Through experience and judicious design, the electric power grid has evolved into a robust network. The system is subject to numerous disturbances on a daily basis, yet few disturbances result in a significant loss of power to customers and very few lead to a general collapse of the system. (Those very few are devastating however.) Historically, this robustness arises from excellent anticipation of and conservative preparation for future power generation and transmission requirements. As the industry transitions into a competitive era, there is a need for less conservative operation while maintaining reliability. In this talk we will discuss some of the challenges with the analysis of dynamic phenomena that affect system reliability.One of greatest difficulties is to account for the many unknowns and uncertainties inherent in the system. It is particularly difficult to perform uncertainty analyses when studies require dynamic time-step simulations, and such studies are not usually done. Consequently it is common that "post-mortem" simulation studies made after a major blackout fail to reproduce the event without significant modification of parameter values from their nominal values. Even with speedy computers, a standard Monte Carlo approach remains computationally prohibitive. In this presentation we focus on our efforts to identify critical parametric uncertainties and quantify their effect in time-step simulation studies. We present a particular technique that is motivated by orthogonal polynomials and guassian quadrature integration that was developed for the study of global climate change, and discuss its applicability to power system studies. We show results that suggest that this is an enabling method which may reduce computation times by two or three orders of magnitude, making studies possible that were previously deemed infeasible.