Towards improved scalability in smart grid modeling: Simplifying generator dynamics analysis via spectral graph sparsification

Abstract-Smart-grid technologies focus on the complex interactions between different components of the electricity grid, together with the computing, control and communication functionalities that will bring together this future smarter infrastructure. Investigating these complex dynamic interactions is crucial for the efficiency and robustness of the emerging smart grid. In particular, it is one of the key elements for smart-grids to establish the dynamics among generators when a disturbance or fault appears on transmission and distribution systems. In small-signal stability analysis, eigenvalues from a system matrix construction is an important component of the generator dynamics. Such methods allow us certain mathematical tractability for generators, and help to reveal their stability or system mode. However, the recent trends in electricity grids, accompanied by increases in size and more tangled interconnections, raise challenges to using this approach. In general, the complexity of obtaining eigenvalues increases with the grid size and we especially emphasize that a system matrix becomes fully dense under the existence of algebraic buses. This hampers a fast diagnosis of generators, and the model complexity is not acceptable for analyzing large-scale electricity grids through eigenvalues. For this reason, we propose here a complexity reduction method for investigating generator dynamics, by utilizing a spectral sparsifier. This is based on finding a sparse counterpart which conserves the dense system matrix properties. We explain the reasoning for this sparsification and test the proposed method in several electricity grids. Our results show that the generator dynamics can be analyzed based on much simpler grid topologies, while staying within a controllable small error-bound.