The scale-up of AI models for analyzing large-scale power systems necessitates a thorough understanding of their scaling properties. Existing studies on these properties provide only partial insights, showing predictable decreases in loss function with increased model scales; yet no scaling law for power system AI models has been established, resulting in unpredictable performance. This letter introduces and explores the concept of “emergent abilities” in graph neural networks (GNN) used for analyzing large-scale power systems–a phenomenon where model performance improves dramatically once its scale exceeds a threshold. We further introduce an empirical power-law formula to quantify the relationship between this threshold and the power system size. Our theory precisely predicts the threshold for the emergence of these abilities in large-scale power systems, including both a synthetic 10,000-bus and a real-world 19,402-bus system.

With the growing penetration of distributed renewable energy, distributed control approaches are widely utilized in voltage control of active distribution networks (ADNs), suffering from limited applicability for control devices or heavy communication burden. This paper develops an innovative distributed voltage control strategy of ADNs with global sensitivities (DVC-GS), which integrates network information from global optimization view to coordinate energy storages, PV inverters and the OLTC within little communication and computing time. The global sensitivities of voltage violations across all buses with respect to nodal voltage and active/reactive power injection are formulated to quantify the ability of each controllable resource for alleviating voltage violations in the entire ADN. The back-and-forth communication combined with modified DistFlow model is newly developed for real-time update of global sensitivities at each bus with high accuracy and no iteration. Then the coordinated control of various devices is implemented on basis of global sensitivities to effectively ensure voltage security of ADNs. Comprehensive simulations based on a modified 11-bus system demonstrate the significant efficiency and superiority of the global sensitivities and DVC-GS.

When renewable energy penetration increases and the power network becomes more complex, vulnerability and security concerns typically also become more prevalent. A proper evaluation method focused on risk prediction and failure identification is required in modern power systems. In our work, a novel evaluation framework with high efficiency and accuracy is proposed, where the influence of over/under-voltage on renewable energy generators is considered during the cascading failure risk evaluation process. A graph convolutional network and a long short-term memory network are applied to describe the complex network topological structure and extract the system's electrical features, respectively. The neural network model trained with offline simulation data can reduce the numerical effort of evaluating cascading failure risk in real-time. Finally, the proposed method is verified based on the benchmark of both an IEEE 39-bus test system and a real-world French power system. The results show that the proposed cascade neural network model can achieve better evaluation results with shorter training and evaluation times.

Power flow calculation in quasi-steady states is the basis of cascading failure analysis. However, in recent years, data-driven analysis methods that are based on sufficient data have put forward higher requirements on the speed of power flow calculation. To build a more accurate and efficient neural network for power flow calculation, a physics-informed graph neural network-based model is proposed for faster calculation. Via minimizing the physics-informed loss function and using a pre-training/fine-tuning method, the proposed model is trained to follow the physical equations directly and can generalize to dynamic power networks. Physics-informed $LOSS$ makes the proposed model more interpretable, since the calculation error can be evaluated by $LOSS$ . Then cascading failures are simulated with the proposed model, and a pre-set factor $\zeta$ is introduced to balance the speed and accuracy of simulations. Finally, the accuracy of cascading failure simulations with the proposed model is verified in the IEEE 39-bus system, the 118-bus system, the 300-bus system, and a real-world French system. Experimental results show that compared with AC power flow, the proposed physics-informed graph neural network-based power flow model can reduce the simulation time significantly while maintaining high accuracy if $\zeta$ is properly pre-set.

Commutation failures (CFs) are usually triggered by the voltage dips caused by the faults in the receiving-end systems. To reduce the probability of CFs, counter measures to reduce the voltage dips should be implemented, among which adding dynamic var sources (DVSs) is very helpful. In this paper, an optimal allocation method for DVSs is proposed to maximize the benefit of DVSs to be installed. Firstly, the probability of CFs is quantified based on the concept of area of vulnerability (AOV), where the detailed ac network is considered. In order to find the most effective locations for installing DVSs, a 0-1 nonlinear programming model is formulated based on the quantitative index. Then, we introduce penalty functions to transform the binary programming to an unconstrained optimization problem, which can be solved by the gradient iteration method efficiently. Moreover, the sensitivity analysis in the calculation of gradient provides a better understanding of the relationships between the DVSs and CFs. In case studies, the 37-bus system and 1648-bus system are used to show the effectiveness of the proposed method.