Dynamic optimization under uncertainty of the synthesis/design and operation/control of a proton exchange membrane fuel cell system

► Multi-level optimization strategy for dynamic PEMFC system synthesis/design is proposed and evaluated. ► Physical decomposition is applied and the global optimum solution is found within 6 iterations for the 41 decision variable dynamic system. ► We developed and showed how to define and integrate the uncertainties into optimization objective functions. Proton exchange membrane fuel cell (PEMFC) systems with their own fuel conversion unit typically consist of a fuel processing subsystem, a fuel cell stack subsystem, a work recovery-air supply subsystem, and a power electronics subsystem. Since these subsystems have different physical characteristics, their integration into a single system level unit makes the optimization problem of synthesis/design and operation/control highly complex. Thus, dynamic system/subsystem/component modeling and highly effective optimization strategies are required. Furthermore, uncertainties in the results of system optimization can be affected by any number of sources of uncertainty such as the load profiles and cost models. These uncertainties can be taken into account by treating the problem probabilistically. The difficulty with doing this, particularly when large-scale dynamic optimization with a large number of degrees of freedom is being used, is that the traditional probabilistic approaches are simply too computationally intensive. This difficulty can be overcome by the use of approximate approaches such as the response sensitivity analysis (RSA) method based on Taylor series expansion. Thus, in this paper, a stochastic modeling and uncertainty analysis methodology for energy system synthesis/design and operation/control which uses the RSA method is proposed and employed for calculating the uncertainties on the system outputs. Their effects on the development and control optimization of a 5kWe PEMFC system are assessed by taking the uncertainties into account in the objectives and constraints. It is shown that these uncertainties significantly affect the reliability of being able to meet certain constraints (e.g., that on the CO concentration) during the synthesis/design and operation/control optimization process.