finally, there are not many studies that present experimental validation of the results.

The ultimate goal of the proposed thesis project is the development of distributed parameter models of PEM fuel cells, based on first principles, the discretization and order reduction of these models and the nonlinear controllers design for PEMFC.


The main objectives to be achieved in the thesis are:

1. Review and analysis of the state of the art in modeling and control of PEMFC, in order to study variables and factors that affect reliability, performance and durability of PEM fuel cells. This review will allow the definition of new indicators of performance of the PEMFC, as well as the setting of new control objectives.
2. Development of distributed parameter models of PEM fuel cells that take into account the spatial variations of variables of interest such as gas concentration, temperature, concentration of liquid water inside the stack, among other variables whose variation influences significantly the performance and fuel cell durability. This phase includes the discretization of these models.
3. Mathematical definition of control objectives.
4. Order reduction of the discretized models obtained in the previous phase, depending on the inputs and outputs set by the control objectives, to make possible the numerical simulations and allow the application of nonlinear control techniques.
5. Proposal of nonlinear controllers for PEM fuel cells.
6. Simulation and experimental validation of the proposed controllers.

The work is under the scope of the following projects:

  • DICOPEM: Avances en el modelo y diseño de controladores para sistemas basados en pila de combustible PEM (web)
  • DISCPICO: Design and implementation of control systems for PEM fuel cells and their integration into distributed electrical power generation systems (web)