Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection

摘要

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 compression enables the real-time monitoring of power transmission systems using a limited number of measurements, thereby minimizing communication bandwidth. The ID perspective gives a rigorous error bound on the quality of the data compression. We propose selecting rows and columns used in an ID via the discrete empirical interpolation method (DEIM), a greedy algorithm that aims to control the error bound. This bound leads to a computable estimate for 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. Numerical tests using synthetic PMU data illustrate DEIM's excellent performance for data compression, and validate the proposed DEIM-based fault-detection method.