Because of the lack of accurate information about load models and renewable distributed energy resources, parameters of the power system remain largely uncertain. For security purposes, it is necessary to quantify this uncertainty over the system’s dynamic behavior. When tackling the dynamics of the electrical power system, we are faced with two major challenges: a large parameter space together with non-linear and discontinuous dynamics. It is thus necessary to strike a balance between computational tractability and accuracy. In this talk, we will introduce the differential-algebraic equation formulation of the power system used in most commercial software. We then will introduce trajectory sensitivity techniques to analyze the effect of local parameter variation. Recent advances in differentiable programming and heterogeneous computing architectures have made trajectory sensitivities a thriving area of research where it is now possible to obtain second- and higher-order sensitivities in a computationally scalable fashion. We will show how these sensitivities, while local, can provide satisfactory approximations over a range of typical scenarios. Also, we will show how they can be used both in a setting where parametric uncertainty is represented as a bounded set or as a probability distribution function. Finally, we will show how these sensitivities can be connected with statistical global variance-based measures. Numerical examples and illustrations using realistic power system models will be given to illustrate the techniques.