基于图Transformer的电力系统暂态稳定判别

熊学侨; 田芳; 黄彦浩; 李东琦; 张海岩; 马辰宇

doi:10.12204/j.issn.1000-7229.2026.07.010

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电力建设 ›› 2026, Vol. 47 ›› Issue (7) : 129-140. DOI: 10.12204/j.issn.1000-7229.2026.07.010

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基于图Transformer的电力系统暂态稳定判别

熊学侨 ¹ ,
田芳 ¹ ,
黄彦浩 ¹ ,
李东琦 ¹ ,
张海岩 ² ,
马辰宇 ¹

作者信息 +

Transient Stability Assessment of Power Systems Based on Graph Transformer

Author information +

文章历史 +

摘要

【目的】 针对传统电力系统暂态稳定判别方法难以处理高维非线性动态行为、效率与泛化能力不足的问题，提出基于图Transformer的电力系统暂态稳定智能判别方法。【方法】 融合短路故障起始时刻电气量与故障信息构建节点输入特征；采用图神经网络建模电网拓扑关系，结合拉普拉斯位置编码注入结构信息，利用Transformer多头自注意力机制挖掘节点间全局复杂依赖关系；通过PSASP平台生成多拓扑、多故障场景样本，采用最大池化聚合节点特征完成模型构建，并在IEEE 39节点与某区域1947节点系统开展试验验证。【结果】 IEEE 39节点特征消融实验表明，故障持续时间是影响暂态稳定判别最主要的因素；在1947节点系统验证集上，模型准确率达98.33%、召回率达97.36%，综合性能优于传统机器学习与主流深度学习对比模型；在电网拓扑变化场景下，模型各项性能指标波动小于0.25%，能够保持稳定且优异的判别效果。【结论】 所提方法兼具图神经网络拓扑建模与Transformer全局特征捕捉优势，在高维数据处理、复杂扰动适应与拓扑泛化方面性能突出，判别准确、鲁棒性强，可为电力系统紧急控制与安全防御提供可靠的决策依据。

Abstract

[Objective] Traditional methods for transient stability assessment of power systems often struggle to handle high-dimensional nonlinear dynamic behaviors， exhibiting insufficient efficiency and generalization ability. An intelligent transient stability assessment method based on Graph Transformer is proposed. [Methods] Node input features are constructed by fusing electrical quantities and fault information at the initial moment of short-circuit faults. A graph neural networks is employed to model the grid topology， augmented with Laplacian position encoding to inject structural information. The Transformer multi-head self-attention is adopted to capture global complex dependencies among nodes. Multi-topology and multi-fault samples are generated through the PSASP platform. The model is built with max-pooling for feature aggregation and verified on the IEEE 39-bus system and a regional 1947-bus system. [Results] Feature ablation experiments on the IEEE 39-bus system show that fault duration is the most important factor affecting transient stability assessment. On the 1947-bus validation set， the model achieves 98.33% accuracy and 97.36% recall， outperforming traditional machine learning and mainstream deep learning models. Under variations in grid topology， the model's performance indicators fluctuate by less than 0.25%， demonstrating stable and excellent results. [Conclusions] The proposed method integrates the advantages of graph neural network topology modeling and Transformer global feature capture. It exhibits outstanding performance in high-dimensional data processing， adapting to complex disturbances and generalizing across topological changes. With high accuracy and strong robustness， the method provides reliable decision support for power system emergency control and security defense.

导出引用

熊学侨, 田芳, 黄彦浩, 等. 基于图Transformer的电力系统暂态稳定判别[J]. 电力建设. 2026, 47(7): 129-140 https://doi.org/10.12204/j.issn.1000-7229.2026.07.010

XIONG Xueqiao, TIAN Fang, HUANG Yanhao, et al. Transient Stability Assessment of Power Systems Based on Graph Transformer[J]. Electric Power Construction. 2026, 47(7): 129-140 https://doi.org/10.12204/j.issn.1000-7229.2026.07.010

中图分类号： TM712

附录A

对于任意节点对（i，j），注意力分数α_ij表示节点j对节点i的影响权重，计算如下：

（A1）

${\alpha }_{ij}=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}{\mathrm{x}}_{j}\left({\mathit{e}}_{ij}\right)=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}{\mathrm{x}}_{j}\left(\frac{{\mathit{Q}}_{i}{\mathit{K}}_{j}^{\mathrm{T}}}{\sqrt{{d}_{k}}}\right)$

式中：softmax操作将节点间原始注意力分数e_ij转换为物理可解释的影响权重；d_k是查询向量和键向量的维度；Q_i和K_j是节点i和节点j的查询向量和键向量。定义为：

（A2）

${\mathit{Q}}_{i}={\mathit{h}}_{i}^{\text{'}}{\mathit{W}}_{q},{\mathit{K}}_{j}={\mathit{h}}_{j}^{\text{'}}{\mathit{W}}_{k}$

式中： ${\mathit{W}}_{q}\mathrm{、}{\mathit{W}}_{k}\in {\mathbb{R}}^{d\times {d}_{k}}$是可学习的线性变换矩阵。

节点的值向量V_j计算如下：

（A3）

${\mathit{V}}_{j}={\mathit{h}}_{j}^{\text{'}}{\mathit{W}}_{v}$

式中： ${\mathit{W}}_{v}\in {\mathbb{R}}^{d\times {d}_{v}}$是可学习线性变换矩阵；d_v是值向量的维度。

附录B

节点i的平均有功功率通量定义为：

（B1）

${\Phi }_{i}^{P}=\frac{1}{2}\left(\sum _{j\in {\mathcal{N}}_{\mathrm{i}\mathrm{n}}}\left|{P}_{ji}\right|+\sum _{k\in {\mathcal{N}}_{out}}|{P}_{ik}|\right)$

式中：P_ji表示从节点j流向节点i的有功功率；P_ik表示从节点i流向节点k的有功功率； ${\mathcal{N}}_{\mathrm{i}\mathrm{n}}$表示输入邻居节点集合； ${\mathcal{N}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$表示输出节点集合。

节点i的平均无功功率通量 ${\Phi }_{i}^{Q}$同理定义为：

（B2）

${\Phi }_{i}^{Q}=\frac{1}{2}\left(\sum _{j\in {\mathcal{N}}_{in}}|{Q}_{ji}|+\sum _{k\in {\mathcal{N}}_{out}}|{Q}_{ik}|\right)$

式中：Q_ji表示从节点j流向节点i的无功功率；Q_ik表示从节点i流向节点k的无功功率。

附录C

1）平均池化。

平均池化将所有节点的特征进行平均，认为所有节点对全局表示的贡献是相等的，对于每个特征维度，计算该列上所有元素的平均值：

（C1）

${\mathit{h}}_{\mathrm{G}}=\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{m}\mathrm{P}\mathrm{o}\mathrm{o}\mathrm{l}\left({\mathit{H}}^{\left(L\right)}\right)=\frac{1}{N}\sum _{i=1}^{N}{\mathit{h}}_{i}$

2）求和池化。

求和池化通过累加所有节点的特征信号，捕捉电网中特征分布的总体强度或规模信息。对于每个特征维度，将该列上所有元素进行加和：

（C2）

${\mathit{h}}_{\mathrm{G}}=\mathrm{S}\mathrm{u}\mathrm{m}\mathrm{P}\mathrm{o}\mathrm{o}\mathrm{l}\left({\mathit{H}}^{\left(L\right)}\right)=\sum _{i=1}^{N}{\mathit{h}}_{i}$

附录D

1）召回率：

（D1）

${\lambda }_{\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}^{}=\frac{{N}_{\mathrm{T}\mathrm{P}}}{{N}_{\mathrm{T}\mathrm{P}}+{N}_{\mathrm{F}\mathrm{N}}}$

召回率用来衡量模型对失稳样本的识别覆盖率，高召回率代表几乎无失稳漏判，能最大程度避免因漏判失稳引发的系统崩溃、大停电等严重事故，是暂态稳定判别最核心的安全指标。

2）预测精度：

（D2）

${\lambda }_{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}=\frac{{N}_{\mathrm{T}\mathrm{P}}}{{N}_{\mathrm{T}\mathrm{P}}+{N}_{\mathrm{F}\mathrm{P}}}$

预测精度用来衡量模型判失稳的精准度，高精确率可减少稳定样本误判为失稳的情况，避免不必要的紧急控制措施，兼顾电网运行的经济性。

3）F1分数：

（D3）

${F}_{1}=\frac{2\times {\lambda }_{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}\times {\lambda }_{\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}{{\lambda }_{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}+{\lambda }_{\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}$

F1分数兼顾失稳识别覆盖率与判失稳精准度的平衡指标，解决样本不平衡场景下准确率的片面性问题。

4）准确率：

（D4）

${\lambda }_{\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}}=\frac{{N}_{\mathrm{T}\mathrm{P}}+{N}_{\mathrm{T}\mathrm{N}}^{}}{{N}_{\mathrm{T}\mathrm{P}}+{N}_{\mathrm{T}\mathrm{N}}^{}+{N}_{\mathrm{F}\mathrm{P}}+{N}_{\mathrm{F}\mathrm{N}}}$

准确率用来衡量模型对稳定、失稳样本的整体判别性能，反映模型的综合识别能力。

5）特异度：

（D5）

${\lambda }_{\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}}=\frac{{N}_{\mathrm{T}\mathrm{N}}}{{N}_{\mathrm{T}\mathrm{N}}+{N}_{\mathrm{F}\mathrm{P}}}$

高特异度可减少稳定误报，降低不必要的控制成本，保障电网供电可靠性。

6）马修斯相关系数：

（D6）

${\lambda }_{\mathrm{M}\mathrm{C}\mathrm{C}}=\frac{{N}_{\mathrm{T}\mathrm{P}}\times {N}_{\mathrm{T}\mathrm{N}}-{N}_{\mathrm{F}\mathrm{P}}\times {N}_{\mathrm{F}\mathrm{N}}}{\sqrt{({N}_{\mathrm{T}\mathrm{P}}+{N}_{\mathrm{F}\mathrm{P}})({N}_{\mathrm{T}\mathrm{P}}+{N}_{\mathrm{F}\mathrm{N}})({N}_{\mathrm{T}\mathrm{N}}+{N}_{\mathrm{F}\mathrm{P}})({N}_{\mathrm{T}\mathrm{N}}+{N}_{\mathrm{F}\mathrm{N}})}}$

马修斯相关系数是类别不平衡电网稳定/失稳数据集下鲁棒性最优的综合评价指标，对失稳漏判和稳定误报两类错误均高度敏感，能客观反映模型在复杂工况下的真实性能。

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脚注

利益冲突声明（Conflict of Interests）：所有作者声明不存在利益冲突。

作者贡献声明（Authors' Contributions）：熊学侨提出基于图Transformer的电力系统暂态稳定判别核心概念、基本框架，提出研究方向，设计论文整体框架，进行实验，开展对比实验，完成实验数据整理与分析；田芳设计研究思路、研究方案，开展研究方案可行性调查分析，实施核心研究过程；黄彦浩确定研究对象范围（39节点系统、1947节点区域电网），收集仿真数据，完成数据采集、清洗与分析；李东琦承担图Transformer模型相关技术开发；张海岩绘制模型原理图、训练结果图等核心图谱；马辰宇负责文献调研与整理。所有作者均阅读并同意了论文终稿内容。