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

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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.