AMPS: Rank Minimization Algorithms for Wide-Area Phasor Measurement Data Processing

当前的监控和数据采集（SCADA）系统通常每2 - 4秒提供测量，仅提供对电力系统行为的稳态视图。得益于2009年的《美国复苏和再投资法案》，现在已经安装了2000多个相量测量单元（PMU），每天提供TB级的数据，为电力系统运行条件和能源需求提供动态可见性。PMU可以以每秒30或60个样本的采样率直接测量母线电压相量和线路电流相量。在这个项目中要解决的问题是（i）在使用PMU数据，以提高广域态势感知和防止停电的数据质量问题，（ii）网络数据安全，以检测和防止复杂的攻击。通过开发实时PMU数据恢复方法，预计该项目将提高PMU测量的数据质量，并作为建立基于PMU的监测系统的第一步。该系统可以增强PMU数据的系统可见性，从而提供低成本的解决方案，以满足能源需求并提高电网可靠性。PI希望利用RPI的资源及其与行业的联系，将开发的技术整合到实践中。该项目将大数据分析与一般动力系统相结合，所开发的方法可应用于其他应用，如通信网络监控和视频处理。此外，预计该项目中的研究可以融入现有的高中生推广活动中。在数学上，该项目中解决的问题涉及最小化矩阵的秩。这种类型的问题通常使用凸优化近似来解决。PI建议使用非凸方法，这可以更好地捕捉问题的结构，因此可能会导致更好的解决方案。PI最近研究了一种非凸方法来最小化对称半正定矩阵的秩。PI提出了一种方法，将这种方法扩展到更一般的复杂矩阵的秩最小化问题。PI还将为感兴趣的问题开发相关的交替方向方法。为了便于公用事业和ISO的测试和采用，PI打算在开源数据集中器平台上实现他们的方法。据设想，要开发的方法的分析将表明，它们可以成功地应用于压缩传感，低秩矩阵理论和低秩张量分析的广泛的问题。

The current Supervisory Control and Data Acquisition (SCADA) systems typically provide measurements every 2-4 seconds, offering only a steady state view into power system behavior. Thanks to the American Recovery and Reinvestment Act of 2009, more than two thousand phasor measurement units (PMUs) have now been installed and provide terabytes of data daily, offering dynamic visibility into power system operating conditions and energy demand. PMUs can directly measure bus voltage phasors and line current phasors at sampling rates of 30 or 60 samples per second. The problems to addressed in this project are (i) data quality issues in the use of PMU data to improve wide-area situational awareness and prevent blackouts, and (ii) cyber data security, to detect and prevent sophisticated attacks. Through developing real-time PMU data recovery methods, it is envisioned that this project will improve the data quality of PMU measurements and serve as a first step towards building a PMU-based monitoring system. The system can enhance system visibility from PMU data, resulting in a lower-cost solution to meet energy demand and improve grid reliability. The PIs expect to leverage the resources at RPI and thier connections to industry to integrate the developed technology into practice. This project connects big data analysis with general dynamical systems, and the developed methods can be applied to other applications such as monitoring of communication networks and video processing. Further, it is envisaged that the research in this project can be integrated into the existing outreach activities to high school students.Mathematically, the problems addressed in this project involve minimizing the rank of a matrix. Problems of this type are often addressed using convex optimization approximations. The PIs propose instead to use nonconvex approaches, which better capture the structure of the problem and may therefore lead to better solutions. The PIs recently investigated a nonconvex approach to minimizing the rank of a symmetric positive semidefinite matrix. The PIs propose a method to extend this approach to more general rank minimization problems over complex matrices. The PIs will also develop related alternating direction methods for the problems of interest. To facilitate testing and adoption from utilities and ISOs, the PIs intend to implement thier methods on an open-source data concentrator platform. It is envisioned that the analysis of the methods to be developed will show that they can be successfully applied to a broad range of problems in compressed sensing, low-rank matrix theory, and low-rank tensor analysis.