Application of the Extra Element Theorem for Grid Strength Analysis in IBR-Dominated Systems

Stability is one of the major concerns in maintain the security of power systems as their generation mix transitions to include high shares of inverter-based resources (IBRs). Most of the stability problems in IBR-dominated power systems are a consequence of low levels of grid strength, which is a measure of voltage stiffness at various nodes in the system. Grid-forming resources and synchronous condensers can provide the much needed grid strength to ensure system stability; however, system planners lack tools for the optimal sizing and placement of these grid strengthening devices (GSD). This paper presents a new method for performing grid strength analysis in large power systems by leveraging the Extra Element Theorem. The method shows the impact of the size of GSDs on grid strength without requiring analysis for each particular size; this not only significantly reduces computation, but also guides the sizing and placement of GSDs. The paper also introduces a sensitivity index to optimize the allocation of GSDs in large power systems. The proposed method is demonstrated through case studies on an IEEE 9-bus system and a larger 100+ bus system.