This paper critically evaluates a number of uncertainty importance measures for use in power system stability studies. Sensitivity analysis of uncertain system parameters is vital as new technologies proliferate and the total level of system uncertainty grows. Accurate assessment of the importance of different uncertainties can guide power system operators towards parameters which will require the greatest levels of mitigation or increased monitoring in order to reduce the uncertainty and its subsequent impact. Local and global sensitivity analysis techniques are described and evaluated within this paper, including nonparametric methods, variance-based approaches, and distribution-based techniques. The techniques are illustrated using a large 295-bus realistic network model of a generic distribution system. Numerical experiments on dynamic models are used in order to assess the impact of uncertainties on the mitigation of system frequency excursions using single-site and distributed energy storage devices. Robin Preece (GS'10-M'13) received the B.Eng. degree in electrical and electronic engineering and Ph.D. degree from the University of Manchester, Manchester, U.K., in 2009 and 2013, respectively. He is currently a Lecturer in power systems engineering with the University of Manchester, Manchester, U.K. Jovica V. Milanović (M'95-SM'98-F'10) received the Dipl.Ing. and M.Sc. degrees from the University of Belgrade, Belgrade, Yugoslavia, the Ph.D. degree from the University of Newcastle, Newcastle, Australia, and the D.Sc. degree from the University of Manchester, Manchester, U.K., all in electrical engineering.Currently, he is a Professor of electrical power engineering,