(453g) Estimation of Optimal Operating Profile of PEMFC Using Dynamic Optimization Technique

Typically fuel cells are operated to deliver the maximum power and operating conditions are decided from the polarization curve, which is a steady state representation of the system; but due to various dynamics taking place in the system, the operating conditions chosen from polarization curve might not be sufficient to provide the optimum performance from the cell for extended operations. PEMFC operating temperature changes with time, this change in operating temperature affects the cathode and anode gas temperatures, which in turn affects the rate of condensation/vaporization of water vapor at the cathode and anode.  Due to the change in the concentration of water at the membrane, transportation of protons will change. This affects the production of current from the PEMFC. These types of many known/unknown phenomena take place in PEMFC, which decreases the overall efficiency of the PEMFC.

There are various potential manipulated variables in PEMFC¹, of which some variables are more effective toward attaining the required power density obtained from the fuel cell. To increase the efficiency of PEMFC, it's critical to operate it at optimal operating conditions. This can be achieved either by  designing a control algorithm for the PEMFC and force the system dynamics to follow the optimal operating conditions or to estimate the optimal operating conditions by implementing dynamic optimization on the PEMFC models. In the literature, a number of attempts have been reported for controlling the PEMFC by designing the control algorithm based on reduced order models, empirical models or using model identification (identifying simpler models). But to our knowledge, open or closed-loop control of PEMFC using full-order physics based models directly has not been reported.

The key component of control/optimization scheme is the dynamic model used for optimization and control. To address complex nonlinear dynamics of the PEMFC, researchers have used two/three dimensional physics based models ^{[2, 3]} but models in general are computationally very expensive and hence are not useful in designing the controllers or optimization approaches. We have recently developed and implemented a model reformulation approach to develop physics based efficient models and algorithms (CPU time < 15 ms) for lithium-ion batteries.  To use PEMFC efficiently there is a need to have computationally efficient models sufficient enoughto capture all the required nonlinear dynamics of the system and from our experience in battery domain, we believe that model reformulation approach will be useful for finding computationally efficient physics based models for the PEMFC.

In this talk, as a first step, we will present the mathematical reformulation of available steady state physics based models⁵ that applies various mathematical techniques to solve for the dependent variables without losing accuracy. The approach considers each dependent variable separately and finds a suitable mathematical method to minimize the computational cost associated with that particular variable. The dependency of the chosen variable with other dependent/independent variable is kept constant.  After mathematical reformulation we plan to validate this model and the optimum profiled predicted using experimental data. For optimization, our goal is to estimate optimum operating profile of the manipulated variables, so that the efficiency of system is not compromised for delivering the load requirement. In optimization, we will formulate the objective function, which will maximize the available power density using inlet conditions of manipulated variables as control variables. This will be done for a randomly varying noisy load requirement as needed for vehicular applications. After estimating the optimum profile, we plan to consider the dynamic models of the PEMFC and mathematically reformulate the model and validate using experimental setup. This model then can be used for control or dynamic optimization purposes, which will facilitate optimum use of PEMFC for better production of power and helps in increased efficiency of the device.

When steady state models are used, the equations are simpler and only the disturbance variable changes with time. After we make progress in efficient simulation (improved computation time) of steady state models and optimization, we plan to explore the applicability of more detailed dynamic and 2D models for the same purpose. There are different methods to solve constrained optimization problems. (reference). Irrespective of the method used the most efficient and stable model for the problem with minimal number of state variables is advantageous for obtaining optimal profiles and for estimating uncertainties.

Acknowledgements

The authors are thankful for the partial financial support by the National Science Foundation (CBET ? 0828002) and the
United States government.

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