Electromigration has become a major reliability problem in modern chips, especially in power grids. It is important to identify EM-weak wires that carry high density currents over an extended period of time. In this paper, we first indicate that the conventional current estimation approach based on the assumption that the worst case power configuration produces currents of the highest density can potentially underestimate currents carried by some power grid wires. We propose a linear programming-based algorithm that for each wire finds the worst case configuration of current sources and computes the true worst case current value. Our method considers global and local constraints among current sources and provides practical information to designers for EM reliability improvement purpose.