An apparatus and article of manufacture for estimating loss rates of links in a smart grid include identifying end-to-end passage rates from a source to each of multiple receiver and/or load meters in a smart grid, and estimating a loss in at least one link of the grid by identifying the sparsest solution of link loss rates that matches the end-to-end passage rates. Also, a system includes a memory, a processor coupled thereto, and software modules executing on the processor, including a monitoring module for monitoring power flow of receiver and/or load meters in a smart grid, a measurement collector module for collecting measurements to compute end-to-end passage rates from a source to each receiver and/or load meter, and a processing module for estimating a loss in a link of the grid by identifying the sparsest solution of link loss rates matching the end-to-end passage rates.