Integration of Renewable Energy Sources into Smart Grids: A Study on Impact and Solutions for Efficient Integration of Renewable Energy Sources, Such as Solar and Wind Energy, into Existing Electrical Grids

This paper focuses on the mathematical modeling of electrical grid stability, taking into account the integration of renewable energy sources. Through the “Stability Margins" model, the study examines the effects of adding solar, wind, and hydroelectric energy to the stability of a theoretical electrical grid composed of ten nodes. Using the admittance matrix and Kirchhoff’s power law, a model is developed that analyzes the eigenvalues of the Jacobian matrix to assess the grid’s stability. Stability margins are calculated to estimate how far the grid is from becoming unstable. The results provide a deeper understanding of the impact of renewable energy on electrical grid stability and help identify solutions to maintain grid stability under increasing integration of renewable energy sources.