Technical and economic uncertainties are not rigorously treated or characterized in most preliminary cost and performance estimates of advanced power system designs. Nor do current design methods rigorously address the issues of design under uncertainty. However, process costs and other important quality measures, such as controllability, safety, and environmental compliance, largely depend on the process synthesis stage. This conceptual design stage involves identifying the basic flowsheet structures from a typically large number of alternatives. This paper describes recent developments in on-going research to develop and demonstrate advanced computer-based methods for dealing with uncertainties that are critical to the design of advanced coal-based power systems. Results are presented illustrating the use of these new modeling tools for the environmental control design of an advanced energy system based on an integrated gasification combined cycle (IGCC) for electric power generation.