Distributed Optimization Algorithm for the Economic Dispatch Problem over Delayed Communication Network

This work investigates the economic dispatch problem (EDP) when communication links suffer heterogeneous delays, adopting general convex cost models that subsume the quadratic forms used in existing works. Additionally, each generator is characterized by a bounded output limitation. A distributed primal-dual method is developed through the local communication among generators to address the global equality coupled constraint across all generators. Given the inherent delays in open communication environments, passivity-based scattering transformation is then provided to tackle heterogeneous time delays. Furthermore, we introduce the adaptive penalty function method to handle private bounded constraints. A fully distributed optimization scheme is then developed building on the Karush-Kuhn-Tucker (KKT) conditions to address the EDP over a connected network. We prove its convergence using Filippov solution and differential inclusion. Furthermore, a modified distributed optimization approach incorporating a maximal projection operator is proposed to account for transmission losses. The effectiveness of our developed methods is demonstrated via two practical case simulations.