3V-GM: A Tri-Layer “Point–Line–Plane” Critical Node Identification Algorithm for New Power Systems

With the increasing penetration of renewable energy, the stochastic and intermittent nature of its generation increases operational uncertainty and vulnerability, posing significant challenges for grid stability. However, traditional algorithms typically identify critical nodes by focusing solely on the network topology or power flow, or by combining the two, which leads to the inaccurate and incomplete identification of essential nodes. To address this, we propose the Three-Dimensional Value-Based Gravity Model (3V-GM), which integrates structural and electrical–physical attributes across three layers. In the plane layer, we combine each node’s global topological position with its real-time supply–demand voltage state. In the line layer, we introduce an electrical coupling distance to quantify the strength of electromagnetic interactions between nodes. In the point layer, we apply eigenvector centrality to detect latent hub nodes whose influence is not immediately apparent. The performance of our proposed method was evaluated by examining the change in the load loss rate as nodes were sequentially removed. To assess the effectiveness of the 3V-GM approach, simulations were conducted on the IEEE 39 system, as well as six other benchmark networks. The simulations were performed using Python scripts, with operational parameters such as bus voltages, active and reactive power flows, and branch impedances obtained from standard test cases provided by MATPOWER v7.1. The results consistently show that removing the same number of nodes identified by 3V-GM leads to a greater load loss compared to the six baseline methods. This demonstrates the superior accuracy and stability of our approach. Additionally, an ablation experiment, which decomposed and recombined the three layers, further highlights the unique contribution of each component to the overall performance.