[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84855-en":3,"doc-seo-84855-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84855,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Causal Structural Dynamic Graph Learning for Online Transient Stability Trajectory Prediction in Power Systems","Power systems feature dynamically coupled generators, motivating Graph Neural Networks for online transient stability trajectory prediction. Existing GNN methods often assume fixed admittance-based topology, missing state-dependent coupling, or rely on data-driven adjacency that ignores directional effects. The proposed C-DNR framework fuses a measurement-inferred dynamic structural graph with a nonlinear causal graph, then learns edge-wise weights for each generator pair. The fused graph is propagated through a GRU to predict post-fault trajectories, cutting autoregressive error by 73% on the IEEE 39-bus benchmark.","Causal–Structural Dynamic Graph Learning for Online Transient Stability Trajectory Prediction in  \nPower Systems  \nIbrahim Shahbaz, Omar Al-Refai∗ , Isaac Lagoy∗ , Ahmad Al-Khateeb†, Sathvik Sankaranarayanan†, and Eman Hammad  \niSTAR Lab, Texas A&M University, College Station, TX, USA  \n{i.shahbaz, omaralrefai, isaac lagoy, ahmad.alkhateeb, sath440, [eman.hammad](eman.hammad}@tamu.edu)[}](eman.hammad}@tamu.edu)[@tamu.edu](eman.hammad}@tamu.edu)  \narXiv :2607 .05729v1 [ ee ss . SY] 7 Jul 2026  \nAbstract—Power systems consist of dynamically coupled generators, motivating the use of Graph Neural Networks (GNNs) for online transient stability prediction. Traditional GNN frameworks are often constrained by fixed admittance-based topologies that fail to capture state-dependent coupling, or by datadriven methods that neglect directional influences. This paper proposes Causal Dynamic Network Representation (C-DNR), a novel framework that fuses two complementary representations of inter-generator interactions prior to temporal modeling: a dynamic structural graph inferred from measurements and a directional causal graph obtained via nonlinear causal discovery. An end-to-end learned edge-wise fusion mechanism adaptively weights these representations for each generator pair, and the resulting graph is propagated through a Gated Recurrent Unit (GRU) to predict post-fault trajectories. Evaluated on the IEEE 39-bus system, C-DNR reduces autoregressive prediction error by 73% compared to a dynamic structural baseline. Among the evaluated causal methods, only Peter–Clark Momentary Conditional Independence (PCMCI) achieves consistent improvements, owing to its ability to isolate directional dependencies from misleading oscillatory correlations. The learned fusion weights further provide interpretable diagnostics aligned with the electrical topology, offering transparent, pairwise insight into the prediction process.  \nIndex Terms—Smart grid, transient stability assessment, graph neural networks, dynamic graph learning, causal discovery.  \nI. INTRODUCTION  \nThe rapid integration of inverter-based resources (IBRs) reduces system inertia and accelerates post-fault dynamics, increasing the need for reliable online transient stability assessment (TSA) [1] . In this context, conventional timedomain simulation of differential-algebraic equations is computationally intensive for real-time applications and requires precise contingency information that is typically unavailable at fault inception [2]. Machine learning(ML)-based TSA methods have been developed to enable faster prediction [3], [4]; however, many approaches provide only binary stability classification or scalar stability margins. In practice, grid operators require full post-fault trajectories of generator states to support timely remedial actions, such as load shedding and controlled islanding.  \n∗ Equal contribution as second authors.†Equal contribution as third authors.  \nTrajectory prediction in complex networked systems, such as traffic forecasting, has been effectively addressed using spatio-temporal GNNs (STGNNs) [5] . The Temporal Graph Convolutional Network (T-GCN) [6] exemplifies this approach by combining a Graph Convolutional Network (GCN) [7] to model spatial dependencies with a Gated Recurrent Unit (GRU) [8] to capture temporal dynamics. This formulation has led to a broad class of STGNN architectures, including attention-based methods for dynamic spatio-temporal correlations [9], and graph attention mechanisms with learnable edge weights [10] . Motivated by their success in networked timeseries prediction, variants of STGNNs have been adopted for various power-system applications [11], [12] .  \nA key limitation of existing graph-based TSA methods is their reliance on the fixed admittance topology of the physical network. This static-graph assumption (i) cannot adapt to post-contingency topology changes, (ii) fails to capture the state-dependent coupling that arises during lar","cbCaieVeg26jliAG","https://ap.wps.com/l/cbCaieVeg26jliAG","pdf",2683717,1,7,"English","en",105,"# Abstract\n# Introduction\n## Motivation for online transient stability trajectory prediction\n## Limitations of existing graph-based TSA methods\n## Causal discovery for directional modeling\n# Method (C-DNR)","[{\"question\":\"What problem does this work address in transient stability assessment?\",\"answer\":\"It targets online prediction of post-fault transient stability trajectories for generator states, not just binary stability labels or scalar margins, enabling faster remedial decision-making.\"},{\"question\":\"How does C-DNR improve over correlation-based dynamic graph learning?\",\"answer\":\"C-DNR combines a dynamic structural graph inferred from measurements with a directional causal graph from nonlinear causal discovery, then uses an end-to-end learned edge-wise fusion to weight their contributions.\"},{\"question\":\"What modeling approach is used to generate the final trajectory predictions?\",\"answer\":\"After edge-wise fusion, the resulting graph representation is propagated through a GRU to predict post-fault 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problem does this work address in transient stability assessment?","Question",{"text":75,"@type":76},"It targets online prediction of post-fault transient stability trajectories for generator states, not just binary stability labels or scalar margins, enabling faster remedial decision-making.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does C-DNR improve over correlation-based dynamic graph learning?",{"text":80,"@type":76},"C-DNR combines a dynamic structural graph inferred from measurements with a directional causal graph from nonlinear causal discovery, then uses an end-to-end learned edge-wise fusion to weight their contributions.",{"name":82,"@type":73,"acceptedAnswer":83},"What modeling approach is used to generate the final trajectory predictions?",{"text":84,"@type":76},"After edge-wise fusion, the resulting graph representation is propagated through a GRU to predict post-fault 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