Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection

arXiv:2510.20116v2 Announce Type: replace Abstract: This work investigates the reduction of phasor measurement unit (PMU) data through low-rank matrix approximations. To reconstruct a PMU data matrix from fewer measurements, we propose the framework of interpolatory matrix decompositions (IDs). In contrast to methods relying on principal component analysis or singular value decomposition, IDs recover the complete data matrix using only a few of its rows (PMU datastreams) and/or a few of its columns (snapshots in time). This row-/column-based compression enables real-time monitoring of power transmission systems using measurements from a smaller subset of pilot datastreams, thereby minimizing communication bandwidth. The ID perspective gives a rigorous error bound on the quality of the data compression. We propose selecting the pilot measurements used in an ID via the discrete empirical interpolation method (DEIM), a greedy algorithm that aims to control the error bound. This bound yields a computable estimate of the reconstruction error during online operations. A violation of this estimate suggests a change in the system's operating conditions and thus serves as a tool for fault detection. Following a disturbance, DEIM can be used to localize the event source across all buses with high accuracy. Numerical tests on synthetic PMU data demonstrate DEIM's excellent performance in data compression and validate the proposed DEIM-based fault-detection and localization method.