An electric power system or power grid is optimized using a computer-implemented tool the represents in computer memory the optimization function and at least one constraint, which the processor operates upon using a linear programming solver algorithm. The constraints are represented in memory as data structures that include both real and reactive power terms, corresponding to at least one of a power flow model and a transmission line model. The transmission line model is represented using a piecewise linear representation. The power flow model may also include for each node in the power system a real power loss term representing transmission line loss allocated to that node.