Distributed event‐triggered scheme for economic dispatch in power systems with uncoordinated step‐sizes

Abstract

Considering potential applications in power systems, economic dispatch problem (EDP) in time-varying balanced communication networks is studied, aiming to minimise the total cost of generating electricity. This is equivalent to dealing with the problem of optimising the sum of local functions while a single generator possesses only its local function. The variables of generators, satisfying some local constraints, are coupled by a linear constraint. In order to resolve the EDP, the authors design a fully distributed primal-dual optimisation algorithm with time-varying uncoordinated step-sizes. In consideration of saving computation and communication resources, an event-triggered scheme is introduced into the algorithm, based on which each generator is only allowed to interact with their neighbouring generators at some independent event-triggered sampling time instants. The proposed algorithm is able to achieve a linear convergence rate under the strong convexity and smoothness of the local objective functions. The Zeno-like behaviour is rigorously excluded, which means that the interval between any two consecutive sampling time instants of each generator is not less than two. Effectiveness of the algorithm and correctness of the theoretical analysis are verified by numerical experiments.