Compressive Sensing in Power Engineering: A Comprehensive Survey of Theory and Applications, and a Case Study

Compressive Sensing (CS) is a transformative signal processing framework that enables sparse signal acquisition at rates below the Nyquist limit, offering substantial advantages in data efficiency and reconstruction accuracy. This survey explores the theoretical foundations of CS, including sensing matrices, sparse bases, and recovery algorithms, with a focus on its applications in power engineering. CS has demonstrated significant potential in enhancing key areas such as state estimation (SE), fault detection, fault localization, outage identification, harmonic source identification (HSI), Power Quality Detection condition monitoring, and so on. Furthermore, CS addresses challenges in data compression, real-time grid monitoring, and efficient resource utilization. A case study on smart meter data recovery demonstrates the practical application of CS in real-world power systems. By bridging CS theory and its application, this survey underscores its potential to drive innovation, efficiency, and sustainability in power engineering and beyond.