  Economic dispatch problem for a networked power system has been considered.
The objective is to minimize the total generation cost while meeting the
overall supply-demand balance and generation capacity. In particular, a more
practical scenario has been studied by considering the power losses. A
non-convex optimization problem has been formulated where the non-convexity
comes from the nonlinear equality constraint representing the supply-demand
balance with the power losses. It is shown that the optimization problem can be
solved using convex relaxation and dual decomposition. A simple distributed
algorithm is proposed to solve the optimization problem. Specifically, the
proposed algorithm does not require any initialization process and hence robust
to various changes in operating condition. In addition, the behavior of the
proposed algorithm is analyzed when the problem is infeasible.
