Distributed event-triggered aggregative optimization with applications to price-based energy management

TL;DR

This paper introduces a novel distributed continuous-time algorithm with event-triggered communication for aggregative optimization, specifically applied to price-based energy management, ensuring exponential convergence and practical implementation.

Contribution

It proposes a new distributed algorithm combining gradient dynamics with a dynamic average consensus estimator, with convergence analysis and event-triggered communication implementation.

Findings

Algorithm achieves exponential convergence under convexity.

Event-triggered communication reduces communication load.

Simulations demonstrate effectiveness in energy management applications.

Abstract

This paper studies a distributed continuous-time aggregative optimization problem, which is a fundamental problem in the price-based energy management. The objective of the distributed aggregative optimization is to minimize the sum of local objective functions, which have a specific expression that relies on agents' own decisions and the aggregation of all agents' decisions. To solve the problem, a novel distributed continuous-time algorithm is proposed by combining gradient dynamics with a dynamic average consensus estimator in a two-time scale. The exponential convergence of the proposed algorithm is established under the assumption of a convex global cost function by virtue of the stability theory of singular perturbation systems. Motivated by practical applications, the implementation of the continuous-time algorithm with event-triggered communication is investigated. Simulations on the price-based energy management of distributed energy resources are given to illustrate the proposed method.