Application of Orthogonal Projectors in Power System Dynamics

This paper explores the application of orthogonal projectors to simplify the analysis of complex power system dynamics. By leveraging modal information, orthogonal projections map high-dimensional dynamics onto a lower-dimensional subspace, enabling projected state variables to effectively depict the system's progression over time. A theoretical framework and its practical application are presented, illustrating how this approach enhances the analysis of high-dimensional dynamics. The method is validated using a two-machine infinite bus system and extended to the New England 39-bus system. Results demonstrate that complex trajectories in an n-dimensional space can be efficiently projected onto a 2D subspace, facilitating the observation of specific dynamics, such as those with an electromechanical nature.