Distributed power generation is one of the most powerful applications of fuel cell power plants. Several types of configurations have been hypothesized and tested for these kinds of applications at the conceptual level, but hybrid power plants are one of the most efficient. These are designs that combine the fuel cell cycle with other thermodynamic cycles to provide higher efficiency. The power plant in focus is the high-pressure (HP)-low-pressure (LP) solid oxide fuel cells (SOFC)/steam turbine (ST)/gas turbine (GT) configuration which is a part of the Vision-21 program. This program is a new approach that the U.S. Department of Energy's (DOE's) Office of Fossil Energy has begun for developing 21st century energy plants that would have virtually no environmental impact. The overall goal is to effectively eliminate, at competitive costs, environmental concerns associated with the use of fossil fuels for producing electricity and transportation fuels. In this design, coal is gasified in an entrained bed gasifier and the syngas produced is cleaned in a transport bed desulfurizer and passed over to cascaded SOFC modules (at two pressure levels). This module is integrated with a reheat GT cycle. The heat of the exhaust from the GT cycle is used to convert water to steam, which is eventually used in a steam bottoming cycle. Since this hybrid technology is new and futuristic, the system level models used for predicting the fuel cells' performance and for other modules such as the desulfurizer have significant uncertainties in them. Also, the performance curves of the SOFC would differ depending on the materials used for the anode, cathode, and electrolyte. The accurate characterization and quantification of these uncertainties is crucial to the credibility of the model predictions. We have utilized the uncertainty analysis of the (HP-LP)SOFC/ST/GT conceptual design to illustrate the concept of "value of research", which deals with the examination of tradeoffs inherent in allocating scarce resources to reduce uncertainty. Research activities introduce their own costs, and though reducing uncertainty is profitable, the time required to achieve a reduction tempers the benefit and, therefore, needs to be minimized. The "value of research" methodology developed in this work optimizes the objective but, beyond that, limits the extent to which the uncertainty reduction contributes to this goal. The framework developed in this work forms the basis for optimal design and synthesis of any power plant under uncertainties in the face of multiple objectives.