A Distributed Solution to the Adjustable Robust Economic Dispatch Problem

Abstract

The problem of maintaining balance between consumption and production of electric energy in the presence of a high share of intermittent power sources in a transmission grid is addressed. A distributed, asynchronous optimization algorithm, based on the ideas of cutting-plane approximations and adjustable robust counterparts, is presented to compute economically optimal adjustable dispatch strategies. These strategies guarantee satisfaction of the power balancing constraint as well as of the operational constraints for all possible realizations of the uncertain power generation or demand. The communication and computational effort of the proposed distributed algorithm increases for each computational unit only slowly with the number of participants, making it well suited for large scale networks. A distributed implementation of the algorithm and a numerical study are presented, which show the performance in asynchronous networks and its robustness against packet loss.

Constraint-Coupled Distributed Optimization: A Relaxation and Duality Approach

“…A special coupling associated to peak minimization problems arising in demand-side management is considered in [30], where a (simplified) algorithmic approach, similar to the one proposed in this paper, is proposed for that set-up. An alternative approach to constraint-coupled problems has been proposed in [32], and customized to MPC in [33], [34], where agents employ a cutting-plane consensus scheme to iteratively approximate their local problems. This approach enforces agents to eventually agree on the complete solution vector and this may be an undesirable feature in some applications.…”

Consensus-based Approach for the Economic Dispatch Problem

“…Mudumbai et al (2012) present a distributed iterative procedure for load-frequency control and ED that requires adjusting some parameters with an initial centralized intervention. Finally, Lorenzen et al (2013) present a distributed optimization algorithm based on the ideas of cutting-plane consensus algorithm and adjustable robust counterparts. The cited papers do not consider losses in their models and, to the best knowledge of the authors, no distributed approach has yet been proposed to solve the ED in the more realistic case with non-negligible losses.…”