Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
LAPACK: a portable linear algebra library for high-performance computers
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Problems of learning on manifolds
Problems of learning on manifolds
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
A tutorial on spectral clustering
Statistics and Computing
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
Computer Science Review
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Clustering is an important data analysis technique with numerous applications in the analysis of electric power grids. Standard clustering techniques are oblivious to the rich structural and dynamic information available for power grids. Therefore, by exploiting the inherent topological and electrical structure in the power grid data, we propose new methods for clustering with applications to model reduction, locational marginal pricing, phasor measurement unit (PMU or synchrophasor) placement, and power system protection. We focus our attention on model reduction for analysis based on time-series information from synchrophasor measurement devices, and spectral techniques for clustering. By comparing different clustering techniques on two instances of realistic power grids we show that the solutions are related and therefore one could leverage that relationship for a computational advantage. Thus, by contrasting different clustering techniques we make a case for exploiting structure inherent in the data with implications for several domains including power systems.