Load flow studies are one of the most essential engineering applications for grid operators because they provide a clear picture of the operating conditions of the power system. Traditionally, the load flow problem is assumed to be deterministic; that is, the system variables contain no randomness. Unfortunately, this assumption is just that, an assumption that helps us deal with complexities of the underlying physics in the flow of electricity. The reality is that most of the variables (e.g., generation and electrical demand) involved in the analysis of power systems are, in fact, a stochastic process. Therefore, it is much more accurate to assess the power system’s response to a range of possible inputs. The research presented here seeks to understand and quantify the impact that uncertainty, i.e., sources of randomness, has on the power system. The first part of this work uses numerical methods, namely Monte Carlo simulations, to (1) quantify the impact that ocean wave energy has on power system reliability and (2) understand the power system’s failure risk from large earthquakes. Lastly, we propose a new method that couples the Karhuen-Loève expansion with anisotropic sparse grids to solve the Probabilistic Load Flow (PLF) problem. This new method proves capable of solving high-dimensional problems with an accuracy comparable to Monte Carlo simulations and a significant decrease in computational time.