Discovering Clusters in Power Networks From Orthogonal Structure of Spectral Embedding

Abstract

This paper presents an integrated approach to parti-5 tion similarity graphs, the task that arises in various contexts in 6 power system studies. The approach is based on orthogonal trans-7 formation of row-normalized eigenvectors obtained from spectral 8 clustering to closely fit the axes of the canonical coordinate system. 9 We select the number of clusters as the number of eigenvectors 10 that allows the best alignment with the canonical coordinate axes, 11 which is a more informative approach than the popular spectral 12 eigengap heuristic. We show a link between the two relevant meth-13 ods from the literature and on their basis construct a robust and 14 time-efficient algorithm for eigenvector alignment. Furthermore, 15 a graph partitioning algorithm based on the use of aligned eigen-16 vector columns is proposed, and its efficiency is evaluated by com-17 parison with three other methods. Finally, the proposed integrated 18 approach is applied to the adaptive reconfiguration of secondary 19 voltage control helping to achieve demonstrable improvements in 20 control performance. 21 Index Terms-Power network partitioning, spectral clustering, 22 number of clusters, adaptive network zone division.23

Isoperimetric clustering‐based network partitioning algorithm for voltage–apparent power coupled areas

“…The proposed partitioning technique on the New England 39‐bus system is compared with results in [16, 33]. In [16], bulk power system is partitioned considering the volt–var interactions of buses with respect to pilot buses.…”

“…The number of clusters obtained in the proposed isoperimetric clustering‐based partitioning was 2, whereas in [33] the number of clusters obtained for the base case was 5. On close observation of the clusters formed based on VCAs in [33], there are clusters with single generators serving loads. Such technique for clustering will not be efficient in cases where the partitioning of system aims at forming clusters suitable for localised reactive power market.…”

A parallel approach for ultra-fast state estimation in large power system using graph partitioning theory

“…While these advancements have undoubtedly marked progress, many existing multi-area state estimation methods rely heavily on geographical information for delineating network areas, often overlooking a distinct approach to zone partitioning. Noteworthy exceptions include the application of spectral clustering for power system network partitioning during emergency conditions [13] and the use of the k-means algorithm to expedite load flow in [14]. In reference [15], a state estimation method based on Gaussian process regression is presented, utilizing data from the SCADA unit of the New York Independent System Operator.…”

Probabilistic Optimal Power Flow-Based Spectral Clustering Method Considering Variable Renewable Energy Sources

“…Consequently, hierarchical clustering can be obtained for the connection strength determined by the chosen electrical weighting (Sánchez-García et al, 2014). This method has been studied from various perspectives, such as to improve the calculation efficiency and partition quality through orthogonal conversion (Tyuryukanov et al, 2018), to island power systems according to the minimum active flow disruptions (Amini et al, 2020), and to prevent cascading failures through tree partitioning (Bialek and Vahidinasab, 2022). As described above, numerous studies have focused on clustering; these studies and their findings are summarized and compared in Table 1.…”