In smart grids, power electronics circuits are used to process power from distributed energy resources (DERs). Stability analysis is mandatory for the design of power electronics circuits. Stability analysis foundations, such as root analysis, are also used in load variance analysis and cost and utility function modeling in smart grids. Traditionally, paper-and-pencil proof methods are used to conduct stability analysis. But traditional techniques cannot guarantee accurate analysis of the systems due to their inherent limitations. However, an accurate and exhaustive stability analysis is direly needed in the safety- and mission-critical operations of smart grids, such as integration of electric vehicles and renewable energy sources. Therefore, in this chapter, we provide a logical framework for stability analysis using HOL Light theorem prover which is a formal method technique and ensures an accurate analysis and verification of stability analysis.