Abstract: Analyzing the vulnerability of power systems in cascading failures is generally regarded as a challenging problem. Although existing studies can extract some critical rules, they fail to capture the complex subtleties under different operational conditions. In recent years, several deep learning methods have been applied to address this issue. However, most of the existing deep learning methods consider only the grid topology of a power system in terms of topological connections, but do not encompass a power system's spatial information such as the electrical distance to increase the accuracy in the process of graph convolution. In this paper, we construct a novel power-weighted line graph that uses power system topology and spatial information to optimize the edge weight assignment of the line graph. Then we propose a multi-graph convolutional network (MGCN) based on a graph classification task, which preserves a power system's spatial correlations and captures the relationships among physical components. Our model can better handle the problem with power systems that have parallel lines, where our method can maintain desirable accuracy in modeling systems with these extra topology features. To increase the interpretability of the model, we present the MGCN using layer-wise relevance propagation and quantify the contributing factors of model classification.

连锁故障中电力系统脆弱性的多图卷积网络分析

[1]Bach S, Binder A, Montavon G, et al., 2015. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PLoS ONE, 10(7):e0130140.

[2]Bandyopadhyay S, Biswas A, Murty MN, et al., 2019. Beyond node embedding: a direct unsupervised edge representation framework for homogeneous networks.

[3]Bolz V, Rueß J, Zell A, 2019. Power flow approximation based on graph convolutional networks. Proc 18^th IEEE Int Conf on Machine Learning and Applications, p.1679-1686.

[4]Bruna J, Zaremba W, Szlam A, et al., 2014. Spectral networks and locally connected networks on graphs. Proc 2^nd Int Conf on Learning Representations, p.1-14.

[5]Bucolo M, Buscarino A, Famoso C, et al., 2021. Chaos addresses energy in networks of electrical oscillators. IEEE Access, 9:153258-153265.

[6]Chen G, Dong ZY, Hill DJ, et al., 2010. Attack structural vulnerability of power grids: a hybrid approach based on complex networks. Phys A Stat Mech Appl, 389(3):595-603.

[7]Chen KJ, Hu J, Zhang Y, et al., 2020. Fault location in power distribution systems via deep graph convolutional networks. IEEE J Sel Area Commun, 38(1):119-131.

[8]Defferrard M, Bresson X, Vandergheynst P, 2016. Convolutional neural networks on graphs with fast localized spectral filtering. Proc 30^th Int Conf on Neural Information Processing Systems, p.3844-3852.

[9]di Muro MA, Valdez LD, Rêgo HHA, et al., 2017. Cascading failures in interdependent networks with multiple supply-demand links and functionality thresholds. Sci Rep, 7(1):15059.

[10]Eppstein MJ, Hines PDH, 2012. A “random chemistry” algorithm for identifying collections of multiple contingencies that initiate cascading failure. IEEE Trans Power Syst, 27(3):1698-1705.

[11]Fang JY, Wu JJ, Zheng ZB, et al., 2021. Revealing structural and functional vulnerability of power grids to cascading failures. IEEE J Emerg Sel Top Circ Syst, 11(1):133-143.

[12]Gambuzza LV, Buscarino A, Fortuna L, et al., 2017. Analysis of dynamical robustness to noise in power grids. IEEE J Emerg Sel Top Circ Syst, 7(3):413-421.

[13]Gao HY, Ji SW, 2019. Graph U-Nets. Proc 36^th Int Conf on Machine Learning, p.2083-2092.

[14]Ge LJ, Liao WL, Wang SX, et al., 2020. Modeling daily load profiles of distribution network for scenario generation using flow-based generative network. IEEE Access, 8:77587-77597.

[15]Henaff M, Bruna J, LeCun Y, 2015. Deep convolutional networks on graph-structured data. https://arxiv.org/abs/1506.05163

[16]Hu JL, Li TH, Dong SB, 2020. GCN-LRP explanation: exploring latent attention of graph convolutional networks. Proc Int Joint Conf on Neural Networks, p.1-8.

[17]Kim C, Kim K, Balaprakash P, et al., 2019. Graph convolutional neural networks for optimal load shedding under line contingency. Proc IEEE Power & Energy Society General Meeting, p.1-5.

[18]Kipf TN, Welling M, 2017. Semi-supervised classification with graph convolutional networks. Proc 5^th Int Conf on Learning Representations, p.1-14.

[19]Knyazev B, Lin X, Amer MR, et al., 2018. Spectral multigraph networks for discovering and fusing relationships in molecules. https://arxiv.org/abs/1811.09595

[20]Kohlbrenner M, Bauer A, Nakajima S, et al., 2020. Towards best practice in explaining neural network decisions with LRP. Proc Int Joint Conf on Neural Networks, p.1-7.

[21]León-Montiel RD, Quiroz-Juárez MA, Quintero-Torres R, et al., 2015. Noise-assisted energy transport in electrical oscillator networks with off-diagonal dynamical disorder. Sci Rep, 5:17339.

[22]Li Q, Liao YX, Wu KM, et al., 2021. Parallel and distributed optimization method with constraint decomposition for energy management of microgrids. IEEE Trans Smart Grid, 12(6):4627-4640.

[23]Li X, Qi ZT, 2021. Impact of cascading failure based on line vulnerability index on power grids. Energy Syst, early access.

[24]Liao WL, Yang DC, Wang YS, et al., 2021. Fault diagnosis of power transformers using graph convolutional network. CSEE J Power Energy Syst, 7(2):241-249.

[25]Liu YX, Zhang N, Wu D, et al., 2021. Searching for critical power system cascading failures with graph convolutional network. IEEE Trans Contr Netw Syst, 8(3):1304-1313.

[26]Lonapalawong S, Yan JZ, Li JY, et al., 2022. Reducing power grid cascading failure propagation by minimizing algebraic connectivity in edge addition. Front Inform Technol Electron Eng, 23(3):382-397.

[27]Luo B, Wang HT, Liu HQ, et al., 2019. Early fault detection of machine tools based on deep learning and dynamic identification. IEEE Trans Ind Electron, 66(1):509-518.

[28]Mei SW, He F, Zhang XM, et al., 2009. An improved OPA model and blackout risk assessment. IEEE Trans Power Syst, 24(2):814-823.

[29]Montavon G, Binder A, Lapuschkin S, et al., 2019. Layer-wise relevance propagation: an overview. In: Samek W, Montavon G, Vedaldi A, et al. (Eds.), Explainable AI: Interpreting, Explaining and Visualizing Deep Learning. Springer, Cham, p.193-209.

[30]Owerko D, Gama F, Ribeiro A, 2018. Predicting power outages using graph neural networks. Proc IEEE Global Conf on Signal and Information Processing, p.743-747.

[31]Pizzuti C, Socievole A, van Mieghem P, 2020. Comparative network robustness evaluation of link attacks. Proc Int Conf on Complex Networks and Their Applications, p.735-746.

[32]Ren WD, Wu JJ, Zhang X, et al., 2018. A stochastic model of cascading failure dynamics in communication networks. IEEE Trans Circ Syst II Expr Briefs, 65(5):632-636.

[33]Schnake T, Eberle O, Lederer J, et al., 2020. Higher-order explanations of graph neural networks via relevant walks. https://arxiv.org/abs/2006.03589v3

[34]Schneider CM, Moreira AA, Andrade JSJr, et al., 2011. Mitigation of malicious attacks on networks. Proc Natl Acad Sci USA, 108(10):3838-3841.

[35]Song JJ, Cotilla-Sanchez E, Ghanavati G, et al., 2016. Dynamic modeling of cascading failure in power systems. IEEE Trans Power Syst, 31(3):2085-2095.

[36]Springenberg JT, Dosovitskiy A, Brox T, et al., 2015. Striving for simplicity: the all convolutional net. Proc 3^rd Int Conf on Learning Representations, p.1-14.

[37]Tong HJ, Qiu RC, Zhang DX, et al., 2021. Detection and classification of transmission line transient faults based on graph convolutional neural network. CSEE J Power Energy Syst, 7(3):456-471.

[38]Wu J, Barahona M, Tan YJ, et al., 2011. Spectral measure of structural robustness in complex networks. IEEE Trans Syst Man Cybern Part A Syst Humans, 41(6):1244-1252.

[39]Ying R, He RN, Chen KF, et al., 2018. Graph convolutional neural networks for web-scale recommender systems. Proc 24^th ACM SIGKDD Int Conf on Knowledge Discovery & Data Mining, p.974-983.

[40]Zeiler MD, Fergus R, 2014. Visualizing and understanding convolutional networks. Proc 13^th European Conf on Computer Vision, p.818-833.

[41]Zhang X, Tse CK, 2015. Assessment of robustness of power systems from a network perspective. IEEE J Emerg Sel Top Circ Syst, 5(3):456-464.

[42]Zhang X, Zhan CJ, Tse CK, 2017. Modeling the dynamics of cascading failures in power systems. IEEE J Emerg Sel Top Circ Syst, 7(2):192-204.

[43]Zhou BL, Khosla A, Lapedriza À, et al., 2016. Learning deep features for discriminative localization. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.2921-2929.

[44]Zhu YH, Yan J, Sun Y, et al., 2014. Revealing cascading failure vulnerability in power grids using risk-graph. IEEE Trans Parall Distrib Syst, 25(12):3274-3284.

[45]Zimmerman RD, Murillo-Sánchez CE, Thomas RJ, 2011. MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans Power Syst, 26(1):12-19.