  This paper studies two fundamental problems in power systems: the economic
dispatch problem (EDP) and load shedding. For the EDP, an extension of the
problem considering the transmission losses is presented. Because the
optimization problem is non-convex owing to quadratic equality constraints
modeling the transmission losses, a convex relaxation method is presented.
Under a particular assumption, it is shown that a distributed algorithm can be
designed to solve the considered EDP. Furthermore, this work aims to handle an
overloading problem by employing an optimal load shedding method. Emphasis is
placed on scheduling the load shedding when there exist some priorities on the
loads. First, a novel optimization problem is proposed to obtain the load
shedding according to the predefined priority order. Then, a distributed
algorithm solving the optimization problem is presented. Finally, this paper
presents how to integrate the proposed algorithms, i.e., the EDP and the load
shedding, in a distributed manner. Simulation results are presented to
demonstrate the effectiveness of the proposed method.
