Comparative Analysis of Weighted Least Squares and Graph Convolutional Neural Network Approaches for Power System Inertia Estimation Using Transient Phasor Data

System inertia has decreased due to the increased integration of renewable energy sources like solar and wind, posing a threat to grid dependability and frequency stability. For reliable operation, a real-time inertia estimate is essential, particularly in grids that rely heavily on renewable energy sources. This study compares and contrasts two ways to figure out inertia: one uses a Graph Convolutional Network (GCN), and the other uses the more common Weighted Least Squares (WLS) method. Known for its ease of use and resilience to noise, WLS uses transient phasor data (frequency, ROCOF, and power deviations) to estimate inertia. However, since it relies on localized measurements and linearity assumptions, it has trouble estimating inertia in complicated, renewable-rich networks. By incorporating topological and geographical information, the GCN-based approach, on the other hand, represents the power grid as a graph, improving accuracy and flexibility. Simulations on the IEEE 30-bus system in PSS/E that include wind, solar, and regular generators show that the GCN-based method works better than WLS in terms of accuracy, noise resilience, and handling complex grid situations. This study talks about how to make grid stability better in power systems that use renewable energy. It does this by pointing out the problems with old methods and the benefits of using advanced machine learning models like GCNs.