Sizing and Placement of Grid Strengthening Devices Using Extra Element Theorem

Stability is a major concern in maintaining the reliability of power systems with high shares of inverter-based resources (IBRs). Many 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 strengthening devices (GSDs) - such as synchronous condensers, pumped hydro storage, and energy storage systems with GFM control - can provide the much-needed grid strength to ensure system stability. However, system planners lack tools to optimally size and place GSDs. This paper presents a new grid-strength assessment method for large power systems using the Extra Element Theorem. This method provides an intuitive expression for the grid-strength improvement achieved at a node in the grid from a GSD of any size and at any point in the grid. These gains can be used to achieve specific objectives on grid-strength improvement using the minimum aggregate capacity of GSDs. The method provides a framework for optimizing the size and location of GSDs for improving system strength and stability using the sensitivity indices introduced in this paper. The proposed method is demonstrated on an IEEE 9-bus system and an actual utility grid.