Cyberattacks on power grids pose significant risks to national security. Power grid attacks typically lead to abnormal readings in power output, frequency, current, and voltage. Due to the interconnected structure of power grids, abnormalities can spread throughout the system and cause widespread power outages if not detected and dealt with promptly. Our research proposes a novel anomaly detection system for power grids that prevents overfitting. We created a network graph to represent the structure of the power grid, where nodes represent power grid components like generators and edges represent connections between nodes such as overhead power lines. We combine the capabilities of Long Short-Term Memory (LSTM) models with a Graph Isomorphism Network (GIN) in a hybrid model to pinpoint anomalies in the grid. We train our model on each category of nodes that serves a similar structural purpose to prevent overfitting of the model. We then assign each node in the graph a unique signature using a GIN. Our model achieved a 99.92% accuracy rate, which is significantly higher than a version of our model without structural encoding, which had an accuracy level of 97.30%. Our model allows us to capture structural and temporal components of power grids and develop an attack detection system with high accuracy without overfitting.