PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks

TL;DR

PowerFlowNet introduces a graph neural network that reframes power flow as a node-regression problem on a bus-edge graph, leveraging a mask-based encoding and a stack of PowerFlowConv layers to integrate local and higher-order information. The model achieves near-Newton-Raphson accuracy while delivering substantial speedups, notably ≈4× on IEEE 14-bus and ≈145× on the large 6470rte network, outperforming DC PF and other baselines. Key contributions include the mask encoder, the PowerFlowConv layer combining one-step message passing with high-order TAGConv, and a dual loss framework (MSE and Masked L2) to handle unknown features while honoring PF physics. The results demonstrate strong scalability, interpretability through subgraph analyses, and robust generalization, making PowerFlowNet a promising tool for real-world PF analysis in planning and operation across large-scale grids.

Abstract

Accurate and efficient power flow (PF) analysis is crucial in modern electrical networks' operation and planning. Therefore, there is a need for scalable algorithms that can provide accurate and fast solutions for both small and large scale power networks. As the power network can be interpreted as a graph, Graph Neural Networks (GNNs) have emerged as a promising approach for improving the accuracy and speed of PF approximations by exploiting information sharing via the underlying graph structure. In this study, we introduce PowerFlowNet, a novel GNN architecture for PF approximation that showcases similar performance with the traditional Newton-Raphson method but achieves it 4 times faster in the simple IEEE 14-bus system and 145 times faster in the realistic case of the French high voltage network (6470rte). Meanwhile, it significantly outperforms other traditional approximation methods, such as the DC relaxation method, in terms of performance and execution time; therefore, making PowerFlowNet a highly promising solution for real-world PF analysis. Furthermore, we verify the efficacy of our approach by conducting an in-depth experimental evaluation, thoroughly examining the performance, scalability, interpretability, and architectural dependability of PowerFlowNet. The evaluation provides insights into the behavior and potential applications of GNNs in power system analysis.

Figures (7)

• Figure 1: A message passing step of node $i$ consisting of message creation, aggregation, and update of the hidden state.
• Figure 2: Interpreting the PF problem of the IEEE 9-case into a GNN node regression problem. In detail, Fig. \ref{['fig:pf_a']} shows the standard IEEE 9-case, and Fig. \ref{['fig:pf_b']} illustrates how each bus is transformed into a load, generator, or reference node while keeping the same line connectivity. Each node has different known and unknown features $\boldsymbol x = (V^m, \theta, P, Q)$ depending on its type. The ultimate goal of this GNN problem is to approximate all the features for all nodes, thus solving the PF problem.
• Figure 3: The PowerFlowNet model architecture consists of a mask encoder and $L$ PowerFlowConv layers. The input graph with incomplete feature information is fed node-by-node to the mask encoder to generate encoded graph features, where each node $n \in \mathcal{N}$ with $(\boldsymbol x_i, \boldsymbol m_i)$. Then, the encoded graph features are processed by a series of $L$ sequential PowerFlowConv layers, each comprising a 1-step message passing and a high-order TAGConv. Finally, the complete output graph is produced.
• Figure 4: Probability density function of the actual not-normalized error for every node in the test dataset. The brighter the color, the highest the probability of the prediction error of PowerFlowNet being in that region.
• Figure 5: Illustration of graph coverage defined as the number of nodes included in a subgraph, plotted per K-hop size and sorted from slowest to fastest growth for every node.