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.

翻译：本研究通过低秩矩阵逼近探讨相量测量单元(PMU)数据的降维问题。为从较少测量值重构PMU数据矩阵，我们提出插值矩阵分解(ID)框架。与依赖主成分分析或奇异值分解的方法不同，ID仅需利用矩阵的少数行(PMU数据流)和/或少数列(时间快照)即可恢复完整数据矩阵。这种压缩方式使得仅需有限测量值即可实现电力传输系统的实时监测，从而最小化通信带宽需求。ID框架为数据压缩质量提供了严格的误差界。我们建议通过离散经验插值法(DEIM)——一种旨在控制误差界的贪心算法——来选择ID中使用的行与列。该误差界可导出在线运行期间重构误差的可计算估计量。若该估计量被突破，则暗示系统运行条件发生变化，从而可作为故障检测工具。使用合成PMU数据的数值测试表明，DEIM在数据压缩方面具有优异性能，并验证了所提出的基于DEIM的故障检测方法。