GMT: A Graph-Based State Estimation Framework via Improved Graph Neural Networks

Abstract

State estimation is an essential tool for situational awareness and control to ensure safe operation. To address challenges such as unknown physical models, missing data, and amplitude distortions in state estimation for complex systems, this paper proposes a Graph structures with Multibranch Transformer(GMT). The framework learns spatiotemporal dependencies among nodes in a data-driven manner. First, a Gumbel-Softmax differentiable sampling strategy was adopted to adaptively construct a globally sparse directed graph, which breaks the locality constraint of fixed distance metrics. Second, a spatiotemporal encoding module combining influence propagation convolution and hierarchical dilated convolution was designed, which enhances robustness against structured noise by aggregating neighborhood feature discrepancies and modeling multi-scale temporal dependencies. Meanwhile, a hybrid multi-branch attention mechanism was introduced, which reduces the quadratic complexity of self-attention and ensures scalability in high-dimensional scenarios. Experiments were conducted on modified IEEE 30, 39, and 118 node systems. The results show that GMT achieves AUC values of 0.92, 0.83, and 0.80 for anomaly detection on these three systems, respectively, significantly outperforming the compared methods. The mean absolute error (MAE) for state estimation is below 0.41 and the root mean square error (RMSE) below 0.85 in all cases. By optimizing the decision threshold via Youden’s index, the framework balances the trade-off between high recall and high accuracy requirements.