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## Compressive sensing for smart-grid security and reliability

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Communication, Control and Security Challenges for the Smart Grid — Recommend this title to your library

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This chapter aims to introduce the applications of a newly born theorem in signal processing and system identification, widely known as compressive sensing-sparse recovery (CS-SR), in smart power grid monitoring, security, and reliability. We will discuss how the sparse nature of the electrical power networks can be exploited to mathematical model and reformulate some of the most famous monitoring and security problems in power engineering as compressive system identification (CSI) problems. First, a short background on CS-SR theorems and techniques is presented. Next, the state-of-the-art in CS-SR applications in smart grid technology will be discussed, and finally, three distinctive monitoring problems are specifically addressed in detail, within comprehensive mathematical descriptions, and their specific features are explored through variety of case studies.

Chapter Contents:

• 13.1 Introduction
• 13.2 Mathematical modeling of a compressive sensing or sparse recovery problem
• 13.2.1 Sparse modeling
• 13.2.2 Sparse-recovery problem
• 13.3 Applications of CS-SR in smart grid
• 13.3.1 Power network model: a sparse interconnected graph
• 13.3.2 DC power-flow model and weighted Laplacian matrix of PN
• 13.4 Sparse recovery-based power line outage identification in smart grid
• 13.4.1 POI-SRP formulations
• 13.4.1.1 Distributed POI-SRP
• 13.4.1.2 Binary POI-SRP
• 13.4.1.3 Structured POI-SRP
• 13.4.2 Measurement matrix structure and its properties in POI-SRP
• 13.4.3 Addressing high coherence by support selection modification: BLOOMP algorithm
• 13.4.4 Case studies and discussion
• 13.4.4.1 Single-line outage
• 13.4.4.2 Multiple-line outages
• 13.5 Sparse recovery-based smart-grid topology identification
• 13.5.1 Sparse setup of topology identification problem
• 13.5.1.1 l1 Minimization versus reweighted l1 minimization PNTI-SRP
• 13.5.1.2 Noisy reweighted l1-minimization based PNTI
• 13.5.2 Case studies and discussion
• 13.5.2.1 Setup
• 13.5.2.2 Results
• 13.6 Modeling and analyzing the dynamic behavior of transmission lines using structured sparsity
• 13.6.1 Line parameters dynamical modeling
• 13.6.1.1 Dynamical current wave analysis in transmission lines
• 13.6.1.2 Power network modeling under dynamical behavior
• 13.6.1.3 Mathematical formulation of LPDM
• 13.6.2 Structured sparse LPDM
• 13.6.2.1 Block OMP recovery algorithm for block sparse signals
• 13.6.2.2 BOMP guarantee condition
• 13.6.3 Case studies
• 13.7 Conclusions
• Acknowledgements
• References

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