As phasor measurement units (PMUs) become more widely used in transmission power systems, a fast state estimation (SE) algorithm that can take advantage of their high sample rates is needed. To accomplish this, we present a method that uses graph neural networks (GNNs) to learn complex bus voltage estimates from PMU voltage and current measurements. We propose an original implementation of GNNs over the power system's factor graph to simplify the integration of various types and quantities of measurements on power system buses and branches. Furthermore, we augment the factor graph to improve the robustness of GNN predictions. This model is highly efficient and scalable, as its computational complexity is linear with respect to the number of nodes in the power system. Training and test examples were generated by randomly sampling sets of power system measurements and annotated with the exact solutions of linear SE with PMUs. The numerical results demonstrate that the GNN model provides an accurate approximation of the SE solutions. Furthermore, errors caused by PMU malfunctions or communication failures that would normally make the SE problem unobservable have a local effect and do not deteriorate the results in the rest of the power system.

翻译：随着相量测量单元（PMU）在输电系统中日益普及，亟需一种能够利用其高采样率优势的快速状态估计算法。为此，我们提出一种基于图神经网络（GNN）的方法，可从PMU电压和电流测量值中学习复杂的母线电压估计值。我们提出一种在电力系统因子图上实现的原始GNN架构，以简化不同类型与数量测量值在电力系统母线和支路上的集成。此外，我们通过增强因子图设计提升GNN预测的鲁棒性。该模型具有高度高效性和可扩展性，其计算复杂度与电力系统节点数呈线性关系。训练与测试样本通过随机采样电力系统测量值集生成，并标注了基于PMU的线性状态估计精确解。数值结果表明，GNN模型能够准确逼近状态估计解。同时，因PMU故障或通信失效而通常导致状态估计问题不可观测的误差仅产生局部影响，不会恶化电力系统其余部分的估计结果。