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Smart grid calls for low-cost, fine-grained and long-lasting monitoring solutions, to be able to provide reliable service to customers, enhance situational awareness capabilities and refine the operation of the grid and the microgrids, in addition to enabling prompt utility reaction to emergencies. Wireless Sensor Networks (WSNs) are promising candidates for monitoring the smart grid, given their capability to cover a large geographic region at low-cost. However, they do not provide long-lasting operation capability due to the limited battery lifetime of the sensors. Particularly, when sensors are deployed in hard-to-reach or hazardous environments, replacing the batteries of the sensors increase the cost of monitoring significantly. In the literature, energy-efficient protocols and ambient energy harvesting have been proposed to extend the lifetime of the sensors while neither of those offer a concrete solution for the smart grid. In this context, recent advances in Radio Frequency (RF) energy harvesting offers a unique solution to make WSNs operationally ready for smart grid monitoring tasks. Studies on RF energy harvesting have focused on uniform power delivery to all sensors, however it becomes essential to differentiate between critical zones and less critical zones in smart grid monitoring tasks. In this paper, we propose the Differentiated RF Power Transmission (DRIFT) scheme which is based on an Integer Linear Programming (ILP) model that maximizes the power received by the high priority sensor nodes. We compare the performance of DRIFT with a path length minimizing approach, namely Sustainable wireless Rechargeable Sensor network (SuReSense). We show that DRIFT is able to provide more power to high priority nodes than SuReSense. We also show that there is a tradeoff between power maximization and path length minimization.