Shannon’s Nyquist theorem has always dictated the conventional signal acquisition policies. Power system is not an exception to this. As per this theory, the sampling rate must be at least twice the maximum frequency present in the signal. Recently, compressive sampling (CS) theory has shown that the signals can be reconstructed from samples obtained at sub-Nyquist rate. Signal reconstruction in this theory is exact for “sparse signals” and is near exact for compressible signals provided certain conditions are satisfied. CS theory has already been applied in communication, medical imaging, MRI, radar imaging, remote sensing, computational biology, machine learning, geophysical data analysis, and so forth. CS is comparatively new in the area of computer based power system monitoring. In this paper, subareas of computer based power system monitoring where compressive sampling theory has been applied are reviewed. At first, an overview of CS is presented and then the relevant literature specific to power systems is discussed. 1. Introduction Operation of electric power system has become increasingly complex due to high load growth, increasing market pressure, increasing interconnections of transmission lines, and penetration of variable renewable energy sources. As a result, system operators are forced to operate power grids near their operating limits. The occurrence of major blackouts in many power systems around the world has necessitated the use of better system monitoring and control methodologies. The analysis of the August 14, 2003, blackout has shown that the problems developed hours before the system collapse. If the system operators were aware of the overall worsening system conditions that were developing, certain actions could have been taken. Better system monitoring is only possible if the operator has better knowledge about the grid. As a result, power utilities are looking for new computer based smart devices and smart solutions for grid monitoring and control. An overview of smart grids can be found in [1, 2]. Computer technologies are being used to make traditional power generation, transmission, and distribution systems more efficient. Phasor Measurement Unit (PMU) based Wide Area Measurement Systems (WAMS) are being installed to monitor power system dynamics accurately. Communication networks are being upgraded to allow two way communications and send more and more information to control centers. Utilities are installing wireless smart meters [3, 4] with communication facilities in distribution systems. In [5], different smart grid
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