This paper presents a method for accurately treating active power losses in linear (DC) optimal power flow models. Quadratic nodal losses are approximated by iteratively adding linear constraints. In each iteration a linear programming problem is solved, and constraints on the nodal loss functions are built as linearizations around the current system operating state. The performance of the proposed model — in terms of computational time and convergence properties — is demonstrated on the IEEE 118 bus test system. © Copyright 2012 IEEE - All rights reserved.