Abstract
Modern power systems are shifting toward decarbonization and incorporation of distributed energy resources (DERs) to replace fossil fuel generators. Although promising, DERs introduce uncertainty because of their intermittent nature. This study provides a comprehensive survey of current approaches for modeling system uncertainties and methods of analysis, particularly in the context of static voltage stability studies within modern power systems. Emphasis is placed on evaluating various models applied to different system random variables (RVs), focusing on their suitability for those particular RVs. Additionally, the study examines the characteristics and frameworks of prominent probabilistic methods (PM), evaluates their efficacy, and discusses static voltage stability analysis approaches, emphasizing solution structures and appropriate applications. It concludes by thoroughly reviewing both numerical and analytical PM methods and offering insights into their strengths and limitations. The provided comprehensive survey reveals that, considering system uncertainties, voltage stability studies have gained the most share, followed by small-signal stability studies, whereas the frequency stability studies have gained the least share.