Priority-Considered Load Shedding in Economic Dispatch: Distributed Optimization Approach

This article studies two fundamental problems in power systems: 1) the economic dispatch problem (EDP) and 2) load shedding. In particular, convex optimization problems are formulated for both the EDP and the load shedding problem. For the EDP, an extension of the problem considering the transmission losses is presented. Furthermore, emphasis is placed on scheduling the load shedding when there exist some priorities on the loads. To solve the EDP and the load shedding problem in a distributed setting, we develop a method that combines the dual decomposition approach and the extragradient-based strategy. Notably, this work provides a fixed step size-based scheme for a strongly convex resource allocation problem considering general nonaffine coupled constraints. We show that the proposed algorithm converges to the optimal solution under the assumption that the underlying graph is undirected. In addition, the method has an ergodic convergence rate of O(1/k) in terms of the optimality residuals and the constraint violations. Simulation results are presented to demonstrate the effectiveness of the proposed optimization problems and distributed algorithm.