Due to system complexity and structural variations, real time power line outage detection (POD) and localization is a critical and challenging monitoring goal for modern smart grid (SG). Online monitoring of power lines status plays a major role in system-wide cascading blackout prevention. In this work, we aim to address the multiple POD problems by exploiting the compressive system identification (CSI) - a time efficient approach in complex network analysis. We consider a power network (PN) as a single graph and the mathematical formulation of POD is initialized using the DC power-flow model and graph theory concepts. The POD sparse recovery problem (POD-SRP) reported earlier is improved and generalized in case of large-scale multiple outages. The technical challenges from sparse recovery perspective are addressed through developing new SRP solvers. Moreover, a new sparse-based mathematical formulation for POD is termed as `Binary-POD-SRP' to specifically address the signal dynamic range issue. Finally, using the IEEE standard test-beds, it is discussed how the inherent challenges within large-scale multiple-outages can be solved by applying these new techniques and formulations.