Comparison of Different Optimization Methods for the Microstructure of Proton Exchange Membrane Fuel Cells

Abstract

Proton exchange membrane fuel cells (PEMFCs) have attracted much attention in the research and commercial sectors because they are environmental friendly and have relatively high power density compared to most other energy storage devices based on electrochemical processes. A significant part of the research on PEMFCs is related to decreasing the cost and improving the structure of PEMFCs by optimizing numerically the microstructure of these devices including the non-uniform porosity, carbon, nafion, and catalyst (i.e. platinum) distributions and the geometrical characteristics. The existing optimization techniques can generally be divided into heuristic and non-heuristic techniques. Heuristic techniques usually use stochastic approaches that search the optimization space using trial-and-error methods. Examples of such techniques include the genetic algorithm, particle swarm optimization, differential evolution, simulating annealing, harmony search, memetic algorithms, etc. These techniques can be applied to optimize a small number of design variables and often need to be used with simplified (often purely mathematic and not based on fundamental physics) models, such as compact, reduced-order models, or equivalent circuit models. On the other hand, non-heuristic techniques are deterministic and often require evaluating the gradient of the objective function. In general, these techniques have local convergence and their rate of convergence can be increased, using second-order derivatives such as the Hessian matrix, or taking advantage of the particular functional form of the objective function. Non-heuristic techniques usually require between a few tens of iterations to optimize the objective function compared to heuristic techniques which require at least tens of thousands of iterations.In this presentation we will make a thorough critical review of the different optimization methods used in the literature for PEMFCs. In additional, we will present the results of our efforts to develop a full-cell optimization algorithm for PEMFCs using the adjoint method [1-3]. The advantages and disadvantages of different methods, including the adjoint method, will be discussed in detail and examples of sample simulations results will be presented.